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 basis transform matrix $T$ . This transformation is special and combines two things using the decomposition $T = F B$ . 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 Pyehtim

    CondaPkg Found dependencies: /home/runner/.julia/packages/DimensionalData/KlTtO/CondaPkg.toml
    CondaPkg Found dependencies: /home/runner/.julia/packages/PythonCall/L4cjh/CondaPkg.toml
    CondaPkg Found dependencies: /home/runner/.julia/packages/Pyehtim/Fm109/CondaPkg.toml
    CondaPkg Resolving changes
             + ehtim (pip)
             + libstdcxx-ng
             + numpy
             + numpy (pip)
             + openssl
             + pandas
             + python
             + setuptools (pip)
             + uv
             + xarray
    CondaPkg Initialising pixi
             │ /home/runner/.julia/artifacts/cefba4912c2b400756d043a2563ef77a0088866b/bin/pixi
             │ init
             │ --format pixi
             └ /home/runner/work/Comrade.jl/Comrade.jl/examples/intermediate/PolarizedImaging/.CondaPkg
✔ Created /home/runner/work/Comrade.jl/Comrade.jl/examples/intermediate/PolarizedImaging/.CondaPkg/pixi.toml
    CondaPkg Wrote /home/runner/work/Comrade.jl/Comrade.jl/examples/intermediate/PolarizedImaging/.CondaPkg/pixi.toml
             │ [dependencies]
             │ openssl = ">=3, <3.6, >=3, <3.6"
             │ uv = ">=0.4"
             │ libstdcxx-ng = ">=3.4,<15.0"
             │ pandas = "<2"
             │ xarray = "*"
             │ numpy = ">=1.24, <2.0"
             │ 
             │     [dependencies.python]
             │     channel = "conda-forge"
             │     build = "*cpython*"
             │     version = ">=3.8,<4, >=3.6,<=3.10"
             │ 
             │ [project]
             │ name = ".CondaPkg"
             │ platforms = ["linux-64"]
             │ channels = ["conda-forge"]
             │ channel-priority = "strict"
             │ description = "automatically generated by CondaPkg.jl"
             │ 
             │ [pypi-dependencies]
             │ ehtim = ">=1.2.10, <2.0"
             │ numpy = ">=1.24, <2.0"
             └ setuptools = "*"
    CondaPkg Installing packages
             │ /home/runner/.julia/artifacts/cefba4912c2b400756d043a2563ef77a0088866b/bin/pixi
             │ install
             └ --manifest-path /home/runner/work/Comrade.jl/Comrade.jl/examples/intermediate/PolarizedImaging/.CondaPkg/pixi.toml
✔ The default environment has been installed.
/home/runner/work/Comrade.jl/Comrade.jl/examples/intermediate/PolarizedImaging/.CondaPkg/.pixi/envs/default/lib/python3.10/site-packages/ehtim/__init__.py:58: UserWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html. The pkg_resources package is slated for removal as early as 2025-11-30. Refrain from using this package or pin to Setuptools<81.
  import pkg_resources

For reproducibility we use a stable random number genreator

julia

using StableRNGs
rng = StableRNG(42)

StableRNGs.LehmerRNG(state=0x00000000000000000000000000000055)

Now we will load some synthetic polarized data.

julia

fname = Base.download(
    "https://de.cyverse.org/anon-files/iplant/home/shared/commons_repo/curated/EHTC_M87pol2017_Nov2023/hops_data/April11/SR2_M87_2017_101_lo_hops_ALMArot.uvfits",
    joinpath(__DIR, "m87polarized.uvfits")
)
obs = Pyehtim.load_uvfits_and_array(
    fname,
    joinpath(__DIR, "..", "..", "Data", "array.txt"), polrep = "circ"
)

Python: <ehtim.obsdata.Obsdata object at 0x7f137e7f6fb0>

Notice that, unlike other non-polarized tutorials, we need to include a second argument. This is the array file of the observation and is required to determine the feed rotation of the array.

Now we scan average the data since the data to boost the SNR and reduce the total data volume.

julia

obs = scan_average(obs).add_fractional_noise(0.01).flag_uvdist(uv_min = 0.1e9)

Python: <ehtim.obsdata.Obsdata object at 0x7f137f504d00>

Now we extract our observed/corrupted coherency matrices.

julia

dvis = extract_table(obs, Coherencies())

EHTObservationTable{Comrade.EHTCoherencyDatum{Float64}}
  source:      M87
  mjd:         57854
  bandwidth:   1.856e9
  sites:       [:AA, :AP, :AZ, :JC, :LM, :PV, :SM]
  nsamples:    189

##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. As always Comrade requires this to be a two argument function where the first argument is typically a NamedTuple of parameters we will fit and the second are additional metadata required to build the model.

julia

using StatsFuns: logistic
function sky(θ, metadata)
    (; c, σ, p, p0, pσ, angparams) = θ
    (; mimg, ftot) = metadata
    # Build the stokes I model
    rast = apply_fluctuations(CenteredLR(), mimg, σ .* c.params)
    brast = baseimage(rast)
    brast .= ftot .* brast
    # The total polarization fraction is modeled in logit space so we transform it back
    pim = logistic.(p0 .+ pσ .* p.params)
    # Build our IntensityMap
    pmap = PoincareSphere2Map(rast, pim, angparams)
    # Construct the actual image model which uses a third order B-spline pulse
    m = ContinuousImage(pmap, BSplinePulse{3}())
    # Finally find the image centroid and shift it to be at the center
    x0, y0 = centroid(pmap)
    ms = shifted(m, -x0, -y0)
    return ms
end

sky (generic function with 1 method)

Now, we define the model metadata required 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

using Distributions
using VLBIImagePriors
fovx = μas2rad(200.0)
fovy = μas2rad(200.0)
nx = ny = 32
grid = imagepixels(fovx, fovy, nx, ny)

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

┌ 32×32 IntensityMap{Float64, 2} ┐
├────────────────────────────────┴─────────────────────────────────────── dims ┐
  ↓ X Sampled{Float64} LinRange{Float64}(-4.69663253574863e-10, 4.69663253574863e-10, 32) ForwardOrdered Regular Points,
  → Y Sampled{Float64} LinRange{Float64}(-4.69663253574863e-10, 4.69663253574863e-10, 32) ForwardOrdered Regular Points
└──────────────────────────────────────────────────────────────────────────────┘
  ↓ →          -4.69663e-10  -4.39362e-10  -4.09062e-10  -3.78761e-10  -3.4846e-10  -3.18159e-10  -2.87858e-10  -2.57557e-10  -2.27256e-10  -1.96956e-10  -1.66655e-10  -1.36354e-10  -1.06053e-10  -7.57521e-11  -4.54513e-11  -1.51504e-11  1.51504e-11  4.54513e-11  7.57521e-11  1.06053e-10  1.36354e-10  1.66655e-10  1.96956e-10  2.27256e-10  2.57557e-10  2.87858e-10  3.18159e-10  3.4846e-10  3.78761e-10  4.09062e-10  4.39362e-10  4.69663e-10
 -4.69663e-10   1.25675e-11   4.60978e-11   1.55054e-10   4.78251e-10   1.3527e-9    3.50847e-9    8.34459e-9    1.81997e-8    3.63993e-8    6.67567e-8    1.12271e-7    1.73145e-7    2.44865e-7    3.1755e-7     3.77633e-7    4.11812e-7   4.11812e-7   3.77633e-7   3.1755e-7    2.44865e-7   1.73145e-7   1.12271e-7   6.67567e-8   3.63993e-8   1.81997e-8   8.34459e-9   3.50847e-9   1.3527e-9   4.78251e-10  1.55054e-10  4.60978e-11  1.25675e-11
 -4.39362e-10   4.60978e-11   1.69087e-10   5.6874e-10    1.75423e-9    4.96172e-9   1.28691e-8    3.06081e-8    6.67567e-8    1.33513e-7    2.44865e-7    4.11812e-7    6.351e-7      8.98167e-7    1.16478e-6    1.38516e-6    1.51053e-6   1.51053e-6   1.38516e-6   1.16478e-6   8.98167e-7   6.351e-7     4.11812e-7   2.44865e-7   1.33513e-7   6.67567e-8   3.06081e-8   1.28691e-8   4.96172e-9  1.75423e-9   5.6874e-10   1.69087e-10  4.60978e-11
 -4.09062e-10   1.55054e-10   5.6874e-10    1.913e-9      5.90051e-9    1.66892e-8   4.32864e-8    1.02953e-7    2.24542e-7    4.49084e-7    8.23623e-7    1.38516e-6    2.13621e-6    3.02106e-6    3.91783e-6    4.65912e-6    5.0808e-6    5.0808e-6    4.65912e-6   3.91783e-6   3.02106e-6   2.13621e-6   1.38516e-6   8.23623e-7   4.49084e-7   2.24542e-7   1.02953e-7   4.32864e-8   1.66892e-8  5.90051e-9   1.913e-9     5.6874e-10   1.55054e-10
 -3.78761e-10   4.78251e-10   1.75423e-9    5.90051e-9    1.81997e-8    5.14764e-8   1.33513e-7    3.1755e-7     6.92582e-7    1.38516e-6    2.5404e-6     4.27243e-6    6.58898e-6    9.31823e-6    1.20843e-5    1.43707e-5    1.56713e-5   1.56713e-5   1.43707e-5   1.20843e-5   9.31823e-6   6.58898e-6   4.27243e-6   2.5404e-6    1.38516e-6   6.92582e-7   3.1755e-7    1.33513e-7   5.14764e-8  1.81997e-8   5.90051e-9   1.75423e-9   4.78251e-10
 -3.4846e-10    1.3527e-9     4.96172e-9    1.66892e-8    5.14764e-8    1.45597e-7   3.77633e-7    8.98167e-7    1.95892e-6    3.91783e-6    7.18534e-6    1.20843e-5    1.86365e-5    2.63559e-5    3.41794e-5    4.06464e-5    4.43252e-5   4.43252e-5   4.06464e-5   3.41794e-5   2.63559e-5   1.86365e-5   1.20843e-5   7.18534e-6   3.91783e-6   1.95892e-6   8.98167e-7   3.77633e-7   1.45597e-7  5.14764e-8   1.66892e-8   4.96172e-9   1.3527e-9
 -3.18159e-10   3.50847e-9    1.28691e-8    4.32864e-8    1.33513e-7    3.77633e-7   9.79458e-7    2.32956e-6    5.0808e-6     1.01616e-5    1.86365e-5    3.13427e-5    4.8337e-5     6.83588e-5    8.86505e-5    0.000105424   0.000114965  0.000114965  0.000105424  8.86505e-5   6.83588e-5   4.8337e-5    3.13427e-5   1.86365e-5   1.01616e-5   5.0808e-6    2.32956e-6   9.79458e-7   3.77633e-7  1.33513e-7   4.32864e-8   1.28691e-8   3.50847e-9
 -2.87858e-10   8.34459e-9    3.06081e-8    1.02953e-7    3.1755e-7     8.98167e-7   2.32956e-6    5.54065e-6    1.20843e-5    2.41685e-5    4.43252e-5    7.45458e-5    0.000114965   0.000162586   0.000210847   0.000250741   0.000273435  0.000273435  0.000250741  0.000210847  0.000162586  0.000114965  7.45458e-5   4.43252e-5   2.41685e-5   1.20843e-5   5.54065e-6   2.32956e-6   8.98167e-7  3.1755e-7    1.02953e-7   3.06081e-8   8.34459e-9
 -2.57557e-10   1.81997e-8    6.67567e-8    2.24542e-7    6.92582e-7    1.95892e-6   5.0808e-6     1.20843e-5    2.63559e-5    5.27119e-5    9.6674e-5     0.000162586   0.000250741   0.000354602   0.000459862   0.000546871   0.000596367  0.000596367  0.000546871  0.000459862  0.000354602  0.000250741  0.000162586  9.6674e-5    5.27119e-5   2.63559e-5   1.20843e-5   5.0808e-6    1.95892e-6  6.92582e-7   2.24542e-7   6.67567e-8   1.81997e-8
 -2.27256e-10   3.63993e-8    1.33513e-7    4.49084e-7    1.38516e-6    3.91783e-6   1.01616e-5    2.41685e-5    5.27119e-5    0.000105424   0.000193348   0.000325171   0.000501483   0.000709204   0.000919723   0.00109374    0.00119273   0.00119273   0.00109374   0.000919723  0.000709204  0.000501483  0.000325171  0.000193348  0.000105424  5.27119e-5   2.41685e-5   1.01616e-5   3.91783e-6  1.38516e-6   4.49084e-7   1.33513e-7   3.63993e-8
 -1.96956e-10   6.67567e-8    2.44865e-7    8.23623e-7    2.5404e-6     7.18534e-6   1.86365e-5    4.43252e-5    9.6674e-5     0.000193348   0.000354602   0.000596367   0.000919723   0.00130069    0.00168678    0.00200593    0.00218748   0.00218748   0.00200593   0.00168678   0.00130069   0.000919723  0.000596367  0.000354602  0.000193348  9.6674e-5    4.43252e-5   1.86365e-5   7.18534e-6  2.5404e-6    8.23623e-7   2.44865e-7   6.67567e-8
 -1.66655e-10   1.12271e-7    4.11812e-7    1.38516e-6    4.27243e-6    1.20843e-5   3.13427e-5    7.45458e-5    0.000162586   0.000325171   0.000596367   0.00100297    0.00154678    0.00218748    0.00283681    0.00337356    0.00367889   0.00367889   0.00337356   0.00283681   0.00218748   0.00154678   0.00100297   0.000596367  0.000325171  0.000162586  7.45458e-5   3.13427e-5   1.20843e-5  4.27243e-6   1.38516e-6   4.11812e-7   1.12271e-7
 -1.36354e-10   1.73145e-7    6.351e-7      2.13621e-6    6.58898e-6    1.86365e-5   4.8337e-5     0.000114965   0.000250741   0.000501483   0.000919723   0.00154678    0.00238547    0.00337356    0.00437497    0.00520274    0.00567363   0.00567363   0.00520274   0.00437497   0.00337356   0.00238547   0.00154678   0.000919723  0.000501483  0.000250741  0.000114965  4.8337e-5    1.86365e-5  6.58898e-6   2.13621e-6   6.351e-7     1.73145e-7
 -1.06053e-10   2.44865e-7    8.98167e-7    3.02106e-6    9.31823e-6    2.63559e-5   6.83588e-5    0.000162586   0.000354602   0.000709204   0.00130069    0.00218748    0.00337356    0.00477093    0.00618714    0.00735779    0.00802372   0.00802372   0.00735779   0.00618714   0.00477093   0.00337356   0.00218748   0.00130069   0.000709204  0.000354602  0.000162586  6.83588e-5   2.63559e-5  9.31823e-6   3.02106e-6   8.98167e-7   2.44865e-7
 -7.57521e-11   3.1755e-7     1.16478e-6    3.91783e-6    1.20843e-5    3.41794e-5   8.86505e-5    0.000210847   0.000459862   0.000919723   0.00168678    0.00283681    0.00437497    0.00618714    0.00802372    0.00954187    0.0104055    0.0104055    0.00954187   0.00802372   0.00618714   0.00437497   0.00283681   0.00168678   0.000919723  0.000459862  0.000210847  8.86505e-5   3.41794e-5  1.20843e-5   3.91783e-6   1.16478e-6   3.1755e-7
 -4.54513e-11   3.77633e-7    1.38516e-6    4.65912e-6    1.43707e-5    4.06464e-5   0.000105424   0.000250741   0.000546871   0.00109374    0.00200593    0.00337356    0.00520274    0.00735779    0.00954187    0.0113473     0.0123743    0.0123743    0.0113473    0.00954187   0.00735779   0.00520274   0.00337356   0.00200593   0.00109374   0.000546871  0.000250741  0.000105424  4.06464e-5  1.43707e-5   4.65912e-6   1.38516e-6   3.77633e-7
 -1.51504e-11   4.11812e-7    1.51053e-6    5.0808e-6     1.56713e-5    4.43252e-5   0.000114965   0.000273435   0.000596367   0.00119273    0.00218748    0.00367889    0.00567363    0.00802372    0.0104055     0.0123743     0.0134942    0.0134942    0.0123743    0.0104055    0.00802372   0.00567363   0.00367889   0.00218748   0.00119273   0.000596367  0.000273435  0.000114965  4.43252e-5  1.56713e-5   5.0808e-6    1.51053e-6   4.11812e-7
  1.51504e-11   4.11812e-7    1.51053e-6    5.0808e-6     1.56713e-5    4.43252e-5   0.000114965   0.000273435   0.000596367   0.00119273    0.00218748    0.00367889    0.00567363    0.00802372    0.0104055     0.0123743     0.0134942    0.0134942    0.0123743    0.0104055    0.00802372   0.00567363   0.00367889   0.00218748   0.00119273   0.000596367  0.000273435  0.000114965  4.43252e-5  1.56713e-5   5.0808e-6    1.51053e-6   4.11812e-7
  4.54513e-11   3.77633e-7    1.38516e-6    4.65912e-6    1.43707e-5    4.06464e-5   0.000105424   0.000250741   0.000546871   0.00109374    0.00200593    0.00337356    0.00520274    0.00735779    0.00954187    0.0113473     0.0123743    0.0123743    0.0113473    0.00954187   0.00735779   0.00520274   0.00337356   0.00200593   0.00109374   0.000546871  0.000250741  0.000105424  4.06464e-5  1.43707e-5   4.65912e-6   1.38516e-6   3.77633e-7
  7.57521e-11   3.1755e-7     1.16478e-6    3.91783e-6    1.20843e-5    3.41794e-5   8.86505e-5    0.000210847   0.000459862   0.000919723   0.00168678    0.00283681    0.00437497    0.00618714    0.00802372    0.00954187    0.0104055    0.0104055    0.00954187   0.00802372   0.00618714   0.00437497   0.00283681   0.00168678   0.000919723  0.000459862  0.000210847  8.86505e-5   3.41794e-5  1.20843e-5   3.91783e-6   1.16478e-6   3.1755e-7
  1.06053e-10   2.44865e-7    8.98167e-7    3.02106e-6    9.31823e-6    2.63559e-5   6.83588e-5    0.000162586   0.000354602   0.000709204   0.00130069    0.00218748    0.00337356    0.00477093    0.00618714    0.00735779    0.00802372   0.00802372   0.00735779   0.00618714   0.00477093   0.00337356   0.00218748   0.00130069   0.000709204  0.000354602  0.000162586  6.83588e-5   2.63559e-5  9.31823e-6   3.02106e-6   8.98167e-7   2.44865e-7
  1.36354e-10   1.73145e-7    6.351e-7      2.13621e-6    6.58898e-6    1.86365e-5   4.8337e-5     0.000114965   0.000250741   0.000501483   0.000919723   0.00154678    0.00238547    0.00337356    0.00437497    0.00520274    0.00567363   0.00567363   0.00520274   0.00437497   0.00337356   0.00238547   0.00154678   0.000919723  0.000501483  0.000250741  0.000114965  4.8337e-5    1.86365e-5  6.58898e-6   2.13621e-6   6.351e-7     1.73145e-7
  1.66655e-10   1.12271e-7    4.11812e-7    1.38516e-6    4.27243e-6    1.20843e-5   3.13427e-5    7.45458e-5    0.000162586   0.000325171   0.000596367   0.00100297    0.00154678    0.00218748    0.00283681    0.00337356    0.00367889   0.00367889   0.00337356   0.00283681   0.00218748   0.00154678   0.00100297   0.000596367  0.000325171  0.000162586  7.45458e-5   3.13427e-5   1.20843e-5  4.27243e-6   1.38516e-6   4.11812e-7   1.12271e-7
  1.96956e-10   6.67567e-8    2.44865e-7    8.23623e-7    2.5404e-6     7.18534e-6   1.86365e-5    4.43252e-5    9.6674e-5     0.000193348   0.000354602   0.000596367   0.000919723   0.00130069    0.00168678    0.00200593    0.00218748   0.00218748   0.00200593   0.00168678   0.00130069   0.000919723  0.000596367  0.000354602  0.000193348  9.6674e-5    4.43252e-5   1.86365e-5   7.18534e-6  2.5404e-6    8.23623e-7   2.44865e-7   6.67567e-8
  2.27256e-10   3.63993e-8    1.33513e-7    4.49084e-7    1.38516e-6    3.91783e-6   1.01616e-5    2.41685e-5    5.27119e-5    0.000105424   0.000193348   0.000325171   0.000501483   0.000709204   0.000919723   0.00109374    0.00119273   0.00119273   0.00109374   0.000919723  0.000709204  0.000501483  0.000325171  0.000193348  0.000105424  5.27119e-5   2.41685e-5   1.01616e-5   3.91783e-6  1.38516e-6   4.49084e-7   1.33513e-7   3.63993e-8
  2.57557e-10   1.81997e-8    6.67567e-8    2.24542e-7    6.92582e-7    1.95892e-6   5.0808e-6     1.20843e-5    2.63559e-5    5.27119e-5    9.6674e-5     0.000162586   0.000250741   0.000354602   0.000459862   0.000546871   0.000596367  0.000596367  0.000546871  0.000459862  0.000354602  0.000250741  0.000162586  9.6674e-5    5.27119e-5   2.63559e-5   1.20843e-5   5.0808e-6    1.95892e-6  6.92582e-7   2.24542e-7   6.67567e-8   1.81997e-8
  2.87858e-10   8.34459e-9    3.06081e-8    1.02953e-7    3.1755e-7     8.98167e-7   2.32956e-6    5.54065e-6    1.20843e-5    2.41685e-5    4.43252e-5    7.45458e-5    0.000114965   0.000162586   0.000210847   0.000250741   0.000273435  0.000273435  0.000250741  0.000210847  0.000162586  0.000114965  7.45458e-5   4.43252e-5   2.41685e-5   1.20843e-5   5.54065e-6   2.32956e-6   8.98167e-7  3.1755e-7    1.02953e-7   3.06081e-8   8.34459e-9
  3.18159e-10   3.50847e-9    1.28691e-8    4.32864e-8    1.33513e-7    3.77633e-7   9.79458e-7    2.32956e-6    5.0808e-6     1.01616e-5    1.86365e-5    3.13427e-5    4.8337e-5     6.83588e-5    8.86505e-5    0.000105424   0.000114965  0.000114965  0.000105424  8.86505e-5   6.83588e-5   4.8337e-5    3.13427e-5   1.86365e-5   1.01616e-5   5.0808e-6    2.32956e-6   9.79458e-7   3.77633e-7  1.33513e-7   4.32864e-8   1.28691e-8   3.50847e-9
  3.4846e-10    1.3527e-9     4.96172e-9    1.66892e-8    5.14764e-8    1.45597e-7   3.77633e-7    8.98167e-7    1.95892e-6    3.91783e-6    7.18534e-6    1.20843e-5    1.86365e-5    2.63559e-5    3.41794e-5    4.06464e-5    4.43252e-5   4.43252e-5   4.06464e-5   3.41794e-5   2.63559e-5   1.86365e-5   1.20843e-5   7.18534e-6   3.91783e-6   1.95892e-6   8.98167e-7   3.77633e-7   1.45597e-7  5.14764e-8   1.66892e-8   4.96172e-9   1.3527e-9
  3.78761e-10   4.78251e-10   1.75423e-9    5.90051e-9    1.81997e-8    5.14764e-8   1.33513e-7    3.1755e-7     6.92582e-7    1.38516e-6    2.5404e-6     4.27243e-6    6.58898e-6    9.31823e-6    1.20843e-5    1.43707e-5    1.56713e-5   1.56713e-5   1.43707e-5   1.20843e-5   9.31823e-6   6.58898e-6   4.27243e-6   2.5404e-6    1.38516e-6   6.92582e-7   3.1755e-7    1.33513e-7   5.14764e-8  1.81997e-8   5.90051e-9   1.75423e-9   4.78251e-10
  4.09062e-10   1.55054e-10   5.6874e-10    1.913e-9      5.90051e-9    1.66892e-8   4.32864e-8    1.02953e-7    2.24542e-7    4.49084e-7    8.23623e-7    1.38516e-6    2.13621e-6    3.02106e-6    3.91783e-6    4.65912e-6    5.0808e-6    5.0808e-6    4.65912e-6   3.91783e-6   3.02106e-6   2.13621e-6   1.38516e-6   8.23623e-7   4.49084e-7   2.24542e-7   1.02953e-7   4.32864e-8   1.66892e-8  5.90051e-9   1.913e-9     5.6874e-10   1.55054e-10
  4.39362e-10   4.60978e-11   1.69087e-10   5.6874e-10    1.75423e-9    4.96172e-9   1.28691e-8    3.06081e-8    6.67567e-8    1.33513e-7    2.44865e-7    4.11812e-7    6.351e-7      8.98167e-7    1.16478e-6    1.38516e-6    1.51053e-6   1.51053e-6   1.38516e-6   1.16478e-6   8.98167e-7   6.351e-7     4.11812e-7   2.44865e-7   1.33513e-7   6.67567e-8   3.06081e-8   1.28691e-8   4.96172e-9  1.75423e-9   5.6874e-10   1.69087e-10  4.60978e-11
  4.69663e-10   1.25675e-11   4.60978e-11   1.55054e-10   4.78251e-10   1.3527e-9    3.50847e-9    8.34459e-9    1.81997e-8    3.63993e-8    6.67567e-8    1.12271e-7    1.73145e-7    2.44865e-7    3.1755e-7     3.77633e-7    4.11812e-7   4.11812e-7   3.77633e-7   3.1755e-7    2.44865e-7   1.73145e-7   1.12271e-7   6.67567e-8   3.63993e-8   1.81997e-8   8.34459e-9   3.50847e-9   1.3527e-9   4.78251e-10  1.55054e-10  4.60978e-11  1.25675e-11

For the image metadata we specify the grid and the total flux of the image, which is 1.0. Note that we specify the total flux out front since it is degenerate with an overall shift in the gain amplitudes.

julia

skymeta = (; mimg = mimg ./ flux(mimg), ftot = 0.6);

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)
skyprior = (
    c = cprior,
    σ = Exponential(0.1),
    p = cprior,
    p0 = Normal(-2.0, 2.0),
    pσ = truncated(Normal(0.0, 1.0); lower = 0.01),
    angparams = ImageSphericalUniform(nx, ny),
)

skym = SkyModel(sky, skyprior, grid; metadata = skymeta)

SkyModel
  with map: sky
   on grid: ComradeBase.RectiGrid

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.

For the complex gain matrix, we used the JonesG jones matrix. The first argument is now a function that converts from the parameters to the complex gain matrix. In this case, we will use a amplitude and phase decomposition of the complex gain matrix. Note that since the gain matrix is a diagonal 2x2 matrix the function must return a 2-element tuple. The first element of the tuple is the gain for the first polarization feed (R) and the second is the gain for the second polarization feed (L).

julia

function fgain(x)
    gR = exp(x.lgR + 1im * x.gpR)
    gL = gR * exp(x.lgrat + 1im * x.gprat)
    return gR, gL
end
G = JonesG(fgain)

Comrade.JonesG{typeof(Main.var"##225".fgain)}(Main.var"##225".fgain)

Similarly we provide a JonesD function for the leakage terms. Since we assume that we are in the small leakage limit, we will use the decomposition 1 d1 d2 1 Therefore, there are 2 free parameters for the JonesD our parameterization function must return a 2-element tuple. For d-terms we will use a re-im parameterization.

julia

function fdterms(x)
    dR = complex(x.dRx, x.dRy)
    dL = complex(x.dLx, x.dLy)
    return dR, dL
end
D = JonesD(fdterms)

Comrade.JonesD{typeof(Main.var"##225".fdterms)}(Main.var"##225".fdterms)

Finally we define our response Jones matrix. This matrix is a basis transform matrix plus the feed rotation angle for each station. These are typically set by the telescope so there are no free parameters, so no parameterization is necessary.

julia

R = JonesR(; add_fr = true)

Comrade.JonesR{Nothing}(nothing, true)

Finally, we build our total Jones matrix by using the JonesSandwich function. The first argument is a function that specifies how to combine each Jones matrix. In this case we will use the standard decomposition J = adjoint(R)_G_D*R, where we need to apply the adjoint of the feed rotaion matrix R because the data has feed rotation calibration.

julia

js(g, d, r) = adjoint(r) * g * d * r
J = JonesSandwich(js, G, D, R)

Comrade.JonesSandwich{Base.Splat{typeof(Main.var"##225".js)}, Tuple{Comrade.JonesG{typeof(Main.var"##225".fgain)}, Comrade.JonesD{typeof(Main.var"##225".fdterms)}, Comrade.JonesR{Nothing}}}(splat(js), (Comrade.JonesG{typeof(Main.var"##225".fgain)}(Main.var"##225".fgain), Comrade.JonesD{typeof(Main.var"##225".fdterms)}(Main.var"##225".fdterms), Comrade.JonesR{Nothing}(nothing, true)))

Note

This is a general note that for arrays with non-zero leakage, feed rotation calibration does not remove the impact of feed rotations on the instrument model. That is, when modeling feed rotation must be taken into account. This is because the R and D matrices are not commutative. Therefore, to recover the correct instrumental terms we must include the feed rotation calibration in the instrument model. This is not ideal when doing polarized modeling, especially for interferometers using a mixture of linear and circular feeds. For linear feeds R does not commute with G or D and applying feed rotation calibration before solving for gains can mix gains and leakage with feed rotation calibration terms breaking many of the typical assumptions about the stabilty of different instrument effects.

For the instrument prior, we will use a simple IID prior for the complex gains and d-terms. The IIDSitePrior function specifies that each site has the same prior and each value is independent on some time segment. The current time segments are

ScanSeg() which specifies each scan has an independent value
TrackSeg() which says that the value is constant over the track.
IntegSeg() which says that the value changes each integration time

For the released EHT data, the calibration procedure makes gains stable over each scan so we use ScanSeg for those quantities. The d-terms are typically stable over the track so we use TrackSeg for those.

julia

intprior = (
    lgR = ArrayPrior(IIDSitePrior(ScanSeg(), Normal(0.0, 0.2)); LM = IIDSitePrior(ScanSeg(), Normal(0.0, 1.0))),
    lgrat = ArrayPrior(IIDSitePrior(ScanSeg(), Normal(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),
    dRx = ArrayPrior(IIDSitePrior(TrackSeg(), Normal(0.0, 0.2))),
    dRy = ArrayPrior(IIDSitePrior(TrackSeg(), Normal(0.0, 0.2))),
    dLx = ArrayPrior(IIDSitePrior(TrackSeg(), Normal(0.0, 0.2))),
    dLy = ArrayPrior(IIDSitePrior(TrackSeg(), Normal(0.0, 0.2))),
)

(lgR = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}, Base.Pairs{Symbol, Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}, Tuple{Symbol}, @NamedTuple{LM::Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}}}, Comrade.NoReference, Nothing}(Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}(Comrade.ScanSeg(), Distributions.Normal{Float64}(μ=0.0, σ=0.2)), Base.Pairs{Symbol, Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}, Tuple{Symbol}, @NamedTuple{LM::Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}}}(:LM => Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}(Comrade.ScanSeg(), Distributions.Normal{Float64}(μ=0.0, σ=1.0))), Comrade.NoReference(), false, nothing), lgrat = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Comrade.NoReference, Nothing}(Comrade.IIDSitePrior{Comrade.ScanSeg, Distributions.Normal{Float64}}(Comrade.ScanSeg(), Distributions.Normal{Float64}(μ=0.0, σ=0.1)), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), Comrade.NoReference(), false, nothing), gpR = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.ScanSeg, VLBIImagePriors.DiagonalVonMises{Float64, Float64, Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Comrade.SEFDReference{Float64}, Nothing}(Comrade.IIDSitePrior{Comrade.ScanSeg, VLBIImagePriors.DiagonalVonMises{Float64, Float64, Float64}}(Comrade.ScanSeg(), VLBIImagePriors.DiagonalVonMises{Float64, Float64, Float64}(μ=0.0, κ=0.10132118364233778, lnorm=-1.739120733481688)), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), Comrade.SEFDReference{Float64}(0.0, 0), true, nothing), gprat = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.ScanSeg, VLBIImagePriors.DiagonalVonMises{Float64, Float64, Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Comrade.SingleReference{Float64}, Nothing}(Comrade.IIDSitePrior{Comrade.ScanSeg, VLBIImagePriors.DiagonalVonMises{Float64, Float64, Float64}}(Comrade.ScanSeg(), VLBIImagePriors.DiagonalVonMises{Float64, Float64, Float64}(μ=0.0, κ=99.99999999999999, lnorm=1.3823902436480708)), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), Comrade.SingleReference{Float64}(:AA, 0.0), true, nothing), dRx = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Comrade.NoReference, Nothing}(Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}(Comrade.TrackSeg(), Distributions.Normal{Float64}(μ=0.0, σ=0.2)), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), Comrade.NoReference(), false, nothing), dRy = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Comrade.NoReference, Nothing}(Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}(Comrade.TrackSeg(), Distributions.Normal{Float64}(μ=0.0, σ=0.2)), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), Comrade.NoReference(), false, nothing), dLx = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Comrade.NoReference, Nothing}(Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}(Comrade.TrackSeg(), Distributions.Normal{Float64}(μ=0.0, σ=0.2)), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), Comrade.NoReference(), false, nothing), dLy = Comrade.ArrayPrior{Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, Comrade.NoReference, Nothing}(Comrade.IIDSitePrior{Comrade.TrackSeg, Distributions.Normal{Float64}}(Comrade.TrackSeg(), Distributions.Normal{Float64}(μ=0.0, σ=0.2)), Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}(), Comrade.NoReference(), false, nothing))

Finally, we can build our instrument model which takes a model for the Jones matrix J and priors for each term in the Jones matrix.

julia

intmodel = InstrumentModel(J, intprior)

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; admode = set_runtime_activity(Enzyme.Reverse))

VLBIPosterior
ObservedSkyModel
  with map: sky
   on grid: VLBISkyModels.FourierDualDomainObservedInstrumentModel
  with Jones: JonesSandwich
  with reference basis: PolarizedTypes.CirBasis()Data Products: Comrade.EHTCoherencyDatum

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)

TransformedVLBIPosterior(
VLBIPosterior
ObservedSkyModel
  with map: sky
   on grid: VLBISkyModels.FourierDualDomainObservedInstrumentModel
  with Jones: JonesSandwich
  with reference basis: PolarizedTypes.CirBasis()Data Products: Comrade.EHTCoherencyDatum
Transform: Params to ℝ^5689
)

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
using OptimizationOptimisers
xopt, sol = comrade_opt(
    post, Optimisers.Adam();
    initial_params = prior_sample(rng, post), maxiters = 25_000
)

((sky = (c = (params = [0.006196768010070597 0.012532920514229195 0.01916429631039211 0.02623125080360275 0.0338700970224518 0.042214673241194586 0.051309598973525064 0.061130897218443295 0.07141721576456544 0.08176076840746735 0.09171723191589562 0.10114158079010942 0.11035299841498157 0.1196787346654339 0.12868517650148859 0.13581247472348792 0.13872913001417778 0.1360860658586299 0.12893156137315587 0.11961568844503521 0.11014065479772524 0.10166669522075616 0.09446035877140163 0.08812301099611487 0.0819052793672862 0.07516256657369239 0.06731986992565857 0.05836257438946372 0.0481656425062368 0.037055520866257595 0.025097825087925022 0.01270662825673901; 0.012252886595333686 0.02479775887210279 0.037921041802479974 0.05192112715920419 0.06710134646570208 0.08372138538018767 0.10199208727308609 0.1218517634828346 0.14283287401292116 0.16394430867101156 0.18402000017602624 0.2026033130851004 0.22066843119321525 0.23963231150003383 0.25914704802499305 0.27554283495855997 0.28271111480256067 0.27661265554296127 0.2601289821519635 0.23947096595174464 0.21929946522498114 0.20205460333451955 0.1881067963542621 0.1762249149715628 0.16452979248920077 0.1514063262517803 0.13599167995875278 0.11790735427769763 0.09745789453439697 0.07487121516205798 0.05080706983974277 0.025627699588869412; 0.018045341775381824 0.036514466618055096 0.055855532783095435 0.07652183667263181 0.09897701325641989 0.12372900565397749 0.15119054048416103 0.18152853040557257 0.21411204054972446 0.2470662837351258 0.2777403692714144 0.3046915582985969 0.32997046929831825 0.3579951362477143 0.39103315653949094 0.4232656412406568 0.4393233415543986 0.42792053373227534 0.3960122643652718 0.3585716747656921 0.32487844861511495 0.2987050901770813 0.2796491595927121 0.26437430657293237 0.2488377047257706 0.23025029179901357 0.2073880272837421 0.18013664408178628 0.14886687228417295 0.1144384707676309 0.07754156547432965 0.039181951647653826; 0.023428261395017344 0.04742043328476806 0.072551527847697 0.09943354018726239 0.12873661061412137 0.1611872834812491 0.1976486516853103 0.23887601087454294 0.28462111073478896 0.3319969778930648 0.37498007923561205 0.4087196991533225 0.4358877498883077 0.46694574821935786 0.5147247173886381 0.5777932584238109 0.6196910050596293 0.6009891511616148 0.5379671152169879 0.47179426438141564 0.4200282673413506 0.3864944847272338 0.36703397958164036 0.3530267143476789 0.3365522197215629 0.3136700145124149 0.2835031720821861 0.24653257972167025 0.20378710300292519 0.1564812738164873 0.1060221624811026 0.05345946751686553; 0.028288773039715713 0.05725232215127483 0.08760301835603411 0.12008724905906684 0.15552714260066586 0.1949028069750706 0.23953577397756892 0.2912720306621754 0.35170977090003935 0.4188122340577373 0.4812749389258896 0.5212048680090704 0.5372398861979125 0.5501708740975483 0.596705265396437 0.7051485687991506 0.816436403187573 0.8033798767129117 0.6833395429840124 0.5686423498143162 0.4928907921083953 0.4577444489254853 0.44822510463915505 0.44377582822449385 0.43040350385927817 0.4043717922186208 0.36666269911307925 0.3190592855071049 0.26348052632185 0.20203005593065196 0.13659090559500928 0.06887351657485336; 0.03251362224912441 0.0657870545607222 0.1006295504590151 0.13791753708239476 0.1785822487971986 0.22358176154316625 0.27429839263791467 0.3335712634718274 0.40639183800881745 0.4964615105076533 0.5928052514059814 0.6526464503785732 0.637669052131663 0.5890124195116815 0.5905166006308352 0.7159253643958778 0.944533138722639 1.0109546692240101 0.8245736780718813 0.6405162497872117 0.5354395339888053 0.5105401658439674 0.526703191739978 0.5405351307939404 0.5336591374085233 0.5053501840411283 0.45966802021116443 0.3998817807380914 0.3294094719378752 0.2517601019964101 0.1697885269295227 0.08537476438958325; 0.03602793223345388 0.07283771076057709 0.11128904831891218 0.15237967424069293 0.1971099507118708 0.24592154696795993 0.2986477851683404 0.35685618844248673 0.4279724504250445 0.5245817903112464 0.6455282143804337 0.7344037683012398 0.675268530701457 0.540561155877199 0.4869341747280918 0.6011400921654225 0.900847377656042 1.122722040230514 0.9170380638009018 0.6743832649948638 0.5574568621345458 0.5537424642871998 0.5999871250879496 0.6392085403049865 0.6452877164680262 0.6183887813731119 0.565280037798766 0.4912059221002378 0.40276569746511204 0.3061794670523527 0.2055370441705339 0.10313319210415442; 0.038812081755876235 0.0783112210255691 0.11931250830221315 0.16285114168287093 0.21005188607036512 0.2607967795652262 0.3116582753104457 0.3574512778985936 0.4001655090481582 0.45510122275651815 0.5272470500523078 0.5662577445029546 0.48760196272307127 0.35963935167513944 0.31910930509146607 0.43740801664182916 0.7140797245438533 0.9214276047060704 0.7667478066524501 0.5907891151391582 0.5231653063816291 0.5601566013008686 0.646006354131586 0.7282646263697631 0.7678702590576616 0.7515639233365983 0.6895657898346136 0.5961447499317297 0.48442403481053664 0.3650337819771907 0.24344215771320737 0.12161881507821756; 0.04095176827533074 0.08234908722574633 0.1247578304047827 0.16898805114306842 0.216136821794323 0.26616608747864623 0.31417823252895344 0.3481064275587636 0.3564852605225494 0.3442301608731162 0.3235629342956652 0.28375407011969794 0.2186358623496868 0.1706962718280595 0.19486138950246648 0.30621219391437887 0.4435059161490978 0.47855347840977686 0.4138986800112434 0.3558001339241657 0.38917530152910107 0.5144836936190408 0.6868512365181025 0.8499824895456387 0.9440190319330926 0.9385718436271744 0.851624330252573 0.7203056797460236 0.5738644318506569 0.4264468731010704 0.2819038679536366 0.14016147412831148; 0.042677964458367953 0.08546036842888032 0.12843666982863908 0.17171201553024998 0.2155812108758983 0.2598149373719247 0.3007867490224928 0.3270047027878025 0.32018427462383436 0.273851263830046 0.20803790534896205 0.14912749288875318 0.12363885127416015 0.16540793845505725 0.2806464935396977 0.395895027939786 0.3984486665021706 0.3094681083570406 0.21900780374228 0.1832304741977865 0.259429662369526 0.4382111427895155 0.6956899308422972 0.9786138213556654 1.1819552572404295 1.1932013112148487 1.0494872489069722 0.8550252365267613 0.6631768491434729 0.4851293578401294 0.31786882549122314 0.1573119279408083; 0.044305711989782864 0.08839023179470905 0.13182876816650352 0.17377534035263328 0.2130791876337192 0.2481021078033176 0.27575879537076725 0.28870095768806514 0.2736562770816754 0.22482390884170592 0.16510843228850525 0.13879694191994044 0.19560349576412708 0.3921845757429166 0.7027173727285675 0.8435398032125411 0.5709819208902246 0.3806115573118353 0.295141807430928 0.2342726850479698 0.2163862345452412 0.3204594972352398 0.5556045162510334 0.928775919398126 1.37462708127988 1.4691336331810405 1.2350482810974772 0.9684792544094327 0.7361243442501473 0.5330340063187688 0.3473250007256762 0.17140144867175985; 0.046160067741740154 0.09194467935545347 0.13668447361030478 0.1789972484154545 0.2164970493251364 0.24522354847562589 0.2584433027470848 0.2474348272175724 0.20944590311716912 0.16245394663451795 0.148863648387339 0.22208887510453598 0.43126456660683654 0.8478815679760098 0.98300861329124 0.7268966419847186 0.38406488688010926 0.47542137068946344 0.671382626217176 0.5117924721596375 0.2093679240953046 0.15219549480328612 0.3029260256585631 0.6672475140962228 1.3258198411690334 1.631572725718177 1.3162168394966913 1.0240806095276362 0.778599311807857 0.5638025290693484 0.36724616722121733 0.18116861142523183; 0.048443040831898744 0.09666475001294682 0.1442268370298679 0.19007125230910524 0.23183170162167024 0.263178760568854 0.26887111604257763 0.23076908943041635 0.1617141754779021 0.11877338723325884 0.17623889738871365 0.40283241092605654 0.7415031309545711 0.5377049559687783 0.08840468986092818 -0.1792206148537516 -0.2505615337944633 -0.07195137377349546 0.3055178564704216 0.4811793429557715 0.1408075265200763 0.0012513196278252899 0.09266804030823207 0.3874431684348538 0.8500845138810323 1.21148828918353 1.201704777050549 1.0109640928031174 0.789742625413092 0.5771622963010189 0.37715690020127285 0.18628671595373408; 0.05101953121137394 0.10224374483368032 0.15388913756033662 0.20595322247800038 0.25715002290245764 0.2996696604372008 0.30782782283016913 0.25119296384425627 0.17267391956799688 0.1388387532296202 0.24653998248681883 0.5797753366396821 0.8836772922536705 0.120312919094128 -0.386050452813161 -0.6054185463508801 -0.61253080632096 -0.41963495567894826 -0.059089238881742875 0.21809386771782288 0.037262331461231854 -0.08844660546795276 -0.009006354379583602 0.2547836353207025 0.6389853498398048 0.9737447919935618 1.0645878400935307 0.9592463682074481 0.7754195179733036 0.5747471401985648 0.37769837860699307 0.18698868323155757; 0.05347799913024842 0.10753277931036948 0.16290156715421328 0.22007785166202343 0.27704308073831563 0.3214154956669933 0.3177004482584468 0.23121869623938307 0.11475302820231804 0.07107505538999728 0.18302519152894145 0.4328175087618345 0.7962461938555506 -0.04646488370791933 -0.5332734751353347 -0.7219090832676335 -0.6906238967896985 -0.4588157309296376 -0.0543999861282285 0.1772177427950713 -0.02457435096351208 -0.12708654469286246 -0.02816192728081675 0.2550514868982885 0.6513774680993195 0.9842754773073775 1.043804817798318 0.9288018683734517 0.7542538370383635 0.5624435759013819 0.37100971765316276 0.18402742978397177; 0.05536426377901567 0.11134823632415901 0.16867436739222008 0.22735707164299387 0.2826991951753498 0.3143259392756683 0.2809535175120298 0.16608765779552537 0.03132101775703814 -0.028667952185643386 0.07971062345788492 0.4169593892070065 0.6661131554301687 -0.005215716769154591 -0.4290192949317993 -0.5729654279416689 -0.4926016968020276 -0.18788321505394603 0.391252621622201 0.4495761014613081 -0.0016216622170531065 -0.11657252891268177 -0.010335104789659369 0.3044161294352515 0.7888047050156246 1.2742222226920297 1.2246965884935097 0.9694099765317082 0.7462721763596941 0.547138502707223 0.359491541964418 0.17821018505847022; 0.056527705545960094 0.11356624353967873 0.17150993821404067 0.23007274393610674 0.2845192046528764 0.3131001352634133 0.27184097475848545 0.14535834470737236 0.006098762922447518 -0.06610642562343175 0.006915194725394255 0.27566588608894627 0.5316404276559793 0.22399814394742384 -0.048292672607727 -0.11184932086342636 0.01144494619950693 0.19446256798509354 0.4645334623737585 0.20712469370019201 -0.013696142112148393 -0.05270649265540216 0.055516464215667014 0.3056435868452438 0.6961461226715279 1.1392305358931598 1.1988631780086196 0.9517458599289899 0.7195433292534603 0.5220137645516865 0.3419804568493151 0.1695276814568414; 0.057106268539434596 0.11466260512963744 0.17309175787865522 0.2328755701058511 0.2935938475318017 0.3442650439509029 0.3492190383884422 0.26726167346960017 0.11731521765980493 -0.022021467679088594 -0.0703949196548875 0.011206375706272791 0.15628482006838695 0.3282857908891407 0.589494725574462 0.7339510307990825 0.6203706952782309 0.14688065303333575 0.05280639975249545 -0.014083810233256793 0.00893707497161687 0.10332138197468445 0.18846006044816233 0.3136768058711374 0.5216395921339524 0.7660979886579442 0.8766673489231664 0.7945537552402754 0.6408361548014658 0.4776992873022094 0.3169381209687134 0.1580876085348385; 0.057305290139574964 0.11511237591758024 0.17399526310478555 0.2352636906326451 0.3025775440123214 0.3776452599807047 0.4438062996119846 0.4421258424409016 0.30388454099135553 0.08140626829744124 -0.1039032878513975 -0.17665999103068866 -0.10788722350532276 0.15063759899149523 0.6005572171738696 0.47035170509911317 -0.014861715491901843 -0.29546249106286876 -0.341379521279149 -0.22832964764042904 0.02943973886838397 0.32269065472972996 0.41164986416216987 0.35907746786578215 0.398574025315073 0.5225660248451892 0.6274709676870157 0.6308007494304128 0.5493398394736928 0.42756853118729277 0.28995101508815646 0.14609384856535867; 0.057009865193745644 0.11459777045433728 0.17330286318771262 0.23408335098941593 0.30091947804952784 0.38051512899088963 0.46936285538923467 0.5197842035169284 0.43033148529574583 0.19914026939536345 -0.04779904518719093 -0.20216898346332526 -0.2059582395438522 -0.017311981315210008 0.2991833413321614 0.10615518957654785 -0.26603737253283116 -0.480019449391619 -0.5035047925299958 -0.35047383498145906 -0.022800595469141437 0.42523595945895337 0.6806519357741971 0.5265136625091954 0.46613528744564087 0.5058487855545701 0.5599040430364614 0.5599487167195066 0.49680219458308555 0.3933916446970634 0.2696438851074919 0.13660483101602855; 0.056063207706883396 0.11278133360182427 0.1707222118305001 0.23054406793341237 0.2952625289063574 0.37154594071134306 0.4650675477246065 0.556041024838474 0.5629541349922594 0.42191575622145283 0.18296714766057087 -0.020560920590810317 -0.0930295563534638 0.000689058886562433 0.17912407544698652 0.06405890356893877 -0.21759410253618272 -0.40755465595881873 -0.43566623505157237 -0.2981285366130607 0.007032004807987901 0.46637019592294743 0.9276158345920632 0.8542785813698459 0.7329592311491457 0.6785341373692483 0.6387720075617878 0.5783196612907099 0.49002097660270716 0.3808974846731681 0.25917616688513123 0.1309301893611631; 0.05445422237787154 0.10972400921549899 0.16666492229358917 0.2261911514541856 0.28980613933830085 0.36073046805601044 0.4444645786904529 0.5401947579101725 0.6214119604622321 0.6346162182047038 0.47989576716296484 0.2539451218175969 0.1156362747288787 0.13248439308888102 0.24319190818475261 0.23502660050347363 0.080213847500878 -0.0946717573669798 -0.1429051900754076 -0.05847714022437236 0.1651050223568772 0.5129086651507427 0.907475957449018 1.0845554331143632 1.0826021621902173 0.9370397752141709 0.7785518578913109 0.6375208572962463 0.508342952699242 0.382316696119574 0.25574195600027866 0.12815124368020203; 0.05205541533209755 0.10503615480844077 0.15999748676883693 0.2181460969260939 0.28073769043492647 0.34904037878358185 0.42576145375880975 0.518483676853526 0.6256561673562023 0.6856358558131587 0.5779184543514524 0.35895404778912743 0.1965620935197572 0.18406299824974473 0.28898304228578553 0.4181735815681246 0.5527681246452282 0.4976623579783699 0.37296129491749935 0.335982943578355 0.42907674286163405 0.6473290105175934 0.9572869585091619 1.223731540522336 1.2986659132772373 1.1206987649392899 0.8831728376785624 0.6858392789504983 0.5256051765655471 0.3851945773303791 0.2537261314830783 0.12611953628725978; 0.048775734097167074 0.09842590685565879 0.14991887968191472 0.20428688620780205 0.2624172274313957 0.324703509665783 0.39184304293704575 0.467536447317272 0.5490282606851107 0.5946543759093746 0.5269685353100569 0.3644231140546952 0.2314308129614653 0.2074575665484828 0.29222434516045404 0.45765775769882683 0.6747957700004086 0.8197554680057341 0.7798595704840561 0.6739177994128219 0.6534528892461673 0.7453659866741518 0.9371543886198783 1.1539190907638333 1.2350886595257267 1.0926652144423974 0.8787700413588683 0.6858319464041238 0.5227070128460497 0.3796694245965291 0.2481754026409931 0.12277234028173802; 0.0446804575784225 0.09007100925946505 0.13689098684545986 0.18577994392082403 0.23706270177087618 0.2905066400836769 0.34595224957247084 0.40417545102353686 0.4585291689052793 0.4821541556935825 0.438420801594682 0.34017639998662175 0.2566996856549095 0.2481763161926532 0.3281939698417816 0.47681000860378675 0.6503687182091038 0.7827453278495956 0.841253363465894 0.8433279247024583 0.8623841655786104 0.9143860714435732 1.018855769700939 1.1178675412430912 1.1178234631012416 0.9933153688469512 0.8194759720012227 0.650700345323161 0.4993395081524276 0.3629150949761319 0.23682721330801892 0.11696273790558503; 0.039931218467164555 0.08038567838323916 0.12183990246045748 0.16465374137279612 0.20889821783852003 0.25433052846751003 0.300805926967064 0.34778107004524556 0.3897813731821119 0.41105343549753 0.3941561975572058 0.3493553550450824 0.31774395365224306 0.34020924783426515 0.43035913570248385 0.5667632478049016 0.7089855788383995 0.8431589573613214 0.9985869920041436 1.1719564638486697 1.2790482974855577 1.2200496022880398 1.1670785150812573 1.1254113941781902 1.035205756836127 0.8984254849566681 0.7460630241648194 0.5979532894314069 0.46142080917847667 0.3361899470249469 0.21954445708830098 0.10844413088573604; 0.03471859407403925 0.06979732977013807 0.10554012122833452 0.14213222703679956 0.17956740544087454 0.2176342566116525 0.2559871226344372 0.29358663898594656 0.32690976113598863 0.3490459269134525 0.35574152832232553 0.35692831520408586 0.3748139605788211 0.43049949756605443 0.5322437676219614 0.6650269943941596 0.8031101225126097 0.970453523214278 1.2357065903963445 1.5788689424440914 1.838954386377711 1.5324316780270146 1.2572103759089825 1.0809121148039627 0.9385575033758454 0.79885298206583 0.6619987091801238 0.5325317777259512 0.4125040237192743 0.30131401802745544 0.19704654635374932 0.09737962856137158; 0.02920482203822035 0.058640862093503054 0.0885011266003377 0.11888419311762263 0.14976117494620153 0.18096372696594562 0.21209120908008394 0.2421908968979761 0.26939776581169406 0.29185983122943215 0.31105884261468936 0.33506767938782245 0.3763738455898462 0.44455591430666963 0.5427256355158395 0.6640739786075337 0.7959849548900602 0.9591817490538899 1.2038031242246379 1.4851215725612716 1.6212683126411704 1.405616230586798 1.1523501339719564 0.9609690974401218 0.8131285216765102 0.6848830168094951 0.5668420419643612 0.45704748256887534 0.35504189981159584 0.2599244336778456 0.17022254735734257 0.08419402357289903; 0.02350399441912401 0.04714858552286024 0.07105579912803534 0.09527829669077549 0.11979328591673839 0.1444737578100134 0.16905420957339193 0.19303737758507053 0.21585621239471064 0.237550310097515 0.2601572179034727 0.2890962516953931 0.3316194535116123 0.39230966800770617 0.4719472840527699 0.5683369170570803 0.677614502994292 0.8060851041390822 0.9612931188410196 1.1085597542071939 1.1638799258862351 1.0703509441289578 0.923650152330587 0.7849239840891642 0.665100957564007 0.5593228832869567 0.46299793514543347 0.3739480314486261 0.2910901126907158 0.21348260058271945 0.13998056134122216 0.06927735466557856; 0.017689365779265817 0.03547169953867306 0.053401023360704646 0.07152073848593483 0.08980784012581955 0.10819655999576135 0.12655005677025155 0.1447205259143242 0.1627165418978 0.18107860422514324 0.20150106177790483 0.22722699727623985 0.26218870986970344 0.30880805031758024 0.367462829977547 0.4375966149590338 0.517993532724961 0.6075099153253151 0.7006629296542408 0.7764543625328807 0.8016678029169295 0.7591501260018723 0.6786209766181106 0.5893415852240166 0.5039726106308354 0.4251902342954755 0.35253082465815155 0.28514859172273405 0.22229959141849595 0.16323983638520542 0.10713072343973859 0.05305755680450321; 0.011822581116203703 0.02368493918700222 0.03564388353534686 0.047698186525273745 0.05985443126084818 0.07206834241551063 0.08431511171990334 0.0965820958089938 0.10903890134146497 0.12221799953957206 0.1372596647571642 0.15595307641101 0.18031047930909289 0.2116329631808754 0.25027540933222975 0.295928727432103 0.347581632810168 0.40267924288347146 0.4554812489628056 0.4948517138746508 0.5072107602332462 0.4868067769875633 0.4436941345541152 0.39105749334378664 0.33721518078144497 0.28566917326439534 0.2373561431219788 0.19225756728726195 0.15004299955256978 0.11027481407638964 0.07242624298370669 0.035873617122462224; 0.005912610573946271 0.011856746062442781 0.017828843402197665 0.023856257105816823 0.029919679387616527 0.036023959685544 0.0421556676321003 0.04834601302428015 0.0547291661811262 0.061597922447086846 0.06951494669405234 0.07927174073116004 0.09172255633950571 0.10744974505388746 0.12664678899146414 0.14912928486505794 0.17419209724862603 0.20021853355594366 0.224164349953372 0.24127388179543044 0.24651313244502443 0.23799302365118546 0.21900812033940623 0.19463501129145513 0.16875231100670388 0.1433847500618212 0.11933003433013545 0.0967485006062152 0.07556283401403206 0.05556800957973218 0.03650202460717265 0.018094699763919093], hyperparams = 26.03182426500241), σ = 2.8404241261312713, p = (params = [0.0056704842510277315 0.011331887082770883 0.017085799102499945 0.022894939751059995 0.028778980647107464 0.03475387662590939 0.04075541713932338 0.046760139155534806 0.05271487462525525 0.05845741200252633 0.06402642476725738 0.06911748553984919 0.07379520209598382 0.07775605541729899 0.08094147029206691 0.08310560968067209 0.0839755704443678 0.08332878421808268 0.08124240646383331 0.07801594122994399 0.07397109900023166 0.06935434430098456 0.0643291393248523 0.058925030973537205 0.05323566786191932 0.047190942773234115 0.0409259838116404 0.034380591637989295 0.027702022222059496 0.020853441679352488 0.013959765564107935 0.006976557139227051; 0.01127967740718464 0.02265756106236649 0.03411173165072867 0.04573878224858223 0.05754523925557052 0.06949626170374963 0.08158027340126156 0.09367182366115644 0.10562112335125817 0.11730554799536863 0.12844085137644262 0.1388696550087243 0.14828105076811623 0.1564235272009355 0.16297555678490355 0.16754630979305138 0.16947070888301655 0.16812544711568095 0.16370088796289456 0.1569515032458452 0.14861143482720915 0.13922887071777532 0.12907845068424337 0.118288658024856 0.10681237433140674 0.09476611853365513 0.0821045256188947 0.06902180885791181 0.055543566503218844 0.04185169505568703 0.027960713930712762 0.014016471443497918; 0.016899172889939036 0.033860818550091744 0.05105065698943265 0.06848205813433993 0.08621156216799003 0.10425074250286828 0.12249124834477945 0.14082045256432774 0.15899536297989494 0.1767222968926912 0.19371584395647667 0.2096324031242593 0.22407550527239395 0.2366256826549182 0.2470273654333704 0.2547362503987381 0.2582236471998425 0.25599785626781607 0.24854485991367045 0.23757229379210232 0.22444545160253204 0.21001539370837322 0.1946723657797874 0.17842564541942707 0.16122253389720684 0.1429886349311439 0.1239136613861245 0.1040838454622328 0.08375248756672993 0.06303733470338718 0.042135472693749884 0.021078650484247497; 0.022391582241110892 0.044966328783905773 0.06778486983555063 0.09102458902062108 0.11472925753393694 0.13890411705388203 0.16349515210995527 0.18827315204097617 0.21291609514497511 0.2369799207962376 0.25999616283452126 0.2815728841464691 0.3012191080537458 0.31825968303343405 0.3329635096315113 0.34540926510853975 0.35204252572761946 0.3484530439237654 0.3363098890318865 0.3199791028970678 0.3014952409140821 0.28184200856296243 0.2613430785920212 0.23976857684451192 0.21678567420820088 0.1923405213916593 0.16658412258622543 0.1398532272788849 0.11241539545724395 0.084565314794926 0.056455066584964124 0.02826220217577785; 0.027820144126814907 0.055813028064381945 0.0842485235705768 0.11322627983030277 0.14291840579759355 0.17336138849218574 0.20446670392461572 0.2359557989263954 0.26736148783808156 0.29809330259969574 0.32738454471567147 0.35447036998808223 0.3791009219350592 0.40000060361923534 0.41809839704183394 0.4361463049145889 0.44878462333488034 0.4439552065787865 0.42522177054145616 0.4027764439652052 0.37885154902032236 0.35432967109905666 0.3292022860982251 0.3026560173406997 0.2739976593223597 0.24315149893346505 0.21048102491155177 0.1764947099491363 0.1416862926225522 0.10643269185369512 0.07100278436851999 0.03549577219682815; 0.03303628954300428 0.06638245430987497 0.10023107512183263 0.13490985086514082 0.17055804264242247 0.20732557596679901 0.2451129060030483 0.2835201248335797 0.3218060047218096 0.35916745687157847 0.3949552832697471 0.4281892768709195 0.45719429922139687 0.4797660481134623 0.49789596994280755 0.5173359161554872 0.5364081515078194 0.5334669313431833 0.5098518099847796 0.48268649178256623 0.45457604175152133 0.4269837906196305 0.39869413110637814 0.3677083096767685 0.33340595323112915 0.29592103812927434 0.2559056538365883 0.21419357347817816 0.17158964586422784 0.1286512829620727 0.08569092542100434 0.04281858982667829; 0.038068480168284444 0.07646125968955894 0.11560203792631225 0.15575357522232372 0.19729739100919205 0.24036700563311322 0.2848284221073207 0.3300306523617957 0.37475984674290447 0.41775737611529273 0.4585896951535448 0.4974456617508468 0.5293842099046803 0.5504125861013027 0.566726218379651 0.5847149748246188 0.6049860264318142 0.6055574617979932 0.5836806360892213 0.5556933092748217 0.527388597000078 0.49922755308309585 0.46898208821317994 0.43471842980106484 0.3954193008209996 0.3511246671665389 0.30312174156536903 0.252963015578404 0.20200836150161908 0.15106835960654968 0.10043681149853817 0.0501218660802137; 0.04276147203988317 0.08597948484955299 0.13004215851986997 0.17544878138711623 0.22263932427063035 0.27191282899389607 0.3229884819774912 0.37455991913635406 0.42442255720296823 0.4707149771042705 0.512775292366564 0.550521263862695 0.5809332058986029 0.6013962507863694 0.6175919916382637 0.636050984825029 0.6554543714689408 0.6592253877766308 0.6399058305298891 0.6165662227208931 0.5917535754774527 0.5653935000911761 0.5360420513759084 0.5022428576158419 0.46065152572686324 0.40966120922682725 0.3523192989966505 0.2925819969990261 0.2326201687225317 0.17337292541922344 0.11500361133719171 0.057320346990760884; 0.047103666241353224 0.09471229826828782 0.14334782671274632 0.193554642906643 0.24595679769165701 0.3010342692913825 0.3585559642091587 0.41656691749595415 0.4712875571624341 0.5192713022102987 0.5598543748277948 0.593504392140455 0.6199099485692356 0.6386302596493384 0.6522594763841278 0.6675532646123898 0.6805910761458553 0.6828943015866599 0.6747560342049571 0.6591602418550717 0.6410266025646184 0.6211225884896184 0.5987969039426515 0.5710349633340212 0.5303224357670634 0.4725348009833423 0.40377535706670514 0.3325561534469553 0.2627386750797276 0.1950235391370093 0.12904741384125726 0.06423093227602142; 0.05100212737703226 0.10254564285298642 0.15523969219874534 0.20967545879325106 0.2665111525069077 0.32628196898216627 0.38884050425169797 0.4522440420108892 0.51217520717886 0.564032139432401 0.6060429136889856 0.6385430763070902 0.6616692317105183 0.6744969706959675 0.6778186442721612 0.685842738667889 0.6975052930033175 0.7034471367717469 0.700989521473094 0.6917809011081418 0.6805005626130178 0.6656076676748873 0.6489638482316131 0.6279290692613956 0.5922195301459562 0.5315526177575278 0.4523970558460653 0.37006394522219016 0.2908241677948349 0.21516540835521916 0.14209664596446955 0.0706554411465612; 0.05437835743913898 0.10937183227236001 0.16551844608020927 0.22346926115510224 0.28377870355825746 0.34674728802123495 0.4119467799927944 0.4776635798813235 0.5403181786194282 0.5955344845336014 0.640513880703814 0.6742154926720751 0.6957865628727037 0.7016824472991325 0.6816130745404719 0.6888006725647061 0.7051578326386679 0.717232719037415 0.7225784191663566 0.7229412867739 0.7119872515251995 0.6956442656307343 0.6773114195941231 0.6556001606052695 0.625532295382444 0.5727146156787016 0.4900479462047752 0.401211157688788 0.3151582711662305 0.23295568659811608 0.15369677868030787 0.07636666014080447; 0.05727238814926246 0.1151059571404275 0.17412739360859564 0.23485348072493545 0.2976656688189741 0.3624027003687413 0.4279869972761303 0.4925413301814796 0.5537031779383873 0.6087484287135859 0.6555025624707465 0.69171072423919 0.7140039367977159 0.7116653946866061 0.611416602734955 0.6618031242733775 0.6952834569307026 0.7210466610185724 0.733917999384533 0.7437751787863314 0.7281989169332685 0.7092964023560437 0.6906150891923402 0.6718057626205977 0.6535382110475684 0.606050798905731 0.5175740439573051 0.4258102251535533 0.3353768897486689 0.24796555333385484 0.16352706604444978 0.08121792563395404; 0.059620278723872384 0.11984266080135758 0.18118330040386788 0.24408612997919665 0.30864629065287863 0.37417120220982686 0.438846201254134 0.5006507997037241 0.5587590699321218 0.611398699332217 0.6568540873203985 0.6911762192003515 0.7085715274037445 0.6992150702132972 0.6587058489304438 0.6624808808396303 0.6809876495358341 0.7029492323759173 0.7241634299099493 0.7407645857512247 0.7268669128563555 0.7104305945435305 0.6941394421636481 0.6761609615687583 0.6518876219422342 0.6078734600108997 0.535713557901418 0.44615984494266153 0.3521811500456918 0.26021328319435455 0.1714385526929944 0.08509421555981701; 0.06148701436218618 0.12357563318437766 0.18680510776591 0.25151738522242084 0.3175678738660068 0.3838287092027591 0.4479801625043958 0.50823450548564 0.5655278620083692 0.6162337153116555 0.6568766177096221 0.678492213147936 0.6760115013866156 0.6733342259576878 0.6533072443603443 0.6483917800769993 0.6569760377252768 0.6738851490135654 0.6940465318386788 0.7114665337752125 0.7112678504634444 0.7036576681294461 0.6930455545533104 0.6786049720931325 0.6562310132490989 0.6169916088341508 0.5505329560223085 0.4614221999438114 0.3645297396648254 0.26903847370682604 0.1770557001248047 0.08783113934728608; 0.0628361920535965 0.12628576446352183 0.19093358782896883 0.25708095365723366 0.3243999081826648 0.3914479519030286 0.45581677258152936 0.5152677513597684 0.5688959229686839 0.6148162094037474 0.6479680884930351 0.6502219872647256 0.6346518134886132 0.6480317137173564 0.6295555978168865 0.6179628138574733 0.6195889770846392 0.632699071818519 0.6517605807902518 0.6787656743674991 0.6915609988114368 0.6944705636443234 0.6908600859247054 0.6817596671151994 0.664825990143883 0.6307613467370164 0.563683506942908 0.4708558763173624 0.37118036481536304 0.2736536085847869 0.17999866432989847 0.08926818823439925; 0.06361822761538677 0.12791170309354394 0.19343677493633518 0.2605756995288369 0.32895065431545506 0.39680830638046877 0.4613600699225511 0.520076599147313 0.5706546685399022 0.611197320760588 0.6411818615449478 0.6580192984005583 0.6633303043081511 0.6293150631793119 0.5921852701522438 0.5707463497474605 0.5663578415381758 0.5772984150996956 0.5850622208205624 0.6390120786365624 0.6718665595204804 0.6852038031086122 0.6872021797535184 0.6823945044631821 0.672357264901449 0.6523644907246157 0.5779807233837212 0.4747538999679015 0.37174513130783515 0.27376176253325896 0.18012430282740927 0.08936397375667622; 0.0638778643070247 0.12840974051411858 0.19427495873378614 0.2619221141483847 0.3312406586703878 0.40053480638739586 0.4661423369416287 0.5242704517938133 0.5735502653867882 0.6107873391652822 0.6349163866595651 0.6431458238944551 0.6269765505706829 0.5846065342366491 0.5301754884964783 0.502657658063629 0.4960648473637372 0.5200614136757832 0.5519885806707596 0.620670306522431 0.6633860114670141 0.6815015678402848 0.6831635225618633 0.6744392574518819 0.6549412763604417 0.6249443616364265 0.5588129542206147 0.463065585467179 0.3644853884589479 0.26928281375668095 0.17753073321522547 0.08816596164979867; 0.06347969328984 0.12769982524151446 0.1933374994302081 0.261031537540585 0.331190585363901 0.4030114083341191 0.47310414607814655 0.5351629382820547 0.5835114016378442 0.6163461483378141 0.6338384286214518 0.6327695699890449 0.6037273994454685 0.5410975576930412 0.4444190468464814 0.4215428007398572 0.4191945966097699 0.5119480452588652 0.5758345517803456 0.6290263835302163 0.6650752090281354 0.6832122303168263 0.6819540001548313 0.666659247032449 0.6379462142727511 0.5943571282254125 0.5273500364077998 0.4420620275591373 0.35130538953185014 0.26102359179457163 0.17263392724398482 0.08587373314839111; 0.06246073277386374 0.12568249468830023 0.19044404110985513 0.25752452911800416 0.3277470223704082 0.4011374901247585 0.47521012779380833 0.5427753054056513 0.5934105187269647 0.6239283928053527 0.6374542169402142 0.6339387109602874 0.6095401100705825 0.5559581493819135 0.44450642646546207 0.48822819059016653 0.5098840059392109 0.5603459843513368 0.6066546473973443 0.6469494064570912 0.677547037550991 0.6930318898436151 0.6871932640366666 0.6618358772540249 0.6225313268815166 0.5696520097600731 0.5012317070532141 0.42101247225099997 0.3360470328355454 0.2506564052257748 0.16620471782981816 0.08279946479514001; 0.060721055162690094 0.12223072894363288 0.1853130468511704 0.25080005872788036 0.3196523956758407 0.3922908005781441 0.46649043949738567 0.5354696061092081 0.5897951821687176 0.6250286973101878 0.6413975245160213 0.6416680480942261 0.6278685070665283 0.6035314553201558 0.5724399918403548 0.5734258312904589 0.5853304239648452 0.6100738968660695 0.6381784200770562 0.6659396668961896 0.69004911016023 0.7062817479503908 0.7009743448079626 0.6623487093331235 0.6128130566765423 0.5526549045287142 0.4813336417558857 0.4025106240861281 0.3209885797342541 0.23951227406078246 0.15892729628088367 0.07920822627738139; 0.05826769741327276 0.11728504478875867 0.1778124587892708 0.24065618296323338 0.306780207505929 0.3767198739282487 0.44913691739835226 0.5191774061981509 0.5791863882502457 0.625247419073633 0.6494535286894657 0.6534799734271882 0.647086015089095 0.6379656606108461 0.6305904553006072 0.6329321243892003 0.6395968627678766 0.6511471323337252 0.6663980941373069 0.683836404939217 0.7007899198392944 0.7141281247079152 0.7111324846600057 0.6612451896914856 0.6038736559091531 0.5371879546395854 0.4625024490316836 0.3841458433092173 0.3053853599304707 0.2275888415303829 0.15095270080326273 0.07523432323432111; 0.05514095568696366 0.11096631647054954 0.16816203768704693 0.22745151246663234 0.2894676562815859 0.3544390267681379 0.4216027681144826 0.4886001936515397 0.5522788094324661 0.6105351438295706 0.6462749607707662 0.6553271730719682 0.654377868738493 0.6553560153204712 0.6619187318585346 0.6719402671589273 0.6784484639461151 0.6816759535875185 0.6887244535986625 0.6972678292283824 0.7047696037752991 0.7074920753824318 0.6950777899986006 0.6483573820879591 0.5896561381399206 0.5176980006740585 0.4408312723410072 0.36387969381508345 0.28840752282808124 0.21461464048305814 0.1422455992986455 0.07085894419411663; 0.051419798106042976 0.10340915101339372 0.15658984918743102 0.21151275633288394 0.26863296577521717 0.3280185231145524 0.3892495413638958 0.4520144836890183 0.5153387460491341 0.5727440310763614 0.60972708357656 0.6259833644867774 0.6356650685397798 0.6502230182697829 0.6705488363940112 0.6898090122885719 0.704334213155946 0.7069105808148998 0.7052474995655288 0.7043704444045705 0.700787796640086 0.6925408220447337 0.6726782120331753 0.6282338003996498 0.5676221587521806 0.49377137003000304 0.41658524340046993 0.3417077401539812 0.2698574294484174 0.20042707918215788 0.13270625715277942 0.06609753133802014; 0.04716789329273865 0.09482851705896267 0.14340268300101117 0.19334854505134566 0.24495547767502954 0.29828346227488 0.3531556923627547 0.40947323878030756 0.4660813169751574 0.5177642141084926 0.5556099804126013 0.5795198143564786 0.5996069020163961 0.6232972454671589 0.6503081933550764 0.6752179709594948 0.692148534312235 0.6985510728510973 0.6997726220016413 0.6953684835099824 0.68318927804541 0.6619814907162352 0.6310840566391485 0.5868440147680201 0.5294747987104164 0.45863801642085184 0.385694516332885 0.3157427175252064 0.24902354923561743 0.18478251000782112 0.12228069948773576 0.06086433287859533; 0.04254169174554949 0.08541767809722173 0.12902912679734324 0.1736148807825702 0.2193926955280515 0.26638408193972213 0.31450776851494644 0.36358023384270255 0.4120997144468251 0.4563619961158942 0.4922996659437783 0.520789672806033 0.5468540081717931 0.5746818906738139 0.6041620444966919 0.6308217171442851 0.649591180923338 0.6608538376176709 0.6667601221457119 0.6656417850662156 0.6546080041730581 0.6257623449421617 0.5854858341340855 0.535898221256797 0.47795766231964226 0.4139404759939053 0.3490119154793068 0.2861688757307364 0.2258549317823708 0.16762088903932665 0.11090907368986595 0.05521775753327554; 0.037584243288666976 0.07545847063828376 0.11380323619384464 0.15288573183367182 0.1927687615496072 0.23350789752890436 0.275042160269624 0.3170777921033763 0.35843694684920874 0.3968083060821627 0.43000986446685735 0.45871189492402126 0.48577742144850133 0.5135124927941986 0.5419069437458189 0.5678152383311754 0.587457850213194 0.6029902640086725 0.6176815003234156 0.6287524222444407 0.6259826743536396 0.5876650639178416 0.5359363845812963 0.4818082498670383 0.42470167094416383 0.3667098853884813 0.3096571652992491 0.25430269286208007 0.20086708229794573 0.14913628654353223 0.09871357332903084 0.04913497573216645; 0.032453299661095523 0.06506644574329419 0.09806857135813532 0.13150945273677306 0.16553540788423982 0.20007008174635862 0.23505103820452064 0.2701284368862645 0.3045254232647254 0.33703727255509625 0.3667617840811529 0.39406511353563484 0.42004573452343114 0.4454747213358921 0.4704706167495231 0.49370599784262237 0.513155318621539 0.5315840944793299 0.5522386264012512 0.5725953083925052 0.5864271437533457 0.5379520112272899 0.47811756617534823 0.42234998459822043 0.36935289244809943 0.3180592183932028 0.2684898148472161 0.22065013815271342 0.17442249398604867 0.12956790432591384 0.085783137568636 0.04271762974529017; 0.02715209270369102 0.054452739935959324 0.08195415300592958 0.10980962120298793 0.13795785503735059 0.16646213093550283 0.1950966414893353 0.22361346577333058 0.25149979131811595 0.2782239457225518 0.3034849603225697 0.3273801802943083 0.35019136244427795 0.3720982381665415 0.39328016028368634 0.4135254689444774 0.4313539075465526 0.44765695629737257 0.46479750951054105 0.47928012663707575 0.4835424996043849 0.4511685038952861 0.40366973236363385 0.3558284795415742 0.31039302752989917 0.2671220330971781 0.22559414709291262 0.1855560336777961 0.1467880352098662 0.10911924698389382 0.07227275359402474 0.03599201698236365; 0.021794071770040325 0.04365120575068422 0.06568677284062062 0.08787913566139467 0.11031662560196889 0.1328541825037623 0.15547481110294883 0.1778741611189858 0.19983152348154726 0.22104498449426457 0.2413122197861888 0.2606259718837771 0.27911745041886216 0.29680912555460903 0.3137558421107481 0.32994273068502483 0.34447772701824003 0.3569790671524152 0.3672655023931017 0.37315298217244114 0.3698983056961104 0.34973032180080826 0.3185181544477344 0.28366281629685813 0.2486306049189565 0.21448442366346498 0.18141791184290434 0.149376903190423 0.11829531375820897 0.08798194640336895 0.05830077726043398 0.029045681328876482; 0.016364691977576548 0.03279088029823731 0.049287518369173264 0.06592499973347163 0.08263381623448608 0.09944898477322592 0.11619229328286759 0.1328162169077686 0.14907602936561154 0.1648742129844378 0.18003124037441062 0.1945299805364826 0.20842269284772552 0.22169387533150642 0.23425542939639662 0.24600093089688008 0.256514812464038 0.2651340324290149 0.2710214782048545 0.27271868091199436 0.2680480216913071 0.25469653527107095 0.23453917815105615 0.21084826430540018 0.18593546015718898 0.1609781256721763 0.1364388794075011 0.1125078161772811 0.08915958683772066 0.06636246125641554 0.043994362302047 0.021915003792314387; 0.010923806286428295 0.021868915138816586 0.03287601900747356 0.04392487790353839 0.055052122719708184 0.06616844106348714 0.07728357534079203 0.08824248914154317 0.09902261865140825 0.10946151232155248 0.11954579441845636 0.12919574869977843 0.1384433947081087 0.14725053859641846 0.1555257688046058 0.16311987044166074 0.16976740958959693 0.17500480869829899 0.17819127034240903 0.17845305854670013 0.17476719814149005 0.16642298858794036 0.15415151128069807 0.13941373251969627 0.12349759441709258 0.10723754819620819 0.09107430163651956 0.07518126717559162 0.059633913361896294 0.04441010883017222 0.029441885231472172 0.014682321219891615; 0.005462356917014994 0.010940375032986723 0.0164333537785815 0.021964596258539304 0.027497336615478655 0.03306025685377361 0.038569053056235106 0.044048702139385776 0.04938919706391368 0.054611325890281975 0.05962024800072441 0.06445135267457693 0.06906407643412463 0.07344265514237322 0.07753825376519419 0.0812684395292359 0.0844759494638741 0.08691995748904832 0.0883063997076397 0.08823978003221525 0.08629136978321239 0.08225493740324058 0.07640696179403189 0.0693242872731254 0.061576940938917524 0.053574794164539974 0.04555217375099472 0.03763786863581802 0.029871494610228852 0.022245709906712034 0.014765362918331807 0.0073475235447039685], hyperparams = 25.83417528178972), p0 = 0.5913564056470484, pσ = 2.0693843732667494, angparams = ([0.5217074118593911 0.18929723746537358 0.2806949841900168 -0.958361653639645 0.936560018260044 0.8765535607189785 0.8124254528693095 0.9932932804914382 0.9249822568509711 0.6721384530455942 0.516344088469046 0.6713000568574887 0.8456756982714291 0.8251756943267515 0.9239676927891054 -0.019113571374214305 -0.2888331637211274 -0.38838211809955037 -0.44746198640335283 -0.28346731584837376 -0.10113426125625513 -0.20009129915916526 -0.43573994207498556 -0.6280708065080393 -0.42623930122768583 0.2535021969139365 0.3643476709434237 0.3938026255475579 0.2167188744892029 0.172430144894575 -0.16868450305432287 -0.18736242211439932; 0.5209405800389155 -0.27180530790012053 0.48281378380390166 0.6460329114960921 0.984090403742237 0.8342327454828015 0.8002235496093266 0.9136216944113862 0.9782824661397802 0.7860531591136547 0.6616521768957345 0.7610734733777111 0.8674931601671299 0.8358282239894573 0.8877827652602694 0.6327811649428513 0.03731862636171709 0.0877307870587758 0.44667182631091495 0.6783235112261357 0.5750690435681484 0.09096810577396264 -0.5268327627906123 -0.5367651591771129 -0.31630470437154296 -0.010380132138529258 -0.21437886495551767 -0.5531513415546143 -0.5859529502131053 -0.20274182534183255 -0.7751365243466264 -0.10482158460050474; -0.5938349387001388 0.06872032529205029 0.5557675984400725 0.7364655132128046 0.7699843845374008 0.6784058722895491 0.7000584096629942 0.7269702033520422 0.874753625496528 0.9866229088724695 0.8240294462584286 0.7758337000113278 0.8148275781121376 0.7951382112432035 0.6635254930433488 0.5328478822083507 0.6092773873678033 0.8347281217175667 0.879016373872443 0.7371335677377924 0.4064746609793222 -0.1702509928231409 -0.7359060700828206 -0.7019860411300465 -0.5664664474300989 -0.7033680581087394 -0.9253828843874321 -0.948983677651312 -0.8769362778910457 -0.7066674772337651 -0.9081970131982123 -0.6704202645653776; 0.2693987798758111 -0.2357940708499723 0.10254878576904083 0.005197850280495294 0.22297531477425575 0.30785692796594166 0.32015564392184065 0.345568208797478 0.3854198788231563 0.5688020913152123 0.9582651795467011 0.8839100856318898 0.7289466834506886 0.6470848482940366 0.4271536743771303 0.2886262366201051 0.39315215668886755 0.6385257529268792 0.8106977292693848 0.5334623267514789 0.033168600872919764 -0.5194890343436209 -0.9244967057399528 -0.6267904904198537 -0.4446639024301499 -0.5354750260800143 -0.7825219946438494 -0.9604413535279694 -0.5511526748362647 -0.11019340695637199 0.24392626558713226 0.4742265064101805; -0.15469255301163595 -0.35280334689652987 -0.4227267719530703 -0.7242574249342019 -0.6815016906787408 -0.4312353584342122 -0.351237297845566 -0.33196464721439783 -0.25289616677895693 -0.09771898204197908 0.16249542288171834 0.6521362214460911 0.3675592932267085 0.10370182728643848 -0.02884137498791755 0.10081006374501382 0.26087639517747974 0.4317129991643938 0.47141245608831944 0.01024926889853254 -0.4009510954971301 -0.7622890620032738 -0.6445967792161071 0.23131072667969743 0.10396127054133163 -0.10273029885716112 -0.23596048541157216 -0.036680217834983264 0.3267832364524334 0.45432941814593353 0.8091529651786733 0.7245700321003375; -0.3879563102150017 -0.5207182112958704 -0.706773621471828 -0.8940996600972149 -0.9942262408510338 -0.812987108593097 -0.6593331029090634 -0.631324560626567 -0.6658263714548169 -0.6460438114311626 -0.5133760876457264 -0.4402731124740091 -0.3827681125232761 -0.4150641480170411 -0.5505317429783608 -0.10866419716970631 0.21738529030189224 0.25719084155548566 -0.13871297864550278 -0.5282745328012414 -0.7370589165880063 0.5546659582074803 0.8795823992954216 0.981853584480521 0.8725130990812039 0.6499075101777169 0.4719030056276042 0.4390416010173107 0.49962502424261146 0.5253549261064806 0.661148506491785 0.38484097712788556; -0.5164450680218242 -0.48594544158453684 -0.7678064931651075 -0.984512097369509 -0.8731118903169074 -0.7964146702459116 -0.741361098965529 -0.7085883459453013 -0.7340319584593642 -0.8517751000321887 -0.9969148630297521 -0.7733750845012577 -0.5635178185076541 -0.4728664478240278 -0.35447867854858617 0.1556149582318945 0.5590047735439856 0.40639303444396235 -0.7122456839691234 -0.44364984917777794 0.22910174323830884 0.7677939916547403 0.9636755760078005 0.9839404556126492 0.963410012689899 0.9188051439088962 0.557595296976782 0.447159038528075 0.3947289294289015 0.22721663901713737 -0.6029289131752303 -0.7858425994470252; -0.28753832867722007 -0.3677177751561742 -0.5555887293410087 -0.9492527099967606 -0.5550375194092341 -0.3631412857567987 -0.33238052245408856 -0.3688548519215522 -0.44156940304012177 -0.5218595571711216 -0.6459174880734238 -0.7311028762135383 -0.5954406433352988 -0.41165196308367835 -0.040159296949221185 0.4915210490875853 0.5844018687661605 0.37793087491118843 -0.4075144567470005 0.02676200353265489 0.45034496799577367 0.7838980950563388 0.9130918503233225 0.2878362032515885 -0.3024977458658235 -0.5612027216770143 -0.7253146753430539 -0.23694373128677876 -0.14717184228890692 -0.4043882603191923 -0.7613157679608394 -0.7967937165273826; -0.028753844883799312 -0.019158504701856146 -0.04831168978634452 0.00044366493867150405 0.09865762830103841 0.0734790408382227 0.05272063610539462 0.05403892221844845 0.10207938105610943 0.2660626903247396 0.6715376108506909 0.9911186858474831 0.1806451339000346 -0.1579434911562096 0.40694148992062235 0.6834559842081381 0.5898906334939245 0.06775723036682936 -0.44059484583006414 0.07047825278861455 0.46832324193176617 0.38109034350522586 -0.19673585184785547 -0.6272766339982075 -0.7147983247794973 -0.6736639370479902 -0.5848057265159186 -0.49650371008725147 -0.4436967597014319 -0.32735029012718025 -0.1382888722709247 -0.022318306647632753; -0.0272246508870579 0.11293190381111382 0.30093432142941257 0.564334346205428 0.558592465305157 0.36879906847710103 0.2210386646006475 0.1654537052849744 0.20729568814088487 0.3500763440815406 0.5451766055726236 0.6274508466671489 0.5642710735118703 0.45304720638701124 0.5324714633399257 0.40557231260548693 -0.3217477578633277 -0.7365564187262956 -0.7743224147440316 0.12528742482092373 0.11725506122312208 -0.12529219582719528 -0.5614416488287286 -0.8088643571720238 -0.7822496316998511 -0.5964303036857974 -0.3951696116230934 -0.2445262747974405 -0.0019382580503089328 0.6543379568726003 0.5613702240658417 0.5582274069431666; -0.11711455610979415 0.04240760115280088 0.29930178121624657 0.5508851604667485 0.5381265021524242 0.3833928515055193 0.20965606598369554 0.1136756113142797 0.13485842956872737 0.25151246874223804 0.40334647821115005 0.5234590307357121 0.5963834551991661 0.6400119716489099 0.2118270425068181 -0.17977128337787832 0.2625152154507474 0.6345595382658981 0.05594421059466565 0.16664275989732683 0.01149009187919211 -0.13635577071567304 -0.3499691984388509 -0.6947834227826976 -0.8442621022497482 0.07418984467551586 0.1007611180143763 0.16414675875022278 0.5351119902968474 0.9232715901255616 0.7767691350535946 0.7273571572474689; -0.7901032220683217 -0.40644098566760434 0.07355048690498381 0.24660701868073573 0.23405199477307076 0.1637842863568392 0.07446990298771897 0.015427480308731794 0.044071328333582176 0.16059947827312626 0.3179533106714606 0.5078177363152305 0.7617074073904764 0.8074615953548995 -0.604229538976267 0.8619477628074129 0.9735155025951385 0.4476280329322248 -0.6938105213797577 0.379746712267298 -0.04370660577280611 -0.2445247289746023 -0.28333572405106405 0.4435571813139829 0.704278098353874 0.8192879362063716 0.8641048387030026 0.16803367836078856 0.1645064142874711 0.5772058926364998 0.8169431689743072 0.7438023492887811; -0.15490873436364974 -0.23983556668509673 -0.2746665367436031 -0.232956268379939 -0.18819586174088998 -0.14528490657256754 -0.08305670619837473 0.051937430346600276 0.80700361119371 0.009007459051106916 -0.24571455765747635 0.12297396370447256 -0.5814452839647791 0.44451610000728037 0.43255875147773437 0.39845694037829005 -0.5523273088017092 -0.6411659685594914 -0.7309413839394387 -0.048007787191045 -0.4564905299421463 -0.7295886570752724 -0.5418139475219147 -0.3800894003363713 -0.24505279691396373 -0.4547590796398034 -0.47130895342526874 -0.4719839655125983 -0.45227859440788293 -0.3953002694173058 -0.27972838347613604 -0.1944795469433078; 0.4426144719802261 0.0648542079482808 -0.1390057875214486 -0.2709451997405056 -0.3129960509178834 -0.2447082343644817 -0.04940632751431132 0.8428314603102051 0.3436678269595593 0.036613902859469076 -0.2970764713563326 0.2845405023526801 -0.08708261288842237 0.9522710699773044 0.7512002747926045 -0.2721720623472856 -0.5523173247243254 -0.6805134660523492 -0.8886997318592705 -0.3388951043114368 -0.2869800542879453 -0.9922652239998789 -0.2707223261273196 -0.07466487689317705 -0.07631317368231075 -0.4330677261321664 -0.5876183636500943 -0.5875794319347379 -0.5508470842721173 -0.49677016522003764 -0.4042244054965023 -0.09330118027562083; 0.7600716117710059 0.1417070920686171 -0.07370554694334366 -0.1515283608525695 -0.15507207614662277 -0.034267402193992956 0.24886774291861763 0.6659951794462067 0.6715672000087838 0.08955195181485238 -0.11090276109559352 -0.27173231190154495 -0.9142057640948478 0.7689284795315602 0.4829539591332919 -0.027165610351856745 -0.4179037996794834 -0.5333164166318686 -0.5019541349682799 -0.31572103579977356 -0.02416418877221995 0.3624530925711095 0.5017155916724595 0.7725358895132853 0.999790116843932 0.3222275484934881 -0.394935765196174 -0.6011144023307098 -0.6378398260297335 -0.6196728637515994 -0.5702552346106565 -0.0016557757433493673; 0.2702236271024279 0.059800669569454554 -0.14479401270383593 -0.10647063446898375 -0.01053051777292243 0.1718094231274857 0.392833671287086 0.4200182233254634 0.28840790586563153 0.012067061526695934 -0.1476340898135767 0.32671473572500614 0.7978513012968902 0.6364219117683549 0.35274126849750165 -0.06976627583114327 -0.4886684750896254 -0.5198471426054092 0.629580961466152 -0.7171517145372334 -0.09815515472939586 0.11812472279355002 0.8126405043645062 0.8833612613709302 0.7479849657297291 0.27355525356610505 -0.08662016495630698 -0.40394117384152567 -0.7307248903657538 -0.9553862775310423 -0.9598101045863979 -0.9249678661948092; 0.029456520636994502 -0.16378574154547632 -0.35025490668970677 -0.27307819402778793 -0.14177075638350622 -0.053764106736295884 -0.03375746210171348 -0.5145097292235724 -0.3472816459004691 -0.3411606167382923 -0.29557081140811226 -0.9474553318814417 -0.9697406389935177 0.6113260235631403 -0.19789066748359163 -0.5450784516690197 -0.9307813223730144 0.9574646421697594 0.9466244149739429 -0.7493885412858395 -0.11379658518304095 -0.07807704476082752 0.0025253035262266716 0.3871354537320159 0.6448181579547 -0.2995997590003545 -0.3716759001916153 -0.475285480763529 -0.6153747671536643 -0.7054097010554559 -0.686793252546788 -0.6857659919266068; -0.0228076831175957 -0.29728032481243444 -0.5469274593247782 -0.790128628663953 -0.5899684916237911 -0.5018550756069723 -0.497992211708678 -0.48965233190700885 -0.4339431290848978 -0.31344227951470205 -0.06369611164707589 0.17321250738794908 0.351208626022729 -0.28319405630014 -0.2192141029422487 0.25597157852697056 0.14099774036472507 -0.6354932909930423 -0.7642949234638712 -0.7437373882526407 0.1038730236881831 0.6579106564347987 0.2260959496512675 -0.2593128346688399 -0.44778877686412233 -0.5944220077807958 -0.6128843357759688 -0.49874796770248603 -0.4762335537058846 -0.5465469081287401 -0.6224868128011424 -0.6458804356893345; -0.005916009595908913 -0.10204793990248591 -0.3565304046605527 -0.8445119667787581 -0.808051810771346 -0.730328241998088 -0.6905523120933085 -0.5961451671830846 -0.44940986980773423 -0.30722717692278617 -0.15795334693738391 0.04117946107292927 0.3026494451450762 0.575366187261185 -0.3537613912797806 0.7111373829611762 0.47561159532048486 -0.8964848205389795 -0.6298845669263395 -0.30294871183379746 0.07072205031422639 0.4691754939886463 0.33616748798827567 -0.2868003849407863 -0.023852805665922926 0.152040742969643 0.269016426345192 0.31403985374420057 0.18201662747623062 -0.27325707520548975 -0.5000092663807394 -0.4208896562976347; 0.07186475869669134 0.04552556295336574 -0.11144627484197946 -0.5481460806657595 -0.772182599227013 -0.6725485525784204 -0.7074974707876606 -0.8615899720530887 -0.9422586466523132 -0.8045436156683367 -0.7813951085832956 -0.8362849160361474 -0.3263229838485603 0.3549903177583247 0.5867991872556726 0.515725994911222 -0.8872251776783079 -0.9783260125548198 -0.6768938371058247 -0.07835402466786043 0.37913196704914776 -0.0447074993421003 -0.43345244494898766 -0.1975962356405242 0.5778524818898746 0.7492431352159744 0.8714896770257677 0.9721483894983771 0.9545881674393782 0.6205908444594184 0.24017357874054676 0.01513738297769361; 0.32524961743194836 0.24573797783690055 0.021587962086847972 -0.8512754114775803 -0.5587233849431313 -0.39875381069503807 -0.3540292120408753 -0.41364088831780693 -0.6107845312856645 -0.6009342601861638 -0.5505028865428618 -0.5691758786442175 -0.630820590422722 -0.7642616972353382 0.054589185030648676 -0.9326365387119199 -0.9137621699169277 -0.9663432592954173 -0.39608652807074185 0.24901160897041402 0.3274836524010423 -0.07191663520845745 -0.4575650174566538 -0.08484173868620236 0.7166103060231986 0.8333742582201106 0.9235541039721809 0.9916434782790761 0.9754109684817689 0.7702727995802077 0.5209164019498956 0.10231040648626952; 0.38729161509039944 0.5128478726154032 0.2323099882762708 -0.011069404586580508 -0.1445130560453342 -0.17832483366810675 -0.10178727502736441 0.02495294195105148 0.048251458689593234 -0.09075940708876658 -0.17049543708237758 -0.21481444315254286 -0.2220731137784415 -0.15043564981157193 -0.1270827161634035 -0.4384058347557287 -0.5702393255362954 0.6438670008526088 0.09801673321707098 0.18012741504539082 0.1405065042040543 -0.09226783006711622 -0.34996935655569317 0.6033851248968898 0.35688043063931074 0.607999213234413 0.793584775837203 0.9401402130972422 0.7952965099851993 0.4938509066563481 0.40747689038161183 0.059831481624258366; 0.5143650352446746 0.7082022924960023 0.511975390360796 0.28968852156675406 0.20605900881362266 0.1919489274323735 0.4540995492094889 0.7642934817821967 0.6824757440875255 0.5916069553219707 0.4840838366700691 0.4545438739202768 0.7953230196155225 0.46382422121232225 0.3921768660762702 0.5269220324702791 0.420674796069035 -0.10778541786798358 -0.6305315281043552 -0.7913640709286361 -0.4899627971927089 -0.24471866219795138 0.0035600538814633703 0.40880494703954307 0.27725339690685835 -0.09469025124339514 -0.34064339642139196 -0.5054682677079851 -0.5712066563690514 -0.2828152779848992 0.23544287225817864 0.1982164663280682; 0.7972153507221302 0.9849457824792422 0.8500026952875989 0.6409841566567615 0.4599910266354257 0.3595143463871106 0.4226889577067035 0.5112482940670021 0.49557199958634274 0.5053914946736628 0.5014954510576924 0.4791115984510892 0.3456450715636225 0.20271735219906145 0.16782860564788007 0.19049007631107343 0.2997717228896596 -0.4443197061174715 -0.6617169331614249 -0.8867315883772086 -0.8315406116567814 -0.49158823346031116 0.1484209752464 0.5488165988405143 0.3904003662735548 0.1769939751342506 -0.055810020977636224 -0.2722183439621886 -0.32052904291641016 -0.18118657530586482 0.11186501535605732 0.5267717445098963; 0.4678849573960568 0.6006153659507011 0.7411113286921511 0.7460354144692477 0.6330977020328971 0.37154435926234214 -0.4688297311597244 -0.38639224483971246 -0.28313684019854335 -0.2591026239695303 -0.26173712066979754 -0.16204217411098382 0.04362981277288196 0.1318683235983155 0.11060439619758229 0.04942884196300014 -0.054129926194209 -0.13377447207415927 0.2036325960762817 0.6332420984894245 0.6325536494976635 0.40692861209820685 0.2862197646008126 0.3452754724525989 0.3982693290036457 0.43996664446614714 0.6019586717634688 0.9801401276368553 0.5566269235012733 0.20105615971302546 0.1183974833982362 0.268488329342256; -0.5171866574157704 0.07784650093681665 0.31249074752252676 0.28488018382435804 0.12654473579632144 -0.39678624684121094 -0.5151506761608864 -0.4337152489926018 -0.4296687941916442 -0.4990964779955446 -0.5947939433728041 -0.5050943130222523 0.05080263629715059 0.440289455041013 0.35256561226617994 0.16367033258732575 -0.11441229056860319 -0.3845161235540868 0.34239149088603416 0.6969346058147039 0.7394027023604355 0.8307633795651209 0.30097910123036525 -0.2543451462753504 -0.5809872081174183 -0.7709842870513386 -0.0021135208460781314 0.285742606298096 0.4481963129865816 0.48018205058132823 0.08699020967211395 -0.5202757629672601; -0.9276571775619019 -0.47308601256135496 -0.2508133234806216 -0.12663248323457696 -0.2218082333218825 -0.13431532826366988 -0.11294871274028577 -0.1869963477189607 -0.30317211586844256 -0.41764720002669076 -0.39364073347482537 -0.08858789173481627 0.29554008887847544 0.6109870826812844 0.6588755141373445 0.4569656053006026 0.22887440524936586 -0.3583428985882245 -0.42260179985973273 -0.3288768554189719 0.022535570028608922 0.07171114178633219 -0.027605183591121282 -0.3814644092541959 -0.6539164571302397 -0.7844595315378423 -0.6669495958550746 -0.3703007479850562 -0.08643249862360541 -0.012448066490516645 -0.0076046019822621465 -0.4380690699971877; -0.820101809175052 -0.5267029465486498 -0.3452641080054652 -0.25285918847727096 0.23220145217211532 0.5021022207208716 0.5070594686632499 0.43843621247800385 0.2205042223259428 -0.13202702867293173 0.07512060285707078 0.32961607658665776 0.4873041364236842 0.6361497243389148 0.6143019303676723 0.4267855243864604 0.5076555425116402 0.8572503797185171 -0.11009743858109815 -0.9202485717323565 -0.6968310592589293 -0.33463970499226525 -0.13998304888949198 -0.06692999944043601 -0.21935338508458066 -0.6219835846376025 -0.8061312123418916 -0.7269303814086885 -0.4761148133103747 -0.31807246716536564 0.16340907815392294 -0.11883176855844645; -0.2766285540944993 -0.8916032023791702 -0.7081187368151319 0.6643482125957277 0.8626780602931389 0.8410486999407888 0.8270440306980171 0.7920726398527935 0.365896899709719 0.1764619611999497 0.367063749467053 0.619886339605821 0.5680456086769617 0.3466013314870768 0.12246174578027104 0.24885217490678102 0.5596320759495691 0.9241406323662128 0.7893297055049202 -0.5074574258877054 -0.9782083546537541 -0.6142754024396911 -0.25190902482146776 0.024824647436968692 0.19031305163539275 0.15468598074211962 -0.4876988906156562 -0.8983297158403278 -0.7688904151125137 -0.18775627832143624 -0.7218848895773078 0.2756739495277357; -0.8113028492772362 -0.861067123267525 0.05935489627862134 0.2951107169175826 0.6783021760525577 0.9291003497517948 0.981595712240606 0.5604986369036176 -0.04043219048568756 0.015112052247059214 0.3483079509936365 0.749859411639598 0.458080224259905 -0.0846183792959267 -0.3792453456012421 0.03938570892399711 0.5241015227727446 0.7872274348826797 0.9616707178107783 0.64739603340783 -0.6513494558407098 -0.9858518692680832 -0.551557924451315 0.0005398377532203222 0.37188063763312423 0.6133098742847141 0.7909863087885104 0.9835227487689584 -0.82811146718371 -0.9782313951534188 -0.34347031032662384 -0.11180191596335765; 0.5140226199179218 -0.8387829267517873 -0.4203873165818007 0.01118745160827197 0.3820226696518215 0.5708994695294575 0.410495407096959 -0.46412136200381304 -0.7463937848723254 -0.29686402882978263 0.141923644584504 0.9495801757098364 0.10218172615652732 -0.16987703125304932 -0.2683725596713518 0.004342595297648759 0.4441746878430906 0.6060951320791189 0.806797914888678 0.9315485531692232 0.5294695431213765 0.10200837924777684 -0.08170147025547043 -0.15008268201355834 0.19103846624998067 0.8127786889447737 0.9063995917291546 0.9164706347596149 0.8747923218195859 0.9743869282723379 -0.8319767771554856 -0.5869369104393343; 0.2925250061038943 -0.3364124613624598 0.003228089797213553 -0.5782676979112457 0.015985867976256188 -0.11702976749873839 -0.23953782719768416 -0.4998798502903713 -0.43028117560440804 -0.22983326325919456 -0.3480675966753467 -0.906399536771102 -0.36786834780265043 -0.14658272470292824 0.02702949466414526 0.12824201884304906 0.26751629418222156 0.23233279387643926 0.3007534182414199 0.7147956334323369 0.7817224262868789 0.5924536921588796 0.33649239585896573 0.047709124980329316 -0.28270317568027575 -0.40438013947836715 0.5717717892439216 0.37478333610672365 0.9774311914159097 0.8214373465620004 0.3605372128622835 0.2710444767508314], [-0.37899960711111425 -0.7991333750143056 -0.42840968953051456 0.252036222724544 0.24207448972751475 -0.22341762457602302 -0.4750283112273842 0.11483934169976674 0.3722382431768162 0.740422467828288 0.8324513378989148 0.5355723590276876 -0.2775015934589904 -0.5454966658718726 0.3027345384866973 0.991740822274696 0.9559673525841521 0.8911696349110356 0.723068506434823 0.26969210567944885 0.697474991879434 0.9171502789370615 0.8108394240832575 0.6703636217005351 -0.8442463000706333 -0.9083729773508014 -0.8006288788103426 -0.3223432348906262 0.14193764005870743 0.6638058503100105 0.8445274310477612 0.8996378410160007; -0.40823671293515407 -0.8760602131166999 -0.8149709507701104 -0.6818752501274143 0.0526374145860756 -0.5053960130500847 -0.5701461452982384 -0.3989076644987711 0.2072755903083315 0.6144656244110961 0.7112681231188647 0.4604847994797586 -0.09913117819208454 -0.45829459810057477 -0.4598174719304427 0.5573082996091437 0.9496785189217267 0.993969644755744 0.8490419282204353 0.5524710104449451 0.6381279920595423 0.9693440232251854 0.7925594700452077 0.5573682125838739 -0.410762516512172 -0.9981567865300796 -0.7075161170173476 0.0014319173593133566 0.4346780770993377 0.748385212003108 0.6292348803938429 -0.921473008926958; -0.7764547994082432 -0.9976314246443044 -0.7397182785207148 -0.14143124714648458 -0.19085193897436448 -0.4783834011475397 -0.5844125745401331 -0.6219056664944732 -0.44970334602552064 0.09328256987502748 0.5271878199493075 0.5054860377967539 0.21841149733579074 -0.23847508118662794 -0.6613683384733988 -0.8422217551334347 -0.6017318376936998 -0.028007116545091356 0.4182104285542558 0.6676563285444302 0.8418681826463691 0.9055279662878668 0.6735249726958948 0.29642832195654983 0.2231995891761361 0.35177580149539933 0.3579616688011131 0.13117659821955782 -0.1985830231989516 -0.5691177310124409 0.09983957841002315 0.5853996063857666; -0.8072119216429559 -0.8455927331421697 -0.6505633848215691 -0.06450286733494646 0.21074551354879786 0.023421918964148396 -0.27676888354912005 -0.5819468906456959 -0.7701700516206009 -0.7761138211829778 -0.2804919465205818 0.4459823447489176 0.5531360329452075 0.22178486932573344 -0.6024884447329422 -0.9407187662100837 -0.8970257116816099 -0.5925452362383266 0.11668468497575836 0.8041494299393022 0.9926142432966091 0.8084527835224038 0.347318777033903 0.15170943124602804 0.3530165910959293 0.46881580376853144 0.3901234789279175 -0.10142281171233397 -0.8145520554619726 -0.889010811993742 -0.387227010119137 -0.760853343124529; -0.16363734131186114 -0.6664403883711986 -0.7787127082220757 -0.4620013178105377 0.40988495106008244 0.5836978305735048 0.4310748896678668 0.04194239164451329 -0.5003943768333384 -0.8792169938192682 -0.9855717649309418 -0.24747956196217186 0.9046604943411358 0.9072587781482357 -0.13627234005142652 -0.909793866373731 -0.9649846616964328 -0.7927155045939406 -0.09346486969440569 0.7774944070276502 0.8977891831726705 0.6243781925985943 -0.66958917235116 -0.05317325308578626 0.35970311329465776 0.35402330019759554 -0.03432517515412637 -0.7821189683401811 -0.9450900348291457 -0.8790681522036767 -0.47448657030723745 0.21327402594829056; 0.7688819617945879 0.29127693566084856 -0.2665316678041061 -0.38004633967350193 0.09145619826995241 0.5789054236091716 0.6883992412821315 0.5592411212858676 0.18556683607451657 -0.43616935794109657 -0.8566214176924333 -0.49936745263235544 0.4318526288606265 0.827902320113956 0.7794018274897618 -0.5759013745800802 -0.9357032323625856 -0.9262263037585411 -0.2647804286599143 0.31078463535207035 0.20915509129805426 -0.8257967124756082 -0.4643434980500698 -0.1385190539524775 0.11295989575832102 -0.07754280436267844 -0.5252449387983084 -0.7575276351379755 -0.8272333374716154 -0.8508794407489924 -0.586959873312597 0.018997600007465167; 0.8251242409120146 0.7442100895410272 0.403024090839541 -0.1551653811812886 -0.22708110527959302 0.12684662229634705 0.5150360901708699 0.6961333557418842 0.6538786534474149 0.38929436153748137 -0.06616476435643073 -0.14305643697670894 0.18714260649820064 0.5093248674452261 0.8217933725766832 0.9221250779924334 0.19993195817349835 -0.2892279364685118 -0.5664299048728328 -0.684855753757421 -0.8798217983724277 -0.6302132959847894 -0.25835556494722034 0.09386250236858476 0.2560545063184593 -0.15111997808977642 -0.6019410085157529 -0.6891038911776618 -0.7278514209119797 -0.8474257190109704 -0.761324856865569 -0.06733058721753844; 0.8571077429394055 0.9194595616514307 0.8301470769061449 0.09417649509550986 -0.48506811614276957 -0.4382136122270465 -0.2371755962596264 0.06401152687010879 0.41782294814221543 0.6842765470986711 0.6797085970385509 0.36112645367696256 0.1677540331110875 0.25408578887623906 0.5681958510445619 0.8332525542035875 0.7659824610107002 0.646694552520769 -0.9043896491612257 -0.9202022610596179 -0.7440732750727507 -0.39267139420547076 0.27500172723799 0.9403355937146095 0.8633617124051575 0.7322811387301023 0.6716527143755167 0.08746242771813693 -0.14572872870380055 -0.3209720261908944 -0.5313432295856874 -0.5708444556472322; -0.13308430524960999 0.16358415030849519 0.3349748150362256 -0.03199770280515802 -0.7027933557194598 -0.7544887070796151 -0.7149926135636172 -0.6472636463698929 -0.5585789690651524 -0.4402007530734906 -0.2318496296931291 -0.12312854682001785 -0.9758865581116662 -0.6502668885541691 0.06651102245056191 0.5192603044855972 0.7747559227584025 0.9970852884357918 -0.8546081592768063 -0.8000019557260173 -0.28704435406288953 0.38111132524520597 0.8552196317427557 0.7786683694598432 0.645770035021996 0.64667037970592 0.7510704704100456 0.8657810923499667 0.7764019748232602 -0.04558096443434038 -0.7689895909164637 -0.9772697680369969; -0.4859691825539457 -0.5084785428220926 -0.48854466613551445 -0.5794600020490616 -0.7959231283031393 -0.9163875359683401 -0.9540309407432019 -0.9564585764506107 -0.9524559150879593 -0.9312151769780053 -0.8246556858854296 -0.6512544498499149 -0.5503166621294294 -0.5374494289405267 -0.43262327096835723 0.6276811323886166 0.1306767625392071 -0.47039886333337544 -0.5924690503581812 0.17047720761478966 0.990667372164038 0.9920897884293559 0.8274284163725081 0.5773821272843169 0.5513748310397769 0.6968704060000873 0.8353295988912931 0.9285173664003175 0.9999085278621214 -0.10463545138299174 -0.6834643432877191 -0.8029662409456158; -0.8161716201877117 -0.8553819847133174 -0.8892290348692816 -0.8312801708420404 -0.7159713880829052 -0.7217887433625756 -0.8063628254487719 -0.87158774186654 -0.8841920441506912 -0.8389347592009324 -0.7414078710791678 -0.6367520499997443 -0.5677266150932029 -0.5164620234701798 -0.44719835777806477 0.69059993659597 -0.7914728552315324 -0.5542935665196047 0.5149095986202966 0.6959778466161259 0.7066417832514988 0.6477827599896956 0.46447179376732844 -0.046759454036284724 0.42558890388982523 0.9615040079402419 0.9357651715023072 0.9267699600722527 0.8296285626619213 -0.061219670164383136 -0.46175399494573705 -0.5898832020788108; -0.19113717734385388 -0.7952762588053606 -0.7286399014179888 -0.487101198255474 -0.2792549750043072 -0.21717847539239524 -0.26137953133716285 -0.3561687158179077 -0.42582221027891415 -0.4169774105262774 -0.3669177536554131 -0.37357788710991163 -0.4997052738789753 -0.5650743314866828 0.7089039542690693 -0.29110459809221945 0.11723662661455443 0.5658549661549124 -0.7012816456906037 0.8934336610161919 0.7315187078457295 0.534828005810196 0.3822156803347105 -0.4181973313300615 -0.40578792608076003 -0.3075995879811521 0.05868957585440114 0.3254674241712547 0.4626204801012895 0.6738995819983884 0.42481254689609743 0.052679924154965925; 0.832741839692599 0.9176988634435873 0.8446332479408417 0.6973760816606911 0.5766105034471058 0.49961031442510223 0.4464485510476019 0.38912410229724786 0.1945527853423349 0.9640753618869894 0.9008765977278784 0.9285628055324245 -0.16743045900207243 -0.5758642346598428 -0.8828996391072329 -0.9080450066289242 0.21552948706156458 0.5738664902329459 0.6537572873080721 0.27196475240655005 0.3745209518769319 0.6652792340706322 0.7136038815890009 0.8431442067018141 0.9090708326205762 -0.12124595456691795 -0.08015134973316729 0.11289202338001919 0.3455939141722833 0.6376255334178174 0.9250291631816 0.9575070902240009; 0.8627505652209131 0.8272390991845207 0.828110361738174 0.9059836822942299 0.9496231277059605 0.9403728719005101 0.9354377704567953 0.39548005204461056 -0.5617116115695372 -0.5877413394756805 -0.4520131000137671 0.5463614108110363 -0.34245899099557026 -0.19417215323948062 0.12403449099087845 0.3775671687078237 0.37668691527856435 0.34420686926305755 0.26480215842142973 -0.589483449639597 -0.5605864253538898 -0.0726075489793514 0.5411244801323936 0.5543121219791928 0.5108897934152147 0.3950192367702809 0.37732762799650965 0.44146494105623485 0.5412112396987524 0.6765668583114466 0.8731254940223236 0.9145557454445482; 0.6172990084912297 0.5738910867595015 0.5305850704243827 0.6246325964657171 0.8046720312451359 0.9785126742625538 0.9349114733680675 0.44903388868901184 -0.6833926654402708 -0.9767588291965539 -0.9293654793422536 0.7966223759268775 -0.4015772922588256 0.6360323112377472 0.8366333572386204 0.8434169333114949 0.5375073175051942 0.21576477855078072 -0.08949573850969837 -0.6405333501168208 -0.9607093528994695 -0.731916710163606 -0.3578247508666206 -0.2660789642362383 -0.008196582037040809 0.7070796573634568 0.8613743775322255 0.7990563565733709 0.73924744523665 0.7243915799248737 0.8027846213115803 0.745131265694866; 0.718400704621928 0.9779943073431373 0.6279619166199425 0.485320748022541 0.5087219467782437 0.7055710385417762 0.9149706053538855 0.7437982415206952 0.49412853757385833 0.045227249842541145 -0.854412959388224 -0.8199643643987583 0.5411877068512627 0.7573268730049487 0.9326681012405292 0.9916454727656939 0.6126346831503982 0.0012816055435925712 -0.7566680020192167 -0.45847350873511356 0.5354468333573368 0.3264180866793258 -0.5789338430251425 -0.46643963533157223 -0.12649735986544083 0.2228059874964689 0.3827482975801942 0.44949544994214086 0.43049601878021365 0.2781570436299577 0.042068076369493224 -0.3672857139714719; 0.6295711972557353 0.8141459175117975 0.9327912723561176 0.60428138819037 0.27506270037306807 0.10441677794910485 0.06822563138140153 0.8467963709034787 0.4892608988439457 0.46507359621800887 0.49517321018234023 -0.3045622906054968 -0.19656403114379678 0.6136538952957074 0.8797577900534429 0.18193873194652624 0.29077840514394804 0.18744235052629032 0.2962879233251134 0.13492323147864466 0.6132660352130158 0.5862205705824173 0.6419965408561226 -0.2626224141369061 -0.2528565395279642 -0.01851324895388853 -0.10093065444009078 -0.28633456082087516 -0.541126619346117 -0.7018609230001334 -0.6497297350621137 -0.5010017839637518; 0.06892667349655626 0.40563712718096545 0.6095852592193161 0.5013659184170353 -0.054879261568920576 -0.388928623536567 -0.641855455963097 -0.8191675046344686 -0.8989506355177727 -0.9495584027879239 -0.9787735457793296 -0.7978792275874673 -0.4725612234512511 0.27185588647441417 -0.018378618612018408 -0.3898473400468617 0.32866939269038364 0.733691299592341 -0.14165613365664445 -0.31041558984974416 -0.1865306689866596 0.2587709965620581 0.6459748540027392 -0.1440188244058858 -0.2764665403374722 -0.48984707666416666 -0.7531389551989679 -0.8654545370623105 -0.8783886006781872 -0.818650485548702 -0.6353447352142935 -0.409753978802292; -0.9443699004784908 -0.8280375377756474 -0.7327953999858636 -0.5354705144600634 -0.25726465515805147 -0.33116965531037407 -0.5381447204745 -0.754734967142136 -0.8874256791820357 -0.9482411169629162 -0.9456245230128173 -0.7215858089001698 -0.2856056236703109 0.12929519247497945 -0.3881514802667233 0.37770033411532855 -0.6693843746766452 -0.21391912608275157 -0.5852907255797402 -0.7493324014551569 -0.7797730617942146 -0.6425647216309797 0.5127803957717253 -0.824493349938698 -0.8840150138034587 -0.8503808791132665 -0.8206959616655101 -0.79471409176946 -0.7183665814970086 -0.4017892998136849 -0.16517326257614695 -0.10827296985172599; -0.9951276952664679 -0.9797559379587377 -0.9700522374071909 -0.8292699513894924 0.0806508139921273 0.31222050656947764 0.2829579728574605 0.06776903761578118 -0.3235520479476167 -0.5364091959895756 -0.5624143077132068 -0.5345691685884856 -0.28929583095654227 0.10939972842180974 0.4279487779553832 0.7146014222283767 0.4571504706645717 -0.2065689325728999 -0.7310326622881772 -0.9933988225777741 -0.9094558000473854 0.9819364023537493 0.7963233571337235 -0.08021341403640077 -0.7645369615704958 -0.6609409629217383 -0.4868900967478131 -0.19836354186161845 0.2176367411072925 0.6831423710263509 0.7165902377717425 0.3185146759286145; -0.8259456732173207 -0.9417670833495746 -0.8516602489278752 0.04106665376080802 0.7851874232705159 0.8111892103223678 0.8179081463539966 0.8504736685346438 0.7611222566210216 0.30311036655024903 0.09203242107478696 0.02972513724175742 -0.027338298188162115 -0.43293327017272265 -0.9648618242977868 0.18833383159428166 -0.01701823967994338 -0.2572354357167628 -0.5017849534603861 -0.17837406482385354 0.25662708108078264 0.7626685465059222 0.843371778876502 -0.8775394458261524 -0.6899077269676057 -0.5472932114610088 -0.3813792994734934 -0.12694114656184652 0.20305007123489272 0.6307645242792976 0.8476645612801468 0.7408129402248972; 0.728849803666515 0.8158145326206719 0.43622199328720035 0.4439890091217804 0.6617620823069602 0.9098306896384584 0.9948009272488595 0.998672307983951 0.6337768895458873 0.010423502053976153 -0.07835603788403708 -0.059504250427721485 -0.004363646249144058 0.05122533461095168 -0.6344901143768775 -0.4561192671425539 -0.3238914773902151 -0.22418949449316183 -0.44730954133812256 -0.13589989242587072 -0.13835943491223615 -0.32243665469268934 -0.5623176302339786 0.41269225954315203 -0.09627958608392304 0.05164655966697987 0.145140590306571 0.3062176197239049 0.4515059164652515 0.5995688349283361 0.6319737320597708 0.9007840694839434; 0.8003095618647051 0.6610031654773668 0.28172476464139484 0.10371986092774939 0.0669235695775793 0.03896355162119487 -0.1735085684349243 -0.6162309024662841 -0.7305506704852919 -0.768208011964764 -0.706864502873046 -0.5403053798474318 0.13052358094961689 0.7722078315553372 0.7304303793413507 0.7627200553835722 -0.22028084906846465 -0.29603394971194885 -0.3224288077876464 -0.593658003543338 -0.7067822373579263 -0.8213395955505407 -0.8448161431253257 -0.4325710033010494 0.8948480793885762 0.9942287930803023 0.9102822385730129 0.8049069129476162 0.8028130899255891 0.8442227651573814 0.6723411330864297 0.6480277521694936; 0.06627300245548795 -0.1423997327367211 -0.34323991587885855 -0.37486968015882155 -0.41320486121444416 -0.49843489896302584 -0.7681474231435027 -0.7928753048704219 -0.6254338351877576 -0.6148651467175358 -0.6229778882448003 -0.45138137025412667 0.16117267938672145 0.6064039710334387 0.7590618548195907 0.8341436793512528 0.8907319126811754 -0.40221183773026237 -0.5480154137890255 -0.4330556541084556 -0.5519718551374038 -0.8374400758132363 -0.756235890977523 0.20169381802136815 0.6920842760496506 0.8995387878790598 0.9933187928216699 0.8908614776120773 0.6578615049045925 0.6339337539068944 0.9056839324931282 0.778662724655528; -0.725158339814244 -0.5460039448010097 -0.5114678044545813 -0.6195858376491086 -0.7705053457073278 -0.9233361089042469 -0.09962020763992392 0.5869534773613091 0.6318798390037746 0.5304960505886437 0.23598558516676077 0.01959823685615203 0.3987876707313326 0.7819116081945776 0.8800429927789584 0.9043234758392324 0.8522302049167007 0.0638889940662158 -0.5814412274828351 0.05566553035346359 0.7570828860762726 0.7438759729639953 0.6287222147730048 0.8520588952568457 0.8778755536457871 0.6887676775546593 0.5283114484308032 0.1943192305063308 -0.01537011389640211 0.09419847694036586 0.35503815954414697 0.7842705068191014; -0.25998081100560316 0.06698666936245365 0.022934412219593556 -0.02813627996276412 -0.09462022630673897 0.3558914172412823 0.8253830827568335 0.9001186193956023 0.902543238066696 0.8580189437956292 0.7322021382393284 0.5040417606070228 0.52655146570709 0.840700486867088 0.9287359129900911 0.921284385375136 0.8014886523395096 -0.059983152748091954 -0.5319588668478615 0.05192652366353097 0.32209408488892644 0.5060539992450046 0.40495339579892353 0.11977889068870863 -0.04572370468612186 -0.6361830875203426 -0.7632037853633746 -0.7648463599533977 -0.8459292778525863 -0.8476923691050148 -0.30912803996860005 0.04433341206063792; -0.36679382952205447 0.7994850481678614 0.811952668272813 0.8368840630494466 0.9141488406277135 0.9619287483533118 0.8750952027676774 0.8892655862094798 0.8685474737382288 0.7623635373110839 0.5042599507503922 0.2290030558863249 0.22759139731366979 0.5079051711806754 0.750769983450967 0.6567613505714487 0.31655744192885826 -0.9220725541411343 -0.6630011859661831 -0.3686148857545769 -0.14783487701436016 -0.3286318962548156 -0.7036406959709717 -0.923923721164042 -0.6732154363076521 -0.6092536851414854 -0.6479460531737232 -0.6547445254280674 -0.7309147851969005 -0.7838769414114097 -0.9408262098522133 -0.8939983562528244; 0.1701695816099782 0.7861844144550124 0.9384023401199971 0.9614489134423068 0.8284081390231809 0.4552074560397195 0.35294979578046254 0.4233649695762095 0.4500053922550709 -0.1252700389737497 -0.4470835807989783 -0.21889823677407896 0.1105409621676021 0.5128917355062352 0.7227214867253136 0.31497535244309705 -0.05472083290930014 -0.5130886531153783 -0.18957286007567445 -0.08723577281862625 -0.25321778447289467 -0.4067086701976575 -0.5635103683784806 -0.7492010022238518 -0.895990712377386 -0.7660688252851118 -0.5026129256289681 -0.39636216546754804 -0.47781329773873826 -0.5951198051428737 -0.5443732207301998 -0.9722176789471414; -0.09546083420328028 0.12152190823852972 0.6702452297326794 0.7290845348858189 0.27386575757672277 0.06475770655188486 -0.03842277412555966 -0.41166550856742834 -0.9182121061251658 -0.9300537849753872 -0.9246894023017767 -0.6273695395296485 0.03850178468626443 0.6526364375430034 0.9310660518754579 0.3871784545732625 0.12902075864714216 0.058478767150861595 0.15512355705520425 0.14987575480706444 -0.12051534520080603 -0.34390425381152157 -0.47252917321350324 -0.582801731697368 -0.6848194784567674 -0.8015985070504983 -0.7058687172895419 -0.16225797614181184 -0.15414803340858133 0.3390503772558456 -0.5907787820848055 -0.874963587735204; -0.28515311170288943 -0.5022567866944024 -0.8713905351363213 -0.8241593557917692 -0.6285086822348607 -0.33904918885922486 -0.12095087184509087 -0.8005207898721434 -0.8315392058542105 -0.7984946825672414 -0.8265100254885394 -0.6253988732186037 0.03902299170489823 0.4727039574047857 0.8497700713701585 0.821675658670661 0.47809394595992355 0.3212888371543022 0.23467958417824564 0.09011640381682685 -0.08690942083326178 -0.13870648748068148 -0.27864664026300395 -0.3721563969538756 -0.479537329923674 -0.5653558701356061 -0.5127416047338759 -0.14327465984064605 0.3715552305764007 -0.12153976308517044 -0.9057061954588729 -0.5765233731753925; -0.8464089990666743 -0.4330818180292902 -0.8978239798172765 -0.9313917953118533 -0.574380082402342 -0.2672468683590345 0.17516087157522478 0.2859550456867781 0.020807419035071217 -0.0606581279597649 0.025701526214114808 -0.0069899967415740045 -0.14586465194864662 -0.05638293382766272 0.21675540532429624 0.8202754036771723 0.8523080380082141 0.5830066125884877 0.23864417827903578 -0.3608142481591147 -0.32429570812757363 0.0610504193070471 0.581585254545569 0.9509682425679568 0.6189501915788675 -0.16177569217163532 -0.38730410075435123 -0.37500464798363436 -0.05441259429252547 -0.03832979354417709 -0.2661552973668392 -0.13594221221936867; 0.6426978751226899 -0.8871935999544313 -0.9999864150842335 -0.78591053386768 -0.8281018566044737 0.06296322555636595 0.24915654961902597 0.5557179928295671 0.8951581510874959 0.9731499961565659 0.9202167314045144 0.4183024116648284 -0.7811150549697136 -0.6652436072520267 -0.3361289130326146 0.15496489337799396 0.7828469834570186 0.9491829409109999 0.383108826569916 -0.5477360818044489 -0.450352121979209 0.06184772749535175 0.4558558969697286 0.6901795488899618 0.8203031961878832 0.6263731715610255 0.47794935567729324 -0.9228013389992472 0.09892801198433399 0.238600431089922 -0.5876093347088489 0.13283893397492894], [0.7643171293518133 0.5705719979338479 0.8588803547450218 0.1342411385076458 0.25348623950800436 -0.42630789368681343 -0.33810203646614867 0.013430730751576029 0.07646250602433681 -0.002114018103839994 -0.20103122228493966 -0.5123655744765157 -0.4558787985647635 -0.1466917210173568 0.23374238359618008 0.12682591542438343 -0.05197907586800289 -0.23446964015206437 -0.5262601122316606 -0.9202784627382645 -0.7094367462310752 0.3446720729134691 0.39073025379770565 0.3951451337330159 0.3249126696606031 -0.3325585214344209 -0.47565131461291715 -0.8608218927467496 -0.965860567460282 -0.7277565789643126 -0.5082508796226377 0.39439457119931925; -0.7496423802591599 0.3982968460724275 -0.3204890007002141 -0.3430562935256523 0.16969201468582595 -0.22052345987968258 -0.18594527058306623 -0.07853709126905233 -0.0004960905184795252 -0.06747167898107365 -0.2373058234517291 -0.45685984455724815 -0.48747166745719245 -0.30225360433659393 -0.020239916361633404 0.5375829763676795 0.3109952263702934 0.06578490941080578 -0.2821561335569318 -0.4844099469827062 -0.5119455643715175 -0.2282476032064915 0.30707772060517535 0.6334223231735887 0.8551172370038032 0.059793664887946386 -0.6733963516541196 -0.8330795537936377 -0.6838962709547263 -0.631518271083367 0.056805227924707366 0.3740319895689903; -0.21089810348817123 0.0030095604214837248 -0.3793932589629188 -0.6615253208901308 -0.6088510367555315 -0.5575973403358091 -0.4103415233430475 -0.29111452286060113 -0.18047990263220656 -0.13369217570799427 -0.20748126227716138 -0.3775790453921823 -0.5369845768543509 -0.5575704983892081 -0.3497511128595826 0.0820710034423406 0.5164299185252793 0.5499496015424439 0.22897653135770762 -0.10425512106714685 -0.3550159334867168 -0.38863054655198526 0.06932796816763452 0.647569183949166 0.7932828671586996 0.6176788488483401 0.12461926396797031 -0.28674497315722114 -0.437661452969945 -0.4203880170358296 -0.40646063007474054 0.45589907841920296; -0.5251982587165637 -0.47893014710827475 -0.7524965308005069 -0.9979039845887138 -0.9517711581679574 -0.9511443242828135 -0.9060349600120103 -0.7361524499288914 -0.5082220071923926 -0.27223430622204386 -0.055245937456286434 -0.14072209737806907 -0.4033326936213826 -0.7294468252357063 -0.6742013144672718 -0.17816592950026414 0.20193131077916898 0.49109571965191046 0.5737193356072037 0.2622244082178354 -0.11669107901135133 -0.27665003164939217 0.15708439832029492 0.7642760820477416 0.8231969996827003 0.7024800627643988 0.48524529785232334 0.2593565493634705 -0.18093003610099162 -0.4444290598302219 -0.8891317222947956 -0.4429575723184138; -0.9743167013713394 -0.6568005840178986 -0.46358234902504364 -0.5118651822198943 -0.6062588329224505 -0.687991939066077 -0.8311478810055293 -0.9423589065653056 -0.828039248141104 -0.4662922670687218 0.04736595521469152 0.7165697559128674 0.21561436858691574 -0.40758734093495114 -0.9902514955432861 -0.40263190603386584 0.02735158368037227 0.43037892040486614 0.8769461867057671 0.6288063291091847 0.18224379714492409 -0.1704912272156009 0.36897876970675386 0.9714257320450108 0.9272570973109683 0.9295773171791153 0.9711562344313986 0.6220486162528366 0.004188369649054036 -0.14430510589854667 -0.34660348172030186 -0.6553720000411397; -0.5082424915247318 -0.8025025178632496 -0.6553105508452911 -0.23696113081013484 0.05612437795850454 -0.06261367085007329 -0.3023017433136834 -0.537288253559109 -0.7226618797367174 -0.6264053678767032 -0.05142702970397117 0.7461847852133684 0.816695707703631 0.37722606137542597 -0.29907790168922144 -0.8102652028874481 -0.2778544520186269 0.2756042547671787 0.9542798510677905 0.7901512060502791 0.6426494388562219 -0.10200717852315845 -0.10353704007906775 0.12952223876563987 0.47535350412296595 0.7560471821957755 0.7081139085954988 0.48310905040003427 0.2570210896524688 0.0025256536453912197 -0.4672908724601218 -0.9227873609435764; -0.22902942774959056 -0.45826670229086686 -0.49804093331418176 -0.08160658439094264 0.43140444899448477 0.59129823898698 0.43025753539261397 0.11532955828427158 -0.18341153324179443 -0.3506124342351245 -0.04222534580117423 0.6175968219738516 0.8046274374251938 0.7190170386883671 0.4460947424521936 -0.35421649497437896 -0.8046992452189501 -0.866713275727097 0.4145639257498283 0.5780548484961351 0.41644446731091916 0.11542784734572936 -0.06768889323098995 -0.15182559223622188 -0.07922901768202628 0.3646366132860192 0.5716244458177174 0.5702496132628699 0.5607328966168522 0.47983564864700873 -0.2384558407251883 -0.6147503565832912; 0.42742019902530204 0.13920399535197342 -0.04665827400822541 0.3000834556174855 0.6757531167147872 0.8222513220651109 0.9128367459913288 0.9272802287559502 0.7940027999349485 0.509340956216836 0.3475439852922262 0.5788577276386593 0.7856901581663153 0.8752045893278285 0.8219128334101433 0.2531743257461883 -0.2678531784515735 -0.6625363458172132 -0.12653588436578914 0.3905273279908654 0.49350214905651246 0.48095005222972464 0.3010603309791138 -0.18143674184437691 -0.4038584743433395 -0.3857665602958044 0.15100083775926806 0.967578416430187 0.9783167107167612 0.8564152575234335 0.3715813152294512 -0.1981322304908934; 0.9906875310109777 0.9863433365037939 0.9409877012593918 0.9994878439363908 0.7045198162824059 0.652186799503659 0.697141375244728 0.7603483195045668 0.823145998764079 0.8575744526341099 0.7037634449331004 0.050230583531835744 0.12252657383279748 0.7431062018658356 0.9110295866072434 0.5130854254757294 0.22755724701031335 -0.03506972081341161 0.2748109821777342 0.5958436764105258 0.8356308274992845 0.8423326586669377 0.4794730295642124 -0.014127803885525208 -0.26841091028517117 -0.35776293817554994 -0.3064235805420685 -0.06250732756159934 0.4475859235063046 0.9438030320119164 0.6241243440758947 0.21082147345395458; 0.8735518141426573 0.8536368997361342 0.819001003281655 0.5880075269230777 0.23341129264980182 0.15563139468724393 0.20240274913203032 0.24044139190568728 0.22328508121268387 0.10141423706918518 -0.15074968813614 -0.4268173808168578 -0.6154264594413251 -0.7112639032851495 -0.7275377970561239 0.6644753534113821 0.9377643435544951 0.4860139415775666 0.22227285572612537 0.9773640994356224 -0.0694939446798151 0.007727700757385764 0.012061954226494318 -0.11121299739385491 -0.28995052923094466 -0.3982995481877186 -0.3821850850906731 -0.2793964946571547 0.013385778435935077 0.7489280743233417 0.46662614905998734 0.2088716784036925; 0.5658162839185272 0.5162589036446452 0.3459626675036309 -0.0741540123145936 -0.4447525594393305 -0.5762212520981336 -0.5530129543966521 -0.4768780385175129 -0.44723330939776723 -0.4826281673003123 -0.5363077355553602 -0.5661602864581303 -0.5674621263833547 -0.5689039061732327 -0.8689896045773027 0.7005383738570736 -0.5519569558294318 -0.5386026684957536 -0.8554170623442255 -0.6984590378779432 -0.7074781748942858 -0.7495229146948525 -0.8135032347438014 -0.717697393672701 -0.32572317631800957 -0.26458629908193293 -0.3379212051643855 -0.33786577615892294 -0.15928466924365645 0.3792383457035711 0.4282673919174128 0.3506984084739048; -0.5824117769364561 -0.44982374031402056 -0.6809362818484732 -0.8378051091963337 -0.9312552403493309 -0.9622932075873839 -0.962359067160987 -0.9342942998455819 -0.9037329048187267 -0.8946159213255709 -0.8742294059830767 -0.7762478398979086 -0.41242752670501676 0.16940121582148965 -0.3638156784007601 0.41509537116289685 0.1962731249737835 -0.6924141112160047 0.1638017516396798 -0.2399348409159919 -0.6804190713696485 -0.8088057004750809 -0.8795635515315158 -0.792696675263123 0.5825191149019289 0.4838902469161058 -0.4998783466165425 -0.9305028956106861 -0.8711601064380365 -0.46118619980231274 0.3900489182985482 0.6663204115014915; -0.5315489746422603 -0.316713904000419 -0.4595138409952193 -0.6777890363159286 -0.7950488317946759 -0.8539799937014045 -0.8909462805483693 -0.9197200314989085 -0.5575790394516734 -0.26547610492078766 -0.35783475490990696 0.35021210777550765 0.7961711016819643 0.6861383388748593 0.18270510059749767 0.12917558825354278 -0.8052835427095479 -0.5094933288561193 -0.19577053541401165 0.9611089562674271 0.8070628554693466 -0.15844220454630667 -0.44408011265066916 -0.38031551961115934 -0.33695600306742696 -0.8823228422671124 -0.8783186389671629 -0.8743492021819244 -0.8221976158609985 -0.6611893648057637 -0.2570468415316103 0.21297389039854756; 0.24444609099893755 0.5580944404774016 0.5430567371991738 0.3252418579367754 0.015792005438152575 -0.23625567046698503 -0.35002170276194067 0.3650077505288887 0.7525772320106738 0.8082199824235542 0.8410884184093931 0.787734670620418 -0.9354883526900916 -0.2355355263874712 -0.6483159663282627 -0.885079319378542 -0.7436750235602134 -0.6468562851774284 -0.37428946483786135 0.7332525969096468 0.7767788025878638 0.1006869856122502 -0.7961744275833406 -0.8289530913058056 -0.8562522516797796 -0.8101926605222609 -0.7157712762130882 -0.67812913002279 -0.6353407619322458 -0.5435776753894841 -0.2724967920715257 0.3935513667026741; 0.20305929945602139 0.8065780313121942 0.8444210889079781 0.7660765466256163 0.5731104372905829 0.20331918614439787 -0.2529928526645405 -0.5956668429275201 -0.2863074583289867 0.1947373552062565 0.3521084824146061 -0.5399577213460868 0.05443803117146279 -0.06489909419130871 -0.25845715101949435 -0.5365723681085754 -0.7324222128266048 -0.8179359144137613 -0.8602514511332425 -0.700026610166814 -0.27650249769660906 -0.5769971274355903 -0.7875550220397268 -0.576532986224455 0.018776003411453274 0.6294503674910781 0.3194681879309485 -0.013054283982035111 -0.21604066987825551 -0.3020966415964219 -0.17420051430684066 0.6669157782588855; -0.6409989227403782 0.19987749929259682 0.7646558213733353 0.8678293470116191 0.8608664757449833 0.6874962048591104 0.0922523606280819 -0.5199508322767091 -0.8201572216284637 -0.9989038401657043 -0.49817935560837295 0.47001693860570576 0.2656109315746075 0.1463665181852005 0.07552357530704872 -0.1084984935377266 -0.6211939040708558 -0.8542583366945986 -0.17629902915104806 -0.5248766141908213 0.8388457869284729 0.9378154309636599 0.06671593562516316 0.045901508699706564 0.6515496212794304 0.9356949370292154 0.9197829568558037 0.7967341893987244 0.5298247940728549 0.09932632976416678 -0.27747944083196224 0.09765065703561726; -0.7763841967595312 -0.5570822702844451 0.08498201313242786 0.7485133958943161 0.9509161705944033 0.9930793308238651 0.9970986395412745 0.13496534651155606 -0.80001201946163 -0.8168941080015185 -0.816970860778563 -0.09782742575862904 -0.14479528564474867 0.4997093051994168 0.43227944036604476 0.8184056325220362 -0.221571769464173 0.2193782674375788 0.12694756187864364 -0.6482380240288605 0.7816361732000298 0.8063804422897674 0.7667033744355594 -0.8838300787236253 0.7212996004364973 0.9538853411286394 0.9228597012607319 0.831935232488021 0.5731455991156313 0.098936335197202 -0.3258317044615508 -0.5279414899229415; -0.9973609794209449 -0.8643395915563437 -0.5738259021506982 0.3526031281986363 0.8055590887953525 0.7725775099506014 0.5831169099999621 0.2986723844096842 0.05984242326477382 -0.009632087389247592 0.19479515251566606 0.5773960213482653 -0.8082935055395927 -0.9197257762319612 -0.9755036665482807 0.8845889454683443 -0.9338608394833655 0.24051061100361906 -0.6291158953363094 -0.5920277517932552 0.976942528748372 0.707241924300173 -0.7291070631583754 -0.9549949905589857 -0.8503243283526365 -0.6377400082709391 -0.23907008412232741 0.04731711097374758 0.04043598055297454 -0.17634585259026989 -0.45699806927836667 -0.6441584740181923; -0.3288320116726873 -0.5513075856507891 -0.579566193210181 -0.008418201194371373 0.5299690258076952 0.5974506827693731 0.48325745114587537 0.273835843192981 0.10250089193610892 0.08031342267003674 0.2843325547102554 0.6910992492975455 0.909303437297622 0.8076116045224865 -0.8509943045676307 0.5929806743598807 -0.5707172411408823 -0.3880123374832114 -0.5105685055879954 -0.5888319200991826 -0.6220549523148482 -0.6057928147112769 -0.7899668890098149 -0.4878076004990907 -0.4668495464621709 -0.5037221187478141 -0.504071721942806 -0.5194309218783222 -0.6714308616011635 -0.87401140118729 -0.8501226540113762 -0.9006269267688736; -0.06750056719105528 -0.1949505710491079 -0.21582025976527114 0.10884494463793719 0.6302614375427245 0.6709670630531505 0.6475971853131082 0.5030607096545987 0.0863870075755281 -0.2549014416301656 -0.27039199463292873 0.12191531161027011 0.8999006791881734 0.9284468610098685 0.6874056715525237 0.4726219477785722 -0.062007509745639865 -0.014404487296645684 0.08605800343961496 0.08378201548924623 0.17073107309922855 0.18385358640818428 0.4218863458930865 0.9769961800689496 0.2856041728796455 0.04232927903735528 -0.0586836989838611 -0.12481752303192756 -0.20345928217932668 -0.38494610620402603 -0.6548397385660067 -0.9477970567873043; 0.4604632789419349 -0.22953781162994966 -0.5236494822770728 -0.5231096479348916 0.26703724357380804 0.42774696201464607 0.4535301325705782 0.32495500402498867 -0.21825482083627593 -0.7395959171225067 -0.8297449037982036 -0.8216783040737669 -0.7754469679809853 -0.4779883280128423 -0.25702466980902117 -0.3077652588198778 -0.40589293704978857 -0.0032612613997147215 0.7689781029142659 0.9519327243015555 0.9093387700224986 0.6427788778038974 0.28170604784877534 -0.4719389795257765 -0.10245485626230451 -0.07718475513192932 -0.03997057629369203 0.023003419227135728 0.08569778956870913 0.09389317939861609 -0.1005529399337042 -0.663874060586763; 0.5646088633522791 -0.26727085123292016 -0.8693344821871618 -0.8959638542157591 -0.7356540783909202 -0.3747110485283952 -0.0032350869096539597 0.04506630619427206 -0.772009488939007 -0.9958182969949018 -0.982238075652336 -0.974840499360843 -0.975020251445148 -0.9872917908904976 -0.7624121444537387 -0.7744388537473261 -0.7549314025034957 0.7315561193592515 0.8889920664647868 0.974210107516701 0.9803645184558256 0.9420834629932175 0.7492131420363879 0.6823573037392742 -0.9291752254177941 -0.7922560126505194 -0.5908954328854442 -0.14955650800984213 0.40453166575959815 0.6297844823250096 0.6592205896294325 0.4301258582910267; 0.3081123426701182 -0.24804098075178468 -0.8114877427618123 -0.9514844985188127 -0.9762483908932922 -0.9806311492618537 -0.8738926570737405 -0.1900393342201451 -0.022859934069657306 -0.24465825301389832 -0.5157571266137071 -0.7081383785599182 -0.5919669663805033 0.4342374427676484 0.559167923480814 0.37498171797178403 -0.8800619657080702 -0.9490765007695469 -0.7060238352740109 0.14599000675455442 0.5102894534697151 0.5152805499462592 0.5350448675870186 0.8035924603797125 0.3498249115174396 -0.05042681161394278 -0.23526224221706873 -0.3108483421693403 -0.17092132214506253 0.45530587666792666 0.7018005804093316 0.7353708349496648; 0.6000463096449521 0.09800062087999052 -0.39960202470869866 -0.6697850653848915 -0.7859198420218433 -0.7888675974062864 -0.48091951650023246 0.3316231788343746 0.6026947079810195 0.6054091909308483 0.6003339598311017 0.7527993987890461 0.9244202788359217 0.7688822400291725 0.6290140377480706 0.5176078177784371 0.3416629536357438 -0.8005033643560336 -0.5116735351931752 -0.16177110563611274 0.06218747704834744 0.23882028419983875 0.6372428825058305 0.811245921166383 0.607130059261033 0.3993783943420677 0.1010099865645792 -0.36367980548459067 -0.6815272357079759 -0.7518639641493966 -0.40892888472590433 0.3408751830480331; 0.5052019881595277 0.5840726619570903 0.43491916891597737 0.24401752015449718 0.07422137102679038 0.09698050883502554 0.877652834217767 0.7114679532777248 0.721499410105752 0.8071181887195674 0.9358442622877939 0.986589196637342 0.9160048215539489 0.6092823501480568 0.4618343841708006 0.4239762264894649 0.5203591345579012 0.9889502449863122 0.7876927477122585 0.7719493464154095 0.16340558165989508 -0.5301486975393754 -0.723039848834615 -0.39342151331150954 0.26592490271896013 0.5762190886400413 0.5987760607653809 -0.03956471725460066 -0.830620387200025 -0.9750400338363373 -0.9273240756027362 -0.5593154647787901; 0.8154311370679754 0.994712374719255 0.9496439045499919 0.958150108602017 0.9874378170881957 0.8461099062483888 0.23100334965062252 0.04095795171441466 -0.028291884313024547 -0.12126911288648883 -0.3318134923187797 -0.7005866388368764 -0.8486239721496057 -0.3152267234247901 0.1146607734573416 0.3527706103046457 0.5869631742603978 0.9211673963581958 0.7744597025996757 0.7152522571499681 0.5912182712177035 0.23182225307695464 -0.863379596616391 -0.9596674235960878 -0.8126273480714908 0.029228552359348667 0.6461544049502789 0.5773744093844211 0.2890047091260555 -0.22548358179840536 -0.9470335571279264 -0.8528468086613781; -0.07010312077527098 0.3701530527698372 0.5270915871547033 0.5325310124337308 0.3393125473801883 -0.23801780539458303 -0.47058577792290934 -0.41741955287609545 -0.39206116107412653 -0.49434062476029333 -0.7686149068412698 -0.9693862934004717 -0.9278244509251276 -0.6072290522402087 0.047196279718690066 0.5998724564170459 0.9205476047338379 -0.14619361111565093 -0.6179297259096289 0.8694613734777807 0.9887552767098816 0.941731696879565 0.7100195242473175 -0.029152391715555174 -0.34521622703942084 -0.11590164158004355 0.36789149047694386 0.6589286474753412 0.6769734115622632 0.6207914193705812 0.3388040921887018 -0.09414047444668637; -0.546328963246954 -0.3232616162877978 0.013919187494385107 -0.10806580237625434 -0.5097278105119546 -0.7353091403709163 -0.7863314421396824 -0.7928024912446214 -0.8653745055626442 -0.9832986733619202 -0.8913322426605881 -0.9183881554075148 -0.8662074660884816 -0.5764161655201254 0.31671247366042277 0.8477291097558942 0.8598206095476688 -0.04314881825386537 -0.9756744768315968 -0.3814872031474909 0.6710493487655863 0.8500613656841151 0.8141626439192302 0.6589523757007627 0.38611492561852623 0.16209557479353673 0.3123022822184964 0.5607755828947036 0.7382473413771694 0.7380124139593083 0.8227729150432178 0.20167249570505408; -0.9562237563419979 -0.43620655121773994 -0.22212425935032376 -0.16455149167111993 -0.4251871483426979 -0.5370693845026443 -0.5608224868131392 -0.4507243528505504 0.15167724597975474 0.3222749343377853 0.10106291653208703 -0.47132620003608283 -0.8220959792133717 -0.6737456474089928 0.3436846343168334 0.8877868208970129 0.8186364171025449 0.3775504276282729 -0.5940499120899327 -0.8485424085055718 0.16906941313178345 0.7102081343999772 0.8445460459179596 0.8122351127661125 0.703422507674744 0.5775050483383333 0.5137111503990106 0.40825980798579614 0.620520679223806 0.921841863680291 0.3603645887685863 0.3980484815814767; -0.510367896365747 -0.07938217335902403 0.48698617183919074 0.4833953051295456 0.3806349882995046 0.14770980883135096 -0.14778614383889233 0.21215028402447708 0.5539925875856807 0.6018121532411278 0.4422247720803851 -0.21584047848449753 -0.8880538915293343 -0.8771491883021869 -0.36614722946289013 0.5685928929213674 0.704800519766948 0.5263520199334971 0.14182708935611757 -0.7568073795166974 -0.7537842124550224 0.09410952232052693 0.7862187391846479 0.9281698792686119 0.7948262329360137 0.551564808710708 0.3338213685252295 0.11025141496370715 -0.41973576038998744 -0.1682005455561796 0.248444024745106 0.8093955348093969; 0.1391853171554616 -0.32997475764390005 0.1310976938096925 0.363846347449408 0.7239794201574891 0.77630722464967 0.8948811037346299 0.8383442450318354 0.6651792008301701 0.952991259088648 0.9895438902131206 -0.31344637475081594 -0.9840134136034796 -0.9838509841564606 -0.9386124138738773 -0.5719522742225375 0.27618807908032783 0.5410655972690304 0.5404868922599376 -0.04505964284922429 -0.7838968660460867 -0.9929084232020974 -0.8093722638275049 -0.2704340773401697 0.7618431365821563 0.5596601006142954 -0.1686277369002059 -0.13947433317273566 -0.48143292707069296 -0.2215873212502436 -0.48680180767694464 -0.7981383201556187; 0.708073839452282 0.3157755089299172 0.004092564384836335 0.21897740136426463 0.5603496828885238 0.9911304988480222 0.9383723371473364 0.664302376722493 0.11640444348092782 0.012480227566247176 -0.17902546016653534 -0.05884702317467026 -0.5045117933057753 -0.7320959280237644 -0.9414280430504044 -0.9795610580374283 -0.5617700889503263 0.2123045396903079 0.8733699149961163 0.4348015491181861 -0.4313849956465555 -0.8032269176583741 -0.8239953086802239 -0.7220637296580269 -0.4971735922031967 -0.6664333070488289 -0.6668143927904262 0.08930363776415343 -0.18665881841504983 0.5179869882119467 -0.724381244859722 -0.9533565488542428])), instrument = (lgR = [0.0654313367581995, 0.06543133675816755, -0.0037171254178809607, 0.11834139469996612, 0.11462207399485871, 0.047074456453534974, 0.030764561787936996, 0.07784209088768204, 0.06295709638012165, -0.0037201334259482927, 0.05923639990785286, 0.0461034598516216, 0.023408835223680775, 0.06950852158514086, 0.03551676213977647, 0.02298679961374393, 0.0585059269454808, 0.0506109809730355, -0.02105899843274571, -0.00776503700762341, 0.026103591626343407, 0.10876074334793787, 0.05475248083806108, -0.07365410143595019, -0.17165217539521288, -0.02610465686767877, 0.10569230309451001, 0.14702509456134194, -0.06888266580749938, -0.12770463665518636, 0.03249941344602081, 0.031136793087147775, -0.01658361022460968, -0.26001375963159373, 0.033398325690692184, 0.031343149833702684, 0.010893415359110249, -0.026082045891684613, -0.19071971690206052, 0.02744388736371025, 0.007929617456584843, 0.009304522505275227, -0.07495422690601172, 0.08811118144434178, 0.0261910218930862, 0.013507988909065504, -0.01716813659010199, -0.06140679495915015, 0.12667039232581356, 0.03509416418539042, 0.0111060181484078, 0.004785234769595854, -0.30900792764301166, 0.15868289204936772, 0.1514471055662453, 0.02010426909176173, -0.007723768729873238, 0.0400149568880292, -0.19380708416417744, 0.14317133450914002, 0.1652778441525135, 0.03383753104159152, 0.06753037662162671, 0.057441669962252896, 0.15859889680797454, -0.08456662356539416, 0.20723436902882886, 0.022975778457050403, 0.03647552669331706, 0.02268313056509434, 0.07413715562520513, 0.2674517995540393, -0.15282930905716383, 0.20401763294565545, -0.02111802726496309, 0.027208629822357003, -0.003619988176361489, 0.14762062830953698, 0.16518652033098694, 5.516225097772204e-5, 0.0076917803526905144, 0.019922512049697458, -0.007450062574899993, 0.1917977138773326, 0.09337370654094214, -0.7797880023858506, 0.033653899415523075, 0.029946269401681536, -0.010949697925744278, 0.1706489812549202, 0.07148139467261647, 0.024236395553170413, -0.04947112991674129, 0.037447757331271016, -0.04731750097461927, 0.13123871279873242, 0.1119379231493105, 0.1069773421954554, -0.03328315114812067, 0.010004916686208114, 0.13990196595244603, 0.15686826127128045, -0.09102982512468961, -0.040183505595639386], lgrat = [0.005125644446776219, 0.01703776312126654, -0.0024081129989068353, 0.018566990783630447, 0.012363823669023678, 0.01965850586145898, -0.007492825958080688, -0.026977705066778258, -0.006048500593188905, -0.002957434637136203, 0.02553226677389895, -0.021468024712508433, -0.005961591792974111, 0.03432673683568079, 0.015085749519126121, -0.06306034648706481, 0.014583662211204294, 0.007167114279264744, 0.02528322730482621, -0.02057877119524306, 0.003521757706393402, 0.013339963979878125, 0.01722649482431868, -0.035494002257559706, -0.017873604043852374, 0.01896984019995512, -0.0003487062029641723, -0.031888486264531, 0.007179043211616932, -0.009234874971345574, 0.02472646341292331, 0.012657841777114535, 0.002373824383671985, -0.006346282220993162, 0.0230130170996704, -0.0008489414425397793, -0.014731633129321577, 0.022486192406158925, -0.006657528141962751, 0.011813134161829058, 0.06490054394089578, 0.01640743087482918, -0.010384406887498166, 0.02847442086080018, 0.0318893403112016, -0.02561476447616061, 0.0325885858310456, 0.007504210358139129, -0.012155443158799897, 0.019748432384369786, -0.03160679256819454, 0.017577388641755575, -0.07725025343066136, -0.013564495362041863, 0.010713759350081233, 0.031392721900904114, 0.014549009169567246, 0.016933092091177087, -0.04845005843217951, -0.008802116596600011, 0.009509403597096911, 0.032398011588005426, -0.06998173713022414, 0.017636314254447668, 0.0396513585728934, -0.0041769033376947, -0.006060560555730962, -0.019698513290306596, 0.021883930044678476, 0.01560876946209655, 0.0061792768171502815, 0.06686526027733528, 0.041688876638038226, -0.004854408098352971, 0.04836201101993649, 0.03944144269108456, 0.004456228617511184, -0.019540180839428913, 0.04130045901100827, 0.002393792684759943, 0.03168391900902592, 0.012375389994145655, -0.0544755441641335, -0.02153180022411875, 0.02334231933283249, 0.02238600270434996, -0.07419642898660227, 0.00556894293058157, 0.03451967097874344, 0.0040779971879996045, 0.017863725128910497, 0.008720357379401576, -0.04959859001352957, -0.0026407583758240203, -0.026438422209096556, 0.01900806438844183, 0.027966135435493925, 0.012824815166077802, 0.01924220820031534, 0.018954192934522718, 0.0053697771388899005, 0.039207616784569244, -0.023192251455369736, 0.017525865041963115], gpR = [0.0, 1.7936888345007576, 0.0, 0.6650874717091262, 1.7122034254505163, 0.0, 0.5096154940670303, 1.633523482588496, 0.0, 0.40755175913415276, 1.4340101172804105, 0.0, 0.42602255443367754, 1.318303175418448, 0.0, 0.43760959526616444, 1.1204286054498944, 0.0, 0.3644212623141748, 1.2811546944973051, 1.0075191565027342, 0.0, 0.3382964464257941, 1.048298371025753, 1.6825480996517743, 0.760710315256752, 0.0, 0.2643052731569828, 1.0324428992700658, 1.6936648646224082, 0.0, 0.2567966622697634, 0.775397594802419, 1.7019393272850638, 0.3669938935415418, 0.0, 0.1557647773466659, 0.7165899063414995, 1.652218042555165, 0.0, 0.25480781388730855, 0.541124281585436, 1.5505973620652127, -0.09583357852901297, 0.0, 0.2032283387723387, 0.4278658753072586, 1.4950144982016895, -0.19232134142383028, 0.0, 0.24823559104635246, 0.11731464181177248, 0.8747502522704695, 1.3293637352519623, -0.5842524310579007, 0.0, 0.20862153543555945, 0.06627883146372511, 0.7463921469727741, 1.2240001518285646, -0.7364680812399724, 0.0, 0.2222166943262871, -0.198360671994668, 0.2815194837001649, 0.9584039119602719, -1.0760719441698194, -2.093763236988714, 0.0, 0.25578463293398424, -0.33470826108982, 0.12301038652167753, 0.8516605756370754, -1.2087602528214534, -2.1912767936239534, 0.0, 0.29552665100342285, -0.8768064991997431, -0.3208878383700844, -0.24727395219064263, -1.5309943447324672, 0.0, 0.39726469841989565, -1.4693068446926585, -0.5033238713082842, -1.473264490204648, -0.878337285473024, 0.0, 0.5416636303644565, -2.1084188746382324, -0.60175948149831, -2.2305212873257654, -0.08078255222826058, 0.0, 0.6630089192919589, -2.529639408768337, -0.6935693573914818, -2.6472470087217843, 0.1571044484853464, 0.0, -2.6881461955299, -0.6448186626080679, -2.763935377597494, 0.3658602245638919], gprat = [0.0, 0.0016870478182497088, 0.0, -0.09110762126379157, 0.003071394728017386, 0.0, 0.049118938346048704, 0.007547743545544321, 0.0, 0.056689904607392656, -0.010653883582202539, 0.0, 0.03844303591608486, 0.015902552880152947, 0.0, -0.06660464073056005, -0.015416521637813041, 0.0, -0.046934222088211186, -0.001144483050206091, 0.007608688440347948, 0.0, 0.02481638156699937, 0.0533493797707359, 0.002204716457363949, 0.002052073062179976, 0.0, -0.010923173409653764, -0.00891504412287425, -0.009746569292393481, 0.0, -0.05076041939675502, 0.034784763813836855, -0.0426374972248027, 0.01038651663415116, 0.0, 0.0174252104377913, 0.0021409448867522746, -0.01194763160478729, 0.0, -0.0636690127617765, -0.04023082755598395, 0.0022010533000995404, 0.02315969455425068, 0.0, 0.03282396917466998, -0.02364653148400908, 0.0030364623910265716, -0.0023985806876574145, 0.0, -0.04353274065412105, -0.012896337077316744, 0.0003381358458511883, -0.0019087869222325082, -0.005060469431118264, 0.0, -0.012260117081093647, -0.04761102755792379, 0.0006806958579523467, 0.039809468925102225, 0.013616949468145458, 0.0, -0.00898728692497297, -0.08767646875995361, 0.00018292847080717673, 0.04431860158363925, -0.021718953321670398, -0.2423888147388693, 0.0, 0.03475830611087936, -0.05186717411625086, -0.00012048752821858244, 0.03069155010239869, -0.03618723715201533, 0.052501716766353596, 0.0, -0.020691472183441917, -0.07297034772694033, -0.00028990057899580535, -0.03992244134143341, 0.20696503930993812, 0.0, 0.029277636392835905, 0.04421530462343942, -0.00038114362043639716, -0.015817970614936172, 0.0912241315289682, 0.0, 0.04245664919424827, 0.14030969516980168, -0.0004038852746228727, -0.022960649248482845, -0.1551351423598355, 0.0, 0.04935320240150557, 0.1378568970028282, -0.0005668344720675123, -0.0490960516989265, 0.04043452514204596, 0.0, 0.10610260639010552, -0.0005679436737464627, -0.04442126304203775, -0.02066255965862851], dRx = [0.007696016531371016, -0.08760092154595413, 0.03266453107679881, -6.838516903170392e-8, 0.018017872678774475, -0.16224306476728956, -0.012273667858231283], dRy = [-0.07275357574979102, 0.023624110678146657, 0.06528166085747943, -6.14194716968859e-14, 0.04620560663512691, -0.016144545861231683, 0.09701567456422493], dLx = [0.01162213487454992, 0.049760717745096036, -0.043843481071671596, 0.05489481484592177, 0.004692406121097824, 0.116274340721647, 0.06979063068828495], dLy = [-0.06532300937277145, 0.04412739220610292, 0.08722460871044418, 0.025836569971541105, 0.016934031368860025, -0.059306687946460594, 0.049848241288855906])), retcode: Default
u: [0.006196768010070597, 0.012252886595333686, 0.018045341775381824, 0.023428261395017344, 0.028288773039715713, 0.03251362224912441, 0.03602793223345388, 0.038812081755876235, 0.04095176827533074, 0.042677964458367953, 0.044305711989782864, 0.046160067741740154, 0.048443040831898744, 0.05101953121137394, 0.05347799913024842, 0.05536426377901567, 0.056527705545960094, 0.057106268539434596, 0.057305290139574964, 0.057009865193745644, 0.056063207706883396, 0.05445422237787154, 0.05205541533209755, 0.048775734097167074, 0.0446804575784225, 0.039931218467164555, 0.03471859407403925, 0.02920482203822035, 0.02350399441912401, 0.017689365779265817, 0.011822581116203703, 0.005912610573946271, 0.012532920514229195, 0.02479775887210279, 0.036514466618055096, 0.04742043328476806, 0.05725232215127483, 0.0657870545607222, 0.07283771076057709, 0.0783112210255691, 0.08234908722574633, 0.08546036842888032, 0.08839023179470905, 0.09194467935545347, 0.09666475001294682, 0.10224374483368032, 0.10753277931036948, 0.11134823632415901, 0.11356624353967873, 0.11466260512963744, 0.11511237591758024, 0.11459777045433728, 0.11278133360182427, 0.10972400921549899, 0.10503615480844077, 0.09842590685565879, 0.09007100925946505, 0.08038567838323916, 0.06979732977013807, 0.058640862093503054, 0.04714858552286024, 0.03547169953867306, 0.02368493918700222, 0.011856746062442781, 0.01916429631039211, 0.037921041802479974, 0.055855532783095435, 0.072551527847697, 0.08760301835603411, 0.1006295504590151, 0.11128904831891218, 0.11931250830221315, 0.1247578304047827, 0.12843666982863908, 0.13182876816650352, 0.13668447361030478, 0.1442268370298679, 0.15388913756033662, 0.16290156715421328, 0.16867436739222008, 0.17150993821404067, 0.17309175787865522, 0.17399526310478555, 0.17330286318771262, 0.1707222118305001, 0.16666492229358917, 0.15999748676883693, 0.14991887968191472, 0.13689098684545986, 0.12183990246045748, 0.10554012122833452, 0.0885011266003377, 0.07105579912803534, 0.053401023360704646, 0.03564388353534686, 0.017828843402197665, 0.02623125080360275, 0.05192112715920419, 0.07652183667263181, 0.09943354018726239, 0.12008724905906684, 0.13791753708239476, 0.15237967424069293, 0.16285114168287093, 0.16898805114306842, 0.17171201553024998, 0.17377534035263328, 0.1789972484154545, 0.19007125230910524, 0.20595322247800038, 0.22007785166202343, 0.22735707164299387, 0.23007274393610674, 0.2328755701058511, 0.2352636906326451, 0.23408335098941593, 0.23054406793341237, 0.2261911514541856, 0.2181460969260939, 0.20428688620780205, 0.18577994392082403, 0.16465374137279612, 0.14213222703679956, 0.11888419311762263, 0.09527829669077549, 0.07152073848593483, 0.047698186525273745, 0.023856257105816823, 0.0338700970224518, 0.06710134646570208, 0.09897701325641989, 0.12873661061412137, 0.15552714260066586, 0.1785822487971986, 0.1971099507118708, 0.21005188607036512, 0.216136821794323, 0.2155812108758983, 0.2130791876337192, 0.2164970493251364, 0.23183170162167024, 0.25715002290245764, 0.27704308073831563, 0.2826991951753498, 0.2845192046528764, 0.2935938475318017, 0.3025775440123214, 0.30091947804952784, 0.2952625289063574, 0.28980613933830085, 0.28073769043492647, 0.2624172274313957, 0.23706270177087618, 0.20889821783852003, 0.17956740544087454, 0.14976117494620153, 0.11979328591673839, 0.08980784012581955, 0.05985443126084818, 0.029919679387616527, 0.042214673241194586, 0.08372138538018767, 0.12372900565397749, 0.1611872834812491, 0.1949028069750706, 0.22358176154316625, 0.24592154696795993, 0.2607967795652262, 0.26616608747864623, 0.2598149373719247, 0.2481021078033176, 0.24522354847562589, 0.263178760568854, 0.2996696604372008, 0.3214154956669933, 0.3143259392756683, 0.3131001352634133, 0.3442650439509029, 0.3776452599807047, 0.38051512899088963, 0.37154594071134306, 0.36073046805601044, 0.34904037878358185, 0.324703509665783, 0.2905066400836769, 0.25433052846751003, 0.2176342566116525, 0.18096372696594562, 0.1444737578100134, 0.10819655999576135, 0.07206834241551063, 0.036023959685544, 0.051309598973525064, 0.10199208727308609, 0.15119054048416103, 0.1976486516853103, 0.23953577397756892, 0.27429839263791467, 0.2986477851683404, 0.3116582753104457, 0.31417823252895344, 0.3007867490224928, 0.27575879537076725, 0.2584433027470848, 0.26887111604257763, 0.30782782283016913, 0.3177004482584468, 0.2809535175120298, 0.27184097475848545, 0.3492190383884422, 0.4438062996119846, 0.46936285538923467, 0.4650675477246065, 0.4444645786904529, 0.42576145375880975, 0.39184304293704575, 0.34595224957247084, 0.300805926967064, 0.2559871226344372, 0.21209120908008394, 0.16905420957339193, 0.12655005677025155, 0.08431511171990334, 0.0421556676321003, 0.061130897218443295, 0.1218517634828346, 0.18152853040557257, 0.23887601087454294, 0.2912720306621754, 0.3335712634718274, 0.35685618844248673, 0.3574512778985936, 0.3481064275587636, 0.3270047027878025, 0.28870095768806514, 0.2474348272175724, 0.23076908943041635, 0.25119296384425627, 0.23121869623938307, 0.16608765779552537, 0.14535834470737236, 0.26726167346960017, 0.4421258424409016, 0.5197842035169284, 0.556041024838474, 0.5401947579101725, 0.518483676853526, 0.467536447317272, 0.40417545102353686, 0.34778107004524556, 0.29358663898594656, 0.2421908968979761, 0.19303737758507053, 0.1447205259143242, 0.0965820958089938, 0.04834601302428015, 0.07141721576456544, 0.14283287401292116, 0.21411204054972446, 0.28462111073478896, 0.35170977090003935, 0.40639183800881745, 0.4279724504250445, 0.4001655090481582, 0.3564852605225494, 0.32018427462383436, 0.2736562770816754, 0.20944590311716912, 0.1617141754779021, 0.17267391956799688, 0.11475302820231804, 0.03132101775703814, 0.006098762922447518, 0.11731521765980493, 0.30388454099135553, 0.43033148529574583, 0.5629541349922594, 0.6214119604622321, 0.6256561673562023, 0.5490282606851107, 0.4585291689052793, 0.3897813731821119, 0.32690976113598863, 0.26939776581169406, 0.21585621239471064, 0.1627165418978, 0.10903890134146497, 0.0547291661811262, 0.08176076840746735, 0.16394430867101156, 0.2470662837351258, 0.3319969778930648, 0.4188122340577373, 0.4964615105076533, 0.5245817903112464, 0.45510122275651815, 0.3442301608731162, 0.273851263830046, 0.22482390884170592, 0.16245394663451795, 0.11877338723325884, 0.1388387532296202, 0.07107505538999728, -0.028667952185643386, -0.06610642562343175, -0.022021467679088594, 0.08140626829744124, 0.19914026939536345, 0.42191575622145283, 0.6346162182047038, 0.6856358558131587, 0.5946543759093746, 0.4821541556935825, 0.41105343549753, 0.3490459269134525, 0.29185983122943215, 0.237550310097515, 0.18107860422514324, 0.12221799953957206, 0.061597922447086846, 0.09171723191589562, 0.18402000017602624, 0.2777403692714144, 0.37498007923561205, 0.4812749389258896, 0.5928052514059814, 0.6455282143804337, 0.5272470500523078, 0.3235629342956652, 0.20803790534896205, 0.16510843228850525, 0.148863648387339, 0.17623889738871365, 0.24653998248681883, 0.18302519152894145, 0.07971062345788492, 0.006915194725394255, -0.0703949196548875, -0.1039032878513975, -0.04779904518719093, 0.18296714766057087, 0.47989576716296484, 0.5779184543514524, 0.5269685353100569, 0.438420801594682, 0.3941561975572058, 0.35574152832232553, 0.31105884261468936, 0.2601572179034727, 0.20150106177790483, 0.1372596647571642, 0.06951494669405234, 0.10114158079010942, 0.2026033130851004, 0.3046915582985969, 0.4087196991533225, 0.5212048680090704, 0.6526464503785732, 0.7344037683012398, 0.5662577445029546, 0.28375407011969794, 0.14912749288875318, 0.13879694191994044, 0.22208887510453598, 0.40283241092605654, 0.5797753366396821, 0.4328175087618345, 0.4169593892070065, 0.27566588608894627, 0.011206375706272791, -0.17665999103068866, -0.20216898346332526, -0.020560920590810317, 0.2539451218175969, 0.35895404778912743, 0.3644231140546952, 0.34017639998662175, 0.3493553550450824, 0.35692831520408586, 0.33506767938782245, 0.2890962516953931, 0.22722699727623985, 0.15595307641101, 0.07927174073116004, 0.11035299841498157, 0.22066843119321525, 0.32997046929831825, 0.4358877498883077, 0.5372398861979125, 0.637669052131663, 0.675268530701457, 0.48760196272307127, 0.2186358623496868, 0.12363885127416015, 0.19560349576412708, 0.43126456660683654, 0.7415031309545711, 0.8836772922536705, 0.7962461938555506, 0.6661131554301687, 0.5316404276559793, 0.15628482006838695, -0.10788722350532276, -0.2059582395438522, -0.0930295563534638, 0.1156362747288787, 0.1965620935197572, 0.2314308129614653, 0.2566996856549095, 0.31774395365224306, 0.3748139605788211, 0.3763738455898462, 0.3316194535116123, 0.26218870986970344, 0.18031047930909289, 0.09172255633950571, 0.1196787346654339, 0.23963231150003383, 0.3579951362477143, 0.46694574821935786, 0.5501708740975483, 0.5890124195116815, 0.540561155877199, 0.35963935167513944, 0.1706962718280595, 0.16540793845505725, 0.3921845757429166, 0.8478815679760098, 0.5377049559687783, 0.120312919094128, -0.04646488370791933, -0.005215716769154591, 0.22399814394742384, 0.3282857908891407, 0.15063759899149523, -0.017311981315210008, 0.000689058886562433, 0.13248439308888102, 0.18406299824974473, 0.2074575665484828, 0.2481763161926532, 0.34020924783426515, 0.43049949756605443, 0.44455591430666963, 0.39230966800770617, 0.30880805031758024, 0.2116329631808754, 0.10744974505388746, 0.12868517650148859, 0.25914704802499305, 0.39103315653949094, 0.5147247173886381, 0.596705265396437, 0.5905166006308352, 0.4869341747280918, 0.31910930509146607, 0.19486138950246648, 0.2806464935396977, 0.7027173727285675, 0.98300861329124, 0.08840468986092818, -0.386050452813161, -0.5332734751353347, -0.4290192949317993, -0.048292672607727, 0.589494725574462, 0.6005572171738696, 0.2991833413321614, 0.17912407544698652, 0.24319190818475261, 0.28898304228578553, 0.29222434516045404, 0.3281939698417816, 0.43035913570248385, 0.5322437676219614, 0.5427256355158395, 0.4719472840527699, 0.367462829977547, 0.25027540933222975, 0.12664678899146414, 0.13581247472348792, 0.27554283495855997, 0.4232656412406568, 0.5777932584238109, 0.7051485687991506, 0.7159253643958778, 0.6011400921654225, 0.43740801664182916, 0.30621219391437887, 0.395895027939786, 0.8435398032125411, 0.7268966419847186, -0.1792206148537516, -0.6054185463508801, -0.7219090832676335, -0.5729654279416689, -0.11184932086342636, 0.7339510307990825, 0.47035170509911317, 0.10615518957654785, 0.06405890356893877, 0.23502660050347363, 0.4181735815681246, 0.45765775769882683, 0.47681000860378675, 0.5667632478049016, 0.6650269943941596, 0.6640739786075337, 0.5683369170570803, 0.4375966149590338, 0.295928727432103, 0.14912928486505794, 0.13872913001417778, 0.28271111480256067, 0.4393233415543986, 0.6196910050596293, 0.816436403187573, 0.944533138722639, 0.900847377656042, 0.7140797245438533, 0.4435059161490978, 0.3984486665021706, 0.5709819208902246, 0.38406488688010926, -0.2505615337944633, -0.61253080632096, -0.6906238967896985, -0.4926016968020276, 0.01144494619950693, 0.6203706952782309, -0.014861715491901843, -0.26603737253283116, -0.21759410253618272, 0.080213847500878, 0.5527681246452282, 0.6747957700004086, 0.6503687182091038, 0.7089855788383995, 0.8031101225126097, 0.7959849548900602, 0.677614502994292, 0.517993532724961, 0.347581632810168, 0.17419209724862603, 0.1360860658586299, 0.27661265554296127, 0.42792053373227534, 0.6009891511616148, 0.8033798767129117, 1.0109546692240101, 1.122722040230514, 0.9214276047060704, 0.47855347840977686, 0.3094681083570406, 0.3806115573118353, 0.47542137068946344, -0.07195137377349546, -0.41963495567894826, -0.4588157309296376, -0.18788321505394603, 0.19446256798509354, 0.14688065303333575, -0.29546249106286876, -0.480019449391619, -0.40755465595881873, -0.0946717573669798, 0.4976623579783699, 0.8197554680057341, 0.7827453278495956, 0.8431589573613214, 0.970453523214278, 0.9591817490538899, 0.8060851041390822, 0.6075099153253151, 0.40267924288347146, 0.20021853355594366, 0.12893156137315587, 0.2601289821519635, 0.3960122643652718, 0.5379671152169879, 0.6833395429840124, 0.8245736780718813, 0.9170380638009018, 0.7667478066524501, 0.4138986800112434, 0.21900780374228, 0.295141807430928, 0.671382626217176, 0.3055178564704216, -0.059089238881742875, -0.0543999861282285, 0.391252621622201, 0.4645334623737585, 0.05280639975249545, -0.341379521279149, -0.5035047925299958, -0.43566623505157237, -0.1429051900754076, 0.37296129491749935, 0.7798595704840561, 0.841253363465894, 0.9985869920041436, 1.2357065903963445, 1.2038031242246379, 0.9612931188410196, 0.7006629296542408, 0.4554812489628056, 0.224164349953372, 0.11961568844503521, 0.23947096595174464, 0.3585716747656921, 0.47179426438141564, 0.5686423498143162, 0.6405162497872117, 0.6743832649948638, 0.5907891151391582, 0.3558001339241657, 0.1832304741977865, 0.2342726850479698, 0.5117924721596375, 0.4811793429557715, 0.21809386771782288, 0.1772177427950713, 0.4495761014613081, 0.20712469370019201, -0.014083810233256793, -0.22832964764042904, -0.35047383498145906, -0.2981285366130607, -0.05847714022437236, 0.335982943578355, 0.6739177994128219, 0.8433279247024583, 1.1719564638486697, 1.5788689424440914, 1.4851215725612716, 1.1085597542071939, 0.7764543625328807, 0.4948517138746508, 0.24127388179543044, 0.11014065479772524, 0.21929946522498114, 0.32487844861511495, 0.4200282673413506, 0.4928907921083953, 0.5354395339888053, 0.5574568621345458, 0.5231653063816291, 0.38917530152910107, 0.259429662369526, 0.2163862345452412, 0.2093679240953046, 0.1408075265200763, 0.037262331461231854, -0.02457435096351208, -0.0016216622170531065, -0.013696142112148393, 0.00893707497161687, 0.02943973886838397, -0.022800595469141437, 0.007032004807987901, 0.1651050223568772, 0.42907674286163405, 0.6534528892461673, 0.8623841655786104, 1.2790482974855577, 1.838954386377711, 1.6212683126411704, 1.1638799258862351, 0.8016678029169295, 0.5072107602332462, 0.24651313244502443, 0.10166669522075616, 0.20205460333451955, 0.2987050901770813, 0.3864944847272338, 0.4577444489254853, 0.5105401658439674, 0.5537424642871998, 0.5601566013008686, 0.5144836936190408, 0.4382111427895155, 0.3204594972352398, 0.15219549480328612, 0.0012513196278252899, -0.08844660546795276, -0.12708654469286246, -0.11657252891268177, -0.05270649265540216, 0.10332138197468445, 0.32269065472972996, 0.42523595945895337, 0.46637019592294743, 0.5129086651507427, 0.6473290105175934, 0.7453659866741518, 0.9143860714435732, 1.2200496022880398, 1.5324316780270146, 1.405616230586798, 1.0703509441289578, 0.7591501260018723, 0.4868067769875633, 0.23799302365118546, 0.09446035877140163, 0.1881067963542621, 0.2796491595927121, 0.36703397958164036, 0.44822510463915505, 0.526703191739978, 0.5999871250879496, 0.646006354131586, 0.6868512365181025, 0.6956899308422972, 0.5556045162510334, 0.3029260256585631, 0.09266804030823207, -0.009006354379583602, -0.02816192728081675, -0.010335104789659369, 0.055516464215667014, 0.18846006044816233, 0.41164986416216987, 0.6806519357741971, 0.9276158345920632, 0.907475957449018, 0.9572869585091619, 0.9371543886198783, 1.018855769700939, 1.1670785150812573, 1.2572103759089825, 1.1523501339719564, 0.923650152330587, 0.6786209766181106, 0.4436941345541152, 0.21900812033940623, 0.08812301099611487, 0.1762249149715628, 0.26437430657293237, 0.3530267143476789, 0.44377582822449385, 0.5405351307939404, 0.6392085403049865, 0.7282646263697631, 0.8499824895456387, 0.9786138213556654, 0.928775919398126, 0.6672475140962228, 0.3874431684348538, 0.2547836353207025, 0.2550514868982885, 0.3044161294352515, 0.3056435868452438, 0.3136768058711374, 0.35907746786578215, 0.5265136625091954, 0.8542785813698459, 1.0845554331143632, 1.223731540522336, 1.1539190907638333, 1.1178675412430912, 1.1254113941781902, 1.0809121148039627, 0.9609690974401218, 0.7849239840891642, 0.5893415852240166, 0.39105749334378664, 0.19463501129145513, 0.0819052793672862, 0.16452979248920077, 0.2488377047257706, 0.3365522197215629, 0.43040350385927817, 0.5336591374085233, 0.6452877164680262, 0.7678702590576616, 0.9440190319330926, 1.1819552572404295, 1.37462708127988, 1.3258198411690334, 0.8500845138810323, 0.6389853498398048, 0.6513774680993195, 0.7888047050156246, 0.6961461226715279, 0.5216395921339524, 0.398574025315073, 0.46613528744564087, 0.7329592311491457, 1.0826021621902173, 1.2986659132772373, 1.2350886595257267, 1.1178234631012416, 1.035205756836127, 0.9385575033758454, 0.8131285216765102, 0.665100957564007, 0.5039726106308354, 0.33721518078144497, 0.16875231100670388, 0.07516256657369239, 0.1514063262517803, 0.23025029179901357, 0.3136700145124149, 0.4043717922186208, 0.5053501840411283, 0.6183887813731119, 0.7515639233365983, 0.9385718436271744, 1.1932013112148487, 1.4691336331810405, 1.631572725718177, 1.21148828918353, 0.9737447919935618, 0.9842754773073775, 1.2742222226920297, 1.1392305358931598, 0.7660979886579442, 0.5225660248451892, 0.5058487855545701, 0.6785341373692483, 0.9370397752141709, 1.1206987649392899, 1.0926652144423974, 0.9933153688469512, 0.8984254849566681, 0.79885298206583, 0.6848830168094951, 0.5593228832869567, 0.4251902342954755, 0.28566917326439534, 0.1433847500618212, 0.06731986992565857, 0.13599167995875278, 0.2073880272837421, 0.2835031720821861, 0.36666269911307925, 0.45966802021116443, 0.565280037798766, 0.6895657898346136, 0.851624330252573, 1.0494872489069722, 1.2350482810974772, 1.3162168394966913, 1.201704777050549, 1.0645878400935307, 1.043804817798318, 1.2246965884935097, 1.1988631780086196, 0.8766673489231664, 0.6274709676870157, 0.5599040430364614, 0.6387720075617878, 0.7785518578913109, 0.8831728376785624, 0.8787700413588683, 0.8194759720012227, 0.7460630241648194, 0.6619987091801238, 0.5668420419643612, 0.46299793514543347, 0.35253082465815155, 0.2373561431219788, 0.11933003433013545, 0.05836257438946372, 0.11790735427769763, 0.18013664408178628, 0.24653257972167025, 0.3190592855071049, 0.3998817807380914, 0.4912059221002378, 0.5961447499317297, 0.7203056797460236, 0.8550252365267613, 0.9684792544094327, 1.0240806095276362, 1.0109640928031174, 0.9592463682074481, 0.9288018683734517, 0.9694099765317082, 0.9517458599289899, 0.7945537552402754, 0.6308007494304128, 0.5599487167195066, 0.5783196612907099, 0.6375208572962463, 0.6858392789504983, 0.6858319464041238, 0.650700345323161, 0.5979532894314069, 0.5325317777259512, 0.45704748256887534, 0.3739480314486261, 0.28514859172273405, 0.19225756728726195, 0.0967485006062152, 0.0481656425062368, 0.09745789453439697, 0.14886687228417295, 0.20378710300292519, 0.26348052632185, 0.3294094719378752, 0.40276569746511204, 0.48442403481053664, 0.5738644318506569, 0.6631768491434729, 0.7361243442501473, 0.778599311807857, 0.789742625413092, 0.7754195179733036, 0.7542538370383635, 0.7462721763596941, 0.7195433292534603, 0.6408361548014658, 0.5493398394736928, 0.49680219458308555, 0.49002097660270716, 0.508342952699242, 0.5256051765655471, 0.5227070128460497, 0.4993395081524276, 0.46142080917847667, 0.4125040237192743, 0.35504189981159584, 0.2910901126907158, 0.22229959141849595, 0.15004299955256978, 0.07556283401403206, 0.037055520866257595, 0.07487121516205798, 0.1144384707676309, 0.1564812738164873, 0.20203005593065196, 0.2517601019964101, 0.3061794670523527, 0.3650337819771907, 0.4264468731010704, 0.4851293578401294, 0.5330340063187688, 0.5638025290693484, 0.5771622963010189, 0.5747471401985648, 0.5624435759013819, 0.547138502707223, 0.5220137645516865, 0.4776992873022094, 0.42756853118729277, 0.3933916446970634, 0.3808974846731681, 0.382316696119574, 0.3851945773303791, 0.3796694245965291, 0.3629150949761319, 0.3361899470249469, 0.30131401802745544, 0.2599244336778456, 0.21348260058271945, 0.16323983638520542, 0.11027481407638964, 0.05556800957973218, 0.025097825087925022, 0.05080706983974277, 0.07754156547432965, 0.1060221624811026, 0.13659090559500928, 0.1697885269295227, 0.2055370441705339, 0.24344215771320737, 0.2819038679536366, 0.31786882549122314, 0.3473250007256762, 0.36724616722121733, 0.37715690020127285, 0.37769837860699307, 0.37100971765316276, 0.359491541964418, 0.3419804568493151, 0.3169381209687134, 0.28995101508815646, 0.2696438851074919, 0.25917616688513123, 0.25574195600027866, 0.2537261314830783, 0.2481754026409931, 0.23682721330801892, 0.21954445708830098, 0.19704654635374932, 0.17022254735734257, 0.13998056134122216, 0.10713072343973859, 0.07242624298370669, 0.03650202460717265, 0.01270662825673901, 0.025627699588869412, 0.039181951647653826, 0.05345946751686553, 0.06887351657485336, 0.08537476438958325, 0.10313319210415442, 0.12161881507821756, 0.14016147412831148, 0.1573119279408083, 0.17140144867175985, 0.18116861142523183, 0.18628671595373408, 0.18698868323155757, 0.18402742978397177, 0.17821018505847022, 0.1695276814568414, 0.1580876085348385, 0.14609384856535867, 0.13660483101602855, 0.1309301893611631, 0.12815124368020203, 0.12611953628725978, 0.12277234028173802, 0.11696273790558503, 0.10844413088573604, 0.09737962856137158, 0.08419402357289903, 0.06927735466557856, 0.05305755680450321, 0.035873617122462224, 0.018094699763919093, -0.41660034225741893, 1.0439533812100463, 0.0056704842510277315, 0.01127967740718464, 0.016899172889939036, 0.022391582241110892, 0.027820144126814907, 0.03303628954300428, 0.038068480168284444, 0.04276147203988317, 0.047103666241353224, 0.05100212737703226, 0.05437835743913898, 0.05727238814926246, 0.059620278723872384, 0.06148701436218618, 0.0628361920535965, 0.06361822761538677, 0.0638778643070247, 0.06347969328984, 0.06246073277386374, 0.060721055162690094, 0.05826769741327276, 0.05514095568696366, 0.051419798106042976, 0.04716789329273865, 0.04254169174554949, 0.037584243288666976, 0.032453299661095523, 0.02715209270369102, 0.021794071770040325, 0.016364691977576548, 0.010923806286428295, 0.005462356917014994, 0.011331887082770883, 0.02265756106236649, 0.033860818550091744, 0.044966328783905773, 0.055813028064381945, 0.06638245430987497, 0.07646125968955894, 0.08597948484955299, 0.09471229826828782, 0.10254564285298642, 0.10937183227236001, 0.1151059571404275, 0.11984266080135758, 0.12357563318437766, 0.12628576446352183, 0.12791170309354394, 0.12840974051411858, 0.12769982524151446, 0.12568249468830023, 0.12223072894363288, 0.11728504478875867, 0.11096631647054954, 0.10340915101339372, 0.09482851705896267, 0.08541767809722173, 0.07545847063828376, 0.06506644574329419, 0.054452739935959324, 0.04365120575068422, 0.03279088029823731, 0.021868915138816586, 0.010940375032986723, 0.017085799102499945, 0.03411173165072867, 0.05105065698943265, 0.06778486983555063, 0.0842485235705768, 0.10023107512183263, 0.11560203792631225, 0.13004215851986997, 0.14334782671274632, 0.15523969219874534, 0.16551844608020927, 0.17412739360859564, 0.18118330040386788, 0.18680510776591, 0.19093358782896883, 0.19343677493633518, 0.19427495873378614, 0.1933374994302081, 0.19044404110985513, 0.1853130468511704, 0.1778124587892708, 0.16816203768704693, 0.15658984918743102, 0.14340268300101117, 0.12902912679734324, 0.11380323619384464, 0.09806857135813532, 0.08195415300592958, 0.06568677284062062, 0.049287518369173264, 0.03287601900747356, 0.0164333537785815, 0.022894939751059995, 0.04573878224858223, 0.06848205813433993, 0.09102458902062108, 0.11322627983030277, 0.13490985086514082, 0.15575357522232372, 0.17544878138711623, 0.193554642906643, 0.20967545879325106, 0.22346926115510224, 0.23485348072493545, 0.24408612997919665, 0.25151738522242084, 0.25708095365723366, 0.2605756995288369, 0.2619221141483847, 0.261031537540585, 0.25752452911800416, 0.25080005872788036, 0.24065618296323338, 0.22745151246663234, 0.21151275633288394, 0.19334854505134566, 0.1736148807825702, 0.15288573183367182, 0.13150945273677306, 0.10980962120298793, 0.08787913566139467, 0.06592499973347163, 0.04392487790353839, 0.021964596258539304, 0.028778980647107464, 0.05754523925557052, 0.08621156216799003, 0.11472925753393694, 0.14291840579759355, 0.17055804264242247, 0.19729739100919205, 0.22263932427063035, 0.24595679769165701, 0.2665111525069077, 0.28377870355825746, 0.2976656688189741, 0.30864629065287863, 0.3175678738660068, 0.3243999081826648, 0.32895065431545506, 0.3312406586703878, 0.331190585363901, 0.3277470223704082, 0.3196523956758407, 0.306780207505929, 0.2894676562815859, 0.26863296577521717, 0.24495547767502954, 0.2193926955280515, 0.1927687615496072, 0.16553540788423982, 0.13795785503735059, 0.11031662560196889, 0.08263381623448608, 0.055052122719708184, 0.027497336615478655, 0.03475387662590939, 0.06949626170374963, 0.10425074250286828, 0.13890411705388203, 0.17336138849218574, 0.20732557596679901, 0.24036700563311322, 0.27191282899389607, 0.3010342692913825, 0.32628196898216627, 0.34674728802123495, 0.3624027003687413, 0.37417120220982686, 0.3838287092027591, 0.3914479519030286, 0.39680830638046877, 0.40053480638739586, 0.4030114083341191, 0.4011374901247585, 0.3922908005781441, 0.3767198739282487, 0.3544390267681379, 0.3280185231145524, 0.29828346227488, 0.26638408193972213, 0.23350789752890436, 0.20007008174635862, 0.16646213093550283, 0.1328541825037623, 0.09944898477322592, 0.06616844106348714, 0.03306025685377361, 0.04075541713932338, 0.08158027340126156, 0.12249124834477945, 0.16349515210995527, 0.20446670392461572, 0.2451129060030483, 0.2848284221073207, 0.3229884819774912, 0.3585559642091587, 0.38884050425169797, 0.4119467799927944, 0.4279869972761303, 0.438846201254134, 0.4479801625043958, 0.45581677258152936, 0.4613600699225511, 0.4661423369416287, 0.47310414607814655, 0.47521012779380833, 0.46649043949738567, 0.44913691739835226, 0.4216027681144826, 0.3892495413638958, 0.3531556923627547, 0.31450776851494644, 0.275042160269624, 0.23505103820452064, 0.1950966414893353, 0.15547481110294883, 0.11619229328286759, 0.07728357534079203, 0.038569053056235106, 0.046760139155534806, 0.09367182366115644, 0.14082045256432774, 0.18827315204097617, 0.2359557989263954, 0.2835201248335797, 0.3300306523617957, 0.37455991913635406, 0.41656691749595415, 0.4522440420108892, 0.4776635798813235, 0.4925413301814796, 0.5006507997037241, 0.50823450548564, 0.5152677513597684, 0.520076599147313, 0.5242704517938133, 0.5351629382820547, 0.5427753054056513, 0.5354696061092081, 0.5191774061981509, 0.4886001936515397, 0.4520144836890183, 0.40947323878030756, 0.36358023384270255, 0.3170777921033763, 0.2701284368862645, 0.22361346577333058, 0.1778741611189858, 0.1328162169077686, 0.08824248914154317, 0.044048702139385776, 0.05271487462525525, 0.10562112335125817, 0.15899536297989494, 0.21291609514497511, 0.26736148783808156, 0.3218060047218096, 0.37475984674290447, 0.42442255720296823, 0.4712875571624341, 0.51217520717886, 0.5403181786194282, 0.5537031779383873, 0.5587590699321218, 0.5655278620083692, 0.5688959229686839, 0.5706546685399022, 0.5735502653867882, 0.5835114016378442, 0.5934105187269647, 0.5897951821687176, 0.5791863882502457, 0.5522788094324661, 0.5153387460491341, 0.4660813169751574, 0.4120997144468251, 0.35843694684920874, 0.3045254232647254, 0.25149979131811595, 0.19983152348154726, 0.14907602936561154, 0.09902261865140825, 0.04938919706391368, 0.05845741200252633, 0.11730554799536863, 0.1767222968926912, 0.2369799207962376, 0.29809330259969574, 0.35916745687157847, 0.41775737611529273, 0.4707149771042705, 0.5192713022102987, 0.564032139432401, 0.5955344845336014, 0.6087484287135859, 0.611398699332217, 0.6162337153116555, 0.6148162094037474, 0.611197320760588, 0.6107873391652822, 0.6163461483378141, 0.6239283928053527, 0.6250286973101878, 0.625247419073633, 0.6105351438295706, 0.5727440310763614, 0.5177642141084926, 0.4563619961158942, 0.3968083060821627, 0.33703727255509625, 0.2782239457225518, 0.22104498449426457, 0.1648742129844378, 0.10946151232155248, 0.054611325890281975, 0.06402642476725738, 0.12844085137644262, 0.19371584395647667, 0.25999616283452126, 0.32738454471567147, 0.3949552832697471, 0.4585896951535448, 0.512775292366564, 0.5598543748277948, 0.6060429136889856, 0.640513880703814, 0.6555025624707465, 0.6568540873203985, 0.6568766177096221, 0.6479680884930351, 0.6411818615449478, 0.6349163866595651, 0.6338384286214518, 0.6374542169402142, 0.6413975245160213, 0.6494535286894657, 0.6462749607707662, 0.60972708357656, 0.5556099804126013, 0.4922996659437783, 0.43000986446685735, 0.3667617840811529, 0.3034849603225697, 0.2413122197861888, 0.18003124037441062, 0.11954579441845636, 0.05962024800072441, 0.06911748553984919, 0.1388696550087243, 0.2096324031242593, 0.2815728841464691, 0.35447036998808223, 0.4281892768709195, 0.4974456617508468, 0.550521263862695, 0.593504392140455, 0.6385430763070902, 0.6742154926720751, 0.69171072423919, 0.6911762192003515, 0.678492213147936, 0.6502219872647256, 0.6580192984005583, 0.6431458238944551, 0.6327695699890449, 0.6339387109602874, 0.6416680480942261, 0.6534799734271882, 0.6553271730719682, 0.6259833644867774, 0.5795198143564786, 0.520789672806033, 0.45871189492402126, 0.39406511353563484, 0.3273801802943083, 0.2606259718837771, 0.1945299805364826, 0.12919574869977843, 0.06445135267457693, 0.07379520209598382, 0.14828105076811623, 0.22407550527239395, 0.3012191080537458, 0.3791009219350592, 0.45719429922139687, 0.5293842099046803, 0.5809332058986029, 0.6199099485692356, 0.6616692317105183, 0.6957865628727037, 0.7140039367977159, 0.7085715274037445, 0.6760115013866156, 0.6346518134886132, 0.6633303043081511, 0.6269765505706829, 0.6037273994454685, 0.6095401100705825, 0.6278685070665283, 0.647086015089095, 0.654377868738493, 0.6356650685397798, 0.5996069020163961, 0.5468540081717931, 0.48577742144850133, 0.42004573452343114, 0.35019136244427795, 0.27911745041886216, 0.20842269284772552, 0.1384433947081087, 0.06906407643412463, 0.07775605541729899, 0.1564235272009355, 0.2366256826549182, 0.31825968303343405, 0.40000060361923534, 0.4797660481134623, 0.5504125861013027, 0.6013962507863694, 0.6386302596493384, 0.6744969706959675, 0.7016824472991325, 0.7116653946866061, 0.6992150702132972, 0.6733342259576878, 0.6480317137173564, 0.6293150631793119, 0.5846065342366491, 0.5410975576930412, 0.5559581493819135, 0.6035314553201558, 0.6379656606108461, 0.6553560153204712, 0.6502230182697829, 0.6232972454671589, 0.5746818906738139, 0.5135124927941986, 0.4454747213358921, 0.3720982381665415, 0.29680912555460903, 0.22169387533150642, 0.14725053859641846, 0.07344265514237322, 0.08094147029206691, 0.16297555678490355, 0.2470273654333704, 0.3329635096315113, 0.41809839704183394, 0.49789596994280755, 0.566726218379651, 0.6175919916382637, 0.6522594763841278, 0.6778186442721612, 0.6816130745404719, 0.611416602734955, 0.6587058489304438, 0.6533072443603443, 0.6295555978168865, 0.5921852701522438, 0.5301754884964783, 0.4444190468464814, 0.44450642646546207, 0.5724399918403548, 0.6305904553006072, 0.6619187318585346, 0.6705488363940112, 0.6503081933550764, 0.6041620444966919, 0.5419069437458189, 0.4704706167495231, 0.39328016028368634, 0.3137558421107481, 0.23425542939639662, 0.1555257688046058, 0.07753825376519419, 0.08310560968067209, 0.16754630979305138, 0.2547362503987381, 0.34540926510853975, 0.4361463049145889, 0.5173359161554872, 0.5847149748246188, 0.636050984825029, 0.6675532646123898, 0.685842738667889, 0.6888006725647061, 0.6618031242733775, 0.6624808808396303, 0.6483917800769993, 0.6179628138574733, 0.5707463497474605, 0.502657658063629, 0.4215428007398572, 0.48822819059016653, 0.5734258312904589, 0.6329321243892003, 0.6719402671589273, 0.6898090122885719, 0.6752179709594948, 0.6308217171442851, 0.5678152383311754, 0.49370599784262237, 0.4135254689444774, 0.32994273068502483, 0.24600093089688008, 0.16311987044166074, 0.0812684395292359, 0.0839755704443678, 0.16947070888301655, 0.2582236471998425, 0.35204252572761946, 0.44878462333488034, 0.5364081515078194, 0.6049860264318142, 0.6554543714689408, 0.6805910761458553, 0.6975052930033175, 0.7051578326386679, 0.6952834569307026, 0.6809876495358341, 0.6569760377252768, 0.6195889770846392, 0.5663578415381758, 0.4960648473637372, 0.4191945966097699, 0.5098840059392109, 0.5853304239648452, 0.6395968627678766, 0.6784484639461151, 0.704334213155946, 0.692148534312235, 0.649591180923338, 0.587457850213194, 0.513155318621539, 0.4313539075465526, 0.34447772701824003, 0.256514812464038, 0.16976740958959693, 0.0844759494638741, 0.08332878421808268, 0.16812544711568095, 0.25599785626781607, 0.3484530439237654, 0.4439552065787865, 0.5334669313431833, 0.6055574617979932, 0.6592253877766308, 0.6828943015866599, 0.7034471367717469, 0.717232719037415, 0.7210466610185724, 0.7029492323759173, 0.6738851490135654, 0.632699071818519, 0.5772984150996956, 0.5200614136757832, 0.5119480452588652, 0.5603459843513368, 0.6100738968660695, 0.6511471323337252, 0.6816759535875185, 0.7069105808148998, 0.6985510728510973, 0.6608538376176709, 0.6029902640086725, 0.5315840944793299, 0.44765695629737257, 0.3569790671524152, 0.2651340324290149, 0.17500480869829899, 0.08691995748904832, 0.08124240646383331, 0.16370088796289456, 0.24854485991367045, 0.3363098890318865, 0.42522177054145616, 0.5098518099847796, 0.5836806360892213, 0.6399058305298891, 0.6747560342049571, 0.700989521473094, 0.7225784191663566, 0.733917999384533, 0.7241634299099493, 0.6940465318386788, 0.6517605807902518, 0.5850622208205624, 0.5519885806707596, 0.5758345517803456, 0.6066546473973443, 0.6381784200770562, 0.6663980941373069, 0.6887244535986625, 0.7052474995655288, 0.6997726220016413, 0.6667601221457119, 0.6176815003234156, 0.5522386264012512, 0.46479750951054105, 0.3672655023931017, 0.2710214782048545, 0.17819127034240903, 0.0883063997076397, 0.07801594122994399, 0.1569515032458452, 0.23757229379210232, 0.3199791028970678, 0.4027764439652052, 0.48268649178256623, 0.5556933092748217, 0.6165662227208931, 0.6591602418550717, 0.6917809011081418, 0.7229412867739, 0.7437751787863314, 0.7407645857512247, 0.7114665337752125, 0.6787656743674991, 0.6390120786365624, 0.620670306522431, 0.6290263835302163, 0.6469494064570912, 0.6659396668961896, 0.683836404939217, 0.6972678292283824, 0.7043704444045705, 0.6953684835099824, 0.6656417850662156, 0.6287524222444407, 0.5725953083925052, 0.47928012663707575, 0.37315298217244114, 0.27271868091199436, 0.17845305854670013, 0.08823978003221525, 0.07397109900023166, 0.14861143482720915, 0.22444545160253204, 0.3014952409140821, 0.37885154902032236, 0.45457604175152133, 0.527388597000078, 0.5917535754774527, 0.6410266025646184, 0.6805005626130178, 0.7119872515251995, 0.7281989169332685, 0.7268669128563555, 0.7112678504634444, 0.6915609988114368, 0.6718665595204804, 0.6633860114670141, 0.6650752090281354, 0.677547037550991, 0.69004911016023, 0.7007899198392944, 0.7047696037752991, 0.700787796640086, 0.68318927804541, 0.6546080041730581, 0.6259826743536396, 0.5864271437533457, 0.4835424996043849, 0.3698983056961104, 0.2680480216913071, 0.17476719814149005, 0.08629136978321239, 0.06935434430098456, 0.13922887071777532, 0.21001539370837322, 0.28184200856296243, 0.35432967109905666, 0.4269837906196305, 0.49922755308309585, 0.5653935000911761, 0.6211225884896184, 0.6656076676748873, 0.6956442656307343, 0.7092964023560437, 0.7104305945435305, 0.7036576681294461, 0.6944705636443234, 0.6852038031086122, 0.6815015678402848, 0.6832122303168263, 0.6930318898436151, 0.7062817479503908, 0.7141281247079152, 0.7074920753824318, 0.6925408220447337, 0.6619814907162352, 0.6257623449421617, 0.5876650639178416, 0.5379520112272899, 0.4511685038952861, 0.34973032180080826, 0.25469653527107095, 0.16642298858794036, 0.08225493740324058, 0.0643291393248523, 0.12907845068424337, 0.1946723657797874, 0.2613430785920212, 0.3292022860982251, 0.39869413110637814, 0.46898208821317994, 0.5360420513759084, 0.5987969039426515, 0.6489638482316131, 0.6773114195941231, 0.6906150891923402, 0.6941394421636481, 0.6930455545533104, 0.6908600859247054, 0.6872021797535184, 0.6831635225618633, 0.6819540001548313, 0.6871932640366666, 0.7009743448079626, 0.7111324846600057, 0.6950777899986006, 0.6726782120331753, 0.6310840566391485, 0.5854858341340855, 0.5359363845812963, 0.47811756617534823, 0.40366973236363385, 0.3185181544477344, 0.23453917815105615, 0.15415151128069807, 0.07640696179403189, 0.058925030973537205, 0.118288658024856, 0.17842564541942707, 0.23976857684451192, 0.3026560173406997, 0.3677083096767685, 0.43471842980106484, 0.5022428576158419, 0.5710349633340212, 0.6279290692613956, 0.6556001606052695, 0.6718057626205977, 0.6761609615687583, 0.6786049720931325, 0.6817596671151994, 0.6823945044631821, 0.6744392574518819, 0.666659247032449, 0.6618358772540249, 0.6623487093331235, 0.6612451896914856, 0.6483573820879591, 0.6282338003996498, 0.5868440147680201, 0.535898221256797, 0.4818082498670383, 0.42234998459822043, 0.3558284795415742, 0.28366281629685813, 0.21084826430540018, 0.13941373251969627, 0.0693242872731254, 0.05323566786191932, 0.10681237433140674, 0.16122253389720684, 0.21678567420820088, 0.2739976593223597, 0.33340595323112915, 0.3954193008209996, 0.46065152572686324, 0.5303224357670634, 0.5922195301459562, 0.625532295382444, 0.6535382110475684, 0.6518876219422342, 0.6562310132490989, 0.664825990143883, 0.672357264901449, 0.6549412763604417, 0.6379462142727511, 0.6225313268815166, 0.6128130566765423, 0.6038736559091531, 0.5896561381399206, 0.5676221587521806, 0.5294747987104164, 0.47795766231964226, 0.42470167094416383, 0.36935289244809943, 0.31039302752989917, 0.2486306049189565, 0.18593546015718898, 0.12349759441709258, 0.061576940938917524, 0.047190942773234115, 0.09476611853365513, 0.1429886349311439, 0.1923405213916593, 0.24315149893346505, 0.29592103812927434, 0.3511246671665389, 0.40966120922682725, 0.4725348009833423, 0.5315526177575278, 0.5727146156787016, 0.606050798905731, 0.6078734600108997, 0.6169916088341508, 0.6307613467370164, 0.6523644907246157, 0.6249443616364265, 0.5943571282254125, 0.5696520097600731, 0.5526549045287142, 0.5371879546395854, 0.5176980006740585, 0.49377137003000304, 0.45863801642085184, 0.4139404759939053, 0.3667098853884813, 0.3180592183932028, 0.2671220330971781, 0.21448442366346498, 0.1609781256721763, 0.10723754819620819, 0.053574794164539974, 0.0409259838116404, 0.0821045256188947, 0.1239136613861245, 0.16658412258622543, 0.21048102491155177, 0.2559056538365883, 0.30312174156536903, 0.3523192989966505, 0.40377535706670514, 0.4523970558460653, 0.4900479462047752, 0.5175740439573051, 0.535713557901418, 0.5505329560223085, 0.563683506942908, 0.5779807233837212, 0.5588129542206147, 0.5273500364077998, 0.5012317070532141, 0.4813336417558857, 0.4625024490316836, 0.4408312723410072, 0.41658524340046993, 0.385694516332885, 0.3490119154793068, 0.3096571652992491, 0.2684898148472161, 0.22559414709291262, 0.18141791184290434, 0.1364388794075011, 0.09107430163651956, 0.04555217375099472, 0.034380591637989295, 0.06902180885791181, 0.1040838454622328, 0.1398532272788849, 0.1764947099491363, 0.21419357347817816, 0.252963015578404, 0.2925819969990261, 0.3325561534469553, 0.37006394522219016, 0.401211157688788, 0.4258102251535533, 0.44615984494266153, 0.4614221999438114, 0.4708558763173624, 0.4747538999679015, 0.463065585467179, 0.4420620275591373, 0.42101247225099997, 0.4025106240861281, 0.3841458433092173, 0.36387969381508345, 0.3417077401539812, 0.3157427175252064, 0.2861688757307364, 0.25430269286208007, 0.22065013815271342, 0.1855560336777961, 0.149376903190423, 0.1125078161772811, 0.07518126717559162, 0.03763786863581802, 0.027702022222059496, 0.055543566503218844, 0.08375248756672993, 0.11241539545724395, 0.1416862926225522, 0.17158964586422784, 0.20200836150161908, 0.2326201687225317, 0.2627386750797276, 0.2908241677948349, 0.3151582711662305, 0.3353768897486689, 0.3521811500456918, 0.3645297396648254, 0.37118036481536304, 0.37174513130783515, 0.3644853884589479, 0.35130538953185014, 0.3360470328355454, 0.3209885797342541, 0.3053853599304707, 0.28840752282808124, 0.2698574294484174, 0.24902354923561743, 0.2258549317823708, 0.20086708229794573, 0.17442249398604867, 0.1467880352098662, 0.11829531375820897, 0.08915958683772066, 0.059633913361896294, 0.029871494610228852, 0.020853441679352488, 0.04185169505568703, 0.06303733470338718, 0.084565314794926, 0.10643269185369512, 0.1286512829620727, 0.15106835960654968, 0.17337292541922344, 0.1950235391370093, 0.21516540835521916, 0.23295568659811608, 0.24796555333385484, 0.26021328319435455, 0.26903847370682604, 0.2736536085847869, 0.27376176253325896, 0.26928281375668095, 0.26102359179457163, 0.2506564052257748, 0.23951227406078246, 0.2275888415303829, 0.21461464048305814, 0.20042707918215788, 0.18478251000782112, 0.16762088903932665, 0.14913628654353223, 0.12956790432591384, 0.10911924698389382, 0.08798194640336895, 0.06636246125641554, 0.04441010883017222, 0.022245709906712034, 0.013959765564107935, 0.027960713930712762, 0.042135472693749884, 0.056455066584964124, 0.07100278436851999, 0.08569092542100434, 0.10043681149853817, 0.11500361133719171, 0.12904741384125726, 0.14209664596446955, 0.15369677868030787, 0.16352706604444978, 0.1714385526929944, 0.1770557001248047, 0.17999866432989847, 0.18012430282740927, 0.17753073321522547, 0.17263392724398482, 0.16620471782981816, 0.15892729628088367, 0.15095270080326273, 0.1422455992986455, 0.13270625715277942, 0.12228069948773576, 0.11090907368986595, 0.09871357332903084, 0.085783137568636, 0.07227275359402474, 0.05830077726043398, 0.043994362302047, 0.029441885231472172, 0.014765362918331807, 0.006976557139227051, 0.014016471443497918, 0.021078650484247497, 0.02826220217577785, 0.03549577219682815, 0.04281858982667829, 0.0501218660802137, 0.057320346990760884, 0.06423093227602142, 0.0706554411465612, 0.07636666014080447, 0.08121792563395404, 0.08509421555981701, 0.08783113934728608, 0.08926818823439925, 0.08936397375667622, 0.08816596164979867, 0.08587373314839111, 0.08279946479514001, 0.07920822627738139, 0.07523432323432111, 0.07085894419411663, 0.06609753133802014, 0.06086433287859533, 0.05521775753327554, 0.04913497573216645, 0.04271762974529017, 0.03599201698236365, 0.029045681328876482, 0.021915003792314387, 0.014682321219891615, 0.0073475235447039685, -0.429719734190616, 0.5913564056470484, 0.7224070902087865, 4.8771777582271e-5, -3.5430749346480894e-5, 7.145212850668355e-5, 9.523859703336848e-5, -7.463402408496118e-5, -0.00013704996559742752, -5.525156521259365e-5, -7.22428745570976e-5, -1.962237241142358e-5, 4.235483342680529e-5, -0.00012690973024109307, -8.257158690266794e-5, -4.3004061158934244e-5, -4.5490685211791326e-5, -0.00027085709168425497, -9.221052264608853e-5, 0.00018274997901422782, -0.00012080047299262493, -0.00047576430448019756, 0.0007601285884884592, -0.00021098860875204823, -0.00011458895146513015, 0.00034157212364659535, 0.00017033427392668435, -1.3771531792191955e-5, -6.374016233979954e-5, 0.00047448558217453647, -9.393076966282817e-6, -0.00016766958569671702, 0.00030139374268996157, -9.338371644993665e-5, -0.0006507913421337786, 0.0004511653305560863, -0.00045947881611714514, -0.00011115444350679098, -0.0003386973578704192, -0.000135869184362514, 0.0007303910590216706, -0.0004662172596661641, 0.0004193756474685948, 0.0008174531105471417, 0.00023161180705457446, 0.0007919249882060482, 0.0006431690151931424, 0.0002115691874771482, 0.0003831437401871663, 0.0010186035021194047, -0.000908857331789128, 3.435594660788079e-5, 0.0007342861265024315, -0.0009055181479096236, -1.744288527188752e-5, 5.2713818048697136e-5, -0.0007627628395659166, -5.408264582952654e-6, -0.0008633187967606165, -0.0003006098103188151, 6.558972148039736e-5, -0.0009082358245358223, -6.160659942540096e-5, 0.00021149457814165494, -0.0005370737500146981, 0.00029941768325038407, 0.0002945499312199859, 0.0005543178606889338, 0.00042940640950305653, 0.000329739186049008, 0.000513046971380892, 0.00019751869999361447, 0.0004276156187073116, 3.554794940027737e-5, 0.0003218567902881483, 0.0001675326900673016, -0.0002596529883541039, 0.0001808945698420268, -0.00020608502376589873, -0.00010359538639778841, 0.00032492745675573824, -0.0004595591151317548, -0.00018170877324958222, -3.472891595161326e-5, -0.00014869791276023522, 3.08545369825969e-5, -9.905840422057276e-5, -3.894851716133717e-5, -1.344061516488242e-5, -0.00013463359740962177, -9.929988784308608e-5, -3.4901482270682824e-5, -6.246677786597098e-5, 7.614716600425197e-5, -0.00012538679050683475, 2.0618873645062067e-5, 7.339774091141117e-6, 1.6125996457826136e-5, 1.7766351296411396e-5, 2.521340336065536e-5, -0.00010644039180383286, 7.599721011688106e-5, -4.6789016702437355e-5, -0.00015080645871316307, 6.85634799680182e-5, 1.3207638644942591e-5, -0.00019173883856841284, 5.784196503458115e-7, -0.0001731872574493522, -0.0006210753554747897, -0.000351767109276771, -0.00020748104924422987, -0.0003919286828039679, -0.0003862595848792299, -0.0001868896523937218, 0.00010454146614248858, -0.000288024143106705, -0.00031163551903980435, 0.0004772599507725421, -0.00029388521715812755, -0.00022719057455970255, 0.0005680784563848772, 8.600572999656905e-5, -1.267025240497137e-5, 0.00010818445938845129, 0.0006523065983460548, 7.747557367684098e-5, -0.0003488355856764444, 0.0005856273230759829, 3.705403717667832e-5, -0.0007473979899882826, 0.00045108603383420655, -0.0005657030279018777, -0.001106901625301635, -0.000626085116637074, -0.0003492205087129636, 0.0013362457802510428, -0.00046116175428107534, 0.000144453876050874, 0.0018425619258712284, 0.0012430790179982693, 0.000558580991585239, 0.0022621637888725404, 0.0031793691476152534, 0.00010476906881651772, 0.0017134181544437566, 0.0003501796824187391, -0.0004319933760018764, 0.0021473520231088793, -0.0014693333398875102, -0.0007668860892192391, 0.0010464112292066703, -0.002229713687053512, -0.00019979346289498637, -0.0016211643981967794, -0.0010793716341819285, 5.696260722858123e-5, -0.0012258926425793432, -0.0002439265346160197, 0.0002341036103289045, -0.0008971794927334645, -0.00021867043459286643, 0.0006315376211587306, 0.001004620661894321, -0.0003291260559040833, 0.0006996819334904103, 0.000653050657651036, -0.0002450568076892324, 0.0005672843362226138, -8.201582188665385e-5, 5.644393646254442e-5, 0.00042981620579938303, -0.000390734831657851, 0.00041797781026825753, 2.7502813333781853e-5, 2.366608442456044e-5, 0.00035142734013068736, -0.00025391651846932083, 0.0004291026464722058, 0.00019866994999755665, -0.0001083809955490686, 0.0001617751525449753, -6.651835921110882e-5, -0.00018429964749164056, 2.5119296107404548e-5, -9.016647025095058e-5, -0.0004752543625513205, -0.0002772138461072809, -4.38139178447765e-5, -0.00011414551409287481, -5.8935804707740314e-5, -4.4904512416334166e-5, -1.977111625153216e-5, -5.214077900466191e-5, 1.855827299367932e-5, 4.5144098884514346e-5, -6.890101525347274e-5, 0.00013813349667241769, 8.187098698558378e-5, -0.00013819505230038828, -5.4345488230731704e-5, 0.0001468779016794579, -0.0001954922685093862, -0.00010026580524703506, 8.88111411990989e-5, -0.0005634125864588722, -0.0006516905602302284, -0.00019625370699364418, -0.0003615225384603948, -0.00021522117956391574, -0.00033885162577868, -0.00012778446480338025, -0.00031417845657769826, -0.0003666215422978026, 0.0001924408234132878, -0.00023781061598787242, -0.0003580001077219523, 0.0005349149960438686, -3.0064805563780086e-5, -6.480745949803472e-5, 0.0004493501853139063, 0.0012622829507146303, 0.0009745359076630245, -0.0015820871390968222, 0.0026522261811776403, 0.0007440273716639771, -0.002210513879778987, 0.0008600205890876689, 0.00024072973850044238, -0.0023848284397619, -0.0022286951448276422, -0.0008469889453671209, 0.0026045947656274907, -0.0014170024065561751, -0.000483513198456747, 0.002880472078311244, 0.0018889508460656161, -0.00030239422925982124, 0.002176849234306361, 0.0034644348348347406, -0.0007172396761610291, 0.0031106203447735137, 0.0037877359944312613, -0.0013415977367558494, 0.0035729140005088564, 0.00032551057617138485, -0.0025256885245700626, 0.002815039668803738, -0.002649904427823674, -0.0017192677871268646, -0.0035337000976114405, -0.0027947952642151082, -0.00028357291967902315, -0.0024682794072100204, -0.0005491505326158296, 5.281106022133739e-5, -0.0020834333742716076, -0.0012810141240823547, 0.0003931442973124162, 0.0007382299413625149, -0.0014711975867454997, 0.0008924813580885775, 0.0004911058329915973, -0.0014145947175740546, 0.001074477238780009, -0.00043388506777359523, -0.000505131668993859, 0.0006552244442003238, -0.0004521941507647907, 0.0003845166841909268, 0.00023047158737553685, 1.6914838060584818e-5, 0.0007003917391421705, -0.0001519724345027886, 0.0004919771485265145, 0.0003193745475488187, -0.0001524864171226968, 0.0004144468172237227, 6.147430274577616e-6, -0.00020163791757063566, 0.00019085337720732063, -6.32502301785753e-5, 2.421750833927934e-5, -0.0003555377715154709, 0.00019869618880754715, -6.370048962808548e-5, -0.00013604555812774677, 1.9864983921714664e-5, 4.59696289994185e-7, -0.00014240311575458835, 5.828018371408204e-7, -0.0009620652180180609, 0.0002530102103345534, 0.0001347599099931354, 0.0005051051585409879, -0.0005331287310474225, -0.0002682208606500792, 0.0002166378974244357, -4.160326242333736e-5, -0.0001945935716466504, 1.9124141334108966e-6, -2.373215627232827e-5, -0.00036715287684905326, -0.0005657203182610333, -0.00036087104329312036, -0.0003998199035632777, -0.000766124795625549, -0.0003256492953804967, -0.00020304425335915531, -0.0010274070826374847, -0.0001619259042440876, -8.516216612993013e-5, -0.0010278490737225712, 0.00010197413421204603, 0.000324929809151615, 9.756458841138112e-7, -7.036487295216255e-5, 0.002197933882443524, 0.002371776457636891, -0.002435346351401941, 0.002471269768793725, 0.0023618879776771415, -0.0035640652217418475, -0.0003179310004175235, 0.0015704698694957609, -0.0031020112864097527, -0.005335402404770365, -0.0014724178938266609, 0.0044078188086753775, -0.00428401739198293, -0.0017981547351115224, 0.006012650712437023, 0.0021584999013291263, -0.0011311788640980245, 0.004662963335531312, 0.005718860766053139, -0.0008109377458960242, 0.003696464432665912, 0.0066098561166462655, -0.0020865731956969465, 0.004617275838320005, 0.0057193434798175355, -0.005829929891316463, 0.003699306730866407, 0.002601666921413631, -0.006947580671934484, -0.004405176886768925, -6.925435542797028e-5, -0.0037749205557079325, -0.005710937825057514, 0.0007495830644261817, -0.004778432741551895, 0.00023051792671423642, -0.0029363520141796116, -4.670135759813271e-5, 0.0018731711649399713, -0.0037800342397329616, 0.0007612607992032336, 0.0002725612454234303, -0.0025003677945348263, 0.0014156633572916253, -0.0008279288410628411, -0.0014792724039734877, 0.0011209399892789535, -0.0009309458086596127, 0.0003666434476444469, 0.0003743758574909173, -3.6975348008616686e-5, 0.001259154861870126, -0.00011550589866210384, 0.0007633511032035479, 0.0004857400848931837, -0.00015798271589147322, 0.0006006991932989411, -6.751792986920267e-5, 0.0002651467592319561, 0.00029098355044231833, -6.567383476943556e-5, 0.00019566976324170406, -0.0005464493723087927, 0.0003205096917346619, 4.957944073179143e-6, -0.0004127649971651904, 0.00016124582300323437, -6.937220091150518e-5, -9.428218738634254e-5, 2.6269743818290586e-5, 0.00032402919211722814, 8.375245559203183e-5, 8.770067032458653e-5, 0.00023932857425020145, 1.2801300914221629e-5, 4.126871655486696e-5, 0.0002745129196543642, -6.804205908802363e-5, -0.0002170660588587938, 0.00018314157112155099, 0.00017309658020763646, -0.0007817406399068497, -0.0006872034647897338, 0.00041331424761855817, -0.0006113310887442598, -0.00115353807000756, 0.00010611086502026513, 6.511757985306333e-5, -0.0028969782385864086, -0.0007534532832330977, 0.00143139649640181, -0.0021386943172339336, -0.001869085218905747, 0.0026038408216246265, 0.00047260012143007394, -0.0033665944638339735, 0.003374864736348562, 0.0035692528729725304, -0.0050857308123719806, 0.0014914342362627744, 0.003909402320349624, -0.005201416757360203, -0.003231055673524627, 0.002186125486222501, -0.0026083367441634125, -0.008698241675230407, -0.001873187903909585, 0.0057392325757482775, -0.007913435720418145, -0.0033572378640335404, 0.010185785768053766, 0.00016938718060662976, -0.0018650389284420605, 0.00967772341863631, 0.006892751437936222, -0.00013133485981937077, 0.006344695199979336, 0.01073658298226168, -0.0016438857863968698, 0.0031894565215413754, 0.011026234300862803, -0.006180836043972681, -0.000574945480627614, 0.008439482315186271, -0.008615712541950515, -0.0027430398478161507, 0.005650702989128889, -0.007527309267629836, 0.0007861917896266322, 0.0061438483133318044, -0.004646094646763871, 0.006529268654711441, 0.002220562699342054, -0.0010585783240877427, 0.00484749970143569, -0.005388768895504345, 0.0012016721741555827, 0.0003902774832294812, -0.005693177566731435, 0.0020681972071627643, -0.0018578387195955267, -0.0035336281105580072, 0.0019388739854442685, -0.0023596875579245963, 0.00022730438759414924, 0.00018626896242643205, -0.00013927731776277333, 0.0014534703201378517, -0.00029648160138581015, 0.001221903750439132, 0.0004535446043230899, 0.00019576962230859521, 0.0006984329640355709, -0.00042975278582730605, 0.0005839886124262359, 0.00018539301173828898, -0.0002878297990999634, 0.00022130062011909766, -0.0002050551598378395, 0.00012418470988832415, 9.36149412217118e-5, -0.000140752269235813, 0.00017741169895897348, 2.9151341967226244e-6, -0.0001510101324584159, 0.00010218366154013306, 0.0003216104474688244, -8.197267734943657e-5, -0.000156413798987537, 0.0004556830073860439, -0.0002760624974200641, -0.00012045654398161121, 0.0004745420014886302, -0.0003346271397877888, -0.0003900369509106444, 0.0003672201629606897, 2.793830548396226e-5, -0.0011345509619355091, -0.000737407384278507, 0.0009981164160914027, -0.00117645811334557, -0.0022020562872537993, 0.0015680228066469056, -0.0001695953430332346, -0.004178688381840983, 0.0006655483966685982, 0.0031024680656560402, -0.002489395819260908, -0.0030040294976314374, 0.005636673889240696, 0.0005924340519973892, -0.0060831605424132434, 0.0052583384851177, 0.003551745230290897, -0.008825334275961357, 0.0014988190345666776, 0.004269056801881412, -0.00803707511048646, -0.006416189675938045, 0.001983882806909995, -0.002630634799868314, -0.0116560446194426, -0.0020636871927089506, 0.007096672541888495, -0.012130286740770239, -0.0038810232802044342, 0.014914124232054474, -0.00374696732026179, -0.0005795445248968688, 0.01654901237335309, 0.0034386184417892355, 0.0029595953231188743, 0.012154192172840729, 0.011842834435531552, -0.0008996913916631343, 0.0017473158575252632, 0.016618241786534576, -0.008199363505304957, -0.006354358692372092, 0.01262245645806582, -0.010963173823252535, -0.004971285905938939, 0.008968509376142533, -0.00904949190218904, 0.0042010899214126205, 0.009028212134955197, -0.004829627288966364, 0.009824963277113916, 0.0051807866034372175, -0.0019039952043724375, 0.009714369189243859, -0.004000833898161834, 0.0018856396493566632, 0.0003827644092596723, -0.009633380093222012, 0.0026994494410119817, -0.003742548309707295, -0.005923291285176965, 0.0017230896142850368, -0.004282102042690116, 0.0004497608519571671, -0.0011952948358602482, 0.0010721016077095225, 0.0025488554846852546, -0.00021131119309323947, 0.0015133515594452451, -0.0003744608086474672, 0.0006333939942042444, 0.0005742369917396497, -0.0009275808275170689, 0.0006339704337479763, 4.8813429369919856e-5, -0.0004048351904828708, 0.0011529805681784171, -0.000420748013404335, 0.00018330263179579373, 0.0001924736675626234, -9.009989961995379e-5, 0.0002617250613437006, -2.5390096713893485e-5, 1.3660134685921298e-5, 0.00021502990016716953, 0.00017406484350871658, -0.00010177638866923309, -7.243948088973243e-5, 0.0003843086066166869, -0.0002738135746872393, -8.930050593940696e-5, 0.0005425559968120375, -0.00045292870216608164, -0.00031802096961870945, 0.0005390341789264258, -0.00046598550026719077, -0.0015254574455290247, -0.000808186776763655, 0.0009918907466871674, -0.001912447029640763, -0.0026388340560376785, 0.0027551648082446314, -0.001209895471554584, -0.0047035433698596, 0.003267631105195397, 0.0027297560942325066, -0.003192146994734903, -0.002277809064245642, 0.008766786494844336, 0.0006238407607332878, -0.008460473334815618, 0.008249240487195489, 0.0030056120306936164, -0.012972603134082257, 0.0027522068998009604, 0.0033312120010832442, -0.012812248044238505, -0.008786787931926053, 0.0012869949105701703, -0.004517182285219582, -0.016631567544562263, -0.0016144256964314102, 0.00867790267560505, -0.017317885999739078, -0.001062013538592033, 0.02010769929110184, -0.007523890275522716, 0.005896176584291088, 0.022149930211970037, -0.005993908717858495, 0.009027787259335503, 0.021027118033483717, 0.0021200695021715175, -0.0007625569115066556, 0.0015411681895705174, 0.02252374472776164, -0.011170206955516565, -0.014397129332676076, 0.01307959524429526, -0.01564658452693243, -0.012193322227974743, 0.01094968248633155, -0.014555576233595009, 0.005821386669050557, 0.013323228122628223, -0.00644049603015404, 0.014879377154378337, 0.008250615822173448, -0.001356092691686073, 0.013253545364703315, -4.310045350925839e-5, 0.005769336158636056, -0.0022044268915206175, -0.011102808875276277, 0.004369260295999897, -0.007940202780845703, -0.004971179186738922, -0.0038903611564306212, -0.0008266510428833633, 0.007282785770915209, -0.0026807862481549424, 0.0042952008414392775, 0.0012021154813115545, -0.000285894884942838, 0.0022150340295118767, -0.0011911429849082288, 0.0008095159173935654, 0.0005634811997068633, -0.0012553711311953759, 0.000655018095341177, -3.0430801010929398e-5, -0.00044417088268783696, 0.0008571121080467758, -0.00010561217357052832, -0.0001290442609989806, 0.00019455780659021808, 8.301899213712073e-5, 0.00042413654742918757, -8.183542028513304e-5, 8.512154924925244e-5, 0.0003205844166358759, 0.0005809293389234019, 6.716399291761765e-5, 7.854986729509564e-6, 0.0006004586592138925, -0.000262173679587804, -5.1616852807284374e-5, 0.0010515091476193841, -0.0008995409911712601, -0.0004210758327938483, 0.0010650851417168142, -0.0017936342832343144, -0.0022689154166875302, -0.0013980692631184962, 0.00017664040153649477, -0.00396874496471312, -0.004032224277657092, 0.0035718325675070475, -0.0034316211901385214, -0.006103101070776031, 0.0059958257190405005, 0.000993338310860674, -0.004390541624913105, 0.0007619400198569948, 0.011037573238098055, 0.0008557142206945342, -0.010249514313004335, 0.012040226617604996, 0.0030147083857083156, -0.017427495419591262, 0.004381048337364028, 0.0023297440190183584, -0.01786290221082991, -0.009773457518216311, 0.0003603731093302244, -0.008319804984149333, -0.021824337813239128, 0.001309373937957183, 0.009810053265608907, -0.023186696596757192, 0.02350957494928672, 0.01103134892599833, 0.010181367773067164, 0.018293038540906754, 0.012333714245186663, -0.016361314393107413, 0.011379364574773735, 0.02015139079758703, -0.014086793745729857, -0.013282108444930996, 0.021860113794323795, 0.0034841408565380485, -0.013520950847122038, -0.02261997512109413, 0.008247350958726791, -0.017687683136823295, -0.02239305740608481, 0.008124735202985825, -0.025349142073242865, 0.0019938567281555194, 0.014800726347955973, -0.011019360128260144, 0.02265655039882174, 0.008656775275273056, 0.0005019084090118651, 0.020087492296807535, 0.0009064725949500922, 0.013310407724920398, -0.010731852043792948, -0.0033095938700722677, 0.007400250053281758, -0.01147676302337776, 0.004800200754346034, -0.004188335291383144, 0.006362337744775989, 0.007712024185778806, -0.0031010228713535984, 0.006435762708736582, 0.0002928454679082836, -0.0008599390705249626, 0.004089460735372839, -0.0019195849902838413, 0.001290466065055049, 0.0012461062996674142, -0.002333485880328861, 0.0012942488719190606, -0.0006726625731831878, -0.0007364848321634854, 0.00034903464618892666, -0.0004985016416872223, 0.00013211057877397979, -0.0003217800908259039, 0.0001982555600887446, 0.0005812326460153358, -0.00017369306722553158, 0.00019309512602061114, 0.00023082490184614455, 0.00045344088425329775, 0.0001824770549800762, 3.74831258514448e-5, 0.0010200785453325745, 0.00021613121972735284, -5.17285458913224e-7, 0.0019857515569661377, -0.0010208578661633724, -0.000409701928871198, 0.001501985160979876, -0.0030013604708127146, -0.0019805462956845273, -0.001797638973801924, -0.003556908139509942, -0.005885876576362357, -0.006043473000501278, 0.0016843252410600718, -0.006559349022385072, -0.009265464564319021, 0.008253713510781774, -0.002315148601303501, -0.007341479124754767, 0.006946673457243267, 0.013200993865486675, 0.0021050200254117053, -0.011518681867885391, 0.01697442513178523, 0.004763896286027981, -0.02188854595667782, 0.005131351156670616, 0.0033426617816741714, -0.021915982286718302, -0.011085326261001067, 0.0012366148951366142, -0.011948314421683776, -0.02535820029895341, 0.02206667780449088, 0.005319844385535312, -0.015246421259401531, 0.011648165238983309, -0.019038470159115323, 0.025507607247123993, 0.021354814485147134, -0.021730846281349542, -0.009104141265757969, 0.008818444216926132, 0.015108618231209237, -0.025077366330621107, -0.01022736776448383, 0.014408625403408325, -0.023560177267146595, -0.013612889015011181, -0.02820027420893457, 0.001877269650542878, -0.015281254778717043, -0.030175078056381664, 0.003485331208661558, -0.032701816736104415, -0.011229124629597005, 0.0029981280619203418, -0.020909610988994957, 0.02605627596283738, -0.007471740305133744, 0.001482779894824202, 0.019476128911840425, -0.02372405270017583, 0.017037504535335528, -0.018237659681703367, -0.0005706814253303459, 0.010140707393442543, -0.012798022329533577, 0.012332719940419028, -0.0040207101931883545, 0.008973066548920834, 0.010245717337798088, -0.004209274136334354, 0.008841814812418332, -0.0002771630114098097, -0.0020829981553286063, 0.005967510502836356, -0.0026937262121024905, 0.0011026661394509774, 0.0022503229342998488, -0.00432744169323688, 0.0007825689963758054, -0.00196384371368151, 0.0003244026124670385, -3.203867171163882e-5, -0.0006589158616363018, 0.000438986521163673, -0.0006737639897881559, 1.8782698825207497e-5, 0.0006004522027901061, -0.0002768701198365848, 0.0005760013651913793, 7.490198048009907e-5, 0.00051757383987315, 0.0005701552977154918, -1.6278795873200835e-6, 0.0012117651911211942, 0.0009472489820427735, -0.00010401310780044456, 0.0013006887957809684, 0.00012297666351246948, -0.0001762496222854743, 0.0026137601250565893, -0.0035663992613367422, -0.0012509714453235044, -0.000787972482051574, -0.007089705422679012, -0.003760021516451674, -0.008044742138208754, -0.0054313189773478295, -0.007800198019689281, -0.01447127309301542, 0.006613934851074041, -0.005956746429229565, -0.011275606887261189, 0.014784884632719425, 0.01100512257553528, 0.006797646287505526, -0.011246706598489623, 0.02191020389627997, 0.009727667679451655, -0.02587593230119501, 0.0028180253046300586, 0.00734003058809594, -0.024483107436961943, -0.014084810698953879, 0.005210900443303914, -0.013529482142300861, -0.029027208252159223, 0.0003337507690471184, 0.03572160490805905, -0.00983660915672529, 0.0015279654340239802, -0.024527525904918402, 0.03372850474232582, 0.003515634261707511, -0.03834563888063906, 0.007645007217853563, 0.0004378156112267506, 0.001640929400261279, -0.036242103711113055, -0.011704389380589987, 0.015955541741040254, -0.028025646143364877, -0.010794060558119834, -0.0327000904888571, -0.0003317016923869206, -0.01099749709703772, -0.03394321763960472, 0.0028748974667982393, -0.027926633432730212, -0.01861937960181612, -0.008847921956309006, -0.022301768169779117, 0.011248979418424692, -0.027447755562932184, -0.0036956911666332945, 0.0004244413411448079, -0.04054937115418174, 0.020413308561530376, -0.02650690132461695, -0.00844189603582269, 0.013574255391839407, -0.016514596349655557, 0.016260619857816655, -0.004780171349624189, 0.009787095102559935, 0.014890483092643451, -0.006507359255997167, 0.011187090596498346, -0.001581140558991288, -0.0038600574995940567, 0.007046059663339388, -0.0045688878935092455, -0.0011087533660215118, -0.0010520086589077876, -0.008257670606185784, 0.0005582927237176632, -0.002942516660740699, 0.0010196177672167034, 3.0815486858081576e-5, -0.0016282369855945373, 0.001227175117982047, -0.00016468313183127284, -3.364964937925819e-5, 0.000528664876553752, -0.0001037786992178382, 0.0004394152496154511, 5.635310417653065e-6, 0.0004619447750389433, 0.0007447486174515088, -0.00017985162380683938, 0.0016436692001364575, 0.001766924598501809, -0.000589512566633772, 0.002860270466100842, 0.0018299100333560065, -0.0007201836408338391, 0.0048450094037711935, -0.0014181733277808988, -0.00027932465063843865, 0.0014417057746861134, -0.008744274021200035, 0.00042024427485721724, -0.008419932345746754, -0.014049533191084932, -0.0008434598363080783, -0.024184503697442013, -0.0016051139847141822, -0.0010243593204646493, -0.017006763315735994, 0.017896470442354057, 0.009150701767345, 0.018547438046289954, -0.0064035380495533955, 0.01943749491201985, 0.016656983932691907, -0.025196012391927185, -0.004605911382614348, 0.013918670393480895, -0.025584484660558134, -0.01850689420613074, 0.012797490621619154, -0.014768289411405693, -0.0351873757835236, -0.012810816741531497, 0.04696899162284976, -0.018656426027846194, -0.015135068064036026, -0.02302857915105116, 0.042850685557084996, -0.006818348165667895, -0.057137778615325166, 0.021647776858489114, -0.006725023109964317, -0.038920190483068245, -0.022693049305915407, -0.012431270783167962, 0.020826252196627648, -0.034360585011465, -0.0026102535329421907, -0.04010993826399662, 0.007982665219367004, -0.005915392781886334, -0.035413877491448184, 0.010648326068425144, -0.02791216165029778, -0.020089963321875515, -0.009658654092196985, -0.020789452021342292, 0.0034755559854694534, -0.03133487996002172, -0.007066554760936525, -0.003247636664258836, -0.04071099654426806, 0.01849503378502756, -0.027006650236463123, -0.019705151791900438, 0.01531765006042361, -0.01902820308218061, 0.018336568151688656, -0.005832486265050827, 0.0052586453182983245, 0.020854125666440206, -0.00965018895718372, 0.011879557731869382, -0.005383482691941717, -0.0046546085767536554, 0.005962626557869318, -0.009088494236922982, 0.000607764497774893, -0.00361713721154084, -0.007211338463855147, 0.0013614392990874977, -0.003429672621094297, 0.00037484231675547896, 0.0008868806756887374, -0.0021045048434228347, 0.0011260168007939482, 0.00013180092825011016, 2.38683626141513e-5, 0.0009189645858950461, -0.00021188384908050052, 0.0005601758534855187, -0.00010898056568843502, 0.0005439622289973852, 0.0004339804998228027, -0.0004151757729002226, 0.0028657249181759607, 0.0017338966741986194, -0.0017202473696149247, 0.004320010090653248, 0.002814655748950351, -0.0021024419100248316, 0.0066987964436326115, 0.003379919511599696, -0.0010664757657820319, 0.008441764160626853, -0.003203570094645626, 0.009275842508242623, -0.008619764380683407, -0.009776726443468864, 0.01460897077463433, -0.020693887428616945, -0.0038278887722949847, 0.016525589414922093, -0.02139460408189939, 0.010567811660013715, 0.016939383369297345, 0.031144883510832184, -0.0038691877192169283, 0.0015784443327717555, 0.02064569760683402, -0.021428933450525788, -0.01404403647631117, 0.02117675517755559, -0.02576007190610357, -0.02290425243161367, 0.03183369676060899, -0.02341856994010878, -0.048660841438291934, 0.01361168756827439, 0.10278034809711516, 0.03876412250257226, 0.05994187028622994, 0.11509758556496852, 0.16594575835734413, -0.043481161024754245, 0.12747128069240826, -0.08640116614808478, 0.034718065240560515, -0.08713282011893035, 0.04994595270540919, -0.07774932697764096, -0.024992748808879122, -0.008027836518250037, 0.008864829929653475, -0.04083460117071356, 0.029550507688494147, 0.0017220411020536393, -0.030175247300688476, 0.02890036153657052, -0.030980888920081155, -0.019803571384066625, 0.004516456836932355, -0.021792608745343018, 0.0011381161959187066, -0.03146042280967718, -0.008701264146240997, -0.002410276484193421, -0.03948684530196481, 0.016158385836339665, -0.01920708494369922, -0.025173308458883808, 0.014895323983706386, -0.014033205983492635, 0.023404131680287304, -0.003922702583613015, 0.00047443238016069237, 0.023883263797505796, -0.00929779447546567, 0.0092784190523434, -0.012896424315661613, -0.0011780931433107327, 0.0030454154021915154, -0.012891460933432162, 0.0029535904221532766, -0.001961481194295395, -0.00822939975416372, 0.0034603093774888466, -0.003502081852885723, -0.00263102179486345, 0.0023614893156050057, -0.001969532867324956, -0.0006797340620180019, 0.001069509192711659, -7.872811547007637e-6, -0.00035303367508440786, -0.0006164226438410005, 0.00028447838735890337, -4.002058268556188e-5, 0.0005909842163579743, -0.00019392665779998953, -0.00031858214097283793, 0.002990019928841741, -0.0003416790033327638, -0.0016801861586573318, 0.005157240199642811, 0.0013823790264120175, -0.0033987048557655966, 0.007016422644573025, 0.005324170169365463, -0.0038822491535667187, 0.005234775197398507, 0.012884164283454264, 0.0030707773403660208, -0.008538444508017119, 0.0096333774589009, 0.018218108436969593, -0.01650005741004816, 0.005479620430217897, 0.023559856450280643, -0.018854911122629017, 0.005312011230968338, 0.024879252479593043, 0.006092145996552054, -0.03291117374564282, 0.004132133316471105, 0.01987448854014924, -0.019382992870561253, -0.021676259318676443, 0.032246196605410914, -0.030696733601213194, -0.03068243281056697, 0.06410158048680954, -0.04205275873970296, -0.03470788919938232, -0.07017091807595469, -0.020206112846837692, 0.09608480572688227, -0.021122618312439886, -0.08306630123433549, -0.2269105479749912, -0.18558620580583432, -0.08152126024045062, 0.011051065365633977, 0.14640788801405874, 0.0993094189988429, 0.04874032976078888, -0.14200191088748176, -0.028783436428049092, -0.02120279012993959, 0.018276340391203072, -0.024591337272335402, -0.04206231324820691, 0.015390311005868466, -0.014523599642497557, 0.0462398425743266, -0.014070123794318082, -0.012473617722947975, 0.038801171187637096, -0.02691525837181672, -0.0011664447393625347, -0.03308604033179055, -0.009541906705006226, -0.0001874945809267302, -0.04189409567185746, 0.028493347260034392, 0.00467615500355883, -0.021207886510945878, 0.010896411388934624, 0.005080945639727768, 0.02914221692472695, 0.0010377979615479177, 0.00948573934822507, 0.02178849452151703, 0.000997018374007555, 0.010333744947799548, -0.01665452335795196, 0.004830029561047723, 0.0037195399819927566, -0.01516349116100447, 0.0056314203194249585, 0.0012774416918517357, -0.010010131170171613, 0.0038195480229974467, 0.00025888663398492174, -0.005527786896253027, 0.001708675012451637, 0.00014555880674612062, -0.0033125103722130384, 0.0001566903906008086, -0.000223675897328971, -0.0015089336609735375, -0.0003330680749054615, -0.0007072217253603078, -0.0004567850775071386, 0.0009637782706355975, -0.0006371222963618909, -0.000171331140956613, 0.0024905041519653424, -0.0013655731723737127, -0.0009006202888839895, 0.004798131707468752, -0.001439038939775924, -0.0033645681337431533, 0.0066944474937488336, 0.0022944860577764695, -0.007546527296839536, 0.0016376842843335232, 0.014327649586086946, -0.006436717656852232, -0.009539048882242116, 0.019026940146525124, 0.008669449906254288, -0.013982640974963701, 0.015060714909842452, 0.02126130359454562, -0.01388585239544533, 0.008570827000765566, 0.029522419016746404, -0.005397348789926894, -0.02222134751090302, 0.025393913545072682, 0.017945849962545852, -0.021289143114114034, -0.028174183864686037, 0.05420061385699913, -0.04373755483634525, -0.04817869400285049, 0.09947954271659773, -0.06961734950685204, 0.0208702873084021, 0.04754429683307092, -0.06159295491832209, 0.07338758900179819, 0.1206654296570819, -0.0246041983598652, -0.029845488734345907, 0.07586543750763113, 0.06275339104416797, -0.006403193932512563, 0.0754133112634879, 0.08974003903076486, 0.017343814834695846, 0.06862375239528323, 0.06888506516003774, 0.05609433642257173, -0.030126498333177182, 0.028920331230595096, -0.09784144987586228, 0.041698957946048706, 0.009370510316750685, 0.0585306593945479, 0.021109803715000684, 0.006505548680995338, 0.0552108889039333, -0.03220663088502224, -0.018244172226264187, -0.020142830267886852, -0.007659495756057135, 0.002608159924503544, -0.05026838579676951, 0.01869169591927118, 0.03111927603993072, 0.01749937555171208, 0.007027772390820978, 0.021022714824768394, 0.026655485184926483, 0.0035795090421409507, 0.021224654983960197, 0.016538707872067904, 0.01038128953071614, 0.019822312487516397, -0.007432519326148511, 0.011543214449809828, 0.009595715649792568, -0.011472214992505624, 0.00873046797152505, 0.0070388851843807484, -0.007910689384597906, 0.0030379905303954554, 0.005720414600082388, -0.005905438643128793, -0.00038742982579115817, 0.0021643006329352264, -0.004016074995106067, -0.00022944437440822034, -7.615359701051957e-5, -0.00132883811251934, -0.000122878594266171, -0.0005576659832824954, -0.0006137075067056042, 0.001117741532870119, 0.0003662238081933495, 0.0002827626681933594, 0.0023922979659712356, -0.0012390648319183612, -5.4540268901445e-5, 0.004214800242945905, -0.004201097716515767, -0.002221664564370947, 0.004673969133324667, -0.006592504203487954, -0.007377195427528458, -0.0005024043043573179, -0.0023738053485786374, -0.017249753659998444, -0.013203965028749286, 0.01869319000180268, -0.007173090752973015, -0.010236047064665438, 0.023730385346638273, 0.012881583732305057, -0.0013393448789430836, 0.01894978899395298, 0.027411454581921502, 0.016066945668734844, 0.002626001551951922, 0.03596945318474092, 0.02271566059123022, -0.018456056453322715, -0.03103734716890894, 0.030094207262702222, -0.06353334261408086, -0.1234571042478736, -0.15990962483024215, 0.18761175688283357, -0.09628398627944387, 0.039806245753801955, -0.08124889368249119, 0.016813448138573755, 0.038168134863166316, 0.006302134515500637, -0.032940631236580496, 0.022642118942985838, 0.03922351526067152, -0.01211713341278051, 0.01923880861587905, 0.050868511014692724, 0.004119119992702328, -0.017484331478038892, 0.07772967273940172, 0.038193398014223, -0.026008240277603494, -0.0021804962473501847, -0.11573677701728356, -0.10661518260213572, -0.1169795290441895, -0.25646923438035757, 0.047254570732289204, 0.034462446841935175, 0.05535634785056782, 0.0030605755522892077, -0.05409555957146116, -0.014410242986977023, -0.006556562897277165, -0.03273517019626444, -0.03933503571273547, 0.01784593163747326, 0.033238091644916985, 0.025444827065260408, 0.006594035668877427, 0.029823765300572073, 0.024714148015015595, 0.003472804370114506, 0.027631968133995575, 0.014500874492840066, 0.009693496007443934, 0.02553481551043154, 0.003152501863624866, 0.014886342303052209, 0.016962565347629875, 0.001066331894641582, 0.009813549905386992, 0.011545565831820457, 0.005059521242371607, 0.0012395971882895606, 0.009424550112877914, 0.003478886436274431, -0.002188480431719935, 0.004903699397303172, -0.00211289619266821, -0.000636225495763931, 0.0005138577333719983, -0.00222514980323763, 2.0529684083814734e-5, -0.0002552996451372551, -0.000715041866361874, -2.4610135134774027e-5, 0.001276939572254872, 0.00016329773521008445, 0.002914870167606393, 0.0025672087392753728, 0.0024763451683469774, 0.0037775170290355346, -0.005970760377342991, 0.0005818257394748391, 0.003485693419632745, -0.011360911785089987, -0.0021516817574669597, 0.0019652068421442672, -0.017735661150467, -0.007848968120928078, -0.0029784404313847783, -0.015785217055996188, -0.022209032075718123, 0.005271815060020912, 0.031239110485376927, -0.011999899456522951, 0.017891120019757092, 0.030329975657602152, 0.009215418660613654, 0.026821831487781545, 0.020378067801020777, 0.020135738275657115, 0.023196421673422507, 0.03589977858646534, 0.03800419804376542, -0.02016063606372283, 0.07744804245556548, 0.07856259875676341, 0.10348269552890418, -0.03494908832215614, 0.049835024537449965, 0.03472954259792514, -0.07914528407664971, 0.011258955837497276, -0.011280311384494542, 0.01564846588167359, -0.036682568506341114, -0.0010296563316629546, 0.03196797621580316, -0.02033766696431389, -0.0032290346680687023, 0.04589692615589527, -0.005021701286084057, -0.048052829597384154, 0.016039289127318626, 0.07214870865047626, 0.020621107676402677, -0.03140615853809904, 0.07126261438410528, 0.10103740407378313, 0.05366313484731649, 0.0842498642860891, 0.05850152489351359, 0.08106101554688946, 0.053612005049209495, -0.06200451979923062, 0.01252100717186211, -0.020461172484586634, -0.030366543321667022, -0.031593478889825354, -0.05364214875334305, 0.028431569597311572, 0.04115471929734979, 0.020233199895348056, 0.008953897225667735, 0.039208534748837655, 0.024329914152703098, 0.001849988681558383, 0.03384639672566935, 0.015868290437442742, 0.005228424369441569, 0.02943029231709624, 0.011269204544174143, 0.012341706394111786, 0.01773778084331121, 0.016201328163732667, 0.008132474038728256, 0.00600191133536026, 0.016153628890939815, 0.00297341891140966, 0.004626215299704556, 0.010607751865316357, 0.00028012302864297055, 0.005844004852450276, 0.004044003969494561, 1.5407974556739646e-5, 0.002910421460692023, -0.002029345468517804, 0.00010249605365241979, 0.0001238540235813925, -0.0007829036353779084, -0.0003185213019105947, 0.0010542278518374155, -5.7321821027350384e-5, 0.00012174341323380696, 0.0030981071823951724, 0.0010145502139001534, 0.004378111117666594, -0.0043238907320064315, 0.003710933007967166, 0.0049268722057105386, -0.011241273821090506, 0.0025305463689161947, 0.00557840725554806, -0.02063458993535137, 0.0005848680665397739, 0.007275183641876583, -0.031314965425128724, -0.00929889120529376, 0.023334605892600963, 0.008345784633890017, -0.03359066082783666, 0.026168249045448358, 0.034299034406739565, -0.011993884783657906, 0.026388673611764613, 0.034658596040690604, 0.010179741088241412, -0.01754998143707175, 0.007127865543025474, 0.05115108472246168, 0.026382046726110043, -0.07954081371364781, -0.055470134081525554, 0.14833460188455783, 0.017863350186823546, 0.029906145075259353, -0.034984841397571756, 0.013651805371904684, -0.051007286029165926, -0.024091492127948227, 0.016430681146321374, -0.03243831068452363, -0.0167206368447398, 0.021506061118103388, -0.029304748717496807, -0.022202794392665853, 0.02783523513627421, -0.028224125829956613, -0.09711108928692525, 0.030337746349112113, -0.02311721923366471, 0.017195459901600835, 0.04008306337585051, -0.11388953168662944, 0.05604234588444819, -0.0788750127717037, -0.06724885041686822, -0.05077594129355985, 0.026162744300752806, -0.00354869288408093, -0.05956577578897971, -0.0011093747174834164, -0.02645910334068238, -0.05263529308285491, -0.029896434840651378, -0.06968308541479751, 0.04730790219066414, -0.024772163580004992, -0.09896928882948494, 0.020470686407980474, 0.06082592941826118, 0.0233313373045398, -0.002345078166325747, 0.03692128526211224, 0.02254358967203701, -0.004117216932726321, 0.02884220422823858, 0.021122334916480325, 0.007383749036824032, 0.010212503684695704, 0.029697914375347034, 0.01170402058493198, -0.001261591179772034, 0.019823201503338123, 0.007769934382385199, 0.0017913248216747865, 0.011365951876730685, 0.004153693532401728, 0.003789066898161335, 0.005585798234474413, 0.002061462408302555, 0.003955653099414611, 0.0012818185237212763, 0.0005715624862701043, 0.0016725933259562958, -0.0012002510341815463, -0.0007785633421070969, 0.001786467442774628, -0.00047002541608429153, 0.00021850208697015593, 0.002475578403492613, 0.00016384373695147255, 0.005762845494721821, -0.00019335719164453787, 0.0037967746636494277, 0.007591881444065232, -0.007045186765211254, 0.005838982161949153, 0.008850140354247376, -0.016250711677025246, 0.00882279166590977, 0.00868905566606186, -0.03129206259466445, 0.009311143029013634, 0.018640515143804586, -0.01326636352694687, -0.03975457395236232, 0.0183806858707971, 0.03145201996802525, -0.03222248632984463, 0.0033371814954552257, 0.04910847972894005, -0.001727255124149708, -0.0336739125184179, -0.021505711945383928, 0.022219602647297068, 0.04836539392834533, -0.04224761441602445, -0.041051672320367126, 0.07382638645128174, 0.09332531551493482, -0.11419845943092077, -0.043877987276217126, 0.03927236907670063, -0.03486701243843703, -0.03916153037466383, 0.0198080838047314, -0.037224659501549656, -0.02813797034112167, 0.011383829093172839, -0.04315459975161277, -0.03717140571435605, 9.164055300542032e-5, -0.06108330817978316, 0.13948906407905654, 0.027307700871793603, 0.03196031253415964, -0.0705470769198624, 0.08144818722931471, 0.02669944878253826, -0.044719124810762276, -0.010670873482221793, -0.019355120968579626, -0.03707463876977185, -0.007828135466007028, -0.0005458723946144503, -0.03499723676168818, -0.009316078278270927, -0.00011811034665962198, 0.04340924067751117, -0.015114760829389062, 0.04932120393236513, -0.008177614473985892, -0.022459916747928948, -0.07200586019083662, -0.03003547693666085, -0.027189035753920253, -0.05411306319931334, -0.006508469088113542, 0.003108362428970164, 0.04811495047879956, -0.014829781408138665, -0.0023133933505913745, 0.03552701770222317, -0.011785776475891315, -0.030326653773455618, -0.00480825831794246, 0.020292323126379287, -0.012145530626553644, -0.0010213932629768606, 0.013432311060473578, 0.0008499842592053695, 0.005487665629345606, 0.006554276584772966, 0.002674977787865341, 0.0043822872104453585, 0.0026974403241190907, 0.002594684337142927, 0.002408024883916313, 0.0002918851763389084, 0.001192480947106566, 0.0002667232075641152, -0.0003941517521480861, 0.0006369227496287932, -0.0004635619373816001, 0.0012118731149337167, 0.002303550449464927, -0.0007655227223426452, 0.005333778159105632, 0.0025376565397820356, 0.0013894053150831694, 0.008423200054237327, 0.0012123611665993473, 0.005960979739216469, 0.00797508711086787, -0.0015811853674887843, 0.014835675511322536, -0.003826022323205541, -0.0073032519429183824, 0.026321228542726543, -0.02638448114066557, -0.020982870769174267, 0.015357136345975814, -0.01818599321103717, -0.040359854104487294, -0.005646868953798812, -0.018504956663639535, -0.03589349058774429, 0.011542044497389775, -0.036438700977363306, -0.02788089580421199, 0.010459898836670383, 0.004330754202306007, 0.039860190792381595, -0.06621956048879797, -0.1691128995282993, -0.17093394930487363, 0.03992587070099856, -0.12013241243687516, 0.1074469742692981, -0.03217547565386243, -0.06649043451463416, 0.01981187789605631, -0.028003461978381914, -0.0357593587884734, -0.006375702480486465, -0.06128456395985754, 0.17889720982567267, -0.21500935163345464, -0.05009586747453302, 0.1475442689066439, 0.04618049602499947, 0.019786501288772476, -0.06793804205432408, -0.01259178894189396, -0.05592200188991878, -0.035884438655964176, -0.033343933540805545, -0.029087018765745192, -0.024029397904188485, -0.025951299539361244, 0.0030550167458050486, -0.013672517999880847, -0.0173211238505723, 0.02654436899134254, 0.004598708453226899, -0.020986683614572944, 0.04170936121538934, -0.043475086926445486, -0.02223143462516619, -0.04868027409027517, -0.038429887837283426, -0.031826555781786406, -0.02971596400417808, 0.010606599244668188, -0.03028549555950342, 0.04102850655494136, 0.015148759882660484, -0.023535973748870738, 0.034265174181516665, -0.016083208519429976, -0.025232231206925172, -0.023516919794135824, -0.0032632096040081347, -0.005618804448411908, -0.028918296049523975, 0.012854707104036604, 0.0025262800537899327, -0.00967445868543608, 0.006939924533179137, 0.0016935720028810797, 0.0010234992899987398, 0.002965446466392765, 0.0008771546407633173, 0.0019866002566516195, 0.0004403764171460865, 0.000560964837601523, 0.0012788267420469936, -0.00016213706576958102, 0.00015425794873464403, -0.0005263790260713365, 0.001471810753279348, 0.0011987388916804029, -0.0010510615615783121, 0.003412296690594593, 0.003090676615553471, -0.00048261186325665787, 0.00459636323340437, 0.0069286296118488645, 0.0022593509764283195, 0.0001373084901081332, 0.010416019342781618, 0.008424059167067222, -0.010591291571696644, 0.0062308714212722365, 0.01584161508719732, -0.012712196080941743, -0.01962363031354676, 0.01656339248901071, 0.0009282955031247611, -0.03191912069903755, 0.013546248956244915, 0.0025303232263896277, -0.028721817718751378, 0.021392089532084674, 0.0049059607074120075, 0.0066754862530130086, 0.03827127802746177, 0.0112626372955423, 0.04703802347608466, -0.04720571607347043, 0.030197499079395416, 0.07104594005555707, -0.019079644151272074, -0.0042607000685912135, 0.02413692250846184, 0.08529859915426606, -0.040227867040151466, -0.06997345648486919, 0.08703928619818542, -0.02610253698621412, -0.0529567040725512, -0.057875365944262055, -0.12966491623020557, -0.08289449484516359, -0.09490053614968148, -0.08619619295839588, 0.015519144281481058, -0.07456165490105654, -0.061766637107585357, -0.025779700460982075, -0.04916730539599005, -0.017615949739936097, -0.0435723982539378, -0.034239569618727976, -0.0028559412005414596, -0.03620858836537811, 0.003053787101740141, 0.009463797688410344, -0.006779186196708246, 0.036178629394092235, 0.007629937118405622, -0.005756523144165417, 0.04126613296812429, -0.03886121207652424, -0.02915253601234579, 0.007169075299166012, -0.0446324055294821, -0.021797256153213308, -0.008142524394464496, 0.02979449426797281, 0.002619103071315521, 0.03632076962634755, 0.03367594906550865, 0.0025090947578902748, 0.03456105978926874, -0.016015987589880463, -0.0179511915734218, 0.04234193540241826, -0.030182038551383412, -0.0028611328929476093, -0.01251190365944489, -0.008867040994400461, 0.0026188491765908955, -0.014826978457442455, 0.005744923134730218, 0.0007996833258010468, -0.006715827714040242, 0.003016813315016283, -0.0011684943574768994, -0.00014592533052082808, 0.0006916042480272227, -0.0005299649064092979, 0.00042069450952713483, -7.250121449302156e-5, 0.0005000064603392919, -0.0005085816128859026, 0.001626359648216702, 0.0018046974155377232, -0.0014478393808354845, 0.0015430540167541312, 0.0031958894502308573, -0.0013477070399875758, 0.00014651579064026854, 0.004384678787465307, -0.0005154599606874875, -0.004324942271972807, 0.009684189501488001, 0.001965810571236015, -0.011257677022715533, 0.003194589214645138, 0.009815687265495388, 0.005176751504625436, -0.019880332441595885, 0.009409921951149326, 0.012934520278039797, -0.02137079694174866, 0.014174053243307436, 0.015098118406663318, -0.009253928179454151, 0.026939626412306995, 0.00423667289465453, 0.035794903516184924, -0.002510962927283307, 0.0005886826689385666, 0.036204042171440784, -0.0362468938100291, -0.0026260576073056977, 0.043952401099514087, -0.04088214234283753, -0.021714499690031953, 0.017815342400362158, 0.03839064553463239, -0.019374587747468756, -0.037846291844244755, 0.052441864325566995, -0.0013902240856488801, -0.05527192716042879, -0.01590785586321114, -0.005728347891789829, 0.03124874844814906, 0.04895515175271196, -0.006986116583305841, 0.037649179118059935, 0.04798563527122636, 0.0060028927961932625, -0.010779734423544194, 0.056458174219738165, 0.003871680196579599, -0.04268869338149823, -0.03405441201663229, 0.01688539422479282, -0.040504418114217615, 0.007603847014379252, 0.015195683747785746, 0.011907843144626331, 0.042194547018000655, 0.006422213568767155, -0.006324076207674088, 0.04481009863871631, -0.02242301768266719, -0.032345701953037376, 0.02335326172515424, -0.035141111903582906, -0.023326467110686155, 0.002628058160146085, 0.025598772695650453, 0.03063833830984026, 0.006612849906777202, 0.033239431121954516, 0.014479557777211768, 0.02657788366399866, 0.0013727379678477346, -0.009005254732499862, 0.06022931337109964, -0.022806941924497125, -0.008287695027349825, 0.021963119069411986, -0.016320808594256605, -0.002010724885282054, 0.0028208198363260033, -0.005410853872864635, -0.0007219690936827611, -0.0062617941700774515, 0.0022198839351235135, -0.0013596605169352936, -0.0032866103108983914, 0.0009195607110587835, -0.0005297610809006727, -0.0005074495498626775, -0.0001944655577520796, 0.0008913637988531269, 0.0003349813169405523, 0.0001037201715418114, 0.0011052283381800731, -0.000260243745400277, -0.0004668028245177186, 0.002482822598174634, -0.0010655669832879426, -0.00289563165895058, 0.004506315475344043, -0.0015420471600634022, -0.0067047294824145644, 0.005491731529101404, -0.001499559175887231, 0.007371016680476346, -0.010974102975440447, -0.0013555845699498874, 0.01442775056160873, -0.011842447758000368, 0.002169024774182539, 0.020399291069004944, -0.010218443080020094, 0.012515708568448764, 0.011891683120037461, 0.011892337841962072, 0.026284457817516284, -0.004298517951109553, 0.034036563383067715, 0.000265121544140226, -0.005727047763848089, 0.02720737661183494, -0.031480541747711026, -0.010063868947893486, 0.022011838977218857, -0.033287899379435944, -0.026815534811518923, 0.024451885713405667, -0.005823435452871828, -0.03763572501435888, -0.002753938847456571, 0.0038189665538735235, 0.013748779375314739, -0.027763486021770815, -0.021886987220962724, 0.005172751660788211, 0.01429404158630533, 0.0410674938599303, -0.0036023174622524206, 0.027047035458495208, 0.03720476815404087, 0.035250353968013334, 0.013864753726438703, 0.03789348588408324, 0.02656062734433539, -0.03637641422991727, -0.034294709347738477, -0.002515840491514298, 0.055256844992157925, 0.010346056120393672, -0.005124917835020836, 0.054349228448579624, 0.04580565991836717, -0.006434912864833691, -0.022487271846175032, 0.06570247714021699, -0.011274081001789366, -0.03783875347734403, 0.023738748024217205, -0.019989789849394896, -0.03405340076822539, 0.009711313184458007, 0.01508443824784011, 0.027574741231317836, -0.019652084057130894, 0.03097034202129302, 0.018865378305511146, 0.00864218939175959, 0.002862350690870465, -0.013117344276706633, 0.037589226806755444, -0.008626278046944607, -0.010484057990994161, 0.021912718628311373, -0.007731514031514367, -0.004328515439949275, 0.008938961473307836, -0.00657580360728979, -0.0009251964206419046, 0.0006277268985807004, 0.0001904114551205612, 0.00011395827736600951, -0.0018533883104264078, 0.00038790869824806214, 4.049476234150802e-5, -0.0005259123407456234, -0.0002792269864107105, 0.0005195948936230453, 0.0002503842790906008, -0.000983614480976639, 0.0014797351775206042, 0.0005733244287477922, -0.0016772714141901, 0.0015350929002649139, 0.00015801176799420605, -0.003910885959730191, 0.0014692579435049155, 0.0006645120140171822, -0.004815800634802427, -0.005002519505584542, 0.0027566507476865193, 0.009260007669102262, -0.004888483849251347, -0.0010900101979488372, 0.014268245296982585, -0.0038252298452748335, -0.0010022062990348226, 0.02142514766904109, 0.006452749099916921, 0.007064198466160753, -0.005958745446014401, 0.02590293552560135, 0.014522303406152775, -0.021024854524392865, 0.030985521148766227, 0.00045169579674216736, -0.014592125874906338, 0.01936636398354534, -0.033919389631939766, -0.010805772970443021, 0.014576827123627916, -0.03354453125442523, -0.018180623325825738, 0.023945052419478422, -0.01490115433816056, -0.009176546189351695, 0.018342239656246546, -0.026987546664559634, 0.018559790021692783, -0.013236886297495467, -0.029133748446728447, 0.03287251122689205, -0.02341873085609265, 0.0026987583452609556, 0.00010002575898590316, 0.025429098165245263, 0.030368661093013585, 0.010443253780037158, 0.029837240986750422, -0.03367707429135632, 0.01743761154596204, 0.026598840367822472, -0.040977001753381016, -0.032469741287169965, 0.05965224948749719, 0.0316033296463472, -0.04244898575885113, 0.07824085160604967, 0.026134288149438172, -0.018726004501949306, -0.030088241378959817, 0.04008856320670557, 0.00017561108124261753, -0.04167326711484292, 0.026392804951493324, 0.005842334858022198, -0.02976791723279437, 0.025083963363733926, 0.009807339132460935, 0.0215432082022378, -0.02477500816092917, 0.009429310749475912, 0.012686699483234181, -0.027048637190999005, -0.0007160278541445157, -0.01825114967852977, 0.0184166047897987, -0.0024401679059446613, -0.009823045908006669, 0.014192386647322773, -0.002381872822878066, -0.0044679002528470345, 0.007985427579924044, -0.002287082181211238, -0.0011554321632380904, 0.0032601233509832253, -0.0001618326071622956, 0.0011519922191847566, -0.0016031880847491157, 0.0003194517744227924, 0.00043277047850171597, -0.0007822666030892431, -0.000274755725994301, 0.00029325713224045844, 0.00017286010903062133, -0.00037153680490841564, 0.00038579777640261733, 0.0004384407260530253, -0.001344478566160174, 0.0005677342595471591, 0.001240256695879509, -0.002656631043594429, 0.0006430154745715436, 0.0032393592380201815, 0.0015698201764573927, -0.00036086716228049927, 0.006592706425611691, 0.008607091905896003, -0.0012142810770686694, 0.0011354134980350373, 0.012453173881641095, 0.001187964227199226, -0.0019215700391377452, 0.005303975406597016, 0.0173276217747031, -0.003343345992354268, -0.017750135835124824, 0.022034089234809397, -0.0003997764693093818, -0.031786736545396085, 0.022689952157335228, -0.004370446314313819, -0.030436105645144595, -0.002048373113534635, -0.031439889005381784, 0.01673106295186787, -0.015774484489370685, -0.029900672414489383, -0.013139335483024457, 0.02914670754464486, -0.013147152215109039, -0.0026012478812617425, 0.019311666915610197, -0.02887987715441669, 0.027983035440798974, -0.009637995059316522, -0.020883357272207543, 0.03702722882422425, -0.01955142008752592, 0.001924021054945806, 0.016626604952713345, -0.011279047396689284, -0.03795853214321088, -0.010897152551762563, -0.006052130438821767, -0.04013193605160505, -0.010885852999641555, -0.03129463514655938, -0.01851532323513909, -0.009688387276590379, -0.003932962677365708, 0.04790332836844879, -0.006349831198328495, -0.06567790143340145, -0.035321445579797404, 0.029858689567454955, 0.020422197293471996, 0.03376665095931598, 0.019215635361383744, -0.02033274481518657, 0.03777238952130424, 0.02152650156163879, 0.007911135154772505, 0.031819895071971145, 0.01069641972398247, 0.02639625545504467, -0.012187954171583923, -0.006427975054429505, 0.0030271296019179243, -0.0242533358696223, -0.006918050989347961, -0.016755826384373614, -0.0005286934441510743, -0.0007913319855586999, -0.008858011678305588, 0.007790977083691278, 0.00017359699470483216, -0.00407549107749943, 0.005679902400545637, 1.495244811418799e-6, -0.0010308003066886084, 0.0025708487185504237, -0.00011957711859478902, 0.0007576759743083071, -0.00021546608379011017, 3.786334917578803e-5, 0.0005477465634589407, -0.0005730507766488273, -0.0002945811165569669, -0.0005834727511226066, 0.00022455258521784683, -0.0001888037974669651, -0.0002451861192791109, 0.0005104235864798665, -0.00052492675712777, 0.00020683208523650012, 0.0007351104462264215, -0.001359155368522492, 0.001079027086173049, 0.002516175959765714, 0.0005837501482435912, 0.0020197593259112566, 0.005206616513983463, 0.006257375519180961, 0.0008101110311256967, 0.0034090781935402245, 0.011179014168017113, 0.0029711513438879325, -0.0009193409862043221, -0.0046488680859785025, 0.013268378909627945, -0.006206607481496737, -0.01708657929703854, 0.01543652318219756, -0.006416109472825981, -0.028778682028618018, 0.020284881319273296, -0.01066717547266115, -0.03958040661873851, 0.019952313177974974, -0.015270442353694695, 0.04132452088391241, -0.023810184733784052, 0.03418013904636215, -0.009954107447519202, 0.036926690326607434, -0.013687239247456446, -0.00310031527171794, 0.020755517720751838, -0.03478628661647494, 0.04094486412448475, -0.00033567839103196197, 0.000768942296518844, 0.033822253325586894, -0.005719935488560074, 0.0294616567909277, 0.02759743369350228, -0.010821952666043976, 0.03087074650524089, -0.017177798444874146, -0.010605639873171351, -0.03261962041010878, -0.0008013809328596634, -0.029700186483129713, -0.015684709391795126, 0.018589253280133868, -0.02459480865112289, 0.009187757211250806, 0.026647074598815344, -0.02565414216385799, -0.0038097724451986183, 0.014586240055245083, -0.003935091516573181, -0.03797678922055613, 0.011371414938246676, 0.036701764273925436, 0.014347900761470639, 0.012694496647214993, 0.022504234834007212, 0.01974181165678558, 0.009927939094022847, 0.021883420072870287, 0.0066288966925535445, -0.011344668922974964, -0.0008928256669828387, -0.015867798968412106, -0.008643500511791002, -0.008898595386033912, -0.0045630853950193485, -0.0017508594092980228, -0.007151718988994346, 0.003081935345237233, 0.000926555365755782, -0.0033341021904994294, 0.00342467262901171, 0.0010884060016034243, -0.0014034914837290214, 0.0023262669647588635, 0.0001293518102922516, 0.00041909008867720935, 0.000515842651011856, -0.00015060934482858152, 0.00043701428765827703, -0.0002648678735483343, 7.567671521628706e-5, -0.0002711719423105646, -9.927699572515458e-5, -5.470126356995901e-6, -0.0005260090790314489, 3.151009042272935e-5, -0.0005535758812758563, 0.0002768601688395562, 0.0004861354011669012, -0.0006944946261113927, 0.00060803966664299, 0.0009110950180286619, -0.0002794473023757842, 0.0009630153646875548, 0.002528639325741771, 0.0032420954875031225, -0.0003868260824433798, 0.0037715784467025185, 0.006943581578391087, -0.0011420418169699326, 0.0027556267916048643, -0.006457635593108076, 0.008426197099497964, -0.0044389304865680435, -0.012073798383718342, 0.01159000408943615, -0.0064120362500428235, -0.016864829136836443, 0.019704901402697077, -0.011262428793362773, 0.0031195712566005934, 0.04042979574085207, -0.011125455473270767, 0.04032274497007515, -0.015139072834998898, 0.023815538051557467, -0.01975059118375957, -0.005265819614272712, -0.03832006556859354, -0.016786523924319438, 0.015311692533252949, -0.03140459946215045, 0.0131747047644472, 0.028909898530597816, 0.025735921072978455, 0.01414115203286817, 0.011517721929838616, 0.0483697687703799, -0.013966157586145105, -0.0008630145537641679, 0.04446636752234702, -0.020194659357803943, -0.016641871803469443, -0.021666328058674498, 0.004355866995316877, -0.024362851249139263, -0.014431306431479248, 0.019613560875710524, -0.017302001449475354, 0.001108088752771537, 0.02227533228148221, -0.014628647357947982, -0.0020630779636757867, 0.016846889564387336, 0.0014310608766440816, -0.021952412538236665, -0.0026633964179975126, 0.027965132327651028, -0.0014183782138077151, 0.004043597874880425, 0.02055083020922785, 0.00912418417299128, 0.007573139259792119, 0.011855747714907466, 0.00991845054007793, -0.00941515589852595, -0.0077689818711062205, 0.00035693513055107387, -0.006542512371412668, -0.005081268838116782, -0.0009666374024647721, -0.0031945790726060777, -0.003934617404505354, 0.00083254147502815, 0.00040403174548580645, -0.0020937336559436644, 0.0015084131838423807, 0.0009623819361691178, -0.0008871343830233219, 0.0008654939872749251, 0.0006448958545923912, -0.00012836024698279367, 0.00044405996832360783, -8.884317013413363e-5, 0.00013761550782448868, -0.00014641680414267683, 0.00012431267274978807, -0.0002731685248539292, -0.0001622886350923422, -9.248449827828372e-5, -0.00030522725791894687, -0.0002905077594196631, -0.0007081195430082769, 0.00027391867474804027, 9.536089086999052e-5, -0.0005112105320686093, 0.0002548621413842392, 0.0003170038779699453, -0.0001828297754298551, -2.659625002073161e-5, 0.0007524830945261671, 0.0013408837607437663, -0.0014924516276619943, 0.0020120627109160307, 0.002838154005942565, -0.00306387319606684, 0.002909562221181732, -0.0055095075369906935, 0.005101890004282545, 0.0011470059575633311, -0.007142494413658951, 0.009173160240970944, -0.0037424885102856848, -0.007238876286807253, 0.01530190441579244, -0.0070010204941391525, 0.0024893520985949497, 0.023118530633403377, -0.008348506624506459, 0.025056565846945864, 0.0017018296346221077, -0.014495040585885221, -0.015488617966082157, -0.002634012416824821, -0.028864170206366942, -0.018741661706082272, 0.012034591145759381, -0.0228290059459484, -0.013081938802828687, 0.02853235357806584, 0.010582134241215917, -0.0035013379345221717, 0.015471352823759974, 0.037179229108957115, -0.013923621278178113, -0.0037810366694692493, 0.03457191861679091, -0.01667549003840497, -0.02049156816686186, -0.006504670740548603, 0.006189529535039661, -0.018882571458660072, -0.01159768142462747, 0.017847882914684796, -0.009971383102014163, -0.0012018269591431911, 0.01775815029233186, -0.007333182635760925, -0.0007685564906719104, 0.014077417825316485, 0.0025746521296394244, -0.010481907104410075, -0.005641288103482455, 0.015074897729474474, -0.0038961039672583894, -0.0006943458400417764, 0.012358117046890554, 0.0012566894393731837, 0.006708152572052194, 0.005887437074796847, 0.006672685950913369, -1.7140097009180445e-5, -0.006189381544627731, 0.005240141919729911, -0.0035856924069269224, -0.003483524478314757, 0.0019778791863348704, -0.002314678136333752, -0.0014431734340273946, 0.0008967265545744722, -0.000744407830200921, -0.0010774152050682295, 0.0007841121031376614, 0.00045147105066689803, -0.0002926573929761005, 0.00019053513608089935, 0.0011910594556153733, -0.0005089391209036676, -0.0002215862212943574, 0.00011330376954725194, 9.471167460452541e-5, -0.00013213765651401516, 0.00015192171130730644, -0.00012435401060322023, -0.0003320890379921739, -0.00014814965246770035, 3.835081707449786e-7, -0.0002231223846002164, -0.0003842607506313019, 5.311579038098991e-5, -0.00011610825477825749, -0.0007471248246860955, -7.889654078450891e-5, 0.00020175278351207591, -1.9797145759331966e-5, -0.00042212735177928843, 0.00033573375111210763, 0.0005462840584094641, -0.0009425650551601841, 0.0006011156393730154, 0.0011468407066281816, -0.0017673631200653915, 0.0014625343850402262, -0.0009202778702022112, 0.00033969979398080477, 0.0037580272729320634, -0.003543479441364763, 0.006178961887163563, -0.000446106294171008, -0.002567460364709461, 0.009749183551550921, -0.0029335883297826773, 0.0022840814948438272, 0.012895887386965002, -0.004701359764525934, 0.0029417275493442596, 0.005697884480294255, -0.0162901034451277, -0.00956927305549405, 0.002288837495437727, -0.017727056156336476, -0.012675919093798598, 0.009523774270231674, -0.014629358211217403, -0.013203532037183559, 0.01755134490643475, -0.00028673852449881166, -0.009326382979455903, 0.010378161438249243, 0.01839537205997736, -0.010644660877131942, -0.006412849583463668, 0.01863231421954357, -0.009644889179008036, -0.01673633506295304, 0.0009150278721232885, 0.005071117445853725, -0.012833047930663578, -0.00838777364862305, 0.013476940081443997, -0.002749923362411231, -0.0017303513508709588, 0.01139019082738159, -0.0014580682622904663, 0.0002642213057600494, 0.009709499486481966, 0.0031625280783021386, -0.0015445768806523759, -0.004922154589607996, 0.007838031601345021, -0.003026982486989231, -0.0020807948886598245, 0.006809607251804567, -0.002779912144591725, 0.006929907649755967, 0.001373899796580351, -0.0002797353450104569, 0.0013352141269992322, -0.0035739635682063182, 0.0026979472118822557, -0.0014147193004044754, -0.0025014254548430905, 0.0025174107269434996, -0.0016113994533382993, -0.0008786230333648806, 0.0012430811682005607, -0.000781567895185466, -0.0001411682399614064, 0.000355195595993171, 0.00057621433751522, -8.394001390016654e-5, 6.459275712020337e-5, 0.00034577688342455986, -0.00014148619009873286, -5.262252647607952e-5, 0.00011129288935326233, -0.0002740282649254188, 2.6518948200246414e-5, 4.681756506563329e-5, 3.066264862427588e-5, -0.00020865390736261923, -0.00018372932174445797, 0.0001362961108969604, -0.00021444008082965974, -0.0002501030092490264, -5.663605548087242e-5, -0.00012482143706419262, -0.000291579020533498, -0.00043092649523239165, -9.571831022518405e-5, 0.0001487257145700937, -0.0004301297468283666, 1.906212435196094e-6, 0.0003817861463798627, -0.0006321265203819723, 0.00019640147429669176, 0.000525115432742697, -0.0009682746446214656, 0.0007459536803801975, -0.00019749400368286713, -0.00019555744927640458, 0.0013128305052404023, -0.0017701647772370606, 0.0030975196432226613, 0.0017856809166493103, -7.831890373454929e-6, 0.004040315463903607, 5.408771513003185e-5, 0.004494410432758256, 0.006968057780341505, -0.001337833373589714, 0.0016084876176743071, 0.004523345288075736, -0.00851790643110585, -0.005097079486735273, 0.0038947667929636457, -0.009265984845765896, -0.0068812519369126236, 0.006760879739205753, -0.007936757720017411, -0.008187625805004277, 0.009489343894655035, -0.00277320432409493, -0.00911160315141862, 0.005367969441177251, 0.0066065263781524995, -0.007532867072675116, -0.006623987707319329, 0.007015935397215747, -0.005640121479268406, -0.010402917592172056, 0.0004788907473599821, 0.001860719476942788, -0.007343717485100904, -0.006863903034160509, 0.009668425918705134, 0.002204306297058616, -0.0020607116915145164, 0.00891423397692648, 0.0018556648453899906, 0.0007831879814822494, 0.00589527609230632, 0.0033468674908707797, 0.00299866254634739, -0.0031685925981031933, 0.00445335779272687, -0.0009481332722021828, -0.0013744568210846632, 0.002820968185965423, -0.0029224489280308043, 0.0017721834320924706, -4.893522042599464e-5, -0.0026445211799941792, 0.0008002636705918632, -0.0015104240024743406, 0.0005160238106431615, -0.00015844038929046521, -0.001339848146807201, 0.0012409676056492685, -0.0002643809069514484, -0.00026532405520279453, 0.00040993998970697133, -0.00038451192333406343, -7.708739196004113e-5, 0.0003103141815104959, -0.00023052890528745128, 0.00010343320187305473, -0.0001168456532570078, 0.00031948830758972646, -1.9872359677238485e-5, -0.0001758270931869308, 0.00011936377682521683, 1.2081076650679322e-5, -2.2794751936939284e-5, 8.073942796846506e-5, 0.0003108232882882476, -0.0003407678507826524, -3.653592699567517e-5, 0.00013486584440229295, -0.00011380535520894381, -0.00013659984714610841, -0.00011001128192393475, -8.126161273749099e-5, -4.7492961018796604e-5, -0.0003831604540190325, -0.00019154732208700998, 0.0002403001164001079, -0.0004649493756319332, -7.632464982360517e-5, 0.0004461166789874806, -0.0007225429732598119, 2.1447142885002366e-6, 0.00016267566024082822, -0.0006067140986746604, 0.000343538137384608, -0.0006075873425644431, -0.0004822556922817642, 0.0012867511782849114, -0.0004929058062747372, -6.863327359984885e-5, 0.001421125957388448, 0.001913170005307939, -0.0003059358011792261, 0.0021897350029587595, 0.003568243999265369, -0.00023660071753248393, 0.0014656737690413077, 0.0032311091403138914, 0.003772385429231864, -0.0025816488788105827, -0.002440168476933844, 0.003936030018466183, -0.004081488352287732, -0.0033946370162191786, 0.004623262550708658, -0.003714492188254074, -0.0042778684295969515, 0.005000786788799377, -0.002085503111994652, -0.005794656684657367, 0.0016870920277609848, 0.000602439028345485, -0.0045427732333970915, -0.004519919430937522, 0.0006371408483208805, -0.0035296985712654242, -0.005286992582393955, -0.0011388733422124494, -0.0016491901549199608, -0.002424921503337533, -0.005274926539566946, 0.003502070928578926, 0.0038550569332614546, -0.0021722985113985685, 0.004120891672056374, 0.003374534679853374, 0.0005023202445387171, 0.0026757810944223514, 0.0032485815692193487, 0.003412295874427685, -0.0008212241273899328, 0.0024514096571406053, 0.0013220932543894998, -0.00040313714304967435, 0.0014104921515369494, -0.0016728849251525057, 0.00019878871850144373, 9.313613938757623e-5, -0.0009640438725706582, 0.0004487724258394909, -0.0007922431927397728, -0.0002107342701963596, -1.0811331160342159e-5, -0.000680808799423688, 0.0005391665943805257, -0.00018936922660539807, -0.00035431352559940344, 0.0004393867891243716, -3.6832962933864186e-5, 6.651298209478538e-5, 0.0001808417140527858, -0.0006425751756252271, -7.983636080055832e-5, -0.00011048663499914597, 0.0001259578481481107, -4.9548471707704385e-6, -2.864433147833021e-5, 0.00023395549738271517, 6.795634842390214e-5, 0.0001475290890682114, -6.994132580156449e-6, 3.5016475807648915e-5, -2.1073506882354754e-5, -7.536686166927109e-5, 6.11807813186161e-5, 5.523197037710933e-6, -0.00016426281964255392, 1.8057679581880543e-5, -7.351529260666518e-5, 7.69644832457437e-5, -0.00012217924404687774, -0.00028054200468777637, 0.00021666007782172219, -0.0001270492745774315, -9.280709650024988e-5, 0.0002073360110524966, -0.00018407047370683994, -0.00014654230410535824, -0.00029169773464456366, -0.0003683298830483198, -0.00011536522305090854, -0.0006146597763906505, -0.0004289879763801557, 0.00030000178341456146, -9.045241299914638e-5, -0.0005029830884248594, 0.0004082291800208971, 0.000562681656515427, -0.00068506100317365, 0.0004677162472651791, 0.001019601802714942, -0.0006061069942293931, 0.0005621518481329622, 0.0017922272052336666, 0.0009319627516167325, 0.0008556975678299687, -0.0005315774036489939, 0.001757864521122598, -0.0004884748946086292, -0.001039432211613969, 0.002245175578039204, -0.000700704706072154, -0.0016385271453666478, 0.0023066590432966245, -0.0005005342416952459, -0.0032236204402757767, 0.0001412899387282639, -0.0009319430926471233, -0.0035046615047184134, -0.003315528774488006, -0.0016626980935072447, -0.002102244428762754, -0.0021456678318014072, -0.0015433606388745949, -0.0013828415099480069, -0.00045680842172615395, -0.002351126216166826, 0.0005085462751046432, 0.0015173163430638758, -0.001386565131704141, 0.0010156855087788198, 0.0016527807686124892, -0.0001960586450598917, 0.0009099050661803865, 0.001411211565778802, 0.0014720544119017126, 0.00034769370135727986, 0.0009928895909884475, 0.0010363942602162658, 0.00010725508278139723, 0.0008683608976778449, -0.00039207701570843597, 5.726262030104415e-5, 0.00017171323865031483, -0.0004484977629013295, 4.623392793156815e-5, -0.00016429669011496542, -0.0005033334371082124, -3.1472353838587926e-6, -0.00038936969280117833, 0.00014021723025341645, 4.432265769217751e-5, -0.00014765439100320629, 0.00022316680740041322, -0.000439258241379992, -0.00035948175756267083, 0.00021927750227712916, -7.793552848701224e-5, -0.0002055103130454679, 5.6373479121200495e-5, -0.0001020416708657927, -3.264385737538265e-5, -5.970607738076356e-5, 4.6039128080927535e-6, -7.503530969088317e-6, -9.250052344598702e-6, -1.3771541358739508e-5, 6.612531795662996e-5, 2.898884999264929e-5, -1.4606148803967888e-5, -0.00012840076725154155, 5.211872075689391e-5, -8.375808521190877e-5, 7.31361396816719e-5, 5.695715937676964e-5, 5.686845847363999e-5, -9.12402747698427e-5, -5.31187396032769e-5, 9.07471038281986e-5, 2.671101386912912e-5, -8.208055577654877e-5, 0.00021241986048144748, 1.0486065109763715e-5, -0.0005093489885837683, -0.00019479823091018178, -1.6690211608977998e-5, -0.00015238710907005396, -0.0002727421238931473, -0.00019539979547580062, -6.782057166726635e-5, -8.551625616452957e-6, -0.0003744569565458791, 8.077970884401396e-5, 0.0003634306512610406, -0.000522766421458066, 0.00013598467070601757, 0.0003190524001397181, -0.0002587499821099779, 0.00015383249870284816, 0.00039389860119887514, 2.7897933443939037e-5, 0.00035286615898922805, -0.00013696008188832716, 0.0006743138368373584, 0.00014998451985063314, -8.024758117788576e-5, 0.000786601908008659, 0.00033849030798802055, -2.0643382859964772e-6, 0.0009289923505917466, 0.0008314771973951205, -0.0012857720045688329, -0.000510553615927598, 0.0001357414518200198, -0.0015234237770044125, -0.0011129715369345584, -0.0011728178826077183, -0.0012626279791190522, -0.0008010257156016101, -0.00125926172607156, -0.0004924276962071333, -0.00012667597862725015, -0.0010537052551780645, 8.291857733015547e-6, 0.00017447390890284708, -0.0005191781410453957, 6.462077087206905e-5, 0.0004679084456160525, -0.0004193127075772557, 4.612274119565784e-5, 0.0006943941447228765, 0.00033157433352734773, 0.00014847684680519333, 0.00048541435061774673, 0.0005508399217707546, 0.0003502541232397126, 0.0005177381527504158, 0.00022665023250961855, 0.00015681883638639916, 0.0004580772229200447, -0.0003266853370289994, -0.00020550844997344338, 1.751165716937114e-5, -0.00033687370849875024, -0.0001031827910743885, -0.00021057237758117487, -2.2173847851295708e-5, -1.793006176820798e-5, -0.00014669413109922948, 3.042957576754214e-5, 8.926034882504838e-5, -0.0002833040814493155, 0.00012888394560353178, -8.618136499581962e-6, -4.444071537068626e-5, 6.239142809883235e-5, -6.191040467184857e-5, -1.4339253880264074e-5, -8.418803708895577e-5, 2.394667631417877e-5, 1.17362692350396e-5, -8.422868807764808e-5, 0.0654313367581995, 0.06543133675816755, -0.0037171254178809607, 0.11834139469996612, 0.11462207399485871, 0.047074456453534974, 0.030764561787936996, 0.07784209088768204, 0.06295709638012165, -0.0037201334259482927, 0.05923639990785286, 0.0461034598516216, 0.023408835223680775, 0.06950852158514086, 0.03551676213977647, 0.02298679961374393, 0.0585059269454808, 0.0506109809730355, -0.02105899843274571, -0.00776503700762341, 0.026103591626343407, 0.10876074334793787, 0.05475248083806108, -0.07365410143595019, -0.17165217539521288, -0.02610465686767877, 0.10569230309451001, 0.14702509456134194, -0.06888266580749938, -0.12770463665518636, 0.03249941344602081, 0.031136793087147775, -0.01658361022460968, -0.26001375963159373, 0.033398325690692184, 0.031343149833702684, 0.010893415359110249, -0.026082045891684613, -0.19071971690206052, 0.02744388736371025, 0.007929617456584843, 0.009304522505275227, -0.07495422690601172, 0.08811118144434178, 0.0261910218930862, 0.013507988909065504, -0.01716813659010199, -0.06140679495915015, 0.12667039232581356, 0.03509416418539042, 0.0111060181484078, 0.004785234769595854, -0.30900792764301166, 0.15868289204936772, 0.1514471055662453, 0.02010426909176173, -0.007723768729873238, 0.0400149568880292, -0.19380708416417744, 0.14317133450914002, 0.1652778441525135, 0.03383753104159152, 0.06753037662162671, 0.057441669962252896, 0.15859889680797454, -0.08456662356539416, 0.20723436902882886, 0.022975778457050403, 0.03647552669331706, 0.02268313056509434, 0.07413715562520513, 0.2674517995540393, -0.15282930905716383, 0.20401763294565545, -0.02111802726496309, 0.027208629822357003, -0.003619988176361489, 0.14762062830953698, 0.16518652033098694, 5.516225097772204e-5, 0.0076917803526905144, 0.019922512049697458, -0.007450062574899993, 0.1917977138773326, 0.09337370654094214, -0.7797880023858506, 0.033653899415523075, 0.029946269401681536, -0.010949697925744278, 0.1706489812549202, 0.07148139467261647, 0.024236395553170413, -0.04947112991674129, 0.037447757331271016, -0.04731750097461927, 0.13123871279873242, 0.1119379231493105, 0.1069773421954554, -0.03328315114812067, 0.010004916686208114, 0.13990196595244603, 0.15686826127128045, -0.09102982512468961, -0.040183505595639386, 0.005125644446776219, 0.01703776312126654, -0.0024081129989068353, 0.018566990783630447, 0.012363823669023678, 0.01965850586145898, -0.007492825958080688, -0.026977705066778258, -0.006048500593188905, -0.002957434637136203, 0.02553226677389895, -0.021468024712508433, -0.005961591792974111, 0.03432673683568079, 0.015085749519126121, -0.06306034648706481, 0.014583662211204294, 0.007167114279264744, 0.02528322730482621, -0.02057877119524306, 0.003521757706393402, 0.013339963979878125, 0.01722649482431868, -0.035494002257559706, -0.017873604043852374, 0.01896984019995512, -0.0003487062029641723, -0.031888486264531, 0.007179043211616932, -0.009234874971345574, 0.02472646341292331, 0.012657841777114535, 0.002373824383671985, -0.006346282220993162, 0.0230130170996704, -0.0008489414425397793, -0.014731633129321577, 0.022486192406158925, -0.006657528141962751, 0.011813134161829058, 0.06490054394089578, 0.01640743087482918, -0.010384406887498166, 0.02847442086080018, 0.0318893403112016, -0.02561476447616061, 0.0325885858310456, 0.007504210358139129, -0.012155443158799897, 0.019748432384369786, -0.03160679256819454, 0.017577388641755575, -0.07725025343066136, -0.013564495362041863, 0.010713759350081233, 0.031392721900904114, 0.014549009169567246, 0.016933092091177087, -0.04845005843217951, -0.008802116596600011, 0.009509403597096911, 0.032398011588005426, -0.06998173713022414, 0.017636314254447668, 0.0396513585728934, -0.0041769033376947, -0.006060560555730962, -0.019698513290306596, 0.021883930044678476, 0.01560876946209655, 0.0061792768171502815, 0.06686526027733528, 0.041688876638038226, -0.004854408098352971, 0.04836201101993649, 0.03944144269108456, 0.004456228617511184, -0.019540180839428913, 0.04130045901100827, 0.002393792684759943, 0.03168391900902592, 0.012375389994145655, -0.0544755441641335, -0.02153180022411875, 0.02334231933283249, 0.02238600270434996, -0.07419642898660227, 0.00556894293058157, 0.03451967097874344, 0.0040779971879996045, 0.017863725128910497, 0.008720357379401576, -0.04959859001352957, -0.0026407583758240203, -0.026438422209096556, 0.01900806438844183, 0.027966135435493925, 0.012824815166077802, 0.01924220820031534, 0.018954192934522718, 0.0053697771388899005, 0.039207616784569244, -0.023192251455369736, 0.017525865041963115, 0.9180304069410601, -0.2080794364723334, 0.5797750461571177, 0.7392363453011291, -0.07647922497132734, 0.9364851957215946, -0.14547101456007006, 0.9281224674814896, -0.07385039350448451, 0.9366801345428142, -0.09571702463045226, 0.934557529601544, -0.18614358783250295, 0.9205757068103455, 0.01735109212789675, 0.9392729753122149, -0.10846714322237755, 0.9332426620562889, 0.010884942639258903, 0.9393645587814078, -0.1846127571963531, 0.9207700635405651, -0.06869473836555669, 0.9369258266589772, 0.9117276551165114, 0.27171539874192485, -0.1058553440206716, 0.9335368155514088, -0.024539290197676606, 0.9390958891662007, -0.21625534132640786, 0.9118607219526207, 0.9302173132405614, -0.10438834596856801, -0.22942207847853688, 0.9106021660958252, -0.06944666773334246, 0.9368669979562929, -0.01489653219399095, 0.9394412284369315, 0.01044518530238549, 0.9395498641785216, -0.007053535038758294, 0.9393751502855919, -0.23849759838034934, 0.9073171793124397, 0.007774527000709606, 0.9395594475075562, -0.36017416147355547, 0.8670414053540065, -0.09475187158944463, 0.9346481128976931, -0.05522040647114049, 0.937917067910894, -0.046697902050276595, 0.9384193043190224, 0.09289422569242063, 0.9348489378727192, -0.16395808293926253, 0.9248077051362, -0.09529156772180979, 0.9344881712560781, -0.419229213582551, 0.8401803788249705, -0.04843322226343181, 0.9381689765556509, -0.10618433057893531, 0.9335282032865648, -0.05219740214030168, 0.9381243355203948, -0.0905078570955161, 0.9351114299367481, 0.04226704358191705, 0.9384820921487107, -0.28701741584331913, 0.8943152073335402, 0.7206820582749403, 0.6021671505916888, -0.1548831415296158, 0.9264302011320388, -0.35866613071941406, 0.8677810403600319, -0.037204076333624415, 0.9386722112017956, -0.047930089306034776, 0.9383307130113107, -0.12024601868237637, 0.9316506243403444, -0.09881188899247409, 0.9343452642402756, -0.1424377097784745, 0.9285243108256872, 0.012771140160373154, 0.9393309361383511, -0.24573186885970244, 0.9067745678958723, -0.42110953249407485, 0.8396459579341281, -0.24658033680791225, 0.9064693386631074, -0.31283933220333315, 0.8854998407677703, -0.8126521201046415, -0.46850052086891064, 0.03152856235686955, 0.9388934971299765, -0.12770654238476345, 0.9308135001119573, -0.14829025800613016, 0.927683255080742, -0.10009980333408765, 0.9341972430762088, -0.12428484620658807, 0.931164138040077, -0.09147747004883577, 0.9351247085514678, 0.03732470503150059, 0.9386803743959298, -0.48468626944710125, 0.8047451913454133, -0.4036168085733579, 0.8487341497286057, -0.837022674160275, 0.42714130433723313, 0.5759090100928852, 0.7416179003725463, 0.09541032039205039, 0.9345658755955392, -0.5246243957739232, 0.7793191524828494, -0.17048124860583105, 0.9240809800164531, -0.8843055464708104, 0.3176012230155494, 0.5704422629383353, 0.7462560971300654, 0.1351807517247769, 0.9296459999060538, -0.5603894926111671, 0.7540584573137882, -0.09233373400525088, 0.934979894964819, -0.6453679093861092, 0.6827529132869076, 0.6723109851594284, 0.6561605327706277, 0.11371449589569457, 0.9325109507387027, -0.3841357006633298, 0.8573744011818929, -0.08612945140849824, 0.9354910667036281, -0.3802635086928374, 0.8590593984095636, 0.2213506565674809, 0.9128678328196652, -0.14828576345298525, 0.9276688885815043, 0.04577848380587595, 0.9382884097418919, -0.10937192200297416, 0.9330412513393911, 0.19468235884193918, 0.9189977537248539, 0.0015847976308374057, 0.9393901643924867, -0.0854705572480153, 0.9355303047091174, 0.0013004144687326392, 0.9393697698497505, 0.13130461845252264, 0.930229286767561, 0.004205491335750291, 0.9394851513336789, 0.007112258503150016, 0.9393943080298063, -0.017100738219972288, 0.9394132497670578, -0.017140281925444152, 0.9392504488152255, 0.02494786421494637, 0.9392073064742298, -0.09850312311322716, 0.9342474923752927, -0.02942156692150374, 0.9391065038197073, 0.018477750438742443, 0.9392462632875007, -0.0010751572796812868, 0.9394257171905366, 0.021630656870989005, 0.9392676153930298, 0.067347585804035, 0.9370231174261157, 0.05116315273580151, 0.9379496274262334, 0.002071195596385013, 0.9394370117727706, -0.005220370087754941, 0.9394777223830444, -0.033566966068883916, 0.9388105979974257, -0.058467852288425624, 0.9378112235698258, -0.011229415410657806, 0.9395542032983654, -0.03741370367982459, 0.9386670371605059, 0.04104212659527214, 0.9385853055625292, -0.030903255425487497, 0.93922892160168, 0.007829846247913157, 0.9394346346847038, 0.06400632439910368, 0.9372517251987501, -0.030664981813185683, 0.9390472577027429, 0.028832049153538108, 0.9391698532855275, -0.07609807071691456, 0.9363328316631263, -0.039797774047326505, 0.9386898800412031, 0.013293126081158381, 0.9394681646574617, 0.011999822921242664, 0.9394036771848522, 0.09050813140053565, 0.9350633709406848, 0.015580396952876796, 0.9393807523766361, 0.0007848036496169238, 0.9394241403003729, -0.024009018250446774, 0.9391787993696779, -0.07166069271406442, 0.936674325113166, 0.01009965650560946, 0.9394497493988087, 0.0003176405910980173, 0.9393874766294572, -0.004645755429076546, 0.9394304034680856, -0.002500596946039818, 0.9394047914513418, 0.029373481553960717, 0.9389652048661231, -0.03260800864099602, 0.9389370434927743, 0.0003217944228523021, 0.9393811270944068, 0.03918604972413816, 0.938757217644975, 0.017545273095945595, 0.9392750113816821, 0.003074568044846091, 0.9394184606334346, -0.03763037821019194, 0.9387202454087737, -0.0004676213275319874, 0.9394373777533029, 0.004235931837207612, 0.9394053023557312, -0.03318932328165913, 0.9388612099343479, -0.22556505293879028, 0.9122952388952523, 0.04108262037974879, 0.9385267840532259, 0.03363500546034259, 0.9388799131786965, -0.00028502985636274185, 0.9394028282323366, -0.01280186592680199, 0.9393868889327955, -0.013591275268876987, 0.9393185159700981, 0.27310229306211575, 0.8991121226618561, -0.0520630725800233, 0.9379605145311143, -0.019824243506436003, 0.9392568585105726, -0.00015915078843661032, 0.939424596769614, -0.06628770370591432, 0.9371724799407062, 0.14456900609766654, 0.9284885073338687, 0.04692245617200335, 0.9382475945703924, 0.10983970296078502, 0.9330190979755281, -8.571529095151096e-5, 0.9394172899141885, 0.022642617863037416, 0.9391715187266693, -0.10849662300589522, 0.9332198943384185, 0.012380267224302171, 0.9393382221630857, 0.09013697870395654, 0.935115584390006, -2.136385704995228e-5, 0.939415262908026, -0.00670994602472983, 0.9393999449735321, -0.22913248838760453, 0.9111816585573888, 0.006478726613854983, 0.9394002633107466, -0.00230419441464368, 0.9394127184296641, -0.00015307721738495707, 0.9394168147526469, -0.024549430474029747, 0.9391032219255078, 0.18255519844429183, 0.9215223309440477, -0.029825597670690655, 0.9389462554621524, -1.0420042867691961e-6, 0.9394182380926666, 0.004391496639211139, 0.9393931943035638, -0.05735830811471938, 0.9376375399161407, 0.007696016531371016, -0.08760092154595413, 0.03266453107679881, -6.838516903170392e-8, 0.018017872678774475, -0.16224306476728956, -0.012273667858231283, -0.07275357574979102, 0.023624110678146657, 0.06528166085747943, -6.14194716968859e-14, 0.04620560663512691, -0.016144545861231683, 0.09701567456422493, 0.01162213487454992, 0.049760717745096036, -0.043843481071671596, 0.05489481484592177, 0.004692406121097824, 0.116274340721647, 0.06979063068828495, -0.06532300937277145, 0.04412739220610292, 0.08722460871044418, 0.025836569971541105, 0.016934031368860025, -0.059306687946460594, 0.049848241288855906]
Final objective value:     -2471.4149327158602
)

Now let's evaluate our fits by plotting the residuals

julia

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

These look reasonable, although there may be some minor overfitting. Let's compare our results to the ground truth values we know in this example. First, we will load the polarized truth

julia

imgtrue = load_fits(joinpath(__DIR, "..", "..", "Data", "polarized_gaussian.fits"), IntensityMap{StokesParams});

Select a reasonable zoom in of the image.

julia

imgtruesub = regrid(imgtrue, imagepixels(fovx, fovy, nx * 4, ny * 4))
img = intensitymap(Comrade.skymodel(post, xopt), axisdims(imgtruesub))

#Plotting the results gives
fig = imageviz(img, adjust_length = true, colormap = :bone, pcolormap = :RdBu)
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       LM       PV       SM
─────────┼───────────────────┼─────────────────────────────────────────────────────────────
 0.58 hr │ 227.070703125 GHz │ 1.005  missing  missing  missing  missing    1.017  missing
 0.73 hr │ 227.070703125 GHz │ 0.998    1.019  missing  missing  missing    1.012  missing
 0.88 hr │ 227.070703125 GHz │  1.02    0.993  missing  missing  missing    0.973  missing
  1.3 hr │ 227.070703125 GHz │ 0.994    0.997  missing  missing  missing    1.026  missing
 1.45 hr │ 227.070703125 GHz │ 0.979    0.994  missing  missing  missing    1.035  missing
 1.89 hr │ 227.070703125 GHz │ 1.015    0.939  missing  missing  missing    1.015  missing
 2.04 hr │ 227.070703125 GHz │ 1.007    1.026     0.98  missing  missing    1.004  missing
 2.46 hr │ 227.070703125 GHz │ 1.013    1.017    0.965  missing    0.982    1.019  missing
 2.61 hr │ 227.070703125 GHz │   1.0    0.969    1.007  missing    0.991  missing  missing
 3.06 hr │ 227.070703125 GHz │ 1.025    1.013    1.002  missing    0.994    1.023  missing
 3.21 hr │ 227.070703125 GHz │ 0.999    0.985    1.023  missing    0.993  missing  missing
 3.62 hr │ 227.070703125 GHz │ 1.012    1.067    1.017  missing     0.99    1.029  missing
 3.78 hr │ 227.070703125 GHz │ 1.032    0.975    1.033  missing    1.008    0.988  missing
 4.23 hr │ 227.070703125 GHz │  1.02    0.969    1.018    0.926    0.987    1.011  missing
 4.37 hr │ 227.070703125 GHz │ 1.032    1.015    1.017    0.953    0.991     1.01  missing
 4.79 hr │ 227.070703125 GHz │ 1.033    0.932    1.018     1.04    0.996    0.994     0.98
 4.95 hr │ 227.070703125 GHz │ 1.022    1.016    1.006    1.069    1.043    0.995     1.05
 5.63 hr │ 227.070703125 GHz │  1.04    1.004    0.981    1.042    1.002  missing    1.032
 6.15 hr │ 227.070703125 GHz │ 1.012    0.947    0.979    1.024    1.023  missing    0.928
 6.72 hr │ 227.070703125 GHz │ 1.006    1.035    1.004    1.018    1.009  missing    0.952
 7.23 hr │ 227.070703125 GHz │ 0.997    0.974    1.019    1.028    1.013  missing    1.019
 7.44 hr │ 227.070703125 GHz │ 1.019  missing    1.005     1.04    0.977  missing    1.018
─────────┴───────────────────┴─────────────────────────────────────────────────────────────

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), 10_000, n_adapts=5000, 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