Polarized Image and Instrumental Modeling

In this tutorial, we will analyze a simulated simple polarized dataset to demonstrate Comrade's polarized imaging capabilities.

Introduction to Polarized Imaging

The EHT is a polarized interferometer. However, like all VLBI interferometers, it does not directly measure the Stokes parameters (I, Q, U, V). Instead, it measures components related to the electric field at the telescope along two directions using feeds. There are two types of feeds at telescopes: circular, which measure $R / L$ components of the electric field, and linear feeds, which measure $X / Y$ components of the electric field. Most sites in the EHT use circular feeds, meaning they measure the right (R) and left electric field (L) at each telescope. Although note that ALMA actually uses linear feeds. Currently Comrade has the ability to fit natively mixed polarization data however, the publically released EHT data has been converted to circular polarization. For a VLBI array whose feeds are purely circluar the coherency matrices are given by,

C_{i j} = (\begin{matrix} R R^{*} & R L^{*} \\ L R^{*} & L L^{*} \end{matrix}) .

These coherency matrices are the fundamental object in interferometry and what the telescope observes. For a perfect interferometer, these circular coherency matrices are related to the usual Fourier transform of the stokes parameters by

(\begin{matrix} \tilde{I} \\ \tilde{Q} \\ \tilde{U} \\ \tilde{V} \end{matrix}) = \frac{1}{2} (\begin{matrix} R R^{*} + L L^{*} \\ R L^{*} + L R^{*} \\ i (L R^{*} - R L^{*}) \\ R R^{*} - L L^{*} \end{matrix}) .

Note

In this tutorial, we stick to circular feeds but Comrade has the capabilities to model linear (XX,XY, ...) and mixed basis coherencies (e.g., RX, RY, ...).

In reality, the measure coherencies are corrupted by both the atmosphere and the telescope itself. In Comrade we use the RIME formalism ^[1] to represent these corruptions, namely our measured coherency matrices $V_{i j}$ are given by

V_{i j} = J_{i} C_{i j} J_{j}^{†}

where $J$ is known as a Jones matrix and $i j$ denotes the baseline $i j$ with sites $i$ and $j$ .

Comrade is highly flexible with how the Jones matrices are formed and provides several convenience functions that parameterize standard Jones matrices. These matrices include:

JonesG which builds the set of complex gain Jones matrices

G = (\begin{matrix} g_{a} & 0 \\ 0 & g_{b} \end{matrix})

JonesD which builds the set of complex d-terms Jones matrices

D = (\begin{matrix} 1 & d_{a} \\ d_{b} & 1 \end{matrix})

JonesR is the ideal telescope response $R$ . This transformation is special and combines two things using the decomposition $R = F B$ . The first, $B$ , is the transformation from some reference basis to the observed coherency basis (this allows for mixed basis measurements). The second is the feed rotation, $F$ , that transforms from some reference axis to the axis of the telescope as the source moves in the sky. The feed rotation matrix F for circular feeds in terms of the per station feed rotation angle $φ$ is

F = (\begin{matrix} e^{- i φ} & 0 \\ 0 & e^{i φ} \end{matrix})

In the rest of the tutorial, we are going to solve for all of these instrument model terms in while re-creating the polarized image from the first EHT results on M87.

Load the Data

To get started we will load Comrade

julia

using Comrade

Load the Data

julia

using VLBIFiles

For reproducibility we use a stable random number genreator

julia

using StableRNGs
rng = StableRNG(48)

StableRNGs.LehmerRNG(state=0x00000000000000000000000000000061)

Now we will load some synthetic polarized data.

julia

fname = Base.download(
    "https://github.com/ptiede/ComradeTestData/releases/download/Data/eht_2017_data.uvfits",
    joinpath(__DIR, "m87polarized.uvfits")
)
uvd = VLBIFiles.load(VLBIFiles.UVData, fname)

VLBIFiles.UVData("/home/runner/work/Comrade.jl/Comrade.jl/examples/intermediate/PolarizedImaging/m87polarized.uvfits", VLBIFiles.UVHeader(SIMPLE  =                    T / conforms to FITS standard
BITPIX  =                  -32 / array data type
NAXIS   =                    7 / number of array dimensions
NAXIS1  =                    0
NAXIS2  =                    3
NAXIS3  =                    4
NAXIS4  =                    1
NAXIS5  =                    1
NAXIS6  =                    1
NAXIS7  =                    1
EXTEND  =                    T
GROUPS  =                    T / has groups
PCOUNT  =                    9 / number of parameters
GCOUNT  =                 8646 / number of groups
OBSRA   =    187.7059307575226
OBSDEC  =    12.39112323919932
OBJECT  = 'M87     '          
MJD     =              57849.0
DATE-OBS= '2017-04-06'        
BSCALE  =                  1.0
BZERO   =                  0.0
BUNIT   = 'JY      '          
VELREF  =                    3
EQUINOX = 'J2000   '          
ALTRPIX =                  1.0
ALTRVAL =                  0.0
TELESCOP= 'VLBA    '          
INSTRUME= 'VLBA    '          
OBSERVER= 'EHT     '          
CTYPE2  = 'COMPLEX '          
CRVAL2  =                  1.0
CDELT2  =                  1.0
CRPIX2  =                  1.0
CROTA2  =                  0.0
CTYPE3  = 'STOKES  '          
CRVAL3  =                 -1.0
CDELT3  =                 -1.0
CRPIX3  =                  1.0
CROTA3  =                  0.0
CTYPE4  = 'FREQ    '          
CRVAL4  =     2.27070703125e11
CDELT4  =              1.856e9
CRPIX4  =                  1.0
CROTA4  =                  0.0
CTYPE6  = 'RA      '          
CRVAL6  =    187.7059307575226
CDELT6  =                  1.0
CRPIX6  =                  1.0
CROTA6  =                  0.0
CTYPE7  = 'DEC     '          
CRVAL7  =    12.39112323919932
CDELT7  =                  1.0
CRPIX7  =                  1.0
CROTA7  =                  0.0
PTYPE1  = 'UU---SIN'          
PSCAL1  =  4.4039146672722e-12
PZERO1  =                  0.0
PTYPE2  = 'VV---SIN'          
PSCAL2  =  4.4039146672722e-12
PZERO2  =                  0.0
PTYPE3  = 'WW---SIN'          
PSCAL3  =  4.4039146672722e-12
PZERO3  =                  0.0
PTYPE4  = 'BASELINE'          
PSCAL4  =                  1.0
PZERO4  =                  0.0
PTYPE5  = 'DATE    '          
PSCAL5  =                  1.0
PZERO5  =                  0.0
PTYPE6  = 'DATE    '          
PSCAL6  =                  1.0
PZERO6  =                  0.0
PTYPE7  = 'INTTIM  '          
PSCAL7  =                  1.0
PZERO7  =                  0.0
PTYPE8  = 'TAU1    '          
PSCAL8  =                  1.0
PZERO8  =                  0.0
PTYPE9  = 'TAU2    '          
PSCAL9  =                  1.0
PZERO9  =                  0.0
HISTORY AIPS SORT ORDER='TB', "M87", Dates.Date("2017-04-06"), [:RR, :LL, :RL, :LR], 2.27070703125e11 Hz), VLBIFiles.FrequencyWindow[VLBIFiles.FrequencyWindow(1, 1, 2.270707f11 Hz, 1.856f9 Hz, 1, 1, 1.0f0)], VLBIFiles.AntArray[VLBIFiles.AntArray("VLBA", 2.270707f11 Hz, {1 = Antenna AA, 2 = Antenna AP, 3 = Antenna AZ, 4 = Antenna JC, 5 = Antenna LM, 6 = Antenna PV, 7 = Antenna SM}, [0.0, 0.0, 0.0])])

Unlike non-polarized tutorials, we also need an array file describing the antenna feed rotation parameters. We pass it via the arrayfile keyword on the data product.

julia

dvis = extract_table(
    uvd, Coherencies(;
        time_average = VLBI.GapBasedScans(),
    )
)

EHTObservationTable{Comrade.EHTCoherencyDatum{Float64}}
  source:      M87
  mjd:         57849
  bandwidth:   1.856e9
  sites:       [:AA, :AP, :AZ, :JC, :LM, :PV, :SM]
  nsamples:    274

Often the EHT does not take into acount feed offsets. To load those we read in the standard ehtim style array.txt files.

julia

Comrade.reset_mounts!(dvis, Comrade.load_array_txt(joinpath(__DIR, "../../Data/array.txt")))

EHTObservationTable{Comrade.EHTCoherencyDatum{Float64}}
  source:      M87
  mjd:         57849
  bandwidth:   1.856e9
  sites:       [:AA, :AP, :AZ, :JC, :LM, :PV, :SM]
  nsamples:    274

Inflate noise by 1% and drop short (uvdist < 0.1 Gλ) baselines.

julia

add_fractional_noise!(dvis, 0.01)
dvis = flag(d -> hypot(d.baseline.U, d.baseline.V) < 0.1e9, dvis)

EHTObservationTable{Comrade.EHTCoherencyDatum{Float64}}
  source:      M87
  mjd:         57849
  bandwidth:   1.856e9
  sites:       [:AA, :AP, :AZ, :JC, :LM, :PV, :SM]
  nsamples:    242

##Building the Model/Posterior

To build the model, we first break it down into two parts:

The image or sky model. In Comrade, all polarized image models are written in terms of the Stokes parameters. In this tutorial, we will use a polarized image model based on Pesce (2021)^[2], and parameterizes each pixel in terms of the Poincare sphere. This parameterization ensures that we have all the physical properties of stokes parameters. Note that we also have a parameterization in terms of hyperbolic trig functions VLBISkyModels.PolExp2Map
The instrument model. The instrument model specifies the model that describes the impact of instrumental and atmospheric effects. We will be using the $J = G D R$ decomposition we described above. However, to parameterize the R/L complex gains, we will be using a gain product and ratio decomposition. The reason for this decomposition is that in realistic measurements, the gain ratios and products have different temporal characteristics. Namely, many of the EHT observations tend to demonstrate constant R/L gain ratios across an nights observations, compared to the gain products, which vary every scan. Additionally, the gain ratios tend to be smaller (i.e., closer to unity) than the gain products. Using this apriori knowledge, we can build this into our model and reduce the total number of parameters we need to model.

First we specify our sky model with the @sky macro. Each name ~ dist line contributes an entry to the prior; everything else is the model body. The metadata fields (mimg, ftot, cprior) are passed as keyword arguments and are in scope inside both the prior expressions and the body.

julia

using Distributions
using VLBIImagePriors
@sky function sky(grid; mimg, ftot, cprior)
    σs ~ ntuple(Returns(VLBITruncated(VLBIGaussian(0.0, 0.5); lower = 0.0)), 4)
    as ~ ntuple(Returns(cprior), 4)
    # Build the stokes I model
    δs = ntuple(Val(4)) do i
        σs[i] .* as[i].params
    end

    # Convert hyperbolic polarization parameterization to Stokes parameters.
    pmap = VLBISkyModels.PolExp2Map!(δs..., axisdims(mimg))

    # We now add a mean image. Namely, we assume that `pmap` are multiplicative fluctuations
    # about some mean image `mimg`. We also compute the total flux of the Stokes I image
    # for normalization purposes below.
    bpmap = baseimage(pmap)
    bmimg = baseimage(mimg)
    ft = zero(ftot)
    bpmapI = stokes(bpmap, :I)
    bpmapQ = stokes(bpmap, :Q)
    bpmapU = stokes(bpmap, :U)
    bpmapV = stokes(bpmap, :V)

    @inbounds for i in eachindex(bpmap, bmimg)
        bpmapI[i] = bmimg[i] * bpmapI[i]
        bpmapQ[i] = bmimg[i] * bpmapQ[i]
        bpmapU[i] = bmimg[i] * bpmapU[i]
        bpmapV[i] = bmimg[i] * bpmapV[i]
        ft += bpmapI[i]
    end

    # Renormlize to get the correct total flux.
    @inbounds for i in eachindex(bpmap)
        bpmap[i] *= ftot / ft
    end

    m = ContinuousImage(pmap, BSplinePulse{3}())
    x, y = centroid(pmap)
    return shifted(m, -x, -y)
end

sky (generic function with 1 method)

Now, we define the metadata needed to build the model. We specify our image grid and cache model needed to define the polarimetric image model. Our image will be a 10x10 raster with a 60μas FOV.

julia

fovx = μas2rad(200.0)
fovy = μas2rad(200.0)
nx = ny = 48
grid = imagepixels(fovx, fovy, nx, ny)

fwhmfac = 2 * sqrt(2 * log(2))
mpr = modify(Gaussian(), Stretch(μas2rad(50.0) ./ fwhmfac))
mimg_raw = intensitymap(mpr, grid)
mimg = mimg_raw ./ Comrade.flux(mimg_raw)

┌ 48×48 IntensityMap{Float64, 2} ┐
├────────────────────────────────┴─────────────────────────────────────── dims ┐
  ↓ X Sampled{Float64} LinRange{Float64}(-4.747133960864206e-10, 4.747133960864206e-10, 48) ForwardOrdered Regular Points,
  → Y Sampled{Float64} LinRange{Float64}(-4.747133960864206e-10, 4.747133960864206e-10, 48) ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
  ↓ →          -4.74713e-10  -4.54513e-10  -4.34312e-10  -4.14112e-10  -3.93911e-10  -3.73711e-10  -3.5351e-10   -3.33309e-10  -3.13109e-10  -2.92908e-10  -2.72708e-10  -2.52507e-10  -2.32307e-10  -2.12106e-10  -1.91905e-10  -1.71705e-10  -1.51504e-10  -1.31304e-10  -1.11103e-10  -9.09026e-11  -7.0702e-11   -5.05014e-11  -3.03009e-11  -1.01003e-11  1.01003e-11  3.03009e-11  5.05014e-11  7.0702e-11   9.09026e-11  1.11103e-10  1.31304e-10  1.51504e-10  1.71705e-10  1.91905e-10  2.12106e-10  2.32307e-10  2.52507e-10  2.72708e-10  2.92908e-10  3.13109e-10  3.33309e-10  3.5351e-10   3.73711e-10  3.93911e-10  4.14112e-10  4.34312e-10  4.54513e-10  4.74713e-10
 -4.74713e-10   3.56129e-12   8.6349e-12    2.01457e-11   4.52256e-11   9.76927e-11   2.03056e-10   4.06112e-10   7.81542e-10   1.44722e-9    2.57865e-9    4.42107e-9    7.29353e-9    1.15778e-8    1.76843e-8    2.59912e-8    3.67571e-8    5.00187e-8    6.54937e-8    8.25168e-8    1.00037e-7    1.16696e-7    1.30987e-7    1.41474e-7    1.47028e-7   1.47028e-7   1.41474e-7   1.30987e-7   1.16696e-7   1.00037e-7   8.25168e-8   6.54937e-8   5.00187e-8   3.67571e-8   2.59912e-8   1.76843e-8   1.15778e-8   7.29353e-9   4.42107e-9   2.57865e-9   1.44722e-9   7.81542e-10  4.06112e-10  2.03056e-10  9.76927e-11  4.52256e-11  2.01457e-11  8.6349e-12   3.56129e-12
 -4.54513e-10   8.6349e-12    2.09366e-11   4.88463e-11   1.09656e-10   2.36871e-10   4.9234e-10    9.84681e-10   1.89497e-9    3.509e-9      6.25233e-9    1.07195e-8    1.76843e-8    2.8072e-8     4.28782e-8    6.30196e-8    8.91231e-8    1.21278e-7    1.58799e-7    2.00075e-7    2.42556e-7    2.82948e-7    3.17599e-7    3.43026e-7    3.56492e-7   3.56492e-7   3.43026e-7   3.17599e-7   2.82948e-7   2.42556e-7   2.00075e-7   1.58799e-7   1.21278e-7   8.91231e-8   6.30196e-8   4.28782e-8   2.8072e-8    1.76843e-8   1.07195e-8   6.25233e-9   3.509e-9     1.89497e-9   9.84681e-10  4.9234e-10   2.36871e-10  1.09656e-10  4.88463e-11  2.09366e-11  8.6349e-12
 -4.34312e-10   2.01457e-11   4.88463e-11   1.13961e-10   2.55835e-10   5.52633e-10   1.14866e-9    2.29732e-9    4.42107e-9    8.18671e-9    1.45871e-8    2.50093e-8    4.12584e-8    6.54937e-8    1.00037e-7    1.47028e-7    2.07929e-7    2.82948e-7    3.70488e-7    4.66786e-7    5.65897e-7    6.60135e-7    7.40976e-7    8.00299e-7    8.31718e-7   8.31718e-7   8.00299e-7   7.40976e-7   6.60135e-7   5.65897e-7   4.66786e-7   3.70488e-7   2.82948e-7   2.07929e-7   1.47028e-7   1.00037e-7   6.54937e-8   4.12584e-8   2.50093e-8   1.45871e-8   8.18671e-9   4.42107e-9   2.29732e-9   1.14866e-9   5.52633e-10  2.55835e-10  1.13961e-10  4.88463e-11  2.01457e-11
 -4.14112e-10   4.52256e-11   1.09656e-10   2.55835e-10   5.74329e-10   1.24062e-9    2.57865e-9    5.1573e-9     9.92496e-9    1.83785e-8    3.27468e-8    5.6144e-8     9.2622e-8     1.47028e-7    2.24576e-7    3.30067e-7    4.66786e-7    6.35197e-7    8.31718e-7    1.0479e-6     1.27039e-6    1.48195e-6    1.66344e-6    1.79661e-6    1.86714e-6   1.86714e-6   1.79661e-6   1.66344e-6   1.48195e-6   1.27039e-6   1.0479e-6    8.31718e-7   6.35197e-7   4.66786e-7   3.30067e-7   2.24576e-7   1.47028e-7   9.2622e-8    5.6144e-8    3.27468e-8   1.83785e-8   9.92496e-9   5.1573e-9    2.57865e-9   1.24062e-9   5.74329e-10  2.55835e-10  1.09656e-10  4.52256e-11
 -3.93911e-10   9.76927e-11   2.36871e-10   5.52633e-10   1.24062e-9    2.67989e-9    5.57019e-9    1.11404e-8    2.14391e-8    3.96998e-8    7.07371e-8    1.21278e-7    2.00075e-7    3.17599e-7    4.85111e-7    7.12985e-7    1.00831e-6    1.3721e-6     1.79661e-6    2.26359e-6    2.7442e-6     3.20119e-6    3.59322e-6    3.88089e-6    4.03325e-6   4.03325e-6   3.88089e-6   3.59322e-6   3.20119e-6   2.7442e-6    2.26359e-6   1.79661e-6   1.3721e-6    1.00831e-6   7.12985e-7   4.85111e-7   3.17599e-7   2.00075e-7   1.21278e-7   7.07371e-8   3.96998e-8   2.14391e-8   1.11404e-8   5.57019e-9   2.67989e-9   1.24062e-9   5.52633e-10  2.36871e-10  9.76927e-11
 -3.73711e-10   2.03056e-10   4.9234e-10    1.14866e-9    2.57865e-9    5.57019e-9    1.15778e-8    2.31555e-8    4.45616e-8    8.25168e-8    1.47028e-7    2.52078e-7    4.15859e-7    6.60135e-7    1.00831e-6    1.48195e-6    2.0958e-6     2.85194e-6    3.73429e-6    4.70491e-6    5.70388e-6    6.65374e-6    7.46857e-6    8.0665e-6     8.38319e-6   8.38319e-6   8.0665e-6    7.46857e-6   6.65374e-6   5.70388e-6   4.70491e-6   3.73429e-6   2.85194e-6   2.0958e-6    1.48195e-6   1.00831e-6   6.60135e-7   4.15859e-7   2.52078e-7   1.47028e-7   8.25168e-8   4.45616e-8   2.31555e-8   1.15778e-8   5.57019e-9   2.57865e-9   1.14866e-9   4.9234e-10   2.03056e-10
 -3.5351e-10    4.06112e-10   9.84681e-10   2.29732e-9    5.1573e-9     1.11404e-8    2.31555e-8    4.6311e-8     8.91231e-8    1.65034e-7    2.94057e-7    5.04156e-7    8.31718e-7    1.32027e-6    2.01663e-6    2.9639e-6     4.19159e-6    5.70388e-6    7.46857e-6    9.40981e-6    1.14078e-5    1.33075e-5    1.49371e-5    1.6133e-5     1.67664e-5   1.67664e-5   1.6133e-5    1.49371e-5   1.33075e-5   1.14078e-5   9.40981e-6   7.46857e-6   5.70388e-6   4.19159e-6   2.9639e-6    2.01663e-6   1.32027e-6   8.31718e-7   5.04156e-7   2.94057e-7   1.65034e-7   8.91231e-8   4.6311e-8    2.31555e-8   1.11404e-8   5.1573e-9    2.29732e-9   9.84681e-10  4.06112e-10
 -3.33309e-10   7.81542e-10   1.89497e-9    4.42107e-9    9.92496e-9    2.14391e-8    4.45616e-8    8.91231e-8    1.71513e-7    3.17599e-7    5.65897e-7    9.70223e-7    1.6006e-6     2.54079e-6    3.88089e-6    5.70388e-6    8.0665e-6     1.09768e-5    1.43729e-5    1.81087e-5    2.19536e-5    2.56096e-5    2.87458e-5    3.10471e-5    3.2266e-5    3.2266e-5    3.10471e-5   2.87458e-5   2.56096e-5   2.19536e-5   1.81087e-5   1.43729e-5   1.09768e-5   8.0665e-6    5.70388e-6   3.88089e-6   2.54079e-6   1.6006e-6    9.70223e-7   5.65897e-7   3.17599e-7   1.71513e-7   8.91231e-8   4.45616e-8   2.14391e-8   9.92496e-9   4.42107e-9   1.89497e-9   7.81542e-10
 -3.13109e-10   1.44722e-9    3.509e-9      8.18671e-9    1.83785e-8    3.96998e-8    8.25168e-8    1.65034e-7    3.17599e-7    5.88113e-7    1.0479e-6     1.79661e-6    2.9639e-6     4.70491e-6    7.18644e-6    1.05622e-5    1.49371e-5    2.03263e-5    2.6615e-5     3.35328e-5    4.06526e-5    4.74225e-5    5.32299e-5    5.74915e-5    5.97486e-5   5.97486e-5   5.74915e-5   5.32299e-5   4.74225e-5   4.06526e-5   3.35328e-5   2.6615e-5    2.03263e-5   1.49371e-5   1.05622e-5   7.18644e-6   4.70491e-6   2.9639e-6    1.79661e-6   1.0479e-6    5.88113e-7   3.17599e-7   1.65034e-7   8.25168e-8   3.96998e-8   1.83785e-8   8.18671e-9   3.509e-9     1.44722e-9
 -2.92908e-10   2.57865e-9    6.25233e-9    1.45871e-8    3.27468e-8    7.07371e-8    1.47028e-7    2.94057e-7    5.65897e-7    1.0479e-6     1.86714e-6    3.20119e-6    5.28108e-6    8.38319e-6    1.28048e-5    1.88196e-5    2.6615e-5     3.62174e-5    4.74225e-5    5.97486e-5    7.24348e-5    8.44972e-5    9.4845e-5     0.000102438   0.00010646   0.00010646   0.000102438  9.4845e-5    8.44972e-5   7.24348e-5   5.97486e-5   4.74225e-5   3.62174e-5   2.6615e-5    1.88196e-5   1.28048e-5   8.38319e-6   5.28108e-6   3.20119e-6   1.86714e-6   1.0479e-6    5.65897e-7   2.94057e-7   1.47028e-7   7.07371e-8   3.27468e-8   1.45871e-8   6.25233e-9   2.57865e-9
 -2.72708e-10   4.42107e-9    1.07195e-8    2.50093e-8    5.6144e-8     1.21278e-7    2.52078e-7    5.04156e-7    9.70223e-7    1.79661e-6    3.20119e-6    5.48841e-6    9.05434e-6    1.43729e-5    2.19536e-5    3.2266e-5     4.5631e-5     6.20943e-5    8.13053e-5    0.000102438   0.000124189   0.00014487    0.000162611   0.000175629   0.000182524  0.000182524  0.000175629  0.000162611  0.00014487   0.000124189  0.000102438  8.13053e-5   6.20943e-5   4.5631e-5    3.2266e-5    2.19536e-5   1.43729e-5   9.05434e-6   5.48841e-6   3.20119e-6   1.79661e-6   9.70223e-7   5.04156e-7   2.52078e-7   1.21278e-7   5.6144e-8    2.50093e-8   1.07195e-8   4.42107e-9
 -2.52507e-10   7.29353e-9    1.76843e-8    4.12584e-8    9.2622e-8     2.00075e-7    4.15859e-7    8.31718e-7    1.6006e-6     2.9639e-6     5.28108e-6    9.05434e-6    1.49371e-5    2.37112e-5    3.62174e-5    5.32299e-5    7.52785e-5    0.000102438   0.000134131   0.000168994   0.000204876   0.000238994   0.000268262   0.000289739   0.000301114  0.000301114  0.000289739  0.000268262  0.000238994  0.000204876  0.000168994  0.000134131  0.000102438  7.52785e-5   5.32299e-5   3.62174e-5   2.37112e-5   1.49371e-5   9.05434e-6   5.28108e-6   2.9639e-6    1.6006e-6    8.31718e-7   4.15859e-7   2.00075e-7   9.2622e-8    4.12584e-8   1.76843e-8   7.29353e-9
 -2.32307e-10   1.15778e-8    2.8072e-8     6.54937e-8    1.47028e-7    3.17599e-7    6.60135e-7    1.32027e-6    2.54079e-6    4.70491e-6    8.38319e-6    1.43729e-5    2.37112e-5    3.76392e-5    5.74915e-5    8.44972e-5    0.000119497   0.000162611   0.00021292    0.000268262   0.000325221   0.00037938    0.000425839   0.000459932   0.000477989  0.000477989  0.000459932  0.000425839  0.00037938   0.000325221  0.000268262  0.00021292   0.000162611  0.000119497  8.44972e-5   5.74915e-5   3.76392e-5   2.37112e-5   1.43729e-5   8.38319e-6   4.70491e-6   2.54079e-6   1.32027e-6   6.60135e-7   3.17599e-7   1.47028e-7   6.54937e-8   2.8072e-8    1.15778e-8
 -2.12106e-10   1.76843e-8    4.28782e-8    1.00037e-7    2.24576e-7    4.85111e-7    1.00831e-6    2.01663e-6    3.88089e-6    7.18644e-6    1.28048e-5    2.19536e-5    3.62174e-5    5.74915e-5    8.78145e-5    0.000129064   0.000182524   0.000248377   0.000325221   0.000409753   0.000496754   0.000579478   0.000650442   0.000702516   0.000730097  0.000730097  0.000702516  0.000650442  0.000579478  0.000496754  0.000409753  0.000325221  0.000248377  0.000182524  0.000129064  8.78145e-5   5.74915e-5   3.62174e-5   2.19536e-5   1.28048e-5   7.18644e-6   3.88089e-6   2.01663e-6   1.00831e-6   4.85111e-7   2.24576e-7   1.00037e-7   4.28782e-8   1.76843e-8
 -1.91905e-10   2.59912e-8    6.30196e-8    1.47028e-7    3.30067e-7    7.12985e-7    1.48195e-6    2.9639e-6     5.70388e-6    1.05622e-5    1.88196e-5    3.2266e-5     5.32299e-5    8.44972e-5    0.000129064   0.00018969    0.000268262   0.000365048   0.000477989   0.000602228   0.000730097   0.000851679   0.000955977   0.00103251    0.00107305   0.00107305   0.00103251   0.000955977  0.000851679  0.000730097  0.000602228  0.000477989  0.000365048  0.000268262  0.00018969   0.000129064  8.44972e-5   5.32299e-5   3.2266e-5    1.88196e-5   1.05622e-5   5.70388e-6   2.9639e-6    1.48195e-6   7.12985e-7   3.30067e-7   1.47028e-7   6.30196e-8   2.59912e-8
 -1.71705e-10   3.67571e-8    8.91231e-8    2.07929e-7    4.66786e-7    1.00831e-6    2.0958e-6     4.19159e-6    8.0665e-6     1.49371e-5    2.6615e-5     4.5631e-5     7.52785e-5    0.000119497   0.000182524   0.000268262   0.00037938    0.000516256   0.000675978   0.000851679   0.00103251    0.00120446    0.00135196    0.00146019    0.00151752   0.00151752   0.00146019   0.00135196   0.00120446   0.00103251   0.000851679  0.000675978  0.000516256  0.00037938   0.000268262  0.000182524  0.000119497  7.52785e-5   4.5631e-5    2.6615e-5    1.49371e-5   8.0665e-6    4.19159e-6   2.0958e-6    1.00831e-6   4.66786e-7   2.07929e-7   8.91231e-8   3.67571e-8
 -1.51504e-10   5.00187e-8    1.21278e-7    2.82948e-7    6.35197e-7    1.3721e-6     2.85194e-6    5.70388e-6    1.09768e-5    2.03263e-5    3.62174e-5    6.20943e-5    0.000102438   0.000162611   0.000248377   0.000365048   0.000516256   0.000702516   0.000919864   0.00115896    0.00140503    0.00163901    0.00183973    0.00198702    0.00206502   0.00206502   0.00198702   0.00183973   0.00163901   0.00140503   0.00115896   0.000919864  0.000702516  0.000516256  0.000365048  0.000248377  0.000162611  0.000102438  6.20943e-5   3.62174e-5   2.03263e-5   1.09768e-5   5.70388e-6   2.85194e-6   1.3721e-6    6.35197e-7   2.82948e-7   1.21278e-7   5.00187e-8
 -1.31304e-10   6.54937e-8    1.58799e-7    3.70488e-7    8.31718e-7    1.79661e-6    3.73429e-6    7.46857e-6    1.43729e-5    2.6615e-5     4.74225e-5    8.13053e-5    0.000134131   0.00021292    0.000325221   0.000477989   0.000675978   0.000919864   0.00120446    0.00151752    0.00183973    0.0021461     0.00240891    0.00260177    0.00270391   0.00270391   0.00260177   0.00240891   0.0021461    0.00183973   0.00151752   0.00120446   0.000919864  0.000675978  0.000477989  0.000325221  0.00021292   0.000134131  8.13053e-5   4.74225e-5   2.6615e-5    1.43729e-5   7.46857e-6   3.73429e-6   1.79661e-6   8.31718e-7   3.70488e-7   1.58799e-7   6.54937e-8
 -1.11103e-10   8.25168e-8    2.00075e-7    4.66786e-7    1.0479e-6     2.26359e-6    4.70491e-6    9.40981e-6    1.81087e-5    3.35328e-5    5.97486e-5    0.000102438   0.000168994   0.000268262   0.000409753   0.000602228   0.000851679   0.00115896    0.00151752    0.00191195    0.00231791    0.00270391    0.00303504    0.00327802    0.00340672   0.00340672   0.00327802   0.00303504   0.00270391   0.00231791   0.00191195   0.00151752   0.00115896   0.000851679  0.000602228  0.000409753  0.000268262  0.000168994  0.000102438  5.97486e-5   3.35328e-5   1.81087e-5   9.40981e-6   4.70491e-6   2.26359e-6   1.0479e-6    4.66786e-7   2.00075e-7   8.25168e-8
 -9.09026e-11   1.00037e-7    2.42556e-7    5.65897e-7    1.27039e-6    2.7442e-6     5.70388e-6    1.14078e-5    2.19536e-5    4.06526e-5    7.24348e-5    0.000124189   0.000204876   0.000325221   0.000496754   0.000730097   0.00103251    0.00140503    0.00183973    0.00231791    0.00281007    0.00327802    0.00367946    0.00397403    0.00413005   0.00413005   0.00397403   0.00367946   0.00327802   0.00281007   0.00231791   0.00183973   0.00140503   0.00103251   0.000730097  0.000496754  0.000325221  0.000204876  0.000124189  7.24348e-5   4.06526e-5   2.19536e-5   1.14078e-5   5.70388e-6   2.7442e-6    1.27039e-6   5.65897e-7   2.42556e-7   1.00037e-7
 -7.0702e-11    1.16696e-7    2.82948e-7    6.60135e-7    1.48195e-6    3.20119e-6    6.65374e-6    1.33075e-5    2.56096e-5    4.74225e-5    8.44972e-5    0.00014487    0.000238994   0.00037938    0.000579478   0.000851679   0.00120446    0.00163901    0.0021461     0.00270391    0.00327802    0.00382391    0.00429219    0.00463582    0.00481782   0.00481782   0.00463582   0.00429219   0.00382391   0.00327802   0.00270391   0.0021461    0.00163901   0.00120446   0.000851679  0.000579478  0.00037938   0.000238994  0.00014487   8.44972e-5   4.74225e-5   2.56096e-5   1.33075e-5   6.65374e-6   3.20119e-6   1.48195e-6   6.60135e-7   2.82948e-7   1.16696e-7
 -5.05014e-11   1.30987e-7    3.17599e-7    7.40976e-7    1.66344e-6    3.59322e-6    7.46857e-6    1.49371e-5    2.87458e-5    5.32299e-5    9.4845e-5     0.000162611   0.000268262   0.000425839   0.000650442   0.000955977   0.00135196    0.00183973    0.00240891    0.00303504    0.00367946    0.00429219    0.00481782    0.00520354    0.00540782   0.00540782   0.00520354   0.00481782   0.00429219   0.00367946   0.00303504   0.00240891   0.00183973   0.00135196   0.000955977  0.000650442  0.000425839  0.000268262  0.000162611  9.4845e-5    5.32299e-5   2.87458e-5   1.49371e-5   7.46857e-6   3.59322e-6   1.66344e-6   7.40976e-7   3.17599e-7   1.30987e-7
 -3.03009e-11   1.41474e-7    3.43026e-7    8.00299e-7    1.79661e-6    3.88089e-6    8.0665e-6     1.6133e-5     3.10471e-5    5.74915e-5    0.000102438   0.000175629   0.000289739   0.000459932   0.000702516   0.00103251    0.00146019    0.00198702    0.00260177    0.00327802    0.00397403    0.00463582    0.00520354    0.00562013    0.00584077   0.00584077   0.00562013   0.00520354   0.00463582   0.00397403   0.00327802   0.00260177   0.00198702   0.00146019   0.00103251   0.000702516  0.000459932  0.000289739  0.000175629  0.000102438  5.74915e-5   3.10471e-5   1.6133e-5    8.0665e-6    3.88089e-6   1.79661e-6   8.00299e-7   3.43026e-7   1.41474e-7
 -1.01003e-11   1.47028e-7    3.56492e-7    8.31718e-7    1.86714e-6    4.03325e-6    8.38319e-6    1.67664e-5    3.2266e-5     5.97486e-5    0.00010646    0.000182524   0.000301114   0.000477989   0.000730097   0.00107305    0.00151752    0.00206502    0.00270391    0.00340672    0.00413005    0.00481782    0.00540782    0.00584077    0.00607008   0.00607008   0.00584077   0.00540782   0.00481782   0.00413005   0.00340672   0.00270391   0.00206502   0.00151752   0.00107305   0.000730097  0.000477989  0.000301114  0.000182524  0.00010646   5.97486e-5   3.2266e-5    1.67664e-5   8.38319e-6   4.03325e-6   1.86714e-6   8.31718e-7   3.56492e-7   1.47028e-7
  1.01003e-11   1.47028e-7    3.56492e-7    8.31718e-7    1.86714e-6    4.03325e-6    8.38319e-6    1.67664e-5    3.2266e-5     5.97486e-5    0.00010646    0.000182524   0.000301114   0.000477989   0.000730097   0.00107305    0.00151752    0.00206502    0.00270391    0.00340672    0.00413005    0.00481782    0.00540782    0.00584077    0.00607008   0.00607008   0.00584077   0.00540782   0.00481782   0.00413005   0.00340672   0.00270391   0.00206502   0.00151752   0.00107305   0.000730097  0.000477989  0.000301114  0.000182524  0.00010646   5.97486e-5   3.2266e-5    1.67664e-5   8.38319e-6   4.03325e-6   1.86714e-6   8.31718e-7   3.56492e-7   1.47028e-7
  3.03009e-11   1.41474e-7    3.43026e-7    8.00299e-7    1.79661e-6    3.88089e-6    8.0665e-6     1.6133e-5     3.10471e-5    5.74915e-5    0.000102438   0.000175629   0.000289739   0.000459932   0.000702516   0.00103251    0.00146019    0.00198702    0.00260177    0.00327802    0.00397403    0.00463582    0.00520354    0.00562013    0.00584077   0.00584077   0.00562013   0.00520354   0.00463582   0.00397403   0.00327802   0.00260177   0.00198702   0.00146019   0.00103251   0.000702516  0.000459932  0.000289739  0.000175629  0.000102438  5.74915e-5   3.10471e-5   1.6133e-5    8.0665e-6    3.88089e-6   1.79661e-6   8.00299e-7   3.43026e-7   1.41474e-7
  5.05014e-11   1.30987e-7    3.17599e-7    7.40976e-7    1.66344e-6    3.59322e-6    7.46857e-6    1.49371e-5    2.87458e-5    5.32299e-5    9.4845e-5     0.000162611   0.000268262   0.000425839   0.000650442   0.000955977   0.00135196    0.00183973    0.00240891    0.00303504    0.00367946    0.00429219    0.00481782    0.00520354    0.00540782   0.00540782   0.00520354   0.00481782   0.00429219   0.00367946   0.00303504   0.00240891   0.00183973   0.00135196   0.000955977  0.000650442  0.000425839  0.000268262  0.000162611  9.4845e-5    5.32299e-5   2.87458e-5   1.49371e-5   7.46857e-6   3.59322e-6   1.66344e-6   7.40976e-7   3.17599e-7   1.30987e-7
  7.0702e-11    1.16696e-7    2.82948e-7    6.60135e-7    1.48195e-6    3.20119e-6    6.65374e-6    1.33075e-5    2.56096e-5    4.74225e-5    8.44972e-5    0.00014487    0.000238994   0.00037938    0.000579478   0.000851679   0.00120446    0.00163901    0.0021461     0.00270391    0.00327802    0.00382391    0.00429219    0.00463582    0.00481782   0.00481782   0.00463582   0.00429219   0.00382391   0.00327802   0.00270391   0.0021461    0.00163901   0.00120446   0.000851679  0.000579478  0.00037938   0.000238994  0.00014487   8.44972e-5   4.74225e-5   2.56096e-5   1.33075e-5   6.65374e-6   3.20119e-6   1.48195e-6   6.60135e-7   2.82948e-7   1.16696e-7
  9.09026e-11   1.00037e-7    2.42556e-7    5.65897e-7    1.27039e-6    2.7442e-6     5.70388e-6    1.14078e-5    2.19536e-5    4.06526e-5    7.24348e-5    0.000124189   0.000204876   0.000325221   0.000496754   0.000730097   0.00103251    0.00140503    0.00183973    0.00231791    0.00281007    0.00327802    0.00367946    0.00397403    0.00413005   0.00413005   0.00397403   0.00367946   0.00327802   0.00281007   0.00231791   0.00183973   0.00140503   0.00103251   0.000730097  0.000496754  0.000325221  0.000204876  0.000124189  7.24348e-5   4.06526e-5   2.19536e-5   1.14078e-5   5.70388e-6   2.7442e-6    1.27039e-6   5.65897e-7   2.42556e-7   1.00037e-7
  1.11103e-10   8.25168e-8    2.00075e-7    4.66786e-7    1.0479e-6     2.26359e-6    4.70491e-6    9.40981e-6    1.81087e-5    3.35328e-5    5.97486e-5    0.000102438   0.000168994   0.000268262   0.000409753   0.000602228   0.000851679   0.00115896    0.00151752    0.00191195    0.00231791    0.00270391    0.00303504    0.00327802    0.00340672   0.00340672   0.00327802   0.00303504   0.00270391   0.00231791   0.00191195   0.00151752   0.00115896   0.000851679  0.000602228  0.000409753  0.000268262  0.000168994  0.000102438  5.97486e-5   3.35328e-5   1.81087e-5   9.40981e-6   4.70491e-6   2.26359e-6   1.0479e-6    4.66786e-7   2.00075e-7   8.25168e-8
  1.31304e-10   6.54937e-8    1.58799e-7    3.70488e-7    8.31718e-7    1.79661e-6    3.73429e-6    7.46857e-6    1.43729e-5    2.6615e-5     4.74225e-5    8.13053e-5    0.000134131   0.00021292    0.000325221   0.000477989   0.000675978   0.000919864   0.00120446    0.00151752    0.00183973    0.0021461     0.00240891    0.00260177    0.00270391   0.00270391   0.00260177   0.00240891   0.0021461    0.00183973   0.00151752   0.00120446   0.000919864  0.000675978  0.000477989  0.000325221  0.00021292   0.000134131  8.13053e-5   4.74225e-5   2.6615e-5    1.43729e-5   7.46857e-6   3.73429e-6   1.79661e-6   8.31718e-7   3.70488e-7   1.58799e-7   6.54937e-8
  1.51504e-10   5.00187e-8    1.21278e-7    2.82948e-7    6.35197e-7    1.3721e-6     2.85194e-6    5.70388e-6    1.09768e-5    2.03263e-5    3.62174e-5    6.20943e-5    0.000102438   0.000162611   0.000248377   0.000365048   0.000516256   0.000702516   0.000919864   0.00115896    0.00140503    0.00163901    0.00183973    0.00198702    0.00206502   0.00206502   0.00198702   0.00183973   0.00163901   0.00140503   0.00115896   0.000919864  0.000702516  0.000516256  0.000365048  0.000248377  0.000162611  0.000102438  6.20943e-5   3.62174e-5   2.03263e-5   1.09768e-5   5.70388e-6   2.85194e-6   1.3721e-6    6.35197e-7   2.82948e-7   1.21278e-7   5.00187e-8
  1.71705e-10   3.67571e-8    8.91231e-8    2.07929e-7    4.66786e-7    1.00831e-6    2.0958e-6     4.19159e-6    8.0665e-6     1.49371e-5    2.6615e-5     4.5631e-5     7.52785e-5    0.000119497   0.000182524   0.000268262   0.00037938    0.000516256   0.000675978   0.000851679   0.00103251    0.00120446    0.00135196    0.00146019    0.00151752   0.00151752   0.00146019   0.00135196   0.00120446   0.00103251   0.000851679  0.000675978  0.000516256  0.00037938   0.000268262  0.000182524  0.000119497  7.52785e-5   4.5631e-5    2.6615e-5    1.49371e-5   8.0665e-6    4.19159e-6   2.0958e-6    1.00831e-6   4.66786e-7   2.07929e-7   8.91231e-8   3.67571e-8
  1.91905e-10   2.59912e-8    6.30196e-8    1.47028e-7    3.30067e-7    7.12985e-7    1.48195e-6    2.9639e-6     5.70388e-6    1.05622e-5    1.88196e-5    3.2266e-5     5.32299e-5    8.44972e-5    0.000129064   0.00018969    0.000268262   0.000365048   0.000477989   0.000602228   0.000730097   0.000851679   0.000955977   0.00103251    0.00107305   0.00107305   0.00103251   0.000955977  0.000851679  0.000730097  0.000602228  0.000477989  0.000365048  0.000268262  0.00018969   0.000129064  8.44972e-5   5.32299e-5   3.2266e-5    1.88196e-5   1.05622e-5   5.70388e-6   2.9639e-6    1.48195e-6   7.12985e-7   3.30067e-7   1.47028e-7   6.30196e-8   2.59912e-8
  2.12106e-10   1.76843e-8    4.28782e-8    1.00037e-7    2.24576e-7    4.85111e-7    1.00831e-6    2.01663e-6    3.88089e-6    7.18644e-6    1.28048e-5    2.19536e-5    3.62174e-5    5.74915e-5    8.78145e-5    0.000129064   0.000182524   0.000248377   0.000325221   0.000409753   0.000496754   0.000579478   0.000650442   0.000702516   0.000730097  0.000730097  0.000702516  0.000650442  0.000579478  0.000496754  0.000409753  0.000325221  0.000248377  0.000182524  0.000129064  8.78145e-5   5.74915e-5   3.62174e-5   2.19536e-5   1.28048e-5   7.18644e-6   3.88089e-6   2.01663e-6   1.00831e-6   4.85111e-7   2.24576e-7   1.00037e-7   4.28782e-8   1.76843e-8
  2.32307e-10   1.15778e-8    2.8072e-8     6.54937e-8    1.47028e-7    3.17599e-7    6.60135e-7    1.32027e-6    2.54079e-6    4.70491e-6    8.38319e-6    1.43729e-5    2.37112e-5    3.76392e-5    5.74915e-5    8.44972e-5    0.000119497   0.000162611   0.00021292    0.000268262   0.000325221   0.00037938    0.000425839   0.000459932   0.000477989  0.000477989  0.000459932  0.000425839  0.00037938   0.000325221  0.000268262  0.00021292   0.000162611  0.000119497  8.44972e-5   5.74915e-5   3.76392e-5   2.37112e-5   1.43729e-5   8.38319e-6   4.70491e-6   2.54079e-6   1.32027e-6   6.60135e-7   3.17599e-7   1.47028e-7   6.54937e-8   2.8072e-8    1.15778e-8
  2.52507e-10   7.29353e-9    1.76843e-8    4.12584e-8    9.2622e-8     2.00075e-7    4.15859e-7    8.31718e-7    1.6006e-6     2.9639e-6     5.28108e-6    9.05434e-6    1.49371e-5    2.37112e-5    3.62174e-5    5.32299e-5    7.52785e-5    0.000102438   0.000134131   0.000168994   0.000204876   0.000238994   0.000268262   0.000289739   0.000301114  0.000301114  0.000289739  0.000268262  0.000238994  0.000204876  0.000168994  0.000134131  0.000102438  7.52785e-5   5.32299e-5   3.62174e-5   2.37112e-5   1.49371e-5   9.05434e-6   5.28108e-6   2.9639e-6    1.6006e-6    8.31718e-7   4.15859e-7   2.00075e-7   9.2622e-8    4.12584e-8   1.76843e-8   7.29353e-9
  2.72708e-10   4.42107e-9    1.07195e-8    2.50093e-8    5.6144e-8     1.21278e-7    2.52078e-7    5.04156e-7    9.70223e-7    1.79661e-6    3.20119e-6    5.48841e-6    9.05434e-6    1.43729e-5    2.19536e-5    3.2266e-5     4.5631e-5     6.20943e-5    8.13053e-5    0.000102438   0.000124189   0.00014487    0.000162611   0.000175629   0.000182524  0.000182524  0.000175629  0.000162611  0.00014487   0.000124189  0.000102438  8.13053e-5   6.20943e-5   4.5631e-5    3.2266e-5    2.19536e-5   1.43729e-5   9.05434e-6   5.48841e-6   3.20119e-6   1.79661e-6   9.70223e-7   5.04156e-7   2.52078e-7   1.21278e-7   5.6144e-8    2.50093e-8   1.07195e-8   4.42107e-9
  2.92908e-10   2.57865e-9    6.25233e-9    1.45871e-8    3.27468e-8    7.07371e-8    1.47028e-7    2.94057e-7    5.65897e-7    1.0479e-6     1.86714e-6    3.20119e-6    5.28108e-6    8.38319e-6    1.28048e-5    1.88196e-5    2.6615e-5     3.62174e-5    4.74225e-5    5.97486e-5    7.24348e-5    8.44972e-5    9.4845e-5     0.000102438   0.00010646   0.00010646   0.000102438  9.4845e-5    8.44972e-5   7.24348e-5   5.97486e-5   4.74225e-5   3.62174e-5   2.6615e-5    1.88196e-5   1.28048e-5   8.38319e-6   5.28108e-6   3.20119e-6   1.86714e-6   1.0479e-6    5.65897e-7   2.94057e-7   1.47028e-7   7.07371e-8   3.27468e-8   1.45871e-8   6.25233e-9   2.57865e-9
  3.13109e-10   1.44722e-9    3.509e-9      8.18671e-9    1.83785e-8    3.96998e-8    8.25168e-8    1.65034e-7    3.17599e-7    5.88113e-7    1.0479e-6     1.79661e-6    2.9639e-6     4.70491e-6    7.18644e-6    1.05622e-5    1.49371e-5    2.03263e-5    2.6615e-5     3.35328e-5    4.06526e-5    4.74225e-5    5.32299e-5    5.74915e-5    5.97486e-5   5.97486e-5   5.74915e-5   5.32299e-5   4.74225e-5   4.06526e-5   3.35328e-5   2.6615e-5    2.03263e-5   1.49371e-5   1.05622e-5   7.18644e-6   4.70491e-6   2.9639e-6    1.79661e-6   1.0479e-6    5.88113e-7   3.17599e-7   1.65034e-7   8.25168e-8   3.96998e-8   1.83785e-8   8.18671e-9   3.509e-9     1.44722e-9
  3.33309e-10   7.81542e-10   1.89497e-9    4.42107e-9    9.92496e-9    2.14391e-8    4.45616e-8    8.91231e-8    1.71513e-7    3.17599e-7    5.65897e-7    9.70223e-7    1.6006e-6     2.54079e-6    3.88089e-6    5.70388e-6    8.0665e-6     1.09768e-5    1.43729e-5    1.81087e-5    2.19536e-5    2.56096e-5    2.87458e-5    3.10471e-5    3.2266e-5    3.2266e-5    3.10471e-5   2.87458e-5   2.56096e-5   2.19536e-5   1.81087e-5   1.43729e-5   1.09768e-5   8.0665e-6    5.70388e-6   3.88089e-6   2.54079e-6   1.6006e-6    9.70223e-7   5.65897e-7   3.17599e-7   1.71513e-7   8.91231e-8   4.45616e-8   2.14391e-8   9.92496e-9   4.42107e-9   1.89497e-9   7.81542e-10
  3.5351e-10    4.06112e-10   9.84681e-10   2.29732e-9    5.1573e-9     1.11404e-8    2.31555e-8    4.6311e-8     8.91231e-8    1.65034e-7    2.94057e-7    5.04156e-7    8.31718e-7    1.32027e-6    2.01663e-6    2.9639e-6     4.19159e-6    5.70388e-6    7.46857e-6    9.40981e-6    1.14078e-5    1.33075e-5    1.49371e-5    1.6133e-5     1.67664e-5   1.67664e-5   1.6133e-5    1.49371e-5   1.33075e-5   1.14078e-5   9.40981e-6   7.46857e-6   5.70388e-6   4.19159e-6   2.9639e-6    2.01663e-6   1.32027e-6   8.31718e-7   5.04156e-7   2.94057e-7   1.65034e-7   8.91231e-8   4.6311e-8    2.31555e-8   1.11404e-8   5.1573e-9    2.29732e-9   9.84681e-10  4.06112e-10
  3.73711e-10   2.03056e-10   4.9234e-10    1.14866e-9    2.57865e-9    5.57019e-9    1.15778e-8    2.31555e-8    4.45616e-8    8.25168e-8    1.47028e-7    2.52078e-7    4.15859e-7    6.60135e-7    1.00831e-6    1.48195e-6    2.0958e-6     2.85194e-6    3.73429e-6    4.70491e-6    5.70388e-6    6.65374e-6    7.46857e-6    8.0665e-6     8.38319e-6   8.38319e-6   8.0665e-6    7.46857e-6   6.65374e-6   5.70388e-6   4.70491e-6   3.73429e-6   2.85194e-6   2.0958e-6    1.48195e-6   1.00831e-6   6.60135e-7   4.15859e-7   2.52078e-7   1.47028e-7   8.25168e-8   4.45616e-8   2.31555e-8   1.15778e-8   5.57019e-9   2.57865e-9   1.14866e-9   4.9234e-10   2.03056e-10
  3.93911e-10   9.76927e-11   2.36871e-10   5.52633e-10   1.24062e-9    2.67989e-9    5.57019e-9    1.11404e-8    2.14391e-8    3.96998e-8    7.07371e-8    1.21278e-7    2.00075e-7    3.17599e-7    4.85111e-7    7.12985e-7    1.00831e-6    1.3721e-6     1.79661e-6    2.26359e-6    2.7442e-6     3.20119e-6    3.59322e-6    3.88089e-6    4.03325e-6   4.03325e-6   3.88089e-6   3.59322e-6   3.20119e-6   2.7442e-6    2.26359e-6   1.79661e-6   1.3721e-6    1.00831e-6   7.12985e-7   4.85111e-7   3.17599e-7   2.00075e-7   1.21278e-7   7.07371e-8   3.96998e-8   2.14391e-8   1.11404e-8   5.57019e-9   2.67989e-9   1.24062e-9   5.52633e-10  2.36871e-10  9.76927e-11
  4.14112e-10   4.52256e-11   1.09656e-10   2.55835e-10   5.74329e-10   1.24062e-9    2.57865e-9    5.1573e-9     9.92496e-9    1.83785e-8    3.27468e-8    5.6144e-8     9.2622e-8     1.47028e-7    2.24576e-7    3.30067e-7    4.66786e-7    6.35197e-7    8.31718e-7    1.0479e-6     1.27039e-6    1.48195e-6    1.66344e-6    1.79661e-6    1.86714e-6   1.86714e-6   1.79661e-6   1.66344e-6   1.48195e-6   1.27039e-6   1.0479e-6    8.31718e-7   6.35197e-7   4.66786e-7   3.30067e-7   2.24576e-7   1.47028e-7   9.2622e-8    5.6144e-8    3.27468e-8   1.83785e-8   9.92496e-9   5.1573e-9    2.57865e-9   1.24062e-9   5.74329e-10  2.55835e-10  1.09656e-10  4.52256e-11
  4.34312e-10   2.01457e-11   4.88463e-11   1.13961e-10   2.55835e-10   5.52633e-10   1.14866e-9    2.29732e-9    4.42107e-9    8.18671e-9    1.45871e-8    2.50093e-8    4.12584e-8    6.54937e-8    1.00037e-7    1.47028e-7    2.07929e-7    2.82948e-7    3.70488e-7    4.66786e-7    5.65897e-7    6.60135e-7    7.40976e-7    8.00299e-7    8.31718e-7   8.31718e-7   8.00299e-7   7.40976e-7   6.60135e-7   5.65897e-7   4.66786e-7   3.70488e-7   2.82948e-7   2.07929e-7   1.47028e-7   1.00037e-7   6.54937e-8   4.12584e-8   2.50093e-8   1.45871e-8   8.18671e-9   4.42107e-9   2.29732e-9   1.14866e-9   5.52633e-10  2.55835e-10  1.13961e-10  4.88463e-11  2.01457e-11
  4.54513e-10   8.6349e-12    2.09366e-11   4.88463e-11   1.09656e-10   2.36871e-10   4.9234e-10    9.84681e-10   1.89497e-9    3.509e-9      6.25233e-9    1.07195e-8    1.76843e-8    2.8072e-8     4.28782e-8    6.30196e-8    8.91231e-8    1.21278e-7    1.58799e-7    2.00075e-7    2.42556e-7    2.82948e-7    3.17599e-7    3.43026e-7    3.56492e-7   3.56492e-7   3.43026e-7   3.17599e-7   2.82948e-7   2.42556e-7   2.00075e-7   1.58799e-7   1.21278e-7   8.91231e-8   6.30196e-8   4.28782e-8   2.8072e-8    1.76843e-8   1.07195e-8   6.25233e-9   3.509e-9     1.89497e-9   9.84681e-10  4.9234e-10   2.36871e-10  1.09656e-10  4.88463e-11  2.09366e-11  8.6349e-12
  4.74713e-10   3.56129e-12   8.6349e-12    2.01457e-11   4.52256e-11   9.76927e-11   2.03056e-10   4.06112e-10   7.81542e-10   1.44722e-9    2.57865e-9    4.42107e-9    7.29353e-9    1.15778e-8    1.76843e-8    2.59912e-8    3.67571e-8    5.00187e-8    6.54937e-8    8.25168e-8    1.00037e-7    1.16696e-7    1.30987e-7    1.41474e-7    1.47028e-7   1.47028e-7   1.41474e-7   1.30987e-7   1.16696e-7   1.00037e-7   8.25168e-8   6.54937e-8   5.00187e-8   3.67571e-8   2.59912e-8   1.76843e-8   1.15778e-8   7.29353e-9   4.42107e-9   2.57865e-9   1.44722e-9   7.81542e-10  4.06112e-10  2.03056e-10  9.76927e-11  4.52256e-11  2.01457e-11  8.6349e-12   3.56129e-12

We use again use a GMRF prior similar to the Imaging a Black Hole using only Closure Quantities tutorial for the log-ratio transformed image. We use the same correlated image prior for the inverse-logit transformed total polarization. The mean total polarization fraction p0 is centered at -2.0 with a standard deviation of 2.0 which logit transformed puts most of the prior mass < 0.8 fractional polarization. The standard deviation of the total polarization fraction pσ again uses a Half-normal process. The angular parameters of the polarizaton are given by a uniform prior on the sphere.

julia

cprior = corr_image_prior(grid, dvis; order = 2)

HierarchicalPrior(
	map: 
	ConditionalMarkov(
Random Field: VLBIImagePriors.GaussMarkovRandomField
Graph: MarkovRandomFieldGraph{2}(
dims: (48, 48)
)
)	hyper prior: 
	VLBIImagePriors.VLBITruncated{VLBIImagePriors.AffineDistribution{VLBIImagePriors.StdInverseGamma{Float64, Float64, 0}, 0, Float64, Float64}, Float64, Int64, Float64}(
untruncated: AffineDistribution(base=StdInverseGamma, loc::0.0, scale::27.59477905945553)
lower: 1.0
upper: 96
logtp: -0.28744561520404394
lcdf: 1.0369068061208359e-12
)

)

The total flux is fixed to 0.6 since it is degenerate with an overall shift in the gain amplitudes.

julia

skym = sky(grid; mimg, ftot = 0.6, cprior)

SkyModel
  with map: _sky_sky
   on grid: 
RectiGrid(
executor: ComradeBase.Serial()
Dimensions: 
(↓ X Sampled{Float64} LinRange{Float64}(-4.747133960864206e-10, 4.747133960864206e-10, 48) ForwardOrdered Regular Points,
→ Y Sampled{Float64} LinRange{Float64}(-4.747133960864206e-10, 4.747133960864206e-10, 48) ForwardOrdered Regular Points)
)
   )

Now we build the instrument model. Due to the complexity of VLBI the instrument model is critical to the success of imaging and getting reliable results. For this example we will use the standard instrument model used in polarized EHT analyses expressed in the RIME formalism. Our Jones decomposition will be given by GDR, where G are the complex gains, D are the d-terms, and R is what we call the ideal instrument response, which is how an ideal interferometer using the feed basis we observe relative to some reference basis.

Given the possible flexibility in different parameterizations of the individual Jones matrices each Jones matrix requires the user to specify a function that converts from parameters to specific parameterization f the jones matrices.

We bundle the whole instrument model — the Jones matrices and their priors — in a single block with the @instrument macro. Each Jones term is its own @jones block: the name ~ ArrayPrior(...) lines inside are that term's priors, and the block builds and returns the Jones matrix. The macro lifts each @jones body — and the combination function — into a named function for us (named functions, unlike closures, serialize reliably).

The individual Jones matrices are:

JonesG — the complex gains, in an amplitude/phase decomposition. The gain matrix is diagonal, so it returns a 2-tuple (R feed, L feed).
JonesD — the leakage (d-)terms in the small-leakage limit [1 d1; d2 1], using a re-im parameterization, returning a 2-tuple.
JonesR — the response matrix (basis transform plus feed rotation). It has no free parameters, so its @jones block has no ~ lines.

We combine them with JonesSandwich using the standard J = adjoint(R)*G*D*R.

Note

For arrays with non-zero leakage, feed rotation calibration does not remove the impact of feed rotations on the instrument model: the R and D matrices do not commute, so feed rotation must be modelled. This is why we keep add_fr = true and apply adjoint(R) in the composition. This is especially important for interferometers using a mixture of linear and circular feeds.

For the instrument prior we use IID priors for the gains and d-terms. The IIDSitePrior segments are ScanSeg() (independent per scan), TrackSeg() (constant over the track), and IntegSeg() (changes each integration time). For released EHT data the gains are stable over a scan, while the d-terms are stable over the track.

julia

@instrument function instrument()
    # Complex gains: amplitude/phase decomposition, returning (gR, gL).
    G = @jones begin
        lgR ~ ArrayPrior(IIDSitePrior(ScanSeg(), VLBIGaussian(0.0, 0.2)); LM = IIDSitePrior(ScanSeg(), VLBIGaussian(0.0, 1.0)))
        lgrat ~ ArrayPrior(IIDSitePrior(ScanSeg(), VLBIGaussian(0.0, 0.1)))
        gpR ~ ArrayPrior(IIDSitePrior(ScanSeg(), DiagonalVonMises(0.0, inv(π^2))); refant = SEFDReference(0.0), phase = true)
        gprat ~ ArrayPrior(IIDSitePrior(ScanSeg(), DiagonalVonMises(0.0, inv(0.1^2))); refant = SingleReference(:AA, 0.0), phase = true)
        gR = exp(complex(lgR, gpR))
        gL = gR * exp(complex(lgrat, gprat))
        return JonesG((gR, gL))
    end
    # Leakage/d-terms (re-im parameterization), returning (dR, dL).
    D = @jones begin
        dRx ~ ArrayPrior(IIDSitePrior(TrackSeg(), VLBIGaussian(0.0, 0.2)))
        dRy ~ ArrayPrior(IIDSitePrior(TrackSeg(), VLBIGaussian(0.0, 0.2)))
        dLx ~ ArrayPrior(IIDSitePrior(TrackSeg(), VLBIGaussian(0.0, 0.2)))
        dLy ~ ArrayPrior(IIDSitePrior(TrackSeg(), VLBIGaussian(0.0, 0.2)))
        return JonesD((complex(dRx, dRy), complex(dLx, dLy)))
    end
    # The ideal response (basis transform + feed rotation); no free parameters.
    R = @jones begin
        return JonesR(; add_fr = true)
    end
    # Combine into the full Jones matrix J = adjoint(R)*G*D*R.
    return JonesSandwich(G, D, R) do g, d, r
        return adjoint(r) * g * d * r
    end
end

instrument (generic function with 1 method)

Building the instrument model is now a single call.

julia

intmodel = instrument()

InstrumentModel
  with Jones: JonesSandwich
  with reference basis: PolarizedTypes.CirBasis()

intmodel = InstrumentModel(JonesR(;add_fr=true)) Putting it all together, we form our likelihood and posterior objects for optimization and sampling, and specifying to use Enzyme.Reverse with runtime activity for AD.

julia

using Enzyme
post = VLBIPosterior(skym, intmodel, dvis);

Reconstructing the Image and Instrument Effects

To sample from this posterior, it is convenient to move from our constrained parameter space to an unconstrained one (i.e., the support of the transformed posterior is (-∞, ∞)). This transformation is done using the asflat function.

julia

tpost = asflat(post);

We can also query the dimension of our posterior or the number of parameters we will sample.

Warning

This can often be different from what you would expect. This difference is especially true when using angular variables, where we often artificially increase the dimension of the parameter space to make sampling easier.

Now we optimize. Unlike other imaging examples, we move straight to gradient optimizers due to the higher dimension of the space. In addition the only AD package that can currently work with the polarized Comrade posterior is Enzyme.

julia

using Optimization, OptimizationLBFGSB
xopt, sol = comrade_opt(
    post, LBFGSB();
    initial_params = prior_sample(rng, post), maxiters = 2_000
)

((sky = (σs = (4.159712568479853, 0.3421561087990353, 0.11637516631029453, 0.011586642265195677), as = ((params = [0.03553909463869862 0.08950466634992969 0.15570650973479433 0.21082934600740083 0.2549598833496592 0.3013113277274086 0.33725526525677735 0.3528893325847083 0.35774841292904547 0.3538384004990176 0.33301854516004836 0.2966714622210386 0.25801994409005397 0.2238518149738415 0.19742085642630006 0.17406890170266298 0.15102856663892858 0.13552326733868997 0.1268067345558267 0.12673370259810798 0.1312646766066671 0.1396152920028447 0.1485543398728005 0.15420509743534155 0.14848994218703146 0.12400382738078182 0.07872629446724361 0.025277934656326845 -0.016231416697530837 -0.033285762636661664 -0.03717305470888821 -0.04708574519381046 -0.06901565779308114 -0.10605388638044634 -0.1477126332413311 -0.1864506878701937 -0.21869632080243787 -0.2367731884369807 -0.2427184786097925 -0.24270788612647437 -0.24203976817450562 -0.2393996749256336 -0.2284651929528563 -0.20969456861764257 -0.1853371835158968 -0.15205534617843916 -0.1074599573386797 -0.05504863324836578; 0.08172653375645228 0.18951223345248894 0.30650482324763373 0.3993625621571946 0.472819483346712 0.5522306194536284 0.6281590377402166 0.6824427640477906 0.7131196912295531 0.7104485237377456 0.6783543182964837 0.6307100965577241 0.5735147157554294 0.515954275934077 0.45944315464860686 0.40342367562246906 0.35686452183377004 0.3277457139607089 0.3146060603195253 0.3134948369799113 0.3164722371997532 0.32092529238779893 0.3225772276194299 0.3186730350312686 0.3013700501001781 0.2607298840803007 0.19048180728530464 0.1014350741780794 0.01831775997966969 -0.03898309733738996 -0.07346567889102076 -0.10673843141462505 -0.15109774171887652 -0.21054635579316233 -0.2789938553109569 -0.34414651711091 -0.4001062489083092 -0.43828892281665205 -0.4555379411873882 -0.45847004129198743 -0.45560922542072074 -0.44930152279667784 -0.4319970669958326 -0.39981013409131777 -0.3534005906972204 -0.2881481779819692 -0.20219870729430003 -0.10317652368373342; 0.14563746920024032 0.29021301218417717 0.42976986094079206 0.5572324550874692 0.6690245993878728 0.7700897763570983 0.8663427451812693 0.950355624544679 1.0078967516847286 1.0340553541904536 1.0305827602164084 0.9979965947374274 0.9376127443830533 0.8595525857475138 0.77076750858554 0.6854031891419052 0.626659533768062 0.593924393676795 0.5830663795780296 0.5788541846358278 0.5743288508744582 0.5612884874733842 0.5406823509716411 0.5127811111093854 0.477391977393994 0.4271461271013861 0.3507846947761956 0.2426330571440337 0.1185864432790707 0.0034622831746540057 -0.08737322516086045 -0.15981796331340264 -0.22790484854620377 -0.2992582160439744 -0.37779450611042736 -0.45495823153478754 -0.5223355510143847 -0.5754379186655764 -0.6076288460330695 -0.6207160071103955 -0.6199812461561338 -0.6089397000805262 -0.5879012336680819 -0.5496484922671949 -0.48546386562960947 -0.3924020592748845 -0.2745649841439755 -0.1407431801433648; 0.1993520154910808 0.37110302913612025 0.5213770005490961 0.6726983874967841 0.8275722652579383 0.968540375865319 1.0886074013356826 1.1900204127168417 1.2737186703140333 1.3351157460761782 1.354574789900466 1.326359717104971 1.2634107162916504 1.1752194246309295 1.0762001262388394 0.99652999546931 0.9538896037189842 0.9388358577167261 0.9371016142269579 0.9300501240674152 0.9107362231896247 0.8727773651390683 0.8228968423882795 0.7659141991677251 0.7052979564070079 0.638587878293382 0.5548304512969336 0.43510088155935855 0.2755216078110752 0.1012678872141224 -0.054801858030182934 -0.17868589919230154 -0.2765991375236698 -0.3582111517437871 -0.43450292849022354 -0.5066711518567666 -0.5710253605318155 -0.6295162599608679 -0.6765978134527625 -0.7054936416092087 -0.7155390598940015 -0.7078263955326152 -0.684813701348606 -0.6407754153186918 -0.5646627033650851 -0.4553925718819981 -0.3198118869982176 -0.16516472352653788; 0.22193598607086046 0.4146891322327484 0.5809426855967136 0.7514800813673023 0.9429195714698883 1.1319459328094177 1.2913061545902975 1.427335767351905 1.5432022224603856 1.6131631231277732 1.6274112109558678 1.601689132020246 1.5476177432309126 1.469942685711735 1.3922251191262118 1.3508605863867742 1.348301505143919 1.3653946096296323 1.3741280746902897 1.3553116182504872 1.3020298589692672 1.2287407832035426 1.147974213188079 1.0646330884791058 0.9787868455041906 0.88657709602568 0.7801638542324327 0.6468387871752125 0.46967250654043635 0.25751098492413294 0.048261343788145034 -0.1268549288412009 -0.2613945507780661 -0.3600599241145086 -0.4350662104350982 -0.4959725612152742 -0.5483257409680097 -0.6019522347029971 -0.6575201905708846 -0.70273614177674 -0.7286287167537284 -0.7329006589645999 -0.713642323684954 -0.66702892695348 -0.5884081296831468 -0.4765119023499504 -0.33555081154770655 -0.17338271881899217; 0.22212251757267232 0.4228946786882029 0.6097231384082429 0.8079021444584451 1.0245878219824252 1.2402495428413243 1.440501327309643 1.6250194725671596 1.7708664363041222 1.8496362824298334 1.876889482165084 1.8738977862620376 1.8383055594515532 1.7811255658145786 1.7404197974370892 1.7512550357091747 1.7991373844401704 1.8499060363296411 1.864210470078623 1.8130034190255058 1.7029121985082107 1.5764533515843788 1.4647551835033448 1.3667846098961989 1.2682130666537377 1.1576758177069852 1.0259398391043182 0.8683174210469237 0.6804686648563121 0.4569077824538462 0.22110570062321402 0.010143194011639586 -0.1567111634768914 -0.2771246348131186 -0.36145016961812954 -0.4211973531189132 -0.46460750645669274 -0.5073064988652666 -0.5596751522740535 -0.6149147996792315 -0.6591996787270024 -0.6802434335801301 -0.671144618993042 -0.6321245501506915 -0.5626279278347178 -0.4590317615098568 -0.32359153061769397 -0.16669519428458732; 0.20600062732576294 0.4059676972442397 0.6099392720958251 0.8334273182573392 1.0708452574966316 1.3057415058566815 1.5376637369171613 1.7580396411528765 1.9275846363058535 2.027420941658059 2.0837693355394946 2.1084085196852245 2.0956967907204196 2.0701273423567432 2.081909976048892 2.1497510326562983 2.2388556977106315 2.3102286943950237 2.315623380575649 2.2271261422817603 2.058389062280028 1.8744325500742123 1.7315849201634337 1.635107998135868 1.548011091730661 1.4390590315877974 1.2969024758917642 1.1162519032442615 0.9080029297728044 0.6762545405830892 0.43016921327865687 0.20184976757768777 0.014080269510477764 -0.12320911259660157 -0.2182277420334738 -0.28480096857924464 -0.32531459177296335 -0.35629811416471474 -0.39947568758999036 -0.45528752853413296 -0.5136210916823762 -0.5579882703128095 -0.5703403345873092 -0.5475931697312133 -0.4936264175463083 -0.4072127421206327 -0.28967645726032565 -0.15014808974209073; 0.18118550567854497 0.37076379514870544 0.5849269501504493 0.8266444590396065 1.0770893198233815 1.3276861101936448 1.586799633435564 1.831888374646546 2.0108076282250273 2.120844122497722 2.2003465298416893 2.249484503361409 2.265348954310976 2.287391298499729 2.354863813199643 2.4618223373626087 2.562412584100047 2.6118794686461904 2.5830842189423158 2.4658884552159264 2.2681016058021632 2.060252312433115 1.9066395402650271 1.8249595258196345 1.774963716151263 1.6952449435992096 1.55944264458195 1.3671897857390145 1.1354151861316746 0.8891849953472408 0.6358882697035955 0.4017117900781452 0.2093575777298913 0.06711718755657765 -0.02798370407723576 -0.09536362767971028 -0.1373489844671608 -0.16087697383076854 -0.19623903743174695 -0.2516165559394249 -0.31561769766563036 -0.37927236858113134 -0.42222351499327776 -0.42614833116365497 -0.39328751360338526 -0.33049365558317756 -0.23959655102784944 -0.1259030296776223; 0.148773424995565 0.3250216014230663 0.5398989275074108 0.7814972926709071 1.0380685370913556 1.3129113516888091 1.5974791101222547 1.844486427275985 2.010045389755696 2.122599473072925 2.2198882611314112 2.2860271946439426 2.3352528768065755 2.4013548940279352 2.5111271957443244 2.6502136695140504 2.7299503368176934 2.697967001003687 2.5870729702820423 2.429370470317478 2.239717996575784 2.0685633558672705 1.952388620273139 1.9152506453848916 1.916075618729707 1.8838106187736363 1.7676893544809595 1.5744840273845313 1.3280718142735326 1.069215156664556 0.8132793710274052 0.5792581290972948 0.3937826136182307 0.2624401511737073 0.1796681432635106 0.12468932084730519 0.08565395097415936 0.06391460700225668 0.033174017068163045 -0.026242223479398696 -0.09860696075918121 -0.17279850230272822 -0.23969204625094834 -0.276404057839325 -0.2734252540593251 -0.23899699530735452 -0.17856692079638814 -0.09575130397209493; 0.11311529513223224 0.26897771125761577 0.4737249308043074 0.7131123252842365 0.9814794565817937 1.2706870986967562 1.5518120593311877 1.7776422259210736 1.9312778368318202 2.0548302411722386 2.1613800424905354 2.239923432094222 2.3099464433718677 2.3996860476305737 2.5594161420508263 2.733126876863413 2.7701111070090665 2.6200968938078075 2.3972065101928712 2.184347545346775 2.0181407140190517 1.9158661910579275 1.880540295790459 1.9152496975635396 1.9733475920057788 1.9816672772512853 1.8822693406854454 1.691364012209059 1.445453066161712 1.191732387464924 0.949044084854729 0.72578759583538 0.5521464417349291 0.4396364773695186 0.3777098106863924 0.3414687010625468 0.3123151742388412 0.2932317139063883 0.26779866312745465 0.20727430966141383 0.12223086560311218 0.03504655957853434 -0.047647129728994514 -0.11209508778558526 -0.1426329740511407 -0.1397094526014192 -0.11065145944433066 -0.06128239351312019; 0.08057388493148786 0.21241073812623515 0.4024636226260616 0.6385718933016885 0.9085480882960302 1.1890397007792894 1.4495545903911384 1.658183333462764 1.8122144168181693 1.9408093363393666 2.0492356457054557 2.13332566992972 2.206360195891259 2.32395928073423 2.525766549321755 2.714827984022826 2.7101929208986406 2.466691397644667 2.1517503522231496 1.8857771824776173 1.7375528172289685 1.697782900680983 1.753239425536467 1.8637758898649115 1.9733307535661702 1.9943712464773535 1.8932178237222246 1.6977990610786733 1.4639442766582813 1.2326704615358868 1.027352895876587 0.8343111215243979 0.6788888016353389 0.5857550766341352 0.5469812689043455 0.53296617232589 0.5167213460930384 0.5001868657172368 0.47987086729806855 0.4257088353967286 0.33493722333949993 0.23349196312461304 0.13489494904612995 0.04922183187611982 -0.009536853563498976 -0.037702423689274685 -0.040515537170748746 -0.02505875081860168; 0.055648502261018355 0.16458180767916145 0.3375886302127666 0.5625011255243989 0.81764780624896 1.076313067137409 1.3186254599234135 1.5210314469268114 1.676636328888798 1.811377585800723 1.9298616835865796 2.0194609908242547 2.102911400930668 2.240081278879328 2.448871481382734 2.6259394410394408 2.5982687844688344 2.3047144625693496 1.9386533754136122 1.6594523471367655 1.5320979537767485 1.5408425387745501 1.656216334798879 1.813655516805305 1.9440654018749064 1.9441436296566765 1.8117035400685342 1.605136335389653 1.3845515601879594 1.1883447336120894 1.0321888760507771 0.8923165271012076 0.7706925043244386 0.7002537544051979 0.6797159915286319 0.6848589932161334 0.6847939682312715 0.6723039119789004 0.6536596970201782 0.6076949660594065 0.5203638147994617 0.4114528213972366 0.29952009438718924 0.1962013530869564 0.11527029302034948 0.060980678693729556 0.02788247753317154 0.009834654588357453; 0.042136718501116326 0.13170482934687439 0.28280712503783983 0.4849639367349465 0.71635006137296 0.9579440742134838 1.1965773642837396 1.40453716420308 1.5741636116124431 1.7298473039658673 1.8636834338992174 1.9587165463584273 2.041762081860734 2.17331456221121 2.364569879724822 2.5273525276107813 2.490592207199661 2.1915161617482073 1.8475095516241329 1.5925831875891856 1.4852307471865431 1.503620531303938 1.6235827201820527 1.7873357456591474 1.9018860879302737 1.8629701011914312 1.684571057289832 1.462443868916573 1.2536826247411048 1.0855007605716085 0.9716796859935759 0.8833868980151439 0.8078932542792694 0.7738207877159662 0.7772911094709362 0.7957585489369455 0.8098885384521891 0.8041527579400364 0.7853122661930088 0.7446615056734514 0.6652692665252531 0.5576447520981376 0.4390766235659352 0.3230483618352204 0.22434243189102038 0.14828727646484766 0.0894818538284453 0.041755855851949616; 0.03521809688188546 0.11040165651065806 0.24136238752355405 0.42146871946301306 0.6341318766759949 0.8708798348476273 1.1197276291907627 1.3465182477675002 1.5435339340164203 1.7279529111080947 1.8761590239093189 1.9663214534701035 2.0378204901918084 2.154595693025732 2.328582656022071 2.4649688063177395 2.4142977016864315 2.15495644469375 1.8684806882477722 1.6503717429773161 1.5367390993882608 1.522127816389481 1.6037502596370958 1.7436124377129865 1.8321821723072629 1.7625403685214254 1.5638823415962961 1.3367478521371754 1.1469827711283689 0.9972232321796564 0.8990501306729011 0.8351734127126141 0.788320097152416 0.7897717263444383 0.8263172281209448 0.8623877060795341 0.8907162240827278 0.8957248743597024 0.8773776175925291 0.8386468268483711 0.7654711011473667 0.6636593356629473 0.547010439607301 0.42493135113466735 0.31323811960530296 0.22009714378189546 0.1401799688430693 0.06786359762407; 0.03536705769104066 0.10521303425813223 0.22394004790866198 0.38805516897382797 0.5936199697506679 0.839815019578356 1.1080086930951925 1.3636047542519647 1.5987442984361335 1.812835453689529 1.966517453622129 2.047903049087762 2.1071704535038354 2.2026619243047114 2.334802300092719 2.406069871712053 2.323920561213718 2.1149755135381447 1.8959079815945128 1.6977297671268161 1.5577673048117229 1.494469229682365 1.5390988385853661 1.65839631087098 1.731851672870717 1.6699526588410998 1.4926295099557418 1.2933089133086415 1.118509261450949 0.9757984002606728 0.8649327120691781 0.7931356961759807 0.7433023754623302 0.7560458969345384 0.8211202781417087 0.8779310675847963 0.9229210745706493 0.9442760819039604 0.9301687469000347 0.8930317131885863 0.8266148339045672 0.7305905329958928 0.6189647593082904 0.49853707593154356 0.3800088113036316 0.2741682911560816 0.1787253179690583 0.0880118136071202; 0.04357247746763321 0.11825434390232346 0.23635498876775562 0.3987224349024902 0.6098137548797519 0.8721613096110843 1.1653141596880696 1.4519024812808956 1.715773699410335 1.9481075207045233 2.108792900108948 2.1827426679135544 2.2162227345899557 2.259369791252463 2.309674498927418 2.2938555207043145 2.175767224255948 2.01941931937526 1.8483019281463484 1.6552000367811779 1.4796966306702979 1.3806307321392697 1.415315315642136 1.5402354074452227 1.6506253636059254 1.6331430236172337 1.5095667021752617 1.3487375979463239 1.1902765772993056 1.0329083211683838 0.8843571944295295 0.7775709518506122 0.7076090930939034 0.701614271810702 0.7701164441025687 0.8441488312544163 0.9066767879370178 0.9494918820587883 0.9463578253474484 0.9104562317497537 0.850444563258073 0.7642588162165032 0.6600837905073412 0.544271564865174 0.42518955135859005 0.3124002369467418 0.20605793543674641 0.10233431945999866; 0.061584657983243196 0.15225194349953555 0.281252602547891 0.4529110099602206 0.6808981318198343 0.964801705928697 1.273627708946224 1.5697871002003236 1.8398169963668067 2.0737261096538515 2.2251042739228333 2.2763312150254436 2.2759817084514045 2.2500420177757077 2.2066610329546554 2.1221812729706673 2.0098913079165666 1.901053313372097 1.7649213590806807 1.5743830588320606 1.3711687634813834 1.2604488986397495 1.3074838979080383 1.480534002258559 1.6397882237569894 1.6757500244483288 1.6004649198745202 1.4792078538969882 1.3253767798664753 1.1395285240175297 0.9367261250302221 0.7820033364024068 0.6853433624639493 0.6554176544503646 0.6999677997052519 0.7713850979344063 0.8481922235101818 0.9120842354100587 0.9275365473773497 0.9009704352523523 0.8471127174731539 0.7688824541332783 0.674675862998459 0.567667077751173 0.4519598615107765 0.3369699346659101 0.22470294931499296 0.11238244139208191; 0.08652203597776917 0.20349841261737245 0.35684453533153093 0.5489249043706567 0.7937319089443642 1.0866225022905582 1.3911942811168763 1.6716532931855028 1.9145040065769017 2.1128458434642354 2.231470821464097 2.2572084657590303 2.2306146199368637 2.164060070540341 2.067846728846338 1.9563384172306941 1.8715416404993706 1.8150813923523805 1.7139808222032455 1.5339004954152247 1.3366863839079164 1.2400697196655268 1.3211061823233439 1.5247870594181883 1.7012233080834904 1.7564815828059779 1.7186924168921665 1.619698387150305 1.450358462720711 1.224237221341356 0.967215105840872 0.7676740495897229 0.6588859530367808 0.6161794836626707 0.6375414127107667 0.6890203379157114 0.7639791672012695 0.8420848416797314 0.8742568882178381 0.8631900219074345 0.8235084597756616 0.7552869654271579 0.6687385927496379 0.5709046639577006 0.4628764708538291 0.349921133247229 0.23528226590585705 0.11838199763780476; 0.1194899175615265 0.2708111493663366 0.45372118855873084 0.6661629864074213 0.9216711635002307 1.2103523315706617 1.4929253594261835 1.7336005548826678 1.9189954590353908 2.059679316658108 2.141662301005601 2.151374633566411 2.119431048768074 2.053283918232822 1.9466181674844258 1.8358907644769267 1.7878369922762216 1.7854101804905973 1.7231127964880277 1.566825239870436 1.3898298556294981 1.3233041340723835 1.4216033624709266 1.6286328718505154 1.8033691881950185 1.8426874055607305 1.8154061063676754 1.7117795988576934 1.5017326731111098 1.2231410288369724 0.9244992939655676 0.6989536516956746 0.5885602923906909 0.5494489433826895 0.5660553987241955 0.6162652858721825 0.6828930901701913 0.7562488739415928 0.7973411139179475 0.8001947550221622 0.7768257082507046 0.7232625805957775 0.6467971381441816 0.557702491144358 0.45787572578843505 0.35039918439624296 0.23766834229967584 0.12014708685162297; 0.1544658053335399 0.3429732078645265 0.5597690391566964 0.7914334711490719 1.0471846274243972 1.319641317175763 1.5665433414230112 1.7574982836197863 1.8885915564140057 1.974574270911518 2.0192828791428172 2.0188780599931646 1.9951575843563965 1.9359358214290867 1.8337268525613992 1.7462595380488906 1.7310997301317066 1.7697905546978367 1.758229249611833 1.6235595191182357 1.4678773253859123 1.4260749525419545 1.540338622931983 1.7502515451916558 1.9109049979307615 1.9268965905125655 1.8616993575270742 1.727985645030639 1.4562401452176092 1.1292785094104756 0.8085467331615988 0.5674252655523595 0.45330448031374887 0.4289769840280424 0.4634730821536156 0.5330997437173619 0.608768937325034 0.6712650095219693 0.706390655173805 0.7179901907468399 0.7092305651752989 0.6716352163099999 0.6081206435053513 0.5290554856044507 0.4386116567810884 0.33867395163304176 0.2310958194492036 0.11729215123197295; 0.18881483015182324 0.4124129480891076 0.6597144056308752 0.9079965210170963 1.1581652988043465 1.4026063407913145 1.611937167301178 1.7683761362813044 1.8678325439119243 1.9219740529351006 1.9412149571382136 1.930491099020228 1.9003011174755942 1.8346547599756857 1.7398099179554338 1.6700520613281338 1.668581760256307 1.7362762509411098 1.7592262484306436 1.6681752174387374 1.5653366760114036 1.564630843715519 1.6800043439141772 1.8424927906145077 1.9531453425480492 1.94266662889069 1.873725132797727 1.6908290865355264 1.3772163172835812 0.9963487487397028 0.6478033130110968 0.3936007579872837 0.2695699019248619 0.2576259473869173 0.32263060898520984 0.4286299157325872 0.5249408499591852 0.5852225069380469 0.6117357112497679 0.6232380257354496 0.6243858992581668 0.6016850845800306 0.5535441298224955 0.4870056117514271 0.4065197336775364 0.3159588094388865 0.21697456563738055 0.11054236798829171; 0.21654016769255663 0.4674325274008622 0.740888985939547 1.0026308551826402 1.2435247330593469 1.4630351718836483 1.6425497748465467 1.7787738007886387 1.878009274990728 1.9362554968752594 1.9522895199893386 1.932311815329546 1.8767614664304817 1.7859132828814357 1.6851582164103733 1.6129009628157456 1.6165868220945458 1.6962148216105664 1.7575041673501686 1.734803021107014 1.691411128043433 1.7135483575313801 1.7880893856478988 1.8624468098321316 1.8640654470324036 1.8501760653093107 1.8182744797999084 1.6463710794364756 1.3041029141497513 0.8809307384516729 0.4868316414380404 0.20543867923207718 0.06780471687025398 0.06651548324726372 0.15875429963200782 0.294487137726697 0.41853464986111505 0.49129019986299893 0.5168838069826089 0.5239073001323002 0.5266547050328104 0.516693153645276 0.48485876735110556 0.4321043458516183 0.3636041308529854 0.2841229234593294 0.19592398162695876 0.10022370957307318; 0.23638748913385876 0.5021593645743072 0.7894287667713998 1.0630172525490127 1.3008458728730887 1.5002861008475672 1.657521552971628 1.7851620041475174 1.9030857354877617 1.9997509773844722 2.0447801369056067 2.027664688980714 1.9459895914407896 1.817097006765222 1.6820598895174748 1.589043838081884 1.5908523942342192 1.6763583063324867 1.7836468171105793 1.8246208384538665 1.8055137704289212 1.8016927228641777 1.8228780352773406 1.805206606469996 1.753598503137176 1.7247917459333362 1.7296706924600602 1.5860866763475308 1.2471120549776784 0.7922547705435253 0.36267133776682 0.04888453187990622 -0.11295097417313597 -0.11675804614883105 -0.009279249360934778 0.14200880610364433 0.2828441145061487 0.3786176236808174 0.4184826413723846 0.42440765841692346 0.4227317901038489 0.41831662992090757 0.402138594782695 0.3649098108989591 0.30875999450306685 0.2423274740906664 0.168322521649865 0.08654108096094763; 0.24704338317934385 0.514069345338739 0.801975730632618 1.0827582876550814 1.322697324762586 1.509973866049411 1.6522422203490694 1.7781509908243511 1.9160403328863345 2.0522198037594954 2.1334615461223136 2.13180333920742 2.0421358087221892 1.876993495675108 1.7012223393360544 1.5846349583468253 1.5764144844252106 1.6758648289274933 1.8228702877340002 1.9088261477174409 1.8870901528061093 1.803669024582043 1.7223697654516807 1.63181242994699 1.5792711855648944 1.600658035316536 1.646486620643528 1.5515101160127986 1.2356881181080432 0.7438475613449153 0.2612614127187628 -0.09023311135112717 -0.2708927528069854 -0.27865452818270287 -0.1682222328217686 -0.014088915937478266 0.13825162868592458 0.2537068721216295 0.30790479921838926 0.31558975130659705 0.3109755679180611 0.3102230264062608 0.305237692418589 0.28255938114348605 0.24151297161472535 0.19023433994204383 0.13272804540546063 0.06870075399623567; 0.24952061570775153 0.5065170114211244 0.7794790725281636 1.0564630445871876 1.301400628181507 1.4882999771991292 1.623961525894946 1.7478027095424478 1.8892565075459844 2.0290467330321627 2.120114025498929 2.124552905969939 2.0223391455654984 1.8416313672859057 1.6609747257145138 1.535706515214776 1.52877979498808 1.652013378676801 1.8440553445819783 1.9828123408974165 1.9403149624719744 1.7523717122071512 1.5378636759260405 1.3787762494634734 1.3339713861448825 1.4236917270002112 1.554083848526466 1.5557715700224215 1.2818067607191246 0.7688809517653497 0.22676910847565127 -0.18156106713898867 -0.39475580521452186 -0.41496331913663 -0.30832900993885687 -0.1600987643161197 -0.009577621040027995 0.1167809822891706 0.18427140159095218 0.19596998765367454 0.18810595699181357 0.18866232939704258 0.19481057044331404 0.18654643052437953 0.16038900749753138 0.12712438334434067 0.0901120352783545 0.04718825806612879; 0.24265472015264283 0.4843381893272036 0.733884796694455 0.9909982993360698 1.2291168612891563 1.419575873266977 1.5618447546432694 1.6866889772260563 1.8150991133468866 1.9272771574169503 1.988594174736914 1.9755614883713386 1.8705107066342217 1.7017565442479021 1.5369346892642168 1.4275586604200001 1.4438464118365724 1.5971491160820894 1.821636750517475 2.001360339000976 1.9571128184837168 1.7039525222302276 1.4034099775046585 1.1942377465168927 1.1485901680702295 1.2658406207212807 1.4683036514979144 1.580111773733588 1.3954093672554817 0.8710595686919286 0.2728540390766044 -0.19933238505079856 -0.4549028025196253 -0.5030860864208979 -0.41906950200883847 -0.2879949477434689 -0.1471311652749748 -0.02500086394615131 0.043437287933039345 0.05905283299253953 0.05282398698725702 0.05535340217256385 0.06937325548721876 0.07575782321329182 0.06811813374312707 0.05503302310165152 0.04023606331705256 0.021730339818264457; 0.22139683209114305 0.44451586888726446 0.6735429981459226 0.9045578106458919 1.119189919145185 1.3022593469249677 1.4513584093826526 1.5805071084561106 1.6943007098155531 1.7671495298478657 1.7876288247328518 1.760732749773801 1.6671405483978372 1.517065372269573 1.3811734117865222 1.3112838414603392 1.3615508223781572 1.5312143705251717 1.774769976203331 1.9872449553117075 1.962772063603386 1.7076236803019789 1.392294426554669 1.1653948370717806 1.0935977453820047 1.2070260236657158 1.4342190921788125 1.6285030106807137 1.5676497367521427 1.0676440363869215 0.40862137266251275 -0.12909559264202508 -0.4418571925068069 -0.5417198399376931 -0.49687200043049906 -0.39362049472095684 -0.27548518428676533 -0.16910337111863089 -0.10561657721896367 -0.09097293500019721 -0.09871181163285397 -0.09279481953998338 -0.06809911350146353 -0.04714180505399838 -0.036458442807469085 -0.02643999860274086 -0.0154217951916163 -0.006784772652818232; 0.18926646120367582 0.38731755866814344 0.5953904229255239 0.8036740688836899 0.9912138736658356 1.153260190696951 1.300071950392699 1.4311890222041497 1.534732226087687 1.5855969365765632 1.579912420620133 1.5440167678568446 1.4734609592985417 1.3605636133421932 1.2650714527144307 1.2405950625055857 1.3121163319553717 1.4904613349691285 1.7399072607265025 1.9804295358247253 2.0239294990261127 1.7901047393129634 1.5167191878362094 1.3015319387465147 1.220081559490516 1.3050799603907646 1.504912990253557 1.7236516381945979 1.7464291225798978 1.2772999338288236 0.5890596485181585 -0.004504800269209564 -0.37869713676613725 -0.5383105769874904 -0.5431329777419196 -0.477083223058081 -0.38804078997045904 -0.3079623241324865 -0.2643759799611378 -0.25627498100931284 -0.2616588183073912 -0.25084279781852603 -0.2183255170444153 -0.18275051725712882 -0.15019480613265912 -0.11501359760346105 -0.07722996687411054 -0.038947251341459294; 0.14600193665051175 0.31477325976966647 0.5004166178951686 0.6850436182400331 0.8498978736897017 0.991285567871866 1.1261673199953983 1.2558532265583051 1.3586163669715319 1.409393522108039 1.410350652810399 1.3900603516992616 1.3530868209745706 1.2877853791584937 1.2287730840487994 1.2248798821561377 1.3074678152629269 1.484182220137226 1.736654388555009 2.008046601395587 2.1311886336551162 1.975496026543727 1.7455536510433565 1.5741945095101098 1.5156952605262088 1.565362944918843 1.7071893127455557 1.8745242905354325 1.8628645368938135 1.3957524360350162 0.7162355098130362 0.11284667871667557 -0.3027447220765371 -0.509277551942363 -0.5603207764451752 -0.5398542995912826 -0.49262347493194075 -0.4506138332746455 -0.42936887693022224 -0.427993791083044 -0.43277695591646376 -0.4166324197451614 -0.3750100607547423 -0.32483460383224894 -0.2703576399691532 -0.2082973889379369 -0.14150344602463943 -0.07210256643743132; 0.09940278662110463 0.23083730350449772 0.38758622141215443 0.5459900380297067 0.6901959315734296 0.8173925159873981 0.942584276799303 1.0699895687157417 1.1794656197958018 1.2503298287480482 1.286972242276645 1.3135226109547116 1.328430037798966 1.3132639947603981 1.2904555142986942 1.302139800882749 1.368055373272966 1.5101980168781823 1.727958000892181 1.9692494541947287 2.1291159209150057 2.093448258167421 1.9808480482516404 1.9092069842729613 1.9045651415509497 1.9492225871654507 1.9777462824474996 1.994100262120523 1.8296974331703406 1.3517151697603933 0.7333121295365204 0.16967390906931182 -0.24047746976076353 -0.472980367938182 -0.5743858641864215 -0.6037949771375236 -0.5990581136130976 -0.5928112354835369 -0.595523052998865 -0.6018582755638221 -0.6031385483466067 -0.5813444225871468 -0.5325159965117046 -0.46698458394399744 -0.3879299683447636 -0.29825449424239886 -0.2037341054006761 -0.10447230091019169; 0.06084162629924418 0.14614953272930573 0.2603751203791135 0.3864415171547344 0.508580942329532 0.6248566320971066 0.744801432595886 0.8736679326571598 0.9977403164846503 1.1004310943624607 1.1861738329416769 1.2738062583435799 1.3557299444348874 1.4043217793980927 1.4207444713378428 1.4401026536435413 1.4986604980361173 1.5978740489668164 1.7311260126250718 1.8719498514128863 1.9801172835966383 2.0343502646095817 2.0645595252909947 2.122224006592067 2.2029764620292434 2.2096081019022904 2.085424817502362 1.8936710795563836 1.6141665750626173 1.1719777765677595 0.6485150841927192 0.16001553584717668 -0.22115924464479517 -0.4659430215450761 -0.60575562656264 -0.6737829896422948 -0.7067042057150351 -0.7382175487449663 -0.7601292453826076 -0.7681079644173866 -0.7645453752810634 -0.7362120142832618 -0.6790417010411776 -0.5975043706805642 -0.4948360788427021 -0.37972590874794243 -0.2592261511688099 -0.13254813286744388; 0.03264215478660132 0.06847031943021066 0.12868307624754544 0.21750768272651322 0.31501559991970374 0.4145989067970394 0.5284551731568826 0.6611327940158903 0.8031722935073518 0.9412247281819972 1.0767864924915176 1.2235062015227776 1.3723345593888707 1.486531388571855 1.5515277389010622 1.5937696588430754 1.6504060075785416 1.7269559402996304 1.8013115711587293 1.8564474478619766 1.8910627884698936 1.9287726048051026 1.9814292232880695 2.026118669393889 2.0315420744390282 1.9797477087901967 1.8242939163596006 1.6027409776143606 1.3100970037370667 0.9263438904726148 0.49683362208805654 0.08063773010388967 -0.2596055287751093 -0.5054787526273005 -0.6651585562015924 -0.7582603700841896 -0.8269346068893515 -0.8820493096084058 -0.9098064974988657 -0.915229563982416 -0.9049575435547695 -0.8713783787504827 -0.8060958730496238 -0.7075952943086355 -0.5834001140904883 -0.4469659796699916 -0.30494810069250045 -0.15568983682244486; 0.0069690700114491445 0.0017469186902042157 0.008614959394102265 0.052350551909647866 0.1225732266356237 0.20292127054257206 0.3030844004837173 0.4340918046585976 0.5904072624889782 0.7609967070850694 0.9393074556883054 1.1305478904812896 1.3271345989472183 1.500526089963915 1.6153491679211973 1.6812606169216944 1.7511218310124013 1.831106590846498 1.89612684643686 1.920309470989986 1.912262696264501 1.922009541786779 1.937048326777757 1.908716090665061 1.8162451237354378 1.6865182643840466 1.5109848388526095 1.2783097684929308 0.992029180512585 0.6588710413289507 0.2940859201423782 -0.05536826282547916 -0.3535991153381834 -0.5849392035833278 -0.748894284732992 -0.8613497775837823 -0.9470687425771626 -1.0100783810317977 -1.0368712047069812 -1.03606029919468 -1.020254389089767 -0.9797497279371169 -0.9022335646395689 -0.7874501095271293 -0.6474911081401021 -0.49684429773738903 -0.3391848364179388 -0.17263455975830555; -0.022692469628183692 -0.05820815075980173 -0.08876745290539219 -0.08767967048285309 -0.05220680729612318 0.004759696768124403 0.08647652887679029 0.20765486701401137 0.3667012595164964 0.5543627382069164 0.7605442494883173 0.9793423159074198 1.1985338079422432 1.3993581746633974 1.555800992378979 1.6516871545900487 1.7312757496637776 1.8217228274626867 1.8955090653263302 1.9284458470302441 1.9191741879755757 1.9022211426421167 1.8749201627417595 1.7894677504076502 1.6304208872950414 1.440165624294201 1.2263079916987663 0.9731052835540577 0.6948886650999716 0.3940036524155654 0.08607020863113787 -0.21062070976824043 -0.47314309099781515 -0.6912528771143868 -0.8532036498941181 -0.965387787445211 -1.0578117330030656 -1.1188064724889935 -1.1348468636287996 -1.1266725953138255 -1.1029668539357347 -1.0511232363623295 -0.9594446468448334 -0.831408103385454 -0.6832024723214535 -0.5253141004192947 -0.35786672843847894 -0.18131679902529715; -0.05026670101287423 -0.10798347569747412 -0.1630981325864053 -0.19503642642967395 -0.1937113490261806 -0.16291672699716597 -0.10340986795826022 -0.001015613976790726 0.15004392414281548 0.33761678381292515 0.5485002081307363 0.7721489705250264 0.9914940229796632 1.1879912135085193 1.352249475013207 1.4631831026792645 1.5393787327483157 1.6122996025929255 1.6735894217481526 1.708682482934877 1.71818604131403 1.7124640529919437 1.6701934053542675 1.568976073262094 1.3984873600140464 1.1889198600372775 0.9520246794796584 0.6925739675384228 0.42903207502647117 0.16092912449690389 -0.11331556044772026 -0.37312624764673125 -0.6055403158709479 -0.8021486610258288 -0.944790431738641 -1.0580099036422148 -1.1497770354291612 -1.195363782375448 -1.1992992328645153 -1.1810399341470414 -1.1447121066591615 -1.0784326839291065 -0.9730507280516834 -0.8372539528433371 -0.6861430624332864 -0.5262831549069328 -0.3577477436458655 -0.18120069392813834; -0.06792693639497564 -0.13867249238223947 -0.21088537233867885 -0.26896935820847545 -0.2965642753809715 -0.29042990198291085 -0.2527295050756548 -0.1755760499327906 -0.04626459749941079 0.12827832161370425 0.32642478027500055 0.5330732093796267 0.7344336716018958 0.9077676206211912 1.0481471893917498 1.1468633042862297 1.2027098111323666 1.2419045515381857 1.2753035397445875 1.3057561035149932 1.3307646490439995 1.3485189412260976 1.3330561129199714 1.2493141196149797 1.1057918518888898 0.9059301453766403 0.6788051903745711 0.43766928055485294 0.19804343536036664 -0.05039594716067678 -0.29112041045739434 -0.5116332251668966 -0.7160169644609155 -0.886976069921673 -1.020023673271204 -1.1313049383233027 -1.2071280853111148 -1.2336313734273803 -1.2208254756929922 -1.1872383279581398 -1.1372841254626453 -1.0577276806048526 -0.942126685926811 -0.8022694187028546 -0.65314361550114 -0.49890104745762703 -0.33771716654761647 -0.17036740442655557; -0.07294117911009869 -0.14718891278616697 -0.22795424325744917 -0.3051342064960542 -0.3563510047040707 -0.3715616341132704 -0.3539509325048079 -0.30214040940817605 -0.2048781449929159 -0.059194068704851284 0.11643990267313423 0.29598656603056267 0.4635879937862919 0.6037486958576314 0.7071781841115992 0.7737537143556872 0.8048583458223499 0.817601106948551 0.8327130656117858 0.8649502166098509 0.9046768561209079 0.9393663293684564 0.9456914477866895 0.894112028340659 0.7792542562886725 0.6149771131990216 0.4194099522447711 0.21145857529129447 -0.006009125101813443 -0.22274488047293126 -0.4279601452073162 -0.6231911206959152 -0.8021355804217375 -0.949533982445107 -1.0685404528967941 -1.162866862482101 -1.2154775826836293 -1.2185625536437386 -1.1877640840088464 -1.1416968894839956 -1.0796492904091586 -0.988402132053517 -0.8664425370331645 -0.7286866211354626 -0.5873524878898347 -0.44389749014928387 -0.2978717671509852 -0.1497962917284731; -0.07068257179222853 -0.1414645856178161 -0.21813007865538384 -0.2991175599990121 -0.3656661405673858 -0.39947953728865043 -0.39997418404684976 -0.3715621582611026 -0.3072336406353409 -0.20014686581506483 -0.0591648474394087 0.09242452782560288 0.2291566716976244 0.3329728697385217 0.3995093306955083 0.43126935451418563 0.4351545425266908 0.4299043312986729 0.43200899206904214 0.4615601138893815 0.5100190540451938 0.5530772976396336 0.5720285274349657 0.5448216608453542 0.46466440290140903 0.34228385666553335 0.18843312088817524 0.014453457854362957 -0.16952363026720263 -0.35348134482202825 -0.532401476245493 -0.697268235795499 -0.8449186888727451 -0.967171094150427 -1.066833369133802 -1.1395357441567966 -1.1661148879571293 -1.1479965326100376 -1.1040313286006673 -1.0472226955319426 -0.9755056438626363 -0.877023969873052 -0.7532563522182271 -0.6206775863502474 -0.490725706691299 -0.3653319064645314 -0.2430885805173207 -0.12174603619294805; -0.06714651247084807 -0.1306732535774157 -0.19395267284468984 -0.26197921537210034 -0.3269961086800912 -0.3714341813307157 -0.38684952243772736 -0.3769998073330576 -0.3410476113524298 -0.27109970459943716 -0.16917029760366858 -0.05197374692448117 0.05864393239447034 0.1390738181736997 0.17906657183267277 0.1870760486773289 0.1721197824868196 0.15360295352664438 0.14356737786184914 0.1554745257336725 0.1917022789547798 0.2302761915527031 0.25424639596699633 0.2473883320835864 0.201307963123946 0.1193267751489463 0.0039481875352840425 -0.13322468630354406 -0.2821793090802011 -0.4345033598806058 -0.5765671756456955 -0.7096366886857859 -0.8320935456970571 -0.9328106901883754 -1.014748962295839 -1.063697109579439 -1.0647391496218424 -1.030808273821457 -0.9781214167311131 -0.9169839848676112 -0.8394081176671909 -0.7318545025286939 -0.6063542685704182 -0.48459599460943287 -0.374091097507014 -0.2723543218954718 -0.17673377063817486 -0.08645790239916731; -0.06405535875576839 -0.11899822835585229 -0.16509942280013798 -0.21104291243119624 -0.2592656412264723 -0.3003976244348674 -0.32400371677716183 -0.3262060528442896 -0.30763439622837724 -0.266583218659011 -0.19941437910465604 -0.11433308013071343 -0.030049467869431454 0.03425435518987094 0.06192533906250121 0.05770074366006745 0.03302617872719531 0.007215956785211929 -0.009042653758727516 -0.013377120870861039 0.0017479703090868934 0.02507860355200394 0.04567737672207382 0.04856230149075791 0.02560696164903278 -0.02890602900092428 -0.11227858926682359 -0.21489589235042758 -0.329648472287805 -0.4435423038780739 -0.5548334443053522 -0.6673444830865417 -0.7692601032558757 -0.854905282174534 -0.9206988331228535 -0.9436444900743094 -0.9261140317551068 -0.8846661715502441 -0.8308913341082139 -0.7667470622595833 -0.6754947125333665 -0.5583452509030102 -0.44056524065463953 -0.33724022859681546 -0.24783956974557642 -0.16960669058720307 -0.103017611127227 -0.04793239939931089; -0.05665872855312371 -0.10316333390191534 -0.13565543845977554 -0.15976928212531913 -0.1836803070002687 -0.20851013635252388 -0.22900569154963088 -0.23776647611087648 -0.22864486261293382 -0.2030031291460758 -0.16292262194002868 -0.10681759756069374 -0.04388596778550277 0.010096432724820604 0.037277505626159876 0.03367316671894027 0.008118397122778868 -0.02528569066082113 -0.04645912990888862 -0.05982485256902002 -0.057720453068036685 -0.04673325062552352 -0.03172325878394674 -0.027044222195426782 -0.03914339803259823 -0.0776591966808216 -0.13583628808435558 -0.21229408160536525 -0.2966565196597037 -0.3874367021200424 -0.4853626830623737 -0.5850227743137681 -0.6752271585958387 -0.7518201663091835 -0.7968183149600995 -0.7996624254798429 -0.7739790074153621 -0.729680021259819 -0.6738789747296168 -0.5979530875902115 -0.49334721246529345 -0.3780563423503459 -0.2743004125068102 -0.1889239196166537 -0.11960093522631787 -0.06587353972969583 -0.03020762901131346 -0.010758096193349546; -0.04232019048663082 -0.07794730289546663 -0.10156970488572813 -0.11225221021490775 -0.11553267090006057 -0.11880383334763371 -0.12465962199384972 -0.13000662314042638 -0.1265579253723702 -0.10881689189385615 -0.08276355481639619 -0.05078755478760659 -0.010660828719576906 0.032345282822869914 0.06451751854417065 0.07270484703443833 0.0607943969982015 0.03256568454781748 0.006759353860780868 -0.009498453044199726 -0.016537413748975528 -0.010737542233101341 -0.003114633077117913 0.0016582439989470754 -0.009472929799116372 -0.037364223497469186 -0.08338227183586418 -0.14407884133644427 -0.21728256180921193 -0.30428071847027666 -0.3986196481087434 -0.4920326592361397 -0.5747323837672932 -0.6354779403339531 -0.6604047360384646 -0.6528563431034606 -0.6216233030945022 -0.5742822877098365 -0.5115887740198983 -0.42316977779257625 -0.3139707290623246 -0.20685111908805157 -0.11885455290702325 -0.05165388032254526 -0.002102326979681507 0.027420339317478868 0.03414556721736118 0.022026468663073468; -0.023671882457811034 -0.045664741455103554 -0.061053210924367406 -0.06474001805092731 -0.057363852583430734 -0.04490137549409457 -0.03367696377493052 -0.02692652168508766 -0.022004265961203685 -0.010520553217936726 0.008570512148237794 0.029372940256557217 0.05257609989895375 0.08036714518198473 0.10992646535183027 0.1290891121450023 0.13392502825641678 0.1266110695554954 0.10905364861983662 0.09645019769602638 0.08619483614892769 0.08529314076950585 0.085136759050911 0.08300851084837578 0.06867983872799713 0.04219606217937545 -0.0012332482703682154 -0.059144674673419974 -0.1352678463217596 -0.22371743372572644 -0.3163446488044791 -0.40264281206066943 -0.47127089808690786 -0.5136870426995349 -0.5257832802892484 -0.5115067683846799 -0.4777777893318329 -0.4278243086280072 -0.35560930626024956 -0.2577757860610043 -0.1510971211142847 -0.05915610691335628 0.010425513540994528 0.06149073261145693 0.09318434795303582 0.10080012960756234 0.08392030411053407 0.04745722273846092; -0.005275221356462344 -0.012828417177711339 -0.01941603599602659 -0.018437616510334227 -0.0076020963769409255 0.010901688945314934 0.03289453064049096 0.051940481987754514 0.06380009745862221 0.07210373007363705 0.08324114499017776 0.09779731312461896 0.11468741424401949 0.13425321342268978 0.15655665330132454 0.17874548023912615 0.19397243350808896 0.20436434826283684 0.2060298828742033 0.2027138071318332 0.1980783594735894 0.19168184914818798 0.18558218278096397 0.1732314895573446 0.153366051643041 0.12036068845536342 0.07321015506007833 0.0089451531363235 -0.07104296747909934 -0.1586271599492428 -0.24452759111759587 -0.31638010962917407 -0.36759198295301015 -0.39541679964932125 -0.3995690485846 -0.38467706975406407 -0.352570936319325 -0.2974903449281774 -0.21497037037032268 -0.11564188214015739 -0.02269484152500032 0.050102521382030654 0.10410854043956383 0.1411124036010819 0.15728006581966802 0.14860751531322616 0.11527817141198045 0.06271209881760542; 0.007754871139223551 0.012580458149979643 0.014649693813146788 0.01975395150102357 0.032555896948782366 0.05083053486407052 0.07228106989260591 0.09544386271021474 0.11424635863426713 0.12471327648634432 0.13077267189819514 0.13755828627110162 0.148121906115095 0.1629545746264063 0.1795290729801026 0.19787744525436943 0.21621065088313354 0.23302437852382177 0.24795727946724622 0.25488916973289094 0.25680266439991584 0.25125203027744064 0.24124021707378637 0.22322099598481196 0.1964489935229885 0.15672470006619152 0.1037460235521627 0.03635712113908584 -0.03951001703314292 -0.11648601989774217 -0.18454627875133983 -0.23605773790670587 -0.27052219001119454 -0.28795977089387215 -0.290710742222286 -0.2791654329960951 -0.24565422083469846 -0.18441031198698837 -0.10132435880278348 -0.014817493507599575 0.058554043586998644 0.11547316361977789 0.1569483043819656 0.18156749804022598 0.18646806888817977 0.1679682640109837 0.12598609567660096 0.06698577854137394; 0.013385179330942798 0.02506127863368746 0.03349955043265847 0.04192981050363827 0.055946102907565 0.0727215238538779 0.08764707694852351 0.10462954901897313 0.12354508482994078 0.13756050846810108 0.14458174388250344 0.14698309866571826 0.1496994433155745 0.15555918687890222 0.163832314490762 0.173649679515363 0.18665018549452564 0.2016392401720231 0.21698812684314178 0.22839893247628287 0.23236104771312704 0.22986742328419849 0.2192610680247482 0.20160989404764262 0.1731829755637886 0.1344096428188499 0.08412312661959687 0.02671235205050812 -0.03321354729349682 -0.08865004485697969 -0.13395989947842427 -0.16739814456223254 -0.18987214915863654 -0.20269452608645822 -0.20482301850175996 -0.19082588876675727 -0.15274091503061793 -0.0937822728790636 -0.025914982389702284 0.03895607362016284 0.09307688598348071 0.13586139897914545 0.16708020141471142 0.18293949397128292 0.18022286233186063 0.15751814667085 0.11621380769453882 0.061422375625527; 0.012099730496740256 0.024259542508540007 0.03590823537131754 0.04564649918042525 0.05504769914885726 0.06685675051914082 0.07886609039864996 0.08959184087953033 0.10198718024638502 0.11425738337682316 0.12118681831565649 0.12220790254168873 0.11980666792213504 0.11712287484906886 0.11595629158251658 0.11689627949798283 0.12153547733823016 0.13055307813833447 0.1409404700054347 0.15019567225350117 0.15429442653184003 0.15347634661483223 0.14667243445217565 0.13373922197068466 0.11280761106316155 0.08393573711615043 0.04827491463865131 0.009707800563928901 -0.028402795995095393 -0.06236243947741149 -0.09079879361344576 -0.11351577130586507 -0.1300293299776608 -0.13862695925423385 -0.1353673289286484 -0.11512410774761032 -0.07889947912600169 -0.03396829917401999 0.011664264296057126 0.05269017584521777 0.08765455447665749 0.1162908924636405 0.1369915805846412 0.14654689099583884 0.1415677218401868 0.12136274710802686 0.08848766334399473 0.04667624413254525; 0.006418837211003674 0.013944646521467199 0.023321388935765 0.030697551693867564 0.0330992753522564 0.03703806749910914 0.046000898969244475 0.05340444328287385 0.05908631017111973 0.06534035758953363 0.06845811270205819 0.06821135042958185 0.06476794996605448 0.060104176499184064 0.05582190643886535 0.053177946183660535 0.05353767085986726 0.05696152978383138 0.0625284196881118 0.06719886815714282 0.07048820666212996 0.07035780222068268 0.06825695425297243 0.061866986831500846 0.05227972139351912 0.037546719108322545 0.020686084454605794 0.001755509663937039 -0.016008768408212123 -0.033102424751487884 -0.04848850658827983 -0.06209826658225425 -0.07227072436843157 -0.07526474639249708 -0.06955636296918075 -0.052520613720067034 -0.030277109517248095 -0.006239409637607038 0.016978443722679284 0.03556625194564913 0.052424481943222905 0.06669053443820275 0.07574963097424169 0.08043931876244932 0.07815360451624069 0.06628058415960549 0.04745916860343939 0.02484587972681608], hyperparams = 95.52853019289508), (params = [0.03407170714978452 0.07026392550645809 0.10430895132071857 0.1319300725299317 0.15777236028805738 0.18180399570625871 0.19138168940606698 0.17583812836163584 0.15018257117798983 0.11194729117842596 0.06262909150933847 0.006256809686211792 -0.04611269698211764 -0.08863441311744581 -0.11391256050980689 -0.13095320323527124 -0.14693438029472647 -0.16218772809902862 -0.17749625045083958 -0.1813442141435629 -0.1741503003150904 -0.16631055942458672 -0.1642145831397098 -0.167177972627237 -0.17251543758791424 -0.1763824036925592 -0.17710454955961585 -0.17555444374367554 -0.17599026958929578 -0.18856695756345163 -0.22226236204479602 -0.27600186899233053 -0.3385864367258205 -0.4050656929486114 -0.47212520580305734 -0.5360089593246715 -0.5825777895377495 -0.5996249002830634 -0.5934611306524482 -0.5739264296346087 -0.5498561798708583 -0.5162312054010522 -0.4717682515461606 -0.41572519668657604 -0.34885507330110754 -0.2723362400875412 -0.18652833354359594 -0.09633334359969012; 0.06823652268948274 0.14174730091230095 0.20713884519112416 0.25355199167785536 0.29381643826437587 0.3353756000200059 0.35507944601670216 0.3360396144455523 0.2792510525274657 0.1990960412123878 0.105425634976917 0.006887665514686524 -0.0841838943942683 -0.16279229878333032 -0.22083722430632483 -0.26586573078680675 -0.3047861133738109 -0.34086800510136384 -0.3746102811734083 -0.3810824711921313 -0.3595306182318709 -0.32346119602921836 -0.2952987890122221 -0.2786185604830178 -0.27376909288629864 -0.27811327871368197 -0.28566059033725644 -0.29345036833227994 -0.301044654107671 -0.3317150827027376 -0.40492769074463186 -0.5200104554782353 -0.654561378776824 -0.7865909440595411 -0.9117016853448112 -1.0203015947119283 -1.0966391540947438 -1.1249134028636711 -1.1172001642237765 -1.0917227387179578 -1.0459715684235757 -0.9752253935923324 -0.880117478925014 -0.7644110569427902 -0.6361515149102411 -0.4916803846365702 -0.33564518984410974 -0.17248602496506737; 0.10709354656984234 0.21308076612651078 0.3014881641267934 0.3650813190706485 0.4154743118142173 0.4572967975103462 0.47863841257037015 0.4538350949358762 0.374084289060911 0.26217385799387816 0.14022615045550824 0.015936106882608464 -0.10414089844614446 -0.21782931984678974 -0.3148754923515477 -0.38942886159953244 -0.45263778767587354 -0.5117789134625885 -0.5558924355778984 -0.5589379133324444 -0.5105887048747363 -0.43361473628833336 -0.3621267292790378 -0.3078870860574945 -0.27904603521852717 -0.2746359683243905 -0.2965043501608718 -0.3243335803797373 -0.35171894689556515 -0.4027071407631045 -0.5193903822091543 -0.6994462502643619 -0.9053415449320026 -1.1025632130758056 -1.2725492951715982 -1.4062062472041261 -1.4915019075108047 -1.53267499199902 -1.5366067079649528 -1.513245406289182 -1.4522603227477395 -1.3463655567360264 -1.2009910912679385 -1.0253468806275252 -0.842872264572015 -0.6499860233396502 -0.4410533292039219 -0.22507316266653865; 0.13656907680021504 0.26886405933222324 0.3786457965135541 0.45690650077911715 0.5110350976800597 0.5462727822212379 0.5554689451191666 0.5193865522335608 0.42993664463513004 0.3122150473686855 0.1744055687443419 0.024974989126881546 -0.12131557878217848 -0.26041142036988285 -0.3800993517754805 -0.4749413278478461 -0.5537960640981086 -0.6166672373658181 -0.6550044161799342 -0.6429203987587604 -0.5673238161695223 -0.4496374306166554 -0.33702712566000775 -0.25159684924515363 -0.19308446062365786 -0.17305808909392645 -0.19768219910624707 -0.2543197809050648 -0.3152577746984713 -0.4036690210758827 -0.5618740217808286 -0.799283111191443 -1.0708298549280724 -1.3191373101350925 -1.5213632850232066 -1.667462000567508 -1.7631266233563785 -1.8178444760980008 -1.8365102953101193 -1.8183885108950042 -1.7436489812758618 -1.6077550362729969 -1.4212964742150487 -1.208076137682003 -0.9868196647603057 -0.7578522909412776 -0.5155002202627879 -0.2620181151533269; 0.15488171116512725 0.30732848780944816 0.43348111009078044 0.527190843722222 0.5837129001941153 0.60367955723639 0.5924003945159432 0.5417945860373335 0.45642049862099904 0.3373273141155973 0.18422056460207803 0.010165496303896128 -0.15484327204334264 -0.30070706417199017 -0.4218954822405733 -0.5144996648817562 -0.586539641731806 -0.6381708796034529 -0.6577043323105597 -0.6222776626479727 -0.517510419738936 -0.3738921110173581 -0.2381512067189537 -0.12778189413307584 -0.04125814198130087 0.005400150641388687 -0.013213249263036854 -0.08823661011514629 -0.1952767821934044 -0.3378193654535251 -0.5428493877302035 -0.8233907729857255 -1.1325168677008768 -1.4197622402790266 -1.6450327398570432 -1.809086998537869 -1.9166923531182936 -1.9839874602170688 -2.0074607438001633 -1.9844989628570775 -1.897545163621981 -1.7396360314071606 -1.5322184816083195 -1.3017577462010028 -1.0631231731846507 -0.8189063496252577 -0.559332801632688 -0.28627176432926754; 0.16438444601684096 0.328956534902252 0.47278291042415643 0.5685565719117158 0.6160244666546679 0.6186356092464641 0.5887910639955648 0.5327661501137597 0.4443448141788905 0.3245046224801007 0.16223024632266866 -0.026049929561107257 -0.1978762606869092 -0.3375898811206055 -0.43768391611350177 -0.5163314023125128 -0.5740804196131117 -0.6041990161914601 -0.5976800853486612 -0.5334788083317991 -0.40278271677306815 -0.23591331442055705 -0.07634456083953625 0.05186607776643041 0.15831081673807712 0.22648489570320204 0.2214971228637823 0.13230436562017905 -0.020148138522858915 -0.21488091312908839 -0.4603690107919768 -0.7660512489750466 -1.0969617024186724 -1.3989880246916975 -1.6448212069788217 -1.824303035162652 -1.9479152738468417 -2.019990349378569 -2.035991976761246 -1.9971126185434034 -1.8944819594834956 -1.7305709774415758 -1.5221247078196778 -1.2923306394000165 -1.0545278052191842 -0.8115037364714549 -0.5576262867465142 -0.2870223609774568; 0.16966212395908403 0.33880438612833 0.4812044705785668 0.5730809810419067 0.6052228791095808 0.5939451342948506 0.5502200223158475 0.48382889085825503 0.38996229428537743 0.26195200501552024 0.09784717639575437 -0.08018331934706203 -0.23704042842104334 -0.34787475249309835 -0.4187274960782016 -0.472468675324584 -0.5067104603193939 -0.5117815276367466 -0.48229766353768544 -0.3988506936139835 -0.24556555101473718 -0.05787599812056085 0.11809474404773734 0.25894844513304494 0.3714377921859073 0.44858441167815494 0.45087601363639906 0.35728695019896994 0.18058248519216735 -0.05009415760655965 -0.3210591494941683 -0.6386978724310847 -0.9741952408386299 -1.2812375543589778 -1.526097102622489 -1.7096336020498026 -1.8353798552276066 -1.9046206920950837 -1.9139969923653175 -1.8608708450313103 -1.7490750492076468 -1.58948403510194 -1.4027941264601502 -1.1917395633027283 -0.9670672592687616 -0.7381401626122247 -0.5094754145936261 -0.2663202762075646; 0.16793420679466328 0.32924606339591916 0.46305234921001404 0.5414809071643458 0.5666046544917417 0.552049352881057 0.5031484301649104 0.4212985947994542 0.30528509227532186 0.1673051372838908 0.012283379577632732 -0.14421686689257435 -0.27324313091858055 -0.3475057441387457 -0.37724309548576834 -0.39716963147971646 -0.3927871028404099 -0.35887479462861793 -0.30551127858386673 -0.21469479652908202 -0.06485926381395461 0.12668901884685052 0.3091603313288943 0.44558716446014335 0.5470702817650958 0.6162746585617599 0.6207751548194562 0.5350947664616025 0.36652639755960076 0.1386928956910513 -0.13417494430811255 -0.4492380198113058 -0.7790651642382258 -1.0740163945840864 -1.3040542953220753 -1.4685710870551592 -1.5822509994195881 -1.6444244557742562 -1.6489459770926267 -1.5933069765051735 -1.4856858584071546 -1.3478817692328644 -1.1949232242544297 -1.0214670150752223 -0.8294010293475653 -0.6333247459751614 -0.4353582649701121 -0.22552555001773597; 0.16178092261770838 0.31468409536117947 0.43304940419342863 0.5004926731586935 0.5231388640323261 0.509873815508943 0.4573240595099787 0.35092964601367493 0.21014902377842173 0.06229908746696314 -0.07972115370811153 -0.21180144261141212 -0.31126622387259 -0.34716331562924063 -0.34076891233267265 -0.3089037418312681 -0.24097364630956655 -0.15947434559532644 -0.07769923295117441 0.008750216393471628 0.1354704219080856 0.30075748936481494 0.45774220728251613 0.567751581617628 0.6388744119951044 0.6878349512178021 0.6924132658594804 0.6339969008541747 0.5090703355230741 0.32212353065688876 0.08148177911146687 -0.20578362196113129 -0.5062335062820525 -0.7718819904604038 -0.9794700018784047 -1.119565140194265 -1.2123758395639546 -1.2622204524393712 -1.2657376987767388 -1.222492378704314 -1.1377974719217905 -1.0297440858386386 -0.917172786969069 -0.7925657331167881 -0.6555867095951814 -0.5085684092588755 -0.3518260013920193 -0.18218516992765252; 0.14820810509171695 0.29016411299322764 0.403129331576995 0.4640423200611441 0.48450829828132524 0.46872960777375244 0.40228394909201254 0.27493333550443805 0.11401129832444708 -0.03589620954960971 -0.16614657610793168 -0.2788848049623969 -0.3503767330652874 -0.3572148952592906 -0.30622851977043103 -0.21010023445031922 -0.07872414387967253 0.04844371504615933 0.15075240446250915 0.23523325673768614 0.3288638314826226 0.44649480105497563 0.549741546571823 0.6067651748754529 0.6390177297945944 0.6654268621104316 0.6790043657780517 0.6655509703547597 0.601781132632967 0.4752284105327902 0.29598181854036537 0.07198193857058903 -0.1657235877575579 -0.3836382288875941 -0.556048313996335 -0.6770413904099972 -0.7548858013995089 -0.7999697023754 -0.804562915543385 -0.7833674354717938 -0.7367704385107445 -0.6705849377781729 -0.601095155053151 -0.5310673866326155 -0.460365685199732 -0.37153232140981124 -0.2617588011071894 -0.1358280457252414; 0.1356968810435616 0.2681399771694841 0.378541330528753 0.4389406088642777 0.45395069961646134 0.4264019106140583 0.3473490410312335 0.20355584808708724 0.03085989017641196 -0.12593165317783303 -0.24959646311676698 -0.34360777475152854 -0.3974356568064421 -0.37240469303398616 -0.27030827740342944 -0.10732074875230574 0.07649975424166557 0.2298658199499956 0.35113218704031857 0.434804578406127 0.503285465678117 0.5635298898290064 0.5938736550829425 0.586511386347319 0.5720945413934854 0.5853865583934642 0.619516938739447 0.6524992103453103 0.6509164373055428 0.5932672368774676 0.48733383391763985 0.34977198682028093 0.19605438400777123 0.050367702546549965 -0.08329923134464001 -0.18837890103509503 -0.2628955336892327 -0.3033834294865398 -0.3214258999967482 -0.3271288215212179 -0.3245888806528243 -0.30608845392743317 -0.2857876312932723 -0.2742554261461134 -0.2647255650612015 -0.23451707454043488 -0.17151278462725775 -0.09027772842769569; 0.12545434156661903 0.24931479506121276 0.354426246796041 0.41650228265814765 0.4243472208655399 0.38488662620178754 0.29372197701619507 0.1425357477331134 -0.0413380576385444 -0.2044846562795399 -0.3265258428889544 -0.4100022030267157 -0.437480824364934 -0.376229864832452 -0.22053375195692657 0.0016646372183743727 0.21293735507948125 0.3800276296282338 0.5089590752217819 0.6086264603946616 0.6698249337127651 0.6879540177095066 0.6499884592121185 0.5736483277985442 0.5124286369586363 0.5052466532058263 0.5577248655919861 0.6328001984817527 0.6845314875340238 0.6897056167845316 0.6562490854249436 0.5975488912318367 0.5280584787916647 0.4531897157691413 0.37082277047790013 0.28042803669632643 0.21116683555311794 0.16710158234743555 0.13282202483779212 0.09178383800828176 0.04688526121718156 0.016720714142964527 -0.016926457152367104 -0.058027637434993326 -0.10321496341373795 -0.11673404367275987 -0.0948683375200746 -0.052578538823678043; 0.11663943368712773 0.2320930358638527 0.33479891422735414 0.39783467084942015 0.4024005611271694 0.349022006660825 0.24609227091360242 0.0860372449418654 -0.10466518405342401 -0.2773082448203999 -0.4033919449773441 -0.4753096412020166 -0.47723626733524416 -0.3770524136297628 -0.1759036486711414 0.0832168092174528 0.31455829073914465 0.4978304924038461 0.6544872507476003 0.7770036136209204 0.8522764316060704 0.8534284422372995 0.7655873115476739 0.6302917034851486 0.5150163241073817 0.47852635550116657 0.5333618272550584 0.6315726823027494 0.7298464223090501 0.7917771584035421 0.816246596022817 0.8114593378579993 0.792219148068495 0.7736569679329849 0.7333104125093534 0.6712827954812071 0.6109466103118951 0.565844824661129 0.50931447445524 0.42492344871214377 0.33110414739749977 0.2492225884058591 0.17403867192962225 0.09154309558787975 0.01637947461231588 -0.028419975401120942 -0.03320362039781481 -0.02165387151006207; 0.1070510962772091 0.21613473536411937 0.3156586424967472 0.38436623858087066 0.38754130795561753 0.3207403778498368 0.2034814965958042 0.03947176345847997 -0.1556021066327956 -0.3370109608867662 -0.4723035880886168 -0.5400862390089848 -0.5190413103712194 -0.39055905769600596 -0.16417491604578788 0.1140685527324503 0.3699281698470901 0.5924166287070709 0.7880724614593175 0.9485463226692152 1.0466287565853862 1.0387362328631604 0.9181961310052378 0.7364297459978796 0.5708591258370144 0.4989306866678916 0.5397631378581973 0.6528340294967574 0.7825639038929226 0.901116312441563 0.9719306078168765 1.0023145121778096 0.9981237484923585 0.9894569186966314 0.9778282190110656 0.9417759867130752 0.8996814004290639 0.8547502903143265 0.7809229131241189 0.6604009912678178 0.5189324004754322 0.39406443426443555 0.2886525342239058 0.19310346484518442 0.10121524267704653 0.040343063004195504 0.010044351773012956 0.0021795520641346195; 0.09723317015952798 0.1993448127736498 0.29146942419115496 0.3597375811283988 0.3620797066834885 0.2879902325607939 0.1612369583165495 -0.004956169819006546 -0.19881066948759163 -0.3880462797597815 -0.5371025601032657 -0.6081002146404381 -0.5795034493992905 -0.4429431611449406 -0.21564100901120872 0.06702012346463032 0.35458633564076114 0.6332369514602048 0.8870377091061584 1.0919169269364204 1.2056270527869581 1.1889861845494283 1.045312771230713 0.8312213951533062 0.6302962337983125 0.5216285518771905 0.540429983778749 0.6518489190167241 0.8084524095377537 0.9623208440158172 1.081671727065076 1.1392930579431921 1.1438426107332857 1.1210184574157158 1.1074740977252913 1.0878257144006993 1.051805361226457 1.0035184105605255 0.9158103464930183 0.781833767859798 0.6211583241437971 0.4690116889423901 0.34897005911071566 0.2495437685479825 0.16005047765941127 0.08489746281835213 0.037492118525599576 0.01157535854099029; 0.09240357217142674 0.18411955604578614 0.2649352891876394 0.3213297435198519 0.3224421792582903 0.24096941361491978 0.10523917665366797 -0.06270319943192611 -0.25339685504799525 -0.44384395089150847 -0.6013302628416842 -0.6796829235761465 -0.6567276226482378 -0.5322538074915203 -0.3199908553326694 -0.04187772086888994 0.2716614524563718 0.6093580491497027 0.929758133113511 1.17274412359097 1.294991033569081 1.266324752796728 1.1054946673539798 0.8767387571705252 0.6606966696042311 0.5282190970762355 0.5216940932485202 0.6232467354751543 0.7833427137215643 0.9581992614407828 1.1030033312621794 1.1851334075541657 1.2011460976274961 1.176212881328367 1.1471047263467935 1.1204958271191783 1.078097693239406 1.0175024778240815 0.9233476886245888 0.7927051306993563 0.6378753225084036 0.48308487737107064 0.35318062718686916 0.2554010527250047 0.1714076520846432 0.09790552628849637 0.045308483127565524 0.014575329196844832; 0.0879883982481991 0.16827179612139162 0.2314037168100471 0.27512084492500694 0.26927019948481706 0.18962237051922098 0.04636716601149941 -0.12589690195219333 -0.3129429664247472 -0.5004346152680315 -0.6581658587764615 -0.7439792590700329 -0.7270677686131908 -0.6193454019786568 -0.4265307790048843 -0.1574766895995178 0.1687310756045939 0.5489671423325514 0.9080262273639447 1.182577712998124 1.3096557980102448 1.2673180006655298 1.1033000209069377 0.8748821593557445 0.6547655980767221 0.5015688754671326 0.48584288982272084 0.5806366927105556 0.7397489197628098 0.9018846727821931 1.0448501160422379 1.1304004829735526 1.1571644536194456 1.1317710338703408 1.0920027623268982 1.0533401865862266 0.999614658446332 0.930555820391912 0.8392346265715604 0.7192780067573585 0.5816843698527283 0.442825502473051 0.3196871150365762 0.22263791790008577 0.1477013660705013 0.08803992701083482 0.042734841437939715 0.015145843423957264; 0.08857454984448464 0.15525316205540546 0.20060320467434856 0.22758406112793095 0.21630805903739184 0.12952054280271938 -0.015043723940896337 -0.18780588102903448 -0.3684361533779092 -0.5444742762318161 -0.6964868158043459 -0.7771848667257688 -0.7654837670661684 -0.6683129690560426 -0.4908927361249823 -0.23828498842713675 0.0910014021461428 0.47454419346784105 0.8533107750271036 1.139063693914226 1.2642287830900107 1.2220440866633988 1.0577090373893792 0.82559199876804 0.5865840376989109 0.41729915327317274 0.40130181277091775 0.501737988390518 0.6607739351566453 0.8089342879175332 0.9322832172730301 1.0103348130795233 1.0317533617599208 1.002195046215682 0.9421857990200956 0.8825656281813112 0.8171051807373585 0.7438151207505407 0.6673222834926577 0.5691088012965972 0.4568260364502811 0.34255067798751465 0.24034350673886415 0.1531668514916027 0.0943596615490033 0.0516155385860982 0.02350285598394558 0.00676475883505399; 0.08507190006938198 0.14447461600280945 0.1734245402959327 0.18476049715832474 0.15392250371333704 0.05976450590513222 -0.0870251555072626 -0.25802478528855105 -0.42785231918408917 -0.5880158158042579 -0.7179464815983838 -0.7818150632248712 -0.7635442232944402 -0.6743058841625161 -0.5125005854802792 -0.2744926019297721 0.03818989357358866 0.40755707863732477 0.7759174650163303 1.0571602149343657 1.1811830045504625 1.1415174425162418 0.9779113759386929 0.7236706082646276 0.4522920550295183 0.26517362653427207 0.2410541217737512 0.3544561017848552 0.5100020428954393 0.6503667106945125 0.7637246474426009 0.8351051072935912 0.8487210865336485 0.8028843497743177 0.7148567972356521 0.6237812249108122 0.5412822493691847 0.4659072665672599 0.4036106335516497 0.339534617250074 0.2624503625172662 0.18412698054814294 0.11302302070713481 0.05774854862519238 0.020734406328424725 -0.0009313280590232383 -0.011299159307511316 -0.009778204887542705; 0.07477877725796216 0.12387696507410996 0.1442540346113573 0.13170919309556225 0.07726373772477255 -0.03173700128785623 -0.18061657762821787 -0.3514300417624187 -0.5155094385535441 -0.6558186742752348 -0.7589684430880158 -0.7883984180991096 -0.7493452481454929 -0.65350983654091 -0.5038070545066942 -0.29168678192498676 -0.007767682653063518 0.3264212045494618 0.6705983188075004 0.9494076937468057 1.0793839000518533 1.0519299075208028 0.8842266045179551 0.6190497585749521 0.318507495999105 0.10575977398385243 0.062465427969513126 0.15326801260585718 0.30951267249316944 0.4322085645082133 0.5408762857346135 0.6156541531427827 0.6190030798579799 0.5502493679965105 0.4323779972011089 0.31390881699523915 0.21419171327616648 0.13503343455284997 0.08432568933055178 0.05165009804483147 0.01918651520433559 -0.013045799752490055 -0.03617241912977848 -0.04968812086227675 -0.05579969689189488 -0.05890070433904851 -0.0484902737199285 -0.02770962420468294; 0.06710174628422551 0.11182630350428387 0.12455706364374268 0.090266486740387 0.00471705744550086 -0.12984862649055762 -0.2934186291928526 -0.47492638752671 -0.6384236526599106 -0.7649283640246148 -0.8316512245667846 -0.8229551351115194 -0.7498683360676055 -0.6414874060154471 -0.5059458104529388 -0.32733141203829963 -0.09400577233351323 0.2031922901637229 0.525366673048694 0.8025021420000793 0.9571472718560946 0.9510246986177702 0.8126809648948864 0.5630088967160708 0.26328588089745514 0.031002520603028452 -0.0658584663754875 -0.014995510316090926 0.10814054820781399 0.21548425812242802 0.2935387746566089 0.35676084027151245 0.3485926282405452 0.25906916037460426 0.12192979507070367 -0.02246268437100991 -0.13315411884151035 -0.20883615965242455 -0.2447545203876648 -0.24672482562594436 -0.23506894708658932 -0.21711542843345966 -0.18796705278174855 -0.15168086739690373 -0.12070784395577515 -0.09801847793913512 -0.07229262758017266 -0.03561932159412595; 0.0676627924472149 0.11563346751778296 0.12288023137305215 0.06779380050276979 -0.04895844591004286 -0.21642155753927084 -0.4086057925286146 -0.6091941151977298 -0.7841268487273363 -0.9020864417368595 -0.9414825973961901 -0.8937598060123172 -0.7922593020811499 -0.6764504002989804 -0.5550751925625332 -0.414357257635481 -0.2205463842272729 0.03436082754523538 0.3235223165075691 0.5946034716167632 0.759780952905249 0.7955713886929956 0.7086086173122074 0.5271099557533981 0.2798038511920756 0.03914460028134336 -0.08942160414769264 -0.09423427164877052 -0.006642051360630427 0.0530854493137023 0.08761097031672349 0.09810198966474314 0.05473627491654255 -0.049686264797862534 -0.19399075344875638 -0.34310654434408333 -0.46155173950165235 -0.5325490056876199 -0.547883281213091 -0.5216523813982835 -0.4745457938786641 -0.4082657565663611 -0.3255204418109398 -0.23913615004085342 -0.16745784729735883 -0.11296241128028535 -0.06802588304966316 -0.027413213974959737; 0.07365469938224072 0.12111944487037528 0.12084216461083733 0.050216342682392355 -0.09302999952174139 -0.29454677567208915 -0.5198339912841634 -0.7464190440212627 -0.9326824365181333 -1.0488140006416 -1.0710268826247726 -1.0022626086046986 -0.8927652619339554 -0.7762511608926017 -0.6592834587709193 -0.5339899563093459 -0.3707747135301651 -0.15567624904498012 0.0854382738994829 0.3013683105406244 0.44542715399991273 0.4996662959004496 0.48572569019146006 0.39648329951990413 0.23965680907241405 0.06428153343073523 -0.05046397795244859 -0.06850217500046556 -0.023139252658146117 0.00012019188419301515 -0.03576595272514752 -0.11041531826349596 -0.21311850483327305 -0.3458762250744041 -0.49094384171040534 -0.6354558275982345 -0.7476466106844188 -0.8088581216654589 -0.8074766177385957 -0.7570523589345084 -0.6712581802710404 -0.5566796170327476 -0.4245380612497759 -0.29475130498981655 -0.18551394295714094 -0.10534855237521645 -0.04745337541395986 -0.013905510870477755; 0.07376290262106777 0.11396484963646122 0.10359706808679332 0.02114076120440922 -0.14055983811651176 -0.36778663454782673 -0.622495049012376 -0.8691667292464255 -1.068397975547547 -1.187886379827715 -1.207156418485538 -1.144274715813054 -1.0449244349076205 -0.9336421937811845 -0.803494635978277 -0.6696723195006501 -0.5161074881554951 -0.33055662216021736 -0.15903604278466846 -0.040381977512710644 0.028085602664954724 0.08603048778736477 0.12370599183825148 0.13416688414351813 0.09808348379172548 0.03431501213910292 0.00021612848423043784 -4.985253549362417e-5 0.035044145670019074 0.022401461040830607 -0.07702893609981476 -0.2308695010604671 -0.40377296978738586 -0.5743417557558139 -0.7337782127863348 -0.8703280117364257 -0.9767013149587906 -1.0242623810671143 -1.0050768132432806 -0.9309961238394748 -0.8093469303249844 -0.647150757706327 -0.4674524098806147 -0.2989124018401699 -0.1702079372231324 -0.07808700663296453 -0.02124897988034187 0.0029244990344433216; 0.06054292827910951 0.09115298369048956 0.07217174350825031 -0.015440906893685633 -0.18460865523344913 -0.42634996602308994 -0.700050816501956 -0.9637998518092926 -1.1753788903217302 -1.3007414423272623 -1.3328493497411875 -1.291519561390861 -1.2114253261296957 -1.0972327323068052 -0.9489378775235443 -0.7882162097265025 -0.6260011418118105 -0.45688520263941296 -0.34906523746157725 -0.34262848487114467 -0.368891415861498 -0.33891726990545257 -0.26542354703800175 -0.17674773331680665 -0.0993181214954983 -0.055363039811380535 0.002571972669474966 0.058211629453048676 0.08645458618065925 0.04012152753119962 -0.09752557104705822 -0.3070997670512631 -0.5175810223678649 -0.7221758760376441 -0.9009913816130505 -1.0417782820911436 -1.133832008804661 -1.162146806627543 -1.1229470740783978 -1.025248128235963 -0.8733713660280729 -0.6726592371357175 -0.45549468328608206 -0.25903607769219744 -0.11561247770947308 -0.02710566265826307 0.016328451471487735 0.01944412054976234; 0.042660874595682345 0.06250382957187266 0.043850932942603546 -0.03944059926825659 -0.20526581006613123 -0.45013897796219365 -0.7352512614392661 -1.0106814348576925 -1.2296252144942528 -1.35877471159551 -1.3990392554847164 -1.380028995317445 -1.3137159680347157 -1.2029610746718282 -1.0397429215087608 -0.861957059868012 -0.6791414792367301 -0.5107791357857773 -0.42380245523873117 -0.4826157776878685 -0.5967973820365011 -0.6183451258118853 -0.5462917970298481 -0.41912704867863443 -0.280501874597009 -0.16704232598969748 -0.046033910387376746 0.06425950970925388 0.09307550919552264 0.028021905090144097 -0.1371272602242372 -0.3619142642085626 -0.5920422624482323 -0.8167522581478679 -1.019935745964316 -1.1637268284795976 -1.235278094980641 -1.2334558322409104 -1.1597750509810507 -1.0392470027880156 -0.8691999501486128 -0.6501048129006739 -0.4091523271883019 -0.19578183795544257 -0.048328799028785854 0.03162830553054394 0.05838530079197482 0.04055126022909493; 0.027670149046799892 0.0442621982656421 0.0318039897412866 -0.039547220550725674 -0.19775849984536772 -0.43791360506930155 -0.726796846504321 -1.0082425550379692 -1.226144430724084 -1.3469095622052278 -1.3895928366571157 -1.3771985979377794 -1.3191025105786025 -1.2103008849484587 -1.0516909214372554 -0.8626604398828284 -0.6588964503950696 -0.4681615980585402 -0.36664695874884307 -0.42930843333983393 -0.5941354798917142 -0.6879750081018988 -0.6617737281053891 -0.5541604594790958 -0.41816058061028816 -0.28926815965107644 -0.1469737895458 -0.01457644598625731 0.03327565389116637 -0.03764170635855812 -0.19703055927746418 -0.4186022040764963 -0.6484957916247791 -0.8933531612269648 -1.107985899995898 -1.245029760231677 -1.2913676769037015 -1.2476070647511288 -1.1403083958777935 -0.9919120920317879 -0.8108354409751809 -0.5873985940366864 -0.34794497212615166 -0.1318474300594793 0.015556301699855682 0.09057759449398037 0.10416570537714885 0.0632678898864421; 0.020902168437661586 0.038115994447631425 0.034703434204853084 -0.026567720476099187 -0.17358830581358992 -0.4049186786675827 -0.6829005054753658 -0.9554070993021803 -1.1655741083954272 -1.2726694089897372 -1.3040016778134043 -1.2964769260324314 -1.241824029148872 -1.1363300244194352 -0.9823452107515654 -0.789263923549425 -0.5680807005650873 -0.35459214997224753 -0.21948649251936458 -0.25057396535271426 -0.4293948253050756 -0.5719496140742 -0.6032345272601354 -0.5437178738140557 -0.447096251652906 -0.3435373960637647 -0.2184233728574255 -0.10986830976928393 -0.0656207950819654 -0.12562498845393683 -0.2625449424682667 -0.46053909955592054 -0.6956213974162784 -0.9385792252230929 -1.1486219154641453 -1.270771577460404 -1.2856156264890946 -1.208808068251004 -1.0691355980724544 -0.902436595223867 -0.7115140438167512 -0.4917463825750325 -0.2553325210515786 -0.05242744680060102 0.08154458976399742 0.14517292280438213 0.14366410372170552 0.08549213248744754; 0.019532895456750285 0.03963538409708137 0.03789121330632394 -0.008757119828376632 -0.13851194264275324 -0.35015516327211366 -0.6022372894473028 -0.8543256210932587 -1.0464628313301982 -1.1459849909229471 -1.1739042045021362 -1.1689600213718128 -1.1203936778234276 -1.0133362429798007 -0.8632289340271921 -0.6624683030913421 -0.4248758928383708 -0.19375062183253655 -0.041812959011854965 -0.04862203110138136 -0.20645070045450764 -0.36133938930605586 -0.4207926613016309 -0.3959377092203178 -0.316030899093689 -0.22907675325657353 -0.16234266562540178 -0.12103824867887528 -0.12172644825970848 -0.19050646053799572 -0.31691543591261556 -0.5042830580561666 -0.7295517189516798 -0.9613655976492494 -1.1412444709965828 -1.227910784737499 -1.21426758526863 -1.1135619749954353 -0.9578817924909601 -0.7798424010628555 -0.5828473413589287 -0.3622041049241115 -0.1433555449465668 0.037010882062437425 0.14941669481339012 0.19469224927400028 0.1759158896455353 0.10213374106302106; 0.021590813689384248 0.04495076783138002 0.048648948178932463 0.011350684222902096 -0.09415580087589459 -0.2707499330512618 -0.49113391106318915 -0.7136371686220222 -0.8918517725928354 -0.9866514258238289 -1.0182458842711712 -1.0166043075499644 -0.9701012445063057 -0.8626346818558406 -0.7105012941322453 -0.5065960211004451 -0.25665185986157363 -0.025222046013616172 0.12226885481866234 0.11949787821465209 -0.017601162135277328 -0.15800454281626578 -0.21604247519817485 -0.17225991432324878 -0.06911500599170817 0.0031729443565523545 0.0030292696058701893 -0.055848125427742756 -0.1262078337887649 -0.23454281841887772 -0.37451336521771683 -0.5548559004840554 -0.7656352879293649 -0.9543511735171496 -1.0778599815114907 -1.1261956553542813 -1.08775129680508 -0.9742480766078693 -0.8129331332028973 -0.6347659990649016 -0.43872017139162134 -0.2258392463559697 -0.027432558532365828 0.12173606600570087 0.20784310833526265 0.22927059524102789 0.19940201388834428 0.11361771867355056; 0.03214491422965842 0.06279057222982846 0.06701256004622445 0.03992993206964643 -0.0419478443921109 -0.18278773360639458 -0.3626369664257269 -0.5506721099985011 -0.707636887712714 -0.8001852475660505 -0.8292908388589207 -0.8287726721833891 -0.7866376317496636 -0.6872895594736058 -0.5443866177824994 -0.3502491207421033 -0.1100762060281667 0.1070438306507097 0.23938406586548652 0.22472535978044125 0.09350735008883451 -0.04710085977503467 -0.09571499856848839 -0.018457267437171826 0.12797961517289255 0.2192796850008565 0.1549722244222444 0.028905517227021976 -0.1240491549345235 -0.27215090303618905 -0.43266999185031035 -0.6122475779994908 -0.7851815368287436 -0.9078567641615041 -0.9724885918837876 -0.9822424374608799 -0.9250709284937733 -0.8063034017164921 -0.6455946594418741 -0.4732303610036366 -0.2902405942426522 -0.10623070925169045 0.06136502536542013 0.18177072290983076 0.2433561115533531 0.24756727519596106 0.20561887038292728 0.11793575626625748; 0.04786972596070577 0.0891069010312262 0.10353635605355362 0.08237061126816138 0.02212321546696242 -0.08384121103791894 -0.22462411825966322 -0.37233207766599785 -0.5054585739325896 -0.5809092244367096 -0.6074960689661164 -0.6048318830532258 -0.5717820953737154 -0.4945864689891583 -0.38450422612763213 -0.2282304318737669 -0.02275535333988934 0.16830762425851342 0.27275643814655076 0.2502105344061118 0.10470322027167131 -0.06144719631014698 -0.15595919230659638 -0.10733741224696071 0.04762152865646983 0.15461013100328846 0.1304924655957342 -0.0012318882918323842 -0.16093220886595455 -0.31924522693139284 -0.4812945983545509 -0.6409986198694049 -0.7636817207667489 -0.8207336713162959 -0.835804048779104 -0.8085691365794331 -0.7363824827701329 -0.6132439994046762 -0.4559487469823716 -0.29455854743768944 -0.14639158352613366 -0.005326664601170228 0.12006110709508513 0.21325215563101882 0.25673207576478074 0.2500784914962671 0.20229212816620323 0.11667779933313102; 0.06453404061812444 0.118226938109493 0.1390229737091932 0.1284219731357133 0.08507805687507528 0.013580045833252218 -0.08336614465448351 -0.19080653340996503 -0.2806818005926449 -0.3374236966167475 -0.35203654139689733 -0.34548700333483967 -0.3298408242839978 -0.28937237827481593 -0.23415737927422167 -0.14691296639448778 -0.009237626586833511 0.13781088540042769 0.21535340683981813 0.18088355863498135 0.03822402354949876 -0.15049317171217158 -0.28174318328395614 -0.28180226766169103 -0.1620934544256933 -0.04103788037757799 -0.017003652456579824 -0.09012049302991172 -0.21384504947124186 -0.3473014491213765 -0.49009609287714506 -0.6126530970101338 -0.6810942160459815 -0.6887876993737493 -0.6624101897797562 -0.6090980683468856 -0.52660172051505 -0.4048470010116835 -0.2527588677016788 -0.11866961548277231 -0.009704236312615312 0.07851868339165703 0.16158576023947488 0.2276477778977881 0.25836141701823984 0.24937685104555127 0.20021784769191148 0.1132875042280622; 0.07353209693140453 0.13104026590427026 0.16308434331907973 0.1641210308925215 0.1464903913791529 0.10958312356905142 0.05708843207236487 0.0034943779287567004 -0.044913535774000306 -0.07509483795343032 -0.08113022952238405 -0.06634748337851068 -0.06786658985805923 -0.0769109927338918 -0.08262190607363129 -0.07380640867497906 -0.025583683863646085 0.04331043920343075 0.07248521059098119 0.025850200893159852 -0.09693728226309976 -0.2562384240690186 -0.3837917148533525 -0.3967735803674335 -0.3035780694367318 -0.19001290180828484 -0.1309983978932557 -0.1577341896463987 -0.22994868314949451 -0.33768808549970636 -0.45819423250115454 -0.5466492688764872 -0.5736384946645339 -0.5409889190608956 -0.4809600839046312 -0.40687927706557653 -0.31129582265664013 -0.19283174675611725 -0.06281131329220216 0.040966511568956386 0.1029678721162146 0.14877258545026 0.19537602019402506 0.23646146275340182 0.2538444403932926 0.24020513388815765 0.193714152888333 0.10638456117515684; 0.06057265271932668 0.1152223892989659 0.15703232515512977 0.1821752868060274 0.19140424857305788 0.19357411539666938 0.19140607013723862 0.19244573545893875 0.19106018410177047 0.19171459950412595 0.20275850143299093 0.22137370666036388 0.20960448727723777 0.15996816107890802 0.0916389916116789 0.02764140766853336 -0.015951642305532532 -0.04134403656671803 -0.08588417299248716 -0.16445262428727833 -0.26457687420636045 -0.36675288854213633 -0.43637572841495065 -0.4265008433542395 -0.3391750612653625 -0.23408611206640617 -0.16701729658551104 -0.16656528698652504 -0.21600049751358633 -0.31683773163465295 -0.41938448387641564 -0.48628123020290065 -0.47750815026687915 -0.4151235834403931 -0.3280306772713964 -0.2285079520993625 -0.1242860645338795 -0.012226254178515607 0.09102068127236247 0.15636166578356944 0.18599286118062702 0.2013936690699942 0.22511634335630074 0.24334436580537896 0.24739715297120388 0.22810110191053187 0.17484548040788114 0.09530927436126897; 0.03217512067441571 0.0715330177158158 0.12148969937676975 0.16671295859456325 0.20928283987132018 0.2551139552299049 0.30552985053753234 0.3589894636179771 0.40739214251789696 0.44946091718393955 0.48625117589393485 0.5184236424299432 0.5031573999648051 0.4243875007365032 0.3053166032144048 0.1780186939687265 0.061137075195331535 -0.045400106248615756 -0.16153861033106118 -0.2771164110383197 -0.3751407001083053 -0.43564993907851574 -0.44842891338641516 -0.40279546290457546 -0.3107992584957267 -0.21352814224481498 -0.1541817906042051 -0.14821284749437869 -0.19885642331681933 -0.2892753881605561 -0.38697854231598766 -0.43124220346111736 -0.4011002867376868 -0.32138304607472606 -0.2106750864664607 -0.09587145435216035 0.01959096979248479 0.11659783598610621 0.18333949707906624 0.21731675580000243 0.23146531144037058 0.2349347332976951 0.2390189089905508 0.2381795894390473 0.2256305738537753 0.197126061928327 0.14599341852972675 0.07788660841182345; -0.002990961131895863 0.01584563809928126 0.06104448363075112 0.12077493275645572 0.1877607518391418 0.2777769726063234 0.386912490964356 0.4983211409975754 0.6035459247620085 0.6896962251448772 0.759367197234017 0.8105008853172087 0.8027905429612098 0.715909222869837 0.5570134435771339 0.3735987952793502 0.18865562594075042 0.02523013162324585 -0.13518775952542092 -0.26986257258246327 -0.36561657795311947 -0.4062930149189377 -0.39268466145313924 -0.33120699764087785 -0.24326230481399974 -0.16453100593506667 -0.11878777307271546 -0.12553571309902586 -0.17122825772478573 -0.255077828934904 -0.33586401484695844 -0.36475907141353225 -0.3303976396359341 -0.24953865545199094 -0.14170701347041798 -0.019374233049240165 0.09765963835718973 0.17817256274273424 0.21581242543610926 0.233907274867937 0.23929924786475174 0.23310023429910695 0.22104487457477356 0.20897759764151377 0.18585617510124794 0.15424026655291007 0.11214950410966207 0.059849004525654795; -0.03505606788059941 -0.040948152983350035 -0.009309732483097976 0.049535660137264376 0.13548609076014842 0.26288917220152985 0.4269573142968232 0.6004915299639146 0.7628428493786422 0.9002793869696946 1.0031117669471488 1.0703275977217215 1.0799028741925287 1.0013526730800524 0.8243640002832593 0.5955023727924247 0.3601068552161942 0.14874282909245667 -0.03145412572393339 -0.16949654482530815 -0.24970617363183092 -0.282117477731223 -0.26246246786793564 -0.20765243742428982 -0.13804637915221005 -0.08516941188983058 -0.06486273301890898 -0.08392254757284612 -0.13190847450802043 -0.19974953438134382 -0.2644894670865952 -0.295578425956231 -0.27809674919073585 -0.22219019989853156 -0.13028230431112445 -0.01890368216967916 0.09230440364190283 0.16379345192693837 0.19399604191462733 0.20607222895138116 0.2101269437847838 0.20342675326353724 0.18420599036168425 0.15643472284373952 0.13443880770927258 0.10690270194628207 0.07556893395282002 0.03861848147391409; -0.06922650845581081 -0.1064835903699022 -0.09380000095479053 -0.03998967909823421 0.060559433052007276 0.2208067756602131 0.43279595557617984 0.6667307881070876 0.8864641853115703 1.0678870035870132 1.2050003639572375 1.290856272137184 1.3074993542205877 1.238223104232853 1.0702069310605842 0.8305353175127659 0.5691410855713576 0.3264932408112487 0.12945892439145915 -0.0062409742362815376 -0.07887023227911087 -0.10315706530450972 -0.09004106649282989 -0.048011755981169184 -0.00532876633444655 0.017384131952858657 0.0066730568239624045 -0.03437821074099081 -0.09215126711410215 -0.15790978610206366 -0.22346917017001486 -0.2736328046664574 -0.28370685397423445 -0.25667283326623674 -0.18922474588514623 -0.09773140188214799 -0.005573318548090555 0.06379823898769746 0.10314229185047247 0.12926016813408467 0.14456508550810498 0.14579782667094643 0.12268186861465254 0.0946212713604856 0.07242939218832897 0.056787884951718645 0.04015837779959928 0.022784882653219932; -0.1037123013982313 -0.17377572017330972 -0.18956454412697324 -0.14162252648714832 -0.030316120515319765 0.1587706434466388 0.4058650298670159 0.6830659113651585 0.955273011731932 1.1835462519907864 1.3577436203193125 1.4678122526427073 1.4892483473581757 1.423975237678997 1.276501953654289 1.0523094272439788 0.7839734847965181 0.5237153882519998 0.31129939313786104 0.16851199797507818 0.0949174372857225 0.07208611428148219 0.07976109328461185 0.10382319858629831 0.1258887562131744 0.11898855605429962 0.0756788144954429 0.003766362468964317 -0.07674751884996758 -0.15803217577655782 -0.24763101149233133 -0.31659096123681674 -0.35216068856349586 -0.3451787790480876 -0.3058475474707306 -0.24568666891366023 -0.17108837840368582 -0.09661300457041593 -0.0386774572953272 0.009313326331844148 0.0514699096168032 0.06471620868061385 0.0457725357853985 0.018589902158117386 0.004220257943830041 0.0071340454708454125 0.008437196292491145 0.0033962343847705185; -0.13397953453661499 -0.23418481073888742 -0.2730626387969051 -0.23676212990278173 -0.11803044712825601 0.083788294492041 0.34900188462508336 0.6490271067903823 0.9576697814036176 1.2340569227596725 1.448063355510515 1.5839703420393727 1.6194414163273252 1.5595734512068689 1.424451941890218 1.2297264821305256 0.9754259917974375 0.7114085611486676 0.4901782366427916 0.3338126263771919 0.245985352098296 0.21164279861310348 0.20489438544477404 0.21434585453268665 0.21420803703978378 0.18678344409234846 0.1192193400026686 0.01973009201217804 -0.0882349541308526 -0.20248621539238326 -0.317088352288528 -0.4085686349930618 -0.4627425914181778 -0.47424231925630855 -0.45460997969900546 -0.41909503203580417 -0.35837223327021117 -0.2833467389086364 -0.20464645419239472 -0.12752051033393286 -0.06732501915442636 -0.03883981871834577 -0.05031182479382978 -0.06773626907231901 -0.06657780874051443 -0.047256991652640336 -0.02691495926182478 -0.01445132636686889; -0.14807586470845924 -0.26914301753468856 -0.33061765621108236 -0.3025105406561426 -0.18703522291362068 0.014766554552597087 0.27835727029885377 0.5849635942537261 0.9106117306001673 1.2187574655431366 1.4705676073027136 1.6336940827551991 1.6884552653682412 1.6338514846492735 1.499630820576004 1.3161307305029895 1.0864786907568753 0.8423808115056121 0.6271425935179669 0.46789977525036186 0.3678987977915215 0.31673365587846297 0.2913570903629842 0.27814141636066075 0.2562091109409612 0.20648085372962197 0.1148378148199019 -0.005400489024614269 -0.13462454376695002 -0.2694325996248199 -0.40600116450186946 -0.519217627682192 -0.5898256086892196 -0.6152045132868325 -0.6152801133777647 -0.5909637771385634 -0.5403580789807158 -0.4546946678474643 -0.3551580496304754 -0.261665648703467 -0.19288188942908777 -0.15804826478830664 -0.151823424298291 -0.1489254800201917 -0.12895586427861777 -0.09782819202522348 -0.06292638713138506 -0.02928621156712609; -0.14616348980952515 -0.2772466342913713 -0.34932604095911407 -0.3379060154397756 -0.23201364226697488 -0.03918020334519484 0.21211724860532763 0.5120487771330253 0.8339430058838391 1.1491962990606057 1.4169406665112754 1.6032473168980277 1.68041039680249 1.6409018093859449 1.509888266185828 1.3228822749332967 1.11047684304396 0.8906708155844902 0.6968013550347846 0.5429121044577574 0.441479504157906 0.37596230895263955 0.33798739334186084 0.3038569176404753 0.2557293042800307 0.17815751879479977 0.06521861221063979 -0.06820747887715456 -0.2093378858031575 -0.3562006612481678 -0.5015405364230124 -0.6289085041565664 -0.7185656742754739 -0.7661640316423655 -0.7756906213745987 -0.7557227563918842 -0.6989375576073639 -0.592830256669663 -0.4719479486918273 -0.37182508046539486 -0.30223023458983567 -0.2600063591486504 -0.23291300699208867 -0.2084285305475336 -0.17293817793558175 -0.1286412660178598 -0.07964232359293165 -0.03894745124826323; -0.13795561557043667 -0.26115441782403115 -0.34056991620004656 -0.3410742477959719 -0.2545634491306998 -0.08267977359979921 0.15176160849661358 0.43572460542456953 0.7425548485327685 1.036138636246733 1.2955523391657828 1.4894002558514234 1.5861100931565522 1.5679057875996116 1.4563450057360319 1.2827063859122205 1.0844238387406981 0.8838566990019371 0.7043253340312591 0.5618461856704041 0.4583257717450095 0.3879091945134208 0.34058322223773346 0.29363876998605903 0.22878236787308212 0.13051280056350223 0.0032577750150209342 -0.14230358691165249 -0.29106813868638975 -0.443566700337632 -0.5944757520515866 -0.7259832299544746 -0.8286581420662519 -0.8857875586102282 -0.9014726129149401 -0.8735961173569337 -0.7968552398530463 -0.6761688932433504 -0.5476799333439631 -0.4478891481755003 -0.37502845657306605 -0.3192314342491291 -0.27707758593625526 -0.2350990955224817 -0.1958531439562277 -0.14145644147236147 -0.08496226665455742 -0.036512578952907014; -0.11740498481761252 -0.22329548925813797 -0.2954634926938232 -0.3075915127945588 -0.2433088523545078 -0.10397760548970557 0.09733318420480992 0.3550301250065946 0.6270044606747471 0.8865037108729092 1.1131603354244024 1.2915840054052588 1.388333402147772 1.3904787780775365 1.309404839402321 1.1694994444705458 1.0047336170826542 0.8285633043663838 0.6666980505381702 0.5333958817203287 0.43705212634268126 0.3670390100617659 0.3160411310203534 0.26547190205155774 0.19197945121194365 0.08664653091004745 -0.045132813047913216 -0.1922945714183446 -0.34534481236544373 -0.4973612152372444 -0.6436860879155925 -0.7670013696336763 -0.8599971006698214 -0.91109958061691 -0.922820111137736 -0.8851843145167172 -0.800842180799855 -0.6810901159625986 -0.5655213232002416 -0.4684677039099383 -0.38897822784782027 -0.3256399427854821 -0.2760266106222566 -0.2364839515983818 -0.19375204569623156 -0.142503715750873 -0.07820589795128463 -0.031143470518924486; -0.09040767990473166 -0.17536272213751622 -0.23447103705306138 -0.2490413747621333 -0.20905882766907452 -0.10703064298168774 0.05314037658753973 0.26417195557249823 0.4922719332220181 0.7028132511870461 0.8863190593310082 1.0282570741239634 1.1084167870074892 1.1195834693369924 1.0654124804903737 0.964215610982079 0.8408772078305008 0.7027207925806527 0.5655140150875718 0.46082893865175706 0.3809611443142306 0.31937536129123506 0.2709375389362586 0.22113742297688357 0.1496055096639474 0.053059359330086014 -0.06259989597189759 -0.19686882379625514 -0.3415000931558716 -0.48663046980598434 -0.6134635555774834 -0.7116702316466743 -0.7792276250368082 -0.8238916129935164 -0.8253907298476235 -0.784042383232982 -0.7053910374302493 -0.605018023524647 -0.5116272648436418 -0.42311177299828256 -0.34698892648298846 -0.2860673239659358 -0.23862803271239486 -0.20466293888891232 -0.1747149745138625 -0.12412054711250264 -0.06322704006487895 -0.022975729822685087; -0.06021981480273057 -0.12125194098925625 -0.16432073590767995 -0.1744345074819335 -0.15076560356440694 -0.08583399095720354 0.023094736332038852 0.17446196619456023 0.3381799700616259 0.49333200364782553 0.6241089327525726 0.7215347329475523 0.775171906973559 0.7838784355281385 0.7494726507210622 0.6774175352525146 0.5948245570353148 0.4999725132882825 0.4089943244415346 0.33645911253810834 0.2837821818324145 0.2411438814653476 0.20258362182436132 0.15450556760577477 0.09231547364158103 0.022668822481077065 -0.06279805817265889 -0.1684898305316568 -0.28620024163975333 -0.398013888561461 -0.49725717115853085 -0.5607365228393105 -0.6029613335357727 -0.6254355290928952 -0.6208420450435279 -0.5809650016832808 -0.5202205660971546 -0.45091584031678483 -0.3876357302990287 -0.3249083969216599 -0.26518269544681655 -0.21310229982655515 -0.17109532336363628 -0.14895193322278819 -0.1283195805947469 -0.08932048653904995 -0.038388041421920586 -0.012934505232451337; -0.030428872037828823 -0.06106666952623352 -0.08752198598098236 -0.09213917467868489 -0.07744248398514164 -0.047396437891474116 0.007498988158210391 0.08586415460247397 0.17481444339074267 0.2581256142151267 0.3267103674327479 0.37374773983369597 0.40029604232492316 0.40207065216318494 0.3804739106745015 0.34278022753386855 0.2998883752072333 0.2533530078003089 0.2078111275604696 0.17471504466426055 0.15092464851762896 0.12955674244825502 0.1063595073082378 0.0770548686822782 0.04187654120254321 0.00026127529553776645 -0.043450446968659046 -0.10166093374947043 -0.1682682776396766 -0.23389202866007738 -0.2857813123521443 -0.3149586399010158 -0.3336727523792887 -0.3409792754834734 -0.3322674606468102 -0.3065047656300648 -0.27090104289049927 -0.24013083301968668 -0.20666024683383463 -0.17783636868266006 -0.14641297623106916 -0.11006176839327216 -0.0864545448843957 -0.07574073882734017 -0.06746526584836486 -0.043959318936336755 -0.017131741706671755 -0.003232490470703261], hyperparams = 95.66273351965651), (params = [0.09433679382731441 0.18634539195901656 0.2673597813506806 0.33402230031116276 0.38814137170943624 0.4181264812408635 0.4108744324924841 0.37710697310768615 0.3344680996401998 0.2945676125766123 0.26418089569589925 0.23768640229173207 0.21367703151831768 0.18901847017898818 0.16144907358108612 0.12798652481661635 0.08720066182238054 0.0425456182638325 -0.0040800450947448335 -0.05155379243195473 -0.10044259413651306 -0.14717560768391139 -0.18801129571823355 -0.21624653240354913 -0.2266895593955113 -0.21982268579332512 -0.19899492774893612 -0.16988948558567038 -0.1349877247728303 -0.09737446112576104 -0.06234267337738967 -0.02959960682693206 0.0017753501069625944 0.034226569169030385 0.07158873252669472 0.11571441977000778 0.1639189693549777 0.21064159349569817 0.25163968672002435 0.2824539105798941 0.3008593741435924 0.30766544294669534 0.3006412558464025 0.27890242348110744 0.24250006449711112 0.19346892797435455 0.13523993178984212 0.06981209949541349; 0.1915477881171562 0.3772302541135705 0.5392948264049255 0.6677073771080899 0.7614260547919052 0.8089430390957609 0.7984453085581419 0.7447731401113837 0.6736972726130841 0.6029377675228997 0.5422073761751253 0.4876248408711197 0.4351384728801555 0.3820704468672404 0.3240248708856205 0.25665384841606653 0.17746114435727722 0.09260549432828404 0.004482273049722952 -0.08589944746869861 -0.17930138372717894 -0.2699316321168915 -0.34972222754857624 -0.4065882587930362 -0.43257193831623786 -0.42660661622479523 -0.3942884753543438 -0.3444686722126552 -0.28228312284735546 -0.21405455701565315 -0.14408800521768356 -0.07516666145753773 -0.007024146218186895 0.06473243790871218 0.14456931250450714 0.2326992586723136 0.32531690912815237 0.4129938597692176 0.4891631823806679 0.5480398968648149 0.5832595620863151 0.5923936099430094 0.5759345821490036 0.5337495798675727 0.4645564233526037 0.3708455102425872 0.2579196001276777 0.13219844277342727; 0.29231895898261684 0.569336711365428 0.8104923987092847 0.9983842788147546 1.1202831650127079 1.1708475609554765 1.154575987471567 1.0902905390411313 1.0023957170689393 0.9113122192156228 0.8264379986952541 0.7439953768371604 0.6592833118669089 0.5718188917791432 0.4782218104477415 0.3740604930729416 0.26020043963278777 0.1424463601537693 0.022047197938400355 -0.10272479293129755 -0.23282880467313927 -0.361040752228802 -0.4745521224629892 -0.5597155911457227 -0.606364969176121 -0.6120401797103376 -0.5812064608160437 -0.5215491076998998 -0.44055702903278576 -0.34635583921587476 -0.24432793929032032 -0.13988135713921931 -0.032062632025337684 0.0819158703791843 0.203488759101522 0.33170784060096653 0.4617207255619984 0.5851675482081845 0.6918637453632995 0.7740500471251761 0.8237514281823828 0.8346158096005069 0.8076141110869378 0.74532324848925 0.6467591899426 0.51541707531405 0.35762869878709924 0.1823652109056407; 0.39169221180699176 0.7570831291036475 1.0731952624282965 1.3162933666386754 1.4643309341304134 1.5166852741691361 1.4930856913281592 1.4194997871306927 1.3170492460034593 1.207294003360333 1.0960841847767515 0.9782835611899887 0.8532621339397504 0.7229265050285537 0.5880260047834083 0.44738266211920297 0.3045776324871315 0.16244176899839505 0.019882044556481838 -0.12808710658652903 -0.2845176064834037 -0.43930485859778884 -0.5766749805848153 -0.6815703422399076 -0.7458356482999484 -0.7671059296517856 -0.7462586337953725 -0.6866832843079868 -0.595749470979461 -0.48105428263402394 -0.3518500407266283 -0.2154354162377888 -0.07147988555177731 0.07988293685533002 0.23660649328038882 0.39626449675250963 0.5543511254913916 0.7033527551366558 0.8330008414151728 0.932497229156917 0.9952899940116106 1.0129966755017215 0.9809532785406592 0.9010524259493502 0.7770820242805524 0.6174450595200494 0.4290443147473694 0.219778788107676; 0.4849354067369121 0.9337004759682357 1.3173897354361954 1.6086733556953883 1.78403272854541 1.8451852576562373 1.8193684916020347 1.7365188602339345 1.6172785238859069 1.4802768515199067 1.329010476433342 1.161182182429812 0.9854931472631446 0.8067660847802665 0.6306074213231257 0.4601055747353696 0.2986035143336711 0.14355296435089357 -0.00985532560403278 -0.17074798198472876 -0.34144651521276465 -0.5083120520360812 -0.6551206999300326 -0.7666860706560975 -0.8380950150924519 -0.8695753780387772 -0.8608547132947679 -0.81086692009028 -0.7224474797069417 -0.5999066210551133 -0.45430233496919287 -0.2944653134432764 -0.12282874907383207 0.057880651751235565 0.2418224113863818 0.42371316333884473 0.5992047269629331 0.7613106032753775 0.9016258360883522 1.0114744209620825 1.0843869697787918 1.111347120952912 1.0811497524311469 0.991090000000956 0.8506781364104768 0.6743127316686501 0.4700907235341329 0.24229004039861654; 0.5699592135061404 1.0934325340789286 1.535535329185824 1.867037591496725 2.0653266007723117 2.137620879632522 2.115776862685783 2.0267541085147855 1.8879703395766065 1.7144483432099415 1.509132708241005 1.2816032645861606 1.0474264102918558 0.8156856657801841 0.6006358281472428 0.4112100185354442 0.24633232783702064 0.0946241296829862 -0.05564721490549331 -0.21799990781365117 -0.38833157687331765 -0.5513955559938796 -0.6894033591157286 -0.7930533854499323 -0.8601583450729882 -0.8945685079704578 -0.8977730326041787 -0.8656538541556342 -0.7952114554111283 -0.6846802011954137 -0.5406313881805129 -0.37317222297945174 -0.18682218314389307 0.01173711104768863 0.21463796309941044 0.4124330345717127 0.597493809069498 0.7630229116374238 0.9040923803393325 1.015962457075786 1.0925047781483106 1.1243673177116085 1.0990484236546296 1.0097387047660749 0.8654940117406312 0.6852412557372863 0.4782675434986529 0.24755426444605433; 0.6430865242951304 1.2317586786012795 1.7230704441115798 2.0846894632555566 2.300069473980064 2.3840453695660093 2.3673527695275607 2.2696847997254865 2.1049093094515947 1.8842237602571836 1.615839413040524 1.32202577350775 1.0225327197260279 0.7374854549517811 0.4938785145681224 0.3027845466686891 0.15351239776775552 0.02411776648727591 -0.11003991090077149 -0.26321786048698737 -0.4242490484077932 -0.5712521539113985 -0.6850684671802405 -0.7649687313824046 -0.8147593230500128 -0.8431368892044643 -0.8546473631955915 -0.8454306229133856 -0.8061477355609338 -0.7276770496352275 -0.6064796206950198 -0.4510709396761432 -0.26702362393638934 -0.06395102733071104 0.1484948003329883 0.35694807307351517 0.5483316516025984 0.7131029016661439 0.8476003867417898 0.9525620616992284 1.0251877284439146 1.0576020656248823 1.0384978930971556 0.959239400840304 0.8244182650685213 0.6515176447074746 0.45365965850314643 0.23483738664767095; 0.7015660273594208 1.341488417581074 1.8707490198789651 2.2548531988521323 2.482985477913122 2.5746258938295896 2.556510656477934 2.44275063092617 2.242253270295732 1.9662196260004865 1.6309171246472023 1.2688376974641558 0.9094217908209319 0.5879179682646635 0.3391295356971864 0.16466335486479888 0.04725429452530114 -0.04953198196095885 -0.16323739788507202 -0.305897326374093 -0.45657139363418453 -0.581646423748479 -0.661769279658939 -0.7039390180979126 -0.7232146900594166 -0.7346045044851537 -0.748764239269662 -0.7633068261613789 -0.7635490842330219 -0.7303063709392824 -0.6510848136701302 -0.5270769669859316 -0.3637557379299863 -0.17052719952607887 0.04106687098905963 0.2530707669480214 0.44802308847616285 0.6130906714919979 0.740651811491129 0.8337834208750945 0.8965276047796986 0.9258810058213709 0.9126011523314036 0.8477209629576163 0.731526850536991 0.5772162594455373 0.3997280668194401 0.20610629017811397; 0.7412496428514023 1.4152111299196415 1.9680114108381712 2.3652950132455004 2.600298934141578 2.6932131670466877 2.667210522742372 2.5296116731650287 2.286247237601502 1.949796683522758 1.5479387323440814 1.1271799824764934 0.7278140585730438 0.39635718470489845 0.162463029360694 0.019655194046047327 -0.056540383872445164 -0.12551526396418244 -0.22969263714879437 -0.3688862338016585 -0.5086231825697769 -0.6058263123867789 -0.6418004466613652 -0.6310189303138819 -0.6065904641866461 -0.5924550227310285 -0.6057478064108137 -0.6445424846964614 -0.6877012597098535 -0.7076448419247917 -0.680613610188507 -0.59979293136672 -0.46932500773326724 -0.29848935337539845 -0.09925649610183938 0.10748246250166466 0.3001247945901131 0.46565031939345614 0.592022033721601 0.6767129692553016 0.7277418736987443 0.7495548809261908 0.7381443185606482 0.6876968374482475 0.5953677605830692 0.46889445914250444 0.32290509181120547 0.165661927881794; 0.7595341960158756 1.448617853868433 2.0106687340767753 2.41142169210996 2.6454606754994234 2.7314231634614097 2.687509092787973 2.5156463779625136 2.2221866151766965 1.8264033059049587 1.3718533659845784 0.914508866456686 0.5010247694413905 0.1831465460624772 -0.019292843582583367 -0.11566107657578865 -0.1493913605957898 -0.20983460413214935 -0.32891342829476283 -0.4788077931743836 -0.6070651240477312 -0.6669579694879789 -0.6455172523118239 -0.5697145017988923 -0.48924265621785085 -0.4445274431539563 -0.458657609473145 -0.5258383920422127 -0.6149712535227798 -0.6892479847434534 -0.7179083719046772 -0.6839339636877712 -0.588037837183807 -0.4401657180135991 -0.25804476989717784 -0.062377157012156605 0.12321915271570026 0.2861829031275496 0.41276438950897015 0.4924578802322575 0.5331775355418334 0.5464371777966256 0.5342415199072429 0.49563239047149327 0.42964320098242514 0.3384451289189383 0.2319222148907026 0.11825595799786892; 0.7568239001512762 1.4420709000171446 1.9987367202518633 2.3920870326519466 2.6156557066241874 2.6841088097797607 2.610070123777319 2.3950527772242305 2.050896161595292 1.6099288729603976 1.12557065426565 0.6547463727807823 0.250204483631781 -0.03525656380279185 -0.19148559696276218 -0.23296252496032713 -0.2388609037234781 -0.3166577877122417 -0.4735546699097248 -0.646493427640524 -0.7595187417868412 -0.7696695334973584 -0.6750172204202837 -0.5201340570100043 -0.37622064575462527 -0.2990091360993692 -0.3191765167996642 -0.41761773906016064 -0.5558024882740502 -0.6867856039082921 -0.7739623247099208 -0.7914421465359631 -0.7319333905299704 -0.6061000762761314 -0.43613713336039467 -0.24668280997516112 -0.06386989309142423 0.0954853784180993 0.22026825539213132 0.2975507947527881 0.32960880479197585 0.33454873484007924 0.32195282081081217 0.2941593730530835 0.2531575983820041 0.19976918452306894 0.13731854974830865 0.0702370702627427; 0.7322848596768756 1.3951026923881467 1.9328250911506428 2.3086070540229575 2.5113612752834653 2.550194827814142 2.4352483978187984 2.1741653248411485 1.7882867652267633 1.3214178256405977 0.82915743641942 0.36868013642101616 -0.0035626722725807768 -0.2423156333752868 -0.34403496737904515 -0.34174079463718793 -0.3459055180145861 -0.4598645050045667 -0.6634989426517001 -0.8560023867120171 -0.9483226245256611 -0.8990672300606702 -0.7234276827676659 -0.4872260136710313 -0.279854451384006 -0.1751188796385519 -0.20021693120514802 -0.3270194092589557 -0.5059754733251561 -0.6891722358042632 -0.8346483456872901 -0.9089258728227739 -0.8927316731320467 -0.7925959600733025 -0.634215061714937 -0.4458429126159089 -0.2571861621626607 -0.09446906411688129 0.029625013451161943 0.1063789986387886 0.13495538058230297 0.13398230270314104 0.12172872316627471 0.10521086618552043 0.08768897186334319 0.06896984555174 0.04828004953072585 0.025110472880877845; 0.6898918141168058 1.3149364625076314 1.8206021985255947 2.1665008312112413 2.3354463867413915 2.333312009818824 2.1728960561273105 1.8694506228200285 1.4555855284474974 0.9809935413663408 0.5016584821746762 0.0745548615336613 -0.24736999775278412 -0.42907214025254575 -0.47873932844242506 -0.4531392488611197 -0.4816263337822069 -0.6445184721081059 -0.8879717703617312 -1.0918492230579202 -1.1577723855724908 -1.048445545969699 -0.795477608027591 -0.4871531047060646 -0.23209943155262247 -0.10910618384566403 -0.13753634831807066 -0.280947504362455 -0.4883664726206564 -0.7096084499386014 -0.9009293343165248 -1.022123260391144 -1.0483675867918254 -0.9765161485152498 -0.8336781227865734 -0.6500152516549313 -0.45502947668353183 -0.28187451184974444 -0.14945842483135016 -0.0666603267756068 -0.03485570910311745 -0.03598701505892778 -0.04557812911143476 -0.051399536289140305 -0.049487642777575315 -0.03980155856701671 -0.02686314716272657 -0.0133900593820689; 0.6361857349244172 1.2115761305143051 1.6718936076810864 1.9738902412590165 2.0973751352373964 2.0468657506691934 1.8407672866597684 1.5036821805284102 1.0760697471754397 0.6074949825318955 0.15633536358065003 -0.21875843511997325 -0.4747599637328567 -0.592084354949019 -0.5962998109151362 -0.5663774716041833 -0.6385445788002544 -0.8549070746455072 -1.1292644516384776 -1.3312375787395239 -1.363702459575709 -1.1970202309757882 -0.8801463194759043 -0.5185271017982221 -0.23099154986882636 -0.09696924677629912 -0.12690638472731525 -0.2796297750000037 -0.5068355478036439 -0.7565835840043814 -0.9807286647281092 -1.133769335357256 -1.1906905082909187 -1.1450979677135351 -1.017445863053464 -0.8414624710750991 -0.6460683674793866 -0.46250846909464366 -0.3141139037488252 -0.21359628915640674 -0.16786727677317698 -0.16159593172079526 -0.16539746015640067 -0.162552118900364 -0.14707817790108585 -0.11841329013762432 -0.08124816354314052 -0.04068280708826319; 0.5771837078618187 1.095287349739182 1.4997976337782373 1.7471135111851661 1.8162324670974561 1.714569104913249 1.467843188928359 1.1093653006545783 0.6808805001250143 0.23192907590592962 -0.17542912833725352 -0.48518389825035063 -0.6683358792799104 -0.7266959816856251 -0.7082948302002731 -0.7066915447396819 -0.8384648174438152 -1.0997636760062381 -1.3818775902502438 -1.5586002638578875 -1.5431389774846778 -1.322411988501282 -0.9550416122249086 -0.5570889077343383 -0.24837248352489513 -0.10581698163004152 -0.1361385400230072 -0.2998629679764371 -0.5454378908530623 -0.8184626888380478 -1.0665839538162771 -1.2434994170530151 -1.3224426604568036 -1.2987895578274342 -1.1833419439224748 -1.0094372816950057 -0.8124511749848803 -0.6215605591128732 -0.4585448002719221 -0.33591596813969044 -0.2651293605272828 -0.2410351646135758 -0.23595866335586996 -0.2271485592985321 -0.20436521208908062 -0.16470810730583188 -0.11292262797623887 -0.055964606361843236; 0.517295270750533 0.9756776199797037 1.3204565505226964 1.50857511457798 1.5203008907279802 1.3693216278623437 1.0902913774519485 0.7223238625653411 0.3064472254000776 -0.10798977098958185 -0.4591082192001893 -0.6965702811552598 -0.8111113085496591 -0.8316819215393672 -0.8260394635502102 -0.8834743015983393 -1.0772073114113114 -1.3604732605410403 -1.6221559077201422 -1.7477076375824927 -1.6709904021727404 -1.3959212229126599 -0.984834294905275 -0.5569257380564466 -0.23049652850881988 -0.08481559073805967 -0.12367322818245856 -0.30580711117733395 -0.5754954134835146 -0.870974954584296 -1.1392202170243078 -1.3383621702615427 -1.4419019241323507 -1.4423214560294908 -1.339095033075631 -1.161748002154469 -0.9555829549190618 -0.7548755886718875 -0.5792271528371287 -0.43699844079564804 -0.33772211343229314 -0.2859482058367026 -0.26573935621588174 -0.2516936933591087 -0.22647495837712098 -0.18236121932270324 -0.12315472846614173 -0.0597393200623031; 0.45904255594245486 0.8587953997128562 1.144108380624356 1.2741288920589497 1.2326750425118003 1.0390973392822285 0.7362564406783245 0.36956056770748585 -0.020182511589146742 -0.3852075508061892 -0.6684462344470363 -0.8345145594670859 -0.8975426939988722 -0.9095823335991658 -0.9427201343267518 -1.0647180949745692 -1.3010981398778503 -1.5829544365445143 -1.8011636867809357 -1.8576370957871295 -1.7117536327685865 -1.3774544967977904 -0.9201593486883346 -0.4578361308860878 -0.11284682715241688 0.024052936079818763 -0.03927281443634445 -0.2532303103005682 -0.5551146571326642 -0.8786379141856723 -1.170394479289527 -1.3966642979474182 -1.5328856986270045 -1.5660218405168655 -1.4842433920215519 -1.306641943237418 -1.088499498316193 -0.8729536800830772 -0.6805256514226765 -0.5195486499350622 -0.3940356802310613 -0.3110197739609442 -0.2679837084857927 -0.24571237905392082 -0.22026911261364515 -0.1766129394976691 -0.11741650248690341 -0.05587558937668656; 0.4016237185861709 0.7439888187521546 0.9742986862957591 1.05321128101052 0.9677855536068358 0.7415054243453344 0.42591329113498266 0.07058421922015935 -0.2819551560956182 -0.5861449599060233 -0.7975883992009267 -0.9035891222928232 -0.9379585471826268 -0.9608725339010784 -1.0348645701086494 -1.1999918006492276 -1.4560099832124085 -1.7253540049083314 -1.895406614433281 -1.8833411216570204 -1.6676963931141098 -1.269936045790515 -0.756059236851363 -0.2460748212364007 0.11235649398206704 0.22550151078173084 0.11488061935871405 -0.14472961649512123 -0.4876724063062005 -0.84395580479494 -1.163177102247886 -1.4170332632397815 -1.5862708537039567 -1.6546196914025206 -1.6044644267370993 -1.4424563571896543 -1.2204401664128732 -0.9910884508967326 -0.777855691670336 -0.5909568001534138 -0.43899493943877865 -0.32863481261008565 -0.26164668737600666 -0.22594671475773564 -0.19947818869684206 -0.16022748365978232 -0.10562124251618907 -0.049100005920304654; 0.3468655293513788 0.636038080375479 0.8166254050319263 0.8524770744970134 0.7348418675230397 0.49062941628701484 0.17411691077419308 -0.15997085292611948 -0.4678473063070119 -0.7088228787936119 -0.8550016954548458 -0.9131172790106059 -0.9322219263306495 -0.9722811584721502 -1.0731493036558648 -1.2617514603264897 -1.5271355423551447 -1.7884845328825607 -1.9259677292615047 -1.8589977448258772 -1.5784235094451369 -1.112808470541692 -0.5302867318842559 0.029628506934637765 0.39687662046881594 0.4712537454595908 0.30033786664784184 -0.021778856131763422 -0.41407898688126576 -0.8112418175152688 -1.1595687808610637 -1.4357120872633833 -1.622150361459274 -1.7085154580419046 -1.683136845556503 -1.5503854525364342 -1.3444707270716874 -1.1120246911645815 -0.8832018972274281 -0.6699886955945279 -0.4883052381157163 -0.3524648326678786 -0.26552699111248107 -0.21705988945551433 -0.18610894965564131 -0.1488920042977018 -0.09830888780575854 -0.04582477165861001; 0.29608801286868414 0.5368629462599414 0.6743054000764169 0.6764406587922024 0.5383457906819779 0.2891250464047357 -0.01617803958275204 -0.32136528318920426 -0.5818649811740523 -0.7612649683656381 -0.8481491196127143 -0.8700792975655428 -0.8819964999532818 -0.9301553958912231 -1.0442319837539296 -1.2502960340514229 -1.5295145576311575 -1.7967262467502665 -1.9237297927088322 -1.827909562981146 -1.5057891323425143 -0.9922981144164652 -0.3661806720898939 0.2186252664808279 0.5864710056318646 0.6305008196794132 0.42321891752227986 0.05257602379036901 -0.3844377616739446 -0.8199486906814758 -1.1974299210891322 -1.4904685923142336 -1.6800418802523231 -1.7607522252420804 -1.739423468234985 -1.6322975771777593 -1.4550112448381782 -1.2321922743107478 -0.9956799611908735 -0.7650125912578765 -0.5605674565046681 -0.4026273031802135 -0.29774118569059854 -0.23479221635453856 -0.1952749612930141 -0.15455366139698226 -0.10243904238538164 -0.04820284020493482; 0.24928854319668195 0.44512904057952596 0.5434626244564966 0.5188001242515309 0.37035327402859486 0.1269425910162511 -0.15822472300974375 -0.4285012541625252 -0.6379710280097829 -0.757199375406784 -0.7931873993307512 -0.7861832704922818 -0.7847289266280516 -0.8288176057319037 -0.95174959550009 -1.175523560850433 -1.4742087338629113 -1.762411240355381 -1.9084081376887319 -1.8215433867654782 -1.5069512474269926 -1.0111971977560728 -0.412947444746037 0.1332133384567288 0.4733019816505662 0.5178199129844827 0.3311454039253573 -0.02464341580556005 -0.460281841312572 -0.9043078552399453 -1.2949941070498099 -1.5927816177323062 -1.7716384718381235 -1.8329089346642216 -1.8001127186057648 -1.7051617057759973 -1.5551923249144621 -1.3508325014202023 -1.1173349730525513 -0.8794717550410975 -0.6613578856999117 -0.48717365347519487 -0.3654041950355757 -0.285421933738199 -0.22975117029674447 -0.1779444708315124 -0.11900568915017604 -0.057399466663830494; 0.20255354643185894 0.353540359023601 0.4149989160210916 0.3677023353745254 0.21529147169490215 -0.014892333677905139 -0.2735600650580532 -0.5060603806453899 -0.6657808655557532 -0.730356892584081 -0.7190749792894958 -0.6781360143044906 -0.6520988592730024 -0.6851800940728847 -0.810286653654323 -1.0442369295762988 -1.360776478721135 -1.6746476530378498 -1.8581673380353605 -1.8251927995966035 -1.5872524587670367 -1.1935153419009972 -0.719453502648299 -0.2900154154186306 -0.012580248333269784 0.053752422962938376 -0.050174556884514825 -0.31667201521735644 -0.6814296660281157 -1.0815848628488054 -1.4530427866211968 -1.7367059718434787 -1.896184998599137 -1.935199202918147 -1.8853864584781574 -1.7869157901543162 -1.64949603092305 -1.4621058412211412 -1.2411257101686723 -1.0101908550000678 -0.7898062251813863 -0.6043240973405136 -0.4658611990166123 -0.3667115152694896 -0.29044750126402624 -0.2199801655700843 -0.14649910118282855 -0.07190205981915566; 0.14862571445355463 0.25035007162585493 0.2737943938235759 0.20612013474700897 0.053299589492538775 -0.15891291927084097 -0.3858680258767547 -0.5769687589874574 -0.6900812973258174 -0.7104363757634133 -0.6591297655399624 -0.5809777102858542 -0.5258123756157393 -0.5400033120429387 -0.6548778687122273 -0.8822149533208451 -1.1961138827823536 -1.518889749445296 -1.7438305791322168 -1.7941950476845796 -1.683495573306005 -1.4606622322317449 -1.1696289908132003 -0.8893310917481312 -0.6839422984815884 -0.600557398049272 -0.6218042235722959 -0.7664232057709272 -1.0148955658155865 -1.330106390616725 -1.648557728534809 -1.898636501404826 -2.0318920223098385 -2.05099352851186 -1.9884348100451203 -1.8825142548553393 -1.7448346347397512 -1.5651455951812672 -1.3586422352552827 -1.1446915255748464 -0.9348623030453207 -0.7475099190380494 -0.5970968043053128 -0.47935938679675055 -0.3805354558503857 -0.28676859342385747 -0.19069450820865427 -0.09399409306585542; 0.08307334290257026 0.12692945064266759 0.10846377701715716 0.021647279738666054 -0.12743883395281846 -0.316309786981464 -0.5083304293962794 -0.6584863553655701 -0.7312710759549254 -0.7175517636544096 -0.638778951706976 -0.5304543056760957 -0.4427714050048225 -0.4272887115627609 -0.5142350538725284 -0.70774837055156 -0.9854166187785427 -1.2885319961277226 -1.531844409599903 -1.6557169410994699 -1.6837512423930567 -1.6417780792908248 -1.5374187808255895 -1.3978500791553516 -1.2702017515817599 -1.1955872431635146 -1.170018789024013 -1.2243010001361296 -1.3749913779855163 -1.6050501254872815 -1.8592749422510932 -2.0629663880517737 -2.1640778496298467 -2.160653612098262 -2.0844991917142908 -1.9711665633573185 -1.8312025392034117 -1.6575467269294824 -1.4647994136507214 -1.2736715220646282 -1.086244097072552 -0.9087634559903761 -0.7540705773967229 -0.6230845353884674 -0.5039046684928478 -0.3832992260406585 -0.25588169531519395 -0.12655830910792734; 0.007044876617691769 -0.015343317387835656 -0.08074379871410232 -0.18844524552710545 -0.3318980419832918 -0.4961390043107135 -0.6525348958406303 -0.7640429645609734 -0.8026272111593628 -0.7650686319055545 -0.6693766375139989 -0.5380075923519458 -0.4182719428986845 -0.3639058746021028 -0.4011886695644134 -0.5354523073836354 -0.7500510493685659 -0.999755209925695 -1.2168285481025316 -1.3700786008926888 -1.4965684715490488 -1.599960036357343 -1.6429736500628895 -1.625460546886812 -1.571945483149028 -1.5317971742618453 -1.505562822058407 -1.5298472420437705 -1.6344018384130137 -1.8165066579343432 -2.0271431899432133 -2.1963375545054737 -2.27073783962937 -2.24658598436363 -2.156600980629037 -2.0354013747759034 -1.8931800790556816 -1.7249213123223108 -1.5483395722137254 -1.3856816724610785 -1.2303639822368566 -1.0751474549074238 -0.9261773364294653 -0.7874181496724582 -0.6502088654406958 -0.5015741597751812 -0.33881952061265164 -0.16915997437374383; -0.07442733414557988 -0.16945465485596808 -0.2894095821785566 -0.4251841851706621 -0.5678860250661484 -0.7096712587354483 -0.8309267015687218 -0.9042363473546389 -0.9112262792249471 -0.8528917125590995 -0.7437527987101495 -0.595760985122903 -0.44614062896175555 -0.34858214024209083 -0.33043460519977336 -0.39323333353643974 -0.5222213528643926 -0.6837675870592106 -0.8268906295158301 -0.9462331775703576 -1.1046917520677069 -1.3071670484552755 -1.469415455881739 -1.5516364912132832 -1.5657174792021271 -1.5616727711088818 -1.5601081891386002 -1.5963222795214413 -1.704450650266508 -1.8854652106890544 -2.0948916713580132 -2.2591196580983137 -2.322712030377255 -2.2854224844496276 -2.18592353793747 -2.0604115681004025 -1.9182111594315783 -1.7576078332673715 -1.6005029716323986 -1.47101544197268 -1.3548397039010815 -1.2297889855902255 -1.0936920836138657 -0.9532385192076779 -0.801402010705524 -0.6265214692746873 -0.4277030022621122 -0.2157083752403388; -0.15905342234814338 -0.32923773162914544 -0.508647406664733 -0.6815196778414211 -0.8346119143010834 -0.961720916412953 -1.051707842122309 -1.087796227272863 -1.0620883098337184 -0.982380277202642 -0.8595056988320262 -0.6969707079263617 -0.5238799184801913 -0.3896844200841772 -0.318360924947596 -0.3083689634489616 -0.3455181649922248 -0.40481483173715277 -0.44263014212872115 -0.4711506905005665 -0.6010282675689789 -0.851650029323027 -1.1014952089969166 -1.2604494285776116 -1.321892726295047 -1.340470223468915 -1.3535982444257086 -1.4189732582818166 -1.5658953076412048 -1.7951093336952777 -2.038631691639667 -2.2252287694127344 -2.3014026145377993 -2.2657278397696845 -2.162775594934991 -2.0355544537654975 -1.8971663129250012 -1.7499105500789993 -1.6184057740338647 -1.525764240344771 -1.4507798733078032 -1.3587097275514504 -1.2402619947180673 -1.1026669987113147 -0.940924158144039 -0.7440038696983944 -0.5130559850943964 -0.2614816285566166; -0.24296419579157694 -0.4865586361587083 -0.7255055947395999 -0.9406985042379563 -1.115489281419864 -1.2407888675779681 -1.3111841416000227 -1.3175709568350111 -1.2624855850017864 -1.1612334491429948 -1.0247991708088477 -0.8511013608189885 -0.6594154476852643 -0.49313340304124353 -0.37460118816595495 -0.30093191312435147 -0.25557243233208454 -0.21466393895236877 -0.13875262026368929 -0.05978412929011104 -0.11854564669430402 -0.3669494584372804 -0.6635949127476134 -0.8643138266989292 -0.9357711510241744 -0.9440070118986429 -0.9593282391234097 -1.055678048365339 -1.2674729958665967 -1.5739144668731369 -1.8764701612862376 -2.0996038846929226 -2.201581493625472 -2.181895540876671 -2.087618788839832 -1.96484241147407 -1.8322664271005658 -1.7025647543197362 -1.6014000206696026 -1.547822428744581 -1.513736810889309 -1.4537177502957475 -1.3539573952975286 -1.2228493744902793 -1.0563357669189841 -0.8445057626069794 -0.5883092430980792 -0.3020765901260124; -0.3216669117749195 -0.6345219757074866 -0.9288092805565331 -1.1869282190787724 -1.391031123300809 -1.528897373250501 -1.595327394203766 -1.5866517523537258 -1.5121611164514992 -1.3936048614753427 -1.244605120463522 -1.0618240348622265 -0.8572023511486881 -0.6657659833521425 -0.5085063911350339 -0.3820262228357776 -0.26940253848351314 -0.15172828129115767 0.00695385050557624 0.1716484852921471 0.18590582684363488 -0.028046067120648673 -0.3156473856103834 -0.49761406646891365 -0.5373960416231857 -0.5110704361988955 -0.5178297031370264 -0.6448616341207221 -0.9283910663134749 -1.3051047671363574 -1.657466076013435 -1.9142296764502453 -2.040777477202355 -2.040459161491102 -1.9582938362619449 -1.8440678807281123 -1.7251365533434657 -1.6202653670151081 -1.5535728748061346 -1.538596675109198 -1.5405388617483016 -1.5083848553882848 -1.4264441421571428 -1.3032609242152506 -1.136309846922961 -0.9163445931407473 -0.644253066888647 -0.33315081522654505; -0.39024143860638644 -0.7656934688491135 -1.1134330757687523 -1.4136221238310984 -1.6483474315608906 -1.807061609627375 -1.8820427422215127 -1.8717475232989946 -1.7897631570055057 -1.6632076057010883 -1.5077881862615339 -1.3215527739242399 -1.1100435091457814 -0.9004086260291222 -0.7138575234557195 -0.5472790281835269 -0.38841062518960023 -0.23179472302800752 -0.05016319089551534 0.12848719265380126 0.1736481745226272 0.024543613632756707 -0.19129960537423385 -0.30064802477171326 -0.27226443805007977 -0.19510983832293585 -0.19605609710570296 -0.36051566006105057 -0.6868159575044824 -1.0808885439868887 -1.4404510360804146 -1.7050341171209082 -1.8449138915019192 -1.8572477496180717 -1.7865604289154797 -1.6844775854744205 -1.5838768874500317 -1.5072023654366236 -1.4759417583331778 -1.4969133491149567 -1.5297107176566702 -1.5202151692323929 -1.4539046087299998 -1.3397564585471153 -1.1746305764274714 -0.9524433732735136 -0.6740213009641496 -0.3504901742593294; -0.44421594156080824 -0.8717869208336884 -1.2675868257512815 -1.6094292972960462 -1.8768226510882573 -2.0594800435832297 -2.1501349924017283 -2.1478276855026563 -2.068557682336114 -1.942254777984941 -1.787124479397065 -1.6035147283715065 -1.3942511981660937 -1.1783880409829455 -0.9760645116746507 -0.7870119019066067 -0.60108296528437 -0.4313069078424952 -0.2760795035887622 -0.14901799614074263 -0.12769858477612295 -0.22521176219385838 -0.3540810780778189 -0.377847991252641 -0.2755233748721522 -0.1479463195329745 -0.14962750864594002 -0.31953678586709594 -0.6108912597918993 -0.9464898124094238 -1.2632840100658822 -1.5036004309474102 -1.629140499284197 -1.6367626173650192 -1.5717695896838142 -1.4852516872688024 -1.4118440813950914 -1.3703464163485322 -1.3733674650305685 -1.423179043808231 -1.47990754194684 -1.489743410698596 -1.4389139333114873 -1.3351059127995497 -1.1745961631455613 -0.9543731799195053 -0.677168172687149 -0.35298816327686966; -0.4796126008754434 -0.9440024840287855 -1.3771922470249003 -1.7555900962536273 -2.0559161353759916 -2.2650883262481627 -2.376117245636117 -2.3868563636103874 -2.315360459919385 -2.1956174172453893 -2.0481811261372305 -1.8750753548954509 -1.6764888827931252 -1.4655035830070746 -1.2593509674619898 -1.064196193933988 -0.8719974956153187 -0.7048135892481145 -0.5853954718974596 -0.5212580020596616 -0.5426979926494662 -0.6225701716041621 -0.6906962371946272 -0.6583122887012919 -0.5292150047247829 -0.3909446986140798 -0.35110140709126103 -0.4455691963741857 -0.6295684234359199 -0.8632535142369774 -1.1000205860092098 -1.2849522375172862 -1.3782529688079188 -1.376765647528092 -1.3228419076723612 -1.262388976112099 -1.2224632721332236 -1.2129052009838115 -1.2436061778046579 -1.3176867902582312 -1.395023554252326 -1.42354780744949 -1.390293180624602 -1.29973675803262 -1.1465845057077255 -0.9314620724374623 -0.6608201416437827 -0.3441802821681978; -0.4960056407258462 -0.9783779945015615 -1.4322346991158645 -1.8359738766269194 -2.1636453390715524 -2.398193754184022 -2.531347514975609 -2.5605289026950135 -2.5016513566862426 -2.3912134544714334 -2.2551955207736065 -2.0960121094890947 -1.9151618864223063 -1.7205580005741692 -1.5224587013598245 -1.3332942651841537 -1.1528036652295106 -1.0013906386854192 -0.9149137962522184 -0.8954874131718586 -0.9410645205047939 -1.0087080598518927 -1.0376565979137196 -0.9743750870332983 -0.8311647611700036 -0.6774409906678508 -0.5820508589243306 -0.5790805933522238 -0.6462744761848734 -0.768881388147786 -0.9143884268745728 -1.0349693977894923 -1.0894122449982715 -1.0798677505180796 -1.0450856282974628 -1.0166767774259737 -1.00969201639204 -1.0305846943972778 -1.088586383149537 -1.185928808273268 -1.2833231991027607 -1.3323015486148584 -1.3185741004162626 -1.2433168903966607 -1.1016500042487136 -0.8954476004804459 -0.6341065168994561 -0.3291214127453814; -0.49244368149765044 -0.9736778460588597 -1.4302842366171615 -1.8430106516778628 -2.1861140468893314 -2.4411533448828067 -2.5965624811168966 -2.6480389406516487 -2.6069328272821806 -2.509228418077686 -2.385117078715103 -2.240288892928831 -2.076972899186456 -1.9025952435954958 -1.7228224168108224 -1.548572915446847 -1.392025378929671 -1.2695655960344945 -1.2098746657453583 -1.2128133235359122 -1.2543061368990942 -1.2942558859494115 -1.285794426367832 -1.1966494532859613 -1.0346483159466708 -0.8500527054596024 -0.6994925497877342 -0.605934607164833 -0.5764706008158134 -0.607756958952693 -0.6748692676780722 -0.7349490179373201 -0.757228571732697 -0.7502518778291306 -0.7423222745482214 -0.7475831749517021 -0.7734976285854357 -0.8253415179882627 -0.9119418691399461 -1.0362137518272911 -1.1569625299300823 -1.2269574050889205 -1.2329511357618428 -1.174228979983946 -1.0458413587874313 -0.8522689070417088 -0.6030989191420646 -0.3120629670946408; -0.46906237244055127 -0.929704817599964 -1.3710819893194535 -1.777322950210894 -2.1247978555040055 -2.392752102515006 -2.56740561538051 -2.6418535078167777 -2.621261070934105 -2.5375075143804544 -2.424419896237346 -2.2923514101905096 -2.1447509381615535 -1.9908540617708406 -1.8360559137274466 -1.687077235652133 -1.5579930979456063 -1.4663136161635255 -1.427989810493489 -1.4333291882951136 -1.4512821884388178 -1.4469302528719634 -1.3905896813805567 -1.264770075453568 -1.0750924429803035 -0.8580840317648865 -0.657838103419594 -0.5010675032265778 -0.40715682309982015 -0.37521006185256967 -0.3803659539227739 -0.3927720061140634 -0.3966587835878303 -0.40147803550772715 -0.42125031137684116 -0.4593380667811475 -0.5187501993750993 -0.6032834500475885 -0.7244661840884011 -0.8801255409207153 -1.0252899994124847 -1.1160030282559146 -1.140495672813691 -1.0975144195828375 -0.9839624516137206 -0.8051325594230205 -0.5696206722994697 -0.29371145400482485; -0.428253149198317 -0.8506003517155213 -1.2599369887744547 -1.644996680826936 -1.9864115088193504 -2.259807770624575 -2.4474056692001906 -2.5415450962324657 -2.5439420018163315 -2.4757488938212147 -2.371805914353879 -2.252021003729209 -2.1197558592592083 -1.9834394475267285 -1.8528707103199948 -1.7326727596840132 -1.6337831323444376 -1.5671552719467563 -1.5396300722959415 -1.5369851813482895 -1.524740983040903 -1.4737584749370276 -1.3656419080770132 -1.1941659559876538 -0.9718083868366371 -0.7224209947780895 -0.48653368758324617 -0.28882020610962544 -0.1536867884358954 -0.0756351432715832 -0.03610970694760201 -0.01882662615226867 -0.02213377175517387 -0.04851970396926798 -0.09783615147320823 -0.1672735105075126 -0.2573080082660215 -0.37729485550499775 -0.5377609240729841 -0.7274866863635447 -0.8971196201367074 -1.0068355222969225 -1.0488610879356906 -1.0228661072661736 -0.9253391534349185 -0.7602259816823357 -0.5380066595460308 -0.277280632060947; -0.37063405909305447 -0.7401606371251148 -1.105665593820287 -1.4587833614176173 -1.7822788508506917 -2.0522480096371916 -2.247214455905097 -2.358487010262313 -2.385953566904408 -2.338837095105905 -2.2439845335954782 -2.130262360832869 -2.011100478192147 -1.8914323352807556 -1.7826555108313722 -1.6900380793337102 -1.6162229995429522 -1.5693601103950465 -1.5456147639447009 -1.5282703995084033 -1.4861341676925761 -1.3933985219835767 -1.2390913571605462 -1.0260545324788592 -0.7699508397731235 -0.4950618610699823 -0.23328789287135435 -0.009360783088707662 0.1560437771343895 0.2674794633375303 0.3350765555745872 0.3597250653797972 0.3419603981452386 0.2916081133579126 0.21557449148369626 0.11847478440743656 -0.004719530748461922 -0.16663469155706973 -0.3707297850375425 -0.5913949825305027 -0.7791811967514779 -0.907206836075715 -0.9711728134676808 -0.9647655767204435 -0.8815588364492838 -0.7271202451475273 -0.516039476415398 -0.2669498931782375; -0.30212879775482626 -0.6097457489875658 -0.9231301207890799 -1.2351196651204919 -1.5315909784688484 -1.790082036311163 -1.9859338939342097 -2.1099923692010427 -2.161381004333075 -2.141611406160183 -2.063519107850434 -1.9537749885114408 -1.8396289517274265 -1.7319148234982147 -1.6406407117500326 -1.5733933843989731 -1.524598168341201 -1.4915648623077615 -1.4682738665154216 -1.437609433459249 -1.371889976244786 -1.2490520098130993 -1.062069427877476 -0.8194920867016942 -0.5376223062914673 -0.24205153048745084 0.040914700415215915 0.28809822761079906 0.48135466182379305 0.6185931791256729 0.6972135643845648 0.7143017592149935 0.6792902004730612 0.6064736037009183 0.5035541703829303 0.3737996352169257 0.21047608289096306 0.005094134853313046 -0.23420405896955981 -0.4744573962596342 -0.6777987800702455 -0.8279886615042419 -0.9168140006559297 -0.9287218280714257 -0.8555286892802706 -0.7081378489335018 -0.5051488726130849 -0.2632692533916421; -0.23279082774641377 -0.4756825422202283 -0.7314672635828188 -0.9947898421653504 -1.2555092394372072 -1.495653861308073 -1.688890411361183 -1.8205516151715602 -1.8888599329052809 -1.893933561845953 -1.8396060338311064 -1.7430443735494154 -1.6324485911179607 -1.532053403375625 -1.4534806934660496 -1.4050640673398613 -1.3812054301299437 -1.3661385485566286 -1.3467211577024283 -1.3066496904755676 -1.225805837970968 -1.0825958905504005 -0.8754634005903037 -0.6123837391125104 -0.311160667676187 0.0031323538611751126 0.3061452918984139 0.5726844442083787 0.7850873718761592 0.9318377542394588 1.00735870789937 1.0149597594694217 0.9670013392716982 0.8747601134353077 0.7455663570891483 0.5812286641168184 0.37718051506133043 0.13431477430609612 -0.13156674529997767 -0.38600526210478364 -0.6032032916431587 -0.772746631011635 -0.8799100056387333 -0.9040250595044049 -0.8381774187536775 -0.6976732763146998 -0.50229013487134 -0.2647393846908645; -0.16974843458277303 -0.35024322276223424 -0.5464955686342424 -0.7570916035953825 -0.976711536723537 -1.1914984866087883 -1.3772011989855135 -1.5122692488843623 -1.5898173951493357 -1.6100602876365788 -1.5770859526369527 -1.502164848948309 -1.4058039691418651 -1.3166230711053626 -1.2515340811011797 -1.2175046340824742 -1.2108182939536547 -1.2139262237438933 -1.2068736495073986 -1.1677011948725915 -1.0809248029555463 -0.9291175897218852 -0.7094920691245382 -0.43371569281955624 -0.11759863705010042 0.21116272367699102 0.5279300493845058 0.8046379575024364 1.0233462718300737 1.1692319573505336 1.2425914779279466 1.2478546416253102 1.1932651932198084 1.0867838848306661 0.9333858530101268 0.733416584402727 0.48900896346635037 0.21257277031436753 -0.07069611985400523 -0.33068757543811195 -0.5544674679326788 -0.7327505085509902 -0.8470603723957457 -0.8772589203984593 -0.8194193813440156 -0.6879883130964102 -0.49944620949186636 -0.26422438170207657; -0.11433804375759643 -0.23779253682220425 -0.37780137456675533 -0.5373194300927848 -0.7146500377499307 -0.8993166538322768 -1.0697827817422605 -1.2023463214383066 -1.2830649093524664 -1.30914661888482 -1.2883342533421056 -1.2341378944858352 -1.163494166770929 -1.0983395872029107 -1.0551752144317195 -1.0394099677989141 -1.0472580770934345 -1.0631574155072387 -1.0687401854100256 -1.0393819092435357 -0.9564953606534063 -0.8069594184592761 -0.5860576554121789 -0.30646471382357227 0.016088853085471616 0.35270427436873797 0.6743247701053942 0.9549661739075904 1.1754520530013897 1.3232797061816897 1.4005889148485453 1.4070702252712441 1.3478851587722542 1.2271038534491319 1.0474014045005529 0.8125486533942168 0.5361218236039405 0.2428886185446837 -0.04125668563090196 -0.29963218743709463 -0.5229200675322451 -0.6986834520930543 -0.8110421846858284 -0.844267419167373 -0.7950422191513 -0.6721424411060323 -0.4885274116594246 -0.2573578592131891; -0.06539087910766747 -0.13909009940239478 -0.23073741846091633 -0.3458226977990579 -0.4832342043145131 -0.6347097182871805 -0.7823853230252683 -0.904666094061788 -0.9837537340250244 -1.0129946134144778 -0.9995233549268465 -0.9600304760359661 -0.913463654862047 -0.8771521495803405 -0.8630947269671286 -0.8714066114557544 -0.899741595364601 -0.9335199651107184 -0.9532103567319051 -0.9389019786150794 -0.8681480487099206 -0.7302652121754598 -0.5196451618919896 -0.2469817837164108 0.07127609740051292 0.4057664418802922 0.725961744436251 1.008217417747306 1.232805144219495 1.3884645034772054 1.4723283345333043 1.4812379389713928 1.4169554315672033 1.2811716011673064 1.0785499114513302 0.8216851839191787 0.5366917823101148 0.24875029856698352 -0.027933690076642495 -0.27977402594403306 -0.49519804004026274 -0.66271877724633 -0.7696617644809274 -0.803376012880796 -0.7596978688722029 -0.6435252236610539 -0.467530703760006 -0.24614627784325122; -0.024371532179278108 -0.05720691746614335 -0.1101688349916364 -0.18962430371702121 -0.2934309671852984 -0.41232168214875187 -0.5326114930908087 -0.6376486662850291 -0.7105990450640833 -0.7420219969377041 -0.7369177759332842 -0.7113485918484461 -0.6833970305665021 -0.667912713176299 -0.6752442714139741 -0.7055510656311605 -0.7548298150129252 -0.8113132143359251 -0.8505275520119482 -0.854662591609313 -0.8031658328063991 -0.6843216157163494 -0.4943913819491758 -0.24000038440438448 0.062074152220728346 0.3840009317927828 0.6964600870709106 0.9769199574997994 1.2054660188195483 1.3680411754291462 1.4561281917630662 1.4651361527275901 1.3939929079993252 1.2471314237596707 1.0357557725509468 0.7817994853676727 0.5122362224181566 0.24079401192744634 -0.021040440594279307 -0.2584251825408146 -0.4613443243319799 -0.6177446259959573 -0.714640633402147 -0.7434941290035335 -0.7023205129616079 -0.5955029486691502 -0.43350239562638804 -0.22875604769933025; 0.0062043452901035315 0.0039434645156203865 -0.020859159212722876 -0.07434061394602935 -0.15155731864164265 -0.24192531418409427 -0.3345836175559376 -0.4190960791265986 -0.48370408743211984 -0.5149928754323948 -0.5157940051816398 -0.5016067756362775 -0.4885140392523632 -0.48745110898308164 -0.5056777403657308 -0.5492820731141917 -0.6124915798001012 -0.6847855427160293 -0.7415419512912723 -0.7610457347559663 -0.7284923421721603 -0.6312212321854288 -0.4678315362723251 -0.24128644820111594 0.03319438237324366 0.32994154999198444 0.6221684115509087 0.8888753338850077 1.1097395456639976 1.2669192008952324 1.3501637895935588 1.3540877428385407 1.2790839920652655 1.1340586106071993 0.9361657424361646 0.7090009699785611 0.46768213526944175 0.22092504125934348 -0.016763596895504898 -0.23330763659913456 -0.41723063355353807 -0.554179711066426 -0.6354443958030412 -0.6575450573051721 -0.6198534435812849 -0.5260290727848006 -0.3829544152371564 -0.20184310740050423; 0.024129936412657697 0.04106057911175079 0.03562101655311009 0.0010862381403915135 -0.05585991605411552 -0.1233606687602675 -0.1916869865937576 -0.2554617600632533 -0.30953189859465247 -0.3409582040419504 -0.34525211182572096 -0.3367150790665039 -0.33119229560695757 -0.33812059549683277 -0.3613112404615344 -0.40772827332095996 -0.4752085597686098 -0.551028135754492 -0.6146229324516952 -0.6426862349631646 -0.6245331559888494 -0.5494949765236797 -0.41568826464320463 -0.22421335085704017 0.011786332962439808 0.2696832254044152 0.5257751694029588 0.760661553030279 0.9544099548185545 1.0901607162574078 1.1596876153879239 1.1587083505380718 1.0903883704188 0.9639456029171009 0.7967796288480435 0.6056494749149218 0.3984409447260795 0.1853943683271586 -0.019119412348239474 -0.20390412512245362 -0.3571811681348817 -0.46909938289998226 -0.53558476889072 -0.5531294671129299 -0.5208112974123512 -0.4404491207939458 -0.31839390947143437 -0.16635512084495377; 0.029338548162996424 0.05362270607660472 0.06002004796805458 0.04121859141322367 0.0016685859027399318 -0.04822267806255905 -0.09947957524885616 -0.1465915518063668 -0.1870701167935873 -0.21381440799638343 -0.22046377933172184 -0.21578199050673286 -0.21371913402098655 -0.2214594282560614 -0.24390212561997804 -0.28372696441765716 -0.34253114866281653 -0.4087954561614747 -0.4657461951915878 -0.49524366845619205 -0.4874964576023287 -0.4359736165490292 -0.3359532231174093 -0.1878965327404137 -0.001140820612491853 0.20493759543302 0.4105506368368982 0.5977858846951042 0.7504117940284658 0.8559940786981891 0.9087792902827847 0.9075266643950091 0.8546167397021036 0.7559713742342399 0.6249675748061795 0.47177829391156223 0.3053457077964453 0.13573977638752965 -0.024543483239894123 -0.16572794891713966 -0.28154190858544936 -0.36876050883787287 -0.42232201282343224 -0.43696129012038726 -0.410391962430444 -0.3443650284691061 -0.24566986899183862 -0.12692170397225147; 0.025115320325267226 0.04630004694576623 0.056023004389688845 0.049363895970867565 0.026183577421624398 -0.0075889081209887166 -0.04524435942880594 -0.08115250793312045 -0.1085447683692626 -0.12403399350174481 -0.12720446760502913 -0.12448144597079032 -0.12444811398350392 -0.13195940517102336 -0.1495448612349563 -0.17853702026594978 -0.2196954710027097 -0.26729087631593385 -0.30784587247719775 -0.33112370655730566 -0.3303532562011928 -0.3014564945026393 -0.23760168438212448 -0.13837295524406223 -0.009828827516078383 0.1337051042255654 0.2777739350283681 0.4075179938747445 0.5125295391304656 0.5846531852042951 0.6219838196207808 0.6228373548789895 0.5878283767630058 0.5207554010805499 0.4285195365673324 0.31945391487670993 0.2009195585279512 0.08281193510883923 -0.024911279156404665 -0.11783862735391935 -0.19501776274817822 -0.2553634785713088 -0.2945510084239049 -0.3061924464741209 -0.2871464702982963 -0.23846598777314168 -0.1676959746099744 -0.08565723046676092; 0.014500242568996125 0.026508981778409536 0.03293417875862423 0.03188476085307077 0.021772010618787172 0.005085253222237055 -0.015489056576164369 -0.037193794733641566 -0.05276102494367326 -0.0575976506595717 -0.05644057850740959 -0.053989906057366706 -0.054295348516364576 -0.059705893555273906 -0.0698252185371563 -0.08630248570899449 -0.10736427316613707 -0.13192388179600423 -0.1524946604108833 -0.16478164226747452 -0.16677437744095003 -0.15499416595379994 -0.1251270201853512 -0.07599402049249834 -0.010712855874596368 0.06313533149667039 0.13744338551261528 0.2039937191926101 0.2577829653593552 0.2950517766180391 0.3155303665364273 0.31695830351155563 0.30017882290640924 0.2665209418919059 0.21835380514996 0.16095344256637575 0.09857021815496979 0.03768184992761848 -0.015783762873213803 -0.06139300072991987 -0.0993201809135985 -0.1301593923494818 -0.15190279782057955 -0.1593945084576129 -0.14942860849753373 -0.12321287401499335 -0.08576424519732467 -0.0435376295533444], hyperparams = 95.53399352881921), (params = [-0.014034011071931418 -0.026388655150283085 -0.03617967367498925 -0.04222073997111765 -0.04302746672411355 -0.038303635266972114 -0.029274322062381137 -0.019364879912667637 -0.011681992731011672 -0.007580885480813641 -0.0070169262595402545 -0.00894200622561169 -0.01114031578771983 -0.011956450271915582 -0.00952638181893044 -0.0025201491642518016 0.010383199463027923 0.030882862591088397 0.060683093765801346 0.09964986338816068 0.145052780012904 0.19217330584041123 0.23635634133375777 0.27396689466264296 0.302643570761916 0.32065042471765426 0.3261855785658783 0.31780359190341634 0.2962126997791445 0.2650398095022218 0.22955350070443975 0.19506933793568831 0.16573863023746624 0.14449494346059308 0.1319552996206237 0.12616337374486444 0.12411529131997555 0.12359305506497874 0.12347589283273243 0.12198289626491382 0.11743333457732655 0.10953949232964325 0.09998642423156967 0.09001533394248491 0.07881749471092002 0.06392148411576468 0.044811081105286525 0.02289792641482786; -0.024290787997462975 -0.04565027461654209 -0.06166823947724305 -0.07044960456150236 -0.07022013736315919 -0.06079337738521508 -0.044636926337433915 -0.02703948451719623 -0.01299852132138902 -0.005371808715704242 -0.0042345427833146215 -0.007746512657897699 -0.01289894255012218 -0.015798614348225645 -0.012571337305559524 -8.33797124140812e-5 0.024663756840446464 0.06514379126299873 0.12379192010949656 0.1999959134135265 0.28852165753558406 0.3805391380084548 0.4671057602594378 0.540781573569316 0.5965590319036425 0.6309330136088808 0.6407769331904408 0.6240979278504297 0.5826991183855568 0.5229257564005372 0.45427739889932206 0.38634110764116036 0.32791473722106645 0.28504737279638975 0.2590093945078264 0.24659661213138986 0.24182611260817247 0.2400328032035485 0.2388312566579378 0.23543444581784093 0.22675055616030035 0.21188703219272323 0.19331292433023417 0.1731531976599372 0.14984732957367033 0.11993966889132722 0.08285242507223008 0.04186037514454396; -0.028112699624948435 -0.052075020459069504 -0.06833914002925055 -0.07471716521538742 -0.07029741509354913 -0.05563719576465451 -0.03389157846940768 -0.010913410003616385 0.007081602695763796 0.016448364204208404 0.01708226401485965 0.011067895908721172 0.0017027437148871274 -0.005220299966852828 -0.0034773004359904 0.012720921601756663 0.04823375993506406 0.10758432574532566 0.19338469172363854 0.3039656257446813 0.43145703329613067 0.5639922682688271 0.6890086632035914 0.7956109928131213 0.8755827401553777 0.9234615714265815 0.9357727511815949 0.9108237769347953 0.8515192195662766 0.7660169582632076 0.6669531284856455 0.5674642418399307 0.48004947928231534 0.4144538716475386 0.3737588915891608 0.3538138206508259 0.3458601826412672 0.3424275120435661 0.33918717666467607 0.33290936164091056 0.3201673382078581 0.29953048965580026 0.272567768784919 0.2415922094898696 0.20547708173639118 0.1615075179795266 0.10964411472281431 0.05463685729122929; -0.023450397634617405 -0.04196883596215748 -0.05153517999545933 -0.05009917940156096 -0.03778712004586566 -0.01606113277743997 0.011529098673852288 0.03826191386891728 0.05742151965248901 0.06580529642491961 0.06350358268634754 0.0520945774380788 0.03607179884624198 0.023360463892380095 0.02275121333864976 0.04190422680490834 0.08731194960795494 0.16422688182857062 0.2751583986952434 0.41633177516957126 0.5775024208155326 0.7446650612269994 0.9025520152301765 1.0373607118298263 1.137771065974696 1.1964788048791108 1.209507919353393 1.1759278184768778 1.0993110798609733 0.989446602792292 0.8608766636540349 0.7306347082203489 0.6146292196412139 0.5256492812756447 0.4690707798212572 0.44055522248120543 0.42913641131614877 0.42368225383294156 0.4178154901857166 0.40855251571793677 0.3922473555886482 0.36598791260540803 0.3306166171445837 0.28891052137806184 0.24097094323100166 0.18534540707094752 0.12369997876459325 0.06097876019104558; -0.008631464663831892 -0.012791098429081396 -0.008589052940687816 0.005524921744114751 0.028868942489469196 0.05940626714626939 0.09274560686921414 0.12186408132930035 0.14048661874910484 0.14530779108800326 0.13651398020966618 0.11645958269238423 0.09176562148506782 0.0725988677075084 0.06984064358912422 0.09214574094352465 0.1468500343348213 0.23961957295202435 0.3726564908303087 0.5402277568793128 0.7296615663336408 0.9247541511747934 1.1088305886974776 1.266201031463146 1.3830557751539732 1.450012323578261 1.4623597639624661 1.4194878089130927 1.325455868665958 1.1912150342305483 1.0337826513913233 0.8736246730123614 0.7296563919511528 0.616966508468958 0.5427031642972712 0.503117110520044 0.48593461825534046 0.4774660830682894 0.46952633059620713 0.45828017661571435 0.43916913780142874 0.40760419290336963 0.3641895568790719 0.31272159140072936 0.25525088196142576 0.19210143266684154 0.12621435607123455 0.06168479689966058; 0.015705243855007447 0.034404715746916316 0.05870241850888874 0.08917473759104223 0.125002155722631 0.164158788169252 0.20211969136914787 0.23248579413017284 0.2492335557905172 0.2487192693505947 0.23127232598694167 0.20080659077166854 0.1666460414242798 0.14165233607372263 0.13778130496782667 0.1640393523286357 0.2273288418398723 0.33391990188713994 0.48572371214517396 0.6753569429192723 0.8876755184079217 1.1043249016826509 1.307823586719044 1.481266689576789 1.6095944328304563 1.6816502034193155 1.6916955272611727 1.6390596972141833 1.528218201497071 1.3708757715473765 1.1867559887546246 0.9991088935722774 0.8289529897392838 0.6922713155951257 0.5975264868016923 0.5427144406043294 0.5158712138983576 0.5025427549027955 0.49255079243401345 0.4801236352165755 0.4592766761362372 0.42386629565087103 0.3739270749008681 0.3146682328146339 0.2506751789177972 0.18450995664650782 0.11911077320198114 0.05759584544059332; 0.04557398384220957 0.09204634900577774 0.13988803263013386 0.1887826145352721 0.2372884697564165 0.28353424830271284 0.324328799795472 0.3544972360970303 0.3678326424140771 0.3610901207427758 0.33485905771978147 0.2945907755419723 0.2522633366228538 0.22296187811800808 0.2199232518089989 0.2520364382024425 0.3249561643916142 0.444881241033406 0.6128426347808357 0.820426320366474 1.0504293282224042 1.282776620163362 1.4988243933538477 1.6815918756309833 1.8158091170306294 1.8893928476753175 1.8957261605877427 1.8335707245993615 1.7077453141139818 1.530688557970751 1.3236937660539365 1.1119767777609104 0.9179953397486295 0.7577677817685077 0.6406390666781091 0.5669292164889796 0.5265655333713928 0.505157913661903 0.4910633529523059 0.4765247649984878 0.4539127594425192 0.41597894558395565 0.36190040061330286 0.2976653069052167 0.22988968484241376 0.16372657984043532 0.10280562449413763 0.04895215657943498; 0.07484384114603457 0.148653589225189 0.21975481858080034 0.2862714530764196 0.3460237485067884 0.3978211967308398 0.43968421648245865 0.4675453039814297 0.4763765080634682 0.4636468584503803 0.43009814868185686 0.38276077529401015 0.3354286524547974 0.30510931288096194 0.3067302599586586 0.3484146646540136 0.4346983429488574 0.5698071965028274 0.7528546356867336 0.9745137829457845 1.2167291415594887 1.4584525783658535 1.6806532403989562 1.8668015770699098 2.002051831393985 2.074104768561419 2.0760893121264425 2.0061041317845296 1.8684147918967529 1.6758676122153937 1.4505856718908094 1.2187781921931786 1.0035978002055932 0.8212621254191952 0.6820370627739428 0.5881880948831739 0.5316182700426539 0.498355826874817 0.4759723175142749 0.45554559629226876 0.4285870479621718 0.3875239997914325 0.3304767552810365 0.26306069442727215 0.19381439475420428 0.13007745505691246 0.07672830046718565 0.03467585471438124; 0.09828392145812113 0.19371277706452172 0.2833502784169491 0.3637880972707748 0.43223132185341756 0.48793411589057795 0.5299109662273853 0.5548749522963778 0.5592350807044626 0.5412333482349148 0.5029699935667894 0.4527201709794768 0.40506540710713385 0.37850793945454364 0.3890669767099752 0.44458476280152615 0.5487313959140383 0.7016059317545013 0.899340250602483 1.1315633310798268 1.3805175402941319 1.6256628225867489 1.848597586406469 2.0335139106070237 2.1667187529786878 2.2364375438249384 2.234855053030686 2.15953963024825 2.0142660446748994 1.8116045282022262 1.5734412306434247 1.3264456330778163 1.0940766389308205 0.8931542801304544 0.7343179877070483 0.6210527368185956 0.5464836086103909 0.4972153728655201 0.46121798965804395 0.4293805804490148 0.3932432252571849 0.3454389408808252 0.28414038606507197 0.21398246657498682 0.1444473459984648 0.08498370459276425 0.041990267391309684 0.015699363107624736; 0.1115774971969246 0.21969542529862882 0.3200854977441248 0.40816334163131696 0.48153948564867943 0.5401220662270495 0.5830293962745211 0.6066775472815727 0.6079395246202334 0.5867376290077385 0.5473594953862727 0.49898236413148167 0.4564126876407012 0.4384199264595107 0.4610383773015343 0.5331510039474672 0.6570857687243119 0.8282472018853623 1.0395702499244424 1.2796022803586726 1.5310244504756683 1.774873374096459 1.994353496253036 2.1751699227681027 2.304649377392803 2.37188460916286 2.3687842411949678 2.291928067685848 2.1442398046284428 1.9378606532773825 1.694143279914365 1.439218666926368 1.1963036982537927 0.9823735189603985 0.8081755686997802 0.6774119233693685 0.5839255052879752 0.5149579028064607 0.4595327674392709 0.4101172520273644 0.35908691911104695 0.2997196744998014 0.23074252055759806 0.156869966887691 0.08756339190600132 0.03364318488528919 0.002509121256916766 -0.005812629807971005; 0.11303030830293584 0.2225346957425563 0.3237261230033369 0.41194536446612656 0.4859823185122372 0.546595319853148 0.5921448873192493 0.6177492162740998 0.6197549781383325 0.5996304519177827 0.5639482279969855 0.5233525909254485 0.49177731263794416 0.48653433550924274 0.5231655646993785 0.6114938521690009 0.7533424764592954 0.9404573508065722 1.1627052922108179 1.4077027886557623 1.6587557250377067 1.898297774143382 2.111003467033249 2.2847315655796483 2.4085743319967503 2.473182357053281 2.470624888010203 2.3962697971503917 2.2519081453867322 2.048926885678063 1.8080701373989898 1.5543435688105993 1.3099051010196572 1.0910242992644423 0.9078268521362161 0.7630513951382687 0.650796854312065 0.5597639915511853 0.4804002015594526 0.40741873037754067 0.3355044960317903 0.25975467452766676 0.17945525356803257 0.09986417640481882 0.030650798714409518 -0.017128153297409934 -0.03626696024546441 -0.027039552215907627; 0.10207831863815943 0.2013227773245372 0.2933148643158156 0.37441002739538276 0.44491262845928425 0.5065330275973337 0.5563445748560539 0.5876835187621079 0.5958042616869483 0.5829746524251141 0.5577254685295681 0.5311706623310047 0.5159074222562936 0.5272447144461525 0.5793230672971502 0.68184706161267 0.8370686820903799 1.0350724044740471 1.2636473912882757 1.5097513103162385 1.7572376549717466 1.9895680736070307 2.192634246735332 2.356051822967625 2.471981246779286 2.5336672901885726 2.533369260338984 2.465268670211767 2.3295806076001595 2.1365434585770635 1.9064006369603963 1.6631035457183545 1.4268709135933648 1.2121689079914486 1.0277007977251744 0.8746835772688532 0.7465992722088836 0.63318770622149 0.5273896243546039 0.42665940999487795 0.328960964090487 0.23235409010082744 0.1375694845718762 0.05029165505553085 -0.019789384736739496 -0.06232437887504704 -0.07055167851399732 -0.04576428043142535; 0.07991265956134679 0.15873920461677385 0.23335000537544426 0.3018155541584023 0.3659129817721526 0.42729859684461 0.48236946672817943 0.5228981620889955 0.542913986704081 0.5444139408275022 0.5363324849111851 0.529159078120422 0.5345151364852869 0.5652350264010649 0.6330902558062599 0.7473389777780692 0.9103491909348239 1.1117656265629698 1.3389651626336 1.579431207689575 1.8184169114189632 2.0399185455889466 2.2306005822661117 2.3817050041888623 2.4887757499158605 2.5477681208447645 2.5514924615148273 2.492928381652901 2.3703660631112258 2.192799040480997 1.9800004214973168 1.7545894846751842 1.534687674999802 1.332590916005247 1.1548355251686493 1.0005451598431836 0.861735397793209 0.7289538754019812 0.5973496302297175 0.46729112491784164 0.3412833762747164 0.2212664048147363 0.11012189656601915 0.013563356481394215 -0.05893308606685812 -0.0979947311688407 -0.09779345181761138 -0.06064128544209742; 0.04913516889724363 0.10011690719811131 0.15214143714148073 0.2050946894274464 0.2613894128876671 0.3221270030786278 0.3831789666132354 0.4352833429221934 0.47176317839837795 0.4938886660944503 0.5088041356349952 0.5251537656773166 0.5530224653840803 0.6030972099495475 0.6852915468889003 0.8076560988507653 0.9716315353991519 1.16796113704141 1.384793557158507 1.6110225605665114 1.8342903534445865 2.0402670274016903 2.216225112970048 2.3549730004837293 2.45412194726578 2.5116391378292557 2.5211350140131987 2.474605052821362 2.368744663414232 2.211266479943032 2.0209097022169487 1.819005297005834 1.6214588959584668 1.4382014123745988 1.2734874717571878 1.1244031510323083 0.9810909388130588 0.8339786650582637 0.6801362551011931 0.5231962963055652 0.37015457271394137 0.22721431714568233 0.09973942299074397 -0.00639089339745544 -0.08265839609290021 -0.1205607124870609 -0.11536297755790378 -0.0702682284418304; 0.01342986251146183 0.03219889139398179 0.05883155554534164 0.09518163222063063 0.14340666706102748 0.20363273673099114 0.2708160132707273 0.3359162134814434 0.39249000326376215 0.44001377666706093 0.48193685177733075 0.5243442779305482 0.574817966719425 0.6421518797717511 0.7349312112404615 0.8601121093546596 1.0185726466114815 1.202169422672149 1.4006494947350563 1.6049990868532602 1.805408524233123 1.9904006736171374 2.148924068611698 2.274973986856015 2.3670311849220376 2.423732556831679 2.4391606316523116 2.4053020175712065 2.318520942522118 2.185112838678374 2.02187971255008 1.8476719558735717 1.6766116137985807 1.5165574273793732 1.3694326171156466 1.2300627524830712 1.0875451961940912 0.9322416778901389 0.7622993169011397 0.5847000776215436 0.410097234860583 0.24818115997843002 0.1065415778259863 -0.008173693402451053 -0.08878515827392279 -0.1278889998613216 -0.12154156457833433 -0.07369714929921871; -0.023642704388521372 -0.03821296001660643 -0.03780375678954247 -0.018614289705751214 0.02128546298207203 0.0808607860490347 0.15442104900641232 0.23370578537964457 0.31218133531381403 0.3871479694203556 0.4582527005020771 0.5276918453802145 0.5999515456920286 0.6818721255272974 0.7808874404139644 0.9034106038494263 1.0503131059071553 1.2150233356472764 1.38976530573057 1.5670156580787054 1.7393689573457285 1.898553232150499 2.0366338689660193 2.1485438858873858 2.2323551388608265 2.285998229971851 2.3045925060857 2.2818223803971978 2.2145601658316934 2.10776262360389 1.9751468279119915 1.8320040780502505 1.6900415110715727 1.555813092799432 1.4291462992737016 1.3029946603890388 1.1659512067602888 1.0091245458262752 0.8317445495281821 0.6425185104133644 0.4547970553330857 0.2806399177945088 0.12902873611623736 0.007274863606535137 -0.07778938755188762 -0.11999739242586759 -0.11628485696499782 -0.07108706523164735; -0.058123464575869206 -0.10412528711022966 -0.12888752741827522 -0.12665027452979358 -0.0954920746795374 -0.037102893149815255 0.04292590961545985 0.13642040555752288 0.23629386083279955 0.33766779769556776 0.4369503157358747 0.5325079166319721 0.6255261890370781 0.719829210743806 0.821572286718124 0.9366977352660455 1.0667616437422083 1.2082933062862573 1.3558497682523958 1.502996437663382 1.6446671932963781 1.7755097291824218 1.8907087842898231 1.9866193315436136 2.0597886988323677 2.106065032194759 2.122489447712937 2.1064511028994155 2.0565649645031607 1.976566941110215 1.8756033470567495 1.7649188219862495 1.653571323720596 1.5464083649397589 1.4419027463751846 1.331923334603138 1.2051852099454954 1.0542262349811276 0.8795861369012145 0.6899258924114644 0.49900857851460423 0.3202202757284574 0.16407107358244102 0.03804876134121233 -0.05120500844811428 -0.09825725361661533 -0.10049800180338059 -0.06258975374775945; -0.0866956545900551 -0.15895425253606815 -0.2052339514809179 -0.21869307500513588 -0.1964657639109214 -0.13993259154328955 -0.0546670069526714 0.050765100711894356 0.1685740989624908 0.29190347830737706 0.4148334366248715 0.5330019153022595 0.6441320192456496 0.7490099149280625 0.8513522115625853 0.956097732987699 1.0660998813851759 1.1814551860239195 1.2996018949824102 1.415753301841716 1.5263576546180386 1.628811906349984 1.7218552873536919 1.8024878232061596 1.8630615157711101 1.8969143665336088 1.9043614677681677 1.888585719461567 1.8512770532357015 1.7944063745697636 1.7228070332166305 1.643268401824381 1.5620701980962226 1.4824215613729483 1.4014804345056433 1.3106695828480401 1.1996405886272201 1.0626434211070386 0.9008538488181176 0.7218978369581098 0.5383762696138968 0.363438643831858 0.20837588710127702 0.08154292207697761 -0.01058132287279285 -0.06315740304426733 -0.07427308460641774 -0.0484321328760205; -0.10642522106424494 -0.1973125686065203 -0.2599224965068324 -0.28619968296155196 -0.27256806269709655 -0.21977411429484142 -0.13295790873872998 -0.020515370947038595 0.10867390850271 0.24639840400928434 0.3856102409829827 0.5201774343824636 0.645349075860631 0.7590079687189715 0.8615760423935042 0.9561657300944071 1.0463311417134393 1.134798430840503 1.2222469497400492 1.307389223821516 1.388518078243587 1.4660330888619912 1.5411223040752418 1.6087455955302497 1.6566013352800437 1.6737022604924499 1.66515737447713 1.6418786519700106 1.6095505043327558 1.5687553898596784 1.520817977009758 1.468727652039406 1.415564771637007 1.362840630577861 1.3067462442668731 1.2384766221005312 1.1490802927058474 1.0341085669413408 0.8946423409380058 0.7362953379324116 0.5693865366857261 0.4067945132970161 0.259687305232291 0.13658564421832708 0.043631294226471516 -0.014639541457036043 -0.03700366148574375 -0.027989619917199216; -0.11614738410770387 -0.2166394747785319 -0.28883192789034423 -0.3243827938304277 -0.3191958996457932 -0.2730243658217942 -0.1903192154527221 -0.07873845818853101 0.052721936482774616 0.19550188415325728 0.34194689980394694 0.4853147609915176 0.6194753193380579 0.7399686008619438 0.844154930253173 0.93222699747818 1.006212897093924 1.0697417181204383 1.1270536244278266 1.1816131398471652 1.2356990425836307 1.292479586207438 1.3531050011148393 1.4104885174949953 1.446149300362507 1.4447651387344225 1.4166188560062976 1.379751840580328 1.3441723085619797 1.3105423752819294 1.2784254545855611 1.2480166846876284 1.2197821886986602 1.192552798674005 1.161489106051488 1.1189271693917846 1.0570107084245692 0.9716296228135605 0.8627418740767665 0.7337775901172148 0.5924275568106651 0.4500450033822662 0.3174968010553876 0.20299040357963494 0.1120204907278758 0.04798932981132153 0.011484760183793397 -0.0013846632471366956; -0.1155533968779139 -0.21673012499182942 -0.29174286339254735 -0.3327494090321013 -0.33556888219617137 -0.29944705835025176 -0.2277229516174333 -0.12645374536302764 -0.0032141568897304405 0.13407030632133313 0.2780854930020629 0.4219698558852605 0.5594657868234687 0.6846154009088586 0.7921366445137025 0.8787675337009334 0.9430400090854759 0.9870761070340446 1.016676268772494 1.0415303497311779 1.0703713068924499 1.1082913499238412 1.1560138243340377 1.2022984534613952 1.2247821198883857 1.2078797744184084 1.1631567484219378 1.1118357363645335 1.0674791062310454 1.0339014430304454 1.0103192055379502 0.9953489357407558 0.9870614427858428 0.9825576814260214 0.9762224829413516 0.9610952375504596 0.9308151672630967 0.8811039732169267 0.8099872244239337 0.7176945527856773 0.6095318119978206 0.494762423916928 0.38301534550979466 0.2810897851069157 0.1936161321066649 0.12301681075783126 0.06946314107965135 0.03038947193362493; -0.10559654843739495 -0.1991033884195851 -0.27067811063935165 -0.3137183403736285 -0.32416910581201225 -0.3012512364285234 -0.2468598814223856 -0.16510619850077551 -0.061267406246405004 0.05889257734356009 0.18987816916164366 0.32585799638968665 0.4608232537547959 0.5880882284042848 0.7003273942426289 0.790310001775579 0.8521356429832863 0.884180461547172 0.8916852794828859 0.8896934986417594 0.8938919946832359 0.913025009023885 0.9450891611173662 0.9762477963660704 0.9847545912702934 0.9579755569515858 0.9050314888013735 0.8443067647372835 0.792356602101816 0.7555575114317368 0.735242709465809 0.7298368300302663 0.7360513749935065 0.750090409803459 0.7662942491516416 0.779049406294064 0.7829539895599086 0.7726710130267083 0.7437963918146445 0.6934984061727371 0.6240722020823809 0.5423425537825153 0.455749442485162 0.3691434723898813 0.2856433374296194 0.2071413918053027 0.1338741429133647 0.06533832536704554; -0.08701279621822641 -0.16558935604895658 -0.22883441957281744 -0.27146189329349263 -0.2895806819007511 -0.2821574189916355 -0.25039420614487323 -0.19624159401903346 -0.12203704285442472 -0.030318977213157586 0.07653868639211578 0.1955015060643679 0.32204525595944195 0.44885377497822876 0.566362792503459 0.6636706564087961 0.7302166027861552 0.7599118600041462 0.7551619095107809 0.7325950354335005 0.7148465535481833 0.7145384207496581 0.7282522465972922 0.740945719925691 0.7349951713822316 0.7020666437851755 0.6474492435218469 0.5847282145434044 0.5291615415318249 0.4902779890099316 0.4713057634391328 0.47129410846642883 0.4871814324494853 0.5157501066179209 0.5522644856456478 0.5919174252278449 0.6298855775953943 0.659869172709299 0.6746505125176687 0.6681909011161374 0.6396029220823473 0.5932384924217986 0.5335526809639863 0.4631235507478342 0.38336667965659577 0.29570788914402996 0.20122618444067272 0.10179271216456814; -0.06099165704329434 -0.11871239179632465 -0.16995053520306508 -0.21070584252612834 -0.23748229012155547 -0.2482501987676693 -0.24323310378467938 -0.22256028196632927 -0.18607131784914077 -0.1323745448660707 -0.05938328430865515 0.03411245675505442 0.14625426563282734 0.2696187718884188 0.39253915360557207 0.5007049726145648 0.5794944798758627 0.6179943411057873 0.614900082607224 0.5839457214433308 0.550954340054011 0.5327347700339901 0.5252894750711161 0.5167682112899064 0.4938753325558395 0.4534715416783032 0.39912032997205105 0.33923395951882657 0.28504209207151837 0.24730219759386662 0.23063243395914473 0.23503933509870206 0.25852133566853863 0.2992297509772005 0.35416116864982866 0.4191126512787915 0.48911568659295607 0.557057955980666 0.6132612296677293 0.6487768683950833 0.6596975494896892 0.6473995573566816 0.6136233906192061 0.5586501895304922 0.4822071842698633 0.38492131329411744 0.26872819512785046 0.13812673104421602; -0.02934973409944576 -0.0613606025262535 -0.09740530941568681 -0.13583106496213934 -0.1727219925070549 -0.204505613356724 -0.22994684105704824 -0.24731051072807533 -0.25354474461103144 -0.24352577976577738 -0.21062467461358383 -0.14910957701478064 -0.05726377476499612 0.05887924816071542 0.18609727163527676 0.3072810577822777 0.40434540786601725 0.4624955147759704 0.47598565613477595 0.4515300530382159 0.4126423612097993 0.3790909069930397 0.3495084081459162 0.3164490025071922 0.27412205506044207 0.2230961332832072 0.16705487430147686 0.11111652188036059 0.0626492699221349 0.030877955094201322 0.020478136823449462 0.03192808546481078 0.06398017356909363 0.11663599969808017 0.18868802483258773 0.27633067868249406 0.3744874127044371 0.47560740692864223 0.5684812716670251 0.641617237631434 0.6880712826230103 0.7058910106225269 0.6947562478011818 0.6531136854153888 0.5788652671476782 0.47154866620992425 0.33388709441378567 0.1730324756047765; 0.006242502512611668 0.004015475048277209 -0.013360955710064747 -0.04800492427887058 -0.09613174820848333 -0.15214180443985523 -0.2117499807726827 -0.2705874181236473 -0.3223404217066063 -0.35830723077572935 -0.36785704425519505 -0.34153454291062024 -0.2743316720875817 -0.1698887660192614 -0.04133097239453163 0.09223768181971251 0.20994298977819134 0.29403483908099476 0.3347257632697024 0.3307536811510281 0.29512660440720956 0.24747060596027223 0.19445235460526075 0.13656393248887258 0.07435295921588787 0.01164983498039822 -0.04703977066034506 -0.09763423854060807 -0.1362369718340537 -0.15647755463453067 -0.15476668306881414 -0.13151377856625077 -0.0876489733063563 -0.021607823711889906 0.06644687451343871 0.17340012672952057 0.29466251138566685 0.4229630304744077 0.5466563933571107 0.6517599357557399 0.7282260534927794 0.7709825859264157 0.7775574314181021 0.7451975162305267 0.670532961833448 0.5522804411639983 0.3938580258130647 0.20492563317688942; 0.045252842351386005 0.07662281022441368 0.08155813743717755 0.05308234987954891 -0.006313476355724356 -0.08855629822728142 -0.1854085826661968 -0.2886968456825083 -0.3879054751933246 -0.4703850345298001 -0.5224842789711616 -0.5320975460647088 -0.49156474711136633 -0.4022623241665269 -0.2766378249668925 -0.1345605863012066 0.0016631462330190612 0.11212749564065909 0.1828710068246697 0.20561502446145444 0.17980237449265368 0.12079316559107345 0.04497206078895706 -0.03577975041884152 -0.1150094569978404 -0.18640737593352721 -0.24424530251049353 -0.28550528981324524 -0.3087115181370314 -0.3114373203405191 -0.2915828508171046 -0.25102815586190225 -0.19106962058666613 -0.11030029087707675 -0.007631712654042407 0.11497623108909398 0.25382572259232417 0.4029332084792947 0.5505567074221416 0.6810317526861955 0.7810154855136646 0.8424841041919704 0.8610389593872676 0.8330172731357257 0.7543883073579251 0.6238793276584561 0.44602403544707375 0.23247899932761926; 0.08732059391024259 0.15527011955804065 0.18504663672164906 0.1648986421520724 0.09545608787376812 -0.013063022218772268 -0.14838221904038634 -0.29711778324007804 -0.44406044444969744 -0.5726942177280894 -0.6662740572549734 -0.7106579247053596 -0.6968998644951135 -0.6251396114531513 -0.5069782056263171 -0.3620531721009975 -0.21349357960808238 -0.0827257572726169 0.013430298350867046 0.06056535217399005 0.04733190801506752 -0.01892668924833233 -0.11297122666915306 -0.21202850696550193 -0.30292300124899796 -0.3760347486416041 -0.42581208413616267 -0.45066070609888115 -0.45234598534766635 -0.43180059806412247 -0.3880755830771211 -0.32478037103071733 -0.24500260254539388 -0.1480147827920743 -0.031958774566364326 0.10257313532727844 0.2535564002784416 0.4164041292885739 0.5796913528738438 0.7269004078334275 0.8424596011353455 0.9158962408603306 0.9410150256990996 0.9127967596335427 0.8271599549163452 0.6839795533594015 0.48901664747416934 0.2549363323174819; 0.13045748296736928 0.23528610417714124 0.290172987533432 0.2792628804153775 0.20180790594250145 0.06937251277658178 -0.1018415059950758 -0.2936974124252507 -0.4862437087145923 -0.6587571321795448 -0.7915064060220514 -0.8686545933742392 -0.8807579291015343 -0.8277776185216061 -0.7209656698813264 -0.5796148201733141 -0.42690623922663934 -0.28546393913113394 -0.1739831063302819 -0.11038310303333497 -0.11245472378292252 -0.18119442509714392 -0.2866088483258475 -0.3973498523036777 -0.492856853705554 -0.5597001174619325 -0.5925138964808013 -0.5926981854511495 -0.5665705983900553 -0.5169032395813348 -0.4437646477481587 -0.35334294113461273 -0.2508690067473203 -0.13660166372278057 -0.008189659222105882 0.1350246406890632 0.2924769368327544 0.4609105497084533 0.6300597439462611 0.7838199551794527 0.9059329431177786 0.9842152809434174 1.0108096520485963 0.9792034197132603 0.8854274948567392 0.7305207309256343 0.5214437936864444 0.2716461952150105; 0.17037971719874448 0.30882791852253977 0.3863961757765715 0.384316272061212 0.3014586794917675 0.15029791576082807 -0.05059466588706768 -0.27965784204702626 -0.5124349780227441 -0.7242234661018089 -0.8921462375627436 -0.9989392331341548 -1.035194152513579 -1.001260722642216 -0.9087453201485545 -0.7767010475614835 -0.6282219840692645 -0.48676760717032946 -0.3723014202913911 -0.30390274795425365 -0.30007671117841284 -0.36513703421386257 -0.4723884161298087 -0.5863875158588425 -0.6788556482235435 -0.7321109403887998 -0.7407094732065272 -0.7110553828640522 -0.6521187455808293 -0.5675635178582146 -0.46061959647065975 -0.3400693328659862 -0.21310285307558072 -0.08112168050933362 0.05821139391516124 0.20655228271913878 0.36456577296606396 0.5302304684601885 0.6952736483986791 0.8452487967410162 0.9647247500470233 1.041054529849083 1.0644953634708916 1.0271496484618265 0.9251930467337001 0.7608593216018553 0.5419906660435097 0.2821064153721189; 0.202143683873592 0.3673463693704605 0.46336852063016865 0.4697601889740718 0.3847525317153151 0.22113681170098307 -0.0012241646687558808 -0.258193626668464 -0.5222506037211812 -0.7654839022579236 -0.9623572019768178 -1.094215481310137 -1.1519982027779345 -1.136667663675764 -1.0598242203950634 -0.9412730016611178 -0.8041625749186625 -0.6719790246575738 -0.5650926205577446 -0.501323858528466 -0.4970953562020966 -0.5549774221877483 -0.6544530787215231 -0.7609634695826116 -0.8430590610572679 -0.8775649072668839 -0.8594035727634612 -0.7986183137972792 -0.705034556530742 -0.5836076209164218 -0.44184502526666997 -0.2909062377770623 -0.13985194356749633 0.008674504478894968 0.15683294723663527 0.3065215106983468 0.45941601968191564 0.6151239934414563 0.7675182855858177 0.9050877415292745 1.014066685190473 1.0818471283171753 1.0976790772411797 1.0527423753279115 0.9433529779211698 0.7726739251916092 0.5488350140389011 0.2851836844327104; 0.2216456139039217 0.40402095174811525 0.5132806913094955 0.5279153204026403 0.4445697010030471 0.2754951642017691 0.040929543781449876 -0.23320623992473938 -0.5171272021651361 -0.7808126507986365 -0.9975929802443729 -1.148206446753217 -1.2233034465718882 -1.2242058004870942 -1.1631520458573208 -1.060520627024888 -0.9395055611619083 -0.8227945542900635 -0.7299190677088698 -0.6763408706460181 -0.6737579262197039 -0.7231386495265997 -0.8072297554046536 -0.8959883743295968 -0.9584648033253553 -0.9724535666545209 -0.9319764064718008 -0.8441364541821057 -0.7185834073894026 -0.5641388667642139 -0.3916160469627751 -0.21423979840251575 -0.04252875511240083 0.11974576370358841 0.27356708739226093 0.4208613009513575 0.5642435533653635 0.7046180328508737 0.8384225483313725 0.9574409528090915 1.0499712190927821 1.104143354845021 1.1086770265255292 1.054650276747549 0.9390391029128098 0.7654297978877025 0.5419073765880951 0.28103732987894725; 0.22745477476191847 0.41581976317900626 0.5319714344309879 0.5539286947596354 0.4760451749875742 0.30859768846857444 0.07167630121810514 -0.20781861926118808 -0.4990294899337488 -0.7710653913294416 -0.9975079840070217 -1.1586628729969675 -1.24510571925522 -1.258754787776584 -1.212106726603656 -1.1259538043757764 -1.0231968071430502 -0.9249726073173791 -0.8485793339131338 -0.8065856918925247 -0.8066123685696508 -0.8470819723184204 -0.9130654987221459 -0.9793606295085995 -1.0193214735596128 -1.0129305552639034 -0.9524417543406707 -0.8417519288991571 -0.6912277976597653 -0.5119065659252982 -0.31682775589778905 -0.12046764422808375 0.06609138991146174 0.2376073343934546 0.3936238451626107 0.5357424543809702 0.6668592938659074 0.7887686073110132 0.9007129898904397 0.9973398108068358 1.0697118639278511 1.107195560655509 1.0987328770324896 1.035864790746552 0.9162385757245647 0.7433126304037557 0.524463200678302 0.27142833836757774; 0.2203037644973669 0.40377730454163224 0.5194552570618747 0.5459351669661325 0.47601688891557886 0.31705803750485956 0.08774480814938655 -0.18543244538399736 -0.47160622226413124 -0.740438434758818 -0.9661651840375809 -1.1292991289297227 -1.2204070002046967 -1.242194157322474 -1.2079315030115785 -1.1377714160221284 -1.0534264118438015 -0.9736053133795752 -0.9130862358676023 -0.8819002424392075 -0.883946282406558 -0.9159353605086342 -0.9643370445916841 -1.0088687571093207 -1.0271657049198786 -1.0015040289090416 -0.9231903054944053 -0.7949258712738624 -0.6269085949096872 -0.43202250422908717 -0.22466008239992585 -0.018503427322269395 0.17538415153586226 0.35033312899479774 0.5043206074609349 0.6384484001820478 0.7556667077872699 0.8581356847098717 0.9470191049450801 1.020278093967003 1.0721333224069258 1.0933272349848122 1.0732953348559935 1.0041158542105912 0.8835361729609211 0.71425163927942 0.5025892182709885 0.2595811004084967; 0.2028533145262063 0.37193828246923993 0.4792626023140036 0.5055451812820311 0.4433131433528985 0.29766529277209663 0.08459024708812057 -0.17178737935183883 -0.44228091151872645 -0.6978538968266512 -0.9135721902728736 -1.0707350549417292 -1.1603484035035228 -1.185933432885676 -1.161366852098412 -1.1058373813799172 -1.0381861227981146 -0.974205538168748 -0.9261738216208271 -0.9021196051222918 -0.9039501547440411 -0.9267406897757389 -0.958750398605788 -0.9831983835516783 -0.9822010560039571 -0.9395643293104966 -0.8472095317694035 -0.7070982230201777 -0.5299089358082534 -0.329709783978959 -0.12043783130594889 0.08539554564514194 0.27714336984346033 0.4476919090937148 0.5942311122479035 0.7172665950892274 0.8192968843803983 0.9028110086101663 0.9705410972592521 1.0234985013914677 1.0583126617081238 1.0669405408653607 1.039435674785483 0.9679416093503147 0.849244975044022 0.6851169046732346 0.48132482561170337 0.2483023706166788; 0.1778863032018917 0.32471606145330284 0.41595997163252846 0.4363357676395469 0.37954083528766064 0.24875426059396247 0.05656439112446305 -0.17587289865538724 -0.42258481763526945 -0.6569745201693734 -0.8553064898202664 -0.9999168632415094 -1.0828172744318005 -1.1084300102087496 -1.0904793327829365 -1.0461579138853727 -0.9912776775656899 -0.938213275093635 -0.8970707774590534 -0.8743991606928606 -0.8712139543100008 -0.8822267812241172 -0.8975437453648893 -0.9033960414800568 -0.8851048007890546 -0.8286890320131193 -0.7271739773976797 -0.582391585662812 -0.4052471792932281 -0.2096651619400849 -0.008911720443509448 0.18586479185223287 0.36518457953777494 0.5226208609504195 0.6550906365835987 0.7631847329175622 0.8491364860091353 0.9158991937250939 0.9674723760996836 1.006289472108276 1.0304421544226123 1.0326833743009731 1.0027719605878935 0.9323127887850857 0.8173654351356878 0.6587636033764351 0.46215996435312034 0.2380928216232039; 0.1462085459941282 0.26435905334128496 0.33384213700914894 0.343274948416827 0.2882146627915417 0.17075088592951015 0.0004208245698019469 -0.20533775178666164 -0.42401671270195623 -0.6318303405136465 -0.8073653119364882 -0.9345622490895555 -1.006890872835039 -1.0289534532859281 -1.0137198022633387 -0.9757601649024776 -0.9273562309030312 -0.878206842502481 -0.8366281202495204 -0.8084987102580484 -0.7942598263202043 -0.7897054145885786 -0.7868333440748141 -0.7748450490455774 -0.7411308247150407 -0.674336030802095 -0.5687859816222814 -0.4270280608625176 -0.25907883594269837 -0.07809847646465519 0.10373573429858123 0.2768309788736019 0.4337482713858587 0.5695864264776318 0.6822693087454356 0.7726012700561042 0.8428109356059209 0.896597104215122 0.9384127529619466 0.9707654104422145 0.9917621599715984 0.9935261617367734 0.9655225125575702 0.8988651109530885 0.7885592572826154 0.6351967246949773 0.4450601001008415 0.2290312561167422; 0.10781277126918912 0.1917900450988825 0.23548867614804156 0.2306040273049936 0.17391270535390427 0.06654241521633235 -0.08391463927169514 -0.2630586540079009 -0.4519963745100899 -0.6304476001961405 -0.7799496405752672 -0.8866084996214569 -0.9455404445471266 -0.9613595172959506 -0.9449689049960711 -0.9078093289309268 -0.8591562697181951 -0.8067737190724573 -0.7575644542641972 -0.7166202767804484 -0.6853135861988278 -0.6611653686798632 -0.6386076654034772 -0.6090158040266136 -0.561645708036414 -0.487381065579035 -0.38260395382266593 -0.25074383816415236 -0.10066009991541652 0.05613512735772913 0.20923606869724268 0.3514512518294915 0.47789112440749726 0.5861814615500982 0.675892334589497 0.7477989856887904 0.8044214360738109 0.8495293221252734 0.8874294231296493 0.9201296802293001 0.944206451943075 0.9502846957234253 0.9275260915721898 0.866508205444975 0.7618555615754937 0.6143726537226016 0.43046589010378145 0.22140180074806293; 0.0638471201362656 0.10944134121123772 0.12419032262949335 0.10206618121480839 0.04048881315896044 -0.05966819724777615 -0.19246745871505797 -0.34627735166197493 -0.5052774588576536 -0.6531509750714616 -0.7749966820852712 -0.8596077670224277 -0.9035808985534717 -0.9110157820424288 -0.8902382770398126 -0.8495124227853476 -0.7956255676914491 -0.7345895421508298 -0.6721834310569095 -0.6131119230101987 -0.5599693407525012 -0.5129180186733426 -0.4693063675072967 -0.4225005465217015 -0.36289961511787316 -0.28345286394363306 -0.1831478127664548 -0.06637428762484 0.05921577714710565 0.18426064530928826 0.3010965315041096 0.405462577102759 0.496220913424733 0.573814926885644 0.6392799594508601 0.6938420385597776 0.7395956134737933 0.7800977078422618 0.819084748761535 0.8572279466870006 0.8886925255784537 0.902653103996497 0.8875385850809493 0.8338526944510704 0.7363386699740113 0.5954593235235649 0.4179578797630348 0.21525906562805702; 0.017732021459292518 0.022780089012495147 0.00635749627306009 -0.03578666299579282 -0.10545801942352735 -0.2012095358625834 -0.31814137362262596 -0.4475178288841624 -0.5773695718774737 -0.6948318621549999 -0.7885863234137298 -0.8505272518249438 -0.8785099529626007 -0.8759300263438445 -0.8481755789746298 -0.8009940212209722 -0.7392384732486424 -0.6671886190230201 -0.5891606352151405 -0.5095222702208049 -0.4326180334663449 -0.3615726423972268 -0.29669345300240363 -0.2329741318056691 -0.16253955337309137 -0.08022988063126178 0.0128376111449204 0.11139240689862975 0.20850794907449513 0.29753465756716885 0.3741371662218683 0.4377729033918916 0.4911392487935943 0.5371940764387354 0.5786179571048464 0.6170789078349974 0.6543991639668215 0.6934993116603643 0.7371900243359636 0.7841249630767476 0.8258953908183246 0.8501280962215517 0.8444279565427344 0.7993489676499815 0.7095655623729744 0.5758011771381696 0.40537325631193283 0.20935256662813218; -0.02599376575962108 -0.06021547377610394 -0.10812185258705577 -0.17184245805042722 -0.25140014076596434 -0.34481174571166384 -0.44805035446307534 -0.5550562460196341 -0.6579144087699079 -0.7471548729280622 -0.8142744259541491 -0.8540084700771762 -0.8654422781586827 -0.8510629887994763 -0.8141917383521338 -0.7584666536941863 -0.6874901467953376 -0.6040406599069165 -0.5107566145507345 -0.4117356509537075 -0.3129137579329242 -0.2200522861151241 -0.1356333409139105 -0.056690842836185744 0.0225674436793088 0.10523210776308614 0.18862320525539258 0.2669859138744998 0.334528787448481 0.3873105736399323 0.42434544495348203 0.44897033513007634 0.46679797248113325 0.4829504964470885 0.5015242029119075 0.5249513918019609 0.5553532669487247 0.5950312119393633 0.645340147444126 0.7024930405778876 0.7559026160625593 0.7916218782747977 0.7963291022269379 0.7600544064352526 0.6778907365981343 0.551832759149799 0.38963144400484057 0.20167090602579843; -0.06354232848614054 -0.13188662978389268 -0.20789618546167798 -0.2913981041447875 -0.3802336200937627 -0.47183908676004754 -0.5631771257701389 -0.6512295285217972 -0.7316164289046942 -0.7973699837395014 -0.841748037050218 -0.8616051975566127 -0.8573681424729013 -0.8306834686047803 -0.7833618832197428 -0.7179047347934329 -0.6371837244701021 -0.5430265861197738 -0.43694725802483997 -0.3229456506050517 -0.2079290912291416 -0.09894084463813402 0.0004747699566588575 0.09113995120862846 0.1764274410510909 0.2568153008626652 0.3287752715847601 0.38669106840745676 0.4264191067849761 0.4463696441888932 0.4487212255069853 0.43980967561738377 0.42722525504119585 0.4174824832141344 0.4155351736026303 0.42511756268562806 0.44916374261745584 0.4896411106024084 0.5462670228375509 0.6128646194471118 0.6772662374667705 0.7243618774886424 0.739584714320664 0.7121832772772947 0.6381383284161647 0.5208613136245995 0.3683898561670284 0.19088093875601533; -0.09186673410651756 -0.18576411553887776 -0.2824643470535005 -0.3797212435316778 -0.47378075957221816 -0.5619038349430722 -0.642773256677776 -0.7158387637713971 -0.7790186555401751 -0.8275355407480168 -0.8553537965841047 -0.8602355579532904 -0.84328143360322 -0.806032267539733 -0.749305365517457 -0.6748878792546916 -0.585576509016556 -0.48323323136995344 -0.36924229367869577 -0.24728546177869962 -0.12433361381464685 -0.007326191698749457 0.1001442068567978 0.19749099397017886 0.285253105918976 0.361502123196581 0.4219195260843133 0.4617897249572007 0.4783082834031757 0.4719424401288722 0.44718000781936423 0.4121995970426155 0.3762690962889829 0.34645375206485063 0.3277379952225017 0.3250444038522347 0.34248865140852136 0.38228058103252943 0.44250072401446683 0.5153073976006746 0.5878945650044952 0.6448579265290664 0.670271984703064 0.6524273574215668 0.5880934816463615 0.4816476427637874 0.3413634133535196 0.17708633206260233; -0.10829792062296503 -0.21617515535651632 -0.32267365051583113 -0.4250459928947455 -0.5186252282024406 -0.6003028358766969 -0.6706323339917971 -0.7313809244559357 -0.7819326962914929 -0.8186345265015907 -0.8363256943102083 -0.8329731811708928 -0.809246977504651 -0.7659346595559903 -0.7032238710503091 -0.6231920867930557 -0.5291283314243905 -0.42361437192683427 -0.30854180104234835 -0.187346929509815 -0.06585131362893575 0.050434909568706034 0.1582552833011294 0.2560148101308302 0.3418297876103583 0.4122766209282999 0.4625224495815834 0.4886870728282325 0.48876581640422906 0.46432256100646807 0.4211370712930539 0.3689197144584182 0.31787239668835093 0.27483831133731906 0.2445061460025195 0.2321194743193458 0.24284037769521352 0.27927300588172044 0.3384811546538257 0.4122129164341026 0.4880388474575446 0.5511442708946661 0.5854580193780301 0.5782406674850602 0.5257660584208536 0.4329334738978876 0.3080613560586686 0.16026146137329178; -0.11050431293071132 -0.21892935796310156 -0.32332050669256074 -0.4208923294382599 -0.5073755908944964 -0.5797760128898035 -0.6392216924589166 -0.6886623927078378 -0.7287854416703397 -0.7569936926690025 -0.7693835264449198 -0.763704625622768 -0.7394705274738961 -0.6961541166832385 -0.633480802203796 -0.5537597499606357 -0.4613019967007645 -0.360090536218734 -0.2526192540190415 -0.1413857201708575 -0.030162543938801214 0.07706084350310442 0.17745145868065246 0.2683336574250441 0.3466710110160733 0.4084318324297653 0.44934181746041096 0.46616004017110746 0.4571323326215302 0.42373853741266193 0.37212216201801435 0.31282268095110605 0.25601942861737 0.2077596358441362 0.17185843391331224 0.15297996136789047 0.15723611196030324 0.1876336726582136 0.24104842578030283 0.3096755086154404 0.38241879757197766 0.44595715529333363 0.48531231317773305 0.48760695697331924 0.44839430229906974 0.3721257103874017 0.26635965739174566 0.13917294033389582; -0.0982077600746684 -0.19335137492052096 -0.2836657622119969 -0.36712988278716263 -0.44011425898579476 -0.5000988285302785 -0.547811654318991 -0.5862316344160607 -0.6166208774165447 -0.6375576567106623 -0.6467077522429461 -0.6419243486489775 -0.6216713775991783 -0.5839101059001298 -0.5279968345517391 -0.45650894007307286 -0.37449890655621093 -0.2867415997306569 -0.19589557735228888 -0.10341282264500151 -0.010843584794521804 0.07927659132769357 0.1643370487444338 0.2407535697844906 0.3053768335902989 0.3546637381974928 0.3859580561328958 0.39658819992968725 0.3848458930370833 0.351511121502841 0.30226778336599675 0.24673926322685552 0.19384088076842731 0.14842985665772576 0.11289168682361482 0.09139949047032275 0.0903053946335686 0.11309680693136301 0.157307341657151 0.2154812084754172 0.278261447847144 0.3348294790679141 0.3725741712783535 0.38035042201959013 0.35388366149530853 0.29628425687595744 0.21340715037434707 0.11192488709005714; -0.07300987575614903 -0.14337227782974224 -0.20964453233886857 -0.27043621002884716 -0.32373217293117384 -0.3677963441726714 -0.4022983553320344 -0.4289494755457806 -0.44924459419619966 -0.46296906420836265 -0.46906823243518786 -0.46605757438748524 -0.45184368887384396 -0.4241186029809009 -0.3818685916778646 -0.3274589895459665 -0.265615211190358 -0.20066830109431003 -0.13482474678809908 -0.06854899020880421 -0.0020176550331597863 0.06348573132893326 0.12544363771590536 0.18066223607437565 0.22633162077705402 0.26023477870785683 0.28100552639713 0.28730025371440004 0.2775195237928518 0.25172301088583604 0.2140197789353967 0.17176751430848516 0.13143994340772905 0.09603834216505742 0.06700711431665443 0.04779062817371439 0.0440270585448345 0.05906204076908872 0.09101482722246299 0.1336966404075609 0.18000022434223753 0.22240637978048639 0.25177065064122944 0.26000731492316864 0.24399189251897435 0.20569572452936408 0.1488687144885712 0.07821454234639476; -0.038824783619592816 -0.07618762629894188 -0.11114989701711074 -0.14308447617693773 -0.17133845784511942 -0.19510675446139705 -0.2136806984565758 -0.22744700989830435 -0.23746713450383647 -0.24397449907615268 -0.24681697299110578 -0.2454867126505959 -0.23816300912714763 -0.22355096893949503 -0.20079857193367617 -0.1713623400597171 -0.13810593180012892 -0.10358718919394262 -0.06908234399600123 -0.034417739388346164 0.0003960046310046239 0.035029738782053135 0.06771709401514844 0.09674627433463212 0.12017399253104369 0.13728507298566803 0.147498590547208 0.15046430860297158 0.14507629684019918 0.1312819597861907 0.11110425407342424 0.088578087916265 0.06685841249873219 0.04746225587789398 0.03107930788087601 0.019573925579973492 0.016477920399578003 0.023958740374770086 0.04075021003238533 0.06339942418665044 0.08797970205955516 0.11074082676515852 0.1267506994266529 0.13167924547533003 0.12404441888933408 0.10491665786248959 0.07616455295733336 0.04010363673504736], hyperparams = 95.57721257230824))), instrument = (lgR = [0.11431658499305342, 0.11433092941919715, 0.06500396522916102, 0.13965143570525512, -0.2422896003185766, 0.24012637103740517, 0.06772150760824902, 0.08038255121153215, -0.08316144688123249, 0.2070293732589647, 0.0963180061210507, 0.12165966683068705, -0.17871643186059671, 0.1532348507400928, -0.5531642845541492, 0.22664931983560155, -0.20626955773816835, 0.037034765562197536, 0.11329849839705346, -0.566651424860414, 0.029715974517968348, 0.1400966488628471, 0.2180839143084571, -0.669231800248953, 0.11447685873975441, 0.11581614116852304, 0.16403086890565205, -0.7658722168708568, 0.16250980058091907, 0.1389698770721194, 0.17291897279462934, -0.8261965329026033, 0.16760499895869607, 0.12712882377200022, 0.18678669036492537, -0.026374072208930885, -0.9398337703539522, 0.22481446363777668, 0.13764340703157518, 0.11316217193339967, -0.022739371230079426, -0.839420750195644, 0.22226489198386307, 0.11685306882339609, 0.18463364151243758, -0.018766276830507113, -0.6733816638767518, 0.24326172130154816, 0.11918189555461342, 0.1453167325704898, -0.024446233803317497, 0.09295281386604873, -0.8000037031200028, 0.23580222449072838, 0.09368529820203851, 0.11763969026006353, -0.00618817762048229, 0.13082628614395378, -0.8261957523470355, 0.22941871420191975, -0.003738579586606355, 0.08009210456783628, -0.008438080849801051, 0.0037799104396504996, 0.1890221786030645, -0.8968514729821023, 0.35978732111717077, 0.05812881768638267, 0.06282895118175788, 0.0683350625590418, 0.012248510106454584, 0.24996168931481616, -0.9000083389395502, 0.03965785970222048, 0.08496430320459111, 0.0831366681709643, 0.02284938482046194, 0.2150806107999883, -0.9484356933706097, 0.058749077931505585, 0.06512375914899543, 0.18495948771323323, 0.027889865066204642, 0.22111885476940593, -0.9381088602972141, 0.08767084830046248, 0.11473860378144145, 0.03056689488575584, 0.19905956984112658, -1.0941665373862355, 0.03226534205927737, 0.07617356996005692, 0.05165049256953663, 0.18027096945531848, -1.0344688393258454, 0.04191055460726883, 0.06864305479432306, 0.12508834439217142, 0.050481040058011156, 0.16472390974751294, -1.2463570105738007, 0.054206807782515784, 0.04165243091040354, 0.12167627334298281, 0.0911782115099837, 0.2093382040467673, -1.1737406743173295, 0.059650014587516356, 0.02946838148005925, 0.07310870532570979, 0.11506853702947191, 0.21876569560770184, -0.9532151537747683, 0.042767310929131656, 0.021691974473682155, 0.0529823103282846, 0.10670048567194627, 0.19201913172485288, -0.9691978934245993, 0.050699855588565663, 0.02682738796378764, 0.047923774525492395, 0.07709600137196873, 0.17448714627136233, -1.0511313090957894, 0.04597620244674346], lgrat = [0.08589801298049121, -0.06910406025467455, 0.0674460211052576, 0.03663159381548992, -0.014072039911932439, -0.048659142875211725, 0.05438932359481428, 0.0783041020828383, 0.015278407849203186, -0.01897524233705677, 0.05303315039842076, 0.0002259001168588567, 0.027836053239900634, -0.028893434361570085, -0.0749850902758356, -0.1075536896846746, 0.0986828882120111, 0.05733952986144613, 0.04624842907256471, 0.12715017731296419, 0.0036932535256885123, 0.026941439385354725, -0.02480341193133555, 0.07048124647270168, -0.007377968824481086, -0.006273417065569522, -0.011152839769953052, 0.13135025912473797, 0.010365160955375917, 0.00808170877750347, 0.04130938817675873, 0.10627948944018498, -0.01579058498531661, 0.014726120535631554, -0.08286445708128844, 0.02128770001914456, 0.1202932607553076, 0.004596286635108509, 0.023878018550042793, -0.06260779586968286, -0.005824910517272144, 0.11418394871085923, -0.014139110389138981, 0.003853871868754215, -0.009295103919326694, 0.012821057395293862, 0.047049878407575, 0.010364101978769816, -0.015789001608338026, -0.004705240218726172, 0.02914392352507765, 3.0954440558515395e-6, 0.05481812257846731, 0.029529546866377047, -0.0065774736892530725, -0.12062604940325253, 0.02332182999911364, 3.4392196555456585e-6, 0.03965522634381669, 0.03734499672122581, -0.09755019503127911, -0.006214886104551827, 0.025758668007918158, 0.02108005461523569, 2.238376892818206e-6, 0.06983199892275094, 0.026151990689769596, -0.09788962575311976, -0.009179556304185665, -0.06623508306505338, 0.012538289911879332, 7.850775284658347e-6, 0.05997882426337129, 0.05172756971260086, -0.054665269173022564, -0.03749788642577309, 0.023450951981442935, 4.811275561712567e-6, 0.07287657064666969, -0.015802315240066842, -0.005705044266655422, -0.026135698784999172, 0.012379194796539017, 4.457893758880863e-8, 0.049311599200385026, 0.012021432646342707, 0.05348089685018997, -0.02260834354031115, -3.5348520800419667e-6, 0.05667395537742617, -0.04360563272721349, -0.06788637679200953, 0.05143038814372461, -2.0676683141617805e-5, 0.0846074680303427, 0.01686540196774415, -0.024261171882996743, -0.0383918615921022, 0.01590556084197583, 6.684036716111854e-6, 0.12544442958274638, -0.021580481756540357, -0.019212803899479852, -0.03907541645753164, 0.009113495315119707, 5.464307334594716e-6, 0.11553681362322497, -0.015673994259293188, -0.004561081600836008, -0.005809598265024069, -0.020072531924403975, -1.7163269038921932e-6, 0.08856599004322722, 0.014631160639729598, -0.017213475821519213, -0.04603775280378557, 0.017641127946134486, -1.1547422813858515e-5, 0.052709140090317005, 0.012140398908537305, -0.0033455859742245065, -0.011221588542027974, 0.03423491359012426, -5.763650854440834e-6, 0.09344042278927166, -0.009514527573372277], gpR = [0.0, -3.0238741809519034, 0.0, -2.285175937252046, 0.09784828375973634, 3.0084013183043576, 0.0, -2.2869355665403273, 0.17309899626811576, 2.7626444098042766, 0.0, -2.2791321620458866, 0.2330730611061003, 2.5587654182769857, 0.0, -2.398633413571032, 0.30618645454994253, 2.310804260474925, 0.0, 0.8208547533388464, -1.769931535144474, 0.0, -2.462999666397879, 0.3827833479939141, 1.9495175929393387, 0.0, -2.431908780661881, 0.413837725298815, 1.7813414066740194, 0.0, -2.497784352416476, 0.42720453510833273, 1.63668307292184, 0.0, -2.493527351697694, 0.08921945205292577, 0.43792747918560004, 1.4869902936209307, 0.0, -2.4721014471551115, -0.037650243219623535, 0.37069307190813, 1.3574231063989093, 0.0, -2.5142673160249833, -0.1815704254539841, 0.24357065580406667, 1.2298757160633544, 0.0, -2.437786445764712, -0.3775906409194788, -1.4528916213721959, 0.1614995816788506, 1.077896402125774, 0.0, -2.5081553620189623, -0.5904865945608664, -1.174191551411501, 0.027670402333640324, 0.8625415531292495, -2.4538074178843834, 0.0, -2.458413017100168, -0.7634337177848343, -0.9307379493139162, -0.1821740528175403, 0.7093157759672519, -2.537116019031691, 0.0, -2.418689599137659, -0.8848621502774796, -0.7130168403005369, -0.381740010952849, 0.5053168752592808, -2.6515628248205023, 0.0, -1.137993429209393, -0.5020727673298055, -0.7252326028725359, -2.819964154934981, 0.0, -2.2184013618289926, -1.4626767131428426, -0.2929293087437911, -1.497960940531256, 0.0, -2.1663846326233243, -1.6722193031277597, -0.1494237054093531, -2.2132454367443244, -2.835958709480634, 0.0, -1.939494763609679, -0.0377791158212681, -2.664671110659403, -2.9053153052826324, 0.0, -2.083997769202213, -2.271489125167288, 0.04933322681788774, -3.0002677733237855, -3.008743158008374, 0.0, -2.0594448016046236, -2.5116835311514736, 0.12811822519965768, 2.927547655868542, -2.9994842101023536, 0.0, -2.0225350005232015, -2.79502730950202, 0.15233565263256926, 2.727349274121474, -3.0287617228493082, 0.0, -1.9192638645183995, -3.0582391016240487, 0.15338874221112841, 2.545752653163966, -2.9415654263894506, 0.0, -1.8815964546780637, -3.121810615577965, 0.172372601839953, 2.373327909271154, -2.9483656523883104], gprat = [0.0, 0.002338772878222198, 0.0, -0.012643499273208307, -0.024825807398199153, 0.014860221742463597, 0.0, -0.028967523427919202, 0.0023458804640759923, 0.03200838318766478, 0.0, -0.04082467437600379, 0.007829746922130596, 0.010219701544065372, 0.0, -0.006214235838459754, 0.018137656503235657, 0.0615753403618756, -0.0275324468927669, 0.005316640617532546, -0.0345726373477434, 0.0, 0.012439189812243569, 0.02180814399688744, 0.022690461218427528, 0.0, -0.07303247464422725, 0.019814232178714232, 0.011000151501858338, 0.0, -0.014727860013569575, 0.009902511035333173, -0.0009179642983818432, 0.0, 0.002750584069302363, 0.05264316255395253, -0.003017745258990216, -0.010421057461054173, 0.0, 0.018393468480409764, 0.021571053625222207, 0.00803607962216928, -0.01268321141149967, 0.0, 0.024240078496864152, -0.008145522093906298, 0.061045155773618624, -0.01216367790922315, 0.0, -0.0062963754772106155, 0.02350783870055027, 1.8818891560713184e-5, 0.07525782716093458, -0.004871432966305738, 0.0, 0.054476494626704175, 0.040082589624510306, 2.1717119514599605e-5, 0.06514064667232244, 0.013371502909690705, 0.10278852900906699, 0.0, 0.05094572596242062, 0.03442454786944774, -2.2227853515778842e-5, 0.08981310403266586, -0.005627178143827742, 0.013522567652989299, 0.0, -0.059026053806855876, -0.03171817699235304, -3.318452056432388e-6, 0.06944562776545347, -0.00042414677345861126, -0.013248760117297205, 0.0, 0.017048110794358598, -8.425536647168533e-6, 0.044409862195208046, 0.05129919113546153, 0.0, 0.05247752778239684, 0.0732751938198159, -1.4363687526570273e-5, 0.005260380916713155, 0.0, 0.009896945213752957, 0.05571146279787901, -1.8241816315336915e-5, 0.06148143399147592, -0.10160923370584933, 0.0, 0.07135276138890288, 1.0398057890169135e-5, 0.04394979502069207, -0.08186259086571318, 0.0, -0.04128426691025202, 0.12234795882579218, -4.649288837551237e-6, 0.031246184378507673, -0.027800126691842147, 0.0, 0.05905953465615085, 0.054892598871760755, -3.871856102593793e-6, 0.03967621960502338, -0.05501678021648523, 0.0, -0.013440035435960684, 0.10224209218747905, -6.494973261805134e-6, 0.017561611741470078, -0.0316844033233769, 0.0, -0.015762479722596565, 0.15028809529816595, -7.595803870117613e-5, 0.0013453510333135124, -0.09956730737510011, 0.0, 0.024869707373606262, 0.0022858041940612512, -1.3310752813011632e-5, 0.006863364839293745, -0.04915941294811505], dRx = [-0.00377079752724891, -0.032168188332715154, 0.022354629417609774, 0.001550811808434439, 0.03937829381434981, -0.12165434566174409, -0.03469547614878778], dRy = [-0.01852636577829295, 0.04952588419975482, 0.09553703177514056, -0.04853945338563308, 0.06209253149182892, 0.04353645597955429, 0.01771975954873608], dLx = [0.0036638472959248185, 0.04043105817204525, -0.022848742165857295, 0.0007040198353262866, -0.003988110066690277, 0.1390477939757669, 0.0028157154631364453], dLy = [-0.02120783053740049, 0.038321079118419824, 0.0935361552046403, 0.00017788755432369805, 0.02226125767580544, -0.0007414240056981892, 0.09418125214449846])), retcode: MaxIters
u: [1.4254459777706436, -1.0724881875883001, -2.150936114296393, -4.457902373251043, 0.03553909463869862, 0.08172653375645228, 0.14563746920024032, 0.1993520154910808, 0.22193598607086046, 0.22212251757267232, 0.20600062732576294, 0.18118550567854497, 0.148773424995565, 0.11311529513223224, 0.08057388493148786, 0.055648502261018355, 0.042136718501116326, 0.03521809688188546, 0.03536705769104066, 0.04357247746763321, 0.061584657983243196, 0.08652203597776917, 0.1194899175615265, 0.1544658053335399, 0.18881483015182324, 0.21654016769255663, 0.23638748913385876, 0.24704338317934385, 0.24952061570775153, 0.24265472015264283, 0.22139683209114305, 0.18926646120367582, 0.14600193665051175, 0.09940278662110463, 0.06084162629924418, 0.03264215478660132, 0.0069690700114491445, -0.022692469628183692, -0.05026670101287423, -0.06792693639497564, -0.07294117911009869, -0.07068257179222853, -0.06714651247084807, -0.06405535875576839, -0.05665872855312371, -0.04232019048663082, -0.023671882457811034, -0.005275221356462344, 0.007754871139223551, 0.013385179330942798, 0.012099730496740256, 0.006418837211003674, 0.08950466634992969, 0.18951223345248894, 0.29021301218417717, 0.37110302913612025, 0.4146891322327484, 0.4228946786882029, 0.4059676972442397, 0.37076379514870544, 0.3250216014230663, 0.26897771125761577, 0.21241073812623515, 0.16458180767916145, 0.13170482934687439, 0.11040165651065806, 0.10521303425813223, 0.11825434390232346, 0.15225194349953555, 0.20349841261737245, 0.2708111493663366, 0.3429732078645265, 0.4124129480891076, 0.4674325274008622, 0.5021593645743072, 0.514069345338739, 0.5065170114211244, 0.4843381893272036, 0.44451586888726446, 0.38731755866814344, 0.31477325976966647, 0.23083730350449772, 0.14614953272930573, 0.06847031943021066, 0.0017469186902042157, -0.05820815075980173, -0.10798347569747412, -0.13867249238223947, -0.14718891278616697, -0.1414645856178161, -0.1306732535774157, -0.11899822835585229, -0.10316333390191534, -0.07794730289546663, -0.045664741455103554, -0.012828417177711339, 0.012580458149979643, 0.02506127863368746, 0.024259542508540007, 0.013944646521467199, 0.15570650973479433, 0.30650482324763373, 0.42976986094079206, 0.5213770005490961, 0.5809426855967136, 0.6097231384082429, 0.6099392720958251, 0.5849269501504493, 0.5398989275074108, 0.4737249308043074, 0.4024636226260616, 0.3375886302127666, 0.28280712503783983, 0.24136238752355405, 0.22394004790866198, 0.23635498876775562, 0.281252602547891, 0.35684453533153093, 0.45372118855873084, 0.5597690391566964, 0.6597144056308752, 0.740888985939547, 0.7894287667713998, 0.801975730632618, 0.7794790725281636, 0.733884796694455, 0.6735429981459226, 0.5953904229255239, 0.5004166178951686, 0.38758622141215443, 0.2603751203791135, 0.12868307624754544, 0.008614959394102265, -0.08876745290539219, -0.1630981325864053, -0.21088537233867885, -0.22795424325744917, -0.21813007865538384, -0.19395267284468984, -0.16509942280013798, -0.13565543845977554, -0.10156970488572813, -0.061053210924367406, -0.01941603599602659, 0.014649693813146788, 0.03349955043265847, 0.03590823537131754, 0.023321388935765, 0.21082934600740083, 0.3993625621571946, 0.5572324550874692, 0.6726983874967841, 0.7514800813673023, 0.8079021444584451, 0.8334273182573392, 0.8266444590396065, 0.7814972926709071, 0.7131123252842365, 0.6385718933016885, 0.5625011255243989, 0.4849639367349465, 0.42146871946301306, 0.38805516897382797, 0.3987224349024902, 0.4529110099602206, 0.5489249043706567, 0.6661629864074213, 0.7914334711490719, 0.9079965210170963, 1.0026308551826402, 1.0630172525490127, 1.0827582876550814, 1.0564630445871876, 0.9909982993360698, 0.9045578106458919, 0.8036740688836899, 0.6850436182400331, 0.5459900380297067, 0.3864415171547344, 0.21750768272651322, 0.052350551909647866, -0.08767967048285309, -0.19503642642967395, -0.26896935820847545, -0.3051342064960542, -0.2991175599990121, -0.26197921537210034, -0.21104291243119624, -0.15976928212531913, -0.11225221021490775, -0.06474001805092731, -0.018437616510334227, 0.01975395150102357, 0.04192981050363827, 0.04564649918042525, 0.030697551693867564, 0.2549598833496592, 0.472819483346712, 0.6690245993878728, 0.8275722652579383, 0.9429195714698883, 1.0245878219824252, 1.0708452574966316, 1.0770893198233815, 1.0380685370913556, 0.9814794565817937, 0.9085480882960302, 0.81764780624896, 0.71635006137296, 0.6341318766759949, 0.5936199697506679, 0.6098137548797519, 0.6808981318198343, 0.7937319089443642, 0.9216711635002307, 1.0471846274243972, 1.1581652988043465, 1.2435247330593469, 1.3008458728730887, 1.322697324762586, 1.301400628181507, 1.2291168612891563, 1.119189919145185, 0.9912138736658356, 0.8498978736897017, 0.6901959315734296, 0.508580942329532, 0.31501559991970374, 0.1225732266356237, -0.05220680729612318, -0.1937113490261806, -0.2965642753809715, -0.3563510047040707, -0.3656661405673858, -0.3269961086800912, -0.2592656412264723, -0.1836803070002687, -0.11553267090006057, -0.057363852583430734, -0.0076020963769409255, 0.032555896948782366, 0.055946102907565, 0.05504769914885726, 0.0330992753522564, 0.3013113277274086, 0.5522306194536284, 0.7700897763570983, 0.968540375865319, 1.1319459328094177, 1.2402495428413243, 1.3057415058566815, 1.3276861101936448, 1.3129113516888091, 1.2706870986967562, 1.1890397007792894, 1.076313067137409, 0.9579440742134838, 0.8708798348476273, 0.839815019578356, 0.8721613096110843, 0.964801705928697, 1.0866225022905582, 1.2103523315706617, 1.319641317175763, 1.4026063407913145, 1.4630351718836483, 1.5002861008475672, 1.509973866049411, 1.4882999771991292, 1.419575873266977, 1.3022593469249677, 1.153260190696951, 0.991285567871866, 0.8173925159873981, 0.6248566320971066, 0.4145989067970394, 0.20292127054257206, 0.004759696768124403, -0.16291672699716597, -0.29042990198291085, -0.3715616341132704, -0.39947953728865043, -0.3714341813307157, -0.3003976244348674, -0.20851013635252388, -0.11880383334763371, -0.04490137549409457, 0.010901688945314934, 0.05083053486407052, 0.0727215238538779, 0.06685675051914082, 0.03703806749910914, 0.33725526525677735, 0.6281590377402166, 0.8663427451812693, 1.0886074013356826, 1.2913061545902975, 1.440501327309643, 1.5376637369171613, 1.586799633435564, 1.5974791101222547, 1.5518120593311877, 1.4495545903911384, 1.3186254599234135, 1.1965773642837396, 1.1197276291907627, 1.1080086930951925, 1.1653141596880696, 1.273627708946224, 1.3911942811168763, 1.4929253594261835, 1.5665433414230112, 1.611937167301178, 1.6425497748465467, 1.657521552971628, 1.6522422203490694, 1.623961525894946, 1.5618447546432694, 1.4513584093826526, 1.300071950392699, 1.1261673199953983, 0.942584276799303, 0.744801432595886, 0.5284551731568826, 0.3030844004837173, 0.08647652887679029, -0.10340986795826022, -0.2527295050756548, -0.3539509325048079, -0.39997418404684976, -0.38684952243772736, -0.32400371677716183, -0.22900569154963088, -0.12465962199384972, -0.03367696377493052, 0.03289453064049096, 0.07228106989260591, 0.08764707694852351, 0.07886609039864996, 0.046000898969244475, 0.3528893325847083, 0.6824427640477906, 0.950355624544679, 1.1900204127168417, 1.427335767351905, 1.6250194725671596, 1.7580396411528765, 1.831888374646546, 1.844486427275985, 1.7776422259210736, 1.658183333462764, 1.5210314469268114, 1.40453716420308, 1.3465182477675002, 1.3636047542519647, 1.4519024812808956, 1.5697871002003236, 1.6716532931855028, 1.7336005548826678, 1.7574982836197863, 1.7683761362813044, 1.7787738007886387, 1.7851620041475174, 1.7781509908243511, 1.7478027095424478, 1.6866889772260563, 1.5805071084561106, 1.4311890222041497, 1.2558532265583051, 1.0699895687157417, 0.8736679326571598, 0.6611327940158903, 0.4340918046585976, 0.20765486701401137, -0.001015613976790726, -0.1755760499327906, -0.30214040940817605, -0.3715621582611026, -0.3769998073330576, -0.3262060528442896, -0.23776647611087648, -0.13000662314042638, -0.02692652168508766, 0.051940481987754514, 0.09544386271021474, 0.10462954901897313, 0.08959184087953033, 0.05340444328287385, 0.35774841292904547, 0.7131196912295531, 1.0078967516847286, 1.2737186703140333, 1.5432022224603856, 1.7708664363041222, 1.9275846363058535, 2.0108076282250273, 2.010045389755696, 1.9312778368318202, 1.8122144168181693, 1.676636328888798, 1.5741636116124431, 1.5435339340164203, 1.5987442984361335, 1.715773699410335, 1.8398169963668067, 1.9145040065769017, 1.9189954590353908, 1.8885915564140057, 1.8678325439119243, 1.878009274990728, 1.9030857354877617, 1.9160403328863345, 1.8892565075459844, 1.8150991133468866, 1.6943007098155531, 1.534732226087687, 1.3586163669715319, 1.1794656197958018, 0.9977403164846503, 0.8031722935073518, 0.5904072624889782, 0.3667012595164964, 0.15004392414281548, -0.04626459749941079, -0.2048781449929159, -0.3072336406353409, -0.3410476113524298, -0.30763439622837724, -0.22864486261293382, -0.1265579253723702, -0.022004265961203685, 0.06380009745862221, 0.11424635863426713, 0.12354508482994078, 0.10198718024638502, 0.05908631017111973, 0.3538384004990176, 0.7104485237377456, 1.0340553541904536, 1.3351157460761782, 1.6131631231277732, 1.8496362824298334, 2.027420941658059, 2.120844122497722, 2.122599473072925, 2.0548302411722386, 1.9408093363393666, 1.811377585800723, 1.7298473039658673, 1.7279529111080947, 1.812835453689529, 1.9481075207045233, 2.0737261096538515, 2.1128458434642354, 2.059679316658108, 1.974574270911518, 1.9219740529351006, 1.9362554968752594, 1.9997509773844722, 2.0522198037594954, 2.0290467330321627, 1.9272771574169503, 1.7671495298478657, 1.5855969365765632, 1.409393522108039, 1.2503298287480482, 1.1004310943624607, 0.9412247281819972, 0.7609967070850694, 0.5543627382069164, 0.33761678381292515, 0.12827832161370425, -0.059194068704851284, -0.20014686581506483, -0.27109970459943716, -0.266583218659011, -0.2030031291460758, -0.10881689189385615, -0.010520553217936726, 0.07210373007363705, 0.12471327648634432, 0.13756050846810108, 0.11425738337682316, 0.06534035758953363, 0.33301854516004836, 0.6783543182964837, 1.0305827602164084, 1.354574789900466, 1.6274112109558678, 1.876889482165084, 2.0837693355394946, 2.2003465298416893, 2.2198882611314112, 2.1613800424905354, 2.0492356457054557, 1.9298616835865796, 1.8636834338992174, 1.8761590239093189, 1.966517453622129, 2.108792900108948, 2.2251042739228333, 2.231470821464097, 2.141662301005601, 2.0192828791428172, 1.9412149571382136, 1.9522895199893386, 2.0447801369056067, 2.1334615461223136, 2.120114025498929, 1.988594174736914, 1.7876288247328518, 1.579912420620133, 1.410350652810399, 1.286972242276645, 1.1861738329416769, 1.0767864924915176, 0.9393074556883054, 0.7605442494883173, 0.5485002081307363, 0.32642478027500055, 0.11643990267313423, -0.0591648474394087, -0.16917029760366858, -0.19941437910465604, -0.16292262194002868, -0.08276355481639619, 0.008570512148237794, 0.08324114499017776, 0.13077267189819514, 0.14458174388250344, 0.12118681831565649, 0.06845811270205819, 0.2966714622210386, 0.6307100965577241, 0.9979965947374274, 1.326359717104971, 1.601689132020246, 1.8738977862620376, 2.1084085196852245, 2.249484503361409, 2.2860271946439426, 2.239923432094222, 2.13332566992972, 2.0194609908242547, 1.9587165463584273, 1.9663214534701035, 2.047903049087762, 2.1827426679135544, 2.2763312150254436, 2.2572084657590303, 2.151374633566411, 2.0188780599931646, 1.930491099020228, 1.932311815329546, 2.027664688980714, 2.13180333920742, 2.124552905969939, 1.9755614883713386, 1.760732749773801, 1.5440167678568446, 1.3900603516992616, 1.3135226109547116, 1.2738062583435799, 1.2235062015227776, 1.1305478904812896, 0.9793423159074198, 0.7721489705250264, 0.5330732093796267, 0.29598656603056267, 0.09242452782560288, -0.05197374692448117, -0.11433308013071343, -0.10681759756069374, -0.05078755478760659, 0.029372940256557217, 0.09779731312461896, 0.13755828627110162, 0.14698309866571826, 0.12220790254168873, 0.06821135042958185, 0.25801994409005397, 0.5735147157554294, 0.9376127443830533, 1.2634107162916504, 1.5476177432309126, 1.8383055594515532, 2.0956967907204196, 2.265348954310976, 2.3352528768065755, 2.3099464433718677, 2.206360195891259, 2.102911400930668, 2.041762081860734, 2.0378204901918084, 2.1071704535038354, 2.2162227345899557, 2.2759817084514045, 2.2306146199368637, 2.119431048768074, 1.9951575843563965, 1.9003011174755942, 1.8767614664304817, 1.9459895914407896, 2.0421358087221892, 2.0223391455654984, 1.8705107066342217, 1.6671405483978372, 1.4734609592985417, 1.3530868209745706, 1.328430037798966, 1.3557299444348874, 1.3723345593888707, 1.3271345989472183, 1.1985338079422432, 0.9914940229796632, 0.7344336716018958, 0.4635879937862919, 0.2291566716976244, 0.05864393239447034, -0.030049467869431454, -0.04388596778550277, -0.010660828719576906, 0.05257609989895375, 0.11468741424401949, 0.148121906115095, 0.1496994433155745, 0.11980666792213504, 0.06476794996605448, 0.2238518149738415, 0.515954275934077, 0.8595525857475138, 1.1752194246309295, 1.469942685711735, 1.7811255658145786, 2.0701273423567432, 2.287391298499729, 2.4013548940279352, 2.3996860476305737, 2.32395928073423, 2.240081278879328, 2.17331456221121, 2.154595693025732, 2.2026619243047114, 2.259369791252463, 2.2500420177757077, 2.164060070540341, 2.053283918232822, 1.9359358214290867, 1.8346547599756857, 1.7859132828814357, 1.817097006765222, 1.876993495675108, 1.8416313672859057, 1.7017565442479021, 1.517065372269573, 1.3605636133421932, 1.2877853791584937, 1.3132639947603981, 1.4043217793980927, 1.486531388571855, 1.500526089963915, 1.3993581746633974, 1.1879912135085193, 0.9077676206211912, 0.6037486958576314, 0.3329728697385217, 0.1390738181736997, 0.03425435518987094, 0.010096432724820604, 0.032345282822869914, 0.08036714518198473, 0.13425321342268978, 0.1629545746264063, 0.15555918687890222, 0.11712287484906886, 0.060104176499184064, 0.19742085642630006, 0.45944315464860686, 0.77076750858554, 1.0762001262388394, 1.3922251191262118, 1.7404197974370892, 2.081909976048892, 2.354863813199643, 2.5111271957443244, 2.5594161420508263, 2.525766549321755, 2.448871481382734, 2.364569879724822, 2.328582656022071, 2.334802300092719, 2.309674498927418, 2.2066610329546554, 2.067846728846338, 1.9466181674844258, 1.8337268525613992, 1.7398099179554338, 1.6851582164103733, 1.6820598895174748, 1.7012223393360544, 1.6609747257145138, 1.5369346892642168, 1.3811734117865222, 1.2650714527144307, 1.2287730840487994, 1.2904555142986942, 1.4207444713378428, 1.5515277389010622, 1.6153491679211973, 1.555800992378979, 1.352249475013207, 1.0481471893917498, 0.7071781841115992, 0.3995093306955083, 0.17906657183267277, 0.06192533906250121, 0.037277505626159876, 0.06451751854417065, 0.10992646535183027, 0.15655665330132454, 0.1795290729801026, 0.163832314490762, 0.11595629158251658, 0.05582190643886535, 0.17406890170266298, 0.40342367562246906, 0.6854031891419052, 0.99652999546931, 1.3508605863867742, 1.7512550357091747, 2.1497510326562983, 2.4618223373626087, 2.6502136695140504, 2.733126876863413, 2.714827984022826, 2.6259394410394408, 2.5273525276107813, 2.4649688063177395, 2.406069871712053, 2.2938555207043145, 2.1221812729706673, 1.9563384172306941, 1.8358907644769267, 1.7462595380488906, 1.6700520613281338, 1.6129009628157456, 1.589043838081884, 1.5846349583468253, 1.535706515214776, 1.4275586604200001, 1.3112838414603392, 1.2405950625055857, 1.2248798821561377, 1.302139800882749, 1.4401026536435413, 1.5937696588430754, 1.6812606169216944, 1.6516871545900487, 1.4631831026792645, 1.1468633042862297, 0.7737537143556872, 0.43126935451418563, 0.1870760486773289, 0.05770074366006745, 0.03367316671894027, 0.07270484703443833, 0.1290891121450023, 0.17874548023912615, 0.19787744525436943, 0.173649679515363, 0.11689627949798283, 0.053177946183660535, 0.15102856663892858, 0.35686452183377004, 0.626659533768062, 0.9538896037189842, 1.348301505143919, 1.7991373844401704, 2.2388556977106315, 2.562412584100047, 2.7299503368176934, 2.7701111070090665, 2.7101929208986406, 2.5982687844688344, 2.490592207199661, 2.4142977016864315, 2.323920561213718, 2.175767224255948, 2.0098913079165666, 1.8715416404993706, 1.7878369922762216, 1.7310997301317066, 1.668581760256307, 1.6165868220945458, 1.5908523942342192, 1.5764144844252106, 1.52877979498808, 1.4438464118365724, 1.3615508223781572, 1.3121163319553717, 1.3074678152629269, 1.368055373272966, 1.4986604980361173, 1.6504060075785416, 1.7511218310124013, 1.7312757496637776, 1.5393787327483157, 1.2027098111323666, 0.8048583458223499, 0.4351545425266908, 0.1721197824868196, 0.03302617872719531, 0.008118397122778868, 0.0607943969982015, 0.13392502825641678, 0.19397243350808896, 0.21621065088313354, 0.18665018549452564, 0.12153547733823016, 0.05353767085986726, 0.13552326733868997, 0.3277457139607089, 0.593924393676795, 0.9388358577167261, 1.3653946096296323, 1.8499060363296411, 2.3102286943950237, 2.6118794686461904, 2.697967001003687, 2.6200968938078075, 2.466691397644667, 2.3047144625693496, 2.1915161617482073, 2.15495644469375, 2.1149755135381447, 2.01941931937526, 1.901053313372097, 1.8150813923523805, 1.7854101804905973, 1.7697905546978367, 1.7362762509411098, 1.6962148216105664, 1.6763583063324867, 1.6758648289274933, 1.652013378676801, 1.5971491160820894, 1.5312143705251717, 1.4904613349691285, 1.484182220137226, 1.5101980168781823, 1.5978740489668164, 1.7269559402996304, 1.831106590846498, 1.8217228274626867, 1.6122996025929255, 1.2419045515381857, 0.817601106948551, 0.4299043312986729, 0.15360295352664438, 0.007215956785211929, -0.02528569066082113, 0.03256568454781748, 0.1266110695554954, 0.20436434826283684, 0.23302437852382177, 0.2016392401720231, 0.13055307813833447, 0.05696152978383138, 0.1268067345558267, 0.3146060603195253, 0.5830663795780296, 0.9371016142269579, 1.3741280746902897, 1.864210470078623, 2.315623380575649, 2.5830842189423158, 2.5870729702820423, 2.3972065101928712, 2.1517503522231496, 1.9386533754136122, 1.8475095516241329, 1.8684806882477722, 1.8959079815945128, 1.8483019281463484, 1.7649213590806807, 1.7139808222032455, 1.7231127964880277, 1.758229249611833, 1.7592262484306436, 1.7575041673501686, 1.7836468171105793, 1.8228702877340002, 1.8440553445819783, 1.821636750517475, 1.774769976203331, 1.7399072607265025, 1.736654388555009, 1.727958000892181, 1.7311260126250718, 1.8013115711587293, 1.89612684643686, 1.8955090653263302, 1.6735894217481526, 1.2753035397445875, 0.8327130656117858, 0.43200899206904214, 0.14356737786184914, -0.009042653758727516, -0.04645912990888862, 0.006759353860780868, 0.10905364861983662, 0.2060298828742033, 0.24795727946724622, 0.21698812684314178, 0.1409404700054347, 0.0625284196881118, 0.12673370259810798, 0.3134948369799113, 0.5788541846358278, 0.9300501240674152, 1.3553116182504872, 1.8130034190255058, 2.2271261422817603, 2.4658884552159264, 2.429370470317478, 2.184347545346775, 1.8857771824776173, 1.6594523471367655, 1.5925831875891856, 1.6503717429773161, 1.6977297671268161, 1.6552000367811779, 1.5743830588320606, 1.5339004954152247, 1.566825239870436, 1.6235595191182357, 1.6681752174387374, 1.734803021107014, 1.8246208384538665, 1.9088261477174409, 1.9828123408974165, 2.001360339000976, 1.9872449553117075, 1.9804295358247253, 2.008046601395587, 1.9692494541947287, 1.8719498514128863, 1.8564474478619766, 1.920309470989986, 1.9284458470302441, 1.708682482934877, 1.3057561035149932, 0.8649502166098509, 0.4615601138893815, 0.1554745257336725, -0.013377120870861039, -0.05982485256902002, -0.009498453044199726, 0.09645019769602638, 0.2027138071318332, 0.25488916973289094, 0.22839893247628287, 0.15019567225350117, 0.06719886815714282, 0.1312646766066671, 0.3164722371997532, 0.5743288508744582, 0.9107362231896247, 1.3020298589692672, 1.7029121985082107, 2.058389062280028, 2.2681016058021632, 2.239717996575784, 2.0181407140190517, 1.7375528172289685, 1.5320979537767485, 1.4852307471865431, 1.5367390993882608, 1.5577673048117229, 1.4796966306702979, 1.3711687634813834, 1.3366863839079164, 1.3898298556294981, 1.4678773253859123, 1.5653366760114036, 1.691411128043433, 1.8055137704289212, 1.8870901528061093, 1.9403149624719744, 1.9571128184837168, 1.962772063603386, 2.0239294990261127, 2.1311886336551162, 2.1291159209150057, 1.9801172835966383, 1.8910627884698936, 1.912262696264501, 1.9191741879755757, 1.71818604131403, 1.3307646490439995, 0.9046768561209079, 0.5100190540451938, 0.1917022789547798, 0.0017479703090868934, -0.057720453068036685, -0.016537413748975528, 0.08619483614892769, 0.1980783594735894, 0.25680266439991584, 0.23236104771312704, 0.15429442653184003, 0.07048820666212996, 0.1396152920028447, 0.32092529238779893, 0.5612884874733842, 0.8727773651390683, 1.2287407832035426, 1.5764533515843788, 1.8744325500742123, 2.060252312433115, 2.0685633558672705, 1.9158661910579275, 1.697782900680983, 1.5408425387745501, 1.503620531303938, 1.522127816389481, 1.494469229682365, 1.3806307321392697, 1.2604488986397495, 1.2400697196655268, 1.3233041340723835, 1.4260749525419545, 1.564630843715519, 1.7135483575313801, 1.8016927228641777, 1.803669024582043, 1.7523717122071512, 1.7039525222302276, 1.7076236803019789, 1.7901047393129634, 1.975496026543727, 2.093448258167421, 2.0343502646095817, 1.9287726048051026, 1.922009541786779, 1.9022211426421167, 1.7124640529919437, 1.3485189412260976, 0.9393663293684564, 0.5530772976396336, 0.2302761915527031, 0.02507860355200394, -0.04673325062552352, -0.010737542233101341, 0.08529314076950585, 0.19168184914818798, 0.25125203027744064, 0.22986742328419849, 0.15347634661483223, 0.07035780222068268, 0.1485543398728005, 0.3225772276194299, 0.5406823509716411, 0.8228968423882795, 1.147974213188079, 1.4647551835033448, 1.7315849201634337, 1.9066395402650271, 1.952388620273139, 1.880540295790459, 1.753239425536467, 1.656216334798879, 1.6235827201820527, 1.6037502596370958, 1.5390988385853661, 1.415315315642136, 1.3074838979080383, 1.3211061823233439, 1.4216033624709266, 1.540338622931983, 1.6800043439141772, 1.7880893856478988, 1.8228780352773406, 1.7223697654516807, 1.5378636759260405, 1.4034099775046585, 1.392294426554669, 1.5167191878362094, 1.7455536510433565, 1.9808480482516404, 2.0645595252909947, 1.9814292232880695, 1.937048326777757, 1.8749201627417595, 1.6701934053542675, 1.3330561129199714, 0.9456914477866895, 0.5720285274349657, 0.25424639596699633, 0.04567737672207382, -0.03172325878394674, -0.003114633077117913, 0.085136759050911, 0.18558218278096397, 0.24124021707378637, 0.2192610680247482, 0.14667243445217565, 0.06825695425297243, 0.15420509743534155, 0.3186730350312686, 0.5127811111093854, 0.7659141991677251, 1.0646330884791058, 1.3667846098961989, 1.635107998135868, 1.8249595258196345, 1.9152506453848916, 1.9152496975635396, 1.8637758898649115, 1.813655516805305, 1.7873357456591474, 1.7436124377129865, 1.65839631087098, 1.5402354074452227, 1.480534002258559, 1.5247870594181883, 1.6286328718505154, 1.7502515451916558, 1.8424927906145077, 1.8624468098321316, 1.805206606469996, 1.63181242994699, 1.3787762494634734, 1.1942377465168927, 1.1653948370717806, 1.3015319387465147, 1.5741945095101098, 1.9092069842729613, 2.122224006592067, 2.026118669393889, 1.908716090665061, 1.7894677504076502, 1.568976073262094, 1.2493141196149797, 0.894112028340659, 0.5448216608453542, 0.2473883320835864, 0.04856230149075791, -0.027044222195426782, 0.0016582439989470754, 0.08300851084837578, 0.1732314895573446, 0.22322099598481196, 0.20160989404764262, 0.13373922197068466, 0.061866986831500846, 0.14848994218703146, 0.3013700501001781, 0.477391977393994, 0.7052979564070079, 0.9787868455041906, 1.2682130666537377, 1.548011091730661, 1.774963716151263, 1.916075618729707, 1.9733475920057788, 1.9733307535661702, 1.9440654018749064, 1.9018860879302737, 1.8321821723072629, 1.731851672870717, 1.6506253636059254, 1.6397882237569894, 1.7012233080834904, 1.8033691881950185, 1.9109049979307615, 1.9531453425480492, 1.8640654470324036, 1.753598503137176, 1.5792711855648944, 1.3339713861448825, 1.1485901680702295, 1.0935977453820047, 1.220081559490516, 1.5156952605262088, 1.9045651415509497, 2.2029764620292434, 2.0315420744390282, 1.8162451237354378, 1.6304208872950414, 1.3984873600140464, 1.1057918518888898, 0.7792542562886725, 0.46466440290140903, 0.201307963123946, 0.02560696164903278, -0.03914339803259823, -0.009472929799116372, 0.06867983872799713, 0.153366051643041, 0.1964489935229885, 0.1731829755637886, 0.11280761106316155, 0.05227972139351912, 0.12400382738078182, 0.2607298840803007, 0.4271461271013861, 0.638587878293382, 0.88657709602568, 1.1576758177069852, 1.4390590315877974, 1.6952449435992096, 1.8838106187736363, 1.9816672772512853, 1.9943712464773535, 1.9441436296566765, 1.8629701011914312, 1.7625403685214254, 1.6699526588410998, 1.6331430236172337, 1.6757500244483288, 1.7564815828059779, 1.8426874055607305, 1.9268965905125655, 1.94266662889069, 1.8501760653093107, 1.7247917459333362, 1.600658035316536, 1.4236917270002112, 1.2658406207212807, 1.2070260236657158, 1.3050799603907646, 1.565362944918843, 1.9492225871654507, 2.2096081019022904, 1.9797477087901967, 1.6865182643840466, 1.440165624294201, 1.1889198600372775, 0.9059301453766403, 0.6149771131990216, 0.34228385666553335, 0.1193267751489463, -0.02890602900092428, -0.0776591966808216, -0.037364223497469186, 0.04219606217937545, 0.12036068845536342, 0.15672470006619152, 0.1344096428188499, 0.08393573711615043, 0.037546719108322545, 0.07872629446724361, 0.19048180728530464, 0.3507846947761956, 0.5548304512969336, 0.7801638542324327, 1.0259398391043182, 1.2969024758917642, 1.55944264458195, 1.7676893544809595, 1.8822693406854454, 1.8932178237222246, 1.8117035400685342, 1.684571057289832, 1.5638823415962961, 1.4926295099557418, 1.5095667021752617, 1.6004649198745202, 1.7186924168921665, 1.8154061063676754, 1.8616993575270742, 1.873725132797727, 1.8182744797999084, 1.7296706924600602, 1.646486620643528, 1.554083848526466, 1.4683036514979144, 1.4342190921788125, 1.504912990253557, 1.7071893127455557, 1.9777462824474996, 2.085424817502362, 1.8242939163596006, 1.5109848388526095, 1.2263079916987663, 0.9520246794796584, 0.6788051903745711, 0.4194099522447711, 0.18843312088817524, 0.0039481875352840425, -0.11227858926682359, -0.13583628808435558, -0.08338227183586418, -0.0012332482703682154, 0.07321015506007833, 0.1037460235521627, 0.08412312661959687, 0.04827491463865131, 0.020686084454605794, 0.025277934656326845, 0.1014350741780794, 0.2426330571440337, 0.43510088155935855, 0.6468387871752125, 0.8683174210469237, 1.1162519032442615, 1.3671897857390145, 1.5744840273845313, 1.691364012209059, 1.6977990610786733, 1.605136335389653, 1.462443868916573, 1.3367478521371754, 1.2933089133086415, 1.3487375979463239, 1.4792078538969882, 1.619698387150305, 1.7117795988576934, 1.727985645030639, 1.6908290865355264, 1.6463710794364756, 1.5860866763475308, 1.5515101160127986, 1.5557715700224215, 1.580111773733588, 1.6285030106807137, 1.7236516381945979, 1.8745242905354325, 1.994100262120523, 1.8936710795563836, 1.6027409776143606, 1.2783097684929308, 0.9731052835540577, 0.6925739675384228, 0.43766928055485294, 0.21145857529129447, 0.014453457854362957, -0.13322468630354406, -0.21489589235042758, -0.21229408160536525, -0.14407884133644427, -0.059144674673419974, 0.0089451531363235, 0.03635712113908584, 0.02671235205050812, 0.009707800563928901, 0.001755509663937039, -0.016231416697530837, 0.01831775997966969, 0.1185864432790707, 0.2755216078110752, 0.46967250654043635, 0.6804686648563121, 0.9080029297728044, 1.1354151861316746, 1.3280718142735326, 1.445453066161712, 1.4639442766582813, 1.3845515601879594, 1.2536826247411048, 1.1469827711283689, 1.118509261450949, 1.1902765772993056, 1.3253767798664753, 1.450358462720711, 1.5017326731111098, 1.4562401452176092, 1.3772163172835812, 1.3041029141497513, 1.2471120549776784, 1.2356881181080432, 1.2818067607191246, 1.3954093672554817, 1.5676497367521427, 1.7464291225798978, 1.8628645368938135, 1.8296974331703406, 1.6141665750626173, 1.3100970037370667, 0.992029180512585, 0.6948886650999716, 0.42903207502647117, 0.19804343536036664, -0.006009125101813443, -0.16952363026720263, -0.2821793090802011, -0.329648472287805, -0.2966565196597037, -0.21728256180921193, -0.1352678463217596, -0.07104296747909934, -0.03951001703314292, -0.03321354729349682, -0.028402795995095393, -0.016008768408212123, -0.033285762636661664, -0.03898309733738996, 0.0034622831746540057, 0.1012678872141224, 0.25751098492413294, 0.4569077824538462, 0.6762545405830892, 0.8891849953472408, 1.069215156664556, 1.191732387464924, 1.2326704615358868, 1.1883447336120894, 1.0855007605716085, 0.9972232321796564, 0.9757984002606728, 1.0329083211683838, 1.1395285240175297, 1.224237221341356, 1.2231410288369724, 1.1292785094104756, 0.9963487487397028, 0.8809307384516729, 0.7922547705435253, 0.7438475613449153, 0.7688809517653497, 0.8710595686919286, 1.0676440363869215, 1.2772999338288236, 1.3957524360350162, 1.3517151697603933, 1.1719777765677595, 0.9263438904726148, 0.6588710413289507, 0.3940036524155654, 0.16092912449690389, -0.05039594716067678, -0.22274488047293126, -0.35348134482202825, -0.4345033598806058, -0.4435423038780739, -0.3874367021200424, -0.30428071847027666, -0.22371743372572644, -0.1586271599492428, -0.11648601989774217, -0.08865004485697969, -0.06236243947741149, -0.033102424751487884, -0.03717305470888821, -0.07346567889102076, -0.08737322516086045, -0.054801858030182934, 0.048261343788145034, 0.22110570062321402, 0.43016921327865687, 0.6358882697035955, 0.8132793710274052, 0.949044084854729, 1.027352895876587, 1.0321888760507771, 0.9716796859935759, 0.8990501306729011, 0.8649327120691781, 0.8843571944295295, 0.9367261250302221, 0.967215105840872, 0.9244992939655676, 0.8085467331615988, 0.6478033130110968, 0.4868316414380404, 0.36267133776682, 0.2612614127187628, 0.22676910847565127, 0.2728540390766044, 0.40862137266251275, 0.5890596485181585, 0.7162355098130362, 0.7333121295365204, 0.6485150841927192, 0.49683362208805654, 0.2940859201423782, 0.08607020863113787, -0.11331556044772026, -0.29112041045739434, -0.4279601452073162, -0.532401476245493, -0.5765671756456955, -0.5548334443053522, -0.4853626830623737, -0.3986196481087434, -0.3163446488044791, -0.24452759111759587, -0.18454627875133983, -0.13395989947842427, -0.09079879361344576, -0.04848850658827983, -0.04708574519381046, -0.10673843141462505, -0.15981796331340264, -0.17868589919230154, -0.1268549288412009, 0.010143194011639586, 0.20184976757768777, 0.4017117900781452, 0.5792581290972948, 0.72578759583538, 0.8343111215243979, 0.8923165271012076, 0.8833868980151439, 0.8351734127126141, 0.7931356961759807, 0.7775709518506122, 0.7820033364024068, 0.7676740495897229, 0.6989536516956746, 0.5674252655523595, 0.3936007579872837, 0.20543867923207718, 0.04888453187990622, -0.09023311135112717, -0.18156106713898867, -0.19933238505079856, -0.12909559264202508, -0.004504800269209564, 0.11284667871667557, 0.16967390906931182, 0.16001553584717668, 0.08063773010388967, -0.05536826282547916, -0.21062070976824043, -0.37312624764673125, -0.5116332251668966, -0.6231911206959152, -0.697268235795499, -0.7096366886857859, -0.6673444830865417, -0.5850227743137681, -0.4920326592361397, -0.40264281206066943, -0.31638010962917407, -0.23605773790670587, -0.16739814456223254, -0.11351577130586507, -0.06209826658225425, -0.06901565779308114, -0.15109774171887652, -0.22790484854620377, -0.2765991375236698, -0.2613945507780661, -0.1567111634768914, 0.014080269510477764, 0.2093575777298913, 0.3937826136182307, 0.5521464417349291, 0.6788888016353389, 0.7706925043244386, 0.8078932542792694, 0.788320097152416, 0.7433023754623302, 0.7076090930939034, 0.6853433624639493, 0.6588859530367808, 0.5885602923906909, 0.45330448031374887, 0.2695699019248619, 0.06780471687025398, -0.11295097417313597, -0.2708927528069854, -0.39475580521452186, -0.4549028025196253, -0.4418571925068069, -0.37869713676613725, -0.3027447220765371, -0.24047746976076353, -0.22115924464479517, -0.2596055287751093, -0.3535991153381834, -0.47314309099781515, -0.6055403158709479, -0.7160169644609155, -0.8021355804217375, -0.8449186888727451, -0.8320935456970571, -0.7692601032558757, -0.6752271585958387, -0.5747323837672932, -0.47127089808690786, -0.36759198295301015, -0.27052219001119454, -0.18987214915863654, -0.1300293299776608, -0.07227072436843157, -0.10605388638044634, -0.21054635579316233, -0.2992582160439744, -0.3582111517437871, -0.3600599241145086, -0.2771246348131186, -0.12320911259660157, 0.06711718755657765, 0.2624401511737073, 0.4396364773695186, 0.5857550766341352, 0.7002537544051979, 0.7738207877159662, 0.7897717263444383, 0.7560458969345384, 0.701614271810702, 0.6554176544503646, 0.6161794836626707, 0.5494489433826895, 0.4289769840280424, 0.2576259473869173, 0.06651548324726372, -0.11675804614883105, -0.27865452818270287, -0.41496331913663, -0.5030860864208979, -0.5417198399376931, -0.5383105769874904, -0.509277551942363, -0.472980367938182, -0.4659430215450761, -0.5054787526273005, -0.5849392035833278, -0.6912528771143868, -0.8021486610258288, -0.886976069921673, -0.949533982445107, -0.967171094150427, -0.9328106901883754, -0.854905282174534, -0.7518201663091835, -0.6354779403339531, -0.5136870426995349, -0.39541679964932125, -0.28795977089387215, -0.20269452608645822, -0.13862695925423385, -0.07526474639249708, -0.1477126332413311, -0.2789938553109569, -0.37779450611042736, -0.43450292849022354, -0.4350662104350982, -0.36145016961812954, -0.2182277420334738, -0.02798370407723576, 0.1796681432635106, 0.3777098106863924, 0.5469812689043455, 0.6797159915286319, 0.7772911094709362, 0.8263172281209448, 0.8211202781417087, 0.7701164441025687, 0.6999677997052519, 0.6375414127107667, 0.5660553987241955, 0.4634730821536156, 0.32263060898520984, 0.15875429963200782, -0.009279249360934778, -0.1682222328217686, -0.30832900993885687, -0.41906950200883847, -0.49687200043049906, -0.5431329777419196, -0.5603207764451752, -0.5743858641864215, -0.60575562656264, -0.6651585562015924, -0.748894284732992, -0.8532036498941181, -0.944790431738641, -1.020023673271204, -1.0685404528967941, -1.066833369133802, -1.014748962295839, -0.9206988331228535, -0.7968183149600995, -0.6604047360384646, -0.5257832802892484, -0.3995690485846, -0.290710742222286, -0.20482301850175996, -0.1353673289286484, -0.06955636296918075, -0.1864506878701937, -0.34414651711091, -0.45495823153478754, -0.5066711518567666, -0.4959725612152742, -0.4211973531189132, -0.28480096857924464, -0.09536362767971028, 0.12468932084730519, 0.3414687010625468, 0.53296617232589, 0.6848589932161334, 0.7957585489369455, 0.8623877060795341, 0.8779310675847963, 0.8441488312544163, 0.7713850979344063, 0.6890203379157114, 0.6162652858721825, 0.5330997437173619, 0.4286299157325872, 0.294487137726697, 0.14200880610364433, -0.014088915937478266, -0.1600987643161197, -0.2879949477434689, -0.39362049472095684, -0.477083223058081, -0.5398542995912826, -0.6037949771375236, -0.6737829896422948, -0.7582603700841896, -0.8613497775837823, -0.965387787445211, -1.0580099036422148, -1.1313049383233027, -1.162866862482101, -1.1395357441567966, -1.063697109579439, -0.9436444900743094, -0.7996624254798429, -0.6528563431034606, -0.5115067683846799, -0.38467706975406407, -0.2791654329960951, -0.19082588876675727, -0.11512410774761032, -0.052520613720067034, -0.21869632080243787, -0.4001062489083092, -0.5223355510143847, -0.5710253605318155, -0.5483257409680097, -0.46460750645669274, -0.32531459177296335, -0.1373489844671608, 0.08565395097415936, 0.3123151742388412, 0.5167213460930384, 0.6847939682312715, 0.8098885384521891, 0.8907162240827278, 0.9229210745706493, 0.9066767879370178, 0.8481922235101818, 0.7639791672012695, 0.6828930901701913, 0.608768937325034, 0.5249408499591852, 0.41853464986111505, 0.2828441145061487, 0.13825162868592458, -0.009577621040027995, -0.1471311652749748, -0.27548518428676533, -0.38804078997045904, -0.49262347493194075, -0.5990581136130976, -0.7067042057150351, -0.8269346068893515, -0.9470687425771626, -1.0578117330030656, -1.1497770354291612, -1.2071280853111148, -1.2154775826836293, -1.1661148879571293, -1.0647391496218424, -0.9261140317551068, -0.7739790074153621, -0.6216233030945022, -0.4777777893318329, -0.352570936319325, -0.24565422083469846, -0.15274091503061793, -0.07889947912600169, -0.030277109517248095, -0.2367731884369807, -0.43828892281665205, -0.5754379186655764, -0.6295162599608679, -0.6019522347029971, -0.5073064988652666, -0.35629811416471474, -0.16087697383076854, 0.06391460700225668, 0.2932317139063883, 0.5001868657172368, 0.6723039119789004, 0.8041527579400364, 0.8957248743597024, 0.9442760819039604, 0.9494918820587883, 0.9120842354100587, 0.8420848416797314, 0.7562488739415928, 0.6712650095219693, 0.5852225069380469, 0.49129019986299893, 0.3786176236808174, 0.2537068721216295, 0.1167809822891706, -0.02500086394615131, -0.16910337111863089, -0.3079623241324865, -0.4506138332746455, -0.5928112354835369, -0.7382175487449663, -0.8820493096084058, -1.0100783810317977, -1.1188064724889935, -1.195363782375448, -1.2336313734273803, -1.2185625536437386, -1.1479965326100376, -1.030808273821457, -0.8846661715502441, -0.729680021259819, -0.5742822877098365, -0.4278243086280072, -0.2974903449281774, -0.18441031198698837, -0.0937822728790636, -0.03396829917401999, -0.006239409637607038, -0.2427184786097925, -0.4555379411873882, -0.6076288460330695, -0.6765978134527625, -0.6575201905708846, -0.5596751522740535, -0.39947568758999036, -0.19623903743174695, 0.033174017068163045, 0.26779866312745465, 0.47987086729806855, 0.6536596970201782, 0.7853122661930088, 0.8773776175925291, 0.9301687469000347, 0.9463578253474484, 0.9275365473773497, 0.8742568882178381, 0.7973411139179475, 0.706390655173805, 0.6117357112497679, 0.5168838069826089, 0.4184826413723846, 0.30790479921838926, 0.18427140159095218, 0.043437287933039345, -0.10561657721896367, -0.2643759799611378, -0.42936887693022224, -0.595523052998865, -0.7601292453826076, -0.9098064974988657, -1.0368712047069812, -1.1348468636287996, -1.1992992328645153, -1.2208254756929922, -1.1877640840088464, -1.1040313286006673, -0.9781214167311131, -0.8308913341082139, -0.6738789747296168, -0.5115887740198983, -0.35560930626024956, -0.21497037037032268, -0.10132435880278348, -0.025914982389702284, 0.011664264296057126, 0.016978443722679284, -0.24270788612647437, -0.45847004129198743, -0.6207160071103955, -0.7054936416092087, -0.70273614177674, -0.6149147996792315, -0.45528752853413296, -0.2516165559394249, -0.026242223479398696, 0.20727430966141383, 0.4257088353967286, 0.6076949660594065, 0.7446615056734514, 0.8386468268483711, 0.8930317131885863, 0.9104562317497537, 0.9009704352523523, 0.8631900219074345, 0.8001947550221622, 0.7179901907468399, 0.6232380257354496, 0.5239073001323002, 0.42440765841692346, 0.31558975130659705, 0.19596998765367454, 0.05905283299253953, -0.09097293500019721, -0.25627498100931284, -0.427993791083044, -0.6018582755638221, -0.7681079644173866, -0.915229563982416, -1.03606029919468, -1.1266725953138255, -1.1810399341470414, -1.1872383279581398, -1.1416968894839956, -1.0472226955319426, -0.9169839848676112, -0.7667470622595833, -0.5979530875902115, -0.42316977779257625, -0.2577757860610043, -0.11564188214015739, -0.014817493507599575, 0.03895607362016284, 0.05269017584521777, 0.03556625194564913, -0.24203976817450562, -0.45560922542072074, -0.6199812461561338, -0.7155390598940015, -0.7286287167537284, -0.6591996787270024, -0.5136210916823762, -0.31561769766563036, -0.09860696075918121, 0.12223086560311218, 0.33493722333949993, 0.5203638147994617, 0.6652692665252531, 0.7654711011473667, 0.8266148339045672, 0.850444563258073, 0.8471127174731539, 0.8235084597756616, 0.7768257082507046, 0.7092305651752989, 0.6243858992581668, 0.5266547050328104, 0.4227317901038489, 0.3109755679180611, 0.18810595699181357, 0.05282398698725702, -0.09871181163285397, -0.2616588183073912, -0.43277695591646376, -0.6031385483466067, -0.7645453752810634, -0.9049575435547695, -1.020254389089767, -1.1029668539357347, -1.1447121066591615, -1.1372841254626453, -1.0796492904091586, -0.9755056438626363, -0.8394081176671909, -0.6754947125333665, -0.49334721246529345, -0.3139707290623246, -0.1510971211142847, -0.02269484152500032, 0.058554043586998644, 0.09307688598348071, 0.08765455447665749, 0.052424481943222905, -0.2393996749256336, -0.44930152279667784, -0.6089397000805262, -0.7078263955326152, -0.7329006589645999, -0.6802434335801301, -0.5579882703128095, -0.37927236858113134, -0.17279850230272822, 0.03504655957853434, 0.23349196312461304, 0.4114528213972366, 0.5576447520981376, 0.6636593356629473, 0.7305905329958928, 0.7642588162165032, 0.7688824541332783, 0.7552869654271579, 0.7232625805957775, 0.6716352163099999, 0.6016850845800306, 0.516693153645276, 0.41831662992090757, 0.3102230264062608, 0.18866232939704258, 0.05535340217256385, -0.09279481953998338, -0.25084279781852603, -0.4166324197451614, -0.5813444225871468, -0.7362120142832618, -0.8713783787504827, -0.9797497279371169, -1.0511232363623295, -1.0784326839291065, -1.0577276806048526, -0.988402132053517, -0.877023969873052, -0.7318545025286939, -0.5583452509030102, -0.3780563423503459, -0.20685111908805157, -0.05915610691335628, 0.050102521382030654, 0.11547316361977789, 0.13586139897914545, 0.1162908924636405, 0.06669053443820275, -0.2284651929528563, -0.4319970669958326, -0.5879012336680819, -0.684813701348606, -0.713642323684954, -0.671144618993042, -0.5703403345873092, -0.42222351499327776, -0.23969204625094834, -0.047647129728994514, 0.13489494904612995, 0.29952009438718924, 0.4390766235659352, 0.547010439607301, 0.6189647593082904, 0.6600837905073412, 0.674675862998459, 0.6687385927496379, 0.6467971381441816, 0.6081206435053513, 0.5535441298224955, 0.48485876735110556, 0.402138594782695, 0.305237692418589, 0.19481057044331404, 0.06937325548721876, -0.06809911350146353, -0.2183255170444153, -0.3750100607547423, -0.5325159965117046, -0.6790417010411776, -0.8060958730496238, -0.9022335646395689, -0.9594446468448334, -0.9730507280516834, -0.942126685926811, -0.8664425370331645, -0.7532563522182271, -0.6063542685704182, -0.44056524065463953, -0.2743004125068102, -0.11885455290702325, 0.010425513540994528, 0.10410854043956383, 0.1569483043819656, 0.16708020141471142, 0.1369915805846412, 0.07574963097424169, -0.20969456861764257, -0.39981013409131777, -0.5496484922671949, -0.6407754153186918, -0.66702892695348, -0.6321245501506915, -0.5475931697312133, -0.42614833116365497, -0.276404057839325, -0.11209508778558526, 0.04922183187611982, 0.1962013530869564, 0.3230483618352204, 0.42493135113466735, 0.49853707593154356, 0.544271564865174, 0.567667077751173, 0.5709046639577006, 0.557702491144358, 0.5290554856044507, 0.4870056117514271, 0.4321043458516183, 0.3649098108989591, 0.28255938114348605, 0.18654643052437953, 0.07575782321329182, -0.04714180505399838, -0.18275051725712882, -0.32483460383224894, -0.46698458394399744, -0.5975043706805642, -0.7075952943086355, -0.7874501095271293, -0.831408103385454, -0.8372539528433371, -0.8022694187028546, -0.7286866211354626, -0.6206775863502474, -0.48459599460943287, -0.33724022859681546, -0.1889239196166537, -0.05165388032254526, 0.06149073261145693, 0.1411124036010819, 0.18156749804022598, 0.18293949397128292, 0.14654689099583884, 0.08043931876244932, -0.1853371835158968, -0.3534005906972204, -0.48546386562960947, -0.5646627033650851, -0.5884081296831468, -0.5626279278347178, -0.4936264175463083, -0.39328751360338526, -0.2734252540593251, -0.1426329740511407, -0.009536853563498976, 0.11527029302034948, 0.22434243189102038, 0.31323811960530296, 0.3800088113036316, 0.42518955135859005, 0.4519598615107765, 0.4628764708538291, 0.45787572578843505, 0.4386116567810884, 0.4065197336775364, 0.3636041308529854, 0.30875999450306685, 0.24151297161472535, 0.16038900749753138, 0.06811813374312707, -0.036458442807469085, -0.15019480613265912, -0.2703576399691532, -0.3879299683447636, -0.4948360788427021, -0.5834001140904883, -0.6474911081401021, -0.6832024723214535, -0.6861430624332864, -0.65314361550114, -0.5873524878898347, -0.490725706691299, -0.374091097507014, -0.24783956974557642, -0.11960093522631787, -0.002102326979681507, 0.09318434795303582, 0.15728006581966802, 0.18646806888817977, 0.18022286233186063, 0.1415677218401868, 0.07815360451624069, -0.15205534617843916, -0.2881481779819692, -0.3924020592748845, -0.4553925718819981, -0.4765119023499504, -0.4590317615098568, -0.4072127421206327, -0.33049365558317756, -0.23899699530735452, -0.1397094526014192, -0.037702423689274685, 0.060980678693729556, 0.14828727646484766, 0.22009714378189546, 0.2741682911560816, 0.3124002369467418, 0.3369699346659101, 0.349921133247229, 0.35039918439624296, 0.33867395163304176, 0.3159588094388865, 0.2841229234593294, 0.2423274740906664, 0.19023433994204383, 0.12712438334434067, 0.05503302310165152, -0.02643999860274086, -0.11501359760346105, -0.2082973889379369, -0.29825449424239886, -0.37972590874794243, -0.4469659796699916, -0.49684429773738903, -0.5253141004192947, -0.5262831549069328, -0.49890104745762703, -0.44389749014928387, -0.3653319064645314, -0.2723543218954718, -0.16960669058720307, -0.06587353972969583, 0.027420339317478868, 0.10080012960756234, 0.14860751531322616, 0.1679682640109837, 0.15751814667085, 0.12136274710802686, 0.06628058415960549, -0.1074599573386797, -0.20219870729430003, -0.2745649841439755, -0.3198118869982176, -0.33555081154770655, -0.32359153061769397, -0.28967645726032565, -0.23959655102784944, -0.17856692079638814, -0.11065145944433066, -0.040515537170748746, 0.02788247753317154, 0.0894818538284453, 0.1401799688430693, 0.1787253179690583, 0.20605793543674641, 0.22470294931499296, 0.23528226590585705, 0.23766834229967584, 0.2310958194492036, 0.21697456563738055, 0.19592398162695876, 0.168322521649865, 0.13272804540546063, 0.0901120352783545, 0.04023606331705256, -0.0154217951916163, -0.07722996687411054, -0.14150344602463943, -0.2037341054006761, -0.2592261511688099, -0.30494810069250045, -0.3391848364179388, -0.35786672843847894, -0.3577477436458655, -0.33771716654761647, -0.2978717671509852, -0.2430885805173207, -0.17673377063817486, -0.103017611127227, -0.03020762901131346, 0.03414556721736118, 0.08392030411053407, 0.11527817141198045, 0.12598609567660096, 0.11621380769453882, 0.08848766334399473, 0.04745916860343939, -0.05504863324836578, -0.10317652368373342, -0.1407431801433648, -0.16516472352653788, -0.17338271881899217, -0.16669519428458732, -0.15014808974209073, -0.1259030296776223, -0.09575130397209493, -0.06128239351312019, -0.02505875081860168, 0.009834654588357453, 0.041755855851949616, 0.06786359762407, 0.0880118136071202, 0.10233431945999866, 0.11238244139208191, 0.11838199763780476, 0.12014708685162297, 0.11729215123197295, 0.11054236798829171, 0.10022370957307318, 0.08654108096094763, 0.06870075399623567, 0.04718825806612879, 0.021730339818264457, -0.006784772652818232, -0.038947251341459294, -0.07210256643743132, -0.10447230091019169, -0.13254813286744388, -0.15568983682244486, -0.17263455975830555, -0.18131679902529715, -0.18120069392813834, -0.17036740442655557, -0.1497962917284731, -0.12174603619294805, -0.08645790239916731, -0.04793239939931089, -0.010758096193349546, 0.022026468663073468, 0.04745722273846092, 0.06271209881760542, 0.06698577854137394, 0.061422375625527, 0.04667624413254525, 0.02484587972681608, 5.300801910529761, 0.03407170714978452, 0.06823652268948274, 0.10709354656984234, 0.13656907680021504, 0.15488171116512725, 0.16438444601684096, 0.16966212395908403, 0.16793420679466328, 0.16178092261770838, 0.14820810509171695, 0.1356968810435616, 0.12545434156661903, 0.11663943368712773, 0.1070510962772091, 0.09723317015952798, 0.09240357217142674, 0.0879883982481991, 0.08857454984448464, 0.08507190006938198, 0.07477877725796216, 0.06710174628422551, 0.0676627924472149, 0.07365469938224072, 0.07376290262106777, 0.06054292827910951, 0.042660874595682345, 0.027670149046799892, 0.020902168437661586, 0.019532895456750285, 0.021590813689384248, 0.03214491422965842, 0.04786972596070577, 0.06453404061812444, 0.07353209693140453, 0.06057265271932668, 0.03217512067441571, -0.002990961131895863, -0.03505606788059941, -0.06922650845581081, -0.1037123013982313, -0.13397953453661499, -0.14807586470845924, -0.14616348980952515, -0.13795561557043667, -0.11740498481761252, -0.09040767990473166, -0.06021981480273057, -0.030428872037828823, 0.07026392550645809, 0.14174730091230095, 0.21308076612651078, 0.26886405933222324, 0.30732848780944816, 0.328956534902252, 0.33880438612833, 0.32924606339591916, 0.31468409536117947, 0.29016411299322764, 0.2681399771694841, 0.24931479506121276, 0.2320930358638527, 0.21613473536411937, 0.1993448127736498, 0.18411955604578614, 0.16827179612139162, 0.15525316205540546, 0.14447461600280945, 0.12387696507410996, 0.11182630350428387, 0.11563346751778296, 0.12111944487037528, 0.11396484963646122, 0.09115298369048956, 0.06250382957187266, 0.0442621982656421, 0.038115994447631425, 0.03963538409708137, 0.04495076783138002, 0.06279057222982846, 0.0891069010312262, 0.118226938109493, 0.13104026590427026, 0.1152223892989659, 0.0715330177158158, 0.01584563809928126, -0.040948152983350035, -0.1064835903699022, -0.17377572017330972, -0.23418481073888742, -0.26914301753468856, -0.2772466342913713, -0.26115441782403115, -0.22329548925813797, -0.17536272213751622, -0.12125194098925625, -0.06106666952623352, 0.10430895132071857, 0.20713884519112416, 0.3014881641267934, 0.3786457965135541, 0.43348111009078044, 0.47278291042415643, 0.4812044705785668, 0.46305234921001404, 0.43304940419342863, 0.403129331576995, 0.378541330528753, 0.354426246796041, 0.33479891422735414, 0.3156586424967472, 0.29146942419115496, 0.2649352891876394, 0.2314037168100471, 0.20060320467434856, 0.1734245402959327, 0.1442540346113573, 0.12455706364374268, 0.12288023137305215, 0.12084216461083733, 0.10359706808679332, 0.07217174350825031, 0.043850932942603546, 0.0318039897412866, 0.034703434204853084, 0.03789121330632394, 0.048648948178932463, 0.06701256004622445, 0.10353635605355362, 0.1390229737091932, 0.16308434331907973, 0.15703232515512977, 0.12148969937676975, 0.06104448363075112, -0.009309732483097976, -0.09380000095479053, -0.18956454412697324, -0.2730626387969051, -0.33061765621108236, -0.34932604095911407, -0.34056991620004656, -0.2954634926938232, -0.23447103705306138, -0.16432073590767995, -0.08752198598098236, 0.1319300725299317, 0.25355199167785536, 0.3650813190706485, 0.45690650077911715, 0.527190843722222, 0.5685565719117158, 0.5730809810419067, 0.5414809071643458, 0.5004926731586935, 0.4640423200611441, 0.4389406088642777, 0.41650228265814765, 0.39783467084942015, 0.38436623858087066, 0.3597375811283988, 0.3213297435198519, 0.27512084492500694, 0.22758406112793095, 0.18476049715832474, 0.13170919309556225, 0.090266486740387, 0.06779380050276979, 0.050216342682392355, 0.02114076120440922, -0.015440906893685633, -0.03944059926825659, -0.039547220550725674, -0.026567720476099187, -0.008757119828376632, 0.011350684222902096, 0.03992993206964643, 0.08237061126816138, 0.1284219731357133, 0.1641210308925215, 0.1821752868060274, 0.16671295859456325, 0.12077493275645572, 0.049535660137264376, -0.03998967909823421, -0.14162252648714832, -0.23676212990278173, -0.3025105406561426, -0.3379060154397756, -0.3410742477959719, -0.3075915127945588, -0.2490413747621333, -0.1744345074819335, -0.09213917467868489, 0.15777236028805738, 0.29381643826437587, 0.4154743118142173, 0.5110350976800597, 0.5837129001941153, 0.6160244666546679, 0.6052228791095808, 0.5666046544917417, 0.5231388640323261, 0.48450829828132524, 0.45395069961646134, 0.4243472208655399, 0.4024005611271694, 0.38754130795561753, 0.3620797066834885, 0.3224421792582903, 0.26927019948481706, 0.21630805903739184, 0.15392250371333704, 0.07726373772477255, 0.00471705744550086, -0.04895844591004286, -0.09302999952174139, -0.14055983811651176, -0.18460865523344913, -0.20526581006613123, -0.19775849984536772, -0.17358830581358992, -0.13851194264275324, -0.09415580087589459, -0.0419478443921109, 0.02212321546696242, 0.08507805687507528, 0.1464903913791529, 0.19140424857305788, 0.20928283987132018, 0.1877607518391418, 0.13548609076014842, 0.060559433052007276, -0.030316120515319765, -0.11803044712825601, -0.18703522291362068, -0.23201364226697488, -0.2545634491306998, -0.2433088523545078, -0.20905882766907452, -0.15076560356440694, -0.07744248398514164, 0.18180399570625871, 0.3353756000200059, 0.4572967975103462, 0.5462727822212379, 0.60367955723639, 0.6186356092464641, 0.5939451342948506, 0.552049352881057, 0.509873815508943, 0.46872960777375244, 0.4264019106140583, 0.38488662620178754, 0.349022006660825, 0.3207403778498368, 0.2879902325607939, 0.24096941361491978, 0.18962237051922098, 0.12952054280271938, 0.05976450590513222, -0.03173700128785623, -0.12984862649055762, -0.21642155753927084, -0.29454677567208915, -0.36778663454782673, -0.42634996602308994, -0.45013897796219365, -0.43791360506930155, -0.4049186786675827, -0.35015516327211366, -0.2707499330512618, -0.18278773360639458, -0.08384121103791894, 0.013580045833252218, 0.10958312356905142, 0.19357411539666938, 0.2551139552299049, 0.2777769726063234, 0.26288917220152985, 0.2208067756602131, 0.1587706434466388, 0.083788294492041, 0.014766554552597087, -0.03918020334519484, -0.08267977359979921, -0.10397760548970557, -0.10703064298168774, -0.08583399095720354, -0.047396437891474116, 0.19138168940606698, 0.35507944601670216, 0.47863841257037015, 0.5554689451191666, 0.5924003945159432, 0.5887910639955648, 0.5502200223158475, 0.5031484301649104, 0.4573240595099787, 0.40228394909201254, 0.3473490410312335, 0.29372197701619507, 0.24609227091360242, 0.2034814965958042, 0.1612369583165495, 0.10523917665366797, 0.04636716601149941, -0.015043723940896337, -0.0870251555072626, -0.18061657762821787, -0.2934186291928526, -0.4086057925286146, -0.5198339912841634, -0.622495049012376, -0.700050816501956, -0.7352512614392661, -0.726796846504321, -0.6829005054753658, -0.6022372894473028, -0.49113391106318915, -0.3626369664257269, -0.22462411825966322, -0.08336614465448351, 0.05708843207236487, 0.19140607013723862, 0.30552985053753234, 0.386912490964356, 0.4269573142968232, 0.43279595557617984, 0.4058650298670159, 0.34900188462508336, 0.27835727029885377, 0.21211724860532763, 0.15176160849661358, 0.09733318420480992, 0.05314037658753973, 0.023094736332038852, 0.007498988158210391, 0.17583812836163584, 0.3360396144455523, 0.4538350949358762, 0.5193865522335608, 0.5417945860373335, 0.5327661501137597, 0.48382889085825503, 0.4212985947994542, 0.35092964601367493, 0.27493333550443805, 0.20355584808708724, 0.1425357477331134, 0.0860372449418654, 0.03947176345847997, -0.004956169819006546, -0.06270319943192611, -0.12589690195219333, -0.18780588102903448, -0.25802478528855105, -0.3514300417624187, -0.47492638752671, -0.6091941151977298, -0.7464190440212627, -0.8691667292464255, -0.9637998518092926, -1.0106814348576925, -1.0082425550379692, -0.9554070993021803, -0.8543256210932587, -0.7136371686220222, -0.5506721099985011, -0.37233207766599785, -0.19080653340996503, 0.0034943779287567004, 0.19244573545893875, 0.3589894636179771, 0.4983211409975754, 0.6004915299639146, 0.6667307881070876, 0.6830659113651585, 0.6490271067903823, 0.5849635942537261, 0.5120487771330253, 0.43572460542456953, 0.3550301250065946, 0.26417195557249823, 0.17446196619456023, 0.08586415460247397, 0.15018257117798983, 0.2792510525274657, 0.374084289060911, 0.42993664463513004, 0.45642049862099904, 0.4443448141788905, 0.38996229428537743, 0.30528509227532186, 0.21014902377842173, 0.11401129832444708, 0.03085989017641196, -0.0413380576385444, -0.10466518405342401, -0.1556021066327956, -0.19881066948759163, -0.25339685504799525, -0.3129429664247472, -0.3684361533779092, -0.42785231918408917, -0.5155094385535441, -0.6384236526599106, -0.7841268487273363, -0.9326824365181333, -1.068397975547547, -1.1753788903217302, -1.2296252144942528, -1.226144430724084, -1.1655741083954272, -1.0464628313301982, -0.8918517725928354, -0.707636887712714, -0.5054585739325896, -0.2806818005926449, -0.044913535774000306, 0.19106018410177047, 0.40739214251789696, 0.6035459247620085, 0.7628428493786422, 0.8864641853115703, 0.955273011731932, 0.9576697814036176, 0.9106117306001673, 0.8339430058838391, 0.7425548485327685, 0.6270044606747471, 0.4922719332220181, 0.3381799700616259, 0.17481444339074267, 0.11194729117842596, 0.1990960412123878, 0.26217385799387816, 0.3122150473686855, 0.3373273141155973, 0.3245046224801007, 0.26195200501552024, 0.1673051372838908, 0.06229908746696314, -0.03589620954960971, -0.12593165317783303, -0.2044846562795399, -0.2773082448203999, -0.3370109608867662, -0.3880462797597815, -0.44384395089150847, -0.5004346152680315, -0.5444742762318161, -0.5880158158042579, -0.6558186742752348, -0.7649283640246148, -0.9020864417368595, -1.0488140006416, -1.187886379827715, -1.3007414423272623, -1.35877471159551, -1.3469095622052278, -1.2726694089897372, -1.1459849909229471, -0.9866514258238289, -0.8001852475660505, -0.5809092244367096, -0.3374236966167475, -0.07509483795343032, 0.19171459950412595, 0.44946091718393955, 0.6896962251448772, 0.9002793869696946, 1.0678870035870132, 1.1835462519907864, 1.2340569227596725, 1.2187574655431366, 1.1491962990606057, 1.036138636246733, 0.8865037108729092, 0.7028132511870461, 0.49333200364782553, 0.2581256142151267, 0.06262909150933847, 0.105425634976917, 0.14022615045550824, 0.1744055687443419, 0.18422056460207803, 0.16223024632266866, 0.09784717639575437, 0.012283379577632732, -0.07972115370811153, -0.16614657610793168, -0.24959646311676698, -0.3265258428889544, -0.4033919449773441, -0.4723035880886168, -0.5371025601032657, -0.6013302628416842, -0.6581658587764615, -0.6964868158043459, -0.7179464815983838, -0.7589684430880158, -0.8316512245667846, -0.9414825973961901, -1.0710268826247726, -1.207156418485538, -1.3328493497411875, -1.3990392554847164, -1.3895928366571157, -1.3040016778134043, -1.1739042045021362, -1.0182458842711712, -0.8292908388589207, -0.6074960689661164, -0.35203654139689733, -0.08113022952238405, 0.20275850143299093, 0.48625117589393485, 0.759367197234017, 1.0031117669471488, 1.2050003639572375, 1.3577436203193125, 1.448063355510515, 1.4705676073027136, 1.4169406665112754, 1.2955523391657828, 1.1131603354244024, 0.8863190593310082, 0.6241089327525726, 0.3267103674327479, 0.006256809686211792, 0.006887665514686524, 0.015936106882608464, 0.024974989126881546, 0.010165496303896128, -0.026049929561107257, -0.08018331934706203, -0.14421686689257435, -0.21180144261141212, -0.2788848049623969, -0.34360777475152854, -0.4100022030267157, -0.4753096412020166, -0.5400862390089848, -0.6081002146404381, -0.6796829235761465, -0.7439792590700329, -0.7771848667257688, -0.7818150632248712, -0.7883984180991096, -0.8229551351115194, -0.8937598060123172, -1.0022626086046986, -1.144274715813054, -1.291519561390861, -1.380028995317445, -1.3771985979377794, -1.2964769260324314, -1.1689600213718128, -1.0166043075499644, -0.8287726721833891, -0.6048318830532258, -0.34548700333483967, -0.06634748337851068, 0.22137370666036388, 0.5184236424299432, 0.8105008853172087, 1.0703275977217215, 1.290856272137184, 1.4678122526427073, 1.5839703420393727, 1.6336940827551991, 1.6032473168980277, 1.4894002558514234, 1.2915840054052588, 1.0282570741239634, 0.7215347329475523, 0.37374773983369597, -0.04611269698211764, -0.0841838943942683, -0.10414089844614446, -0.12131557878217848, -0.15484327204334264, -0.1978762606869092, -0.23704042842104334, -0.27324313091858055, -0.31126622387259, -0.3503767330652874, -0.3974356568064421, -0.437480824364934, -0.47723626733524416, -0.5190413103712194, -0.5795034493992905, -0.6567276226482378, -0.7270677686131908, -0.7654837670661684, -0.7635442232944402, -0.7493452481454929, -0.7498683360676055, -0.7922593020811499, -0.8927652619339554, -1.0449244349076205, -1.2114253261296957, -1.3137159680347157, -1.3191025105786025, -1.241824029148872, -1.1203936778234276, -0.9701012445063057, -0.7866376317496636, -0.5717820953737154, -0.3298408242839978, -0.06786658985805923, 0.20960448727723777, 0.5031573999648051, 0.8027905429612098, 1.0799028741925287, 1.3074993542205877, 1.4892483473581757, 1.6194414163273252, 1.6884552653682412, 1.68041039680249, 1.5861100931565522, 1.388333402147772, 1.1084167870074892, 0.775171906973559, 0.40029604232492316, -0.08863441311744581, -0.16279229878333032, -0.21782931984678974, -0.26041142036988285, -0.30070706417199017, -0.3375898811206055, -0.34787475249309835, -0.3475057441387457, -0.34716331562924063, -0.3572148952592906, -0.37240469303398616, -0.376229864832452, -0.3770524136297628, -0.39055905769600596, -0.4429431611449406, -0.5322538074915203, -0.6193454019786568, -0.6683129690560426, -0.6743058841625161, -0.65350983654091, -0.6414874060154471, -0.6764504002989804, -0.7762511608926017, -0.9336421937811845, -1.0972327323068052, -1.2029610746718282, -1.2103008849484587, -1.1363300244194352, -1.0133362429798007, -0.8626346818558406, -0.6872895594736058, -0.4945864689891583, -0.28937237827481593, -0.0769109927338918, 0.15996816107890802, 0.4243875007365032, 0.715909222869837, 1.0013526730800524, 1.238223104232853, 1.423975237678997, 1.5595734512068689, 1.6338514846492735, 1.6409018093859449, 1.5679057875996116, 1.3904787780775365, 1.1195834693369924, 0.7838784355281385, 0.40207065216318494, -0.11391256050980689, -0.22083722430632483, -0.3148754923515477, -0.3800993517754805, -0.4218954822405733, -0.43768391611350177, -0.4187274960782016, -0.37724309548576834, -0.34076891233267265, -0.30622851977043103, -0.27030827740342944, -0.22053375195692657, -0.1759036486711414, -0.16417491604578788, -0.21564100901120872, -0.3199908553326694, -0.4265307790048843, -0.4908927361249823, -0.5125005854802792, -0.5038070545066942, -0.5059458104529388, -0.5550751925625332, -0.6592834587709193, -0.803494635978277, -0.9489378775235443, -1.0397429215087608, -1.0516909214372554, -0.9823452107515654, -0.8632289340271921, -0.7105012941322453, -0.5443866177824994, -0.38450422612763213, -0.23415737927422167, -0.08262190607363129, 0.0916389916116789, 0.3053166032144048, 0.5570134435771339, 0.8243640002832593, 1.0702069310605842, 1.276501953654289, 1.424451941890218, 1.499630820576004, 1.509888266185828, 1.4563450057360319, 1.309404839402321, 1.0654124804903737, 0.7494726507210622, 0.3804739106745015, -0.13095320323527124, -0.26586573078680675, -0.38942886159953244, -0.4749413278478461, -0.5144996648817562, -0.5163314023125128, -0.472468675324584, -0.39716963147971646, -0.3089037418312681, -0.21010023445031922, -0.10732074875230574, 0.0016646372183743727, 0.0832168092174528, 0.1140685527324503, 0.06702012346463032, -0.04187772086888994, -0.1574766895995178, -0.23828498842713675, -0.2744926019297721, -0.29168678192498676, -0.32733141203829963, -0.414357257635481, -0.5339899563093459, -0.6696723195006501, -0.7882162097265025, -0.861957059868012, -0.8626604398828284, -0.789263923549425, -0.6624683030913421, -0.5065960211004451, -0.3502491207421033, -0.2282304318737669, -0.14691296639448778, -0.07380640867497906, 0.02764140766853336, 0.1780186939687265, 0.3735987952793502, 0.5955023727924247, 0.8305353175127659, 1.0523094272439788, 1.2297264821305256, 1.3161307305029895, 1.3228822749332967, 1.2827063859122205, 1.1694994444705458, 0.964215610982079, 0.6774175352525146, 0.34278022753386855, -0.14693438029472647, -0.3047861133738109, -0.45263778767587354, -0.5537960640981086, -0.586539641731806, -0.5740804196131117, -0.5067104603193939, -0.3927871028404099, -0.24097364630956655, -0.07872414387967253, 0.07649975424166557, 0.21293735507948125, 0.31455829073914465, 0.3699281698470901, 0.35458633564076114, 0.2716614524563718, 0.1687310756045939, 0.0910014021461428, 0.03818989357358866, -0.007767682653063518, -0.09400577233351323, -0.2205463842272729, -0.3707747135301651, -0.5161074881554951, -0.6260011418118105, -0.6791414792367301, -0.6588964503950696, -0.5680807005650873, -0.4248758928383708, -0.25665185986157363, -0.1100762060281667, -0.02275535333988934, -0.009237626586833511, -0.025583683863646085, -0.015951642305532532, 0.061137075195331535, 0.18865562594075042, 0.3601068552161942, 0.5691410855713576, 0.7839734847965181, 0.9754259917974375, 1.0864786907568753, 1.11047684304396, 1.0844238387406981, 1.0047336170826542, 0.8408772078305008, 0.5948245570353148, 0.2998883752072333, -0.16218772809902862, -0.34086800510136384, -0.5117789134625885, -0.6166672373658181, -0.6381708796034529, -0.6041990161914601, -0.5117815276367466, -0.35887479462861793, -0.15947434559532644, 0.04844371504615933, 0.2298658199499956, 0.3800276296282338, 0.4978304924038461, 0.5924166287070709, 0.6332369514602048, 0.6093580491497027, 0.5489671423325514, 0.47454419346784105, 0.40755707863732477, 0.3264212045494618, 0.2031922901637229, 0.03436082754523538, -0.15567624904498012, -0.33055662216021736, -0.45688520263941296, -0.5107791357857773, -0.4681615980585402, -0.35459214997224753, -0.19375062183253655, -0.025222046013616172, 0.1070438306507097, 0.16830762425851342, 0.13781088540042769, 0.04331043920343075, -0.04134403656671803, -0.045400106248615756, 0.02523013162324585, 0.14874282909245667, 0.3264932408112487, 0.5237153882519998, 0.7114085611486676, 0.8423808115056121, 0.8906708155844902, 0.8838566990019371, 0.8285633043663838, 0.7027207925806527, 0.4999725132882825, 0.2533530078003089, -0.17749625045083958, -0.3746102811734083, -0.5558924355778984, -0.6550044161799342, -0.6577043323105597, -0.5976800853486612, -0.48229766353768544, -0.30551127858386673, -0.07769923295117441, 0.15075240446250915, 0.35113218704031857, 0.5089590752217819, 0.6544872507476003, 0.7880724614593175, 0.8870377091061584, 0.929758133113511, 0.9080262273639447, 0.8533107750271036, 0.7759174650163303, 0.6705983188075004, 0.525366673048694, 0.3235223165075691, 0.0854382738994829, -0.15903604278466846, -0.34906523746157725, -0.42380245523873117, -0.36664695874884307, -0.21948649251936458, -0.041812959011854965, 0.12226885481866234, 0.23938406586548652, 0.27275643814655076, 0.21535340683981813, 0.07248521059098119, -0.08588417299248716, -0.16153861033106118, -0.13518775952542092, -0.03145412572393339, 0.12945892439145915, 0.31129939313786104, 0.4901782366427916, 0.6271425935179669, 0.6968013550347846, 0.7043253340312591, 0.6666980505381702, 0.5655140150875718, 0.4089943244415346, 0.2078111275604696, -0.1813442141435629, -0.3810824711921313, -0.5589379133324444, -0.6429203987587604, -0.6222776626479727, -0.5334788083317991, -0.3988506936139835, -0.21469479652908202, 0.008750216393471628, 0.23523325673768614, 0.434804578406127, 0.6086264603946616, 0.7770036136209204, 0.9485463226692152, 1.0919169269364204, 1.17274412359097, 1.182577712998124, 1.139063693914226, 1.0571602149343657, 0.9494076937468057, 0.8025021420000793, 0.5946034716167632, 0.3013683105406244, -0.040381977512710644, -0.34262848487114467, -0.4826157776878685, -0.42930843333983393, -0.25057396535271426, -0.04862203110138136, 0.11949787821465209, 0.22472535978044125, 0.2502105344061118, 0.18088355863498135, 0.025850200893159852, -0.16445262428727833, -0.2771164110383197, -0.26986257258246327, -0.16949654482530815, -0.0062409742362815376, 0.16851199797507818, 0.3338126263771919, 0.46789977525036186, 0.5429121044577574, 0.5618461856704041, 0.5333958817203287, 0.46082893865175706, 0.33645911253810834, 0.17471504466426055, -0.1741503003150904, -0.3595306182318709, -0.5105887048747363, -0.5673238161695223, -0.517510419738936, -0.40278271677306815, -0.24556555101473718, -0.06485926381395461, 0.1354704219080856, 0.3288638314826226, 0.503285465678117, 0.6698249337127651, 0.8522764316060704, 1.0466287565853862, 1.2056270527869581, 1.294991033569081, 1.3096557980102448, 1.2642287830900107, 1.1811830045504625, 1.0793839000518533, 0.9571472718560946, 0.759780952905249, 0.44542715399991273, 0.028085602664954724, -0.368891415861498, -0.5967973820365011, -0.5941354798917142, -0.4293948253050756, -0.20645070045450764, -0.017601162135277328, 0.09350735008883451, 0.10470322027167131, 0.03822402354949876, -0.09693728226309976, -0.26457687420636045, -0.3751407001083053, -0.36561657795311947, -0.24970617363183092, -0.07887023227911087, 0.0949174372857225, 0.245985352098296, 0.3678987977915215, 0.441479504157906, 0.4583257717450095, 0.43705212634268126, 0.3809611443142306, 0.2837821818324145, 0.15092464851762896, -0.16631055942458672, -0.32346119602921836, -0.43361473628833336, -0.4496374306166554, -0.3738921110173581, -0.23591331442055705, -0.05787599812056085, 0.12668901884685052, 0.30075748936481494, 0.44649480105497563, 0.5635298898290064, 0.6879540177095066, 0.8534284422372995, 1.0387362328631604, 1.1889861845494283, 1.266324752796728, 1.2673180006655298, 1.2220440866633988, 1.1415174425162418, 1.0519299075208028, 0.9510246986177702, 0.7955713886929956, 0.4996662959004496, 0.08603048778736477, -0.33891726990545257, -0.6183451258118853, -0.6879750081018988, -0.5719496140742, -0.36133938930605586, -0.15800454281626578, -0.04710085977503467, -0.06144719631014698, -0.15049317171217158, -0.2562384240690186, -0.36675288854213633, -0.43564993907851574, -0.4062930149189377, -0.282117477731223, -0.10315706530450972, 0.07208611428148219, 0.21164279861310348, 0.31673365587846297, 0.37596230895263955, 0.3879091945134208, 0.3670390100617659, 0.31937536129123506, 0.2411438814653476, 0.12955674244825502, -0.1642145831397098, -0.2952987890122221, -0.3621267292790378, -0.33702712566000775, -0.2381512067189537, -0.07634456083953625, 0.11809474404773734, 0.3091603313288943, 0.45774220728251613, 0.549741546571823, 0.5938736550829425, 0.6499884592121185, 0.7655873115476739, 0.9181961310052378, 1.045312771230713, 1.1054946673539798, 1.1033000209069377, 1.0577090373893792, 0.9779113759386929, 0.8842266045179551, 0.8126809648948864, 0.7086086173122074, 0.48572569019146006, 0.12370599183825148, -0.26542354703800175, -0.5462917970298481, -0.6617737281053891, -0.6032345272601354, -0.4207926613016309, -0.21604247519817485, -0.09571499856848839, -0.15595919230659638, -0.28174318328395614, -0.3837917148533525, -0.43637572841495065, -0.44842891338641516, -0.39268466145313924, -0.26246246786793564, -0.09004106649282989, 0.07976109328461185, 0.20489438544477404, 0.2913570903629842, 0.33798739334186084, 0.34058322223773346, 0.3160411310203534, 0.2709375389362586, 0.20258362182436132, 0.1063595073082378, -0.167177972627237, -0.2786185604830178, -0.3078870860574945, -0.25159684924515363, -0.12778189413307584, 0.05186607776643041, 0.25894844513304494, 0.44558716446014335, 0.567751581617628, 0.6067651748754529, 0.586511386347319, 0.5736483277985442, 0.6302917034851486, 0.7364297459978796, 0.8312213951533062, 0.8767387571705252, 0.8748821593557445, 0.82559199876804, 0.7236706082646276, 0.6190497585749521, 0.5630088967160708, 0.5271099557533981, 0.39648329951990413, 0.13416688414351813, -0.17674773331680665, -0.41912704867863443, -0.5541604594790958, -0.5437178738140557, -0.3959377092203178, -0.17225991432324878, -0.018457267437171826, -0.10733741224696071, -0.28180226766169103, -0.3967735803674335, -0.4265008433542395, -0.40279546290457546, -0.33120699764087785, -0.20765243742428982, -0.048011755981169184, 0.10382319858629831, 0.21434585453268665, 0.27814141636066075, 0.3038569176404753, 0.29363876998605903, 0.26547190205155774, 0.22113742297688357, 0.15450556760577477, 0.0770548686822782, -0.17251543758791424, -0.27376909288629864, -0.27904603521852717, -0.19308446062365786, -0.04125814198130087, 0.15831081673807712, 0.3714377921859073, 0.5470702817650958, 0.6388744119951044, 0.6390177297945944, 0.5720945413934854, 0.5124286369586363, 0.5150163241073817, 0.5708591258370144, 0.6302962337983125, 0.6606966696042311, 0.6547655980767221, 0.5865840376989109, 0.4522920550295183, 0.318507495999105, 0.26328588089745514, 0.2798038511920756, 0.23965680907241405, 0.09808348379172548, -0.0993181214954983, -0.280501874597009, -0.41816058061028816, -0.447096251652906, -0.316030899093689, -0.06911500599170817, 0.12797961517289255, 0.04762152865646983, -0.1620934544256933, -0.3035780694367318, -0.3391750612653625, -0.3107992584957267, -0.24326230481399974, -0.13804637915221005, -0.00532876633444655, 0.1258887562131744, 0.21420803703978378, 0.2562091109409612, 0.2557293042800307, 0.22878236787308212, 0.19197945121194365, 0.1496055096639474, 0.09231547364158103, 0.04187654120254321, -0.1763824036925592, -0.27811327871368197, -0.2746359683243905, -0.17305808909392645, 0.005400150641388687, 0.22648489570320204, 0.44858441167815494, 0.6162746585617599, 0.6878349512178021, 0.6654268621104316, 0.5853865583934642, 0.5052466532058263, 0.47852635550116657, 0.4989306866678916, 0.5216285518771905, 0.5282190970762355, 0.5015688754671326, 0.41729915327317274, 0.26517362653427207, 0.10575977398385243, 0.031002520603028452, 0.03914460028134336, 0.06428153343073523, 0.03431501213910292, -0.055363039811380535, -0.16704232598969748, -0.28926815965107644, -0.3435373960637647, -0.22907675325657353, 0.0031729443565523545, 0.2192796850008565, 0.15461013100328846, -0.04103788037757799, -0.19001290180828484, -0.23408611206640617, -0.21352814224481498, -0.16453100593506667, -0.08516941188983058, 0.017384131952858657, 0.11898855605429962, 0.18678344409234846, 0.20648085372962197, 0.17815751879479977, 0.13051280056350223, 0.08664653091004745, 0.053059359330086014, 0.022668822481077065, 0.00026127529553776645, -0.17710454955961585, -0.28566059033725644, -0.2965043501608718, -0.19768219910624707, -0.013213249263036854, 0.2214971228637823, 0.45087601363639906, 0.6207751548194562, 0.6924132658594804, 0.6790043657780517, 0.619516938739447, 0.5577248655919861, 0.5333618272550584, 0.5397631378581973, 0.540429983778749, 0.5216940932485202, 0.48584288982272084, 0.40130181277091775, 0.2410541217737512, 0.062465427969513126, -0.0658584663754875, -0.08942160414769264, -0.05046397795244859, 0.00021612848423043784, 0.002571972669474966, -0.046033910387376746, -0.1469737895458, -0.2184233728574255, -0.16234266562540178, 0.0030292696058701893, 0.1549722244222444, 0.1304924655957342, -0.017003652456579824, -0.1309983978932557, -0.16701729658551104, -0.1541817906042051, -0.11878777307271546, -0.06486273301890898, 0.0066730568239624045, 0.0756788144954429, 0.1192193400026686, 0.1148378148199019, 0.06521861221063979, 0.0032577750150209342, -0.045132813047913216, -0.06259989597189759, -0.06279805817265889, -0.043450446968659046, -0.17555444374367554, -0.29345036833227994, -0.3243335803797373, -0.2543197809050648, -0.08823661011514629, 0.13230436562017905, 0.35728695019896994, 0.5350947664616025, 0.6339969008541747, 0.6655509703547597, 0.6524992103453103, 0.6328001984817527, 0.6315726823027494, 0.6528340294967574, 0.6518489190167241, 0.6232467354751543, 0.5806366927105556, 0.501737988390518, 0.3544561017848552, 0.15326801260585718, -0.014995510316090926, -0.09423427164877052, -0.06850217500046556, -4.985253549362417e-5, 0.058211629453048676, 0.06425950970925388, -0.01457644598625731, -0.10986830976928393, -0.12103824867887528, -0.055848125427742756, 0.028905517227021976, -0.0012318882918323842, -0.09012049302991172, -0.1577341896463987, -0.16656528698652504, -0.14821284749437869, -0.12553571309902586, -0.08392254757284612, -0.03437821074099081, 0.003766362468964317, 0.01973009201217804, -0.005400489024614269, -0.06820747887715456, -0.14230358691165249, -0.1922945714183446, -0.19686882379625514, -0.1684898305316568, -0.10166093374947043, -0.17599026958929578, -0.301044654107671, -0.35171894689556515, -0.3152577746984713, -0.1952767821934044, -0.020148138522858915, 0.18058248519216735, 0.36652639755960076, 0.5090703355230741, 0.601781132632967, 0.6509164373055428, 0.6845314875340238, 0.7298464223090501, 0.7825639038929226, 0.8084524095377537, 0.7833427137215643, 0.7397489197628098, 0.6607739351566453, 0.5100020428954393, 0.30951267249316944, 0.10814054820781399, -0.006642051360630427, -0.023139252658146117, 0.035044145670019074, 0.08645458618065925, 0.09307550919552264, 0.03327565389116637, -0.0656207950819654, -0.12172644825970848, -0.1262078337887649, -0.1240491549345235, -0.16093220886595455, -0.21384504947124186, -0.22994868314949451, -0.21600049751358633, -0.19885642331681933, -0.17122825772478573, -0.13190847450802043, -0.09215126711410215, -0.07674751884996758, -0.0882349541308526, -0.13462454376695002, -0.2093378858031575, -0.29106813868638975, -0.34534481236544373, -0.3415000931558716, -0.28620024163975333, -0.1682682776396766, -0.18856695756345163, -0.3317150827027376, -0.4027071407631045, -0.4036690210758827, -0.3378193654535251, -0.21488091312908839, -0.05009415760655965, 0.1386928956910513, 0.32212353065688876, 0.4752284105327902, 0.5932672368774676, 0.6897056167845316, 0.7917771584035421, 0.901116312441563, 0.9623208440158172, 0.9581992614407828, 0.9018846727821931, 0.8089342879175332, 0.6503667106945125, 0.4322085645082133, 0.21548425812242802, 0.0530854493137023, 0.00012019188419301515, 0.022401461040830607, 0.04012152753119962, 0.028021905090144097, -0.03764170635855812, -0.12562498845393683, -0.19050646053799572, -0.23454281841887772, -0.27215090303618905, -0.31924522693139284, -0.3473014491213765, -0.33768808549970636, -0.31683773163465295, -0.2892753881605561, -0.255077828934904, -0.19974953438134382, -0.15790978610206366, -0.15803217577655782, -0.20248621539238326, -0.2694325996248199, -0.3562006612481678, -0.443566700337632, -0.4973612152372444, -0.48663046980598434, -0.398013888561461, -0.23389202866007738, -0.22226236204479602, -0.40492769074463186, -0.5193903822091543, -0.5618740217808286, -0.5428493877302035, -0.4603690107919768, -0.3210591494941683, -0.13417494430811255, 0.08148177911146687, 0.29598181854036537, 0.48733383391763985, 0.6562490854249436, 0.816246596022817, 0.9719306078168765, 1.081671727065076, 1.1030033312621794, 1.0448501160422379, 0.9322832172730301, 0.7637246474426009, 0.5408762857346135, 0.2935387746566089, 0.08761097031672349, -0.03576595272514752, -0.07702893609981476, -0.09752557104705822, -0.1371272602242372, -0.19703055927746418, -0.2625449424682667, -0.31691543591261556, -0.37451336521771683, -0.43266999185031035, -0.4812945983545509, -0.49009609287714506, -0.45819423250115454, -0.41938448387641564, -0.38697854231598766, -0.33586401484695844, -0.2644894670865952, -0.22346917017001486, -0.24763101149233133, -0.317088352288528, -0.40600116450186946, -0.5015405364230124, -0.5944757520515866, -0.6436860879155925, -0.6134635555774834, -0.49725717115853085, -0.2857813123521443, -0.27600186899233053, -0.5200104554782353, -0.6994462502643619, -0.799283111191443, -0.8233907729857255, -0.7660512489750466, -0.6386978724310847, -0.4492380198113058, -0.20578362196113129, 0.07198193857058903, 0.34977198682028093, 0.5975488912318367, 0.8114593378579993, 1.0023145121778096, 1.1392930579431921, 1.1851334075541657, 1.1304004829735526, 1.0103348130795233, 0.8351051072935912, 0.6156541531427827, 0.35676084027151245, 0.09810198966474314, -0.11041531826349596, -0.2308695010604671, -0.3070997670512631, -0.3619142642085626, -0.4186022040764963, -0.46053909955592054, -0.5042830580561666, -0.5548559004840554, -0.6122475779994908, -0.6409986198694049, -0.6126530970101338, -0.5466492688764872, -0.48628123020290065, -0.43124220346111736, -0.36475907141353225, -0.295578425956231, -0.2736328046664574, -0.31659096123681674, -0.4085686349930618, -0.519217627682192, -0.6289085041565664, -0.7259832299544746, -0.7670013696336763, -0.7116702316466743, -0.5607365228393105, -0.3149586399010158, -0.3385864367258205, -0.654561378776824, -0.9053415449320026, -1.0708298549280724, -1.1325168677008768, -1.0969617024186724, -0.9741952408386299, -0.7790651642382258, -0.5062335062820525, -0.1657235877575579, 0.19605438400777123, 0.5280584787916647, 0.792219148068495, 0.9981237484923585, 1.1438426107332857, 1.2011460976274961, 1.1571644536194456, 1.0317533617599208, 0.8487210865336485, 0.6190030798579799, 0.3485926282405452, 0.05473627491654255, -0.21311850483327305, -0.40377296978738586, -0.5175810223678649, -0.5920422624482323, -0.6484957916247791, -0.6956213974162784, -0.7295517189516798, -0.7656352879293649, -0.7851815368287436, -0.7636817207667489, -0.6810942160459815, -0.5736384946645339, -0.47750815026687915, -0.4011002867376868, -0.3303976396359341, -0.27809674919073585, -0.28370685397423445, -0.35216068856349586, -0.4627425914181778, -0.5898256086892196, -0.7185656742754739, -0.8286581420662519, -0.8599971006698214, -0.7792276250368082, -0.6029613335357727, -0.3336727523792887, -0.4050656929486114, -0.7865909440595411, -1.1025632130758056, -1.3191373101350925, -1.4197622402790266, -1.3989880246916975, -1.2812375543589778, -1.0740163945840864, -0.7718819904604038, -0.3836382288875941, 0.050367702546549965, 0.4531897157691413, 0.7736569679329849, 0.9894569186966314, 1.1210184574157158, 1.176212881328367, 1.1317710338703408, 1.002195046215682, 0.8028843497743177, 0.5502493679965105, 0.25906916037460426, -0.049686264797862534, -0.3458762250744041, -0.5743417557558139, -0.7221758760376441, -0.8167522581478679, -0.8933531612269648, -0.9385792252230929, -0.9613655976492494, -0.9543511735171496, -0.9078567641615041, -0.8207336713162959, -0.6887876993737493, -0.5409889190608956, -0.4151235834403931, -0.32138304607472606, -0.24953865545199094, -0.22219019989853156, -0.25667283326623674, -0.3451787790480876, -0.47424231925630855, -0.6152045132868325, -0.7661640316423655, -0.8857875586102282, -0.91109958061691, -0.8238916129935164, -0.6254355290928952, -0.3409792754834734, -0.47212520580305734, -0.9117016853448112, -1.2725492951715982, -1.5213632850232066, -1.6450327398570432, -1.6448212069788217, -1.526097102622489, -1.3040542953220753, -0.9794700018784047, -0.556048313996335, -0.08329923134464001, 0.37082277047790013, 0.7333104125093534, 0.9778282190110656, 1.1074740977252913, 1.1471047263467935, 1.0920027623268982, 0.9421857990200956, 0.7148567972356521, 0.4323779972011089, 0.12192979507070367, -0.19399075344875638, -0.49094384171040534, -0.7337782127863348, -0.9009913816130505, -1.019935745964316, -1.107985899995898, -1.1486219154641453, -1.1412444709965828, -1.0778599815114907, -0.9724885918837876, -0.835804048779104, -0.6624101897797562, -0.4809600839046312, -0.3280306772713964, -0.2106750864664607, -0.14170701347041798, -0.13028230431112445, -0.18922474588514623, -0.3058475474707306, -0.45460997969900546, -0.6152801133777647, -0.7756906213745987, -0.9014726129149401, -0.922820111137736, -0.8253907298476235, -0.6208420450435279, -0.3322674606468102, -0.5360089593246715, -1.0203015947119283, -1.4062062472041261, -1.667462000567508, -1.809086998537869, -1.824303035162652, -1.7096336020498026, -1.4685710870551592, -1.119565140194265, -0.6770413904099972, -0.18837890103509503, 0.28042803669632643, 0.6712827954812071, 0.9417759867130752, 1.0878257144006993, 1.1204958271191783, 1.0533401865862266, 0.8825656281813112, 0.6237812249108122, 0.31390881699523915, -0.02246268437100991, -0.34310654434408333, -0.6354558275982345, -0.8703280117364257, -1.0417782820911436, -1.1637268284795976, -1.245029760231677, -1.270771577460404, -1.227910784737499, -1.1261956553542813, -0.9822424374608799, -0.8085691365794331, -0.6090980683468856, -0.40687927706557653, -0.2285079520993625, -0.09587145435216035, -0.019374233049240165, -0.01890368216967916, -0.09773140188214799, -0.24568666891366023, -0.41909503203580417, -0.5909637771385634, -0.7557227563918842, -0.8735961173569337, -0.8851843145167172, -0.784042383232982, -0.5809650016832808, -0.3065047656300648, -0.5825777895377495, -1.0966391540947438, -1.4915019075108047, -1.7631266233563785, -1.9166923531182936, -1.9479152738468417, -1.8353798552276066, -1.5822509994195881, -1.2123758395639546, -0.7548858013995089, -0.2628955336892327, 0.21116683555311794, 0.6109466103118951, 0.8996814004290639, 1.051805361226457, 1.078097693239406, 0.999614658446332, 0.8171051807373585, 0.5412822493691847, 0.21419171327616648, -0.13315411884151035, -0.46155173950165235, -0.7476466106844188, -0.9767013149587906, -1.133832008804661, -1.235278094980641, -1.2913676769037015, -1.2856156264890946, -1.21426758526863, -1.08775129680508, -0.9250709284937733, -0.7363824827701329, -0.52660172051505, -0.31129582265664013, -0.1242860645338795, 0.01959096979248479, 0.09765963835718973, 0.09230440364190283, -0.005573318548090555, -0.17108837840368582, -0.35837223327021117, -0.5403580789807158, -0.6989375576073639, -0.7968552398530463, -0.800842180799855, -0.7053910374302493, -0.5202205660971546, -0.27090104289049927, -0.5996249002830634, -1.1249134028636711, -1.53267499199902, -1.8178444760980008, -1.9839874602170688, -2.019990349378569, -1.9046206920950837, -1.6444244557742562, -1.2622204524393712, -0.7999697023754, -0.3033834294865398, 0.16710158234743555, 0.565844824661129, 0.8547502903143265, 1.0035184105605255, 1.0175024778240815, 0.930555820391912, 0.7438151207505407, 0.4659072665672599, 0.13503343455284997, -0.20883615965242455, -0.5325490056876199, -0.8088581216654589, -1.0242623810671143, -1.162146806627543, -1.2334558322409104, -1.2476070647511288, -1.208808068251004, -1.1135619749954353, -0.9742480766078693, -0.8063034017164921, -0.6132439994046762, -0.4048470010116835, -0.19283174675611725, -0.012226254178515607, 0.11659783598610621, 0.17817256274273424, 0.16379345192693837, 0.06379823898769746, -0.09661300457041593, -0.2833467389086364, -0.4546946678474643, -0.592830256669663, -0.6761688932433504, -0.6810901159625986, -0.605018023524647, -0.45091584031678483, -0.24013083301968668, -0.5934611306524482, -1.1172001642237765, -1.5366067079649528, -1.8365102953101193, -2.0074607438001633, -2.035991976761246, -1.9139969923653175, -1.6489459770926267, -1.2657376987767388, -0.804562915543385, -0.3214258999967482, 0.13282202483779212, 0.50931447445524, 0.7809229131241189, 0.9158103464930183, 0.9233476886245888, 0.8392346265715604, 0.6673222834926577, 0.4036106335516497, 0.08432568933055178, -0.2447545203876648, -0.547883281213091, -0.8074766177385957, -1.0050768132432806, -1.1229470740783978, -1.1597750509810507, -1.1403083958777935, -1.0691355980724544, -0.9578817924909601, -0.8129331332028973, -0.6455946594418741, -0.4559487469823716, -0.2527588677016788, -0.06281131329220216, 0.09102068127236247, 0.18333949707906624, 0.21581242543610926, 0.19399604191462733, 0.10314229185047247, -0.0386774572953272, -0.20464645419239472, -0.3551580496304754, -0.4719479486918273, -0.5476799333439631, -0.5655213232002416, -0.5116272648436418, -0.3876357302990287, -0.20666024683383463, -0.5739264296346087, -1.0917227387179578, -1.513245406289182, -1.8183885108950042, -1.9844989628570775, -1.9971126185434034, -1.8608708450313103, -1.5933069765051735, -1.222492378704314, -0.7833674354717938, -0.3271288215212179, 0.09178383800828176, 0.42492344871214377, 0.6604009912678178, 0.781833767859798, 0.7927051306993563, 0.7192780067573585, 0.5691088012965972, 0.339534617250074, 0.05165009804483147, -0.24672482562594436, -0.5216523813982835, -0.7570523589345084, -0.9309961238394748, -1.025248128235963, -1.0392470027880156, -0.9919120920317879, -0.902436595223867, -0.7798424010628555, -0.6347659990649016, -0.4732303610036366, -0.29455854743768944, -0.11866961548277231, 0.040966511568956386, 0.15636166578356944, 0.21731675580000243, 0.233907274867937, 0.20607222895138116, 0.12926016813408467, 0.009313326331844148, -0.12752051033393286, -0.261665648703467, -0.37182508046539486, -0.4478891481755003, -0.4684677039099383, -0.42311177299828256, -0.3249083969216599, -0.17783636868266006, -0.5498561798708583, -1.0459715684235757, -1.4522603227477395, -1.7436489812758618, -1.897545163621981, -1.8944819594834956, -1.7490750492076468, -1.4856858584071546, -1.1377974719217905, -0.7367704385107445, -0.3245888806528243, 0.04688526121718156, 0.33110414739749977, 0.5189324004754322, 0.6211583241437971, 0.6378753225084036, 0.5816843698527283, 0.4568260364502811, 0.2624503625172662, 0.01918651520433559, -0.23506894708658932, -0.4745457938786641, -0.6712581802710404, -0.8093469303249844, -0.8733713660280729, -0.8691999501486128, -0.8108354409751809, -0.7115140438167512, -0.5828473413589287, -0.43872017139162134, -0.2902405942426522, -0.14639158352613366, -0.009704236312615312, 0.1029678721162146, 0.18599286118062702, 0.23146531144037058, 0.23929924786475174, 0.2101269437847838, 0.14456508550810498, 0.0514699096168032, -0.06732501915442636, -0.19288188942908777, -0.30223023458983567, -0.37502845657306605, -0.38897822784782027, -0.34698892648298846, -0.26518269544681655, -0.14641297623106916, -0.5162312054010522, -0.9752253935923324, -1.3463655567360264, -1.6077550362729969, -1.7396360314071606, -1.7305709774415758, -1.58948403510194, -1.3478817692328644, -1.0297440858386386, -0.6705849377781729, -0.30608845392743317, 0.016720714142964527, 0.2492225884058591, 0.39406443426443555, 0.4690116889423901, 0.48308487737107064, 0.442825502473051, 0.34255067798751465, 0.18412698054814294, -0.013045799752490055, -0.21711542843345966, -0.4082657565663611, -0.5566796170327476, -0.647150757706327, -0.6726592371357175, -0.6501048129006739, -0.5873985940366864, -0.4917463825750325, -0.3622041049241115, -0.2258392463559697, -0.10623070925169045, -0.005326664601170228, 0.07851868339165703, 0.14877258545026, 0.2013936690699942, 0.2349347332976951, 0.23310023429910695, 0.20342675326353724, 0.14579782667094643, 0.06471620868061385, -0.03883981871834577, -0.15804826478830664, -0.2600063591486504, -0.3192314342491291, -0.3256399427854821, -0.2860673239659358, -0.21310229982655515, -0.11006176839327216, -0.4717682515461606, -0.880117478925014, -1.2009910912679385, -1.4212964742150487, -1.5322184816083195, -1.5221247078196778, -1.4027941264601502, -1.1949232242544297, -0.917172786969069, -0.601095155053151, -0.2857876312932723, -0.016926457152367104, 0.17403867192962225, 0.2886525342239058, 0.34897005911071566, 0.35318062718686916, 0.3196871150365762, 0.24034350673886415, 0.11302302070713481, -0.03617241912977848, -0.18796705278174855, -0.3255204418109398, -0.4245380612497759, -0.4674524098806147, -0.45549468328608206, -0.4091523271883019, -0.34794497212615166, -0.2553325210515786, -0.1433555449465668, -0.027432558532365828, 0.06136502536542013, 0.12006110709508513, 0.16158576023947488, 0.19537602019402506, 0.22511634335630074, 0.2390189089905508, 0.22104487457477356, 0.18420599036168425, 0.12268186861465254, 0.0457725357853985, -0.05031182479382978, -0.151823424298291, -0.23291300699208867, -0.27707758593625526, -0.2760266106222566, -0.23862803271239486, -0.17109532336363628, -0.0864545448843957, -0.41572519668657604, -0.7644110569427902, -1.0253468806275252, -1.208076137682003, -1.3017577462010028, -1.2923306394000165, -1.1917395633027283, -1.0214670150752223, -0.7925657331167881, -0.5310673866326155, -0.2742554261461134, -0.058027637434993326, 0.09154309558787975, 0.19310346484518442, 0.2495437685479825, 0.2554010527250047, 0.22263791790008577, 0.1531668514916027, 0.05774854862519238, -0.04968812086227675, -0.15168086739690373, -0.23913615004085342, -0.29475130498981655, -0.2989124018401699, -0.25903607769219744, -0.19578183795544257, -0.1318474300594793, -0.05242744680060102, 0.037010882062437425, 0.12173606600570087, 0.18177072290983076, 0.21325215563101882, 0.2276477778977881, 0.23646146275340182, 0.24334436580537896, 0.2381795894390473, 0.20897759764151377, 0.15643472284373952, 0.0946212713604856, 0.018589902158117386, -0.06773626907231901, -0.1489254800201917, -0.2084285305475336, -0.2350990955224817, -0.2364839515983818, -0.20466293888891232, -0.14895193322278819, -0.07574073882734017, -0.34885507330110754, -0.6361515149102411, -0.842872264572015, -0.9868196647603057, -1.0631231731846507, -1.0545278052191842, -0.9670672592687616, -0.8294010293475653, -0.6555867095951814, -0.460365685199732, -0.2647255650612015, -0.10321496341373795, 0.01637947461231588, 0.10121524267704653, 0.16005047765941127, 0.1714076520846432, 0.1477013660705013, 0.0943596615490033, 0.020734406328424725, -0.05579969689189488, -0.12070784395577515, -0.16745784729735883, -0.18551394295714094, -0.1702079372231324, -0.11561247770947308, -0.048328799028785854, 0.015556301699855682, 0.08154458976399742, 0.14941669481339012, 0.20784310833526265, 0.2433561115533531, 0.25673207576478074, 0.25836141701823984, 0.2538444403932926, 0.24739715297120388, 0.2256305738537753, 0.18585617510124794, 0.13443880770927258, 0.07242939218832897, 0.004220257943830041, -0.06657780874051443, -0.12895586427861777, -0.17293817793558175, -0.1958531439562277, -0.19375204569623156, -0.1747149745138625, -0.1283195805947469, -0.06746526584836486, -0.2723362400875412, -0.4916803846365702, -0.6499860233396502, -0.7578522909412776, -0.8189063496252577, -0.8115037364714549, -0.7381401626122247, -0.6333247459751614, -0.5085684092588755, -0.37153232140981124, -0.23451707454043488, -0.11673404367275987, -0.028419975401120942, 0.040343063004195504, 0.08489746281835213, 0.09790552628849637, 0.08803992701083482, 0.0516155385860982, -0.0009313280590232383, -0.05890070433904851, -0.09801847793913512, -0.11296241128028535, -0.10534855237521645, -0.07808700663296453, -0.02710566265826307, 0.03162830553054394, 0.09057759449398037, 0.14517292280438213, 0.19469224927400028, 0.22927059524102789, 0.24756727519596106, 0.2500784914962671, 0.24937685104555127, 0.24020513388815765, 0.22810110191053187, 0.197126061928327, 0.15424026655291007, 0.10690270194628207, 0.056787884951718645, 0.0071340454708454125, -0.047256991652640336, -0.09782819202522348, -0.1286412660178598, -0.14145644147236147, -0.142503715750873, -0.12412054711250264, -0.08932048653904995, -0.043959318936336755, -0.18652833354359594, -0.33564518984410974, -0.4410533292039219, -0.5155002202627879, -0.559332801632688, -0.5576262867465142, -0.5094754145936261, -0.4353582649701121, -0.3518260013920193, -0.2617588011071894, -0.17151278462725775, -0.0948683375200746, -0.03320362039781481, 0.010044351773012956, 0.037492118525599576, 0.045308483127565524, 0.042734841437939715, 0.02350285598394558, -0.011299159307511316, -0.0484902737199285, -0.07229262758017266, -0.06802588304966316, -0.04745337541395986, -0.02124897988034187, 0.016328451471487735, 0.05838530079197482, 0.10416570537714885, 0.14366410372170552, 0.1759158896455353, 0.19940201388834428, 0.20561887038292728, 0.20229212816620323, 0.20021784769191148, 0.193714152888333, 0.17484548040788114, 0.14599341852972675, 0.11214950410966207, 0.07556893395282002, 0.04015837779959928, 0.008437196292491145, -0.02691495926182478, -0.06292638713138506, -0.07964232359293165, -0.08496226665455742, -0.07820589795128463, -0.06322704006487895, -0.038388041421920586, -0.017131741706671755, -0.09633334359969012, -0.17248602496506737, -0.22507316266653865, -0.2620181151533269, -0.28627176432926754, -0.2870223609774568, -0.2663202762075646, -0.22552555001773597, -0.18218516992765252, -0.1358280457252414, -0.09027772842769569, -0.052578538823678043, -0.02165387151006207, 0.0021795520641346195, 0.01157535854099029, 0.014575329196844832, 0.015145843423957264, 0.00676475883505399, -0.009778204887542705, -0.02770962420468294, -0.03561932159412595, -0.027413213974959737, -0.013905510870477755, 0.0029244990344433216, 0.01944412054976234, 0.04055126022909493, 0.0632678898864421, 0.08549213248744754, 0.10213374106302106, 0.11361771867355056, 0.11793575626625748, 0.11667779933313102, 0.1132875042280622, 0.10638456117515684, 0.09530927436126897, 0.07788660841182345, 0.059849004525654795, 0.03861848147391409, 0.022784882653219932, 0.0033962343847705185, -0.01445132636686889, -0.02928621156712609, -0.03894745124826323, -0.036512578952907014, -0.031143470518924486, -0.022975729822685087, -0.012934505232451337, -0.003232490470703261, 5.637202319545611, 0.09433679382731441, 0.1915477881171562, 0.29231895898261684, 0.39169221180699176, 0.4849354067369121, 0.5699592135061404, 0.6430865242951304, 0.7015660273594208, 0.7412496428514023, 0.7595341960158756, 0.7568239001512762, 0.7322848596768756, 0.6898918141168058, 0.6361857349244172, 0.5771837078618187, 0.517295270750533, 0.45904255594245486, 0.4016237185861709, 0.3468655293513788, 0.29608801286868414, 0.24928854319668195, 0.20255354643185894, 0.14862571445355463, 0.08307334290257026, 0.007044876617691769, -0.07442733414557988, -0.15905342234814338, -0.24296419579157694, -0.3216669117749195, -0.39024143860638644, -0.44421594156080824, -0.4796126008754434, -0.4960056407258462, -0.49244368149765044, -0.46906237244055127, -0.428253149198317, -0.37063405909305447, -0.30212879775482626, -0.23279082774641377, -0.16974843458277303, -0.11433804375759643, -0.06539087910766747, -0.024371532179278108, 0.0062043452901035315, 0.024129936412657697, 0.029338548162996424, 0.025115320325267226, 0.014500242568996125, 0.18634539195901656, 0.3772302541135705, 0.569336711365428, 0.7570831291036475, 0.9337004759682357, 1.0934325340789286, 1.2317586786012795, 1.341488417581074, 1.4152111299196415, 1.448617853868433, 1.4420709000171446, 1.3951026923881467, 1.3149364625076314, 1.2115761305143051, 1.095287349739182, 0.9756776199797037, 0.8587953997128562, 0.7439888187521546, 0.636038080375479, 0.5368629462599414, 0.44512904057952596, 0.353540359023601, 0.25035007162585493, 0.12692945064266759, -0.015343317387835656, -0.16945465485596808, -0.32923773162914544, -0.4865586361587083, -0.6345219757074866, -0.7656934688491135, -0.8717869208336884, -0.9440024840287855, -0.9783779945015615, -0.9736778460588597, -0.929704817599964, -0.8506003517155213, -0.7401606371251148, -0.6097457489875658, -0.4756825422202283, -0.35024322276223424, -0.23779253682220425, -0.13909009940239478, -0.05720691746614335, 0.0039434645156203865, 0.04106057911175079, 0.05362270607660472, 0.04630004694576623, 0.026508981778409536, 0.2673597813506806, 0.5392948264049255, 0.8104923987092847, 1.0731952624282965, 1.3173897354361954, 1.535535329185824, 1.7230704441115798, 1.8707490198789651, 1.9680114108381712, 2.0106687340767753, 1.9987367202518633, 1.9328250911506428, 1.8206021985255947, 1.6718936076810864, 1.4997976337782373, 1.3204565505226964, 1.144108380624356, 0.9742986862957591, 0.8166254050319263, 0.6743054000764169, 0.5434626244564966, 0.4149989160210916, 0.2737943938235759, 0.10846377701715716, -0.08074379871410232, -0.2894095821785566, -0.508647406664733, -0.7255055947395999, -0.9288092805565331, -1.1134330757687523, -1.2675868257512815, -1.3771922470249003, -1.4322346991158645, -1.4302842366171615, -1.3710819893194535, -1.2599369887744547, -1.105665593820287, -0.9231301207890799, -0.7314672635828188, -0.5464955686342424, -0.37780137456675533, -0.23073741846091633, -0.1101688349916364, -0.020859159212722876, 0.03562101655311009, 0.06002004796805458, 0.056023004389688845, 0.03293417875862423, 0.33402230031116276, 0.6677073771080899, 0.9983842788147546, 1.3162933666386754, 1.6086733556953883, 1.867037591496725, 2.0846894632555566, 2.2548531988521323, 2.3652950132455004, 2.41142169210996, 2.3920870326519466, 2.3086070540229575, 2.1665008312112413, 1.9738902412590165, 1.7471135111851661, 1.50857511457798, 1.2741288920589497, 1.05321128101052, 0.8524770744970134, 0.6764406587922024, 0.5188001242515309, 0.3677023353745254, 0.20612013474700897, 0.021647279738666054, -0.18844524552710545, -0.4251841851706621, -0.6815196778414211, -0.9406985042379563, -1.1869282190787724, -1.4136221238310984, -1.6094292972960462, -1.7555900962536273, -1.8359738766269194, -1.8430106516778628, -1.777322950210894, -1.644996680826936, -1.4587833614176173, -1.2351196651204919, -0.9947898421653504, -0.7570916035953825, -0.5373194300927848, -0.3458226977990579, -0.18962430371702121, -0.07434061394602935, 0.0010862381403915135, 0.04121859141322367, 0.049363895970867565, 0.03188476085307077, 0.38814137170943624, 0.7614260547919052, 1.1202831650127079, 1.4643309341304134, 1.78403272854541, 2.0653266007723117, 2.300069473980064, 2.482985477913122, 2.600298934141578, 2.6454606754994234, 2.6156557066241874, 2.5113612752834653, 2.3354463867413915, 2.0973751352373964, 1.8162324670974561, 1.5203008907279802, 1.2326750425118003, 0.9677855536068358, 0.7348418675230397, 0.5383457906819779, 0.37035327402859486, 0.21529147169490215, 0.053299589492538775, -0.12743883395281846, -0.3318980419832918, -0.5678860250661484, -0.8346119143010834, -1.115489281419864, -1.391031123300809, -1.6483474315608906, -1.8768226510882573, -2.0559161353759916, -2.1636453390715524, -2.1861140468893314, -2.1247978555040055, -1.9864115088193504, -1.7822788508506917, -1.5315909784688484, -1.2555092394372072, -0.976711536723537, -0.7146500377499307, -0.4832342043145131, -0.2934309671852984, -0.15155731864164265, -0.05585991605411552, 0.0016685859027399318, 0.026183577421624398, 0.021772010618787172, 0.4181264812408635, 0.8089430390957609, 1.1708475609554765, 1.5166852741691361, 1.8451852576562373, 2.137620879632522, 2.3840453695660093, 2.5746258938295896, 2.6932131670466877, 2.7314231634614097, 2.6841088097797607, 2.550194827814142, 2.333312009818824, 2.0468657506691934, 1.714569104913249, 1.3693216278623437, 1.0390973392822285, 0.7415054243453344, 0.49062941628701484, 0.2891250464047357, 0.1269425910162511, -0.014892333677905139, -0.15891291927084097, -0.316309786981464, -0.4961390043107135, -0.7096712587354483, -0.961720916412953, -1.2407888675779681, -1.528897373250501, -1.807061609627375, -2.0594800435832297, -2.2650883262481627, -2.398193754184022, -2.4411533448828067, -2.392752102515006, -2.259807770624575, -2.0522480096371916, -1.790082036311163, -1.495653861308073, -1.1914984866087883, -0.8993166538322768, -0.6347097182871805, -0.41232168214875187, -0.24192531418409427, -0.1233606687602675, -0.04822267806255905, -0.0075889081209887166, 0.005085253222237055, 0.4108744324924841, 0.7984453085581419, 1.154575987471567, 1.4930856913281592, 1.8193684916020347, 2.115776862685783, 2.3673527695275607, 2.556510656477934, 2.667210522742372, 2.687509092787973, 2.610070123777319, 2.4352483978187984, 2.1728960561273105, 1.8407672866597684, 1.467843188928359, 1.0902913774519485, 0.7362564406783245, 0.42591329113498266, 0.17411691077419308, -0.01617803958275204, -0.15822472300974375, -0.2735600650580532, -0.3858680258767547, -0.5083304293962794, -0.6525348958406303, -0.8309267015687218, -1.051707842122309, -1.3111841416000227, -1.595327394203766, -1.8820427422215127, -2.1501349924017283, -2.376117245636117, -2.531347514975609, -2.5965624811168966, -2.56740561538051, -2.4474056692001906, -2.247214455905097, -1.9859338939342097, -1.688890411361183, -1.3772011989855135, -1.0697827817422605, -0.7823853230252683, -0.5326114930908087, -0.3345836175559376, -0.1916869865937576, -0.09947957524885616, -0.04524435942880594, -0.015489056576164369, 0.37710697310768615, 0.7447731401113837, 1.0902905390411313, 1.4194997871306927, 1.7365188602339345, 2.0267541085147855, 2.2696847997254865, 2.44275063092617, 2.5296116731650287, 2.5156463779625136, 2.3950527772242305, 2.1741653248411485, 1.8694506228200285, 1.5036821805284102, 1.1093653006545783, 0.7223238625653411, 0.36956056770748585, 0.07058421922015935, -0.15997085292611948, -0.32136528318920426, -0.4285012541625252, -0.5060603806453899, -0.5769687589874574, -0.6584863553655701, -0.7640429645609734, -0.9042363473546389, -1.087796227272863, -1.3175709568350111, -1.5866517523537258, -1.8717475232989946, -2.1478276855026563, -2.3868563636103874, -2.5605289026950135, -2.6480389406516487, -2.6418535078167777, -2.5415450962324657, -2.358487010262313, -2.1099923692010427, -1.8205516151715602, -1.5122692488843623, -1.2023463214383066, -0.904666094061788, -0.6376486662850291, -0.4190960791265986, -0.2554617600632533, -0.1465915518063668, -0.08115250793312045, -0.037193794733641566, 0.3344680996401998, 0.6736972726130841, 1.0023957170689393, 1.3170492460034593, 1.6172785238859069, 1.8879703395766065, 2.1049093094515947, 2.242253270295732, 2.286247237601502, 2.2221866151766965, 2.050896161595292, 1.7882867652267633, 1.4555855284474974, 1.0760697471754397, 0.6808805001250143, 0.3064472254000776, -0.020182511589146742, -0.2819551560956182, -0.4678473063070119, -0.5818649811740523, -0.6379710280097829, -0.6657808655557532, -0.6900812973258174, -0.7312710759549254, -0.8026272111593628, -0.9112262792249471, -1.0620883098337184, -1.2624855850017864, -1.5121611164514992, -1.7897631570055057, -2.068557682336114, -2.315360459919385, -2.5016513566862426, -2.6069328272821806, -2.621261070934105, -2.5439420018163315, -2.385953566904408, -2.161381004333075, -1.8888599329052809, -1.5898173951493357, -1.2830649093524664, -0.9837537340250244, -0.7105990450640833, -0.48370408743211984, -0.30953189859465247, -0.1870701167935873, -0.1085447683692626, -0.05276102494367326, 0.2945676125766123, 0.6029377675228997, 0.9113122192156228, 1.207294003360333, 1.4802768515199067, 1.7144483432099415, 1.8842237602571836, 1.9662196260004865, 1.949796683522758, 1.8264033059049587, 1.6099288729603976, 1.3214178256405977, 0.9809935413663408, 0.6074949825318955, 0.23192907590592962, -0.10798977098958185, -0.3852075508061892, -0.5861449599060233, -0.7088228787936119, -0.7612649683656381, -0.757199375406784, -0.730356892584081, -0.7104363757634133, -0.7175517636544096, -0.7650686319055545, -0.8528917125590995, -0.982380277202642, -1.1612334491429948, -1.3936048614753427, -1.6632076057010883, -1.942254777984941, -2.1956174172453893, -2.3912134544714334, -2.509228418077686, -2.5375075143804544, -2.4757488938212147, -2.338837095105905, -2.141611406160183, -1.893933561845953, -1.6100602876365788, -1.30914661888482, -1.0129946134144778, -0.7420219969377041, -0.5149928754323948, -0.3409582040419504, -0.21381440799638343, -0.12403399350174481, -0.0575976506595717, 0.26418089569589925, 0.5422073761751253, 0.8264379986952541, 1.0960841847767515, 1.329010476433342, 1.509132708241005, 1.615839413040524, 1.6309171246472023, 1.5479387323440814, 1.3718533659845784, 1.12557065426565, 0.82915743641942, 0.5016584821746762, 0.15633536358065003, -0.17542912833725352, -0.4591082192001893, -0.6684462344470363, -0.7975883992009267, -0.8550016954548458, -0.8481491196127143, -0.7931873993307512, -0.7190749792894958, -0.6591297655399624, -0.638778951706976, -0.6693766375139989, -0.7437527987101495, -0.8595056988320262, -1.0247991708088477, -1.244605120463522, -1.5077881862615339, -1.787124479397065, -2.0481811261372305, -2.2551955207736065, -2.385117078715103, -2.424419896237346, -2.371805914353879, -2.2439845335954782, -2.063519107850434, -1.8396060338311064, -1.5770859526369527, -1.2883342533421056, -0.9995233549268465, -0.7369177759332842, -0.5157940051816398, -0.34525211182572096, -0.22046377933172184, -0.12720446760502913, -0.05644057850740959, 0.23768640229173207, 0.4876248408711197, 0.7439953768371604, 0.9782835611899887, 1.161182182429812, 1.2816032645861606, 1.32202577350775, 1.2688376974641558, 1.1271799824764934, 0.914508866456686, 0.6547463727807823, 0.36868013642101616, 0.0745548615336613, -0.21875843511997325, -0.48518389825035063, -0.6965702811552598, -0.8345145594670859, -0.9035891222928232, -0.9131172790106059, -0.8700792975655428, -0.7861832704922818, -0.6781360143044906, -0.5809777102858542, -0.5304543056760957, -0.5380075923519458, -0.595760985122903, -0.6969707079263617, -0.8511013608189885, -1.0618240348622265, -1.3215527739242399, -1.6035147283715065, -1.8750753548954509, -2.0960121094890947, -2.240288892928831, -2.2923514101905096, -2.252021003729209, -2.130262360832869, -1.9537749885114408, -1.7430443735494154, -1.502164848948309, -1.2341378944858352, -0.9600304760359661, -0.7113485918484461, -0.5016067756362775, -0.3367150790665039, -0.21578199050673286, -0.12448144597079032, -0.053989906057366706, 0.21367703151831768, 0.4351384728801555, 0.6592833118669089, 0.8532621339397504, 0.9854931472631446, 1.0474264102918558, 1.0225327197260279, 0.9094217908209319, 0.7278140585730438, 0.5010247694413905, 0.250204483631781, -0.0035626722725807768, -0.24736999775278412, -0.4747599637328567, -0.6683358792799104, -0.8111113085496591, -0.8975426939988722, -0.9379585471826268, -0.9322219263306495, -0.8819964999532818, -0.7847289266280516, -0.6520988592730024, -0.5258123756157393, -0.4427714050048225, -0.4182719428986845, -0.44614062896175555, -0.5238799184801913, -0.6594154476852643, -0.8572023511486881, -1.1100435091457814, -1.3942511981660937, -1.6764888827931252, -1.9151618864223063, -2.076972899186456, -2.1447509381615535, -2.1197558592592083, -2.011100478192147, -1.8396289517274265, -1.6324485911179607, -1.4058039691418651, -1.163494166770929, -0.913463654862047, -0.6833970305665021, -0.4885140392523632, -0.33119229560695757, -0.21371913402098655, -0.12444811398350392, -0.054295348516364576, 0.18901847017898818, 0.3820704468672404, 0.5718188917791432, 0.7229265050285537, 0.8067660847802665, 0.8156856657801841, 0.7374854549517811, 0.5879179682646635, 0.39635718470489845, 0.1831465460624772, -0.03525656380279185, -0.2423156333752868, -0.42907214025254575, -0.592084354949019, -0.7266959816856251, -0.8316819215393672, -0.9095823335991658, -0.9608725339010784, -0.9722811584721502, -0.9301553958912231, -0.8288176057319037, -0.6851800940728847, -0.5400033120429387, -0.4272887115627609, -0.3639058746021028, -0.34858214024209083, -0.3896844200841772, -0.49313340304124353, -0.6657659833521425, -0.9004086260291222, -1.1783880409829455, -1.4655035830070746, -1.7205580005741692, -1.9025952435954958, -1.9908540617708406, -1.9834394475267285, -1.8914323352807556, -1.7319148234982147, -1.532053403375625, -1.3166230711053626, -1.0983395872029107, -0.8771521495803405, -0.667912713176299, -0.48745110898308164, -0.33812059549683277, -0.2214594282560614, -0.13195940517102336, -0.059705893555273906, 0.16144907358108612, 0.3240248708856205, 0.4782218104477415, 0.5880260047834083, 0.6306074213231257, 0.6006358281472428, 0.4938785145681224, 0.3391295356971864, 0.162463029360694, -0.019292843582583367, -0.19148559696276218, -0.34403496737904515, -0.47873932844242506, -0.5962998109151362, -0.7082948302002731, -0.8260394635502102, -0.9427201343267518, -1.0348645701086494, -1.0731493036558648, -1.0442319837539296, -0.95174959550009, -0.810286653654323, -0.6548778687122273, -0.5142350538725284, -0.4011886695644134, -0.33043460519977336, -0.318360924947596, -0.37460118816595495, -0.5085063911350339, -0.7138575234557195, -0.9760645116746507, -1.2593509674619898, -1.5224587013598245, -1.7228224168108224, -1.8360559137274466, -1.8528707103199948, -1.7826555108313722, -1.6406407117500326, -1.4534806934660496, -1.2515340811011797, -1.0551752144317195, -0.8630947269671286, -0.6752442714139741, -0.5056777403657308, -0.3613112404615344, -0.24390212561997804, -0.1495448612349563, -0.0698252185371563, 0.12798652481661635, 0.25665384841606653, 0.3740604930729416, 0.44738266211920297, 0.4601055747353696, 0.4112100185354442, 0.3027845466686891, 0.16466335486479888, 0.019655194046047327, -0.11566107657578865, -0.23296252496032713, -0.34174079463718793, -0.4531392488611197, -0.5663774716041833, -0.7066915447396819, -0.8834743015983393, -1.0647180949745692, -1.1999918006492276, -1.2617514603264897, -1.2502960340514229, -1.175523560850433, -1.0442369295762988, -0.8822149533208451, -0.70774837055156, -0.5354523073836354, -0.39323333353643974, -0.3083689634489616, -0.30093191312435147, -0.3820262228357776, -0.5472790281835269, -0.7870119019066067, -1.064196193933988, -1.3332942651841537, -1.548572915446847, -1.687077235652133, -1.7326727596840132, -1.6900380793337102, -1.5733933843989731, -1.4050640673398613, -1.2175046340824742, -1.0394099677989141, -0.8714066114557544, -0.7055510656311605, -0.5492820731141917, -0.40772827332095996, -0.28372696441765716, -0.17853702026594978, -0.08630248570899449, 0.08720066182238054, 0.17746114435727722, 0.26020043963278777, 0.3045776324871315, 0.2986035143336711, 0.24633232783702064, 0.15351239776775552, 0.04725429452530114, -0.056540383872445164, -0.1493913605957898, -0.2388609037234781, -0.3459055180145861, -0.4816263337822069, -0.6385445788002544, -0.8384648174438152, -1.0772073114113114, -1.3010981398778503, -1.4560099832124085, -1.5271355423551447, -1.5295145576311575, -1.4742087338629113, -1.360776478721135, -1.1961138827823536, -0.9854166187785427, -0.7500510493685659, -0.5222213528643926, -0.3455181649922248, -0.25557243233208454, -0.26940253848351314, -0.38841062518960023, -0.60108296528437, -0.8719974956153187, -1.1528036652295106, -1.392025378929671, -1.5579930979456063, -1.6337831323444376, -1.6162229995429522, -1.524598168341201, -1.3812054301299437, -1.2108182939536547, -1.0472580770934345, -0.899741595364601, -0.7548298150129252, -0.6124915798001012, -0.4752085597686098, -0.34253114866281653, -0.2196954710027097, -0.10736427316613707, 0.0425456182638325, 0.09260549432828404, 0.1424463601537693, 0.16244176899839505, 0.14355296435089357, 0.0946241296829862, 0.02411776648727591, -0.04953198196095885, -0.12551526396418244, -0.20983460413214935, -0.3166577877122417, -0.4598645050045667, -0.6445184721081059, -0.8549070746455072, -1.0997636760062381, -1.3604732605410403, -1.5829544365445143, -1.7253540049083314, -1.7884845328825607, -1.7967262467502665, -1.762411240355381, -1.6746476530378498, -1.518889749445296, -1.2885319961277226, -0.999755209925695, -0.6837675870592106, -0.40481483173715277, -0.21466393895236877, -0.15172828129115767, -0.23179472302800752, -0.4313069078424952, -0.7048135892481145, -1.0013906386854192, -1.2695655960344945, -1.4663136161635255, -1.5671552719467563, -1.5693601103950465, -1.4915648623077615, -1.3661385485566286, -1.2139262237438933, -1.0631574155072387, -0.9335199651107184, -0.8113132143359251, -0.6847855427160293, -0.551028135754492, -0.4087954561614747, -0.26729087631593385, -0.13192388179600423, -0.0040800450947448335, 0.004482273049722952, 0.022047197938400355, 0.019882044556481838, -0.00985532560403278, -0.05564721490549331, -0.11003991090077149, -0.16323739788507202, -0.22969263714879437, -0.32891342829476283, -0.4735546699097248, -0.6634989426517001, -0.8879717703617312, -1.1292644516384776, -1.3818775902502438, -1.6221559077201422, -1.8011636867809357, -1.895406614433281, -1.9259677292615047, -1.9237297927088322, -1.9084081376887319, -1.8581673380353605, -1.7438305791322168, -1.531844409599903, -1.2168285481025316, -0.8268906295158301, -0.44263014212872115, -0.13875262026368929, 0.00695385050557624, -0.05016319089551534, -0.2760795035887622, -0.5853954718974596, -0.9149137962522184, -1.2098746657453583, -1.427989810493489, -1.5396300722959415, -1.5456147639447009, -1.4682738665154216, -1.3467211577024283, -1.2068736495073986, -1.0687401854100256, -0.9532103567319051, -0.8505275520119482, -0.7415419512912723, -0.6146229324516952, -0.4657461951915878, -0.30784587247719775, -0.1524946604108833, -0.05155379243195473, -0.08589944746869861, -0.10272479293129755, -0.12808710658652903, -0.17074798198472876, -0.21799990781365117, -0.26321786048698737, -0.305897326374093, -0.3688862338016585, -0.4788077931743836, -0.646493427640524, -0.8560023867120171, -1.0918492230579202, -1.3312375787395239, -1.5586002638578875, -1.7477076375824927, -1.8576370957871295, -1.8833411216570204, -1.8589977448258772, -1.827909562981146, -1.8215433867654782, -1.8251927995966035, -1.7941950476845796, -1.6557169410994699, -1.3700786008926888, -0.9462331775703576, -0.4711506905005665, -0.05978412929011104, 0.1716484852921471, 0.12848719265380126, -0.14901799614074263, -0.5212580020596616, -0.8954874131718586, -1.2128133235359122, -1.4333291882951136, -1.5369851813482895, -1.5282703995084033, -1.437609433459249, -1.3066496904755676, -1.1677011948725915, -1.0393819092435357, -0.9389019786150794, -0.854662591609313, -0.7610457347559663, -0.6426862349631646, -0.49524366845619205, -0.33112370655730566, -0.16478164226747452, -0.10044259413651306, -0.17930138372717894, -0.23282880467313927, -0.2845176064834037, -0.34144651521276465, -0.38833157687331765, -0.4242490484077932, -0.45657139363418453, -0.5086231825697769, -0.6070651240477312, -0.7595187417868412, -0.9483226245256611, -1.1577723855724908, -1.363702459575709, -1.5431389774846778, -1.6709904021727404, -1.7117536327685865, -1.6676963931141098, -1.5784235094451369, -1.5057891323425143, -1.5069512474269926, -1.5872524587670367, -1.683495573306005, -1.6837512423930567, -1.4965684715490488, -1.1046917520677069, -0.6010282675689789, -0.11854564669430402, 0.18590582684363488, 0.1736481745226272, -0.12769858477612295, -0.5426979926494662, -0.9410645205047939, -1.2543061368990942, -1.4512821884388178, -1.524740983040903, -1.4861341676925761, -1.371889976244786, -1.225805837970968, -1.0809248029555463, -0.9564953606534063, -0.8681480487099206, -0.8031658328063991, -0.7284923421721603, -0.6245331559888494, -0.4874964576023287, -0.3303532562011928, -0.16677437744095003, -0.14717560768391139, -0.2699316321168915, -0.361040752228802, -0.43930485859778884, -0.5083120520360812, -0.5513955559938796, -0.5712521539113985, -0.581646423748479, -0.6058263123867789, -0.6669579694879789, -0.7696695334973584, -0.8990672300606702, -1.048445545969699, -1.1970202309757882, -1.322411988501282, -1.3959212229126599, -1.3774544967977904, -1.269936045790515, -1.112808470541692, -0.9922981144164652, -1.0111971977560728, -1.1935153419009972, -1.4606622322317449, -1.6417780792908248, -1.599960036357343, -1.3071670484552755, -0.851650029323027, -0.3669494584372804, -0.028046067120648673, 0.024543613632756707, -0.22521176219385838, -0.6225701716041621, -1.0087080598518927, -1.2942558859494115, -1.4469302528719634, -1.4737584749370276, -1.3933985219835767, -1.2490520098130993, -1.0825958905504005, -0.9291175897218852, -0.8069594184592761, -0.7302652121754598, -0.6843216157163494, -0.6312212321854288, -0.5494949765236797, -0.4359736165490292, -0.3014564945026393, -0.15499416595379994, -0.18801129571823355, -0.34972222754857624, -0.4745521224629892, -0.5766749805848153, -0.6551206999300326, -0.6894033591157286, -0.6850684671802405, -0.661769279658939, -0.6418004466613652, -0.6455172523118239, -0.6750172204202837, -0.7234276827676659, -0.795477608027591, -0.8801463194759043, -0.9550416122249086, -0.984834294905275, -0.9201593486883346, -0.756059236851363, -0.5302867318842559, -0.3661806720898939, -0.412947444746037, -0.719453502648299, -1.1696289908132003, -1.5374187808255895, -1.6429736500628895, -1.469415455881739, -1.1014952089969166, -0.6635949127476134, -0.3156473856103834, -0.19129960537423385, -0.3540810780778189, -0.6906962371946272, -1.0376565979137196, -1.285794426367832, -1.3905896813805567, -1.3656419080770132, -1.2390913571605462, -1.062069427877476, -0.8754634005903037, -0.7094920691245382, -0.5860576554121789, -0.5196451618919896, -0.4943913819491758, -0.4678315362723251, -0.41568826464320463, -0.3359532231174093, -0.23760168438212448, -0.1251270201853512, -0.21624653240354913, -0.4065882587930362, -0.5597155911457227, -0.6815703422399076, -0.7666860706560975, -0.7930533854499323, -0.7649687313824046, -0.7039390180979126, -0.6310189303138819, -0.5697145017988923, -0.5201340570100043, -0.4872260136710313, -0.4871531047060646, -0.5185271017982221, -0.5570889077343383, -0.5569257380564466, -0.4578361308860878, -0.2460748212364007, 0.029628506934637765, 0.2186252664808279, 0.1332133384567288, -0.2900154154186306, -0.8893310917481312, -1.3978500791553516, -1.625460546886812, -1.5516364912132832, -1.2604494285776116, -0.8643138266989292, -0.49761406646891365, -0.30064802477171326, -0.377847991252641, -0.6583122887012919, -0.9743750870332983, -1.1966494532859613, -1.264770075453568, -1.1941659559876538, -1.0260545324788592, -0.8194920867016942, -0.6123837391125104, -0.43371569281955624, -0.30646471382357227, -0.2469817837164108, -0.24000038440438448, -0.24128644820111594, -0.22421335085704017, -0.1878965327404137, -0.13837295524406223, -0.07599402049249834, -0.2266895593955113, -0.43257193831623786, -0.606364969176121, -0.7458356482999484, -0.8380950150924519, -0.8601583450729882, -0.8147593230500128, -0.7232146900594166, -0.6065904641866461, -0.48924265621785085, -0.37622064575462527, -0.279854451384006, -0.23209943155262247, -0.23099154986882636, -0.24837248352489513, -0.23049652850881988, -0.11284682715241688, 0.11235649398206704, 0.39687662046881594, 0.5864710056318646, 0.4733019816505662, -0.012580248333269784, -0.6839422984815884, -1.2702017515817599, -1.571945483149028, -1.5657174792021271, -1.321892726295047, -0.9357711510241744, -0.5373960416231857, -0.27226443805007977, -0.2755233748721522, -0.5292150047247829, -0.8311647611700036, -1.0346483159466708, -1.0750924429803035, -0.9718083868366371, -0.7699508397731235, -0.5376223062914673, -0.311160667676187, -0.11759863705010042, 0.016088853085471616, 0.07127609740051292, 0.062074152220728346, 0.03319438237324366, 0.011786332962439808, -0.001140820612491853, -0.009828827516078383, -0.010712855874596368, -0.21982268579332512, -0.42660661622479523, -0.6120401797103376, -0.7671059296517856, -0.8695753780387772, -0.8945685079704578, -0.8431368892044643, -0.7346045044851537, -0.5924550227310285, -0.4445274431539563, -0.2990091360993692, -0.1751188796385519, -0.10910618384566403, -0.09696924677629912, -0.10581698163004152, -0.08481559073805967, 0.024052936079818763, 0.22550151078173084, 0.4712537454595908, 0.6305008196794132, 0.5178199129844827, 0.053752422962938376, -0.600557398049272, -1.1955872431635146, -1.5317971742618453, -1.5616727711088818, -1.340470223468915, -0.9440070118986429, -0.5110704361988955, -0.19510983832293585, -0.1479463195329745, -0.3909446986140798, -0.6774409906678508, -0.8500527054596024, -0.8580840317648865, -0.7224209947780895, -0.4950618610699823, -0.24205153048745084, 0.0031323538611751126, 0.21116272367699102, 0.35270427436873797, 0.4057664418802922, 0.3840009317927828, 0.32994154999198444, 0.2696832254044152, 0.20493759543302, 0.1337051042255654, 0.06313533149667039, -0.19899492774893612, -0.3942884753543438, -0.5812064608160437, -0.7462586337953725, -0.8608547132947679, -0.8977730326041787, -0.8546473631955915, -0.748764239269662, -0.6057478064108137, -0.458657609473145, -0.3191765167996642, -0.20021693120514802, -0.13753634831807066, -0.12690638472731525, -0.1361385400230072, -0.12367322818245856, -0.03927281443634445, 0.11488061935871405, 0.30033786664784184, 0.42321891752227986, 0.3311454039253573, -0.050174556884514825, -0.6218042235722959, -1.170018789024013, -1.505562822058407, -1.5601081891386002, -1.3535982444257086, -0.9593282391234097, -0.5178297031370264, -0.19605609710570296, -0.14962750864594002, -0.35110140709126103, -0.5820508589243306, -0.6994925497877342, -0.657838103419594, -0.48653368758324617, -0.23328789287135435, 0.040914700415215915, 0.3061452918984139, 0.5279300493845058, 0.6743247701053942, 0.725961744436251, 0.6964600870709106, 0.6221684115509087, 0.5257751694029588, 0.4105506368368982, 0.2777739350283681, 0.13744338551261528, -0.16988948558567038, -0.3444686722126552, -0.5215491076998998, -0.6866832843079868, -0.81086692009028, -0.8656538541556342, -0.8454306229133856, -0.7633068261613789, -0.6445424846964614, -0.5258383920422127, -0.41761773906016064, -0.3270194092589557, -0.280947504362455, -0.2796297750000037, -0.2998629679764371, -0.30580711117733395, -0.2532303103005682, -0.14472961649512123, -0.021778856131763422, 0.05257602379036901, -0.02464341580556005, -0.31667201521735644, -0.7664232057709272, -1.2243010001361296, -1.5298472420437705, -1.5963222795214413, -1.4189732582818166, -1.055678048365339, -0.6448616341207221, -0.36051566006105057, -0.31953678586709594, -0.4455691963741857, -0.5790805933522238, -0.605934607164833, -0.5010675032265778, -0.28882020610962544, -0.009360783088707662, 0.28809822761079906, 0.5726844442083787, 0.8046379575024364, 0.9549661739075904, 1.008217417747306, 0.9769199574997994, 0.8888753338850077, 0.760661553030279, 0.5977858846951042, 0.4075179938747445, 0.2039937191926101, -0.1349877247728303, -0.28228312284735546, -0.44055702903278576, -0.595749470979461, -0.7224474797069417, -0.7952114554111283, -0.8061477355609338, -0.7635490842330219, -0.6877012597098535, -0.6149712535227798, -0.5558024882740502, -0.5059754733251561, -0.4883664726206564, -0.5068355478036439, -0.5454378908530623, -0.5754954134835146, -0.5551146571326642, -0.4876724063062005, -0.41407898688126576, -0.3844377616739446, -0.460281841312572, -0.6814296660281157, -1.0148955658155865, -1.3749913779855163, -1.6344018384130137, -1.704450650266508, -1.5658953076412048, -1.2674729958665967, -0.9283910663134749, -0.6868159575044824, -0.6108912597918993, -0.6295684234359199, -0.6462744761848734, -0.5764706008158134, -0.40715682309982015, -0.1536867884358954, 0.1560437771343895, 0.48135466182379305, 0.7850873718761592, 1.0233462718300737, 1.1754520530013897, 1.232805144219495, 1.2054660188195483, 1.1097395456639976, 0.9544099548185545, 0.7504117940284658, 0.5125295391304656, 0.2577829653593552, -0.09737446112576104, -0.21405455701565315, -0.34635583921587476, -0.48105428263402394, -0.5999066210551133, -0.6846802011954137, -0.7276770496352275, -0.7303063709392824, -0.7076448419247917, -0.6892479847434534, -0.6867856039082921, -0.6891722358042632, -0.7096084499386014, -0.7565835840043814, -0.8184626888380478, -0.870974954584296, -0.8786379141856723, -0.84395580479494, -0.8112418175152688, -0.8199486906814758, -0.9043078552399453, -1.0815848628488054, -1.330106390616725, -1.6050501254872815, -1.8165066579343432, -1.8854652106890544, -1.7951093336952777, -1.5739144668731369, -1.3051047671363574, -1.0808885439868887, -0.9464898124094238, -0.8632535142369774, -0.768881388147786, -0.607756958952693, -0.37521006185256967, -0.0756351432715832, 0.2674794633375303, 0.6185931791256729, 0.9318377542394588, 1.1692319573505336, 1.3232797061816897, 1.3884645034772054, 1.3680411754291462, 1.2669192008952324, 1.0901607162574078, 0.8559940786981891, 0.5846531852042951, 0.2950517766180391, -0.06234267337738967, -0.14408800521768356, -0.24432793929032032, -0.3518500407266283, -0.45430233496919287, -0.5406313881805129, -0.6064796206950198, -0.6510848136701302, -0.680613610188507, -0.7179083719046772, -0.7739623247099208, -0.8346483456872901, -0.9009293343165248, -0.9807286647281092, -1.0665839538162771, -1.1392202170243078, -1.170394479289527, -1.163177102247886, -1.1595687808610637, -1.1974299210891322, -1.2949941070498099, -1.4530427866211968, -1.648557728534809, -1.8592749422510932, -2.0271431899432133, -2.0948916713580132, -2.038631691639667, -1.8764701612862376, -1.657466076013435, -1.4404510360804146, -1.2632840100658822, -1.1000205860092098, -0.9143884268745728, -0.6748692676780722, -0.3803659539227739, -0.03610970694760201, 0.3350765555745872, 0.6972135643845648, 1.00735870789937, 1.2425914779279466, 1.4005889148485453, 1.4723283345333043, 1.4561281917630662, 1.3501637895935588, 1.1596876153879239, 0.9087792902827847, 0.6219838196207808, 0.3155303665364273, -0.02959960682693206, -0.07516666145753773, -0.13988135713921931, -0.2154354162377888, -0.2944653134432764, -0.37317222297945174, -0.4510709396761432, -0.5270769669859316, -0.59979293136672, -0.6839339636877712, -0.7914421465359631, -0.9089258728227739, -1.022123260391144, -1.133769335357256, -1.2434994170530151, -1.3383621702615427, -1.3966642979474182, -1.4170332632397815, -1.4357120872633833, -1.4904685923142336, -1.5927816177323062, -1.7367059718434787, -1.898636501404826, -2.0629663880517737, -2.1963375545054737, -2.2591196580983137, -2.2252287694127344, -2.0996038846929226, -1.9142296764502453, -1.7050341171209082, -1.5036004309474102, -1.2849522375172862, -1.0349693977894923, -0.7349490179373201, -0.3927720061140634, -0.01882662615226867, 0.3597250653797972, 0.7143017592149935, 1.0149597594694217, 1.2478546416253102, 1.4070702252712441, 1.4812379389713928, 1.4651361527275901, 1.3540877428385407, 1.1587083505380718, 0.9075266643950091, 0.6228373548789895, 0.31695830351155563, 0.0017753501069625944, -0.007024146218186895, -0.032062632025337684, -0.07147988555177731, -0.12282874907383207, -0.18682218314389307, -0.26702362393638934, -0.3637557379299863, -0.46932500773326724, -0.588037837183807, -0.7319333905299704, -0.8927316731320467, -1.0483675867918254, -1.1906905082909187, -1.3224426604568036, -1.4419019241323507, -1.5328856986270045, -1.5862708537039567, -1.622150361459274, -1.6800418802523231, -1.7716384718381235, -1.896184998599137, -2.0318920223098385, -2.1640778496298467, -2.27073783962937, -2.322712030377255, -2.3014026145377993, -2.201581493625472, -2.040777477202355, -1.8449138915019192, -1.629140499284197, -1.3782529688079188, -1.0894122449982715, -0.757228571732697, -0.3966587835878303, -0.02213377175517387, 0.3419603981452386, 0.6792902004730612, 0.9670013392716982, 1.1932651932198084, 1.3478851587722542, 1.4169554315672033, 1.3939929079993252, 1.2790839920652655, 1.0903883704188, 0.8546167397021036, 0.5878283767630058, 0.30017882290640924, 0.034226569169030385, 0.06473243790871218, 0.0819158703791843, 0.07988293685533002, 0.057880651751235565, 0.01173711104768863, -0.06395102733071104, -0.17052719952607887, -0.29848935337539845, -0.4401657180135991, -0.6061000762761314, -0.7925959600733025, -0.9765161485152498, -1.1450979677135351, -1.2987895578274342, -1.4423214560294908, -1.5660218405168655, -1.6546196914025206, -1.7085154580419046, -1.7607522252420804, -1.8329089346642216, -1.935199202918147, -2.05099352851186, -2.160653612098262, -2.24658598436363, -2.2854224844496276, -2.2657278397696845, -2.181895540876671, -2.040459161491102, -1.8572477496180717, -1.6367626173650192, -1.376765647528092, -1.0798677505180796, -0.7502518778291306, -0.40147803550772715, -0.04851970396926798, 0.2916081133579126, 0.6064736037009183, 0.8747601134353077, 1.0867838848306661, 1.2271038534491319, 1.2811716011673064, 1.2471314237596707, 1.1340586106071993, 0.9639456029171009, 0.7559713742342399, 0.5207554010805499, 0.2665209418919059, 0.07158873252669472, 0.14456931250450714, 0.203488759101522, 0.23660649328038882, 0.2418224113863818, 0.21463796309941044, 0.1484948003329883, 0.04106687098905963, -0.09925649610183938, -0.25804476989717784, -0.43613713336039467, -0.634215061714937, -0.8336781227865734, -1.017445863053464, -1.1833419439224748, -1.339095033075631, -1.4842433920215519, -1.6044644267370993, -1.683136845556503, -1.739423468234985, -1.8001127186057648, -1.8853864584781574, -1.9884348100451203, -2.0844991917142908, -2.156600980629037, -2.18592353793747, -2.162775594934991, -2.087618788839832, -1.9582938362619449, -1.7865604289154797, -1.5717695896838142, -1.3228419076723612, -1.0450856282974628, -0.7423222745482214, -0.42125031137684116, -0.09783615147320823, 0.21557449148369626, 0.5035541703829303, 0.7455663570891483, 0.9333858530101268, 1.0474014045005529, 1.0785499114513302, 1.0357557725509468, 0.9361657424361646, 0.7967796288480435, 0.6249675748061795, 0.4285195365673324, 0.21835380514996, 0.11571441977000778, 0.2326992586723136, 0.33170784060096653, 0.39626449675250963, 0.42371316333884473, 0.4124330345717127, 0.35694807307351517, 0.2530707669480214, 0.10748246250166466, -0.062377157012156605, -0.24668280997516112, -0.4458429126159089, -0.6500152516549313, -0.8414624710750991, -1.0094372816950057, -1.161748002154469, -1.306641943237418, -1.4424563571896543, -1.5503854525364342, -1.6322975771777593, -1.7051617057759973, -1.7869157901543162, -1.8825142548553393, -1.9711665633573185, -2.0354013747759034, -2.0604115681004025, -2.0355544537654975, -1.96484241147407, -1.8440678807281123, -1.6844775854744205, -1.4852516872688024, -1.262388976112099, -1.0166767774259737, -0.7475831749517021, -0.4593380667811475, -0.1672735105075126, 0.11847478440743656, 0.3737996352169257, 0.5812286641168184, 0.733416584402727, 0.8125486533942168, 0.8216851839191787, 0.7817994853676727, 0.7090009699785611, 0.6056494749149218, 0.47177829391156223, 0.31945391487670993, 0.16095344256637575, 0.1639189693549777, 0.32531690912815237, 0.4617207255619984, 0.5543511254913916, 0.5992047269629331, 0.597493809069498, 0.5483316516025984, 0.44802308847616285, 0.3001247945901131, 0.12321915271570026, -0.06386989309142423, -0.2571861621626607, -0.45502947668353183, -0.6460683674793866, -0.8124511749848803, -0.9555829549190618, -1.088499498316193, -1.2204401664128732, -1.3444707270716874, -1.4550112448381782, -1.5551923249144621, -1.64949603092305, -1.7448346347397512, -1.8312025392034117, -1.8931800790556816, -1.9182111594315783, -1.8971663129250012, -1.8322664271005658, -1.7251365533434657, -1.5838768874500317, -1.4118440813950914, -1.2224632721332236, -1.00969201639204, -0.7734976285854357, -0.5187501993750993, -0.2573080082660215, -0.004719530748461922, 0.21047608289096306, 0.37718051506133043, 0.48900896346635037, 0.5361218236039405, 0.5366917823101148, 0.5122362224181566, 0.46768213526944175, 0.3984409447260795, 0.3053457077964453, 0.2009195585279512, 0.09857021815496979, 0.21064159349569817, 0.4129938597692176, 0.5851675482081845, 0.7033527551366558, 0.7613106032753775, 0.7630229116374238, 0.7131029016661439, 0.6130906714919979, 0.46565031939345614, 0.2861829031275496, 0.0954853784180993, -0.09446906411688129, -0.28187451184974444, -0.46250846909464366, -0.6215605591128732, -0.7548755886718875, -0.8729536800830772, -0.9910884508967326, -1.1120246911645815, -1.2321922743107478, -1.3508325014202023, -1.4621058412211412, -1.5651455951812672, -1.6575467269294824, -1.7249213123223108, -1.7576078332673715, -1.7499105500789993, -1.7025647543197362, -1.6202653670151081, -1.5072023654366236, -1.3703464163485322, -1.2129052009838115, -1.0305846943972778, -0.8253415179882627, -0.6032834500475885, -0.37729485550499775, -0.16663469155706973, 0.005094134853313046, 0.13431477430609612, 0.21257277031436753, 0.2428886185446837, 0.24875029856698352, 0.24079401192744634, 0.22092504125934348, 0.1853943683271586, 0.13573977638752965, 0.08281193510883923, 0.03768184992761848, 0.25163968672002435, 0.4891631823806679, 0.6918637453632995, 0.8330008414151728, 0.9016258360883522, 0.9040923803393325, 0.8476003867417898, 0.740651811491129, 0.592022033721601, 0.41276438950897015, 0.22026825539213132, 0.029625013451161943, -0.14945842483135016, -0.3141139037488252, -0.4585448002719221, -0.5792271528371287, -0.6805256514226765, -0.777855691670336, -0.8832018972274281, -0.9956799611908735, -1.1173349730525513, -1.2411257101686723, -1.3586422352552827, -1.4647994136507214, -1.5483395722137254, -1.6005029716323986, -1.6184057740338647, -1.6014000206696026, -1.5535728748061346, -1.4759417583331778, -1.3733674650305685, -1.2436061778046579, -1.088586383149537, -0.9119418691399461, -0.7244661840884011, -0.5377609240729841, -0.3707297850375425, -0.23420405896955981, -0.13156674529997767, -0.07069611985400523, -0.04125668563090196, -0.027933690076642495, -0.021040440594279307, -0.016763596895504898, -0.019119412348239474, -0.024543483239894123, -0.024911279156404665, -0.015783762873213803, 0.2824539105798941, 0.5480398968648149, 0.7740500471251761, 0.932497229156917, 1.0114744209620825, 1.015962457075786, 0.9525620616992284, 0.8337834208750945, 0.6767129692553016, 0.4924578802322575, 0.2975507947527881, 0.1063789986387886, -0.0666603267756068, -0.21359628915640674, -0.33591596813969044, -0.43699844079564804, -0.5195486499350622, -0.5909568001534138, -0.6699886955945279, -0.7650125912578765, -0.8794717550410975, -1.0101908550000678, -1.1446915255748464, -1.2736715220646282, -1.3856816724610785, -1.47101544197268, -1.525764240344771, -1.547822428744581, -1.538596675109198, -1.4969133491149567, -1.423179043808231, -1.3176867902582312, -1.185928808273268, -1.0362137518272911, -0.8801255409207153, -0.7274866863635447, -0.5913949825305027, -0.4744573962596342, -0.38600526210478364, -0.33068757543811195, -0.29963218743709463, -0.27977402594403306, -0.2584251825408146, -0.23330763659913456, -0.20390412512245362, -0.16572794891713966, -0.11783862735391935, -0.06139300072991987, 0.3008593741435924, 0.5832595620863151, 0.8237514281823828, 0.9952899940116106, 1.0843869697787918, 1.0925047781483106, 1.0251877284439146, 0.8965276047796986, 0.7277418736987443, 0.5331775355418334, 0.32960880479197585, 0.13495538058230297, -0.03485570910311745, -0.16786727677317698, -0.2651293605272828, -0.33772211343229314, -0.3940356802310613, -0.43899493943877865, -0.4883052381157163, -0.5605674565046681, -0.6613578856999117, -0.7898062251813863, -0.9348623030453207, -1.086244097072552, -1.2303639822368566, -1.3548397039010815, -1.4507798733078032, -1.513736810889309, -1.5405388617483016, -1.5297107176566702, -1.47990754194684, -1.395023554252326, -1.2833231991027607, -1.1569625299300823, -1.0252899994124847, -0.8971196201367074, -0.7791811967514779, -0.6777987800702455, -0.6032032916431587, -0.5544674679326788, -0.5229200675322451, -0.49519804004026274, -0.4613443243319799, -0.41723063355353807, -0.3571811681348817, -0.28154190858544936, -0.19501776274817822, -0.0993201809135985, 0.30766544294669534, 0.5923936099430094, 0.8346158096005069, 1.0129966755017215, 1.111347120952912, 1.1243673177116085, 1.0576020656248823, 0.9258810058213709, 0.7495548809261908, 0.5464371777966256, 0.33454873484007924, 0.13398230270314104, -0.03598701505892778, -0.16159593172079526, -0.2410351646135758, -0.2859482058367026, -0.3110197739609442, -0.32863481261008565, -0.3524648326678786, -0.4026273031802135, -0.48717365347519487, -0.6043240973405136, -0.7475099190380494, -0.9087634559903761, -1.0751474549074238, -1.2297889855902255, -1.3587097275514504, -1.4537177502957475, -1.5083848553882848, -1.5202151692323929, -1.489743410698596, -1.42354780744949, -1.3323015486148584, -1.2269574050889205, -1.1160030282559146, -1.0068355222969225, -0.907206836075715, -0.8279886615042419, -0.772746631011635, -0.7327505085509902, -0.6986834520930543, -0.66271877724633, -0.6177446259959573, -0.554179711066426, -0.46909938289998226, -0.36876050883787287, -0.2553634785713088, -0.1301593923494818, 0.3006412558464025, 0.5759345821490036, 0.8076141110869378, 0.9809532785406592, 1.0811497524311469, 1.0990484236546296, 1.0384978930971556, 0.9126011523314036, 0.7381443185606482, 0.5342415199072429, 0.32195282081081217, 0.12172872316627471, -0.04557812911143476, -0.16539746015640067, -0.23595866335586996, -0.26573935621588174, -0.2679837084857927, -0.26164668737600666, -0.26552699111248107, -0.29774118569059854, -0.3654041950355757, -0.4658611990166123, -0.5970968043053128, -0.7540705773967229, -0.9261773364294653, -1.0936920836138657, -1.2402619947180673, -1.3539573952975286, -1.4264441421571428, -1.4539046087299998, -1.4389139333114873, -1.390293180624602, -1.3185741004162626, -1.2329511357618428, -1.140495672813691, -1.0488610879356906, -0.9711728134676808, -0.9168140006559297, -0.8799100056387333, -0.8470603723957457, -0.8110421846858284, -0.7696617644809274, -0.714640633402147, -0.6354443958030412, -0.53558476889072, -0.42232201282343224, -0.2945510084239049, -0.15190279782057955, 0.27890242348110744, 0.5337495798675727, 0.74532324848925, 0.9010524259493502, 0.991090000000956, 1.0097387047660749, 0.959239400840304, 0.8477209629576163, 0.6876968374482475, 0.49563239047149327, 0.2941593730530835, 0.10521086618552043, -0.051399536289140305, -0.162552118900364, -0.2271485592985321, -0.2516936933591087, -0.24571237905392082, -0.22594671475773564, -0.21705988945551433, -0.23479221635453856, -0.285421933738199, -0.3667115152694896, -0.47935938679675055, -0.6230845353884674, -0.7874181496724582, -0.9532385192076779, -1.1026669987113147, -1.2228493744902793, -1.3032609242152506, -1.3397564585471153, -1.3351059127995497, -1.29973675803262, -1.2433168903966607, -1.174228979983946, -1.0975144195828375, -1.0228661072661736, -0.9647655767204435, -0.9287218280714257, -0.9040250595044049, -0.8772589203984593, -0.844267419167373, -0.803376012880796, -0.7434941290035335, -0.6575450573051721, -0.5531294671129299, -0.43696129012038726, -0.3061924464741209, -0.1593945084576129, 0.24250006449711112, 0.4645564233526037, 0.6467591899426, 0.7770820242805524, 0.8506781364104768, 0.8654940117406312, 0.8244182650685213, 0.731526850536991, 0.5953677605830692, 0.42964320098242514, 0.2531575983820041, 0.08768897186334319, -0.049487642777575315, -0.14707817790108585, -0.20436521208908062, -0.22647495837712098, -0.22026911261364515, -0.19947818869684206, -0.18610894965564131, -0.1952749612930141, -0.22975117029674447, -0.29044750126402624, -0.3805354558503857, -0.5039046684928478, -0.6502088654406958, -0.801402010705524, -0.940924158144039, -1.0563357669189841, -1.136309846922961, -1.1746305764274714, -1.1745961631455613, -1.1465845057077255, -1.1016500042487136, -1.0458413587874313, -0.9839624516137206, -0.9253391534349185, -0.8815588364492838, -0.8555286892802706, -0.8381774187536775, -0.8194193813440156, -0.7950422191513, -0.7596978688722029, -0.7023205129616079, -0.6198534435812849, -0.5208112974123512, -0.410391962430444, -0.2871464702982963, -0.14942860849753373, 0.19346892797435455, 0.3708455102425872, 0.51541707531405, 0.6174450595200494, 0.6743127316686501, 0.6852412557372863, 0.6515176447074746, 0.5772162594455373, 0.46889445914250444, 0.3384451289189383, 0.19976918452306894, 0.06896984555174, -0.03980155856701671, -0.11841329013762432, -0.16470810730583188, -0.18236121932270324, -0.1766129394976691, -0.16022748365978232, -0.1488920042977018, -0.15455366139698226, -0.1779444708315124, -0.2199801655700843, -0.28676859342385747, -0.3832992260406585, -0.5015741597751812, -0.6265214692746873, -0.7440038696983944, -0.8445057626069794, -0.9163445931407473, -0.9524433732735136, -0.9543731799195053, -0.9314620724374623, -0.8954476004804459, -0.8522689070417088, -0.8051325594230205, -0.7602259816823357, -0.7271202451475273, -0.7081378489335018, -0.6976732763146998, -0.6879883130964102, -0.6721424411060323, -0.6435252236610539, -0.5955029486691502, -0.5260290727848006, -0.4404491207939458, -0.3443650284691061, -0.23846598777314168, -0.12321287401499335, 0.13523993178984212, 0.2579196001276777, 0.35762869878709924, 0.4290443147473694, 0.4700907235341329, 0.4782675434986529, 0.45365965850314643, 0.3997280668194401, 0.32290509181120547, 0.2319222148907026, 0.13731854974830865, 0.04828004953072585, -0.02686314716272657, -0.08124816354314052, -0.11292262797623887, -0.12315472846614173, -0.11741650248690341, -0.10562124251618907, -0.09830888780575854, -0.10243904238538164, -0.11900568915017604, -0.14649910118282855, -0.19069450820865427, -0.25588169531519395, -0.33881952061265164, -0.4277030022621122, -0.5130559850943964, -0.5883092430980792, -0.644253066888647, -0.6740213009641496, -0.677168172687149, -0.6608201416437827, -0.6341065168994561, -0.6030989191420646, -0.5696206722994697, -0.5380066595460308, -0.516039476415398, -0.5051488726130849, -0.50229013487134, -0.49944620949186636, -0.4885274116594246, -0.467530703760006, -0.43350239562638804, -0.3829544152371564, -0.31839390947143437, -0.24566986899183862, -0.1676959746099744, -0.08576424519732467, 0.06981209949541349, 0.13219844277342727, 0.1823652109056407, 0.219778788107676, 0.24229004039861654, 0.24755426444605433, 0.23483738664767095, 0.20610629017811397, 0.165661927881794, 0.11825595799786892, 0.0702370702627427, 0.025110472880877845, -0.0133900593820689, -0.04068280708826319, -0.055964606361843236, -0.0597393200623031, -0.05587558937668656, -0.049100005920304654, -0.04582477165861001, -0.04820284020493482, -0.057399466663830494, -0.07190205981915566, -0.09399409306585542, -0.12655830910792734, -0.16915997437374383, -0.2157083752403388, -0.2614816285566166, -0.3020765901260124, -0.33315081522654505, -0.3504901742593294, -0.35298816327686966, -0.3441802821681978, -0.3291214127453814, -0.3120629670946408, -0.29371145400482485, -0.277280632060947, -0.2669498931782375, -0.2632692533916421, -0.2647393846908645, -0.26422438170207657, -0.2573578592131891, -0.24614627784325122, -0.22875604769933025, -0.20184310740050423, -0.16635512084495377, -0.12692170397225147, -0.08565723046676092, -0.0435376295533444, 5.312515247996559, -0.014034011071931418, -0.024290787997462975, -0.028112699624948435, -0.023450397634617405, -0.008631464663831892, 0.015705243855007447, 0.04557398384220957, 0.07484384114603457, 0.09828392145812113, 0.1115774971969246, 0.11303030830293584, 0.10207831863815943, 0.07991265956134679, 0.04913516889724363, 0.01342986251146183, -0.023642704388521372, -0.058123464575869206, -0.0866956545900551, -0.10642522106424494, -0.11614738410770387, -0.1155533968779139, -0.10559654843739495, -0.08701279621822641, -0.06099165704329434, -0.02934973409944576, 0.006242502512611668, 0.045252842351386005, 0.08732059391024259, 0.13045748296736928, 0.17037971719874448, 0.202143683873592, 0.2216456139039217, 0.22745477476191847, 0.2203037644973669, 0.2028533145262063, 0.1778863032018917, 0.1462085459941282, 0.10781277126918912, 0.0638471201362656, 0.017732021459292518, -0.02599376575962108, -0.06354232848614054, -0.09186673410651756, -0.10829792062296503, -0.11050431293071132, -0.0982077600746684, -0.07300987575614903, -0.038824783619592816, -0.026388655150283085, -0.04565027461654209, -0.052075020459069504, -0.04196883596215748, -0.012791098429081396, 0.034404715746916316, 0.09204634900577774, 0.148653589225189, 0.19371277706452172, 0.21969542529862882, 0.2225346957425563, 0.2013227773245372, 0.15873920461677385, 0.10011690719811131, 0.03219889139398179, -0.03821296001660643, -0.10412528711022966, -0.15895425253606815, -0.1973125686065203, -0.2166394747785319, -0.21673012499182942, -0.1991033884195851, -0.16558935604895658, -0.11871239179632465, -0.0613606025262535, 0.004015475048277209, 0.07662281022441368, 0.15527011955804065, 0.23528610417714124, 0.30882791852253977, 0.3673463693704605, 0.40402095174811525, 0.41581976317900626, 0.40377730454163224, 0.37193828246923993, 0.32471606145330284, 0.26435905334128496, 0.1917900450988825, 0.10944134121123772, 0.022780089012495147, -0.06021547377610394, -0.13188662978389268, -0.18576411553887776, -0.21617515535651632, -0.21892935796310156, -0.19335137492052096, -0.14337227782974224, -0.07618762629894188, -0.03617967367498925, -0.06166823947724305, -0.06833914002925055, -0.05153517999545933, -0.008589052940687816, 0.05870241850888874, 0.13988803263013386, 0.21975481858080034, 0.2833502784169491, 0.3200854977441248, 0.3237261230033369, 0.2933148643158156, 0.23335000537544426, 0.15214143714148073, 0.05883155554534164, -0.03780375678954247, -0.12888752741827522, -0.2052339514809179, -0.2599224965068324, -0.28883192789034423, -0.29174286339254735, -0.27067811063935165, -0.22883441957281744, -0.16995053520306508, -0.09740530941568681, -0.013360955710064747, 0.08155813743717755, 0.18504663672164906, 0.290172987533432, 0.3863961757765715, 0.46336852063016865, 0.5132806913094955, 0.5319714344309879, 0.5194552570618747, 0.4792626023140036, 0.41595997163252846, 0.33384213700914894, 0.23548867614804156, 0.12419032262949335, 0.00635749627306009, -0.10812185258705577, -0.20789618546167798, -0.2824643470535005, -0.32267365051583113, -0.32332050669256074, -0.2836657622119969, -0.20964453233886857, -0.11114989701711074, -0.04222073997111765, -0.07044960456150236, -0.07471716521538742, -0.05009917940156096, 0.005524921744114751, 0.08917473759104223, 0.1887826145352721, 0.2862714530764196, 0.3637880972707748, 0.40816334163131696, 0.41194536446612656, 0.37441002739538276, 0.3018155541584023, 0.2050946894274464, 0.09518163222063063, -0.018614289705751214, -0.12665027452979358, -0.21869307500513588, -0.28619968296155196, -0.3243827938304277, -0.3327494090321013, -0.3137183403736285, -0.27146189329349263, -0.21070584252612834, -0.13583106496213934, -0.04800492427887058, 0.05308234987954891, 0.1648986421520724, 0.2792628804153775, 0.384316272061212, 0.4697601889740718, 0.5279153204026403, 0.5539286947596354, 0.5459351669661325, 0.5055451812820311, 0.4363357676395469, 0.343274948416827, 0.2306040273049936, 0.10206618121480839, -0.03578666299579282, -0.17184245805042722, -0.2913981041447875, -0.3797212435316778, -0.4250459928947455, -0.4208923294382599, -0.36712988278716263, -0.27043621002884716, -0.14308447617693773, -0.04302746672411355, -0.07022013736315919, -0.07029741509354913, -0.03778712004586566, 0.028868942489469196, 0.125002155722631, 0.2372884697564165, 0.3460237485067884, 0.43223132185341756, 0.48153948564867943, 0.4859823185122372, 0.44491262845928425, 0.3659129817721526, 0.2613894128876671, 0.14340666706102748, 0.02128546298207203, -0.0954920746795374, -0.1964657639109214, -0.27256806269709655, -0.3191958996457932, -0.33556888219617137, -0.32416910581201225, -0.2895806819007511, -0.23748229012155547, -0.1727219925070549, -0.09613174820848333, -0.006313476355724356, 0.09545608787376812, 0.20180790594250145, 0.3014586794917675, 0.3847525317153151, 0.4445697010030471, 0.4760451749875742, 0.47601688891557886, 0.4433131433528985, 0.37954083528766064, 0.2882146627915417, 0.17391270535390427, 0.04048881315896044, -0.10545801942352735, -0.25140014076596434, -0.3802336200937627, -0.47378075957221816, -0.5186252282024406, -0.5073755908944964, -0.44011425898579476, -0.32373217293117384, -0.17133845784511942, -0.038303635266972114, -0.06079337738521508, -0.05563719576465451, -0.01606113277743997, 0.05940626714626939, 0.164158788169252, 0.28353424830271284, 0.3978211967308398, 0.48793411589057795, 0.5401220662270495, 0.546595319853148, 0.5065330275973337, 0.42729859684461, 0.3221270030786278, 0.20363273673099114, 0.0808607860490347, -0.037102893149815255, -0.13993259154328955, -0.21977411429484142, -0.2730243658217942, -0.29944705835025176, -0.3012512364285234, -0.2821574189916355, -0.2482501987676693, -0.204505613356724, -0.15214180443985523, -0.08855629822728142, -0.013063022218772268, 0.06937251277658178, 0.15029791576082807, 0.22113681170098307, 0.2754951642017691, 0.30859768846857444, 0.31705803750485956, 0.29766529277209663, 0.24875426059396247, 0.17075088592951015, 0.06654241521633235, -0.05966819724777615, -0.2012095358625834, -0.34481174571166384, -0.47183908676004754, -0.5619038349430722, -0.6003028358766969, -0.5797760128898035, -0.5000988285302785, -0.3677963441726714, -0.19510675446139705, -0.029274322062381137, -0.044636926337433915, -0.03389157846940768, 0.011529098673852288, 0.09274560686921414, 0.20211969136914787, 0.324328799795472, 0.43968421648245865, 0.5299109662273853, 0.5830293962745211, 0.5921448873192493, 0.5563445748560539, 0.48236946672817943, 0.3831789666132354, 0.2708160132707273, 0.15442104900641232, 0.04292590961545985, -0.0546670069526714, -0.13295790873872998, -0.1903192154527221, -0.2277229516174333, -0.2468598814223856, -0.25039420614487323, -0.24323310378467938, -0.22994684105704824, -0.2117499807726827, -0.1854085826661968, -0.14838221904038634, -0.1018415059950758, -0.05059466588706768, -0.0012241646687558808, 0.040929543781449876, 0.07167630121810514, 0.08774480814938655, 0.08459024708812057, 0.05656439112446305, 0.0004208245698019469, -0.08391463927169514, -0.19246745871505797, -0.31814137362262596, -0.44805035446307534, -0.5631771257701389, -0.642773256677776, -0.6706323339917971, -0.6392216924589166, -0.547811654318991, -0.4022983553320344, -0.2136806984565758, -0.019364879912667637, -0.02703948451719623, -0.010913410003616385, 0.03826191386891728, 0.12186408132930035, 0.23248579413017284, 0.3544972360970303, 0.4675453039814297, 0.5548749522963778, 0.6066775472815727, 0.6177492162740998, 0.5876835187621079, 0.5228981620889955, 0.4352833429221934, 0.3359162134814434, 0.23370578537964457, 0.13642040555752288, 0.050765100711894356, -0.020515370947038595, -0.07873845818853101, -0.12645374536302764, -0.16510619850077551, -0.19624159401903346, -0.22256028196632927, -0.24731051072807533, -0.2705874181236473, -0.2886968456825083, -0.29711778324007804, -0.2936974124252507, -0.27965784204702626, -0.258193626668464, -0.23320623992473938, -0.20781861926118808, -0.18543244538399736, -0.17178737935183883, -0.17587289865538724, -0.20533775178666164, -0.2630586540079009, -0.34627735166197493, -0.4475178288841624, -0.5550562460196341, -0.6512295285217972, -0.7158387637713971, -0.7313809244559357, -0.6886623927078378, -0.5862316344160607, -0.4289494755457806, -0.22744700989830435, -0.011681992731011672, -0.01299852132138902, 0.007081602695763796, 0.05742151965248901, 0.14048661874910484, 0.2492335557905172, 0.3678326424140771, 0.4763765080634682, 0.5592350807044626, 0.6079395246202334, 0.6197549781383325, 0.5958042616869483, 0.542913986704081, 0.47176317839837795, 0.39249000326376215, 0.31218133531381403, 0.23629386083279955, 0.1685740989624908, 0.10867390850271, 0.052721936482774616, -0.0032141568897304405, -0.061267406246405004, -0.12203704285442472, -0.18607131784914077, -0.25354474461103144, -0.3223404217066063, -0.3879054751933246, -0.44406044444969744, -0.4862437087145923, -0.5124349780227441, -0.5222506037211812, -0.5171272021651361, -0.4990294899337488, -0.47160622226413124, -0.44228091151872645, -0.42258481763526945, -0.42401671270195623, -0.4519963745100899, -0.5052774588576536, -0.5773695718774737, -0.6579144087699079, -0.7316164289046942, -0.7790186555401751, -0.7819326962914929, -0.7287854416703397, -0.6166208774165447, -0.44924459419619966, -0.23746713450383647, -0.007580885480813641, -0.005371808715704242, 0.016448364204208404, 0.06580529642491961, 0.14530779108800326, 0.2487192693505947, 0.3610901207427758, 0.4636468584503803, 0.5412333482349148, 0.5867376290077385, 0.5996304519177827, 0.5829746524251141, 0.5444139408275022, 0.4938886660944503, 0.44001377666706093, 0.3871479694203556, 0.33766779769556776, 0.29190347830737706, 0.24639840400928434, 0.19550188415325728, 0.13407030632133313, 0.05889257734356009, -0.030318977213157586, -0.1323745448660707, -0.24352577976577738, -0.35830723077572935, -0.4703850345298001, -0.5726942177280894, -0.6587571321795448, -0.7242234661018089, -0.7654839022579236, -0.7808126507986365, -0.7710653913294416, -0.740438434758818, -0.6978538968266512, -0.6569745201693734, -0.6318303405136465, -0.6304476001961405, -0.6531509750714616, -0.6948318621549999, -0.7471548729280622, -0.7973699837395014, -0.8275355407480168, -0.8186345265015907, -0.7569936926690025, -0.6375576567106623, -0.46296906420836265, -0.24397449907615268, -0.0070169262595402545, -0.0042345427833146215, 0.01708226401485965, 0.06350358268634754, 0.13651398020966618, 0.23127232598694167, 0.33485905771978147, 0.43009814868185686, 0.5029699935667894, 0.5473594953862727, 0.5639482279969855, 0.5577254685295681, 0.5363324849111851, 0.5088041356349952, 0.48193685177733075, 0.4582527005020771, 0.4369503157358747, 0.4148334366248715, 0.3856102409829827, 0.34194689980394694, 0.2780854930020629, 0.18987816916164366, 0.07653868639211578, -0.05938328430865515, -0.21062467461358383, -0.36785704425519505, -0.5224842789711616, -0.6662740572549734, -0.7915064060220514, -0.8921462375627436, -0.9623572019768178, -0.9975929802443729, -0.9975079840070217, -0.9661651840375809, -0.9135721902728736, -0.8553064898202664, -0.8073653119364882, -0.7799496405752672, -0.7749966820852712, -0.7885863234137298, -0.8142744259541491, -0.841748037050218, -0.8553537965841047, -0.8363256943102083, -0.7693835264449198, -0.6467077522429461, -0.46906823243518786, -0.24681697299110578, -0.00894200622561169, -0.007746512657897699, 0.011067895908721172, 0.0520945774380788, 0.11645958269238423, 0.20080659077166854, 0.2945907755419723, 0.38276077529401015, 0.4527201709794768, 0.49898236413148167, 0.5233525909254485, 0.5311706623310047, 0.529159078120422, 0.5251537656773166, 0.5243442779305482, 0.5276918453802145, 0.5325079166319721, 0.5330019153022595, 0.5201774343824636, 0.4853147609915176, 0.4219698558852605, 0.32585799638968665, 0.1955015060643679, 0.03411245675505442, -0.14910957701478064, -0.34153454291062024, -0.5320975460647088, -0.7106579247053596, -0.8686545933742392, -0.9989392331341548, -1.094215481310137, -1.148206446753217, -1.1586628729969675, -1.1292991289297227, -1.0707350549417292, -0.9999168632415094, -0.9345622490895555, -0.8866084996214569, -0.8596077670224277, -0.8505272518249438, -0.8540084700771762, -0.8616051975566127, -0.8602355579532904, -0.8329731811708928, -0.763704625622768, -0.6419243486489775, -0.46605757438748524, -0.2454867126505959, -0.01114031578771983, -0.01289894255012218, 0.0017027437148871274, 0.03607179884624198, 0.09176562148506782, 0.1666460414242798, 0.2522633366228538, 0.3354286524547974, 0.40506540710713385, 0.4564126876407012, 0.49177731263794416, 0.5159074222562936, 0.5345151364852869, 0.5530224653840803, 0.574817966719425, 0.5999515456920286, 0.6255261890370781, 0.6441320192456496, 0.645349075860631, 0.6194753193380579, 0.5594657868234687, 0.4608232537547959, 0.32204525595944195, 0.14625426563282734, -0.05726377476499612, -0.2743316720875817, -0.49156474711136633, -0.6968998644951135, -0.8807579291015343, -1.035194152513579, -1.1519982027779345, -1.2233034465718882, -1.24510571925522, -1.2204070002046967, -1.1603484035035228, -1.0828172744318005, -1.006890872835039, -0.9455404445471266, -0.9035808985534717, -0.8785099529626007, -0.8654422781586827, -0.8573681424729013, -0.84328143360322, -0.809246977504651, -0.7394705274738961, -0.6216713775991783, -0.45184368887384396, -0.23816300912714763, -0.011956450271915582, -0.015798614348225645, -0.005220299966852828, 0.023360463892380095, 0.0725988677075084, 0.14165233607372263, 0.22296187811800808, 0.30510931288096194, 0.37850793945454364, 0.4384199264595107, 0.48653433550924274, 0.5272447144461525, 0.5652350264010649, 0.6030972099495475, 0.6421518797717511, 0.6818721255272974, 0.719829210743806, 0.7490099149280625, 0.7590079687189715, 0.7399686008619438, 0.6846154009088586, 0.5880882284042848, 0.44885377497822876, 0.2696187718884188, 0.05887924816071542, -0.1698887660192614, -0.4022623241665269, -0.6251396114531513, -0.8277776185216061, -1.001260722642216, -1.136667663675764, -1.2242058004870942, -1.258754787776584, -1.242194157322474, -1.185933432885676, -1.1084300102087496, -1.0289534532859281, -0.9613595172959506, -0.9110157820424288, -0.8759300263438445, -0.8510629887994763, -0.8306834686047803, -0.806032267539733, -0.7659346595559903, -0.6961541166832385, -0.5839101059001298, -0.4241186029809009, -0.22355096893949503, -0.00952638181893044, -0.012571337305559524, -0.0034773004359904, 0.02275121333864976, 0.06984064358912422, 0.13778130496782667, 0.2199232518089989, 0.3067302599586586, 0.3890669767099752, 0.4610383773015343, 0.5231655646993785, 0.5793230672971502, 0.6330902558062599, 0.6852915468889003, 0.7349312112404615, 0.7808874404139644, 0.821572286718124, 0.8513522115625853, 0.8615760423935042, 0.844154930253173, 0.7921366445137025, 0.7003273942426289, 0.566362792503459, 0.39253915360557207, 0.18609727163527676, -0.04133097239453163, -0.2766378249668925, -0.5069782056263171, -0.7209656698813264, -0.9087453201485545, -1.0598242203950634, -1.1631520458573208, -1.212106726603656, -1.2079315030115785, -1.161366852098412, -1.0904793327829365, -1.0137198022633387, -0.9449689049960711, -0.8902382770398126, -0.8481755789746298, -0.8141917383521338, -0.7833618832197428, -0.749305365517457, -0.7032238710503091, -0.633480802203796, -0.5279968345517391, -0.3818685916778646, -0.20079857193367617, -0.0025201491642518016, -8.33797124140812e-5, 0.012720921601756663, 0.04190422680490834, 0.09214574094352465, 0.1640393523286357, 0.2520364382024425, 0.3484146646540136, 0.44458476280152615, 0.5331510039474672, 0.6114938521690009, 0.68184706161267, 0.7473389777780692, 0.8076560988507653, 0.8601121093546596, 0.9034106038494263, 0.9366977352660455, 0.956097732987699, 0.9561657300944071, 0.93222699747818, 0.8787675337009334, 0.790310001775579, 0.6636706564087961, 0.5007049726145648, 0.3072810577822777, 0.09223768181971251, -0.1345605863012066, -0.3620531721009975, -0.5796148201733141, -0.7767010475614835, -0.9412730016611178, -1.060520627024888, -1.1259538043757764, -1.1377714160221284, -1.1058373813799172, -1.0461579138853727, -0.9757601649024776, -0.9078093289309268, -0.8495124227853476, -0.8009940212209722, -0.7584666536941863, -0.7179047347934329, -0.6748878792546916, -0.6231920867930557, -0.5537597499606357, -0.45650894007307286, -0.3274589895459665, -0.1713623400597171, 0.010383199463027923, 0.024663756840446464, 0.04823375993506406, 0.08731194960795494, 0.1468500343348213, 0.2273288418398723, 0.3249561643916142, 0.4346983429488574, 0.5487313959140383, 0.6570857687243119, 0.7533424764592954, 0.8370686820903799, 0.9103491909348239, 0.9716315353991519, 1.0185726466114815, 1.0503131059071553, 1.0667616437422083, 1.0660998813851759, 1.0463311417134393, 1.006212897093924, 0.9430400090854759, 0.8521356429832863, 0.7302166027861552, 0.5794944798758627, 0.40434540786601725, 0.20994298977819134, 0.0016631462330190612, -0.21349357960808238, -0.42690623922663934, -0.6282219840692645, -0.8041625749186625, -0.9395055611619083, -1.0231968071430502, -1.0534264118438015, -1.0381861227981146, -0.9912776775656899, -0.9273562309030312, -0.8591562697181951, -0.7956255676914491, -0.7392384732486424, -0.6874901467953376, -0.6371837244701021, -0.585576509016556, -0.5291283314243905, -0.4613019967007645, -0.37449890655621093, -0.265615211190358, -0.13810593180012892, 0.030882862591088397, 0.06514379126299873, 0.10758432574532566, 0.16422688182857062, 0.23961957295202435, 0.33391990188713994, 0.444881241033406, 0.5698071965028274, 0.7016059317545013, 0.8282472018853623, 0.9404573508065722, 1.0350724044740471, 1.1117656265629698, 1.16796113704141, 1.202169422672149, 1.2150233356472764, 1.2082933062862573, 1.1814551860239195, 1.134798430840503, 1.0697417181204383, 0.9870761070340446, 0.884180461547172, 0.7599118600041462, 0.6179943411057873, 0.4624955147759704, 0.29403483908099476, 0.11212749564065909, -0.0827257572726169, -0.28546393913113394, -0.48676760717032946, -0.6719790246575738, -0.8227945542900635, -0.9249726073173791, -0.9736053133795752, -0.974205538168748, -0.938213275093635, -0.878206842502481, -0.8067737190724573, -0.7345895421508298, -0.6671886190230201, -0.6040406599069165, -0.5430265861197738, -0.48323323136995344, -0.42361437192683427, -0.360090536218734, -0.2867415997306569, -0.20066830109431003, -0.10358718919394262, 0.060683093765801346, 0.12379192010949656, 0.19338469172363854, 0.2751583986952434, 0.3726564908303087, 0.48572371214517396, 0.6128426347808357, 0.7528546356867336, 0.899340250602483, 1.0395702499244424, 1.1627052922108179, 1.2636473912882757, 1.3389651626336, 1.384793557158507, 1.4006494947350563, 1.38976530573057, 1.3558497682523958, 1.2996018949824102, 1.2222469497400492, 1.1270536244278266, 1.016676268772494, 0.8916852794828859, 0.7551619095107809, 0.614900082607224, 0.47598565613477595, 0.3347257632697024, 0.1828710068246697, 0.013430298350867046, -0.1739831063302819, -0.3723014202913911, -0.5650926205577446, -0.7299190677088698, -0.8485793339131338, -0.9130862358676023, -0.9261738216208271, -0.8970707774590534, -0.8366281202495204, -0.7575644542641972, -0.6721834310569095, -0.5891606352151405, -0.5107566145507345, -0.43694725802483997, -0.36924229367869577, -0.30854180104234835, -0.2526192540190415, -0.19589557735228888, -0.13482474678809908, -0.06908234399600123, 0.09964986338816068, 0.1999959134135265, 0.3039656257446813, 0.41633177516957126, 0.5402277568793128, 0.6753569429192723, 0.820426320366474, 0.9745137829457845, 1.1315633310798268, 1.2796022803586726, 1.4077027886557623, 1.5097513103162385, 1.579431207689575, 1.6110225605665114, 1.6049990868532602, 1.5670156580787054, 1.502996437663382, 1.415753301841716, 1.307389223821516, 1.1816131398471652, 1.0415303497311779, 0.8896934986417594, 0.7325950354335005, 0.5839457214433308, 0.4515300530382159, 0.3307536811510281, 0.20561502446145444, 0.06056535217399005, -0.11038310303333497, -0.30390274795425365, -0.501323858528466, -0.6763408706460181, -0.8065856918925247, -0.8819002424392075, -0.9021196051222918, -0.8743991606928606, -0.8084987102580484, -0.7166202767804484, -0.6131119230101987, -0.5095222702208049, -0.4117356509537075, -0.3229456506050517, -0.24728546177869962, -0.187346929509815, -0.1413857201708575, -0.10341282264500151, -0.06854899020880421, -0.034417739388346164, 0.145052780012904, 0.28852165753558406, 0.43145703329613067, 0.5775024208155326, 0.7296615663336408, 0.8876755184079217, 1.0504293282224042, 1.2167291415594887, 1.3805175402941319, 1.5310244504756683, 1.6587557250377067, 1.7572376549717466, 1.8184169114189632, 1.8342903534445865, 1.805408524233123, 1.7393689573457285, 1.6446671932963781, 1.5263576546180386, 1.388518078243587, 1.2356990425836307, 1.0703713068924499, 0.8938919946832359, 0.7148465535481833, 0.550954340054011, 0.4126423612097993, 0.29512660440720956, 0.17980237449265368, 0.04733190801506752, -0.11245472378292252, -0.30007671117841284, -0.4970953562020966, -0.6737579262197039, -0.8066123685696508, -0.883946282406558, -0.9039501547440411, -0.8712139543100008, -0.7942598263202043, -0.6853135861988278, -0.5599693407525012, -0.4326180334663449, -0.3129137579329242, -0.2079290912291416, -0.12433361381464685, -0.06585131362893575, -0.030162543938801214, -0.010843584794521804, -0.0020176550331597863, 0.0003960046310046239, 0.19217330584041123, 0.3805391380084548, 0.5639922682688271, 0.7446650612269994, 0.9247541511747934, 1.1043249016826509, 1.282776620163362, 1.4584525783658535, 1.6256628225867489, 1.774873374096459, 1.898297774143382, 1.9895680736070307, 2.0399185455889466, 2.0402670274016903, 1.9904006736171374, 1.898553232150499, 1.7755097291824218, 1.628811906349984, 1.4660330888619912, 1.292479586207438, 1.1082913499238412, 0.913025009023885, 0.7145384207496581, 0.5327347700339901, 0.3790909069930397, 0.24747060596027223, 0.12079316559107345, -0.01892668924833233, -0.18119442509714392, -0.36513703421386257, -0.5549774221877483, -0.7231386495265997, -0.8470819723184204, -0.9159353605086342, -0.9267406897757389, -0.8822267812241172, -0.7897054145885786, -0.6611653686798632, -0.5129180186733426, -0.3615726423972268, -0.2200522861151241, -0.09894084463813402, -0.007326191698749457, 0.050434909568706034, 0.07706084350310442, 0.07927659132769357, 0.06348573132893326, 0.035029738782053135, 0.23635634133375777, 0.4671057602594378, 0.6890086632035914, 0.9025520152301765, 1.1088305886974776, 1.307823586719044, 1.4988243933538477, 1.6806532403989562, 1.848597586406469, 1.994353496253036, 2.111003467033249, 2.192634246735332, 2.2306005822661117, 2.216225112970048, 2.148924068611698, 2.0366338689660193, 1.8907087842898231, 1.7218552873536919, 1.5411223040752418, 1.3531050011148393, 1.1560138243340377, 0.9450891611173662, 0.7282522465972922, 0.5252894750711161, 0.3495084081459162, 0.19445235460526075, 0.04497206078895706, -0.11297122666915306, -0.2866088483258475, -0.4723884161298087, -0.6544530787215231, -0.8072297554046536, -0.9130654987221459, -0.9643370445916841, -0.958750398605788, -0.8975437453648893, -0.7868333440748141, -0.6386076654034772, -0.4693063675072967, -0.29669345300240363, -0.1356333409139105, 0.0004747699566588575, 0.1001442068567978, 0.1582552833011294, 0.17745145868065246, 0.1643370487444338, 0.12544363771590536, 0.06771709401514844, 0.27396689466264296, 0.540781573569316, 0.7956109928131213, 1.0373607118298263, 1.266201031463146, 1.481266689576789, 1.6815918756309833, 1.8668015770699098, 2.0335139106070237, 2.1751699227681027, 2.2847315655796483, 2.356051822967625, 2.3817050041888623, 2.3549730004837293, 2.274973986856015, 2.1485438858873858, 1.9866193315436136, 1.8024878232061596, 1.6087455955302497, 1.4104885174949953, 1.2022984534613952, 0.9762477963660704, 0.740945719925691, 0.5167682112899064, 0.3164490025071922, 0.13656393248887258, -0.03577975041884152, -0.21202850696550193, -0.3973498523036777, -0.5863875158588425, -0.7609634695826116, -0.8959883743295968, -0.9793606295085995, -1.0088687571093207, -0.9831983835516783, -0.9033960414800568, -0.7748450490455774, -0.6090158040266136, -0.4225005465217015, -0.2329741318056691, -0.056690842836185744, 0.09113995120862846, 0.19749099397017886, 0.2560148101308302, 0.2683336574250441, 0.2407535697844906, 0.18066223607437565, 0.09674627433463212, 0.302643570761916, 0.5965590319036425, 0.8755827401553777, 1.137771065974696, 1.3830557751539732, 1.6095944328304563, 1.8158091170306294, 2.002051831393985, 2.1667187529786878, 2.304649377392803, 2.4085743319967503, 2.471981246779286, 2.4887757499158605, 2.45412194726578, 2.3670311849220376, 2.2323551388608265, 2.0597886988323677, 1.8630615157711101, 1.6566013352800437, 1.446149300362507, 1.2247821198883857, 0.9847545912702934, 0.7349951713822316, 0.4938753325558395, 0.27412205506044207, 0.07435295921588787, -0.1150094569978404, -0.30292300124899796, -0.492856853705554, -0.6788556482235435, -0.8430590610572679, -0.9584648033253553, -1.0193214735596128, -1.0271657049198786, -0.9822010560039571, -0.8851048007890546, -0.7411308247150407, -0.561645708036414, -0.36289961511787316, -0.16253955337309137, 0.0225674436793088, 0.1764274410510909, 0.285253105918976, 0.3418297876103583, 0.3466710110160733, 0.3053768335902989, 0.22633162077705402, 0.12017399253104369, 0.32065042471765426, 0.6309330136088808, 0.9234615714265815, 1.1964788048791108, 1.450012323578261, 1.6816502034193155, 1.8893928476753175, 2.074104768561419, 2.2364375438249384, 2.37188460916286, 2.473182357053281, 2.5336672901885726, 2.5477681208447645, 2.5116391378292557, 2.423732556831679, 2.285998229971851, 2.106065032194759, 1.8969143665336088, 1.6737022604924499, 1.4447651387344225, 1.2078797744184084, 0.9579755569515858, 0.7020666437851755, 0.4534715416783032, 0.2230961332832072, 0.01164983498039822, -0.18640737593352721, -0.3760347486416041, -0.5597001174619325, -0.7321109403887998, -0.8775649072668839, -0.9724535666545209, -1.0129305552639034, -1.0015040289090416, -0.9395643293104966, -0.8286890320131193, -0.674336030802095, -0.487381065579035, -0.28345286394363306, -0.08022988063126178, 0.10523210776308614, 0.2568153008626652, 0.361502123196581, 0.4122766209282999, 0.4084318324297653, 0.3546637381974928, 0.26023477870785683, 0.13728507298566803, 0.3261855785658783, 0.6407769331904408, 0.9357727511815949, 1.209507919353393, 1.4623597639624661, 1.6916955272611727, 1.8957261605877427, 2.0760893121264425, 2.234855053030686, 2.3687842411949678, 2.470624888010203, 2.533369260338984, 2.5514924615148273, 2.5211350140131987, 2.4391606316523116, 2.3045925060857, 2.122489447712937, 1.9043614677681677, 1.66515737447713, 1.4166188560062976, 1.1631567484219378, 0.9050314888013735, 0.6474492435218469, 0.39912032997205105, 0.16705487430147686, -0.04703977066034506, -0.24424530251049353, -0.42581208413616267, -0.5925138964808013, -0.7407094732065272, -0.8594035727634612, -0.9319764064718008, -0.9524417543406707, -0.9231903054944053, -0.8472095317694035, -0.7271739773976797, -0.5687859816222814, -0.38260395382266593, -0.1831478127664548, 0.0128376111449204, 0.18862320525539258, 0.3287752715847601, 0.4219195260843133, 0.4625224495815834, 0.44934181746041096, 0.3859580561328958, 0.28100552639713, 0.147498590547208, 0.31780359190341634, 0.6240979278504297, 0.9108237769347953, 1.1759278184768778, 1.4194878089130927, 1.6390596972141833, 1.8335707245993615, 2.0061041317845296, 2.15953963024825, 2.291928067685848, 2.3962697971503917, 2.465268670211767, 2.492928381652901, 2.474605052821362, 2.4053020175712065, 2.2818223803971978, 2.1064511028994155, 1.888585719461567, 1.6418786519700106, 1.379751840580328, 1.1118357363645335, 0.8443067647372835, 0.5847282145434044, 0.33923395951882657, 0.11111652188036059, -0.09763423854060807, -0.28550528981324524, -0.45066070609888115, -0.5926981854511495, -0.7110553828640522, -0.7986183137972792, -0.8441364541821057, -0.8417519288991571, -0.7949258712738624, -0.7070982230201777, -0.582391585662812, -0.4270280608625176, -0.25074383816415236, -0.06637428762484, 0.11139240689862975, 0.2669859138744998, 0.38669106840745676, 0.4617897249572007, 0.4886870728282325, 0.46616004017110746, 0.39658819992968725, 0.28730025371440004, 0.15046430860297158, 0.2962126997791445, 0.5826991183855568, 0.8515192195662766, 1.0993110798609733, 1.325455868665958, 1.528218201497071, 1.7077453141139818, 1.8684147918967529, 2.0142660446748994, 2.1442398046284428, 2.2519081453867322, 2.3295806076001595, 2.3703660631112258, 2.368744663414232, 2.318520942522118, 2.2145601658316934, 2.0565649645031607, 1.8512770532357015, 1.6095505043327558, 1.3441723085619797, 1.0674791062310454, 0.792356602101816, 0.5291615415318249, 0.28504209207151837, 0.0626492699221349, -0.1362369718340537, -0.3087115181370314, -0.45234598534766635, -0.5665705983900553, -0.6521187455808293, -0.705034556530742, -0.7185834073894026, -0.6912277976597653, -0.6269085949096872, -0.5299089358082534, -0.4052471792932281, -0.25907883594269837, -0.10066009991541652, 0.05921577714710565, 0.20850794907449513, 0.334528787448481, 0.4264191067849761, 0.4783082834031757, 0.48876581640422906, 0.4571323326215302, 0.3848458930370833, 0.2775195237928518, 0.14507629684019918, 0.2650398095022218, 0.5229257564005372, 0.7660169582632076, 0.989446602792292, 1.1912150342305483, 1.3708757715473765, 1.530688557970751, 1.6758676122153937, 1.8116045282022262, 1.9378606532773825, 2.048926885678063, 2.1365434585770635, 2.192799040480997, 2.211266479943032, 2.185112838678374, 2.10776262360389, 1.976566941110215, 1.7944063745697636, 1.5687553898596784, 1.3105423752819294, 1.0339014430304454, 0.7555575114317368, 0.4902779890099316, 0.24730219759386662, 0.030877955094201322, -0.15647755463453067, -0.3114373203405191, -0.43180059806412247, -0.5169032395813348, -0.5675635178582146, -0.5836076209164218, -0.5641388667642139, -0.5119065659252982, -0.43202250422908717, -0.329709783978959, -0.2096651619400849, -0.07809847646465519, 0.05613512735772913, 0.18426064530928826, 0.29753465756716885, 0.3873105736399323, 0.4463696441888932, 0.4719424401288722, 0.46432256100646807, 0.42373853741266193, 0.351511121502841, 0.25172301088583604, 0.1312819597861907, 0.22955350070443975, 0.45427739889932206, 0.6669531284856455, 0.8608766636540349, 1.0337826513913233, 1.1867559887546246, 1.3236937660539365, 1.4505856718908094, 1.5734412306434247, 1.694143279914365, 1.8080701373989898, 1.9064006369603963, 1.9800004214973168, 2.0209097022169487, 2.02187971255008, 1.9751468279119915, 1.8756033470567495, 1.7228070332166305, 1.520817977009758, 1.2784254545855611, 1.0103192055379502, 0.735242709465809, 0.4713057634391328, 0.23063243395914473, 0.020478136823449462, -0.15476668306881414, -0.2915828508171046, -0.3880755830771211, -0.4437646477481587, -0.46061959647065975, -0.44184502526666997, -0.3916160469627751, -0.31682775589778905, -0.22466008239992585, -0.12043783130594889, -0.008911720443509448, 0.10373573429858123, 0.20923606869724268, 0.3010965315041096, 0.3741371662218683, 0.42434544495348203, 0.4487212255069853, 0.44718000781936423, 0.4211370712930539, 0.37212216201801435, 0.30226778336599675, 0.2140197789353967, 0.11110425407342424, 0.19506933793568831, 0.38634110764116036, 0.5674642418399307, 0.7306347082203489, 0.8736246730123614, 0.9991088935722774, 1.1119767777609104, 1.2187781921931786, 1.3264456330778163, 1.439218666926368, 1.5543435688105993, 1.6631035457183545, 1.7545894846751842, 1.819005297005834, 1.8476719558735717, 1.8320040780502505, 1.7649188219862495, 1.643268401824381, 1.468727652039406, 1.2480166846876284, 0.9953489357407558, 0.7298368300302663, 0.47129410846642883, 0.23503933509870206, 0.03192808546481078, -0.13151377856625077, -0.25102815586190225, -0.32478037103071733, -0.35334294113461273, -0.3400693328659862, -0.2909062377770623, -0.21423979840251575, -0.12046764422808375, -0.018503427322269395, 0.08539554564514194, 0.18586479185223287, 0.2768309788736019, 0.3514512518294915, 0.405462577102759, 0.4377729033918916, 0.44897033513007634, 0.43980967561738377, 0.4121995970426155, 0.3689197144584182, 0.31282268095110605, 0.24673926322685552, 0.17176751430848516, 0.088578087916265, 0.16573863023746624, 0.32791473722106645, 0.48004947928231534, 0.6146292196412139, 0.7296563919511528, 0.8289529897392838, 0.9179953397486295, 1.0035978002055932, 1.0940766389308205, 1.1963036982537927, 1.3099051010196572, 1.4268709135933648, 1.534687674999802, 1.6214588959584668, 1.6766116137985807, 1.6900415110715727, 1.653571323720596, 1.5620701980962226, 1.415564771637007, 1.2197821886986602, 0.9870614427858428, 0.7360513749935065, 0.4871814324494853, 0.25852133566853863, 0.06398017356909363, -0.0876489733063563, -0.19106962058666613, -0.24500260254539388, -0.2508690067473203, -0.21310285307558072, -0.13985194356749633, -0.04252875511240083, 0.06609138991146174, 0.17538415153586226, 0.27714336984346033, 0.36518457953777494, 0.4337482713858587, 0.47789112440749726, 0.496220913424733, 0.4911392487935943, 0.46679797248113325, 0.42722525504119585, 0.3762690962889829, 0.31787239668835093, 0.25601942861737, 0.19384088076842731, 0.13143994340772905, 0.06685841249873219, 0.14449494346059308, 0.28504737279638975, 0.4144538716475386, 0.5256492812756447, 0.616966508468958, 0.6922713155951257, 0.7577677817685077, 0.8212621254191952, 0.8931542801304544, 0.9823735189603985, 1.0910242992644423, 1.2121689079914486, 1.332590916005247, 1.4382014123745988, 1.5165574273793732, 1.555813092799432, 1.5464083649397589, 1.4824215613729483, 1.362840630577861, 1.192552798674005, 0.9825576814260214, 0.750090409803459, 0.5157501066179209, 0.2992297509772005, 0.11663599969808017, -0.021607823711889906, -0.11030029087707675, -0.1480147827920743, -0.13660166372278057, -0.08112168050933362, 0.008674504478894968, 0.11974576370358841, 0.2376073343934546, 0.35033312899479774, 0.4476919090937148, 0.5226208609504195, 0.5695864264776318, 0.5861814615500982, 0.573814926885644, 0.5371940764387354, 0.4829504964470885, 0.4174824832141344, 0.34645375206485063, 0.27483831133731906, 0.2077596358441362, 0.14842985665772576, 0.09603834216505742, 0.04746225587789398, 0.1319552996206237, 0.2590093945078264, 0.3737588915891608, 0.4690707798212572, 0.5427031642972712, 0.5975264868016923, 0.6406390666781091, 0.6820370627739428, 0.7343179877070483, 0.8081755686997802, 0.9078268521362161, 1.0277007977251744, 1.1548355251686493, 1.2734874717571878, 1.3694326171156466, 1.4291462992737016, 1.4419027463751846, 1.4014804345056433, 1.3067462442668731, 1.161489106051488, 0.9762224829413516, 0.7662942491516416, 0.5522644856456478, 0.35416116864982866, 0.18868802483258773, 0.06644687451343871, -0.007631712654042407, -0.031958774566364326, -0.008189659222105882, 0.05821139391516124, 0.15683294723663527, 0.27356708739226093, 0.3936238451626107, 0.5043206074609349, 0.5942311122479035, 0.6550906365835987, 0.6822693087454356, 0.675892334589497, 0.6392799594508601, 0.5786179571048464, 0.5015242029119075, 0.4155351736026303, 0.3277379952225017, 0.2445061460025195, 0.17185843391331224, 0.11289168682361482, 0.06700711431665443, 0.03107930788087601, 0.12616337374486444, 0.24659661213138986, 0.3538138206508259, 0.44055522248120543, 0.503117110520044, 0.5427144406043294, 0.5669292164889796, 0.5881880948831739, 0.6210527368185956, 0.6774119233693685, 0.7630513951382687, 0.8746835772688532, 1.0005451598431836, 1.1244031510323083, 1.2300627524830712, 1.3029946603890388, 1.331923334603138, 1.3106695828480401, 1.2384766221005312, 1.1189271693917846, 0.9610952375504596, 0.779049406294064, 0.5919174252278449, 0.4191126512787915, 0.27633067868249406, 0.17340012672952057, 0.11497623108909398, 0.10257313532727844, 0.1350246406890632, 0.20655228271913878, 0.3065215106983468, 0.4208613009513575, 0.5357424543809702, 0.6384484001820478, 0.7172665950892274, 0.7631847329175622, 0.7726012700561042, 0.7477989856887904, 0.6938420385597776, 0.6170789078349974, 0.5249513918019609, 0.42511756268562806, 0.3250444038522347, 0.2321194743193458, 0.15297996136789047, 0.09139949047032275, 0.04779062817371439, 0.019573925579973492, 0.12411529131997555, 0.24182611260817247, 0.3458601826412672, 0.42913641131614877, 0.48593461825534046, 0.5158712138983576, 0.5265655333713928, 0.5316182700426539, 0.5464836086103909, 0.5839255052879752, 0.650796854312065, 0.7465992722088836, 0.861735397793209, 0.9810909388130588, 1.0875451961940912, 1.1659512067602888, 1.2051852099454954, 1.1996405886272201, 1.1490802927058474, 1.0570107084245692, 0.9308151672630967, 0.7829539895599086, 0.6298855775953943, 0.48911568659295607, 0.3744874127044371, 0.29466251138566685, 0.25382572259232417, 0.2535564002784416, 0.2924769368327544, 0.36456577296606396, 0.45941601968191564, 0.5642435533653635, 0.6668592938659074, 0.7556667077872699, 0.8192968843803983, 0.8491364860091353, 0.8428109356059209, 0.8044214360738109, 0.7395956134737933, 0.6543991639668215, 0.5553532669487247, 0.44916374261745584, 0.34248865140852136, 0.24284037769521352, 0.15723611196030324, 0.0903053946335686, 0.0440270585448345, 0.016477920399578003, 0.12359305506497874, 0.2400328032035485, 0.3424275120435661, 0.42368225383294156, 0.4774660830682894, 0.5025427549027955, 0.505157913661903, 0.498355826874817, 0.4972153728655201, 0.5149579028064607, 0.5597639915511853, 0.63318770622149, 0.7289538754019812, 0.8339786650582637, 0.9322416778901389, 1.0091245458262752, 1.0542262349811276, 1.0626434211070386, 1.0341085669413408, 0.9716296228135605, 0.8811039732169267, 0.7726710130267083, 0.659869172709299, 0.557057955980666, 0.47560740692864223, 0.4229630304744077, 0.4029332084792947, 0.4164041292885739, 0.4609105497084533, 0.5302304684601885, 0.6151239934414563, 0.7046180328508737, 0.7887686073110132, 0.8581356847098717, 0.9028110086101663, 0.9158991937250939, 0.896597104215122, 0.8495293221252734, 0.7800977078422618, 0.6934993116603643, 0.5950312119393633, 0.4896411106024084, 0.38228058103252943, 0.27927300588172044, 0.1876336726582136, 0.11309680693136301, 0.05906204076908872, 0.023958740374770086, 0.12347589283273243, 0.2388312566579378, 0.33918717666467607, 0.4178154901857166, 0.46952633059620713, 0.49255079243401345, 0.4910633529523059, 0.4759723175142749, 0.46121798965804395, 0.4595327674392709, 0.4804002015594526, 0.5273896243546039, 0.5973496302297175, 0.6801362551011931, 0.7622993169011397, 0.8317445495281821, 0.8795861369012145, 0.9008538488181176, 0.8946423409380058, 0.8627418740767665, 0.8099872244239337, 0.7437963918146445, 0.6746505125176687, 0.6132612296677293, 0.5684812716670251, 0.5466563933571107, 0.5505567074221416, 0.5796913528738438, 0.6300597439462611, 0.6952736483986791, 0.7675182855858177, 0.8384225483313725, 0.9007129898904397, 0.9470191049450801, 0.9705410972592521, 0.9674723760996836, 0.9384127529619466, 0.8874294231296493, 0.819084748761535, 0.7371900243359636, 0.645340147444126, 0.5462670228375509, 0.44250072401446683, 0.3384811546538257, 0.24104842578030283, 0.157307341657151, 0.09101482722246299, 0.04075021003238533, 0.12198289626491382, 0.23543444581784093, 0.33290936164091056, 0.40855251571793677, 0.45828017661571435, 0.4801236352165755, 0.4765247649984878, 0.45554559629226876, 0.4293805804490148, 0.4101172520273644, 0.40741873037754067, 0.42665940999487795, 0.46729112491784164, 0.5231962963055652, 0.5847000776215436, 0.6425185104133644, 0.6899258924114644, 0.7218978369581098, 0.7362953379324116, 0.7337775901172148, 0.7176945527856773, 0.6934984061727371, 0.6681909011161374, 0.6487768683950833, 0.641617237631434, 0.6517599357557399, 0.6810317526861955, 0.7269004078334275, 0.7838199551794527, 0.8452487967410162, 0.9050877415292745, 0.9574409528090915, 0.9973398108068358, 1.020278093967003, 1.0234985013914677, 1.006289472108276, 0.9707654104422145, 0.9201296802293001, 0.8572279466870006, 0.7841249630767476, 0.7024930405778876, 0.6128646194471118, 0.5153073976006746, 0.4122129164341026, 0.3096755086154404, 0.2154812084754172, 0.1336966404075609, 0.06339942418665044, 0.11743333457732655, 0.22675055616030035, 0.3201673382078581, 0.3922473555886482, 0.43916913780142874, 0.4592766761362372, 0.4539127594425192, 0.4285870479621718, 0.3932432252571849, 0.35908691911104695, 0.3355044960317903, 0.328960964090487, 0.3412833762747164, 0.37015457271394137, 0.410097234860583, 0.4547970553330857, 0.49900857851460423, 0.5383762696138968, 0.5693865366857261, 0.5924275568106651, 0.6095318119978206, 0.6240722020823809, 0.6396029220823473, 0.6596975494896892, 0.6880712826230103, 0.7282260534927794, 0.7810154855136646, 0.8424596011353455, 0.9059329431177786, 0.9647247500470233, 1.014066685190473, 1.0499712190927821, 1.0697118639278511, 1.0721333224069258, 1.0583126617081238, 1.0304421544226123, 0.9917621599715984, 0.944206451943075, 0.8886925255784537, 0.8258953908183246, 0.7559026160625593, 0.6772662374667705, 0.5878945650044952, 0.4880388474575446, 0.38241879757197766, 0.278261447847144, 0.18000022434223753, 0.08797970205955516, 0.10953949232964325, 0.21188703219272323, 0.29953048965580026, 0.36598791260540803, 0.40760419290336963, 0.42386629565087103, 0.41597894558395565, 0.3875239997914325, 0.3454389408808252, 0.2997196744998014, 0.25975467452766676, 0.23235409010082744, 0.2212664048147363, 0.22721431714568233, 0.24818115997843002, 0.2806399177945088, 0.3202202757284574, 0.363438643831858, 0.4067945132970161, 0.4500450033822662, 0.494762423916928, 0.5423425537825153, 0.5932384924217986, 0.6473995573566816, 0.7058910106225269, 0.7709825859264157, 0.8424841041919704, 0.9158962408603306, 0.9842152809434174, 1.041054529849083, 1.0818471283171753, 1.104143354845021, 1.107195560655509, 1.0933272349848122, 1.0669405408653607, 1.0326833743009731, 0.9935261617367734, 0.9502846957234253, 0.902653103996497, 0.8501280962215517, 0.7916218782747977, 0.7243618774886424, 0.6448579265290664, 0.5511442708946661, 0.44595715529333363, 0.3348294790679141, 0.22240637978048639, 0.11074082676515852, 0.09998642423156967, 0.19331292433023417, 0.272567768784919, 0.3306166171445837, 0.3641895568790719, 0.3739270749008681, 0.36190040061330286, 0.3304767552810365, 0.28414038606507197, 0.23074252055759806, 0.17945525356803257, 0.1375694845718762, 0.11012189656601915, 0.09973942299074397, 0.1065415778259863, 0.12902873611623736, 0.16407107358244102, 0.20837588710127702, 0.259687305232291, 0.3174968010553876, 0.38301534550979466, 0.455749442485162, 0.5335526809639863, 0.6136233906192061, 0.6947562478011818, 0.7775574314181021, 0.8610389593872676, 0.9410150256990996, 1.0108096520485963, 1.0644953634708916, 1.0976790772411797, 1.1086770265255292, 1.0987328770324896, 1.0732953348559935, 1.039435674785483, 1.0027719605878935, 0.9655225125575702, 0.9275260915721898, 0.8875385850809493, 0.8444279565427344, 0.7963291022269379, 0.739584714320664, 0.670271984703064, 0.5854580193780301, 0.48531231317773305, 0.3725741712783535, 0.25177065064122944, 0.1267506994266529, 0.09001533394248491, 0.1731531976599372, 0.2415922094898696, 0.28891052137806184, 0.31272159140072936, 0.3146682328146339, 0.2976653069052167, 0.26306069442727215, 0.21398246657498682, 0.156869966887691, 0.09986417640481882, 0.05029165505553085, 0.013563356481394215, -0.00639089339745544, -0.008173693402451053, 0.007274863606535137, 0.03804876134121233, 0.08154292207697761, 0.13658564421832708, 0.20299040357963494, 0.2810897851069157, 0.3691434723898813, 0.4631235507478342, 0.5586501895304922, 0.6531136854153888, 0.7451975162305267, 0.8330172731357257, 0.9127967596335427, 0.9792034197132603, 1.0271496484618265, 1.0527423753279115, 1.054650276747549, 1.035864790746552, 1.0041158542105912, 0.9679416093503147, 0.9323127887850857, 0.8988651109530885, 0.866508205444975, 0.8338526944510704, 0.7993489676499815, 0.7600544064352526, 0.7121832772772947, 0.6524273574215668, 0.5782406674850602, 0.48760695697331924, 0.38035042201959013, 0.26000731492316864, 0.13167924547533003, 0.07881749471092002, 0.14984732957367033, 0.20547708173639118, 0.24097094323100166, 0.25525088196142576, 0.2506751789177972, 0.22988968484241376, 0.19381439475420428, 0.1444473459984648, 0.08756339190600132, 0.030650798714409518, -0.019789384736739496, -0.05893308606685812, -0.08265839609290021, -0.08878515827392279, -0.07778938755188762, -0.05120500844811428, -0.01058132287279285, 0.043631294226471516, 0.1120204907278758, 0.1936161321066649, 0.2856433374296194, 0.38336667965659577, 0.4822071842698633, 0.5788652671476782, 0.670532961833448, 0.7543883073579251, 0.8271599549163452, 0.8854274948567392, 0.9251930467337001, 0.9433529779211698, 0.9390391029128098, 0.9162385757245647, 0.8835361729609211, 0.849244975044022, 0.8173654351356878, 0.7885592572826154, 0.7618555615754937, 0.7363386699740113, 0.7095655623729744, 0.6778907365981343, 0.6381383284161647, 0.5880934816463615, 0.5257660584208536, 0.44839430229906974, 0.35388366149530853, 0.24399189251897435, 0.12404441888933408, 0.06392148411576468, 0.11993966889132722, 0.1615075179795266, 0.18534540707094752, 0.19210143266684154, 0.18450995664650782, 0.16372657984043532, 0.13007745505691246, 0.08498370459276425, 0.03364318488528919, -0.017128153297409934, -0.06232437887504704, -0.0979947311688407, -0.1205607124870609, -0.1278889998613216, -0.11999739242586759, -0.09825725361661533, -0.06315740304426733, -0.014639541457036043, 0.04798932981132153, 0.12301681075783126, 0.2071413918053027, 0.29570788914402996, 0.38492131329411744, 0.47154866620992425, 0.5522804411639983, 0.6238793276584561, 0.6839795533594015, 0.7305207309256343, 0.7608593216018553, 0.7726739251916092, 0.7654297978877025, 0.7433126304037557, 0.71425163927942, 0.6851169046732346, 0.6587636033764351, 0.6351967246949773, 0.6143726537226016, 0.5954593235235649, 0.5758011771381696, 0.551832759149799, 0.5208613136245995, 0.4816476427637874, 0.4329334738978876, 0.3721257103874017, 0.29628425687595744, 0.20569572452936408, 0.10491665786248959, 0.044811081105286525, 0.08285242507223008, 0.10964411472281431, 0.12369997876459325, 0.12621435607123455, 0.11911077320198114, 0.10280562449413763, 0.07672830046718565, 0.041990267391309684, 0.002509121256916766, -0.03626696024546441, -0.07055167851399732, -0.09779345181761138, -0.11536297755790378, -0.12154156457833433, -0.11628485696499782, -0.10049800180338059, -0.07427308460641774, -0.03700366148574375, 0.011484760183793397, 0.06946314107965135, 0.1338741429133647, 0.20122618444067272, 0.26872819512785046, 0.33388709441378567, 0.3938580258130647, 0.44602403544707375, 0.48901664747416934, 0.5214437936864444, 0.5419906660435097, 0.5488350140389011, 0.5419073765880951, 0.524463200678302, 0.5025892182709885, 0.48132482561170337, 0.46215996435312034, 0.4450601001008415, 0.43046589010378145, 0.4179578797630348, 0.40537325631193283, 0.38963144400484057, 0.3683898561670284, 0.3413634133535196, 0.3080613560586686, 0.26635965739174566, 0.21340715037434707, 0.1488687144885712, 0.07616455295733336, 0.02289792641482786, 0.04186037514454396, 0.05463685729122929, 0.06097876019104558, 0.06168479689966058, 0.05759584544059332, 0.04895215657943498, 0.03467585471438124, 0.015699363107624736, -0.005812629807971005, -0.027039552215907627, -0.04576428043142535, -0.06064128544209742, -0.0702682284418304, -0.07369714929921871, -0.07108706523164735, -0.06258975374775945, -0.0484321328760205, -0.027989619917199216, -0.0013846632471366956, 0.03038947193362493, 0.06533832536704554, 0.10179271216456814, 0.13812673104421602, 0.1730324756047765, 0.20492563317688942, 0.23247899932761926, 0.2549363323174819, 0.2716461952150105, 0.2821064153721189, 0.2851836844327104, 0.28103732987894725, 0.27142833836757774, 0.2595811004084967, 0.2483023706166788, 0.2380928216232039, 0.2290312561167422, 0.22140180074806293, 0.21525906562805702, 0.20935256662813218, 0.20167090602579843, 0.19088093875601533, 0.17708633206260233, 0.16026146137329178, 0.13917294033389582, 0.11192488709005714, 0.07821454234639476, 0.04010363673504736, 5.410302326398203, 0.11431658499305342, 0.11433092941919715, 0.06500396522916102, 0.13965143570525512, -0.2422896003185766, 0.24012637103740517, 0.06772150760824902, 0.08038255121153215, -0.08316144688123249, 0.2070293732589647, 0.0963180061210507, 0.12165966683068705, -0.17871643186059671, 0.1532348507400928, -0.5531642845541492, 0.22664931983560155, -0.20626955773816835, 0.037034765562197536, 0.11329849839705346, -0.566651424860414, 0.029715974517968348, 0.1400966488628471, 0.2180839143084571, -0.669231800248953, 0.11447685873975441, 0.11581614116852304, 0.16403086890565205, -0.7658722168708568, 0.16250980058091907, 0.1389698770721194, 0.17291897279462934, -0.8261965329026033, 0.16760499895869607, 0.12712882377200022, 0.18678669036492537, -0.026374072208930885, -0.9398337703539522, 0.22481446363777668, 0.13764340703157518, 0.11316217193339967, -0.022739371230079426, -0.839420750195644, 0.22226489198386307, 0.11685306882339609, 0.18463364151243758, -0.018766276830507113, -0.6733816638767518, 0.24326172130154816, 0.11918189555461342, 0.1453167325704898, -0.024446233803317497, 0.09295281386604873, -0.8000037031200028, 0.23580222449072838, 0.09368529820203851, 0.11763969026006353, -0.00618817762048229, 0.13082628614395378, -0.8261957523470355, 0.22941871420191975, -0.003738579586606355, 0.08009210456783628, -0.008438080849801051, 0.0037799104396504996, 0.1890221786030645, -0.8968514729821023, 0.35978732111717077, 0.05812881768638267, 0.06282895118175788, 0.0683350625590418, 0.012248510106454584, 0.24996168931481616, -0.9000083389395502, 0.03965785970222048, 0.08496430320459111, 0.0831366681709643, 0.02284938482046194, 0.2150806107999883, -0.9484356933706097, 0.058749077931505585, 0.06512375914899543, 0.18495948771323323, 0.027889865066204642, 0.22111885476940593, -0.9381088602972141, 0.08767084830046248, 0.11473860378144145, 0.03056689488575584, 0.19905956984112658, -1.0941665373862355, 0.03226534205927737, 0.07617356996005692, 0.05165049256953663, 0.18027096945531848, -1.0344688393258454, 0.04191055460726883, 0.06864305479432306, 0.12508834439217142, 0.050481040058011156, 0.16472390974751294, -1.2463570105738007, 0.054206807782515784, 0.04165243091040354, 0.12167627334298281, 0.0911782115099837, 0.2093382040467673, -1.1737406743173295, 0.059650014587516356, 0.02946838148005925, 0.07310870532570979, 0.11506853702947191, 0.21876569560770184, -0.9532151537747683, 0.042767310929131656, 0.021691974473682155, 0.0529823103282846, 0.10670048567194627, 0.19201913172485288, -0.9691978934245993, 0.050699855588565663, 0.02682738796378764, 0.047923774525492395, 0.07709600137196873, 0.17448714627136233, -1.0511313090957894, 0.04597620244674346, 0.08589801298049121, -0.06910406025467455, 0.0674460211052576, 0.03663159381548992, -0.014072039911932439, -0.048659142875211725, 0.05438932359481428, 0.0783041020828383, 0.015278407849203186, -0.01897524233705677, 0.05303315039842076, 0.0002259001168588567, 0.027836053239900634, -0.028893434361570085, -0.0749850902758356, -0.1075536896846746, 0.0986828882120111, 0.05733952986144613, 0.04624842907256471, 0.12715017731296419, 0.0036932535256885123, 0.026941439385354725, -0.02480341193133555, 0.07048124647270168, -0.007377968824481086, -0.006273417065569522, -0.011152839769953052, 0.13135025912473797, 0.010365160955375917, 0.00808170877750347, 0.04130938817675873, 0.10627948944018498, -0.01579058498531661, 0.014726120535631554, -0.08286445708128844, 0.02128770001914456, 0.1202932607553076, 0.004596286635108509, 0.023878018550042793, -0.06260779586968286, -0.005824910517272144, 0.11418394871085923, -0.014139110389138981, 0.003853871868754215, -0.009295103919326694, 0.012821057395293862, 0.047049878407575, 0.010364101978769816, -0.015789001608338026, -0.004705240218726172, 0.02914392352507765, 3.0954440558515395e-6, 0.05481812257846731, 0.029529546866377047, -0.0065774736892530725, -0.12062604940325253, 0.02332182999911364, 3.4392196555456585e-6, 0.03965522634381669, 0.03734499672122581, -0.09755019503127911, -0.006214886104551827, 0.025758668007918158, 0.02108005461523569, 2.238376892818206e-6, 0.06983199892275094, 0.026151990689769596, -0.09788962575311976, -0.009179556304185665, -0.06623508306505338, 0.012538289911879332, 7.850775284658347e-6, 0.05997882426337129, 0.05172756971260086, -0.054665269173022564, -0.03749788642577309, 0.023450951981442935, 4.811275561712567e-6, 0.07287657064666969, -0.015802315240066842, -0.005705044266655422, -0.026135698784999172, 0.012379194796539017, 4.457893758880863e-8, 0.049311599200385026, 0.012021432646342707, 0.05348089685018997, -0.02260834354031115, -3.5348520800419667e-6, 0.05667395537742617, -0.04360563272721349, -0.06788637679200953, 0.05143038814372461, -2.0676683141617805e-5, 0.0846074680303427, 0.01686540196774415, -0.024261171882996743, -0.0383918615921022, 0.01590556084197583, 6.684036716111854e-6, 0.12544442958274638, -0.021580481756540357, -0.019212803899479852, -0.03907541645753164, 0.009113495315119707, 5.464307334594716e-6, 0.11553681362322497, -0.015673994259293188, -0.004561081600836008, -0.005809598265024069, -0.020072531924403975, -1.7163269038921932e-6, 0.08856599004322722, 0.014631160639729598, -0.017213475821519213, -0.04603775280378557, 0.017641127946134486, -1.1547422813858515e-5, 0.052709140090317005, 0.012140398908537305, -0.0033455859742245065, -0.011221588542027974, 0.03423491359012426, -5.763650854440834e-6, 0.09344042278927166, -0.009514527573372277, -0.11227937826175671, -0.9493858833199676, -0.7226276090505822, -0.6266429421558781, 0.09697077507259541, 0.9878671174656307, 0.12655191943659339, -0.9445260971990465, -0.7092057590181093, -0.6171935988278993, 0.17018103805316684, 0.9733037759034299, 0.3589929046489856, -0.901553475014359, -0.7129569817269403, -0.6107468724019606, 0.22097419637427013, 0.930859611535074, 0.5318469383568033, -0.8067861146242263, -0.6351637975663229, -0.6914997978503831, 0.28402957170831855, 0.8984644979729026, 0.7025188473055223, -0.641472826894266, 0.6904116608469492, 0.6431097163446863, -0.950094167074107, -0.191738376517613, -0.5959688480902201, -0.7391064930434688, 0.35380955151798293, 0.8787162265592054, 0.8852170524907559, -0.35225508261662863, -0.8110492245954409, -0.9442013088950143, 0.37880314960127465, 0.8624813815495485, 0.9314539063090292, -0.19906320635090105, -0.5889470267348518, -0.7847603523912692, 0.40360923679306876, 0.886581912356699, 0.8872608289403131, -0.05854346714391579, -0.5670277130975706, -0.7488914304056856, 0.08492286721185689, 0.9493155784827413, 0.4084029771293067, 0.8721879174941599, 0.959210079969192, 0.08057632145645971, -0.5836708233623089, -0.7374922688690152, -0.03658648122768928, 0.9712870052470042, 0.34321289166935914, 0.8830655653837847, 0.9222836980539381, 0.1998325552428095, -0.5509538856689327, -0.7599089769224086, -0.1626564129556355, 0.8859647479313719, 0.2285554189719629, 0.9197233963350736, 0.8372140414483991, 0.29702095580095794, -0.613161690085535, -0.7223730367907573, -0.3567509285667637, 0.899474107564232, -0.9494202612527076, 0.11246273413572588, 0.15229886863969577, 0.9348164670057988, 0.8249260375437051, 0.4430833571593628, -0.5566307229733332, -0.7579471146180198, -0.4674745694326216, 0.6974519472326722, -0.8534788193538925, 0.35743420284137495, 0.026218297648012423, 0.9472795383916607, 0.706920771350469, 0.6054766694559846, -0.6044016797012823, -0.735622386314347, -0.5925867804277556, -0.7280527476782727, -0.6665076379360941, 0.6964490408807679, -0.7613241435651533, 0.566908272422118, -0.17641993342972392, 0.9576773435668912, 0.7142857803896313, 0.832171491137583, -0.5492940239344958, -0.7952381847061741, -0.6214315109895623, -0.7043973711096911, -0.7611820691100112, 0.6230454483230872, -0.6264140034077864, 0.7243555943530533, -0.35621083199675474, 0.8873509791533273, 0.4508670479534345, 0.8149775457280798, -0.4469358806550874, -0.8378584719144538, -0.7596746643657841, 0.3509832467754247, -0.45522268779140296, 0.8291898724687496, -0.5933106297019193, 0.6693724667334195, -0.2996494354529364, -0.8993141796727743, -0.7497875467878367, -0.5671634577023992, -0.9114216440638351, 0.09892834264027361, -0.2547267984437534, 0.8445687708219529, -0.9457481020465661, 0.0690059969536854, -0.7822039939213566, -0.5300837662251604, -0.9815208668191763, -0.09989151813134504, -0.1405690459406719, 0.9337293738820409, -0.760603932317565, -0.5692036930995968, -0.28667340397480684, -0.9085740195728773, -0.867416519730873, -0.3351407271128238, -0.03598053962945304, 0.9519391689798555, -0.44200285896764896, -0.8554271555904807, -0.22641841943852098, -0.9403746758914822, -0.8274322825745237, -0.46631550425267126, -0.7389249989849734, -0.6232635635941732, 0.046731934983684206, 0.9465023938569088, -0.13776359117878212, -0.9683022272770996, -0.12521617210252348, -0.9369900660998951, -0.829771341198533, -0.4411507200213929, -0.5669785786679786, -0.7777744794748277, 0.12383370886655791, 0.961263856428872, 0.21161778319796104, -0.9735153659942041, -0.13381892225276545, -0.9353201539358638, -0.84530745492443, -0.4101442337476319, -0.33221817549234284, -0.9199125410516397, 0.1483968414140716, 0.9665968046845788, 0.3812932277650118, -0.8671953086765998, -0.10635361473098917, -0.9385893358586531, -0.8523187698092897, -0.3096412791611352, -0.08128383756851312, -0.9729099727464997, 0.13059891062159723, 0.8447363882286065, 0.5292865274836387, -0.780604429729219, -0.1936451037998112, -0.9551477239115221, -0.9036677304109074, -0.2902670757335376, -0.01935273807659979, -0.9781708825842694, 0.16205563664032535, 0.9308174888313716, 0.6542473999836671, -0.6770594707581874, -0.18120574636995, -0.9260864430682915, 0.002223784013646446, 0.9508319425786538, -0.011880736818920505, 0.9396214986236394, -0.02399836629735992, 0.9664715221483371, 0.014139457129439991, 0.9514270090757226, -0.027297822984384875, 0.9420959739822949, 0.0022804498705429077, 0.9721065170370715, 0.031061061356282567, 0.970072518761429, -0.038322127247719426, 0.9381785784666588, 0.007373064189620749, 0.9416541292993839, 0.009681324312022689, 0.9472866914304425, -0.005834176921010433, 0.9388285178638905, 0.017041366630776135, 0.9394542156675393, 0.05785936500079066, 0.9384636957256526, -0.025953769532325758, 0.9424230015317445, 0.005018652038377071, 0.9439428226316743, -0.03257880060614376, 0.9419535779017731, 0.011682574907691812, 0.9391264637104785, 0.020482203810436878, 0.9390508716151098, 0.02136064610265715, 0.9412316425961299, -0.07144695948354585, 0.976550337115577, 0.018599205044805958, 0.9385562243268607, 0.010431237651382836, 0.9482430226576419, -0.014024189824251958, 0.952152980925163, 0.009417947214052405, 0.9510354836262732, -0.0009035394515605689, 0.9842857716379215, 0.002583906582771404, 0.9394005059654509, 0.049476685097083486, 0.9389818031029671, -0.002856554976263021, 0.9465829815828186, -0.009869813568979022, 0.9470685984759578, 0.017274141806125295, 0.9390395139370757, 0.021238674853193956, 0.9844387264605645, 0.007584497898779748, 0.9437854015030644, -0.011948812924610398, 0.9420462861807849, 0.022757890034483984, 0.9386699177483564, -0.007793209286746025, 0.9567265102898728, 0.05750619251634564, 0.9408566748459912, -0.01170385954508335, 0.9621499690841254, -0.0059209015690151225, 0.940354231862219, 0.022118097651896082, 0.9407084799944193, 1.7674603186790718e-5, 0.9391946984594033, 0.07072109496375728, 0.9379426948037942, -0.0045841788174468, 0.9410254820151112, 0.05118995729570915, 0.9387408093961994, 0.0384582221925732, 0.9589605987802495, 2.0396586680373068e-5, 0.9391939231837186, 0.06149769066772456, 0.9427398210739474, 0.012567886488268207, 0.9398447975797724, 0.09645704211593194, 0.9350955645284352, 0.04781936697890503, 0.9378213327974338, 0.032335535922354844, 0.9389451377989022, -2.08762616579571e-5, 0.9391937750399311, 0.08586004159432074, 0.9534138472946766, -0.005595753428145543, 0.9944050501993547, 0.012765178397655317, 0.9439331816448595, -0.05541691452734187, 0.9377645481560413, -0.02981505286964216, 0.9396836962045927, -3.1166800877111867e-6, 0.9391969613237192, 0.06554185337394702, 0.9422689202212168, -0.00040600280327683376, 0.9572223681426902, -0.012503309790790748, 0.9436791144502636, 0.016502846426833435, 0.9679223586525515, -7.913235085483237e-6, 0.9391965659487447, 0.04297608767050944, 0.967078681138751, 0.04825479763754361, 0.9398288729514523, 0.04927099345277443, 0.9380349693772112, 0.07084798959319534, 0.9651444125982107, -1.3490313183421323e-5, 0.9391956736415272, 0.004954407280323593, 0.9418256319982538, 0.00930578849574858, 0.9402380694513569, 0.054253681870703604, 0.9728256496423198, -1.7132619749503732e-5, 0.9391948395620565, 0.057880836964828423, 0.9402495292421389, -0.09545781655476572, 0.9362246982418705, 0.06774145879210731, 0.947776319955185, 9.765817717957207e-6, 0.9391963211551612, 0.04151306384782005, 0.9439482419071243, -0.07713777397983858, 0.9401777248880855, -0.0387892110343129, 0.9390301465380562, 0.11508432584396479, 0.9359332167809908, -4.366597623608048e-6, 0.939196891427476, 0.02966532593007756, 0.9490973559777071, -0.02615011068378779, 0.9404048387217477, 0.055442940909583176, 0.9376718602476425, 0.05174584539469607, 0.9417273463328876, -3.6364353847026685e-6, 0.9391969350948797, 0.03814367727087831, 0.9608692627493483, -0.05167768618055991, 0.9383598116548635, -0.012616152830107356, 0.9386428513051518, 0.09580350572217874, 0.933758740978217, -6.10005781684192e-6, 0.9391967558401876, 0.01649952759950107, 0.9394258112478887, -0.02977507422491, 0.9394246597559381, -0.015416051112782273, 0.9779409475740696, 0.14550732343055942, 0.960888945122559, -7.133662870884296e-5, 0.9391583799614777, 0.001266347496317853, 0.9412760691773435, -0.0941720317541023, 0.9426852268570712, 0.023356351941912715, 0.9389550135459199, 0.0021559537173902648, 0.9431910082713503, -1.2501404013508711e-5, 0.9391958658078244, 0.006449604069513579, 0.9396998336832862, -0.04619396455533729, 0.9389198176960636, -0.00377079752724891, -0.032168188332715154, 0.022354629417609774, 0.001550811808434439, 0.03937829381434981, -0.12165434566174409, -0.03469547614878778, -0.01852636577829295, 0.04952588419975482, 0.09553703177514056, -0.04853945338563308, 0.06209253149182892, 0.04353645597955429, 0.01771975954873608, 0.0036638472959248185, 0.04043105817204525, -0.022848742165857295, 0.0007040198353262866, -0.003988110066690277, 0.1390477939757669, 0.0028157154631364453, -0.02120783053740049, 0.038321079118419824, 0.0935361552046403, 0.00017788755432369805, 0.02226125767580544, -0.0007414240056981892, 0.09418125214449846]
Final objective value:     -19112.347351054785
)

Now let's evaluate our fits by plotting the residuals

julia

using CairoMakie
res = residuals(post, xopt)
fig = Figure(; size = (800, 600))
plotfields!(fig[1, 1], res[1], uvdist, x -> Comrade.measurement(x)[1, 1] / noise(x)[1, 1], axis_kwargs = (; ylabel = "RR Residual"))
plotfields!(fig[2, 1], res[1], uvdist, x -> Comrade.measurement(x)[2, 1] / noise(x)[2, 1], axis_kwargs = (; ylabel = "LR Residual"))
plotfields!(fig[1, 2], res[1], uvdist, x -> Comrade.measurement(x)[1, 2] / noise(x)[1, 2], axis_kwargs = (; ylabel = "RL Residual"))
plotfields!(fig[2, 2], res[1], uvdist, x -> Comrade.measurement(x)[2, 2] / noise(x)[2, 2], axis_kwargs = (; ylabel = "LL Residual"))
fig |> DisplayAs.PNG |> DisplayAs.Text

These look reasonable, although there may be some minor overfitting. Let's plot the results

julia

gpl = refinespatial(grid, 2)
img = intensitymap(skymodel(post, xopt), gpl)
fig = imageviz(
    img, adjust_length = true, colormap = :cmr_gothic, pcolormap = :rainbow1,
    pcolorrange = (0.0, 0.3), plot_total = false
);
fig |> DisplayAs.PNG |> DisplayAs.Text

Note

The image looks a little noisy. This is an artifact of the MAP image. To get a publication quality image we recommend sampling from the posterior and averaging the samples. The results will be essentially identical to the results from EHTC VII.

We can also analyze the instrument model. For example, we can look at the gain ratios and products. To grab the ratios and products we can use the caltable function which will return analyze the gprat array and convert it to a uniform table. We can then plot the gain phases and amplitudes.

julia

gphase_ratio = caltable(xopt.instrument.gprat)
gamp_ratio = caltable(exp.(xopt.instrument.lgrat))

┌─────────┬───────────────────┬─────────┬─────────┬─────────┬─────────┬─────────
│      Ti │                Fr │      AA │      AP │      AZ │      JC │      L ⋯
│     Any │               Any │     Any │     Any │     Any │     Any │     An ⋯
├─────────┼───────────────────┼─────────┼─────────┼─────────┼─────────┼─────────
│ 0.92 hr │ 227.070705664 GHz │    1.09 │ missing │ missing │ missing │ missin ⋯
│ 1.22 hr │ 227.070705664 GHz │    1.07 │   1.037 │ missing │ missing │   0.98 ⋯
│ 1.52 hr │ 227.070705664 GHz │   1.056 │   1.081 │ missing │ missing │   1.01 ⋯
│ 1.82 hr │ 227.070705664 GHz │   1.054 │     1.0 │ missing │ missing │   1.02 ⋯
│ 2.12 hr │ 227.070705664 GHz │   0.928 │   0.898 │ missing │ missing │   1.10 ⋯
│ 2.45 hr │ 227.070705664 GHz │ missing │   1.047 │ missing │ missing │   1.13 ⋯
│ 2.75 hr │ 227.070705664 GHz │   1.027 │   0.976 │ missing │ missing │   1.07 ⋯
│ 3.05 hr │ 227.070705664 GHz │   0.994 │   0.989 │ missing │ missing │    1.1 ⋯
│ 3.35 hr │ 227.070705664 GHz │   1.008 │   1.042 │ missing │ missing │   1.11 ⋯
│ 3.68 hr │ 227.070705664 GHz │   1.015 │    0.92 │   1.022 │ missing │   1.12 ⋯
│ 3.98 hr │ 227.070705664 GHz │   1.024 │   0.939 │   0.994 │ missing │   1.12 ⋯
│ 4.28 hr │ 227.070705664 GHz │   1.004 │   0.991 │   1.013 │ missing │   1.04 ⋯
│ 4.58 hr │ 227.070705664 GHz │   0.984 │   0.995 │    1.03 │     1.0 │   1.05 ⋯
│ 4.92 hr │ 227.070705664 GHz │   0.993 │   0.886 │   1.024 │     1.0 │    1.0 ⋯
│ 5.18 hr │ 227.070705664 GHz │   0.994 │   1.026 │   1.021 │     1.0 │   1.07 ⋯
│       ⋮ │                 ⋮ │       ⋮ │       ⋮ │       ⋮ │       ⋮ │        ⋱
└─────────┴───────────────────┴─────────┴─────────┴─────────┴─────────┴─────────
                                                   3 columns and 10 rows omitted

Plotting the phases first, we see large trends in the righ circular polarization phase. This is expected due to a lack of image centroid and the absense of absolute phase information in VLBI. However, the gain phase difference between the left and right circular polarization is stable and close to zero. This is expected since gain ratios are typically stable over the course of an observation and the constant offset was removed in the EHT calibration process.

julia

gphaseR = caltable(xopt.instrument.gpR)
fig = plotcaltable(gphaseR, gphase_ratio, labels = ["R Phase", "L/R Phase"]);
fig |> DisplayAs.PNG |> DisplayAs.Text

Moving to the amplitudes we see largely stable gain amplitudes on the right circular polarization except for LMT which is known and due to pointing issues during the 2017 observation. Again the gain ratios are stable and close to unity. Typically we expect that apriori calibration should make the gain ratios close to unity.

julia

gampr = caltable(exp.(xopt.instrument.lgR))
fig = plotcaltable(gampr, gamp_ratio, labels = ["R Amp", "L/R Amp"], axis_kwargs = (; limits = (nothing, (0.6, 1.3))));
fig |> DisplayAs.PNG |> DisplayAs.Text

To sample from the posterior, you can then just use the sample function from AdvancedHMC like in the other imaging examples. For example

julia

using AdvancedHMC
chain = sample(rng, post, NUTS(0.8), 2_000, n_adapts = 1000, progress = true, initial_params = xopt)

This page was generated using Literate.jl.

Hamaker J.P, Bregman J.D., Sault R.J. (1996) [https://articles.adsabs.harvard.edu/pdf/1996A%26AS..117..137H] ↩︎
Pesce D. (2021) [https://ui.adsabs.harvard.edu/abs/2021AJ....161..178P/abstract] ↩︎

Polarized Image and Instrumental Modeling ​

Introduction to Polarized Imaging ​

Load the Data ​

Load the Data ​

Reconstructing the Image and Instrument Effects ​

Polarized Image and Instrumental Modeling

Introduction to Polarized Imaging

Load the Data

Load the Data

Reconstructing the Image and Instrument Effects