Skip to content

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,

Cij=(RRRLLRLL).

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

(I~Q~U~V~)=12(RR+LLRL+LRi(LRRL)RRLL).

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 Vij are given by

Vij=JiCijJj

where J is known as a Jones matrix and ij denotes the baseline ij 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=(ga00gb)
  • JonesD which builds the set of complex d-terms Jones matrices
D=(1dadb1)
  • JonesR is the basis transform matrix T. This transformation is special and combines two things using the decomposition T=FB. 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=(eiφ00eiφ)

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/48C1z/CondaPkg.toml
    CondaPkg Found dependencies: /home/runner/.julia/packages/PythonCall/IOKTD/CondaPkg.toml
    CondaPkg Found dependencies: /home/runner/.julia/packages/Pyehtim/Fm109/CondaPkg.toml
    CondaPkg Resolving changes
             + ehtim (pip)
             + libstdcxx
             + 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"
             │ libstdcxx = ">=3.4,<15.0"
             │ uv = ">=0.4"
             │ libstdcxx-ng = ">=3.4,<15.0"
             │ pandas = "<2"
             │ xarray = "*"
             │ numpy = ">=1.24, <2.0"

             │     [dependencies.python]
             │     channel = "conda-forge"
             │     build = "*cp*"
             │     version = ">=3.9,<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 0x7ff364b717e0>

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 0x7ff364f73460>

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:

  1. 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

  2. The instrument model. The instrument model specifies the model that describes the impact of instrumental and atmospheric effects. We will be using the J=GDR 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 .+.* 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 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),
= 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: 
RectiGrid(
executor: ComradeBase.Serial()
Dimensions: 
(↓ 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)
)
   )

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)
VLBIPosterior
ObservedSkyModel
  with map: sky
   on grid: 
FourierDualDomain(
Algorithm: VLBISkyModels.NFFTAlg{Float64, AbstractNFFTs.PrecomputeFlags, UInt32}(1, 1.0e-9, AbstractNFFTs.TENSOR, 0x00000000)
Image Domain: RectiGrid(
executor: ComradeBase.Serial()
Dimensions: 
(↓ 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)
)
Visibility Domain: UnstructredDomain(
executor: ComradeBase.Serial()
Dimensions: 
189-element StructArray(::Vector{Float64}, ::Vector{Float64}, ::Vector{Float64}, ::Vector{Float64}) with eltype @NamedTuple{U::Float64, V::Float64, Ti::Float64, Fr::Float64}:
 (U = -4.404687701333328e9, V = -4.521597269333328e9, Ti = 0.5833333432674408, Fr = 2.27070703125e11)
 (U = -4.427688319999995e9, V = -4.558917845333328e9, Ti = 0.7333333566784859, Fr = 2.27070703125e11)
 (U = -4.422283775999995e9, V = -4.545737898666661e9, Ti = 0.7333333566784859, Fr = 2.27070703125e11)
 (U = -4.443824298666661e9, V = -4.596403783111106e9, Ti = 0.8833333253860474, Fr = 2.27070703125e11)
 (U = -4.444612451555551e9, V = -4.594719701333328e9, Ti = 0.8833333253860474, Fr = 2.27070703125e11)
 (U = -4.452459235555551e9, V = -4.700912867555551e9, Ti = 1.300000011920929, Fr = 2.27070703125e11)
 (U = -4.453204522666661e9, V = -4.699246847999995e9, Ti = 1.300000011920929, Fr = 2.27070703125e11)
 (U = -4.442525923555551e9, V = -4.738497991111106e9, Ti = 1.4500000029802322, Fr = 2.27070703125e11)
 (U = -4.446617087999995e9, V = -4.727102591999995e9, Ti = 1.4500000029802322, Fr = 2.27070703125e11)
 (U = -4.373388259555551e9, V = -4.848290346666661e9, Ti = 1.8916667103767395, Fr = 2.27070703125e11)
 (U = -4.374057457777773e9, V = -4.846647935999995e9, Ti = 1.8916667103767395, Fr = 2.27070703125e11)
 (U = 1.854972024888887e9, V = -4.900536604444439e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -4.33647849244444e9, V = -4.885093333333328e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = 1.8543247111111093e9, V = -4.898899640888884e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -4.337125802666661e9, V = -4.883456426666661e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -6.191450481777771e9, V = 1.544323338368054e7, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -4.1988920319999957e9, V = -4.985362616888884e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 1.9771115377777758e9, V = -3.616703032888885e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 2.112877287111109e9, V = -4.853924366222218e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -4.1994733297777734e9, V = -4.983740188444439e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 2.1122959964444423e9, V = -4.852301823999995e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 1.9765302328888867e9, V = -3.6150805831111073e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -6.311769287111104e9, V = -1.3143835066666654e8, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -1.3576575533333316e8, V = 1.2372212337777765e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -6.176003569777771e9, V = -1.368659580444443e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 2.2020455187692285e9, V = -4.835182867692303e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.023443446153844e9, V = -3.5993280459487143e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.2014904845128183e9, V = -4.833565380923072e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.0228883987692285e9, V = -3.5977105394871755e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = -1.7860208246153826e8, V = 1.2358548479999986e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.439166364444442e9, V = -4.776837418666661e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.1385755875555534e9, V = -3.547005681777774e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -3.9131562524444404e9, V = -5.122736583111106e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.438692103111109e9, V = -4.775232839111106e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -3.913630471111107e9, V = -5.121131932444439e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.1381013582222202e9, V = -3.545401116444441e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -6.352322559999993e9, V = -3.4589914133333296e8, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -3.005907564444441e8, V = 1.229831726222221e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -6.051731839999993e9, V = -1.575730865777776e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.511586922666664e9, V = -4.755918350222218e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = 2.170796600888887e9, V = -3.528796735999996e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = 2.170351103999998e9, V = -3.5271960746666627e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = 2.5111413973333306e9, V = -4.754317681777773e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = -3.4079030488888854e8, V = 1.2271216071111097e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = -3.554185649777774e9, V = -5.242140615111105e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.691997553777775e9, V = -4.694789262222218e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.2425047537777753e9, V = -3.4769514666666627e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.2421424639999976e9, V = -3.4753602986666627e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -3.5545479253333297e9, V = -5.24054941866666e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.6916352782222195e9, V = -4.693198023111106e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -4.4949279733333284e8, V = 1.2178377671111097e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -6.246183196444438e9, V = -5.47351347555555e8, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -5.796690360888883e9, V = -1.7651891164444425e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.2622677727179465e9, V = -3.457387467487176e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 2.7506836742564077e9, V = -4.671151025230764e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -3.442546884923073e9, V = -5.272523263999994e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -3.4428772102564063e9, V = -5.270935092512815e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 2.2619374342564077e9, V = -3.455799302564099e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 2.750353309538459e9, V = -4.66956284061538e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -6.193230559179481e9, V = -6.013722551794866e8, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -4.88415901538461e8, V = 1.2137635511794858e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -5.704814683897429e9, V = -1.8151358063589723e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 5.063708287999995e9, V = -4.2083771519999957e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.298526215111109e9, V = -3.400051128888885e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -3.088728042666663e9, V = -5.354635448888883e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.8947912462222195e9, V = -4.600179484444439e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 5.063473251555551e9, V = -4.206796074666662e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.894556095999997e9, V = -4.598598385777773e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.298291107555553e9, V = -3.398470051555552e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -3.0889631217777743e9, V = -5.35305430755555e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.1689170879999976e9, V = 3.918022879999996e8, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -5.983519260444438e9, V = -7.544559466666658e8, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -5.962650044444438e8, V = 1.2001283235555544e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -2.7651820871111083e9, V = 8.08326024888888e8, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -8.152436351999991e9, V = -1.1462582471111097e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -5.38725424355555e9, V = -1.954584263111109e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 5.20314781866666e9, V = -4.164995278222218e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.303663210666664e9, V = -3.3806049066666627e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -2.959920895999997e9, V = -5.380193535999994e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.934449208888886e9, V = -4.575548401777773e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 5.202945521777772e9, V = -4.163416078222218e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -2.96012315733333e9, V = -5.378614286222217e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.9342469404444413e9, V = -4.573969180444439e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.3034609279999976e9, V = -3.379025671111108e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.2686985813333306e9, V = 4.105531208888885e8, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -5.894370119111105e9, V = -8.046451235555547e8, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -6.307860088888882e8, V = 1.1949434986666653e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -2.8994846222222195e9, V = 7.843903822222214e8, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -8.163068671999991e9, V = -1.2151982364444432e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -5.26358409955555e9, V = -1.9995886115555534e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 5.54752803555555e9, V = -4.038701703111107e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.299188743111109e9, V = -3.3265329137777743e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 3.020574414222219e9, V = -4.505591765333328e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -2.5786923022222195e9, V = -5.445258367999994e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.547500060444439e9, V = -4.0388189439999957e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.545354601411759e9, V = -4.037995941647054e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.299206753882351e9, V = -3.325316984470585e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 3.0200180856470556e9, V = -4.504489261176466e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -2.5814593882352915e9, V = -5.443281573647054e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.545326531764701e9, V = -4.0381131670588193e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.5269535999999976e9, V = 4.668900488888884e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -7.213856906666659e8, V = 1.179058869333332e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -5.59926673066666e9, V = -9.396666328888879e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.5269256533333306e9, V = 4.667728097777773e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -3.248339306666663e9, V = 7.121688159999993e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -8.126220359111103e9, V = -1.406556682666665e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -4.877881031111106e9, V = -2.1187254968888867e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 3.248311303111108e9, V = -7.122860568888881e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 8.126192398222214e9, V = 1.4064394311111097e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.658309684512815e9, V = -3.9900336836923037e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 5.658283887589737e9, V = -3.990151154871791e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 3.0433165062564073e9, V = -4.479256681025637e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.290543504410254e9, V = -3.3066006843076887e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -2.4295591712820487e9, V = -5.467004468512815e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 5.658234788102558e9, V = -3.9884589423589706e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 3.0432416295384583e9, V = -4.477681939692303e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.2904686145641003e9, V = -3.305025916717945e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 5.658209004307686e9, V = -3.9885764069743543e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -2.429634061128203e9, V = -5.465429700923072e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.614993171692305e9, V = 4.8922299733333284e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -7.527729985641018e8, V = 1.1726559999999988e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -5.472875690666661e9, V = -9.87747757948717e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.6149673616410227e9, V = 4.891055195897431e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -3.367766186666663e9, V = 6.834330141538454e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -8.087868875487172e9, V = -1.4769707651282036e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -4.720102662564097e9, V = -2.160403784205126e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 3.3677403569230733e9, V = -6.835504902564095e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 8.087843052307683e9, V = 1.47685327753846e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 6.037485539555549e9, V = -3.7629412693333297e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.206725866666664e9, V = -3.2192776817777743e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 3.0838075448888855e9, V = -4.360287900444439e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.037469781333326e9, V = -3.763059541333329e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.037566023111104e9, V = -3.761366407111107e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 3.083888028444441e9, V = -4.358713059555551e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.206806371555553e9, V = -3.217702819555552e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.037550279111104e9, V = -3.7614846791111073e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.9536779662222195e9, V = 5.973466417777772e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = -8.77081679999999e8, V = 1.141010222222221e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.953662200888886e9, V = 5.97228362666666e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = -3.830759658666662e9, V = 5.436635751111104e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 3.8307439288888845e9, V = -5.43781858666666e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.193776597333326e9, V = -3.584673976888885e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.193768718222216e9, V = -3.584792625777774e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 2.0963110399999979e9, V = -3.1565621119999967e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.04824456533333e9, V = -4.2709149368888845e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.193972479999993e9, V = -3.583095103999996e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 2.0965068515555534e9, V = -3.154983210666663e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.0484403768888855e9, V = -4.269336042666662e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.193964600888882e9, V = -3.5832137315555515e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.145532039111108e9, V = 6.862409528888881e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.145524195555552e9, V = 6.861223146666659e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = -9.519335111111101e8, V = 1.114352821333332e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = -4.0974655644444404e9, V = 4.2811187466666627e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 4.0974577137777734e9, V = -4.2823050222222173e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.234329756444438e9, V = -3.385946503111108e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 1.931031367111109e9, V = -3.0921642239999967e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.234330837333326e9, V = -3.3860652231111073e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 2.9449131591111083e9, V = -4.1750833208888845e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.234647921777771e9, V = -3.3843593599999967e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.234648903111104e9, V = -3.3844781297777743e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 1.931349447111109e9, V = -3.090577116444441e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 2.94523125333333e9, V = -4.1734962275555515e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 3.289416654222219e9, V = 7.89136849777777e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 3.2894176639999967e9, V = 7.890181191111102e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = -1.0138817973333323e9, V = 1.0829191111111097e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = -4.303298439111107e9, V = 2.937822586666663e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 4.30329948444444e9, V = -2.939009928888886e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.151253688888882e9, V = -3.205430023111108e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 1.7430493191111093e9, V = -3.038615523555552e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 2.7939210951111083e9, V = -4.091441422222218e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.151262791111104e9, V = -3.205548579555552e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.159540360533327e9, V = -3.2139407530666633e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 2.804326297599997e9, V = -4.0944362495999956e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.159549064533327e9, V = -3.214059332266663e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 1.7550084863999982e9, V = -3.039883980799997e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 3.35733262933333e9, V = 8.86011391999999e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = -1.0508717404444433e9, V = 1.0528258951111101e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 3.357341724444441e9, V = 8.858928017777768e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = -4.408204373333328e9, V = 1.6681450088888872e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 4.408213447111106e9, V = -1.6693308977777758e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.086775295999993e9, V = -3.1345589279999967e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 2.719461119999997e9, V = -4.0595089759999957e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 1.6591904159999983e9, V = -3.0189068799999967e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 6.086787583999993e9, V = -3.1346773919999967e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 3.367314207999996e9, V = 9.24950019999999e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = -1.0602706839999988e9, V = 1.0406020399999988e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 3.367326447999996e9, V = 9.248315599999989e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = -4.427584863999995e9, V = 1.1565201249999988e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 4.427597119999995e9, V = -1.1577047599999988e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
)
   )
ObservedInstrumentModel
  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: 
FourierDualDomain(
Algorithm: VLBISkyModels.NFFTAlg{Float64, AbstractNFFTs.PrecomputeFlags, UInt32}(1, 1.0e-9, AbstractNFFTs.TENSOR, 0x00000000)
Image Domain: RectiGrid(
executor: ComradeBase.Serial()
Dimensions: 
(↓ 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)
)
Visibility Domain: UnstructredDomain(
executor: ComradeBase.Serial()
Dimensions: 
189-element StructArray(::Vector{Float64}, ::Vector{Float64}, ::Vector{Float64}, ::Vector{Float64}) with eltype @NamedTuple{U::Float64, V::Float64, Ti::Float64, Fr::Float64}:
 (U = -4.404687701333328e9, V = -4.521597269333328e9, Ti = 0.5833333432674408, Fr = 2.27070703125e11)
 (U = -4.427688319999995e9, V = -4.558917845333328e9, Ti = 0.7333333566784859, Fr = 2.27070703125e11)
 (U = -4.422283775999995e9, V = -4.545737898666661e9, Ti = 0.7333333566784859, Fr = 2.27070703125e11)
 (U = -4.443824298666661e9, V = -4.596403783111106e9, Ti = 0.8833333253860474, Fr = 2.27070703125e11)
 (U = -4.444612451555551e9, V = -4.594719701333328e9, Ti = 0.8833333253860474, Fr = 2.27070703125e11)
 (U = -4.452459235555551e9, V = -4.700912867555551e9, Ti = 1.300000011920929, Fr = 2.27070703125e11)
 (U = -4.453204522666661e9, V = -4.699246847999995e9, Ti = 1.300000011920929, Fr = 2.27070703125e11)
 (U = -4.442525923555551e9, V = -4.738497991111106e9, Ti = 1.4500000029802322, Fr = 2.27070703125e11)
 (U = -4.446617087999995e9, V = -4.727102591999995e9, Ti = 1.4500000029802322, Fr = 2.27070703125e11)
 (U = -4.373388259555551e9, V = -4.848290346666661e9, Ti = 1.8916667103767395, Fr = 2.27070703125e11)
 (U = -4.374057457777773e9, V = -4.846647935999995e9, Ti = 1.8916667103767395, Fr = 2.27070703125e11)
 (U = 1.854972024888887e9, V = -4.900536604444439e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -4.33647849244444e9, V = -4.885093333333328e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = 1.8543247111111093e9, V = -4.898899640888884e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -4.337125802666661e9, V = -4.883456426666661e9, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -6.191450481777771e9, V = 1.544323338368054e7, Ti = 2.0416667461395264, Fr = 2.27070703125e11)
 (U = -4.1988920319999957e9, V = -4.985362616888884e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 1.9771115377777758e9, V = -3.616703032888885e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 2.112877287111109e9, V = -4.853924366222218e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -4.1994733297777734e9, V = -4.983740188444439e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 2.1122959964444423e9, V = -4.852301823999995e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 1.9765302328888867e9, V = -3.6150805831111073e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -6.311769287111104e9, V = -1.3143835066666654e8, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -1.3576575533333316e8, V = 1.2372212337777765e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = -6.176003569777771e9, V = -1.368659580444443e9, Ti = 2.4583332538604736, Fr = 2.27070703125e11)
 (U = 2.2020455187692285e9, V = -4.835182867692303e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.023443446153844e9, V = -3.5993280459487143e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.2014904845128183e9, V = -4.833565380923072e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.0228883987692285e9, V = -3.5977105394871755e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = -1.7860208246153826e8, V = 1.2358548479999986e9, Ti = 2.612500011920929, Fr = 2.27070703125e11)
 (U = 2.439166364444442e9, V = -4.776837418666661e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.1385755875555534e9, V = -3.547005681777774e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -3.9131562524444404e9, V = -5.122736583111106e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.438692103111109e9, V = -4.775232839111106e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -3.913630471111107e9, V = -5.121131932444439e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.1381013582222202e9, V = -3.545401116444441e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -6.352322559999993e9, V = -3.4589914133333296e8, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -3.005907564444441e8, V = 1.229831726222221e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = -6.051731839999993e9, V = -1.575730865777776e9, Ti = 3.0583332180976868, Fr = 2.27070703125e11)
 (U = 2.511586922666664e9, V = -4.755918350222218e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = 2.170796600888887e9, V = -3.528796735999996e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = 2.170351103999998e9, V = -3.5271960746666627e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = 2.5111413973333306e9, V = -4.754317681777773e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = -3.4079030488888854e8, V = 1.2271216071111097e9, Ti = 3.208333432674408, Fr = 2.27070703125e11)
 (U = -3.554185649777774e9, V = -5.242140615111105e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.691997553777775e9, V = -4.694789262222218e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.2425047537777753e9, V = -3.4769514666666627e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.2421424639999976e9, V = -3.4753602986666627e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -3.5545479253333297e9, V = -5.24054941866666e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.6916352782222195e9, V = -4.693198023111106e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -4.4949279733333284e8, V = 1.2178377671111097e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -6.246183196444438e9, V = -5.47351347555555e8, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = -5.796690360888883e9, V = -1.7651891164444425e9, Ti = 3.6249999403953552, Fr = 2.27070703125e11)
 (U = 2.2622677727179465e9, V = -3.457387467487176e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 2.7506836742564077e9, V = -4.671151025230764e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -3.442546884923073e9, V = -5.272523263999994e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -3.4428772102564063e9, V = -5.270935092512815e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 2.2619374342564077e9, V = -3.455799302564099e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 2.750353309538459e9, V = -4.66956284061538e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -6.193230559179481e9, V = -6.013722551794866e8, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -4.88415901538461e8, V = 1.2137635511794858e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = -5.704814683897429e9, V = -1.8151358063589723e9, Ti = 3.7791666984558105, Fr = 2.27070703125e11)
 (U = 5.063708287999995e9, V = -4.2083771519999957e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.298526215111109e9, V = -3.400051128888885e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -3.088728042666663e9, V = -5.354635448888883e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.8947912462222195e9, V = -4.600179484444439e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 5.063473251555551e9, V = -4.206796074666662e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.894556095999997e9, V = -4.598598385777773e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.298291107555553e9, V = -3.398470051555552e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -3.0889631217777743e9, V = -5.35305430755555e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 2.1689170879999976e9, V = 3.918022879999996e8, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -5.983519260444438e9, V = -7.544559466666658e8, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -5.962650044444438e8, V = 1.2001283235555544e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -2.7651820871111083e9, V = 8.08326024888888e8, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -8.152436351999991e9, V = -1.1462582471111097e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = -5.38725424355555e9, V = -1.954584263111109e9, Ti = 4.225000083446503, Fr = 2.27070703125e11)
 (U = 5.20314781866666e9, V = -4.164995278222218e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.303663210666664e9, V = -3.3806049066666627e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -2.959920895999997e9, V = -5.380193535999994e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.934449208888886e9, V = -4.575548401777773e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 5.202945521777772e9, V = -4.163416078222218e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -2.96012315733333e9, V = -5.378614286222217e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.9342469404444413e9, V = -4.573969180444439e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.3034609279999976e9, V = -3.379025671111108e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 2.2686985813333306e9, V = 4.105531208888885e8, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -5.894370119111105e9, V = -8.046451235555547e8, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -6.307860088888882e8, V = 1.1949434986666653e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -2.8994846222222195e9, V = 7.843903822222214e8, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -8.163068671999991e9, V = -1.2151982364444432e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = -5.26358409955555e9, V = -1.9995886115555534e9, Ti = 4.374999940395355, Fr = 2.27070703125e11)
 (U = 5.54752803555555e9, V = -4.038701703111107e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.299188743111109e9, V = -3.3265329137777743e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 3.020574414222219e9, V = -4.505591765333328e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -2.5786923022222195e9, V = -5.445258367999994e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.547500060444439e9, V = -4.0388189439999957e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.545354601411759e9, V = -4.037995941647054e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.299206753882351e9, V = -3.325316984470585e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 3.0200180856470556e9, V = -4.504489261176466e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -2.5814593882352915e9, V = -5.443281573647054e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.545326531764701e9, V = -4.0381131670588193e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.5269535999999976e9, V = 4.668900488888884e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -7.213856906666659e8, V = 1.179058869333332e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -5.59926673066666e9, V = -9.396666328888879e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 2.5269256533333306e9, V = 4.667728097777773e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -3.248339306666663e9, V = 7.121688159999993e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -8.126220359111103e9, V = -1.406556682666665e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = -4.877881031111106e9, V = -2.1187254968888867e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 3.248311303111108e9, V = -7.122860568888881e8, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 8.126192398222214e9, V = 1.4064394311111097e9, Ti = 4.791666805744171, Fr = 2.27070703125e11)
 (U = 5.658309684512815e9, V = -3.9900336836923037e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 5.658283887589737e9, V = -3.990151154871791e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 3.0433165062564073e9, V = -4.479256681025637e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.290543504410254e9, V = -3.3066006843076887e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -2.4295591712820487e9, V = -5.467004468512815e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 5.658234788102558e9, V = -3.9884589423589706e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 3.0432416295384583e9, V = -4.477681939692303e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.2904686145641003e9, V = -3.305025916717945e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 5.658209004307686e9, V = -3.9885764069743543e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -2.429634061128203e9, V = -5.465429700923072e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.614993171692305e9, V = 4.8922299733333284e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -7.527729985641018e8, V = 1.1726559999999988e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -5.472875690666661e9, V = -9.87747757948717e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 2.6149673616410227e9, V = 4.891055195897431e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -3.367766186666663e9, V = 6.834330141538454e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -8.087868875487172e9, V = -1.4769707651282036e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = -4.720102662564097e9, V = -2.160403784205126e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 3.3677403569230733e9, V = -6.835504902564095e8, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 8.087843052307683e9, V = 1.47685327753846e9, Ti = 4.945833384990692, Fr = 2.27070703125e11)
 (U = 6.037485539555549e9, V = -3.7629412693333297e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.206725866666664e9, V = -3.2192776817777743e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 3.0838075448888855e9, V = -4.360287900444439e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.037469781333326e9, V = -3.763059541333329e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.037566023111104e9, V = -3.761366407111107e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 3.083888028444441e9, V = -4.358713059555551e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.206806371555553e9, V = -3.217702819555552e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.037550279111104e9, V = -3.7614846791111073e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.9536779662222195e9, V = 5.973466417777772e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = -8.77081679999999e8, V = 1.141010222222221e9, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 2.953662200888886e9, V = 5.97228362666666e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = -3.830759658666662e9, V = 5.436635751111104e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 3.8307439288888845e9, V = -5.43781858666666e8, Ti = 5.633333265781403, Fr = 2.27070703125e11)
 (U = 6.193776597333326e9, V = -3.584673976888885e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.193768718222216e9, V = -3.584792625777774e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 2.0963110399999979e9, V = -3.1565621119999967e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.04824456533333e9, V = -4.2709149368888845e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.193972479999993e9, V = -3.583095103999996e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 2.0965068515555534e9, V = -3.154983210666663e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.0484403768888855e9, V = -4.269336042666662e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.193964600888882e9, V = -3.5832137315555515e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.145532039111108e9, V = 6.862409528888881e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 3.145524195555552e9, V = 6.861223146666659e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = -9.519335111111101e8, V = 1.114352821333332e9, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = -4.0974655644444404e9, V = 4.2811187466666627e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 4.0974577137777734e9, V = -4.2823050222222173e8, Ti = 6.1499998569488525, Fr = 2.27070703125e11)
 (U = 6.234329756444438e9, V = -3.385946503111108e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 1.931031367111109e9, V = -3.0921642239999967e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.234330837333326e9, V = -3.3860652231111073e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 2.9449131591111083e9, V = -4.1750833208888845e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.234647921777771e9, V = -3.3843593599999967e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.234648903111104e9, V = -3.3844781297777743e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 1.931349447111109e9, V = -3.090577116444441e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 2.94523125333333e9, V = -4.1734962275555515e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 3.289416654222219e9, V = 7.89136849777777e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 3.2894176639999967e9, V = 7.890181191111102e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = -1.0138817973333323e9, V = 1.0829191111111097e9, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = -4.303298439111107e9, V = 2.937822586666663e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 4.30329948444444e9, V = -2.939009928888886e8, Ti = 6.716666579246521, Fr = 2.27070703125e11)
 (U = 6.151253688888882e9, V = -3.205430023111108e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 1.7430493191111093e9, V = -3.038615523555552e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 2.7939210951111083e9, V = -4.091441422222218e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.151262791111104e9, V = -3.205548579555552e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.159540360533327e9, V = -3.2139407530666633e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 2.804326297599997e9, V = -4.0944362495999956e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.159549064533327e9, V = -3.214059332266663e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 1.7550084863999982e9, V = -3.039883980799997e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 3.35733262933333e9, V = 8.86011391999999e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = -1.0508717404444433e9, V = 1.0528258951111101e9, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 3.357341724444441e9, V = 8.858928017777768e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = -4.408204373333328e9, V = 1.6681450088888872e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 4.408213447111106e9, V = -1.6693308977777758e8, Ti = 7.233333349227905, Fr = 2.27070703125e11)
 (U = 6.086775295999993e9, V = -3.1345589279999967e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 2.719461119999997e9, V = -4.0595089759999957e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 1.6591904159999983e9, V = -3.0189068799999967e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 6.086787583999993e9, V = -3.1346773919999967e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 3.367314207999996e9, V = 9.24950019999999e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = -1.0602706839999988e9, V = 1.0406020399999988e9, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 3.367326447999996e9, V = 9.248315599999989e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = -4.427584863999995e9, V = 1.1565201249999988e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
 (U = 4.427597119999995e9, V = -1.1577047599999988e8, Ti = 7.438888907432556, Fr = 2.27070703125e11)
)
   )
ObservedInstrumentModel
  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 = [0.011774702707330907 0.023718120293101764 0.036026487221095305 0.048767563131383564 0.06207601319376344 0.07586915895953768 0.09000659112194623 0.10399567751539493 0.11697110360366769 0.1275908531997236 0.13454367219657795 0.13735031212253987 0.13683576617785595 0.13434888787430688 0.13063586763793822 0.12563448396188964 0.11876489942135515 0.10983138604420674 0.10004007050653947 0.09088094965969151 0.0831786765352719 0.07706104017633887 0.07226706261631444 0.06823147970387981 0.06427998207294451 0.059684364145557764 0.05415148466131004 0.04733039249638189 0.0394465945950848 0.03046468166977248 0.02076512394618923 0.010511335228925566; 0.023385765528112386 0.047152079301642114 0.07161887263536693 0.09710499815425726 0.12372218713379828 0.15154246865344084 0.18026559922710347 0.2091443724371165 0.23638519635609845 0.2589360915298476 0.273295749570947 0.2780842230712116 0.2756894341364563 0.2697483033782077 0.2623300298486678 0.2527753124993218 0.23913326595419113 0.22021775829183407 0.19937857777450219 0.1803080382944428 0.16471067099623649 0.15273869556767197 0.14376397700915833 0.13648137791674808 0.1292174731488265 0.12053674343890673 0.10950648749791311 0.09597790714247237 0.07988798152404258 0.061805400635417326 0.042066784080013436 0.021303681052311372; 0.03466568624546154 0.06993007910142161 0.10635883552527545 0.1443989175869955 0.18441045012348975 0.2265061579313954 0.2706030053744986 0.31600746826352544 0.36034269877577363 0.3979437094224732 0.42088922059629597 0.42546605971552903 0.41736804898965213 0.4047111000624539 0.39311756735610975 0.38180956038797886 0.36269515484632786 0.33196491339827905 0.2972401457563422 0.2661970651042076 0.24197803093925255 0.22483765145740997 0.21339655184998776 0.20483992074528348 0.19583054726140622 0.18384410627167747 0.1676922666533345 0.14711511191618523 0.12262402840077576 0.09477057150196022 0.06453416516155064 0.03264840575759059; 0.045404427938081846 0.09165954425048292 0.13961877843199705 0.18998032662463732 0.24327803300225914 0.29983897447509184 0.3599056568874644 0.42361836739782704 0.4894273866218617 0.5488164513020544 0.583323087832096 0.5823498568875467 0.5601180509616298 0.5313199501730034 0.5106175306797774 0.5054124209484129 0.49260197705224634 0.449049853456749 0.39184468253737315 0.34308592681446215 0.30893203738527936 0.28891094613582496 0.2793242160866615 0.27376450460369495 0.26574066748287717 0.2516334948076897 0.23043679167315054 0.20249794893474005 0.16872938462783962 0.13039403246100442 0.08866090263441392 0.04486085360255328; 0.05532673821912581 0.1118559101793017 0.1706762039536434 0.23289603186096114 0.29926257737587925 0.37021847988871825 0.4461642155070966 0.5285175520996195 0.6198627507648851 0.7145272305069971 0.7745761226028228 0.756242125843971 0.699358040288324 0.6292304112334648 0.581814957191841 0.5915748913165445 0.6166746191380965 0.5687734321857966 0.4747711084432506 0.3990003159109852 0.3542241715716607 0.33737459339533055 0.33886506901045776 0.3441139106446173 0.3412127364268318 0.3262780156161492 0.29997705320687107 0.26388008100261157 0.21973010127300496 0.16947972859428842 0.11509762042284158 0.058119813592612105; 0.06419901001790289 0.12986070622748577 0.19859798694032532 0.2719168200038022 0.35101158017509865 0.43615910611723496 0.5267147499591365 0.6241240417540181 0.7379027733782042 0.8792426170121185 1.0035493644377973 0.9650012557089869 0.8200771868488187 0.653685620850755 0.5543278722426437 0.5820598363697835 0.692458469979499 0.6756352549971686 0.535263536415673 0.42344700176606287 0.3668011435501139 0.3624072781403834 0.390194124621084 0.4171638605710916 0.424357855921544 0.41015182597860994 0.3788159881147691 0.3334454601146216 0.27705737628209076 0.2130200611824311 0.1441832878505849 0.07270813015419891; 0.07162944890917651 0.14504024770250235 0.22214053237860445 0.30520332396974165 0.39629027959061003 0.49517226569290823 0.5966220830828664 0.6932670806977943 0.797479470182466 0.9464801815812284 1.1179776234101448 1.0735307268024197 0.7996722217953598 0.5282101651365391 0.40037596360224226 0.4511157857418136 0.6677098269164405 0.7579111249746056 0.5720378061585566 0.414798260254997 0.3484426278805875 0.367698809088518 0.4316023076195871 0.4892984838280931 0.5136571450075794 0.5046102009361251 0.46964888580897135 0.41357012933192905 0.342137991346077 0.2615651093121662 0.17620810155643177 0.08854513395310641; 0.07743879859416311 0.1566688174281305 0.239863443031383 0.32991755460720307 0.43029393497053803 0.5410965712256123 0.6493857819452519 0.7211895324721694 0.7452826703517484 0.7676155180252979 0.7896544015288439 0.6794680419513953 0.4496717569229269 0.24514377898311931 0.1718106641407262 0.2657116911970052 0.5342952715324496 0.7568154732912893 0.5430500856547305 0.36060809667850535 0.29984771036291047 0.34088278766425734 0.43689936740220053 0.5360459479596862 0.5994448055514924 0.6110865477444566 0.5768048382813077 0.5073661690089205 0.41618520520485625 0.31519267673039203 0.2107748420064092 0.10545816903235636; 0.08153678658092291 0.16451966060432982 0.25074363252520976 0.34295759275190263 0.445035386798798 0.5586159180352002 0.6683263907123075 0.7224973883022622 0.6784278795092784 0.5821045463568814 0.47079187082684737 0.3188444207514454 0.1350418922680538 0.0010540784291207085 -0.012812391674380634 0.1070301592588348 0.3200866166348216 0.43744188176971005 0.3413887243317023 0.22536736927845494 0.20629421629790037 0.28285663442580367 0.42176806820172613 0.5867987167787974 0.7242460209438548 0.7709945307275976 0.7239608713432147 0.6224737963114712 0.49965723483493985 0.3724544620498219 0.24651886344766583 0.12263831483830037; 0.08429614363684369 0.1692656135193095 0.2556053668072557 0.34422716969072337 0.4362222493706197 0.5295867087597654 0.6094750764146126 0.6354322017453523 0.5681137340786824 0.435189627961309 0.28036153851811246 0.12029534784769368 -0.014288686816249667 -0.07660871308093783 -0.03405049771597276 0.10354712082616059 0.2401165468137526 0.24450987674796726 0.15790728429870335 0.09094283894815061 0.11749846956737385 0.23534161745909646 0.4294476978767074 0.6823130012522917 0.9315450357908425 1.0160254085338503 0.9194191026946393 0.7541007250396965 0.5853284364464268 0.4280869125806694 0.280389895053228 0.13872753158417855; 0.08644564755338985 0.1726217392799953 0.2577763202460607 0.3401163924695506 0.4162831531520802 0.47940040518324406 0.51700428839564 0.510031252330697 0.43906784572673163 0.31188681427414955 0.1650754166448191 0.04191520589009844 -0.012086843441315515 0.03686395039771349 0.1855796060813302 0.35187106524626344 0.37199996412846315 0.22567920149218546 0.12284030904554605 0.08940507883515021 0.10202904434682619 0.1864644646343135 0.3691835180888965 0.6887597161685748 1.133411997545862 1.2866988838155338 1.1038458075143054 0.8648968316196677 0.6552902525891536 0.4736274932312199 0.30826477620421305 0.15202016939629107; 0.08891791672790253 0.17696461671095984 0.26239586594284064 0.34173668897226395 0.4091355353333611 0.4555459020220267 0.469062760725512 0.43360543422366227 0.3360583702671042 0.1961227089596498 0.07391659313107593 0.032578919101669976 0.12228919018958793 0.36965468719065153 0.6853468099538937 0.765735750333134 0.46719129378072416 0.2445076580088917 0.23725166831964908 0.2430036222448592 0.11567722841803277 0.07908771835808799 0.19006697164805283 0.4804254221982978 1.0165558261204883 1.405272973058386 1.1787878369380749 0.9173592377338127 0.6953110922677453 0.5026066070886248 0.32702708890658 0.1612139034266324; 0.09241389871394545 0.18425283228050923 0.2739744104628565 0.3580611073552528 0.4304256337781854 0.48032364880784656 0.4849702029062992 0.40965119202295075 0.25934200677943375 0.10016178331830138 0.02792087061475598 0.11908252605210995 0.40998025020577133 0.6029020316427287 0.14243085473566008 -0.1291282510409239 -0.24710573057843646 -0.18563981468188592 0.18064704807028725 0.46515779622119124 0.0981473353473892 -0.05985431558555199 -0.00975245645365937 0.2275286544937689 0.6418902167560103 1.0247248344956656 1.07996007817201 0.911018128686839 0.707779220185141 0.5155893032187026 0.3363952273956389 0.16602091495024737; 0.09663326602013549 0.19403417505998843 0.2924427259251956 0.3907160633360271 0.4856153544687762 0.5662052787891235 0.5838734893111651 0.45945872258649595 0.2660781335975657 0.0876684051723496 0.051232647661730545 0.2550803644489125 0.6400395967192157 0.18950142439716838 -0.3453533794329606 -0.6018591177183469 -0.6548235944068189 -0.5121203507635133 -0.14655912592871576 0.2717248398173326 0.04587378452025479 -0.14493305406650922 -0.11202896632514109 0.10253115969973749 0.45969480760642184 0.832414277479662 0.9758686608992332 0.8765771205546373 0.6994887252615236 0.5145761008955987 0.33702228299846665 0.1666291518826411; 0.10029527797544593 0.20313070766001273 0.3115723996792432 0.4289945309216076 0.5564738792708125 0.6754255754510978 0.6865734863236103 0.47595678712633066 0.18682139313837978 -0.016421891662214985 -0.03227992824411376 0.18620771663429037 0.6365371387663432 -0.08731073762915298 -0.5759639209026938 -0.7952437996949029 -0.8159300860933574 -0.6517782717220172 -0.3041581517295397 0.08474693231832402 -0.018484090620025314 -0.15517738949413 -0.10712587923312238 0.12090459019601461 0.4724225887733646 0.8075393348846276 0.9060911721002464 0.8215803415323957 0.6699699018399063 0.4997259310147496 0.329588055008474 0.16349833614277565; 0.10152630857724497 0.20655053325921857 0.3197014593980262 0.44722016982909585 0.5902989375038148 0.7064113552228489 0.6300765965662405 0.34456704959732265 0.03970588321772757 -0.15298230597917903 -0.15527908793258718 0.09351415529665347 0.5307061272564677 -0.13511502025633318 -0.570219227530541 -0.7493880005726424 -0.7413247568451432 -0.5511899467235817 -0.17618197085150297 0.13034326815016176 -0.06205141181778999 -0.15518724149018417 -0.057053725927819786 0.22635021189026877 0.6587039938260559 1.049909517129257 1.0062565684710718 0.8220953896856744 0.6471492386622483 0.48029979012916607 0.31745492634968764 0.1578115638287125; 0.09919674361790298 0.2014132635084276 0.3101943907574835 0.42967593548858724 0.5564034341814095 0.6404145861363337 0.537742327545369 0.24952948375243691 -0.028763988687077365 -0.20058926908223532 -0.2032528474457286 0.021271181764497615 0.4653272196733575 0.051154858636754015 -0.3081030900107335 -0.4114795943504895 -0.3720326803230213 -0.17535172900989998 0.2708786955759505 0.2889112847516505 -0.02925440779582557 -0.09634402894491638 0.017094594001136346 0.2792530847994576 0.6834025638345499 1.0687826263758502 1.0346871197096466 0.8192211464358833 0.626270146671058 0.45888779831315923 0.3024937264599277 0.15042022249142406; 0.09374281484778997 0.18920753293854056 0.28800594256409473 0.39139743653459746 0.4949752482157515 0.5665936769288865 0.5201622053227345 0.3234322257858733 0.07327271981804784 -0.12347999146500337 -0.19260051992633365 -0.097018389171935 0.1597528053610985 0.20416479742625615 0.21565131036557875 0.399364607495127 0.4001700235564217 0.19484385718487524 0.1352549559763762 0.020447737878612496 -0.07248056067319857 -0.013270860560190468 0.11761262628837973 0.2955112033890621 0.5446354031429627 0.7754306558717716 0.8234338655324535 0.7209831582758021 0.5743638535667911 0.4269241674296321 0.28334301948699897 0.1414490283636462; 0.08662632338310405 0.1737368399708877 0.26137817570223676 0.34934918824283473 0.43701524239881523 0.5163346097752229 0.5575982377654042 0.5074880431791434 0.3053991200917767 0.04538462667372025 -0.14436290780945915 -0.21397884277297963 -0.16579907354876347 -0.02894909326534188 0.36044071336639677 0.5781278019416313 0.10036241929381524 -0.18765593393334246 -0.2920405572984286 -0.2596922627751172 -0.10503025561572166 0.14634549459634705 0.3079076579273558 0.31243300519769596 0.371477659230333 0.4875978742134196 0.5752528678011055 0.5745317423814192 0.49850517721175835 0.3870332689049201 0.26222398972265826 0.1321356275499248; 0.07907125779479236 0.15788869941442063 0.23560104921973443 0.3110294543975204 0.38480826879403685 0.46159689090717393 0.5409708342789339 0.5837952082712119 0.45821060969797656 0.18005924055385045 -0.08871848538741264 -0.25991420578321933 -0.3048696345945823 -0.209323656427288 0.031112351563059904 0.0927301413064745 -0.22656839609940188 -0.4499097741519567 -0.5113422865368298 -0.41098403786056176 -0.1465645569807952 0.2515928039671206 0.5196536878249469 0.3875106841702371 0.3422438172208117 0.39530078412921915 0.46955844226593496 0.4935640089653014 0.44858982517009116 0.35843541886455477 0.24654075295014583 0.12509721409007865; 0.0717221413293879 0.14288452914886837 0.21238047600695023 0.2786188679964907 0.34209979506508387 0.409770027522281 0.4919087507011104 0.5744016387846375 0.5481434027983401 0.3533502918042106 0.08052822847426688 -0.1466135102414914 -0.2523450778644013 -0.21574192346266052 -0.0712492657673716 -0.07129638992427692 -0.2909473349847776 -0.4671473885926115 -0.5126970979019752 -0.40739666401564006 -0.14070327698869445 0.27646154897743175 0.6578882617088008 0.5625850704668447 0.4979870343116903 0.5049943422843731 0.5232864381045366 0.5072184441856434 0.44525575934701805 0.3515207635035542 0.24076675677894596 0.12196715223523023; 0.06494159724820225 0.12941568178449414 0.19273663253905104 0.25395366486722565 0.31281658209752355 0.37285522509653324 0.4417848439789818 0.5194445923433866 0.566772733007081 0.544449155507164 0.36016869032241766 0.10236821081673957 -0.05702683734215574 -0.06313941802588817 0.04675945107650875 0.07670967306088161 -0.08049026956223188 -0.24442941048375783 -0.3132899340659923 -0.24705684454373852 -0.03515799259323589 0.30956260954947007 0.6931498312480805 0.8066556349518137 0.8447553450018623 0.7834261674769045 0.6886579147821034 0.5859069518187996 0.47701641544088563 0.3624006044767092 0.24347548329996793 0.12221887632929745; 0.058657691643827115 0.11717337946967948 0.1754495052950109 0.2335879833440321 0.29180875089299746 0.35056572550818693 0.41192327838026926 0.4830125637795528 0.5760762899069525 0.6448056050737264 0.5281241172262632 0.26555571066681105 0.07030369582172234 0.01901655995889575 0.0937277729935283 0.1997351251955864 0.2611289289366677 0.18917587336742803 0.08205722198118105 0.06147972101071199 0.1710376035818889 0.408921151461551 0.7568207452463651 1.1034956212301648 1.2626071799537857 1.1257962056875848 0.8806928835816885 0.6784986753949087 0.5176722671478664 0.37850547466675305 0.24895245741602762 0.12363390321928676; 0.05258088761263762 0.10523222022214242 0.1581115252680718 0.21161859239462752 0.26605683372286354 0.3207370462659781 0.3740123979569319 0.4269085105422045 0.48404406730979527 0.5151164521303812 0.4384252693831738 0.2664227261566403 0.1274760900703926 0.08947187132626988 0.14855943559447093 0.27994491393587284 0.4578848188147042 0.6219576229869449 0.544093518538001 0.4251797114183304 0.41247219838533394 0.525859956831442 0.7665851232285615 1.103381371201064 1.370054016821718 1.2361863936939215 0.9537024837744564 0.719700857034855 0.5372919233968293 0.3857284792093478 0.2505070244200441 0.12351221208559347; 0.04654182169613023 0.09313400798864381 0.1399539306885125 0.18706897916912504 0.23421945825748922 0.2799712327339165 0.32192337997386855 0.3590713381746553 0.3891362592689565 0.39545510133348405 0.34885971965098417 0.25818057729164867 0.18299056734952712 0.17007950000044117 0.23085712831840965 0.3571016919147919 0.5162199327275808 0.6347707814683676 0.6549147567688648 0.6180056712860507 0.6156444612223356 0.6819579699288464 0.8354260291398933 1.051569350289597 1.2009879327417288 1.1072699212760382 0.8967116849390955 0.6955373270225748 0.5245870012443935 0.3768308260211087 0.24410151973890967 0.12007931298296207; 0.040437603373075705 0.08096571590347496 0.12147160663545585 0.1619205185830711 0.20183802377453713 0.24016541334050845 0.27565461220508014 0.3075040147734795 0.33313806201030444 0.3423115491390657 0.32115989782645543 0.27800185187922277 0.2517059845747717 0.2771165407219494 0.3609886759924544 0.4829471775055572 0.6018826680932904 0.6908110753321771 0.7637590653387574 0.8590617068600972 0.9631687889047209 0.9843892494362129 1.017446133386084 1.0731044132691323 1.0718963003427924 0.9654084256874532 0.8044004021320368 0.6394542415491484 0.4886748383968323 0.3531664720351077 0.2292839778433024 0.11285256162977407; 0.034465289421505466 0.06883067695983412 0.10317306947550832 0.137237872986259 0.17065726915657187 0.20281145343864693 0.2331112737737281 0.26119930044809475 0.2854500799690736 0.3011541880635457 0.3043732413631062 0.30455099280545417 0.3270139626132321 0.3938024754966926 0.5036164399100312 0.6254856653078963 0.7245514516204014 0.814181712596253 0.9452987445315517 1.1858016339029458 1.5098981914052856 1.4044115579139937 1.2058761890179368 1.074937099333028 0.9701331565735706 0.8458294946904472 0.7064027584013929 0.5677003832460116 0.4378615422435544 0.3183139626315572 0.20733543163166204 0.10221044298107435; 0.028484048600642263 0.05694579509678606 0.08525501772666647 0.11326461706112076 0.14077078779848276 0.16746419780778396 0.19310504523415653 0.2174242268676194 0.23968395322899588 0.2588053865755531 0.27612836173678723 0.30054365756081325 0.3485266761428317 0.43212886899099096 0.5458249570689376 0.6658416278127312 0.7686406461954542 0.8706549955465595 1.0419647059877772 1.3386737451303952 1.7176225576313713 1.547539924591095 1.2296306451707706 1.0075089086173419 0.8543116765445511 0.7250329258851158 0.602808337564273 0.4863077883110239 0.3770838685042031 0.27533681795421994 0.17985751975699213 0.08881265837368814; 0.02265430454962642 0.04526400575431658 0.06769530986809733 0.08997830131919772 0.11182917093858576 0.133266431236547 0.1541949368418801 0.17456351953773724 0.19435364361086568 0.21412816871284068 0.2361038359036484 0.2665256691177318 0.3151829626274686 0.3872805609204566 0.47759271010546944 0.5758420846252931 0.6721263389498989 0.7743986892803021 0.9128069526349856 1.0950694825600704 1.2473384743578504 1.1785685914707602 1.002509349489517 0.8384096653533706 0.706137427935634 0.593871427095746 0.4922089819571615 0.3976316862412824 0.3092420278105454 0.22642235817231074 0.14826455694800453 0.07327184862092255; 0.016901236949690455 0.03375471465772109 0.05055042207764791 0.0671027243957276 0.083503865795526 0.09965388909391047 0.11562171148939003 0.13152857132033535 0.14771001327292657 0.16505165630157384 0.18548524342971584 0.21281049579763212 0.25196387326620273 0.30488998125679634 0.3687998863859282 0.4399762870428185 0.5154624267331903 0.5971290192176831 0.6905822106324543 0.7877285169765996 0.8501025959840237 0.8220494942818932 0.7333999739915055 0.6318200556952012 0.5373757246183354 0.4524592889204947 0.3749776220411486 0.3032083151517695 0.2361990426044537 0.17328863636731237 0.11358717992761645 0.05624062218844433; 0.011225395818408779 0.022431656029247606 0.033555314932619616 0.04460888510023328 0.055521145255671756 0.06633527483565062 0.0771453939821804 0.08807637537559566 0.0995099004873447 0.1121887940895779 0.12742388425960677 0.1472974325228731 0.17407529937476005 0.20854052807878182 0.24961197803940477 0.2957581955762246 0.3459956524255668 0.39976288845809926 0.4557150201761261 0.5062036509851273 0.5339877431965567 0.5214658745535277 0.4769364824809128 0.41911786790899624 0.3601204487541341 0.30439393529869735 0.2526229799772346 0.20448699957313257 0.15946648038807398 0.11710513578961376 0.07687028874430095 0.03803004624117399; 0.00559594116229046 0.011188773608038608 0.01675034229872765 0.02226321542558627 0.027712926799698286 0.03316806106133013 0.03860237531288113 0.04418053295227773 0.05009606404522082 0.05675559952116219 0.06481684718477623 0.07517612419363243 0.08871454057166983 0.10574745476430937 0.1259328375688824 0.14870946033706572 0.17354738890633897 0.1997224928753237 0.22567703377272708 0.24752816335203578 0.2586622024985417 0.2535944469915104 0.23466380183338878 0.2084540259236139 0.18029569176663932 0.1528727416144148 0.12706246551983869 0.10292151947497608 0.0803269591441693 0.0590303229898825 0.03874011791189597 0.01922168060261921], hyperparams = 25.796611756430927), σ = 3.2100458151889106, p = (params = [0.006921166996030833 0.013903872621995102 0.020905608108186244 0.028015335405782684 0.03514789595365393 0.04229740557816008 0.04936438802701279 0.056177014840379 0.06259749051490315 0.06839832423866747 0.07337906880599288 0.07743068077200539 0.08043808508386509 0.08241761013841235 0.08343304867999246 0.08360885283835914 0.08295550026557655 0.08139012799113575 0.07892650510792866 0.0757044132691363 0.07186719050431853 0.06755285441364456 0.06282927792490522 0.05774989115660398 0.052325765744317555 0.046529628064431276 0.040455078884628064 0.03407614982510175 0.027498611614624476 0.020752750073137823 0.013889796519651316 0.0069639092774657725; 0.013846346829326494 0.027742023517862195 0.041802910509590334 0.05599761648346323 0.070352354347282 0.08475475170775007 0.09900857754497353 0.11286734670338901 0.12588780404975614 0.13766929325902025 0.14779916643898228 0.15596299708654598 0.16199703448985406 0.16587945579601865 0.1678034430426234 0.1681030283888413 0.1668358326217838 0.1636850785721974 0.15867172219791612 0.1521012788766063 0.14431300569322308 0.13558983368217684 0.1261225366675488 0.11594359351691147 0.10504576194953116 0.09347130144118673 0.08122189282238784 0.06843154420060368 0.05520482997376417 0.04164361613304058 0.027874802780323196 0.013966695306390952; 0.02068594482838604 0.04152102811288208 0.06257270191413578 0.0839406964176073 0.10560869079208231 0.12745049556323704 0.1492345264236737 0.170476623871781 0.19055984714674337 0.2086981705549996 0.22419673515847588 0.2366071110454303 0.2456820038998405 0.25122704292747366 0.25383469879747533 0.25437123012442636 0.252578478089164 0.24779794739450847 0.2400434026465956 0.2298487684026329 0.21783991699710123 0.2045529643663067 0.19027499601165354 0.17500118254757352 0.15864111208584 0.1411696467769769 0.12266880577565618 0.103332629693372 0.08329952934501646 0.0628278190450647 0.04202954288939101 0.021051473527677; 0.027457184609668984 0.05510153079548635 0.08314622555331298 0.11171086067326357 0.1408200478124072 0.17041434111166656 0.2001394374577938 0.229391743702106 0.25721913652227857 0.28233080722043646 0.3033200493818878 0.3197742374535058 0.331840493351191 0.33860122724301944 0.3412854365659149 0.34254250283499443 0.34129294872864596 0.3347153413193727 0.3234013113013304 0.30899899934545627 0.2925064563582845 0.2746020716144277 0.2556101042684383 0.23536203090084068 0.21354608979281184 0.19008877349162615 0.1651705967363289 0.13900937498069513 0.11201921932660167 0.08439809258341155 0.05642046169961692 0.028267107766059656; 0.03404188237288687 0.06839538303984809 0.10332963347709492 0.13906738658315376 0.17578642277543513 0.21342914203516877 0.2516788593874894 0.28970582388318 0.3261715241173748 0.3592423887290417 0.3859485706892275 0.404650498158567 0.41873349924352693 0.4256554757569343 0.42735934561739347 0.4296951070340857 0.43100325017918883 0.42283150651633744 0.40697601507681486 0.3882001316415715 0.36753152726830507 0.34544798959303635 0.32225767369846636 0.29739776091016035 0.2702431774490288 0.2406802247943961 0.20902906128996732 0.17580459786439503 0.1414585549914405 0.10646111208135473 0.07112392852170059 0.03556684814219508; 0.04039211417292192 0.08120363520923679 0.12283408722622281 0.16568650790743997 0.21002697526231195 0.2559995656697767 0.3033119769729105 0.3508291728930569 0.39646588907672553 0.43773143423178196 0.47071987185003084 0.48945401533813176 0.501568085078237 0.5055467124650512 0.505011043957555 0.5081018661237663 0.5140526836666001 0.5061560190156292 0.48683997291590936 0.46527375946502597 0.44158326262051334 0.4165417451404828 0.39033828869632103 0.36157056758179845 0.3292655129983918 0.2934305597084296 0.25470331374191846 0.21388179477012043 0.17178300891894183 0.1290614552439932 0.08604802096669197 0.04305529428684929; 0.04637971080552565 0.09329474109872951 0.1413201651356499 0.190990442285543 0.24284738115797128 0.2971701509654384 0.3535469440398478 0.4099360747936208 0.46274332449653277 0.5084651737048905 0.5430818297849069 0.5607032380593706 0.5695746866002557 0.568965816404463 0.5675659743963632 0.5714244796785846 0.5820579732456136 0.578785711918 0.5600813647353798 0.5376893532472886 0.5132326629663276 0.48765261906942586 0.45990522224768204 0.4281769002689945 0.39118966380413883 0.3489598357644098 0.3025703496684303 0.25343171716804025 0.20294217266483533 0.15203460487875922 0.1012264907271484 0.05052668966530866; 0.051872772296081636 0.10442617163357705 0.15832117570891907 0.21432900039762376 0.2732587768884306 0.33566980241120453 0.400807808721272 0.46433666763294146 0.5184113170461229 0.5586062839581103 0.5856946943541518 0.6009869320563487 0.6100115595571428 0.6120975474685424 0.6136615685567298 0.6204662508374569 0.6345034384144095 0.64052885134005 0.6241129630639985 0.6026165705929872 0.5796329469978755 0.5550732595336856 0.5274663487694761 0.4951154089587554 0.4557429701508442 0.4077051592103372 0.3528127089608351 0.29431658771610064 0.23466204321487585 0.17519862626522592 0.11632060349994643 0.058006983755855675; 0.05677890807041303 0.11431658523586995 0.1734237571320601 0.2349755856712783 0.30005761360818783 0.3695904886222615 0.4428081200293826 0.5135664318300038 0.5692107519345193 0.6043842742113938 0.6245441288683006 0.63657329948161 0.6426115090522506 0.64411752080149 0.6463822032624257 0.6543181095186557 0.6686091669562827 0.6768614659652387 0.6703974537861014 0.654436931854697 0.635232688349194 0.6139870663410384 0.5901718174754458 0.5625208514321937 0.5255923803775943 0.47262409170407427 0.40666871765593476 0.33636593743539256 0.266372292643466 0.19794396353539845 0.13103699903536872 0.06526815005710361; 0.0609937501018707 0.12279206661875659 0.1862555538716348 0.25226863642853725 0.32183579598636497 0.39553425192117153 0.47208745731144075 0.544770468593596 0.601692701603361 0.6372665382800404 0.6565331246218497 0.6665313590225868 0.6706380821676676 0.6699563279425627 0.6677854039235456 0.6727516899650302 0.6909756058501341 0.7039583931351965 0.704380971814122 0.6952264433286288 0.6814466310628251 0.6646597875404514 0.6464613182197017 0.6260579717197703 0.5959486808481342 0.5396764130508045 0.46089429734053455 0.37727277895014527 0.29651020904764963 0.21934624504177427 0.1448499441111623 0.07195839708002964; 0.06446116053343903 0.12973164700969975 0.19660538064549413 0.26586367016619544 0.338125323522484 0.4131167920651358 0.48814288124340194 0.5571107519783021 0.6124808145683553 0.6506088513116827 0.6735965346528847 0.6859654429431183 0.6910184493784787 0.6879792704106934 0.6735313987694838 0.6640252504164148 0.7012796332647463 0.7228230274705295 0.7312421731308463 0.7320711664666043 0.7214066546050946 0.7043709378032635 0.6856735341386192 0.6670777980970366 0.644693846508094 0.5910915340152959 0.5048402890069325 0.411998246210251 0.32288032809136813 0.23832809080414827 0.15710610076104492 0.07808506562106789; 0.06722736087464397 0.135188183686552 0.20461499993402196 0.27612657197832363 0.34994621490866684 0.4248189969802315 0.4969306063714952 0.5604310055061227 0.6112462530012072 0.6484974362399383 0.6741293651997413 0.6910544663826512 0.701384689414583 0.7002058899867357 0.6587872330848764 0.5964939597023665 0.6957544285504197 0.7323015644447739 0.7517201601938579 0.7616623977362785 0.7486009692242673 0.7280822116281709 0.7069436338486069 0.6870669605790363 0.6686699265951859 0.6253723040819382 0.53480099016797 0.4384143490426501 0.34430761640238666 0.25410378386089283 0.1674106391177941 0.08307471253882112; 0.06933759608594835 0.13937770186010826 0.2107390929876575 0.2838319649472719 0.35840518710124486 0.43238084549322253 0.500777216974637 0.5578526459675083 0.6032192448438698 0.6380448810435339 0.6642190096000695 0.6842845943342564 0.7008063935441983 0.7059870700236209 0.6716034688974581 0.6519482738164033 0.6861012244675265 0.71962893511349 0.7548053658958322 0.7743617738578291 0.7564445987040989 0.7352491689098335 0.7141546168560681 0.6925102232910721 0.666187151774226 0.6206989019075585 0.549076528440304 0.45737286062368465 0.3608288941142503 0.2664549717117313 0.17549528882702203 0.08710643884843106; 0.07084166439060606 0.14237430833776593 0.21519775446163888 0.2895371735988827 0.3645493034494974 0.4377019885560567 0.503150605949244 0.5557902791953444 0.599388070648395 0.6293228889006072 0.648075790725685 0.6555690660222327 0.6426034830740227 0.6581051091702657 0.6491849705303598 0.647875074537672 0.6692519800392777 0.7006802513285134 0.7359289938864447 0.7607118711115746 0.7510779626282333 0.7331995249414117 0.7157032491644921 0.6960944347161214 0.670581391882681 0.629751958353833 0.562783526585757 0.47175734554592264 0.3728008232845574 0.27522796214469375 0.18118403512618017 0.0898861040903098; 0.07173101792753846 0.14421017413156498 0.21810530561911282 0.29362297754318134 0.3695243360841658 0.44199961512400926 0.5051443320314737 0.5557558238536754 0.5924756042787611 0.6152657077763348 0.623315955943344 0.6080222135678784 0.5520103395201044 0.602052458253227 0.609478311557176 0.6160132545061086 0.6367333518063433 0.6692238275625704 0.7057525231209271 0.7341828002800216 0.7357452010923298 0.7272001978373933 0.7148916324715529 0.6993301017404283 0.6775361013024278 0.639912546342801 0.5722567433716478 0.479686610937139 0.37907843769731275 0.2798717798402331 0.18421901455927744 0.0913863683694347; 0.07198023490959486 0.14475555404404877 0.21910312106467447 0.29544602715890994 0.3727025773759517 0.44557260390579984 0.5051775546514286 0.5523776197737857 0.5852641531378843 0.603421098775449 0.6062904194836362 0.5908387880578515 0.5596028112285089 0.5676609578055863 0.5648443791112526 0.5669158666192312 0.5885425313261762 0.6268530125798754 0.6682341202686413 0.7011981904851551 0.7150787996368828 0.7171077482585255 0.7118650519066337 0.7018594002573728 0.6879149747824442 0.6600696003997693 0.5851753523354126 0.48392630913728796 0.38016083789441574 0.2803220910034394 0.18453722713166854 0.09156927681311826; 0.07152608857876759 0.1438827682271491 0.2178462682336231 0.29392169722984407 0.37140144058810926 0.4452925123026637 0.5055289182644755 0.5505325976030221 0.5833997847863283 0.600705441201881 0.6014463941102669 0.5821488145312611 0.5387486577006009 0.5342468506054278 0.5123644750382539 0.4972113937798737 0.5225604731818497 0.5762483512877494 0.6236287408698182 0.6635908519661587 0.6987152695039417 0.7101248736367421 0.7076855604722246 0.6967714965516633 0.6789622223542664 0.648287330208987 0.5761782576634571 0.4763571014991531 0.37435076499862635 0.2764063278466921 0.18219503786404154 0.09047751954890496; 0.07034315216042161 0.1414927570546807 0.21420625412339483 0.28895558490885215 0.3652752227033414 0.4397973713600756 0.5051888834679553 0.5564428988580689 0.5909005136908544 0.6079839672601198 0.6087658909705356 0.5925624842955036 0.5617750960930021 0.5223595663064771 0.4578947173294113 0.39235505919638325 0.43475043318121076 0.5326950289884109 0.6079496901270084 0.6578642818496739 0.6901638449663899 0.7042227599617417 0.701945754409567 0.6873267705134973 0.6610261961651461 0.6168362596402421 0.5457270018392615 0.45611565003683674 0.36157503116335366 0.2683693930375647 0.17741244860632308 0.0882357838896132; 0.06842257622674291 0.13762911588030577 0.20828796857300938 0.28093235349566664 0.3556216058735654 0.43083948276987805 0.5021660977308098 0.5631642646666519 0.6030607931739144 0.6212425565136119 0.6231159390992537 0.6106327607950073 0.584394879368825 0.5417000542390811 0.46707887090456407 0.34319660756925746 0.4665574019033097 0.5550221974086456 0.615903833822229 0.6592619859888188 0.6883512034527114 0.7020352682912581 0.6984400706626801 0.6752831203754291 0.6382410568612168 0.5856657086726731 0.5154813065076332 0.4328419672286532 0.3455200828662917 0.2577331394159582 0.17090868999162598 0.08513738757618823; 0.06586319447525014 0.13240158380004763 0.2003757965022888 0.2703422959327408 0.3428102127775956 0.4174771249580869 0.491276758545865 0.5569653333951532 0.6034393411442058 0.6272906047496257 0.6338489800962085 0.6265269497399455 0.6088894503579882 0.5839836322325036 0.5534275444027026 0.5242148497409167 0.554875087456936 0.5966257832960999 0.6348499320082671 0.6665568912700098 0.6903526300810751 0.7032353996753605 0.6974048233269613 0.6651238046214286 0.6202559003187375 0.5623726501338923 0.4918390157946704 0.412588095380022 0.3297270393798827 0.24628509101017723 0.16349552326816486 0.08150230986175627; 0.06257909560613598 0.125862835523311 0.19043535835340683 0.25695127129185374 0.3261292895339066 0.39827394336011085 0.47177298683439406 0.540605123468096 0.5946522515580901 0.6297679981720425 0.6440421708174764 0.6411994026986014 0.6299184554990163 0.6166464871905615 0.6066908350833411 0.6035034537592989 0.6164444253968672 0.6365961958008298 0.657542826222083 0.6770860621292627 0.693475194989587 0.7037455920368736 0.6990934027039514 0.658958014196013 0.6071934409190408 0.5448819133502064 0.4724435127131234 0.39412454757537274 0.31402376247862307 0.23426579531548608 0.1554493615757727 0.07748561792737424; 0.05879677266257943 0.11811964661989865 0.17865095953702928 0.2409303996231067 0.3055090017608413 0.37249874194529464 0.4409123057314402 0.5073968086196615 0.5670679446541428 0.617460754490871 0.6448286219849384 0.6472159935021812 0.6415538418089229 0.6380919443399999 0.6412716417704877 0.6501978095525148 0.6603662973034253 0.6702794742469387 0.678739208950499 0.6867920668404504 0.6945682834867499 0.698433397026792 0.6895887687505406 0.6499536923320598 0.5957507100746278 0.5281191360461929 0.4524798737349031 0.37454849340818147 0.2972274130822919 0.22130759780040432 0.14671893303883876 0.0731044598030194; 0.05440618805335854 0.10939618192959878 0.16530357386480923 0.222719575643031 0.2819637900227786 0.34294425345872653 0.4048727982850694 0.4668884232741059 0.5287483618535587 0.5852325923673768 0.6189075963128998 0.6274656969720817 0.6299402128777802 0.6369471176857324 0.6504283832132777 0.6670023734603726 0.6845538200192837 0.6938353351183502 0.6942042379259563 0.6918378677712037 0.6897351549010702 0.6858813732525587 0.6744330547323009 0.6412055048943617 0.5805516178682298 0.5079654778241753 0.4298081935847882 0.35289938498772416 0.27884394317730515 0.2071563361631038 0.13718307355486317 0.06831696556002692; 0.04971654926867228 0.09973786908342969 0.1506476653781512 0.20265364303357336 0.2560492011425935 0.31073504087409165 0.36622635944075516 0.4220560913962372 0.4778361510823357 0.5285188636363752 0.5640657850160857 0.5838442967661547 0.5993445372454798 0.6178016651372192 0.6392562112235624 0.6604380580946327 0.679100147609597 0.6949017189133525 0.6942994817684807 0.6853873141997788 0.6743662146800674 0.6600300249906553 0.6397688020167603 0.6066178169947202 0.5533937640710002 0.4784001197246019 0.4011500279083974 0.3278403110312485 0.2583031835176627 0.19155537635353634 0.12672082783159652 0.06307556349263478; 0.04457252865844632 0.08953501349259488 0.13497349283994278 0.18129003807106667 0.2285132117011114 0.27659676208182365 0.3252766096860747 0.3741898996851217 0.4222579364726618 0.46620950139357914 0.5015914357675898 0.5286897715097141 0.5529083963944477 0.5781594153874358 0.6041452257218525 0.6275569506908589 0.6449718961634985 0.6558319026690044 0.6610429245288395 0.6575872912888165 0.6463463530858241 0.6248494187454015 0.5942830173434372 0.5540788236597793 0.5009081109367841 0.4338218796494107 0.36455892303014253 0.29822297352910265 0.23504353371216505 0.17427973167198962 0.11525704315368684 0.05735481896293523; 0.03930940498289701 0.0787640350781361 0.11871699879820806 0.15915605844610645 0.2002478003263416 0.24190288005152627 0.2840086312304479 0.32625852427373664 0.36765630414278655 0.4061247159868139 0.43936829963547996 0.467692766781496 0.4942665336102934 0.5215533316093726 0.5488486967755378 0.5726103251035654 0.5896307873502324 0.6021864892288203 0.6134525765341081 0.6216559573485618 0.6199929543093067 0.5921955418895828 0.549490880635731 0.5004834852781178 0.44472322501491796 0.3842361404865573 0.3240532621309141 0.26571154816938497 0.2096050617881324 0.15547718286380893 0.1028324972563769 0.0511761896966034; 0.033797562338670775 0.06778995062388563 0.10199845783996464 0.13662146939119574 0.17159890978817485 0.20693650266772848 0.2424828298054343 0.2779731114211913 0.312767628481058 0.3457121703240424 0.3757869594346148 0.4032538876292161 0.4296040653924223 0.45584741744476676 0.481295952259791 0.5033602268979867 0.5205248385254488 0.5356610426039641 0.5511337668080696 0.5706989778076148 0.5907725681298315 0.5573701049489369 0.499683861247651 0.4427361642553983 0.38795618336023924 0.3340589518228541 0.28165396548376437 0.2311247272584099 0.18245911063835257 0.13539012348466414 0.0895824463538746 0.04458289619206259; 0.02825101895003419 0.05657974786759113 0.08511186636315736 0.11384785827463542 0.1428400388136439 0.17198268598537841 0.20118883086806835 0.23018729756803444 0.25856792814299034 0.2858123738757245 0.31156316932667255 0.33594973650171517 0.3595684044808517 0.3827144796103373 0.4046997895761485 0.42474070498286554 0.4420159842120193 0.45653767064835715 0.4716194740118045 0.4909290059443632 0.5150153215943734 0.4894570118407436 0.43323366043229417 0.3784612190192704 0.32845187348854754 0.2817597885860133 0.23738665728388633 0.19486959382712868 0.15390579274698582 0.11428370931960763 0.07562394289152138 0.037641861220681964; 0.022623954681380298 0.045305603764188684 0.06810055652464354 0.09103178416618272 0.11407253613697316 0.13721862970791707 0.16028052873383797 0.18314541208338575 0.20552385193363515 0.22719959422827196 0.24796324214853221 0.26784953383167254 0.2871097555329161 0.305779904430629 0.3234268615471498 0.34001613002249914 0.35495465940858534 0.367409422852985 0.37827787990327477 0.3883897602553135 0.39394356713035805 0.3777020510823075 0.3429526862327023 0.3032963965795799 0.26427778614910746 0.2270041948229966 0.19140872845889798 0.15722652204413481 0.12429141321948417 0.09231159077343186 0.061108317036895475 0.030436939390999437; 0.016967846964361866 0.033994418727493654 0.05106058050879576 0.06821236392067921 0.08543038541214952 0.10262869139761946 0.11981868119527722 0.13673935959111605 0.1533928753459267 0.16954134951482167 0.18511419606705096 0.2000775219848455 0.21454041858499573 0.22844495170787688 0.24153734029380083 0.25378322027513117 0.2648779432914715 0.2741345317999425 0.28120262078099734 0.28557867354828265 0.2847099489923909 0.2731571817618601 0.2517256345707426 0.225491704039398 0.19796969500093056 0.17071366755574158 0.1442202795063157 0.11863006950896068 0.09382519270281145 0.06972651142870435 0.04619026998351278 0.022974970661050993; 0.011330066337992054 0.022648982301491788 0.03403577356376244 0.045439179406443306 0.056863193147702856 0.06831141331684334 0.07963293791189222 0.09091336552454567 0.10186350144150712 0.11262846778957787 0.12295752207170488 0.13293669846047218 0.14255826972274863 0.1517544529267179 0.16039482178945 0.1683610792700831 0.1754812191091806 0.18133947765075586 0.18545404327560505 0.18720573526747228 0.1852289509288199 0.17771879376110744 0.16496691573799824 0.14895889200823423 0.1315390229103988 0.11383994631940009 0.09638700170965259 0.07936564624037983 0.06282135512718498 0.04672659912907541 0.030921712842369796 0.015434954833711562; 0.0056489104143004265 0.011338307874374412 0.017003273717873014 0.022707594681458807 0.02841811874322851 0.034089647732665054 0.039791048459524504 0.045326799289881696 0.05086817034345315 0.056155820987129144 0.06135360041480477 0.0663292507285156 0.07111696307072848 0.07571205605335823 0.07998107934672355 0.08391756276870604 0.08737004846399916 0.09016491757755993 0.09203534517745825 0.09262240211961105 0.09134916004130274 0.08763749489191128 0.08164828836597159 0.07400945218071465 0.06559709636847914 0.0568925328999051 0.04824194180387903 0.03975683223241332 0.03150027979309531 0.023403324688209208 0.015541748301454682 0.007701707271502912], hyperparams = 25.908507381038458), p0 = 0.6240335593779779, pσ = 2.0427238352988404, angparams = ([0.733712195164367 -0.012600432909767242 0.9615390727873891 0.8376457219917898 0.8849785092931182 0.7785073549459675 0.597822166840333 0.8914585115530141 0.977698969968017 0.7488017152129427 0.5829487792164157 0.6919956084784668 0.6889211871465959 0.5839949519539485 0.8080693358083386 0.04071103464703921 -0.2859227320191204 -0.45745812092988514 -0.6303420628739718 -0.7752457630535247 -0.782662482977798 -0.883279253277482 -0.7823041017288119 -0.9166220174824383 -0.6230967639589402 -0.011882716805811096 0.48254665409781233 0.38456896533331586 0.8147533410773976 0.11252072192570652 0.5560993872163612 0.853702170540555; 0.20687922889125762 -0.7465420792715394 0.8322600315064747 0.9775186768086849 0.9420603978805119 0.6522701539149465 0.5962364083454805 0.8134483829770875 0.9817797780323784 0.8826808023013969 0.7740218937895228 0.7714233980039988 0.8806403277025062 0.7825917536348178 0.6405486097353981 -0.15583657454462932 -0.47876016252752157 -0.36587899326735707 0.015978625134294207 0.6038668347346429 0.689818718858851 0.25520138587964236 -0.5242187461384314 -0.7595951182132055 0.01650267088800927 0.32124173275749 0.21794673415337867 -0.10673157769588983 -0.504992957913088 -0.5759912740660734 -0.46892190619885205 -0.4558159193739864; -0.34818089697652066 -0.07207243825629532 0.9404414835889516 0.8927188825582951 0.8515787488778884 0.8662922720171167 0.791024455994172 0.7550470925480427 0.7997194048045724 0.9455806800417333 0.8369010632487264 0.7649170026159475 0.8423182083820917 0.8813093737859602 0.6755885035627364 0.17249822889322824 0.028383223197182252 0.7539108283721752 0.8351712018691684 0.8011795374222138 0.6328379816212754 0.1824930069034732 -0.5150462713537983 -0.7851612232698642 -0.6297765324075354 -0.7041696821425297 -0.9989752747155018 -0.9587270048177007 -0.9463501080279827 -0.9779396397924505 0.8452186788383367 -0.7129190855431728; 0.3907461760297889 0.1286660170092463 -0.01859305485788144 0.21082694414944825 0.4145439167991439 0.6025447231896998 0.6360905087880775 0.5364068717897701 0.4383020345087459 0.49634344756258303 0.9140740318270405 0.8184056942580109 0.703463618610183 0.7144443970755916 0.6969533329578723 0.33473447354783875 0.37760908656363146 0.7204326300932753 0.8566988562213069 0.6818260622046545 0.32307818656818277 -0.20992610803902073 -0.7149101735740632 -0.7061339778357181 -0.5465068187398443 -0.656470446742968 -0.8783816532082817 -0.998034702382876 -0.9696769065925068 -0.8653108134042028 0.6604033436059646 0.7656369775787792; -0.08565632753088052 -0.3507831000960948 -0.39994110313260356 -0.6202834672052062 -0.5219661600217506 -0.15568386103920046 -0.04112382958311793 -0.030885788614583257 -0.0701857808702993 -0.04044720467076787 0.1856334222747601 0.9219016522536934 0.5225841150212773 0.4026294578193056 0.46581379695081476 0.43302109161849206 0.45579630694958384 0.6338725215895947 0.6627843417037445 0.23019366590082574 -0.2635369431185347 -0.6667821197345297 -0.7799676053962047 -0.28827222112724704 -0.26664420497686236 -0.4285970214448949 -0.6453325898910888 -0.6476816064118147 -0.14545883524830577 0.5414726922490375 0.8858922309209882 0.9723703192470206; -0.19347288471753932 -0.3184926002170789 -0.633195661451517 -0.7548029964971206 -0.9268237955635195 -0.7373265819625866 -0.5214626064106315 -0.44239329124289173 -0.4349880285828773 -0.38608688668629987 -0.2118352533235155 0.06068868236437943 0.09695540902544926 -0.005393224021176024 -0.0057432993722448256 0.4053804894369512 0.5145593344996736 0.5792683778590074 0.09433402860925341 -0.5543815749701935 -0.8508414190634563 -0.7737156904637028 0.5496515604581206 0.7985933935126304 0.6497543413439545 0.42288029923929177 0.28526662564331734 0.3483606462994553 0.44648486298718204 0.6471886866655393 0.7609652413941701 0.5807992326191945; -0.7420871411850399 -0.3342453788656194 -0.6835098880932419 -0.9001283170648496 -0.9908731198827915 -0.9232713985798606 -0.8083902010030819 -0.7094416706284467 -0.6465975703485056 -0.5869429273205621 -0.4993980962109955 -0.3860927906976432 -0.2607052375042791 -0.35087204430374247 -0.4388383841245975 0.24029327439922563 0.6813816380954306 0.7414786259485188 -0.716809142683327 -0.8040227080378957 -0.3977877034022365 0.4310054208293784 0.8735927454238924 0.9945489661300096 0.9880626892116549 0.9025176737323309 0.641639456647572 0.5143702640438986 0.5044649685742618 0.4097552285631774 0.023489929403846217 -0.712742826635187; -0.35268716243446424 -0.33885375978490273 -0.6255045352864594 -0.9706260723167217 -0.7473033198565929 -0.5717683322639967 -0.5517685990651545 -0.6102649453318385 -0.7080713466832999 -0.7782199980796372 -0.5547126618654122 -0.46118706849280955 -0.14304009131500864 -0.30062752558361094 -0.29950173240908595 0.3334317456741135 0.7441633553664462 0.5721058513163612 -0.41013857558305755 -0.14496103655070108 0.27744042761527027 0.6939108176067286 0.9593720482630906 0.9287117061744248 0.6172919666865282 0.5226441129751211 0.4945410418891012 0.2030571744974128 -0.020645108087906785 -0.425820758063762 -0.8976599320829485 -0.9774151440147202; -0.16950745164158998 -0.1262857834462975 -0.3403557901864477 -0.31686393297557486 -0.12649937183099846 -0.0791396443437305 -0.10491918001111336 -0.14723296216769052 -0.1643915395077647 -0.0820724838196692 0.40902327663593024 0.915280442026058 0.9268334760679416 0.671827501631611 0.25025235335114354 0.3373443273808041 0.38457761598470647 0.07275146780421145 -0.23525521844717914 0.12593079445598349 0.42842745126327914 0.520914436401967 0.20396320017295697 -0.42554690359041214 -0.6581551304466077 -0.6943184334047622 -0.689793305090879 -0.6719796672811813 -0.6227533195380117 -0.6068848077957795 -0.6269324193336562 -0.5506498972870093; -0.055581963371185227 -0.08192809520815823 -0.025839573332282862 0.11393417500949037 0.23419925058592156 0.2175337657459225 0.13611688487274878 0.05798132304541747 0.03401180157352916 0.11563997911489923 0.3207984321168734 0.4804846014877667 0.5025370873601327 0.4585183683229575 0.2602501751769809 0.06422354671758956 -0.17739782164382778 -0.8971543409334141 -0.7216779460320275 -0.4692947490745457 0.00767309248572289 -0.1541229920167561 -0.5337450347684743 -0.8223957230080131 -0.8561515959843905 -0.7495928655197791 -0.5903545262138077 -0.47577068238221315 -0.4222856384880522 0.07388405553804182 0.3712197586943482 0.5016035425397097; -0.1378616924417735 -0.06633591809647375 0.04253463019931974 0.19873737858204651 0.3071615761323945 0.2838718863981904 0.1941978266599861 0.10419922830433558 0.08586939773148278 0.1645708285964335 0.2652302807229403 0.30331931104387366 0.2632269977593188 0.12997930055613632 -0.17448444313238326 -0.16942782958719063 0.7862513335572809 0.3369827658673919 -0.4352035456459855 -0.3147707626788535 -0.1879597153409086 -0.2289717382941155 -0.45185498899825693 -0.8649753330657826 -0.9535387824642096 -0.6027039205703282 -0.1926684132923141 0.043724210465582156 0.5633496211998109 0.969720579534476 0.7932731012604624 0.7959909411087666; -0.8117376808041851 -0.28254615528494714 0.14821622895004324 0.2659931708068555 0.22177704864299286 0.12650773283084038 0.01932277075040333 -0.04701505488648215 3.411913336783882e-5 0.1484668810905423 0.2666154369530928 0.27183188167276856 0.17933082017401242 0.1333698350461408 0.9806375669849511 -0.659805094251024 0.879931683777826 0.9435482668557311 -0.40384364447394827 -0.37377804648683116 -0.09653825426990764 -0.05767516641307593 0.007480015211918956 0.3955830195216698 0.6877637477139988 0.8741590758222568 0.8722462052781528 0.5592582315312705 0.6261447898141248 0.9172911426967404 0.9758584037143282 0.8731019302499902; -0.25856898228645286 0.01473495010336643 0.22637361217861793 0.22994287176236683 0.12741667971842016 0.00017890521972723392 -0.1398209907638025 -0.2842101781167411 -0.33958635724332853 0.06471882745575328 0.15218931884284678 0.3257621823239958 0.5603227122480812 -0.3045317306261077 0.9014532721083274 0.8407126625461683 0.5569462759557732 0.021711105497670666 -0.9098404743258054 0.2704508062285223 -0.9082338376240653 -0.12561571231802504 -0.11217249176751164 -0.15827575817375877 -0.04080242343122723 -0.24462296116716178 0.0224833138543625 -0.04093409247948881 -0.05435331027960247 -0.05611448154255844 -0.013118124480441503 -0.007036451779594069; 0.41896420856615335 0.30055779708759417 0.25480898802085994 0.18668178725962997 0.10106918882587117 -0.005095829143591753 -0.08482665703388077 0.4269288929608559 0.11632855176025195 0.07296801748339257 -0.007152092717091206 0.17235079323386113 -0.39790228761569335 0.6471340890581366 0.7242590313317521 0.19451794705476233 -0.31036278858427585 -0.6390273527483273 -0.8817557976324457 -0.6190090464441798 -0.36662793017203665 -0.4203147261752246 -0.2512913457012274 -0.3753900563223228 -0.42944931331748853 -0.423653271070171 -0.37820211355098404 -0.3736922204917424 -0.38698843402277977 -0.4023356812676665 -0.3977946665931768 -0.2503584867901494; 0.8212725777435366 0.2791680685647699 0.12468769827808049 0.07069395575274089 0.0647064862461743 0.16723661125988304 0.5454595869865191 0.7487958764356663 0.4155010007693856 0.08037775797959808 -0.09191003665597836 0.8078532852886906 -0.9338077729620939 0.8785529611860556 0.6164823230245627 0.13785967569300547 -0.3218967631529418 -0.5609065043902886 -0.6866534851035913 -0.6723673483487157 -0.3049989987995914 0.159520822370373 0.18538116100667712 0.2846245026718873 0.7744431217909703 0.39230983224492516 -0.22557748492547605 -0.4892009971339015 -0.5628481090006199 -0.5673470461977278 -0.5507703493150572 -0.09616876568148532; 0.28100401215509174 -0.06021355330247903 -0.13525546305132866 -0.10717953988665893 -0.03940495522182589 0.10512522893308202 0.8368235179089311 0.5870349866770422 0.2414288460704664 -0.13263607873887198 -0.5345958677918935 -0.5004707664467318 0.6805029377285314 0.8756984828782708 0.6309843908710723 0.1619916594913951 -0.4001098065559751 -0.43735351190260335 0.06693984722561432 0.3445634515367828 -0.7918026424548366 -0.7593813475061371 0.28333671715190045 0.7356230651668493 0.8992980098140018 0.4307237999061543 0.014590336062264326 -0.3562711083623897 -0.7171882552653012 -0.9191579100650501 -0.9313561754852681 -0.8446516569775635; -0.16049000378116865 -0.39761485219258064 -0.5024567936562957 -0.3811589260241489 -0.233185063939432 -0.1096562654712019 -0.039091130986833915 -0.18915991354787964 -0.444045685869267 -0.4952130927224843 -0.47580851071199476 -0.7160038596350602 -0.5964867017719641 0.820737508778196 -0.02633002811524224 -0.4204790101162419 -0.6947384030360537 0.2910235009093283 0.6533804580667222 -0.17820515250503563 -0.2435550712320685 -0.18194206907511845 -0.02519535874330111 0.856079341612776 0.6404634950408656 -0.08930671502447225 -0.3114740651311202 -0.5059113278333653 -0.7606420614368069 -0.9084887122876695 -0.7526581590588982 -0.6219442820838058; -0.6051020704188701 -0.5750229260310638 -0.6540176274516771 -0.6379213289074949 -0.5303346813499245 -0.46023473566205686 -0.47476261810400555 -0.45867338036303507 -0.42167203575826 -0.3851436580339863 -0.32752011037052414 -0.8251996128320866 -0.4110764517910662 0.15988298730270425 -0.1940978155439329 -0.9063371799385658 0.9469948501485931 0.2091888212456624 -0.6131204495618658 -0.6010929314085535 -0.5225680928800973 0.1587128038074451 0.4951841189203634 -0.1045230762891248 -0.5008086980454971 -0.8708597465191046 -0.9159723942794002 -0.8225127112289193 -0.7966561876526911 -0.7625994389591924 -0.6777026296635053 -0.6132178237163175; -0.19303729212901938 -0.40938891440949904 -0.765146690088897 -0.9734636384652006 -0.8676683253540164 -0.8262518367178883 -0.7802275618812954 -0.5124175747203408 -0.3520500392138968 -0.28125053529489663 -0.22886069495842393 -0.13589811058176848 -0.28381507503200676 0.8652314214192598 0.7678438739933563 0.03705128110683331 0.8048381171248281 -0.7022111896956056 -0.804795231235292 -0.48507164515793594 -0.15424095373046193 0.3985962305322386 0.9718680621571785 0.09037082175350092 -0.22363127305116198 -0.3702934969856039 -0.4888396760031168 -0.6158503970107707 -0.781708348717028 -0.750206187180123 -0.5880158414506371 -0.5922942173263521; 0.12419592771433709 0.0472586736214273 -0.17819685351356498 -0.6364966070510857 -0.900578719466956 -0.7769640502722013 -0.8015351205272684 -0.9281366645635504 -0.8651261855548473 -0.8270760754924269 -0.8933825450928072 -0.801445556987352 -0.47319956524944495 -0.006920911779259191 0.3329952424648721 0.30468074483470803 -0.24693376144601392 -0.8113065846997192 -0.8525595915190004 -0.19616032146788623 0.08198796937343217 0.5797080264579353 -0.23653517453141293 -0.7014584847301901 0.531257441205372 0.7130194868343704 0.8862732885808732 0.9988564047795727 0.9052086237930186 0.5912261523259678 0.27889488606714113 0.17047826217235804; 0.6604774638177597 0.487225295586753 0.08787879198946288 -0.5774342740907885 -0.8343042813683421 -0.6216420370684157 -0.5370571409011872 -0.5575211837224686 -0.7033307440342821 -0.7130877367815732 -0.6867077998954338 -0.7299392260703845 -0.8410021449375252 -0.778357852873735 -0.07057875997026786 -0.7182484892312557 -0.9664302826682 -0.9415571617260936 -0.47387309215217654 0.07384224984405577 0.2403789690120056 -0.06541727081974728 -0.40761043569000494 -0.5169931369901137 0.86826439299588 0.9253654282358615 0.979496237909189 0.9985610228687503 0.9595884250851627 0.7987731126950378 0.6518852412105335 0.506149235730977; 0.69439029224329 0.9143800326028599 0.5744712735162576 -0.1346997496334692 -0.547953550992526 -0.5858820285935733 -0.48103100748303296 -0.3785359973075066 -0.3435814609860757 -0.1857965583847196 -0.18616693750444985 -0.20935029746423173 -0.18805520356711933 -0.02174364468326851 0.20367414697866626 -0.14249031481000518 -0.45320133279781905 -0.5942958511655858 -0.4888166070740174 -0.08539468814660124 0.001326411675843417 -0.16604741808854162 -0.6139808576207935 -0.11651160102462053 0.2439570717169755 0.7446140965055235 0.9301927840556593 0.9942561240845224 0.9367705524203399 0.7090827750615318 0.533266852736186 0.20359776511912323; 0.352529889926965 0.8005236017488688 0.6674440113437965 0.29675287342653656 0.06502609040925696 -0.02828646986574983 -0.0021931092551923676 0.5653644652433502 0.6584880482602662 0.5600166984506662 0.4340053161530954 0.3478060583384758 0.3913691067574235 0.6378272853053744 0.6428003473047135 0.8977163341600896 0.059446997034238176 -0.27131425647078394 -0.6396232267815872 -0.7477708853791192 -0.4920721044320918 -0.33745765569478825 -0.1675666706642294 0.07896473011320965 0.8094896371759391 -0.20225136626905352 -0.38984364106023023 -0.5215455204117947 -0.5294950573304407 -0.1251287923030502 0.029835660471845372 -0.06310246612380746; 0.6523176910942551 0.9918486351441366 0.8463344297472335 0.6109865117312178 0.36001241580044724 0.1852800661666113 0.14892354497914315 0.41602569067247913 0.654963510931601 0.7374717862593441 0.7708970461608409 0.7528303879233754 0.40555212226178466 0.11683955206823025 0.06361108117393352 0.1180091223545152 0.22250173283610397 -0.20413989602337515 -0.6276869080406237 -0.9058908874690452 -0.8429295364030248 -0.5465630830795225 0.035941259260102984 0.4844498666871349 0.43741304956639365 -0.04558425229225691 -0.5443811661252157 -0.7269880001561676 -0.7096035077028715 -0.5105918300742897 -0.3133956976993784 0.10828655886094239; 0.7329392094846773 0.8492977798004243 0.8215746744675757 0.8617609262869107 0.6622663140143719 0.15743895381877482 -0.6748928927949785 -0.7439445917696876 -0.28873870208518926 0.07468094461447784 0.292985120853151 0.2806163358665566 0.14846545430642982 0.05436789995738496 0.011604297848629423 -0.00747979974390664 -0.031256028680202365 -0.37102091771793055 -0.21142161553075708 0.14509943993245422 -0.17305422151153213 0.04201830483356495 0.4849887975463907 0.6932283754773241 0.5057912471031834 0.33963234789771324 0.2092760145503544 -0.09399528889845216 -0.10590781285794004 -0.1292962207501981 0.01759176271790332 0.1626049152718456; -0.5694311278124913 0.28281940975234027 0.38818349307406586 0.5892884159422667 0.32835517880925785 -0.37550486554637347 -0.7409002921684076 -0.6637512155275521 -0.5570683828156701 -0.4636147278123543 -0.36359694088033395 -0.1331883971301683 0.2509646245407278 0.360141834321754 0.25568470470607796 0.07503309458903165 -0.2362789028336202 -0.6675694516839932 0.01954069239185446 0.5930223171389934 0.7207546172055576 0.8338783776801275 0.4380814226640844 0.04361783544412695 -0.12563308946691143 -0.036140900488880995 0.30031400963477917 0.4332786233692403 0.5747943211263955 0.528113099351412 0.2698023421359467 0.09422843374513536; -0.77705998841028 -0.41973157974973085 -0.1586580086401582 0.12296205016316099 0.09283781656366313 -0.1678231115233218 -0.44214055344398434 -0.4963942542393822 -0.5257990810870955 -0.5521463994626277 -0.46303670813703107 -0.11841221313597984 0.3387024399914296 0.6094010717957827 0.6470617701066915 0.4780953346802538 -0.06238107315175559 -0.6797209753194794 -0.6134767941756852 0.13770084651773054 0.29799264747032084 0.2760954102718042 0.18325902588724494 -0.23928451004832962 -0.6679150233481213 -0.836122785653467 -0.5631211005473614 -0.16296635749194557 0.057502512754028 0.21036325220035526 0.37115385474696483 -0.3616503627955287; -0.9628106100979312 -0.17326999683807726 -0.5652619632422193 -0.03971050935750319 0.28168638060836904 0.5820346242406269 0.5029768311768181 0.21571653944501426 -0.23402915161724808 -0.5775879956920308 -0.42745793426590517 0.008818622547109288 0.41249575858712434 0.6383289064746578 0.7589791549356631 0.6626802337924712 0.4260911323201238 0.3419424884840805 -0.039062874422710094 -0.8913175600255439 -0.47347758362323183 -0.19563080817540027 -0.06806809384706994 -0.028477969023106987 -0.16563687660180737 -0.5493633868123454 -0.7361753952798518 -0.6375526832824302 -0.4922367007470823 -0.24755496200091856 0.12071067293104158 -0.11038441387077137; -0.058853195623436654 -0.6634742532865304 -0.8505941306333071 0.3061771442551266 0.8731208817466942 0.8707744061112125 0.7770400271995408 0.731111455401838 0.29572597923081984 -0.1635988218571887 -0.1492392387936767 0.18658578636236434 0.5034659410086817 0.5593687960510089 0.6215092899642305 0.5472193055442384 0.553917444401711 0.7746191541274371 0.876982277480991 -0.14187261646182203 -0.879568233978916 -0.5412493998418983 -0.2388341846612898 -0.017689072078807856 0.10785938727538885 0.030249050808747926 -0.46630497341005933 -0.7478187360789608 -0.6737195737805252 -0.5542515253358904 -0.42398070159621615 0.2656572813850231; 0.19604877408377497 -0.0028533923941459947 0.25111868801316606 0.4924835624003209 0.5294676316481325 0.9987088671296002 0.9689393681115689 0.9818633945476088 0.20712313260144238 -0.14912560294716248 -0.024217673168489044 0.402086496587351 0.5196310127206161 0.30618453863493567 0.17895453051653964 0.37370849398385736 0.5761129207331117 0.8045110544659759 0.9890665042505468 0.5749770540037407 -0.5771938325463166 -0.8527824106864981 -0.5609232050801725 -0.13901105846592643 0.1939464339886922 0.4212082661524493 0.42694218543714163 -0.16634905348362578 -0.9203775925340195 -0.765672226935692 -0.9748499979263806 -0.7259775031261007; 0.47649386815017974 -0.5216448198471592 -0.08314441070818361 -0.6028414645128751 0.48654998820677536 0.6449663061798268 0.7644126906533618 0.316363556299976 -0.5475817031302957 -0.45646923891417723 -0.10314729442739282 0.5938565574866382 0.4022867476092785 0.029259196661341833 -0.15178889453239564 -0.01980253025237109 0.45342780406608024 0.7032973434981658 0.9101772658896345 0.8602313040526136 0.1411519523060437 -0.3847921471046936 -0.803769673521568 -0.7875326261268465 0.0700091826691437 0.6206366309501917 0.8816852553455979 0.9362774449912181 0.06407512911221548 -0.3126135815091309 -0.22059449536605447 -0.3182810235111464; 0.9373647650527269 0.200952430052955 -0.21534648688150385 -0.3520601004419193 0.22430147485583238 0.18423263361840342 -0.037914990256618104 -0.4210647956376409 -0.6125870073336525 -0.4049925316093274 -0.24648399813907917 -0.3757869385541894 -0.17720719393227755 -0.13940623616548006 -0.1042913500336265 0.07935279972880235 0.2094843101248226 0.34251160058081637 0.5732227048858246 0.8694121370599571 0.6099715040790081 0.5442609710056409 0.10982460653019932 -0.15817549976265316 -0.2852620248338824 0.5947446667253707 0.749108883258281 0.9489373670326243 0.6208287584073223 -0.06370924801905484 0.016805066579502016 -0.4449460356686828], [-0.6490123337201992 -0.7349875615335038 0.2433361178070228 -0.061954899941444826 -0.4375295598883549 -0.5823218901948579 -0.7397161113276568 -0.42244986556912484 0.20772081335383916 0.6618634754439456 0.7950408229360766 0.5384766155841433 -0.3783409444027308 -0.7042078648268401 -0.4271659641958494 0.9777509171002576 0.9290067667647943 0.8268538224305509 0.6357113877484295 0.18570706300656153 -0.5365815086421116 0.18898918089105898 0.534301910800569 0.37578219660270373 -0.7806730439670354 -0.994715064305233 -0.8614052022224201 -0.6120569786645416 0.524989134270618 0.9934359250260857 -0.06862028036864422 0.11840320481800705; -0.20012616831377622 0.6575883537437859 0.02112682470784811 0.10968343391432142 -0.2901046147614828 -0.7569299963019933 -0.7956998453648613 -0.5729808195964194 -0.16218731297393885 0.44029462177162126 0.586654484077073 0.5283648595918135 0.02420532069613437 -0.5244441160423993 -0.7374739645546179 0.9540519368010288 0.872841978924056 0.9094304433419291 0.9330894975105374 0.6349809338704893 0.5632103211354189 0.8475109431819466 0.8035248235925836 0.6196274842755212 -0.9217019914589729 -0.9444591972033285 -0.9139190870456636 -0.2755861702629053 0.23643881844496237 0.7217222387752371 0.6133005270516648 0.8378346476552554; -0.853137579774821 -0.9565495739472684 -0.04069572421365817 0.14606625502188395 0.10892339174029056 -0.29350041470218524 -0.540602833042537 -0.6116735508793681 -0.5540984996038985 -0.09162406914053352 0.4609385029541844 0.5595624933594594 0.3644093438898942 -0.03856429353174152 -0.5989615317915675 -0.9759510877618961 -0.9141915773312794 0.3037862911137025 0.5218488943854211 0.5959378504531077 0.7281354864072108 0.8878679701825279 0.8225111486250047 0.4879702296406252 0.15169588379140445 0.09919767825080958 -0.04340223422253253 0.14261751354250157 0.07213574888271686 0.19762845980202984 -0.28635496848651365 0.6877950502987283; -0.8756227296773015 -0.9892513315527119 -0.96665095687849 -0.4764053990274576 0.21891074828826226 0.17523807467020522 -0.14604939360001554 -0.5256237821832598 -0.7303382410723291 -0.7585434676882536 -0.22674924804190377 0.5386669972411832 0.6620245822195511 0.5319117767075785 -0.0992579306510487 -0.9049939435587213 -0.9026624617190248 -0.47419403907414603 0.2321337643963743 0.702444337435904 0.9442697669548545 0.9590292684739384 0.6895938462943848 0.32654743695230165 0.3176227505680937 0.3925961305607844 0.3023465233652755 0.02786326379749007 -0.2414533060924629 -0.3989161290944009 0.34034768083478656 0.5350502989340117; -0.23746369770143677 -0.686660032823174 -0.6957320857728454 -0.3532436780549319 0.258909736568913 0.621040410593789 0.5360400393105337 0.1345687283866245 -0.3759869822588893 -0.8058800738788192 -0.9640636989535523 0.09342111912643937 0.8474514383057768 0.8921253586331107 0.5239135569198177 -0.7653407510639363 -0.8860692661424665 -0.6086156066228903 0.14759441219379782 0.8241109839330883 0.9433928226248911 0.7383556614661915 0.2788726358360052 0.15470880154774866 0.30140829074253206 0.3221020274120409 0.06589374040540438 -0.4526573494394954 -0.94270950141397 -0.8346020109247669 -0.4440311023665369 0.18088923140677085; 0.7641951867428679 0.14505265874441484 -0.24919242233658725 -0.42955587490094543 0.09983322574897611 0.5997522033764723 0.720368891543518 0.6169411112792651 0.24788387540628365 -0.38071954930670415 -0.9102075738088902 -0.6885160113170721 0.6708539270538485 0.965804341873741 0.9468976217555556 -0.5218164398002062 -0.8477023522346888 -0.7018693210055356 0.09655038195552614 0.5255872025967933 0.32780508344063575 -0.4599643986311725 -0.6842851605607931 -0.17173525372774018 0.11654519021792405 0.00594202909793231 -0.4897881709018547 -0.7922360947664928 -0.8597331785552401 -0.7600686507551114 -0.5173273020311909 0.694967011088535; 0.5899315754626709 0.7718694166080121 0.3393365918579222 -0.102367989156032 -0.04712375677853952 0.23157604052427852 0.5637142670927907 0.6929018394564819 0.6056622338822173 0.25127395846432354 -0.41587763203768774 -0.6943744859384104 0.23658068582993158 0.5848602899219091 0.7824833879310245 0.26182408999541806 -0.4896327393293447 -0.6420798784437156 -0.19187739888799832 -0.33983263407426534 -0.8226397190586924 -0.8725972356672178 -0.4741414342561626 -0.07558322576112286 0.04464433619121914 -0.15177417433580015 -0.539719379759021 -0.6795287358276724 -0.7214216950411064 -0.8578629714573258 -0.9953823223762084 -0.06825038916185419; 0.7882439078591199 0.9325492458863207 0.739887530484441 0.21632470735694848 -0.3487519822833038 -0.28965351082101504 -0.09785133117521197 0.1248510911641217 0.3645738789718673 0.5972936030829609 0.6859415065334212 0.573849490957787 0.16180526831572184 0.23980100327296858 0.3429327484908906 0.7869766168486828 0.5204414742640819 0.39988819862336894 -0.894362628549442 -0.8970707968824285 -0.8409022154227914 -0.5900478446593327 -0.14396491325131616 0.3682428104519431 0.7253568954276468 0.7986636097372145 -0.2041970026833864 -0.40146340395848706 -0.4022678999103569 -0.42530170011751195 -0.26388911712948926 -0.2113070237645226; -0.07541652471012358 0.05194738507231272 0.22833752482883002 -0.29508960822641483 -0.6275007716498431 -0.6343580089267895 -0.5532564918456288 -0.47596330127273445 -0.4258878366702201 -0.4289010223761434 -0.5504306259432028 -0.38947180046317614 -0.3366067812260559 -0.1912610654725158 0.33884295768784284 0.745955359059858 0.908975460653097 0.978346788129926 -0.8706970692847387 -0.7462282977442211 -0.40388685967004184 0.10568211401689669 0.7489908387854184 0.9044948248925021 0.6911970775815303 0.6192526895662063 0.6844529256189935 0.7206766941353038 0.4424295124939927 -0.06230422248948998 -0.3499509643362863 -0.7937118268250066; -0.454858678993848 -0.5483879590482054 -0.40634573379985145 -0.6622903225378587 -0.8103496646951981 -0.856160156304426 -0.847173502614275 -0.8208485606797629 -0.8256730170109959 -0.8940741487976767 -0.9434044129485601 -0.810688898684753 -0.6364214868791498 -0.44938733053680413 0.2953150224480051 0.9970048743039169 0.8997342838239005 -0.1596537358527369 -0.5934397588491463 -0.0350106267978181 0.8617813809266391 0.9303539179451192 0.8225567621636226 0.5679113104691793 0.451193210959128 0.5381541583606817 0.706556484952531 0.83700693813458 0.9010716750667599 -0.0716963035561288 -0.6589570748846791 -0.796752750558002; -0.5770026698126898 -0.599373225909362 -0.7875491895490286 -0.9290135178431905 -0.9500281906858191 -0.9270677387976239 -0.9468045093474653 -0.9714828231270993 -0.9702892321025285 -0.9275723094908048 -0.8422900407931607 -0.773198091537315 -0.7471383653092389 -0.6986840312737022 -0.47757811345669055 -0.40865372370256614 -0.15443798019862942 -0.9391174897919584 -0.5546508136409026 0.6153747823491237 0.7276618914706646 0.7023761275995809 0.5553179540972437 0.1061280222496022 0.05057701229206004 0.6335465068639471 0.8249061469765484 0.8499802491881242 0.7015392746733211 -0.1793020456125648 -0.5028805878392909 -0.5051286719294807; 0.2517999373461458 -0.8471121760926088 -0.9840978356925636 -0.7690742426159279 -0.5643068711178699 -0.4893766028747524 -0.4763776086295794 -0.48665158556158167 -0.47112290255520584 -0.41166667076488545 -0.3734039642594529 -0.45614082752244395 -0.7318947321509064 -0.9906951881372905 0.17404916573316845 0.671884645457408 -0.29750259773624804 -0.2923051673503666 0.0652761351413293 0.6185175607663977 0.5059257660133519 0.35935389861762196 0.1539098127443733 -0.38478071951799836 -0.5288396814035873 -0.1266828136205808 0.27838360723189964 0.25436605417779556 0.14443076064807478 0.025297467070907305 -0.05292245764687114 -0.19494343758799335; 0.7475829498765884 0.9334039202436163 0.8185759762991672 0.48088981372853096 0.24111899802919837 0.16125745262550575 0.07071950416345527 -0.025365674659872894 0.030979171059689937 0.9548484499082656 0.9848926516483005 0.9191081305529222 0.6667262987636328 -0.3471911349711167 -0.3840967224331035 -0.5243801593480959 -0.2514997529544196 -0.9378097393025873 0.235121274234452 0.7234579175623571 0.35985468940025145 0.3516829431602119 0.3755744424241759 0.7296412961580667 0.9643384387335429 -0.5427224690988899 -0.07492924125788408 0.005182559065307779 0.06911296013865902 0.3931221800207012 0.8800199662247497 0.9483645357077809; 0.8890260813639951 0.8583681442160945 0.8823233367297504 0.9726822692305853 0.9685407696473541 0.8373986093213996 0.7149715190004674 0.2769353086310663 -0.44078923389217856 -0.319331804586121 -0.07778141451755692 0.45882238123770563 -0.4758463029397795 -0.3828492486498631 0.18198363719362756 0.410559141788821 0.4779515121173405 0.4633955063428886 0.38622166189199064 -0.4133834889243534 -0.6387803852691714 -0.18012371735045282 0.2650629316550044 0.48824744214864235 0.5982424959599023 0.4496035587900892 0.29152262696292885 0.2968752606357138 0.3790987481460251 0.5595441701894243 0.8082656109541558 0.8728777427359152; 0.5676504808919112 0.521833713734192 0.450040712016305 0.4871123963351364 0.6265884253910674 0.8892844784862709 0.6926836718797705 -0.3293800804913012 -0.9088380073186917 -0.9208887893016354 -0.8648539696461653 -0.18201220333659285 -0.1805970755812859 0.36029815536740945 0.588818355069677 0.6691449611712547 0.517609708488301 0.3054744297888922 0.0584078242015064 -0.49682802631697986 -0.9431045855780499 -0.9372234294077374 -0.5815009367881027 -0.3258189981010874 0.0323307822829367 0.9188118579214907 0.9709948078497788 0.8096031766591987 0.6907344956335072 0.6758719006373187 0.7646659301698571 0.7541702635849972; 0.7344980946200446 0.897236612113217 0.4815320842563436 0.3050166047668038 0.19654629086652065 0.14812185505927486 0.2340039207356271 0.0732072044711807 -0.007591731882069915 -0.20520651549813212 -0.5862318000063673 -0.846998653312773 0.6091984096463707 0.4790033115239712 0.7750814522598077 0.9495882941181705 0.46294561714092536 -0.03160628622143236 -0.49771368244821795 -0.5992481266175501 0.2777719241366943 -0.21780053511900063 -0.8007645305513339 -0.6158834228724162 -0.11901378598258672 0.34708929403312266 0.5455219469773303 0.6324617500142536 0.6030515298929594 0.38199542166140904 0.09253797125736954 -0.5285755958299557; 0.45074978306427627 0.845938468365557 0.8236419406455416 0.574687678072198 0.32669072151541934 0.10562923410601725 -0.05687039888769319 0.46125536099370334 0.39504198209934094 0.6007001072333943 0.7647784342641363 0.23528143116638803 -0.5009215760092307 0.5284904433552635 0.6603308342903663 0.1920150297395033 -0.18038768176502534 -0.39543870733213987 -0.4207185254450066 -0.6138630694974715 0.8368831834384662 0.7775625859881584 0.7532195282818565 -0.401694225290369 -0.023782719297769962 0.23336296048117428 0.22211525076206395 0.11445313923324789 -0.1179083059528682 -0.4084011722827772 -0.5477127760105729 -0.576160694831452; 0.15574033931623749 0.5182535314330974 0.7223650580781247 0.7206870677851613 0.5336755998694858 0.18692260792549398 -0.3644296917649941 -0.8161505794436452 -0.9036495171867298 -0.9187586108506873 -0.927094562517649 -0.17792261928004247 -0.12995059350725605 0.6974068251908023 0.30378286183121583 0.14989100288434998 0.29150563025366455 0.9471343659851288 0.03872655867851433 0.053352365085281996 0.8016623023576864 0.7434377413653456 0.7906975137874055 -0.09797752306993224 -0.3610809529627487 -0.3737913166181115 -0.33292346842335196 -0.3926324514040203 -0.5366492806608688 -0.638640880889458 -0.5795148747020078 -0.4740437395905548; -0.7092086987084912 -0.6346021898690198 -0.2332314525599837 0.19508857560955453 0.3399087253413366 0.10760853511361522 -0.46881912857458835 -0.8561632488843627 -0.9350140122600109 -0.9575976433093293 -0.9152009095506914 -0.7697363123115739 -0.7983419888295589 -0.5013519304180762 0.533568948872728 -0.8747434629151453 0.006125176373517997 0.6914929245618958 -0.2441473585864323 -0.6541814198671111 -0.8136151897400328 -0.8040981372208604 0.0704938975164263 -0.76824356696827 -0.789097557010089 -0.7976468582090419 -0.8098177193683541 -0.7674310009229977 -0.5650563647293022 -0.26531943612409664 -0.09713432368331 -0.08340060182233729; -0.9795980978543517 -0.864709356749605 -0.9188814566923752 -0.7615782109464863 -0.035959584797235225 0.22278847090494477 0.1764546450880195 -0.14507497153824467 -0.4999516234478067 -0.5502799938736772 -0.4264661250335898 -0.24525134940068233 -0.13068429854474142 0.000996726688857697 0.4451204458232135 0.8336816557151314 0.8745686220205341 0.5229280301595035 -0.49510912879640184 -0.9805346395601052 -0.9925147668366539 0.3601726709827246 0.9484768292851302 -0.1725356587177526 -0.8312377302778859 -0.6989929328919112 -0.4627606737752379 -0.047794762220590536 0.4134285045552402 0.7467627216865982 0.7399818705248444 0.5722004154341088; -0.7379956685614866 -0.8143700331133605 -0.9520057613385698 -0.8087781042171516 0.2611212215592914 0.5119609284565718 0.6000046061258231 0.6780732483280852 0.7097640368626411 0.49814786440751146 0.3724132034248559 0.3524623734199108 0.31305249974268246 -0.4058200469865615 -0.9857587010032323 0.695690500207485 0.2559993927065908 -0.2394769700301344 -0.5982122750949969 -0.49410481282719826 -0.09027243848171077 0.6812818041500867 0.859331073788487 0.8478262945841001 -0.4873347464437719 -0.3784572465697498 -0.20018310033975495 0.011221807406895365 0.2624340235421473 0.5939850444903693 0.7485971005276546 0.5630919635266021; 0.33853262719249 0.4007318950934819 0.14120335746018842 0.2698661790605432 0.6973984852659798 0.8102250694083197 0.8187122988755327 0.855883463847067 0.8625886843627284 0.20332273271772364 0.07184466113332888 0.07562262285044193 0.09244107480581487 -0.0005615597416959255 -0.4317970175121293 -0.5991675282054643 -0.5325789179795933 -0.7050726907548949 -0.7960298212035752 -0.30668322821903193 0.00034576354419937276 0.17585410943028612 0.44376862031852604 -0.005765039814416314 -0.2884095626311306 -0.20853874870793532 -0.05642037277785828 0.09481311905987377 0.25507699181840615 0.5054658203245971 0.6248362673003273 0.8979117204983175; 0.7123676461109482 0.593850645696171 0.28787287020230684 0.13261358223877218 0.07611860711326092 0.06350480012761037 0.08324752546615781 -0.46973789612523953 -0.6702016597381425 -0.638231916898096 -0.5341661573790887 -0.39514314653086957 -0.10810079401711473 0.7034425181976857 0.7445745425455311 -0.11288137719445078 -0.49141024678076906 -0.5804755072975928 -0.6485559025505133 -0.4866379883520181 -0.3561892016224964 -0.4960797055824143 -0.7019302326606351 -0.836410529615497 0.3128355262535982 0.6477825319471271 0.6371987716250775 0.6607828793791851 0.8462544201207516 0.8120214983817634 0.6419943088100488 0.40653265080005657; 0.5071940769899385 0.0029603479903259557 -0.21734450387546358 -0.2687812140886018 -0.2902902768893614 -0.33200795955319556 -0.5286862114967643 -0.8470819736745782 -0.7274084373589432 -0.6306469125944159 -0.5915884648079082 -0.443481011131713 0.10245967845879 0.46417516512144597 0.6273688799631755 0.7856334229442835 0.9749298727318417 -0.26860002784625614 -0.48522557916288306 -0.4154396030668477 -0.4523117139005575 -0.7097692477569554 -0.7823563716750063 -0.3080353545392791 0.4033676964633878 0.8948349070964481 0.8363164216336845 0.5551768333326056 0.4568218209508652 0.7829948384800572 0.9445179038711008 0.9348983037371034; -0.5706181506564024 -0.38465348609808625 -0.4340906888070393 -0.5071447236785696 -0.6934317101991299 -0.9021859705654441 -0.7348976183438773 0.2213224320479189 0.581619634038952 0.6364260092845647 0.5106216845570459 0.38324991992299207 0.4406160451580717 0.5846434754005572 0.7128798174102947 0.8157529370102407 0.9013480796665684 0.5216376548148082 -0.8175941855919928 -0.2994812134680664 0.9440135262874993 0.45038532392666225 0.4539810392313661 0.7193126102507515 0.7541500658584074 0.7237831199911513 0.758494875440775 0.8198956708589907 0.0791865815954887 0.2459367030825916 0.6500225410143528 0.8818963683583051; -0.3281291427023804 0.15239422232929956 0.1197539973483468 0.1447506838720226 -0.005226871670678648 0.050565629021501496 0.4318138966394742 0.7002128880237917 0.8221503028152175 0.8859672686146991 0.9213149070426594 0.97001515498841 0.9679826761965878 0.8987961485842264 0.8955903087386393 0.9019783963218224 0.8245384710315532 0.1284526630299342 -0.38095795709193153 0.1026454980600682 0.3702517745158715 0.5343203746642163 0.509626801446922 0.4607321727254069 0.6599722786490336 0.9089614957476664 -0.3128400122143691 -0.7463316388033279 -0.8116284206044374 -0.7005943574720859 -0.08964003617958295 0.24987945252060206; 0.06481375918769759 0.7833803223237119 0.8455195348484228 0.7352348099337911 0.7562901454142752 0.8349064934699103 0.8958677496803873 0.8484009549339003 0.7957499749377978 0.6941913708096102 0.5441066838209668 0.4089779823406092 0.44836156960128026 0.6198441343117672 0.7585615939623329 0.7724524498368744 0.3218671175706065 -0.5891346418312597 -0.7708290980708694 -0.047939127780537424 0.03126256885023457 -0.18592082612794922 -0.5533303871995648 -0.9632979419434778 -0.6203991333706287 -0.5277332559786098 -0.7060802551221211 -0.7727641116040062 -0.698070174511325 -0.769722075914717 -0.7467177251900404 -0.9208020934435958; 0.2685274515759628 0.9439057258091865 0.7662314868506781 0.9941130224525273 0.9585480248690474 0.6882373739075924 0.5295338138708611 0.5626909839208194 0.2747237774650156 -0.08193983951181573 -0.31075771611952124 -0.18232505872353447 0.17050903693962619 0.49570524910313957 0.6474666940131334 0.377952526284242 -0.18184634939282554 -0.7709453547401405 -0.7601129529908983 -0.3260024617157911 -0.2808166982616288 -0.3997934972846813 -0.5394172140283474 -0.7115856901872039 -0.8612051940347039 -0.7950003450505532 -0.5919171538732003 -0.522245667202486 -0.4798653393988529 -0.6547580195202857 -0.7531663483534362 -0.7512528970733395; -0.07332037934307903 0.03268421168128745 -0.46146005365914705 0.7899536802138493 0.3216864781529671 0.1986355953866733 0.18331635670638527 2.7184896768390018e-5 -0.8317384852245634 -0.9826786277264644 -0.9753505528644465 -0.7548825014130686 0.03065553674864072 0.5449904333109523 0.7832707918752108 0.28943302453662373 -0.10382053461708318 -0.3092784856347291 -0.40554384857976367 -0.3826742273842573 -0.4471514446873014 -0.463556424865185 -0.5210183850271828 -0.602610947279294 -0.704725136892837 -0.8054912399024817 -0.7685243896546748 -0.4661791521205726 -0.5526417319259328 -0.5867338217075236 -0.5793437823381214 -0.7048806338281702; -0.1457804745489067 -0.1320326607627101 -0.963720585011162 -0.7945595519850339 -0.7531502346208491 -0.0014612222877014754 0.12242502148518034 -0.1012354292702324 -0.9477495449313783 -0.8610407897914575 -0.9284636283022165 -0.8886084857897945 0.0033882783120453026 0.47081817674643184 0.9184550985433023 0.5734831571512808 0.15458094046153925 0.011112015713775791 -0.08619657650041815 -0.4788988180272715 -0.584637654265691 -0.49410899943829756 -0.46813526809051925 -0.4956669569255207 -0.5729199916810872 -0.6113686873084478 -0.7451260408359563 -0.7261411791961572 -0.3311940620547155 -0.4281208453326419 -0.0025912180753537785 -0.09608694538354871; -0.624754924167016 -0.5148266453448328 -0.9909476758166763 -0.6800347619853764 0.2677050504464581 -0.10562180829034758 0.43111118730576714 0.21501062247326666 -0.24874636881629147 -0.3964201213453195 -0.7299779167064654 -0.7637386297892068 -0.1070767662327783 0.01435715793817119 0.14539086453768796 0.940973155410516 0.7647733181606182 0.43563460967755985 0.09360215893113749 -0.4696882064179395 -0.6829567749210123 -0.3336343917286836 0.12966528063407562 0.5721900147598277 0.08928146227712881 -0.27429415180727834 -0.36229252698684505 -0.3381760343829186 0.8735859099822935 0.6562778841949398 -0.05455752021295937 -0.9304059299830459; -0.07902715266481093 -0.9775168327312368 -0.691871694060915 -0.8073535143284363 -0.6576394686801378 -0.13817378184229812 0.379387494312201 0.47497791646951165 0.48507981038979825 0.8377379953160611 0.9368973416319405 0.37569066983975863 -0.6750165970158897 -0.523147690800518 -0.3897808047125434 0.3104661403266251 0.7828777920699398 0.9360457867750339 0.6100090589074342 -0.40078341460480416 -0.6143128675873598 -0.04529700186565734 0.263920792585483 0.7552379401730731 0.7656738146786514 0.5052365391708837 0.6286157241895789 -0.08327737312011185 -0.03905718934506654 0.8544853123010966 -0.0027580124269485236 0.2355355652289439], [0.20112037526353863 0.6779635045351043 -0.12739758739385457 -0.5426888931995006 0.1593139112357509 -0.23415275888812684 -0.3089154115233148 -0.16382256639520976 -0.030931987053824488 -0.03511027153721184 -0.16757329941018909 -0.48081702581706004 -0.6182602426882831 -0.4037835796665442 -0.4056515592955374 -0.20578084402483368 -0.23493534987299278 -0.327177052873953 -0.4455781808602746 -0.6037440630076913 -0.3154674663453959 0.42906974984925306 0.3201901943113459 0.13635181620672138 0.04795853591530781 0.10198402760015204 -0.15852382850271426 -0.6910086582456805 -0.2460963268742644 -0.02059490240043546 0.8282781710631498 0.507122554323085; -0.9576797488771518 -0.10125453519454959 0.5539827589687297 0.18007437578667465 0.16840878611077034 -0.04000783685774996 -0.10660160153401549 -0.09997353953210263 -0.09901385234898882 -0.1643631567217772 -0.23817351709781673 -0.3545934519424848 -0.4731666891001726 -0.3354228917222067 -0.2140785607438142 -0.25592941198776264 -0.09452823178584632 -0.19765836943718745 -0.35928912198165763 -0.4818133036026763 -0.45491127627095773 -0.4654003156766839 -0.2820329130927061 0.19767912665998716 0.38754754649478224 -0.06928617432799793 -0.3424195137627196 -0.9553327342252914 -0.8301077024040556 -0.38386333799543937 -0.6355900482268309 0.30044126020512163; -0.38849238468287456 -0.2825216385077291 -0.33751099830337017 -0.4262835275585381 -0.5127858512004416 -0.4042217287740319 -0.2864068555839874 -0.23613418894639673 -0.23113573136953353 -0.31222140779572416 -0.2951818199474805 -0.3190482645844972 -0.3971219786334167 -0.4709634624271787 -0.4299130810847252 -0.13328103888052217 0.4042872154514492 0.5825224048863369 0.17367439361380294 -0.05449245097494761 -0.26331502511638977 -0.4223585798291383 -0.24125245854109975 0.3813225779544742 0.7618201087326886 0.7030681897091758 0.012831468021232334 -0.24597311858053725 -0.31498874070124344 -0.06765391931654582 -0.4512274559087295 0.13669069556065622; -0.2839053736556753 -0.06947560066787914 -0.25542166289677043 -0.8535747743449863 -0.8833070957083373 -0.7786086781831602 -0.7576664432709109 -0.6602933495803802 -0.5239249757101399 -0.4222025458108568 -0.3362342083308744 -0.20012492520730707 -0.2585776282451673 -0.4545756980823784 -0.7102139923162489 -0.2625619819027218 0.20642639837949472 0.5060798739363511 0.46063107274289833 0.2041694729941978 -0.06304833525826836 -0.19024692211421423 0.11560177711964113 0.6282846303752687 0.7748845626236295 0.644138828841879 0.37017867458298676 0.05612816913169069 -0.0377756243920114 -0.30348495539992804 -0.6693510886705456 0.3571011007749161; -0.9676125184328089 -0.6367489426848316 -0.596660689882652 -0.7003337234676847 -0.8127220164988546 -0.7681610142551006 -0.8431903147548484 -0.9904228013338862 -0.9239630649195237 -0.5906956324194296 -0.19005635189215592 0.37599180585894926 0.09344464907579542 -0.20494356340191666 -0.7131143607065349 -0.4761788203757276 0.08444514295607237 0.4772763033596998 0.7341204300940696 0.5175441646274993 0.20139081863773994 0.1011559290558393 0.5602504685534756 0.9449678900629496 0.9154528443474969 0.844129656596436 0.7610544418107321 0.6128701825951576 0.3002341139711315 -0.10122651287540446 -0.1342808077313829 -0.14756370898196808; -0.6152836414517348 -0.9367615437229159 -0.7327799062262828 -0.4957360051650991 -0.36198201476563074 -0.31088069428067705 -0.4573241850282951 -0.6509007920388385 -0.8656436907314372 -0.8402318374737894 -0.35587638026468627 0.7226773733782625 0.7352242224091488 0.2592159068276625 -0.32148391627886086 -0.7505826149985727 -0.1289550824707129 0.41452093149058583 0.9908476748676309 0.6453054794436858 0.41062477625754884 0.43565672532641964 0.4792045295301818 0.5768497156669575 0.7511567842612831 0.906166069109568 0.8238510180479787 0.5010058185879305 0.2480123561732783 -0.05867239548065923 -0.39154101185321766 -0.42390223505853675; -0.3182568320711211 -0.5408305006304523 -0.6462699979923359 -0.4234262717571407 0.12629256447162854 0.30650034587172315 0.16950371086862492 -0.12876162803313113 -0.4637724015810035 -0.7696488795977285 -0.7600311419090396 0.6072696520073055 0.9359820287965344 0.7313188427755524 0.4417472356799733 -0.934723107757891 -0.5440393771072362 -0.19478931428391996 0.6703489514883796 0.4879152239657573 0.406237412911477 0.22980076484124326 0.10966136723684901 0.0718298681139794 0.14744153225559728 0.40302164781245686 0.5449787140664726 0.5231289789830565 0.474411038452296 0.3101157443077435 0.09307123893850455 -0.6980970902813872; 0.5042651159627337 0.12461955495222321 -0.24760960920308833 0.10530265298626024 0.5656056956792257 0.7675817988260978 0.8282370011493785 0.782297195146612 0.6047485880740066 0.1939432553741007 -0.47093323558743344 0.6767593734722093 0.9764008333783166 0.923102686428088 0.8903346799358316 0.5191252984686018 -0.41876195194356103 -0.7160896057696541 0.1786108548572387 0.4174329685864202 0.4646614608741481 0.41271214935017075 0.24265072998864673 -0.043494819979434406 -0.3046440580740809 -0.29829443450049686 0.8448270485622269 0.8930816979242111 0.9152891981301592 0.7986207772648775 0.35294359350107896 -0.0029963241585471627; 0.9826390851368682 0.9906328129450911 0.9121512543660739 0.9013985639527232 0.7682712349848941 0.76897778459692 0.8263771656431845 0.8670532801926809 0.8897162313426831 0.8996154847513292 0.7278228391537197 -0.1028271806895225 -0.16635979824600156 0.7155885779452784 0.9069505001198076 0.5742381100848942 0.16082185552346362 -0.19376476998719466 0.4319046141595816 0.6536702246954859 0.8082854221065247 0.8470415814615838 0.630406009164508 0.028265607852908926 -0.29846008813501507 -0.36667154170916566 -0.23602836453147358 0.17049466059347076 0.6453173091423435 0.7923439997416905 0.6960532049696715 0.25846900505847276; 0.8888274452849528 0.8322009574534908 0.913353962641355 0.740533950901379 0.5371071885139621 0.4686884333085027 0.5135847058867696 0.5681952187478039 0.5631227808690414 0.4327341119925901 0.0841218139398956 -0.3345415628624405 -0.5851702033307288 -0.7666889415293909 -0.9192708435694483 0.04308847480758817 0.3987583621542219 0.4118552818316115 0.35638489702575943 0.882347264121266 0.5072218204492788 0.33269759646857855 0.19625649257769234 -0.03379376006464823 -0.25185140674169904 -0.3853578049046787 -0.3902043912495019 -0.27029917369488665 0.09871512507777938 0.9946862753620556 0.6541952798777575 0.3370147483269419; 0.8050230262459068 0.797716291693546 0.6147821396840311 0.3121495443196358 -0.055661504202563473 -0.24487172109778946 -0.25660947994928685 -0.21298742965203793 -0.226197375314388 -0.3354490319571335 -0.46925513888319415 -0.556921993452336 -0.6103243487963217 -0.7035239909697932 -0.8610890341027055 0.8968257047305238 0.5982957051087405 -0.0670891636198669 -0.7091969746020124 -0.7226570723457576 -0.6596812238576291 -0.6739730843593003 -0.69817550714318 -0.49046357263422374 -0.2969945389468998 -0.4851461715500247 -0.5314214252358738 -0.5249969232378946 -0.4364399734039724 0.16580945107704181 0.34326214645809344 0.33353177729796496; 0.5269523025048093 0.45007625048355904 -0.09789483776502475 -0.5811819357385877 -0.7952186466025324 -0.8628478047099429 -0.8790284435255157 -0.8723301088948033 -0.8820675765063825 -0.8991596840387154 -0.8885300716653526 -0.847374163857609 -0.6573968040578453 -0.027120680326712956 -0.08975995836353642 -0.33649407245740676 0.3704219704932527 0.15580230182452473 -0.9124962120463899 -0.6911772558382355 -0.8571577945432928 -0.9314173880315634 -0.9880565868984537 -0.8339411685204956 0.4973023413411073 0.4688255271321636 -0.4021058624322925 -0.7890045253016833 -0.7662130627751291 -0.39741288062908126 0.21189523207646385 0.4468669550717725; -0.6117694128126759 -0.3585247591440515 -0.5279094228511836 -0.8460917578949784 -0.9620949113881275 -0.9869123577935657 -0.9876481368750228 -0.9584263963413673 -0.9400645706198382 -0.28995846440574025 -0.08261280747759125 0.2216286193590985 0.49144124844776854 0.8869716685663277 -0.19962892080391864 -0.1350098793296177 -0.7915546222231677 0.34647008639604443 -0.3419185541630653 0.6351889505703636 0.21357878806499417 -0.927652844715633 -0.9199788966538509 -0.6652611241574984 0.26150819838600076 -0.8034997998786395 -0.9969353586881368 -0.9991484079727172 -0.9961270583627981 -0.9177723664051893 -0.47475548849476834 0.31710439252416317; -0.18466623566617663 0.41577534751939116 0.3956992659657899 0.13798229390030184 -0.22740667668516534 -0.5465689358460881 -0.6939885916026435 0.8608359629968035 0.8900407402642357 0.944829543888375 0.9969447823853705 0.8716520100057249 -0.7843749521043757 -0.6592753018179363 -0.6650795526312399 -0.8908445203104902 -0.8217282345927636 -0.6139288616286767 -0.27081274199519895 0.6677888075619388 0.6764196775768261 0.889320514442403 -0.9309104692923593 -0.7878430940546673 -0.6765199208588049 -0.7863679455794413 -0.878622626202058 -0.8787600377614062 -0.8405498742410906 -0.7245939008754567 -0.4341268309825234 0.4188138898465525; 0.05730867813576604 0.8060736720078365 0.8842603323829311 0.8704733643005227 0.7766595237319995 0.4256818438431594 -0.4718719844148986 -0.5751638879558472 0.03704584744109203 0.38144888748132594 0.49353840412795263 -0.5605752646030935 0.30884905608899255 -0.31357604122454086 -0.5227260182268325 -0.7302326552249904 -0.7927563708670622 -0.7694603732992483 -0.7246347476260976 -0.5487112730211501 -0.1323984569128412 -0.3101053862793741 -0.7921429704657964 -0.9015713354777781 -0.6318168814044378 0.04333318897585286 -0.07927093681462172 -0.3243841561274698 -0.45396901076654006 -0.4704407540802685 -0.33457142369430953 0.6495989393706207; -0.6176967655348902 0.4374251820394959 0.8659288721058517 0.9462966855306086 0.9797024063717406 0.9833659554283777 0.4949429916211312 -0.806244770296589 -0.9703888281983226 -0.9696896186996593 -0.6087195863459027 -0.17922693217976463 -0.40717692644251235 -0.0608933053279608 -0.03327823372550086 -0.2684041242771188 -0.7909446872365651 -0.8987340809704216 -0.8647543854512943 -0.7226186481197504 -0.5439589447402595 -0.6131092039446483 -0.527727648815642 -0.28203956358193094 0.42083109235258065 0.8330702432340215 0.8379695265698228 0.6877957779131405 0.34924183426856886 -0.0960636986305011 -0.3521539411408382 -0.08468422437540352; -0.8781045448884935 -0.35537379905559663 0.262966013237986 0.7241905452186622 0.9159136959513695 0.9883410182447582 0.9976159788257828 0.8668690899213831 -0.8042171729327322 -0.627633152379653 -0.43441939139330543 0.6572527072108517 0.627121351332924 0.21699721879949882 0.7505131037529187 0.8867511660019417 0.6962749712680715 -0.8711679233431202 -0.6293567345821445 0.7690351458339205 0.49021165281441503 0.6019082225489801 0.6572864946982053 -0.32522286240700576 0.767620279684456 0.9682799385131345 0.9239311241264687 0.8549585997517867 0.6383739388168111 0.08863826557387838 -0.36539897454270753 -0.5303057266469953; -0.7807665663208563 -0.6330575895570616 -0.22461003060920226 0.27141578519334864 0.6587377929505933 0.8678962649628172 0.8011188777023678 0.3514497998578868 0.0749015643873662 0.08687334265420622 0.18228068864553046 -0.5360868777822334 -0.9022909697154122 -0.698613734869598 -0.9327604252211334 0.3950767058627116 0.13500081971031688 -0.24326226554029776 -0.7890396491824572 -0.7973962709659979 0.2902759743455032 0.6497003698792029 0.3599862914882718 -0.989684460571216 -0.7866455322249579 -0.3191917190554601 0.22395655179303958 0.4114761207789853 0.27811233025677295 -0.10285874272934738 -0.45263854867464187 -0.6318595046619349; -0.6780557687415573 -0.6555004022668912 -0.6001280131628297 -0.11962020001959714 0.362786074173451 0.5529270345090913 0.41406953083187936 0.06642831006052334 -0.04253900289064272 0.06248911845075675 0.3317078194145178 0.6237288778381874 0.5311299954401377 -0.004563907851352263 -0.354570108680536 -0.48316775208571433 0.5934627936419897 -0.1695198523687377 -0.5410145128147681 -0.5803035145201378 -0.5605711830058768 -0.4410750851311292 -0.2247289037302369 -0.6337467446760308 -0.5721137118040662 -0.47606954920412337 -0.32439333002114185 -0.17826370164450797 -0.26390028841402025 -0.6056370807104314 -0.8029958240026439 -0.8013937232955072; -0.15799663989879964 -0.5000443441508241 -0.35199822434887884 -0.1219454706990181 0.43320304512372476 0.5888057080365755 0.5713188328667265 0.3428054616338909 -0.04006316611579907 -0.11461716141325057 0.1414011043886607 0.5454693344289645 0.8712082331805668 0.9999755534592091 0.831253244929549 0.4605915117010348 0.41731695728214446 0.2613960613635542 0.16735917510379641 -0.008541013075165325 -0.09051193561737562 -0.7308996176886506 0.21081464730568406 0.6915109837673274 0.16373566174291276 0.054882521458249574 0.01929291981874097 -0.0012423103894075181 -0.09835760790079731 -0.30462612216462326 -0.6120820809500542 -0.8021993808921359; 0.13831815850908552 -0.31529820885527626 -0.29319336332298285 -0.11156897975761164 0.48554307094411076 0.5928382456313992 0.5929284105478824 0.478943420043011 0.03950792923744034 -0.4933098264153768 -0.6242922420450296 -0.5856270157420775 -0.4412635545967279 0.47902937523038636 0.15263820634912864 -0.011568735370726379 0.021836201036806238 0.23689848464582633 0.646209228083136 0.8662607898773713 0.9664723679998777 0.7290923700139091 0.30887511770638 0.11793502667535372 -0.09285358778249025 -0.021654947349372896 0.02266817725598427 0.05244000997175478 0.1015797112127058 0.09562050699120096 -0.12102897741232593 -0.6532536963391052; 0.634994316796953 0.05764637223606898 -0.8062532900686851 -0.9534297157357449 -0.46193317558213776 0.0166608965353779 0.31355915153252767 0.3523833070046845 -0.37133884967244035 -0.961321749079147 -0.979887858913892 -0.9749121354588103 -0.977798490538861 -0.9997634212985311 -0.8786741019969477 -0.7878418517250145 -0.7148204306495206 -0.3868913827407176 0.3569241493696518 0.9479731772394712 0.9999990605393775 0.9703110775120575 0.6527609961508324 0.9931725988682018 -0.9259075933062642 -0.6340831472075185 -0.36270942368015374 -0.049651104464664746 0.23957600122500597 0.4916359655218678 0.5702684480479671 0.3902595190770493; 0.6068401877615135 0.08064349725340074 -0.6867661190847929 -0.9457015226375045 -0.9949761631402152 -0.9975805811979733 -0.9965264872423392 -0.6780186799668092 -0.342378775017705 -0.5282436158715007 -0.7254694355117315 -0.8502310506754835 -0.9138623750919861 -0.3136000282392767 0.1800457277972818 -0.42586755930084025 -0.8688970157058171 -0.7677478490124919 -0.4126225503149326 0.45168813496928323 0.7943514944200086 0.8000170350200319 0.6922538258178803 0.5423854693356669 -0.4968505417310128 -0.7344876963887623 -0.664830550564875 -0.539774264352927 -0.05906302302391753 0.5700560248805513 0.7661286711902358 0.9114544874005355; 0.5632368934576146 0.12738728862209844 -0.486291476030121 -0.7446154319080256 -0.886635559637117 -0.9249010822107517 -0.8356510441111431 -0.3307185428367573 0.20469431991916828 0.2417019571840155 0.23609496506006464 0.4863856492380643 0.9083113400255906 0.8780033799234338 0.7761197837999197 0.6073334930612385 -0.0021730485511976642 -0.9413718329611078 -0.6087407352892087 -0.08228995202456703 0.2913484342290545 0.44440568307924755 0.6217931598066334 0.8187933481780845 0.8037190588251892 0.4440636947383188 -0.06499222164212906 -0.4040632764304574 -0.536448213492147 -0.355267597699223 0.09833140866712825 0.3379928739478726; 0.3703984899286764 0.3615729205273248 0.3695677585565698 0.013127649070296484 -0.2838235237117025 -0.4015886581258704 -0.06667138672115858 0.6305258324993728 0.7604923163441928 0.767713938402588 0.8083472114251334 0.8799852106279106 0.8853335583986669 0.8094665762869904 0.7011902068629491 0.5783521404429636 0.4319660865768652 0.7682692468757627 0.535575063060754 0.9430043241210416 -0.2808748806911686 -0.8918450101056736 -0.7474537325299238 -0.0449865331773945 0.4188470992135035 0.6006561940722507 0.617162112952507 -0.5647441673639332 -0.9912179480169175 -0.9606235607024123 -0.7597112780903816 -0.44251377041383516; 0.7537104592531505 0.9469895366201182 0.9137683272164278 0.7948499244227402 0.9445398648874904 0.9254400105423689 0.5143962633357687 0.26293770237658626 0.11723351247821702 -0.011107794510458147 -0.13775378994219645 -0.20330137717858163 -0.005127944268729842 0.2499266741696924 0.3640650088552794 0.42521172054061107 0.5141095115485503 0.7333832153375553 0.924385848154973 0.798616574523156 0.5860259424673264 0.13837842482211707 -0.7405168400270123 -0.8864667785353804 -0.7407110895928327 0.41531052787043277 0.9010785883455423 0.5052313524044159 0.10426310597710353 -0.47985841721462036 -0.9587342489405918 -0.9636810994732349; 0.6260806266223022 0.4584110290523044 0.5098277674705902 0.6665659070799334 0.6476159014145236 0.5241817913667064 0.04396255318843777 -0.1838710527118762 -0.3005283742252309 -0.46177125750086556 -0.6996748698781259 -0.9048290212746515 -0.8271955996307816 -0.4943921347002269 -0.07678133778282295 0.41802160673580857 0.9447275587910118 0.4369207817271785 0.17166456994724943 0.9893130530302032 0.9540560957525052 0.9429765484033763 0.8125525287834859 0.12165524361239324 -0.4110893295852516 -0.14965392692910412 0.4293545148767026 0.613414699972766 0.7137166752183256 0.6027231769006635 0.5519578380578358 -0.1460565636996632; -0.029811689535625473 -0.2811040536533854 0.30556214011253263 0.10080860100640507 -0.04287734832525492 -0.4330877663267029 -0.6830872911031993 -0.7980258336821482 -0.932607742992017 -0.8122056204762688 -0.8489460267327388 -0.9831987616234223 -0.8948597194362667 -0.5889078987163119 -0.068829663059251 0.6465344504480135 0.8862156916748074 0.5373254084574017 -0.6486157495291741 -0.3150799932483103 0.8348418771143088 0.8954852016764562 0.8392829104717447 0.702021944672045 0.48051018602860623 0.25724369885299586 0.32814611126021936 0.5663797658176035 0.7262453349118679 0.7141487776805314 0.6466601774877477 0.650718345994118; -0.9955704009952769 -0.7474848878289471 -0.25207983618105073 -0.5312520488923982 -0.3663027922790322 -0.4497730915773495 -0.6021660148942602 -0.682258044321346 -0.46984810035193436 -0.08705251344201678 -0.16253906801536128 -0.6287592173383122 -0.8634710674428503 -0.624573436518065 0.014596886083621452 0.7853531409164056 0.8260730968741812 0.5516447991075257 -0.2577523459900371 -0.9129252961738645 0.16252786619306284 0.7015443878593804 0.819449861004835 0.7978390457655873 0.7012337941143095 0.591835160636416 0.4380980875088973 0.47269877945411476 0.49060070529799793 0.5903801056330765 0.6961329948653056 0.6577001603322867; -0.9696973401121324 -0.9912412595547889 0.09045462153085165 0.3551549790089271 0.39042124830428654 -0.050778573691435194 -0.21486883216955138 -0.16029866595801137 0.24263307281516813 0.4861793011440825 0.3706329656495599 -0.22068395556650403 -0.8543840648028421 -0.8273942668075946 -0.3527258254897386 0.7290123661421091 0.8026198573486638 0.5938337194441051 0.1196561756417553 -0.6633681552963345 -0.5701281372509208 0.16916990482296085 0.6827990398150868 0.8573156906509859 0.7963337641185464 0.6699342689425529 0.5123549097669409 0.6671184154861234 0.20788357419714448 0.4800610197579076 0.22284695899164014 0.680972807006015; -0.6185748769100999 -0.6803236047423393 0.10540261268828399 0.4172947293645878 0.8316267882538692 0.7568768047088158 0.47939167968155183 0.9239505032570144 0.7989239778587409 0.7965468732709168 0.6756425658387706 -0.25305670213970677 -0.9092304101992408 -0.9994687445971843 -0.9776613053637834 -0.3379014362094085 0.4577390067816051 0.5617787228789493 0.4035046226514629 -0.19848196965930914 -0.716691125904097 -0.8605946177977127 -0.5806386371273602 0.2288906939892942 0.9935429204798633 0.7345562542155102 0.3022833693666491 0.09498166017584395 -0.48243345210470345 -0.6867110654217297 -0.9738385623923548 -0.1817745733733963; -0.3392668660204512 0.06386675647708494 0.6891585082875158 0.4735335136802351 0.7191656120891796 0.9731219567564099 0.9244606982848704 0.7727227295355774 0.6240470623263896 0.36630056039336795 0.2479294454161861 -0.8471367642874575 -0.7162054203730492 -0.8407629837999887 -0.9149831903296396 -0.9472665458496299 -0.5858486890786933 0.08064792947295675 0.5470874506459138 0.2889553434538843 -0.5005541578372786 -0.8376921732127977 -0.9582715539144097 -0.6360787411932336 -0.5765146890610124 0.6253117789457958 -0.2089931872696872 -0.30427414049735485 0.7829726615245811 -0.5155540541771969 -0.9998549810371059 -0.8640289479265179])), instrument = (lgR = [0.05755100129562894, 0.057551001296848654, -0.010242835890749497, 0.11458860749126752, 0.10442311515907059, 0.041169849800993315, 0.02503688391783294, 0.0663021557100921, 0.05652896110417649, -0.010109454904140256, 0.046496065002990465, 0.039241634732247066, 0.017195501510771986, 0.05650411387359346, 0.02808671617185623, 0.01549607344102931, 0.04365162268338308, 0.03782628865198354, -0.033539035009513905, 0.006710466123679542, 0.015753932297547818, 0.08800186060171834, 0.03462920653773137, -0.052403403893253146, -0.10937815173453733, -0.031173831014268988, 0.08350658381099997, 0.12597340714342087, -0.04641809281094043, -0.06347117387315218, 0.01460886756092407, 0.013728808466115303, 0.002099939769347984, -0.19642505543529912, 0.024337656421894102, 0.01494734341573567, -0.0045500208006439375, -0.008657022333915267, -0.12750074249750268, 0.01495413363248006, -0.0041704105743546336, 0.023379290117620202, -0.011444100733469444, 0.07765026850662347, 0.01555109860674823, 0.0032106711800736817, -0.004578880080126947, 0.002071353478066523, 0.11646129786134037, 0.03061943453308166, 0.006910402120673847, 0.012510396195244376, -0.29982800301919615, 0.22250923172847012, 0.14249873161381438, 0.017739843743807396, -0.009803029268563888, 0.046156408229023685, -0.18883682829220844, 0.20746057094868003, 0.1563150092983598, 0.03657108688647759, 0.07032899925718697, 0.05930256815665265, 0.15956566623931911, -0.017078570969223238, 0.19373924908357473, 0.029327941081879444, 0.04106662270969433, 0.02736654970961926, 0.07433902769045496, 0.27007290689171526, -0.08365864926956201, 0.18546911732883384, -0.00728195098400652, 0.04135923628228456, 0.010448546789663848, 0.13890346505968185, 0.18311047976749034, 0.07819861678617064, 0.03667601329038399, 0.040671941655151506, 0.012680183660143922, 0.17572052292273693, 0.11372237304634528, -0.6933412140911193, 0.057715647880650846, 0.05655458685035344, 0.015082691913656516, 0.14793992432919895, 0.08085629500340144, 0.11677097128648235, -0.04282948724485162, 0.06629457461767821, -0.019921874295802416, 0.106013039241812, 0.10222480753984034, 0.20144700449456826, -0.042627687137497136, 0.03892354687890946, 0.1147260471305238, 0.13864051074928613, 0.003384066361115371, -0.054683532879402114], lgrat = [0.006765321030876906, 0.02351901694368394, -0.0012284061034834332, 0.018757755122287334, 0.015252735582814012, 0.02048132373473891, -0.006641792153497067, -0.027481559181263507, -0.007317508619410595, -0.003842718664508582, 0.019373033694858082, -0.02349771634894664, -0.006968157443751509, 0.027244417942488483, 0.012424167560532079, -0.06509123581934576, 0.006483032966963868, 0.00647987076210725, 0.0245278442058414, -0.015290678102251187, -0.006108084622062229, 0.0120892231738265, 0.01576475479548388, -0.037038247697757556, -0.010331777307181739, 0.013282616967582577, -0.0014721788496030567, -0.03357901379644784, 0.0041168419127466105, -0.001954158378898559, 0.023091762232173928, 0.010869438971812122, -0.0010502638256723415, 0.0002327725373105698, 0.02429216803746726, -0.0030554715883844854, -0.017034024680428472, 0.020188873603441897, 9.489762916038983e-5, 0.010147837212767715, 0.06313668809748343, 0.016616486993414267, -0.005543567149698572, 0.032890826205690914, 0.030265153199348808, -0.02724065309903161, 0.03392205109305394, 0.011761197208664849, -0.008044391041465718, 0.018088783238261037, -0.03316931101591848, 0.021913101028841985, -0.0749431021517506, -0.010917583699509827, 0.011380693760135376, 0.0298904070237073, 0.01310917829293641, 0.021894449338853216, -0.04719290809576986, -0.006731305676418794, 0.008709765750130313, 0.03246424447306024, -0.06987796056229417, 0.02296572938901381, 0.03989466182285997, -0.004244432422867889, -0.0074435953344573385, -0.023657672293521875, 0.022951741155414228, 0.016618375198047482, 0.010935233208738973, 0.06751507653549779, 0.04076105807079613, -0.0028246494255363577, 0.03935881071836712, 0.042628105410730484, 0.007317490232046432, -0.01779115010786911, 0.04575979073543525, -7.125554199045213e-5, 0.025872261176459674, 0.016348931119619704, -0.05079385420922906, -0.022126376757180464, 0.028409206205560866, 0.017743421949481916, -0.07265201580177451, 0.007745443193471236, 0.0372859567288081, 0.002026617194474211, 0.020195730944684295, 0.0032477826987762017, -0.045076251444856295, -0.0013492324768315169, -0.023807816709302255, 0.01450160915499094, 0.025533775085076732, 0.008715262935125092, 0.015645415558978595, 0.02011702789582915, 5.564128881792872e-5, 0.03463309095575714, -0.02595504900706331, 0.008378347464659083], gpR = [0.0, 1.4637656859748394, 0.0, 0.6638881313893761, 1.3773373389262547, 0.0, 0.5094578659549732, 1.2936954996596615, 0.0, 0.4074974586460966, 1.0804869565038153, 0.0, 0.42464403352275365, 0.9600302869198203, 0.0, 0.437464728789003, 0.7495433115773176, 0.0, 0.3643449081932772, 1.2174535456712674, 0.6332275230891753, 0.0, 0.33813158462885295, 0.9697619601958869, 1.604943703219447, 0.3785563179721875, 0.0, 0.26445872747992555, 0.9512681863569893, 1.6158120385211518, 0.0, 0.2566829534863795, 0.6917287817771207, 1.6259757394523462, -0.018839394147456643, 0.0, 0.1559695342367805, 0.6333988819787537, 1.5768683100206524, 0.0, 0.2547863635480981, 0.4600827655277861, 1.4777672046955155, -0.4801226327452863, 0.0, 0.20318898850218434, 0.3476772163116101, 1.4231724604690636, -0.5765356257329035, 0.0, 0.24820520317205677, 0.03887058503943697, 0.8523504866706249, 1.2604155112240358, -0.9722064839650862, 0.0, 0.20870675713268863, -0.011844528368940583, 0.7293994072941797, 1.1561227407682386, -1.127517434170808, 0.0, 0.22229781951866875, -0.2761972285405702, 0.2869746827124912, 0.8933764266159646, -1.4790046202044924, -2.1007147405530597, 0.0, 0.25597714216010087, -0.4127358693196184, 0.1380265435767546, 0.7878181124710407, -1.6155896326440207, -2.177879176583262, 0.0, 0.29560568646094326, -0.9582069633305119, -0.2640468959094217, -0.3104166224236429, -1.4537178955854169, 0.0, 0.3976748953490448, -1.5548783515910496, -0.4141172460791342, -1.5392794503175953, -0.7794628572893164, 0.0, 0.5419671160053234, -2.197185077239733, -0.4772215073167748, -2.3008352293612973, 0.03700359673044074, 0.0, 0.6634990819021924, -2.6196880009253314, -0.5455392710089131, -2.719395160178377, 0.30132801645769286, 0.0, -2.7778357937544875, -0.4906496588116599, -2.8356799904964958, 0.5221574702172098], gprat = [0.0, -0.0034614486394969877, 0.0, -0.09116856684734406, -0.0007325101365563609, 0.0, 0.049024860623068635, 0.004850136933288587, 0.0, 0.05646461009850045, -0.010698842764358988, 0.0, 0.03858110564194073, 0.016700312131842653, 0.0, -0.06664970184126144, -0.012549810437774232, 0.0, -0.04681468043906699, -0.020308921228932048, 0.010882662138134, 0.0, 0.024871613944899257, 0.05184500795113153, 0.003496500916606033, 0.00583535116001408, 0.0, -0.0111681287947521, -0.007603635437017049, -0.007150008788147103, 0.0, -0.050661462406877654, 0.03904312805676568, -0.038243320665282035, 0.012414353096708734, 0.0, 0.01734012271034716, 0.005895707809379809, -0.0075092541278934015, 0.0, -0.06355770290625944, -0.03794003839376107, 0.0065326616261722975, 0.021471924994118062, 0.0, 0.03304718090104154, -0.021980459249066487, 0.0070721126378443565, -0.004787080397349876, 0.0, -0.04329180964832863, -0.012544643949204721, 0.0007558441738970346, 0.0008309380088833725, -0.006738257282483741, 0.0, -0.012153652663081568, -0.047633545170747804, 0.0006536063973829982, 0.04182654536418645, 0.013452410175382788, 0.0, -0.008880187628743597, -0.08869619320731971, 0.00016813026362161705, 0.0442820745401824, -0.014267274472397014, -0.2296657175879998, 0.0, 0.0346280963833271, -0.05324543765310971, -1.7367061641889918e-5, 0.02965026377934854, -0.025707868357978562, 0.05464969986964527, 0.0, -0.0205199468001015, -0.07558478958834379, -0.00033611611820099616, -0.043749053613677744, 0.18731675403401016, 0.0, 0.029020076238794237, 0.041111898425508456, -0.0004323728178040204, -0.021326066343884297, 0.08204493029437272, 0.0, 0.04246507794578358, 0.13567430254446025, -0.00045737854565666567, -0.028015512519297445, -0.14827218842050474, 0.0, 0.04935708319903156, 0.1338349563842532, -0.0005066615927619754, -0.05114403319630658, 0.04485300692787871, 0.0, 0.10236483492455731, -0.0004667734433833256, -0.04454688919109778, -0.022211246351886867], dRx = [0.009160134164017005, -0.09292868484373124, 0.03510119342272539, -2.132277528697243e-8, 0.019302508280167628, -0.1934891415751766, -0.0032793528481479717], dRy = [-0.07810732476837963, 0.022737469581011492, 0.06531813014825595, 1.348784643296338e-14, 0.046701844054095304, -0.022462901329703196, 0.10737022437436909], dLx = [0.013269797082087042, 0.047713909407851925, -0.04433746387879824, 0.0574190368044134, 0.0028309853758902545, 0.11663341613763815, 0.07221420103669189], dLy = [-0.06348921783257913, 0.04555973072826318, 0.08759133608370355, 0.027173265367954846, 0.016189939466356953, -0.058063635350449054, 0.05154141771874011])), retcode: Default
u: [0.011774702707330907, 0.023385765528112386, 0.03466568624546154, 0.045404427938081846, 0.05532673821912581, 0.06419901001790289, 0.07162944890917651, 0.07743879859416311, 0.08153678658092291, 0.08429614363684369, 0.08644564755338985, 0.08891791672790253, 0.09241389871394545, 0.09663326602013549, 0.10029527797544593, 0.10152630857724497, 0.09919674361790298, 0.09374281484778997, 0.08662632338310405, 0.07907125779479236, 0.0717221413293879, 0.06494159724820225, 0.058657691643827115, 0.05258088761263762, 0.04654182169613023, 0.040437603373075705, 0.034465289421505466, 0.028484048600642263, 0.02265430454962642, 0.016901236949690455, 0.011225395818408779, 0.00559594116229046, 0.023718120293101764, 0.047152079301642114, 0.06993007910142161, 0.09165954425048292, 0.1118559101793017, 0.12986070622748577, 0.14504024770250235, 0.1566688174281305, 0.16451966060432982, 0.1692656135193095, 0.1726217392799953, 0.17696461671095984, 0.18425283228050923, 0.19403417505998843, 0.20313070766001273, 0.20655053325921857, 0.2014132635084276, 0.18920753293854056, 0.1737368399708877, 0.15788869941442063, 0.14288452914886837, 0.12941568178449414, 0.11717337946967948, 0.10523222022214242, 0.09313400798864381, 0.08096571590347496, 0.06883067695983412, 0.05694579509678606, 0.04526400575431658, 0.03375471465772109, 0.022431656029247606, 0.011188773608038608, 0.036026487221095305, 0.07161887263536693, 0.10635883552527545, 0.13961877843199705, 0.1706762039536434, 0.19859798694032532, 0.22214053237860445, 0.239863443031383, 0.25074363252520976, 0.2556053668072557, 0.2577763202460607, 0.26239586594284064, 0.2739744104628565, 0.2924427259251956, 0.3115723996792432, 0.3197014593980262, 0.3101943907574835, 0.28800594256409473, 0.26137817570223676, 0.23560104921973443, 0.21238047600695023, 0.19273663253905104, 0.1754495052950109, 0.1581115252680718, 0.1399539306885125, 0.12147160663545585, 0.10317306947550832, 0.08525501772666647, 0.06769530986809733, 0.05055042207764791, 0.033555314932619616, 0.01675034229872765, 0.048767563131383564, 0.09710499815425726, 0.1443989175869955, 0.18998032662463732, 0.23289603186096114, 0.2719168200038022, 0.30520332396974165, 0.32991755460720307, 0.34295759275190263, 0.34422716969072337, 0.3401163924695506, 0.34173668897226395, 0.3580611073552528, 0.3907160633360271, 0.4289945309216076, 0.44722016982909585, 0.42967593548858724, 0.39139743653459746, 0.34934918824283473, 0.3110294543975204, 0.2786188679964907, 0.25395366486722565, 0.2335879833440321, 0.21161859239462752, 0.18706897916912504, 0.1619205185830711, 0.137237872986259, 0.11326461706112076, 0.08997830131919772, 0.0671027243957276, 0.04460888510023328, 0.02226321542558627, 0.06207601319376344, 0.12372218713379828, 0.18441045012348975, 0.24327803300225914, 0.29926257737587925, 0.35101158017509865, 0.39629027959061003, 0.43029393497053803, 0.445035386798798, 0.4362222493706197, 0.4162831531520802, 0.4091355353333611, 0.4304256337781854, 0.4856153544687762, 0.5564738792708125, 0.5902989375038148, 0.5564034341814095, 0.4949752482157515, 0.43701524239881523, 0.38480826879403685, 0.34209979506508387, 0.31281658209752355, 0.29180875089299746, 0.26605683372286354, 0.23421945825748922, 0.20183802377453713, 0.17065726915657187, 0.14077078779848276, 0.11182917093858576, 0.083503865795526, 0.055521145255671756, 0.027712926799698286, 0.07586915895953768, 0.15154246865344084, 0.2265061579313954, 0.29983897447509184, 0.37021847988871825, 0.43615910611723496, 0.49517226569290823, 0.5410965712256123, 0.5586159180352002, 0.5295867087597654, 0.47940040518324406, 0.4555459020220267, 0.48032364880784656, 0.5662052787891235, 0.6754255754510978, 0.7064113552228489, 0.6404145861363337, 0.5665936769288865, 0.5163346097752229, 0.46159689090717393, 0.409770027522281, 0.37285522509653324, 0.35056572550818693, 0.3207370462659781, 0.2799712327339165, 0.24016541334050845, 0.20281145343864693, 0.16746419780778396, 0.133266431236547, 0.09965388909391047, 0.06633527483565062, 0.03316806106133013, 0.09000659112194623, 0.18026559922710347, 0.2706030053744986, 0.3599056568874644, 0.4461642155070966, 0.5267147499591365, 0.5966220830828664, 0.6493857819452519, 0.6683263907123075, 0.6094750764146126, 0.51700428839564, 0.469062760725512, 0.4849702029062992, 0.5838734893111651, 0.6865734863236103, 0.6300765965662405, 0.537742327545369, 0.5201622053227345, 0.5575982377654042, 0.5409708342789339, 0.4919087507011104, 0.4417848439789818, 0.41192327838026926, 0.3740123979569319, 0.32192337997386855, 0.27565461220508014, 0.2331112737737281, 0.19310504523415653, 0.1541949368418801, 0.11562171148939003, 0.0771453939821804, 0.03860237531288113, 0.10399567751539493, 0.2091443724371165, 0.31600746826352544, 0.42361836739782704, 0.5285175520996195, 0.6241240417540181, 0.6932670806977943, 0.7211895324721694, 0.7224973883022622, 0.6354322017453523, 0.510031252330697, 0.43360543422366227, 0.40965119202295075, 0.45945872258649595, 0.47595678712633066, 0.34456704959732265, 0.24952948375243691, 0.3234322257858733, 0.5074880431791434, 0.5837952082712119, 0.5744016387846375, 0.5194445923433866, 0.4830125637795528, 0.4269085105422045, 0.3590713381746553, 0.3075040147734795, 0.26119930044809475, 0.2174242268676194, 0.17456351953773724, 0.13152857132033535, 0.08807637537559566, 0.04418053295227773, 0.11697110360366769, 0.23638519635609845, 0.36034269877577363, 0.4894273866218617, 0.6198627507648851, 0.7379027733782042, 0.797479470182466, 0.7452826703517484, 0.6784278795092784, 0.5681137340786824, 0.43906784572673163, 0.3360583702671042, 0.25934200677943375, 0.2660781335975657, 0.18682139313837978, 0.03970588321772757, -0.028763988687077365, 0.07327271981804784, 0.3053991200917767, 0.45821060969797656, 0.5481434027983401, 0.566772733007081, 0.5760762899069525, 0.48404406730979527, 0.3891362592689565, 0.33313806201030444, 0.2854500799690736, 0.23968395322899588, 0.19435364361086568, 0.14771001327292657, 0.0995099004873447, 0.05009606404522082, 0.1275908531997236, 0.2589360915298476, 0.3979437094224732, 0.5488164513020544, 0.7145272305069971, 0.8792426170121185, 0.9464801815812284, 0.7676155180252979, 0.5821045463568814, 0.435189627961309, 0.31188681427414955, 0.1961227089596498, 0.10016178331830138, 0.0876684051723496, -0.016421891662214985, -0.15298230597917903, -0.20058926908223532, -0.12347999146500337, 0.04538462667372025, 0.18005924055385045, 0.3533502918042106, 0.544449155507164, 0.6448056050737264, 0.5151164521303812, 0.39545510133348405, 0.3423115491390657, 0.3011541880635457, 0.2588053865755531, 0.21412816871284068, 0.16505165630157384, 0.1121887940895779, 0.05675559952116219, 0.13454367219657795, 0.273295749570947, 0.42088922059629597, 0.583323087832096, 0.7745761226028228, 1.0035493644377973, 1.1179776234101448, 0.7896544015288439, 0.47079187082684737, 0.28036153851811246, 0.1650754166448191, 0.07391659313107593, 0.02792087061475598, 0.051232647661730545, -0.03227992824411376, -0.15527908793258718, -0.2032528474457286, -0.19260051992633365, -0.14436290780945915, -0.08871848538741264, 0.08052822847426688, 0.36016869032241766, 0.5281241172262632, 0.4384252693831738, 0.34885971965098417, 0.32115989782645543, 0.3043732413631062, 0.27612836173678723, 0.2361038359036484, 0.18548524342971584, 0.12742388425960677, 0.06481684718477623, 0.13735031212253987, 0.2780842230712116, 0.42546605971552903, 0.5823498568875467, 0.756242125843971, 0.9650012557089869, 1.0735307268024197, 0.6794680419513953, 0.3188444207514454, 0.12029534784769368, 0.04191520589009844, 0.032578919101669976, 0.11908252605210995, 0.2550803644489125, 0.18620771663429037, 0.09351415529665347, 0.021271181764497615, -0.097018389171935, -0.21397884277297963, -0.25991420578321933, -0.1466135102414914, 0.10236821081673957, 0.26555571066681105, 0.2664227261566403, 0.25818057729164867, 0.27800185187922277, 0.30455099280545417, 0.30054365756081325, 0.2665256691177318, 0.21281049579763212, 0.1472974325228731, 0.07517612419363243, 0.13683576617785595, 0.2756894341364563, 0.41736804898965213, 0.5601180509616298, 0.699358040288324, 0.8200771868488187, 0.7996722217953598, 0.4496717569229269, 0.1350418922680538, -0.014288686816249667, -0.012086843441315515, 0.12228919018958793, 0.40998025020577133, 0.6400395967192157, 0.6365371387663432, 0.5307061272564677, 0.4653272196733575, 0.1597528053610985, -0.16579907354876347, -0.3048696345945823, -0.2523450778644013, -0.05702683734215574, 0.07030369582172234, 0.1274760900703926, 0.18299056734952712, 0.2517059845747717, 0.3270139626132321, 0.3485266761428317, 0.3151829626274686, 0.25196387326620273, 0.17407529937476005, 0.08871454057166983, 0.13434888787430688, 0.2697483033782077, 0.4047111000624539, 0.5313199501730034, 0.6292304112334648, 0.653685620850755, 0.5282101651365391, 0.24514377898311931, 0.0010540784291207085, -0.07660871308093783, 0.03686395039771349, 0.36965468719065153, 0.6029020316427287, 0.18950142439716838, -0.08731073762915298, -0.13511502025633318, 0.051154858636754015, 0.20416479742625615, -0.02894909326534188, -0.209323656427288, -0.21574192346266052, -0.06313941802588817, 0.01901655995889575, 0.08947187132626988, 0.17007950000044117, 0.2771165407219494, 0.3938024754966926, 0.43212886899099096, 0.3872805609204566, 0.30488998125679634, 0.20854052807878182, 0.10574745476430937, 0.13063586763793822, 0.2623300298486678, 0.39311756735610975, 0.5106175306797774, 0.581814957191841, 0.5543278722426437, 0.40037596360224226, 0.1718106641407262, -0.012812391674380634, -0.03405049771597276, 0.1855796060813302, 0.6853468099538937, 0.14243085473566008, -0.3453533794329606, -0.5759639209026938, -0.570219227530541, -0.3081030900107335, 0.21565131036557875, 0.36044071336639677, 0.031112351563059904, -0.0712492657673716, 0.04675945107650875, 0.0937277729935283, 0.14855943559447093, 0.23085712831840965, 0.3609886759924544, 0.5036164399100312, 0.5458249570689376, 0.47759271010546944, 0.3687998863859282, 0.24961197803940477, 0.1259328375688824, 0.12563448396188964, 0.2527753124993218, 0.38180956038797886, 0.5054124209484129, 0.5915748913165445, 0.5820598363697835, 0.4511157857418136, 0.2657116911970052, 0.1070301592588348, 0.10354712082616059, 0.35187106524626344, 0.765735750333134, -0.1291282510409239, -0.6018591177183469, -0.7952437996949029, -0.7493880005726424, -0.4114795943504895, 0.399364607495127, 0.5781278019416313, 0.0927301413064745, -0.07129638992427692, 0.07670967306088161, 0.1997351251955864, 0.27994491393587284, 0.3571016919147919, 0.4829471775055572, 0.6254856653078963, 0.6658416278127312, 0.5758420846252931, 0.4399762870428185, 0.2957581955762246, 0.14870946033706572, 0.11876489942135515, 0.23913326595419113, 0.36269515484632786, 0.49260197705224634, 0.6166746191380965, 0.692458469979499, 0.6677098269164405, 0.5342952715324496, 0.3200866166348216, 0.2401165468137526, 0.37199996412846315, 0.46719129378072416, -0.24710573057843646, -0.6548235944068189, -0.8159300860933574, -0.7413247568451432, -0.3720326803230213, 0.4001700235564217, 0.10036241929381524, -0.22656839609940188, -0.2909473349847776, -0.08049026956223188, 0.2611289289366677, 0.4578848188147042, 0.5162199327275808, 0.6018826680932904, 0.7245514516204014, 0.7686406461954542, 0.6721263389498989, 0.5154624267331903, 0.3459956524255668, 0.17354738890633897, 0.10983138604420674, 0.22021775829183407, 0.33196491339827905, 0.449049853456749, 0.5687734321857966, 0.6756352549971686, 0.7579111249746056, 0.7568154732912893, 0.43744188176971005, 0.24450987674796726, 0.22567920149218546, 0.2445076580088917, -0.18563981468188592, -0.5121203507635133, -0.6517782717220172, -0.5511899467235817, -0.17535172900989998, 0.19484385718487524, -0.18765593393334246, -0.4499097741519567, -0.4671473885926115, -0.24442941048375783, 0.18917587336742803, 0.6219576229869449, 0.6347707814683676, 0.6908110753321771, 0.814181712596253, 0.8706549955465595, 0.7743986892803021, 0.5971290192176831, 0.39976288845809926, 0.1997224928753237, 0.10004007050653947, 0.19937857777450219, 0.2972401457563422, 0.39184468253737315, 0.4747711084432506, 0.535263536415673, 0.5720378061585566, 0.5430500856547305, 0.3413887243317023, 0.15790728429870335, 0.12284030904554605, 0.23725166831964908, 0.18064704807028725, -0.14655912592871576, -0.3041581517295397, -0.17618197085150297, 0.2708786955759505, 0.1352549559763762, -0.2920405572984286, -0.5113422865368298, -0.5126970979019752, -0.3132899340659923, 0.08205722198118105, 0.544093518538001, 0.6549147567688648, 0.7637590653387574, 0.9452987445315517, 1.0419647059877772, 0.9128069526349856, 0.6905822106324543, 0.4557150201761261, 0.22567703377272708, 0.09088094965969151, 0.1803080382944428, 0.2661970651042076, 0.34308592681446215, 0.3990003159109852, 0.42344700176606287, 0.414798260254997, 0.36060809667850535, 0.22536736927845494, 0.09094283894815061, 0.08940507883515021, 0.2430036222448592, 0.46515779622119124, 0.2717248398173326, 0.08474693231832402, 0.13034326815016176, 0.2889112847516505, 0.020447737878612496, -0.2596922627751172, -0.41098403786056176, -0.40739666401564006, -0.24705684454373852, 0.06147972101071199, 0.4251797114183304, 0.6180056712860507, 0.8590617068600972, 1.1858016339029458, 1.3386737451303952, 1.0950694825600704, 0.7877285169765996, 0.5062036509851273, 0.24752816335203578, 0.0831786765352719, 0.16471067099623649, 0.24197803093925255, 0.30893203738527936, 0.3542241715716607, 0.3668011435501139, 0.3484426278805875, 0.29984771036291047, 0.20629421629790037, 0.11749846956737385, 0.10202904434682619, 0.11567722841803277, 0.0981473353473892, 0.04587378452025479, -0.018484090620025314, -0.06205141181778999, -0.02925440779582557, -0.07248056067319857, -0.10503025561572166, -0.1465645569807952, -0.14070327698869445, -0.03515799259323589, 0.1710376035818889, 0.41247219838533394, 0.6156444612223356, 0.9631687889047209, 1.5098981914052856, 1.7176225576313713, 1.2473384743578504, 0.8501025959840237, 0.5339877431965567, 0.2586622024985417, 0.07706104017633887, 0.15273869556767197, 0.22483765145740997, 0.28891094613582496, 0.33737459339533055, 0.3624072781403834, 0.367698809088518, 0.34088278766425734, 0.28285663442580367, 0.23534161745909646, 0.1864644646343135, 0.07908771835808799, -0.05985431558555199, -0.14493305406650922, -0.15517738949413, -0.15518724149018417, -0.09634402894491638, -0.013270860560190468, 0.14634549459634705, 0.2515928039671206, 0.27646154897743175, 0.30956260954947007, 0.408921151461551, 0.525859956831442, 0.6819579699288464, 0.9843892494362129, 1.4044115579139937, 1.547539924591095, 1.1785685914707602, 0.8220494942818932, 0.5214658745535277, 0.2535944469915104, 0.07226706261631444, 0.14376397700915833, 0.21339655184998776, 0.2793242160866615, 0.33886506901045776, 0.390194124621084, 0.4316023076195871, 0.43689936740220053, 0.42176806820172613, 0.4294476978767074, 0.3691835180888965, 0.19006697164805283, -0.00975245645365937, -0.11202896632514109, -0.10712587923312238, -0.057053725927819786, 0.017094594001136346, 0.11761262628837973, 0.3079076579273558, 0.5196536878249469, 0.6578882617088008, 0.6931498312480805, 0.7568207452463651, 0.7665851232285615, 0.8354260291398933, 1.017446133386084, 1.2058761890179368, 1.2296306451707706, 1.002509349489517, 0.7333999739915055, 0.4769364824809128, 0.23466380183338878, 0.06823147970387981, 0.13648137791674808, 0.20483992074528348, 0.27376450460369495, 0.3441139106446173, 0.4171638605710916, 0.4892984838280931, 0.5360459479596862, 0.5867987167787974, 0.6823130012522917, 0.6887597161685748, 0.4804254221982978, 0.2275286544937689, 0.10253115969973749, 0.12090459019601461, 0.22635021189026877, 0.2792530847994576, 0.2955112033890621, 0.31243300519769596, 0.3875106841702371, 0.5625850704668447, 0.8066556349518137, 1.1034956212301648, 1.103381371201064, 1.051569350289597, 1.0731044132691323, 1.074937099333028, 1.0075089086173419, 0.8384096653533706, 0.6318200556952012, 0.41911786790899624, 0.2084540259236139, 0.06427998207294451, 0.1292174731488265, 0.19583054726140622, 0.26574066748287717, 0.3412127364268318, 0.424357855921544, 0.5136571450075794, 0.5994448055514924, 0.7242460209438548, 0.9315450357908425, 1.133411997545862, 1.0165558261204883, 0.6418902167560103, 0.45969480760642184, 0.4724225887733646, 0.6587039938260559, 0.6834025638345499, 0.5446354031429627, 0.371477659230333, 0.3422438172208117, 0.4979870343116903, 0.8447553450018623, 1.2626071799537857, 1.370054016821718, 1.2009879327417288, 1.0718963003427924, 0.9701331565735706, 0.8543116765445511, 0.706137427935634, 0.5373757246183354, 0.3601204487541341, 0.18029569176663932, 0.059684364145557764, 0.12053674343890673, 0.18384410627167747, 0.2516334948076897, 0.3262780156161492, 0.41015182597860994, 0.5046102009361251, 0.6110865477444566, 0.7709945307275976, 1.0160254085338503, 1.2866988838155338, 1.405272973058386, 1.0247248344956656, 0.832414277479662, 0.8075393348846276, 1.049909517129257, 1.0687826263758502, 0.7754306558717716, 0.4875978742134196, 0.39530078412921915, 0.5049943422843731, 0.7834261674769045, 1.1257962056875848, 1.2361863936939215, 1.1072699212760382, 0.9654084256874532, 0.8458294946904472, 0.7250329258851158, 0.593871427095746, 0.4524592889204947, 0.30439393529869735, 0.1528727416144148, 0.05415148466131004, 0.10950648749791311, 0.1676922666533345, 0.23043679167315054, 0.29997705320687107, 0.3788159881147691, 0.46964888580897135, 0.5768048382813077, 0.7239608713432147, 0.9194191026946393, 1.1038458075143054, 1.1787878369380749, 1.07996007817201, 0.9758686608992332, 0.9060911721002464, 1.0062565684710718, 1.0346871197096466, 0.8234338655324535, 0.5752528678011055, 0.46955844226593496, 0.5232864381045366, 0.6886579147821034, 0.8806928835816885, 0.9537024837744564, 0.8967116849390955, 0.8044004021320368, 0.7064027584013929, 0.602808337564273, 0.4922089819571615, 0.3749776220411486, 0.2526229799772346, 0.12706246551983869, 0.04733039249638189, 0.09597790714247237, 0.14711511191618523, 0.20249794893474005, 0.26388008100261157, 0.3334454601146216, 0.41357012933192905, 0.5073661690089205, 0.6224737963114712, 0.7541007250396965, 0.8648968316196677, 0.9173592377338127, 0.911018128686839, 0.8765771205546373, 0.8215803415323957, 0.8220953896856744, 0.8192211464358833, 0.7209831582758021, 0.5745317423814192, 0.4935640089653014, 0.5072184441856434, 0.5859069518187996, 0.6784986753949087, 0.719700857034855, 0.6955373270225748, 0.6394542415491484, 0.5677003832460116, 0.4863077883110239, 0.3976316862412824, 0.3032083151517695, 0.20448699957313257, 0.10292151947497608, 0.0394465945950848, 0.07988798152404258, 0.12262402840077576, 0.16872938462783962, 0.21973010127300496, 0.27705737628209076, 0.342137991346077, 0.41618520520485625, 0.49965723483493985, 0.5853284364464268, 0.6552902525891536, 0.6953110922677453, 0.707779220185141, 0.6994887252615236, 0.6699699018399063, 0.6471492386622483, 0.626270146671058, 0.5743638535667911, 0.49850517721175835, 0.44858982517009116, 0.44525575934701805, 0.47701641544088563, 0.5176722671478664, 0.5372919233968293, 0.5245870012443935, 0.4886748383968323, 0.4378615422435544, 0.3770838685042031, 0.3092420278105454, 0.2361990426044537, 0.15946648038807398, 0.0803269591441693, 0.03046468166977248, 0.061805400635417326, 0.09477057150196022, 0.13039403246100442, 0.16947972859428842, 0.2130200611824311, 0.2615651093121662, 0.31519267673039203, 0.3724544620498219, 0.4280869125806694, 0.4736274932312199, 0.5026066070886248, 0.5155893032187026, 0.5145761008955987, 0.4997259310147496, 0.48029979012916607, 0.45888779831315923, 0.4269241674296321, 0.3870332689049201, 0.35843541886455477, 0.3515207635035542, 0.3624006044767092, 0.37850547466675305, 0.3857284792093478, 0.3768308260211087, 0.3531664720351077, 0.3183139626315572, 0.27533681795421994, 0.22642235817231074, 0.17328863636731237, 0.11710513578961376, 0.0590303229898825, 0.02076512394618923, 0.042066784080013436, 0.06453416516155064, 0.08866090263441392, 0.11509762042284158, 0.1441832878505849, 0.17620810155643177, 0.2107748420064092, 0.24651886344766583, 0.280389895053228, 0.30826477620421305, 0.32702708890658, 0.3363952273956389, 0.33702228299846665, 0.329588055008474, 0.31745492634968764, 0.3024937264599277, 0.28334301948699897, 0.26222398972265826, 0.24654075295014583, 0.24076675677894596, 0.24347548329996793, 0.24895245741602762, 0.2505070244200441, 0.24410151973890967, 0.2292839778433024, 0.20733543163166204, 0.17985751975699213, 0.14826455694800453, 0.11358717992761645, 0.07687028874430095, 0.03874011791189597, 0.010511335228925566, 0.021303681052311372, 0.03264840575759059, 0.04486085360255328, 0.058119813592612105, 0.07270813015419891, 0.08854513395310641, 0.10545816903235636, 0.12263831483830037, 0.13872753158417855, 0.15202016939629107, 0.1612139034266324, 0.16602091495024737, 0.1666291518826411, 0.16349833614277565, 0.1578115638287125, 0.15042022249142406, 0.1414490283636462, 0.1321356275499248, 0.12509721409007865, 0.12196715223523023, 0.12221887632929745, 0.12363390321928676, 0.12351221208559347, 0.12007931298296207, 0.11285256162977407, 0.10221044298107435, 0.08881265837368814, 0.07327184862092255, 0.05624062218844433, 0.03803004624117399, 0.01922168060261921, -0.43221718804212866, 1.1662852096845917, 0.006921166996030833, 0.013846346829326494, 0.02068594482838604, 0.027457184609668984, 0.03404188237288687, 0.04039211417292192, 0.04637971080552565, 0.051872772296081636, 0.05677890807041303, 0.0609937501018707, 0.06446116053343903, 0.06722736087464397, 0.06933759608594835, 0.07084166439060606, 0.07173101792753846, 0.07198023490959486, 0.07152608857876759, 0.07034315216042161, 0.06842257622674291, 0.06586319447525014, 0.06257909560613598, 0.05879677266257943, 0.05440618805335854, 0.04971654926867228, 0.04457252865844632, 0.03930940498289701, 0.033797562338670775, 0.02825101895003419, 0.022623954681380298, 0.016967846964361866, 0.011330066337992054, 0.0056489104143004265, 0.013903872621995102, 0.027742023517862195, 0.04152102811288208, 0.05510153079548635, 0.06839538303984809, 0.08120363520923679, 0.09329474109872951, 0.10442617163357705, 0.11431658523586995, 0.12279206661875659, 0.12973164700969975, 0.135188183686552, 0.13937770186010826, 0.14237430833776593, 0.14421017413156498, 0.14475555404404877, 0.1438827682271491, 0.1414927570546807, 0.13762911588030577, 0.13240158380004763, 0.125862835523311, 0.11811964661989865, 0.10939618192959878, 0.09973786908342969, 0.08953501349259488, 0.0787640350781361, 0.06778995062388563, 0.05657974786759113, 0.045305603764188684, 0.033994418727493654, 0.022648982301491788, 0.011338307874374412, 0.020905608108186244, 0.041802910509590334, 0.06257270191413578, 0.08314622555331298, 0.10332963347709492, 0.12283408722622281, 0.1413201651356499, 0.15832117570891907, 0.1734237571320601, 0.1862555538716348, 0.19660538064549413, 0.20461499993402196, 0.2107390929876575, 0.21519775446163888, 0.21810530561911282, 0.21910312106467447, 0.2178462682336231, 0.21420625412339483, 0.20828796857300938, 0.2003757965022888, 0.19043535835340683, 0.17865095953702928, 0.16530357386480923, 0.1506476653781512, 0.13497349283994278, 0.11871699879820806, 0.10199845783996464, 0.08511186636315736, 0.06810055652464354, 0.05106058050879576, 0.03403577356376244, 0.017003273717873014, 0.028015335405782684, 0.05599761648346323, 0.0839406964176073, 0.11171086067326357, 0.13906738658315376, 0.16568650790743997, 0.190990442285543, 0.21432900039762376, 0.2349755856712783, 0.25226863642853725, 0.26586367016619544, 0.27612657197832363, 0.2838319649472719, 0.2895371735988827, 0.29362297754318134, 0.29544602715890994, 0.29392169722984407, 0.28895558490885215, 0.28093235349566664, 0.2703422959327408, 0.25695127129185374, 0.2409303996231067, 0.222719575643031, 0.20265364303357336, 0.18129003807106667, 0.15915605844610645, 0.13662146939119574, 0.11384785827463542, 0.09103178416618272, 0.06821236392067921, 0.045439179406443306, 0.022707594681458807, 0.03514789595365393, 0.070352354347282, 0.10560869079208231, 0.1408200478124072, 0.17578642277543513, 0.21002697526231195, 0.24284738115797128, 0.2732587768884306, 0.30005761360818783, 0.32183579598636497, 0.338125323522484, 0.34994621490866684, 0.35840518710124486, 0.3645493034494974, 0.3695243360841658, 0.3727025773759517, 0.37140144058810926, 0.3652752227033414, 0.3556216058735654, 0.3428102127775956, 0.3261292895339066, 0.3055090017608413, 0.2819637900227786, 0.2560492011425935, 0.2285132117011114, 0.2002478003263416, 0.17159890978817485, 0.1428400388136439, 0.11407253613697316, 0.08543038541214952, 0.056863193147702856, 0.02841811874322851, 0.04229740557816008, 0.08475475170775007, 0.12745049556323704, 0.17041434111166656, 0.21342914203516877, 0.2559995656697767, 0.2971701509654384, 0.33566980241120453, 0.3695904886222615, 0.39553425192117153, 0.4131167920651358, 0.4248189969802315, 0.43238084549322253, 0.4377019885560567, 0.44199961512400926, 0.44557260390579984, 0.4452925123026637, 0.4397973713600756, 0.43083948276987805, 0.4174771249580869, 0.39827394336011085, 0.37249874194529464, 0.34294425345872653, 0.31073504087409165, 0.27659676208182365, 0.24190288005152627, 0.20693650266772848, 0.17198268598537841, 0.13721862970791707, 0.10262869139761946, 0.06831141331684334, 0.034089647732665054, 0.04936438802701279, 0.09900857754497353, 0.1492345264236737, 0.2001394374577938, 0.2516788593874894, 0.3033119769729105, 0.3535469440398478, 0.400807808721272, 0.4428081200293826, 0.47208745731144075, 0.48814288124340194, 0.4969306063714952, 0.500777216974637, 0.503150605949244, 0.5051443320314737, 0.5051775546514286, 0.5055289182644755, 0.5051888834679553, 0.5021660977308098, 0.491276758545865, 0.47177298683439406, 0.4409123057314402, 0.4048727982850694, 0.36622635944075516, 0.3252766096860747, 0.2840086312304479, 0.2424828298054343, 0.20118883086806835, 0.16028052873383797, 0.11981868119527722, 0.07963293791189222, 0.039791048459524504, 0.056177014840379, 0.11286734670338901, 0.170476623871781, 0.229391743702106, 0.28970582388318, 0.3508291728930569, 0.4099360747936208, 0.46433666763294146, 0.5135664318300038, 0.544770468593596, 0.5571107519783021, 0.5604310055061227, 0.5578526459675083, 0.5557902791953444, 0.5557558238536754, 0.5523776197737857, 0.5505325976030221, 0.5564428988580689, 0.5631642646666519, 0.5569653333951532, 0.540605123468096, 0.5073968086196615, 0.4668884232741059, 0.4220560913962372, 0.3741898996851217, 0.32625852427373664, 0.2779731114211913, 0.23018729756803444, 0.18314541208338575, 0.13673935959111605, 0.09091336552454567, 0.045326799289881696, 0.06259749051490315, 0.12588780404975614, 0.19055984714674337, 0.25721913652227857, 0.3261715241173748, 0.39646588907672553, 0.46274332449653277, 0.5184113170461229, 0.5692107519345193, 0.601692701603361, 0.6124808145683553, 0.6112462530012072, 0.6032192448438698, 0.599388070648395, 0.5924756042787611, 0.5852641531378843, 0.5833997847863283, 0.5909005136908544, 0.6030607931739144, 0.6034393411442058, 0.5946522515580901, 0.5670679446541428, 0.5287483618535587, 0.4778361510823357, 0.4222579364726618, 0.36765630414278655, 0.312767628481058, 0.25856792814299034, 0.20552385193363515, 0.1533928753459267, 0.10186350144150712, 0.05086817034345315, 0.06839832423866747, 0.13766929325902025, 0.2086981705549996, 0.28233080722043646, 0.3592423887290417, 0.43773143423178196, 0.5084651737048905, 0.5586062839581103, 0.6043842742113938, 0.6372665382800404, 0.6506088513116827, 0.6484974362399383, 0.6380448810435339, 0.6293228889006072, 0.6152657077763348, 0.603421098775449, 0.600705441201881, 0.6079839672601198, 0.6212425565136119, 0.6272906047496257, 0.6297679981720425, 0.617460754490871, 0.5852325923673768, 0.5285188636363752, 0.46620950139357914, 0.4061247159868139, 0.3457121703240424, 0.2858123738757245, 0.22719959422827196, 0.16954134951482167, 0.11262846778957787, 0.056155820987129144, 0.07337906880599288, 0.14779916643898228, 0.22419673515847588, 0.3033200493818878, 0.3859485706892275, 0.47071987185003084, 0.5430818297849069, 0.5856946943541518, 0.6245441288683006, 0.6565331246218497, 0.6735965346528847, 0.6741293651997413, 0.6642190096000695, 0.648075790725685, 0.623315955943344, 0.6062904194836362, 0.6014463941102669, 0.6087658909705356, 0.6231159390992537, 0.6338489800962085, 0.6440421708174764, 0.6448286219849384, 0.6189075963128998, 0.5640657850160857, 0.5015914357675898, 0.43936829963547996, 0.3757869594346148, 0.31156316932667255, 0.24796324214853221, 0.18511419606705096, 0.12295752207170488, 0.06135360041480477, 0.07743068077200539, 0.15596299708654598, 0.2366071110454303, 0.3197742374535058, 0.404650498158567, 0.48945401533813176, 0.5607032380593706, 0.6009869320563487, 0.63657329948161, 0.6665313590225868, 0.6859654429431183, 0.6910544663826512, 0.6842845943342564, 0.6555690660222327, 0.6080222135678784, 0.5908387880578515, 0.5821488145312611, 0.5925624842955036, 0.6106327607950073, 0.6265269497399455, 0.6411994026986014, 0.6472159935021812, 0.6274656969720817, 0.5838442967661547, 0.5286897715097141, 0.467692766781496, 0.4032538876292161, 0.33594973650171517, 0.26784953383167254, 0.2000775219848455, 0.13293669846047218, 0.0663292507285156, 0.08043808508386509, 0.16199703448985406, 0.2456820038998405, 0.331840493351191, 0.41873349924352693, 0.501568085078237, 0.5695746866002557, 0.6100115595571428, 0.6426115090522506, 0.6706380821676676, 0.6910184493784787, 0.701384689414583, 0.7008063935441983, 0.6426034830740227, 0.5520103395201044, 0.5596028112285089, 0.5387486577006009, 0.5617750960930021, 0.584394879368825, 0.6088894503579882, 0.6299184554990163, 0.6415538418089229, 0.6299402128777802, 0.5993445372454798, 0.5529083963944477, 0.4942665336102934, 0.4296040653924223, 0.3595684044808517, 0.2871097555329161, 0.21454041858499573, 0.14255826972274863, 0.07111696307072848, 0.08241761013841235, 0.16587945579601865, 0.25122704292747366, 0.33860122724301944, 0.4256554757569343, 0.5055467124650512, 0.568965816404463, 0.6120975474685424, 0.64411752080149, 0.6699563279425627, 0.6879792704106934, 0.7002058899867357, 0.7059870700236209, 0.6581051091702657, 0.602052458253227, 0.5676609578055863, 0.5342468506054278, 0.5223595663064771, 0.5417000542390811, 0.5839836322325036, 0.6166464871905615, 0.6380919443399999, 0.6369471176857324, 0.6178016651372192, 0.5781594153874358, 0.5215533316093726, 0.45584741744476676, 0.3827144796103373, 0.305779904430629, 0.22844495170787688, 0.1517544529267179, 0.07571205605335823, 0.08343304867999246, 0.1678034430426234, 0.25383469879747533, 0.3412854365659149, 0.42735934561739347, 0.505011043957555, 0.5675659743963632, 0.6136615685567298, 0.6463822032624257, 0.6677854039235456, 0.6735313987694838, 0.6587872330848764, 0.6716034688974581, 0.6491849705303598, 0.609478311557176, 0.5648443791112526, 0.5123644750382539, 0.4578947173294113, 0.46707887090456407, 0.5534275444027026, 0.6066908350833411, 0.6412716417704877, 0.6504283832132777, 0.6392562112235624, 0.6041452257218525, 0.5488486967755378, 0.481295952259791, 0.4046997895761485, 0.3234268615471498, 0.24153734029380083, 0.16039482178945, 0.07998107934672355, 0.08360885283835914, 0.1681030283888413, 0.25437123012442636, 0.34254250283499443, 0.4296951070340857, 0.5081018661237663, 0.5714244796785846, 0.6204662508374569, 0.6543181095186557, 0.6727516899650302, 0.6640252504164148, 0.5964939597023665, 0.6519482738164033, 0.647875074537672, 0.6160132545061086, 0.5669158666192312, 0.4972113937798737, 0.39235505919638325, 0.34319660756925746, 0.5242148497409167, 0.6035034537592989, 0.6501978095525148, 0.6670023734603726, 0.6604380580946327, 0.6275569506908589, 0.5726103251035654, 0.5033602268979867, 0.42474070498286554, 0.34001613002249914, 0.25378322027513117, 0.1683610792700831, 0.08391756276870604, 0.08295550026557655, 0.1668358326217838, 0.252578478089164, 0.34129294872864596, 0.43100325017918883, 0.5140526836666001, 0.5820579732456136, 0.6345034384144095, 0.6686091669562827, 0.6909756058501341, 0.7012796332647463, 0.6957544285504197, 0.6861012244675265, 0.6692519800392777, 0.6367333518063433, 0.5885425313261762, 0.5225604731818497, 0.43475043318121076, 0.4665574019033097, 0.554875087456936, 0.6164444253968672, 0.6603662973034253, 0.6845538200192837, 0.679100147609597, 0.6449718961634985, 0.5896307873502324, 0.5205248385254488, 0.4420159842120193, 0.35495465940858534, 0.2648779432914715, 0.1754812191091806, 0.08737004846399916, 0.08139012799113575, 0.1636850785721974, 0.24779794739450847, 0.3347153413193727, 0.42283150651633744, 0.5061560190156292, 0.578785711918, 0.64052885134005, 0.6768614659652387, 0.7039583931351965, 0.7228230274705295, 0.7323015644447739, 0.71962893511349, 0.7006802513285134, 0.6692238275625704, 0.6268530125798754, 0.5762483512877494, 0.5326950289884109, 0.5550221974086456, 0.5966257832960999, 0.6365961958008298, 0.6702794742469387, 0.6938353351183502, 0.6949017189133525, 0.6558319026690044, 0.6021864892288203, 0.5356610426039641, 0.45653767064835715, 0.367409422852985, 0.2741345317999425, 0.18133947765075586, 0.09016491757755993, 0.07892650510792866, 0.15867172219791612, 0.2400434026465956, 0.3234013113013304, 0.40697601507681486, 0.48683997291590936, 0.5600813647353798, 0.6241129630639985, 0.6703974537861014, 0.704380971814122, 0.7312421731308463, 0.7517201601938579, 0.7548053658958322, 0.7359289938864447, 0.7057525231209271, 0.6682341202686413, 0.6236287408698182, 0.6079496901270084, 0.615903833822229, 0.6348499320082671, 0.657542826222083, 0.678739208950499, 0.6942042379259563, 0.6942994817684807, 0.6610429245288395, 0.6134525765341081, 0.5511337668080696, 0.4716194740118045, 0.37827787990327477, 0.28120262078099734, 0.18545404327560505, 0.09203534517745825, 0.0757044132691363, 0.1521012788766063, 0.2298487684026329, 0.30899899934545627, 0.3882001316415715, 0.46527375946502597, 0.5376893532472886, 0.6026165705929872, 0.654436931854697, 0.6952264433286288, 0.7320711664666043, 0.7616623977362785, 0.7743617738578291, 0.7607118711115746, 0.7341828002800216, 0.7011981904851551, 0.6635908519661587, 0.6578642818496739, 0.6592619859888188, 0.6665568912700098, 0.6770860621292627, 0.6867920668404504, 0.6918378677712037, 0.6853873141997788, 0.6575872912888165, 0.6216559573485618, 0.5706989778076148, 0.4909290059443632, 0.3883897602553135, 0.28557867354828265, 0.18720573526747228, 0.09262240211961105, 0.07186719050431853, 0.14431300569322308, 0.21783991699710123, 0.2925064563582845, 0.36753152726830507, 0.44158326262051334, 0.5132326629663276, 0.5796329469978755, 0.635232688349194, 0.6814466310628251, 0.7214066546050946, 0.7486009692242673, 0.7564445987040989, 0.7510779626282333, 0.7357452010923298, 0.7150787996368828, 0.6987152695039417, 0.6901638449663899, 0.6883512034527114, 0.6903526300810751, 0.693475194989587, 0.6945682834867499, 0.6897351549010702, 0.6743662146800674, 0.6463463530858241, 0.6199929543093067, 0.5907725681298315, 0.5150153215943734, 0.39394356713035805, 0.2847099489923909, 0.1852289509288199, 0.09134916004130274, 0.06755285441364456, 0.13558983368217684, 0.2045529643663067, 0.2746020716144277, 0.34544798959303635, 0.4165417451404828, 0.48765261906942586, 0.5550732595336856, 0.6139870663410384, 0.6646597875404514, 0.7043709378032635, 0.7280822116281709, 0.7352491689098335, 0.7331995249414117, 0.7272001978373933, 0.7171077482585255, 0.7101248736367421, 0.7042227599617417, 0.7020352682912581, 0.7032353996753605, 0.7037455920368736, 0.698433397026792, 0.6858813732525587, 0.6600300249906553, 0.6248494187454015, 0.5921955418895828, 0.5573701049489369, 0.4894570118407436, 0.3777020510823075, 0.2731571817618601, 0.17771879376110744, 0.08763749489191128, 0.06282927792490522, 0.1261225366675488, 0.19027499601165354, 0.2556101042684383, 0.32225767369846636, 0.39033828869632103, 0.45990522224768204, 0.5274663487694761, 0.5901718174754458, 0.6464613182197017, 0.6856735341386192, 0.7069436338486069, 0.7141546168560681, 0.7157032491644921, 0.7148916324715529, 0.7118650519066337, 0.7076855604722246, 0.701945754409567, 0.6984400706626801, 0.6974048233269613, 0.6990934027039514, 0.6895887687505406, 0.6744330547323009, 0.6397688020167603, 0.5942830173434372, 0.549490880635731, 0.499683861247651, 0.43323366043229417, 0.3429526862327023, 0.2517256345707426, 0.16496691573799824, 0.08164828836597159, 0.05774989115660398, 0.11594359351691147, 0.17500118254757352, 0.23536203090084068, 0.29739776091016035, 0.36157056758179845, 0.4281769002689945, 0.4951154089587554, 0.5625208514321937, 0.6260579717197703, 0.6670777980970366, 0.6870669605790363, 0.6925102232910721, 0.6960944347161214, 0.6993301017404283, 0.7018594002573728, 0.6967714965516633, 0.6873267705134973, 0.6752831203754291, 0.6651238046214286, 0.658958014196013, 0.6499536923320598, 0.6412055048943617, 0.6066178169947202, 0.5540788236597793, 0.5004834852781178, 0.4427361642553983, 0.3784612190192704, 0.3032963965795799, 0.225491704039398, 0.14895889200823423, 0.07400945218071465, 0.052325765744317555, 0.10504576194953116, 0.15864111208584, 0.21354608979281184, 0.2702431774490288, 0.3292655129983918, 0.39118966380413883, 0.4557429701508442, 0.5255923803775943, 0.5959486808481342, 0.644693846508094, 0.6686699265951859, 0.666187151774226, 0.670581391882681, 0.6775361013024278, 0.6879149747824442, 0.6789622223542664, 0.6610261961651461, 0.6382410568612168, 0.6202559003187375, 0.6071934409190408, 0.5957507100746278, 0.5805516178682298, 0.5533937640710002, 0.5009081109367841, 0.44472322501491796, 0.38795618336023924, 0.32845187348854754, 0.26427778614910746, 0.19796969500093056, 0.1315390229103988, 0.06559709636847914, 0.046529628064431276, 0.09347130144118673, 0.1411696467769769, 0.19008877349162615, 0.2406802247943961, 0.2934305597084296, 0.3489598357644098, 0.4077051592103372, 0.47262409170407427, 0.5396764130508045, 0.5910915340152959, 0.6253723040819382, 0.6206989019075585, 0.629751958353833, 0.639912546342801, 0.6600696003997693, 0.648287330208987, 0.6168362596402421, 0.5856657086726731, 0.5623726501338923, 0.5448819133502064, 0.5281191360461929, 0.5079654778241753, 0.4784001197246019, 0.4338218796494107, 0.3842361404865573, 0.3340589518228541, 0.2817597885860133, 0.2270041948229966, 0.17071366755574158, 0.11383994631940009, 0.0568925328999051, 0.040455078884628064, 0.08122189282238784, 0.12266880577565618, 0.1651705967363289, 0.20902906128996732, 0.25470331374191846, 0.3025703496684303, 0.3528127089608351, 0.40666871765593476, 0.46089429734053455, 0.5048402890069325, 0.53480099016797, 0.549076528440304, 0.562783526585757, 0.5722567433716478, 0.5851753523354126, 0.5761782576634571, 0.5457270018392615, 0.5154813065076332, 0.4918390157946704, 0.4724435127131234, 0.4524798737349031, 0.4298081935847882, 0.4011500279083974, 0.36455892303014253, 0.3240532621309141, 0.28165396548376437, 0.23738665728388633, 0.19140872845889798, 0.1442202795063157, 0.09638700170965259, 0.04824194180387903, 0.03407614982510175, 0.06843154420060368, 0.103332629693372, 0.13900937498069513, 0.17580459786439503, 0.21388179477012043, 0.25343171716804025, 0.29431658771610064, 0.33636593743539256, 0.37727277895014527, 0.411998246210251, 0.4384143490426501, 0.45737286062368465, 0.47175734554592264, 0.479686610937139, 0.48392630913728796, 0.4763571014991531, 0.45611565003683674, 0.4328419672286532, 0.412588095380022, 0.39412454757537274, 0.37454849340818147, 0.35289938498772416, 0.3278403110312485, 0.29822297352910265, 0.26571154816938497, 0.2311247272584099, 0.19486959382712868, 0.15722652204413481, 0.11863006950896068, 0.07936564624037983, 0.03975683223241332, 0.027498611614624476, 0.05520482997376417, 0.08329952934501646, 0.11201921932660167, 0.1414585549914405, 0.17178300891894183, 0.20294217266483533, 0.23466204321487585, 0.266372292643466, 0.29651020904764963, 0.32288032809136813, 0.34430761640238666, 0.3608288941142503, 0.3728008232845574, 0.37907843769731275, 0.38016083789441574, 0.37435076499862635, 0.36157503116335366, 0.3455200828662917, 0.3297270393798827, 0.31402376247862307, 0.2972274130822919, 0.27884394317730515, 0.2583031835176627, 0.23504353371216505, 0.2096050617881324, 0.18245911063835257, 0.15390579274698582, 0.12429141321948417, 0.09382519270281145, 0.06282135512718498, 0.03150027979309531, 0.020752750073137823, 0.04164361613304058, 0.0628278190450647, 0.08439809258341155, 0.10646111208135473, 0.1290614552439932, 0.15203460487875922, 0.17519862626522592, 0.19794396353539845, 0.21934624504177427, 0.23832809080414827, 0.25410378386089283, 0.2664549717117313, 0.27522796214469375, 0.2798717798402331, 0.2803220910034394, 0.2764063278466921, 0.2683693930375647, 0.2577331394159582, 0.24628509101017723, 0.23426579531548608, 0.22130759780040432, 0.2071563361631038, 0.19155537635353634, 0.17427973167198962, 0.15547718286380893, 0.13539012348466414, 0.11428370931960763, 0.09231159077343186, 0.06972651142870435, 0.04672659912907541, 0.023403324688209208, 0.013889796519651316, 0.027874802780323196, 0.04202954288939101, 0.05642046169961692, 0.07112392852170059, 0.08604802096669197, 0.1012264907271484, 0.11632060349994643, 0.13103699903536872, 0.1448499441111623, 0.15710610076104492, 0.1674106391177941, 0.17549528882702203, 0.18118403512618017, 0.18421901455927744, 0.18453722713166854, 0.18219503786404154, 0.17741244860632308, 0.17090868999162598, 0.16349552326816486, 0.1554493615757727, 0.14671893303883876, 0.13718307355486317, 0.12672082783159652, 0.11525704315368684, 0.1028324972563769, 0.0895824463538746, 0.07562394289152138, 0.061108317036895475, 0.04619026998351278, 0.030921712842369796, 0.015541748301454682, 0.0069639092774657725, 0.013966695306390952, 0.021051473527677, 0.028267107766059656, 0.03556684814219508, 0.04305529428684929, 0.05052668966530866, 0.058006983755855675, 0.06526815005710361, 0.07195839708002964, 0.07808506562106789, 0.08307471253882112, 0.08710643884843106, 0.0898861040903098, 0.0913863683694347, 0.09156927681311826, 0.09047751954890496, 0.0882357838896132, 0.08513738757618823, 0.08150230986175627, 0.07748561792737424, 0.0731044598030194, 0.06831696556002692, 0.06307556349263478, 0.05735481896293523, 0.0511761896966034, 0.04458289619206259, 0.037641861220681964, 0.030436939390999437, 0.022974970661050993, 0.015434954833711562, 0.007701707271502912, -0.42478155935201506, 0.6240335593779779, 0.7093766844444883, 0.00011217666479613763, -9.92269714039306e-5, 3.0749131700826155e-5, 1.806937436818999e-5, -1.7479544348233196e-5, -8.364626067120217e-5, -7.11340587720664e-5, -0.00017429772646157838, -7.936977693062631e-5, 0.00010799904277675074, -0.00024201495098317936, -7.846912004495515e-5, -3.445697696316658e-5, -9.552453855013701e-5, -0.0003892415565550707, -9.015397658069469e-5, 0.00035609762613132944, -0.0002867082231337381, -0.0009761450379837746, 0.0007759988661415791, -0.0004186365861757949, -0.00031902263407199724, 0.0007130048228595461, 0.0004561322404099283, -0.00011094960967127124, -4.936322207854477e-5, 0.0006431777593718531, -4.341390549088536e-5, -0.0003552805713190263, 0.0006942444700920825, -0.00014469320925343578, -0.0006055951190230769, 0.0008449146614069716, -0.000810389999719758, 0.000251381888485478, 0.0005260774340993197, -0.0004305085803544831, 0.001244700240541763, -0.0010185753104852576, 0.0005545654056094871, 0.0011767666529232646, -0.0002444349750902891, 0.003020482322813813, 0.0020877091108796268, 0.00021077027766896008, 0.0013092973244542973, 0.0034222870439730066, -0.0028780682390845743, -0.0005603440769263344, 0.0015737738498672379, -0.003065864970140254, -0.0012236449890791702, 0.00031494006568162083, -0.001578875933869672, -0.0003600593847635559, -0.0013228389442764747, -0.001264731494292254, 0.0001762145204864967, -0.001389895886763136, -0.00022417242377127227, 0.0008492839824180709, -0.0009489618264645666, 0.00017785829636080222, 0.0007937875191833122, 0.00038699126025164055, 0.0007258894155869822, 0.00029404762948606557, 0.000594190800969783, 0.0005061696150789372, 0.0005742741387285351, 0.0004465131725049675, 0.0004958510037462266, 0.001014172515956392, -0.0007895678632181099, 0.0005125226807029858, -0.00021039587513758788, -0.00012123857436846529, 0.0002784841992816699, -0.000488659416965307, 4.075856979946276e-5, 0.0003937150265636826, -0.0003830389928676252, 0.00010682940500469232, -1.1860109782386827e-5, -9.270856954099608e-6, -1.1549801867331684e-5, -0.0001568273511334581, 5.610144967199939e-5, -4.17166391082398e-5, -0.0002774892461205894, 3.7509902453175986e-5, -4.9181107730981595e-5, -4.8694610453140706e-5, 0.0001025818552723185, -8.64844961053027e-6, -3.712815527778596e-5, -1.287777048265281e-6, -7.511647570216664e-5, 6.928855912760297e-5, -0.0006169533503247702, 0.0005434406837088862, -8.367823657684646e-5, -3.9270701309324885e-5, -0.0005212030217773854, -0.00015393988531099806, 4.674131453613934e-5, -0.0003593715630450977, -2.5238839119199484e-5, -0.00017157393242581031, -0.00033585700690493307, -0.0003114446506530253, -0.0003019750938477551, 0.0001375300091975644, -0.0008881796779136795, -0.0002467323969293471, 0.0005697765872560306, -0.0003992288725304977, -0.00027146725314958556, 0.0007470968667078548, 9.983695707870712e-5, -0.00022120033213653272, 9.099028028365789e-5, 0.0017351779532807446, -0.00024495521801312994, -0.0016396144902811334, 0.0024881814528437385, -0.00027859942851561707, -0.002517264296592084, 0.003350271004920833, -0.0010659227045166691, -0.003195782653135044, 0.0016979402663268729, 3.954512299298917e-5, 0.0025050354815751314, -0.000962195704561237, 0.0010783653996344082, 0.003079722156072592, 0.001491752179216347, 0.0010996058643287252, 0.002055433541438227, 0.003175016904253005, -0.00025001087371316345, 0.0037253890032865537, 0.0018162198699097779, -0.0019459942508920568, 0.004140165758321548, -0.0017392594015701213, -0.003723073383106981, 0.003355511304388457, -0.004098827637920014, -0.00188848684936808, -0.002927382369101155, -0.003023784586893512, 0.0001388375709251609, -0.002540362169473594, -0.0014690412738390531, 0.0012390101056831868, -0.0020709366076280523, -0.000801800872438358, 0.0013634822104146129, 0.0005975533045601946, 8.595966691778901e-5, 0.0020763498129261087, 0.0015402939706006436, 0.00020916823697639643, 0.0013856206837760154, 4.13563043918925e-6, 0.00017796108772108555, 0.0006309104158065482, -0.00028574417198242233, 0.00026859851404284637, 0.000198153560097603, 0.0001067729323079335, 0.0006634952962414315, -0.00030818868009022007, 0.0005751984344126557, 0.0003365891364825756, -0.0001405345523035918, 0.0007655761009642949, -0.0002279958045351676, -0.00032264455405090343, 1.5894185569639808e-5, -0.0003634985488867295, -1.6108766243671092e-6, -7.45387586060692e-5, -0.0005596031507622084, -7.198309378443049e-5, -7.104223656517664e-5, -9.387958239147908e-5, 3.7182942758300026e-5, -0.00018087341579866523, 1.181749307345993e-5, 7.67696085542807e-5, 1.942803890122735e-5, -1.0171466965595213e-5, 0.0001959663942755375, 4.974584269046593e-6, 0.0001304424094106838, 0.0002929266823195522, -1.267581629109497e-5, -0.00010512719685872406, -5.5992130899969875e-6, -0.00029110249674317763, -7.691906086934186e-5, -0.0002806329954617207, -0.0004881853296397227, -0.00041866833732392966, -0.0005237313364331731, -0.00020611303634043225, -0.0006060998565901449, -0.0013474707591862904, 0.000668967842332234, -0.0012740560743947273, -0.0013844934225275243, 0.0016376690520664506, -0.0005480597756805866, -0.0015417999685329489, 0.0010343610972598036, 0.004132013662845278, -0.00019433493727155876, -0.0030560555963167328, 0.006869176311625884, 0.00026233285722685867, -0.0048572193559213725, 0.0037916764415159513, 0.0006197776353718063, -0.004115081282938493, -0.00040935484254941935, 0.0014779286060987425, 0.0053442485632255, -0.0034465697214091464, 0.001746120612877938, 0.006046266175512357, 0.0027115944777700365, 0.0008579186422931675, 0.003096522928577895, 0.006084188209969, -0.0009299734049050971, 0.0033108609579561156, 0.005953850612986376, -0.003563863482719762, 0.005841989743522108, 0.0018651851932493368, -0.004702222095019535, 0.00519362291502762, -0.0016148895753909033, -0.0057716822545560605, -0.0017593199492092076, -0.004526907387695112, -0.0010296288492096304, -0.005309335367934643, -0.002033860416242311, 0.0004320614787843305, -0.004680594802719465, -0.0014415031802242884, 0.0024416777897188126, 0.0006001572535280325, -0.0034268219178286135, 0.0017316966024700164, 0.0007468918183398726, -0.0017818281906766082, 0.002306913617129967, -0.0005924312871785337, -0.0013255190720329836, 0.0018323740335228242, -0.0009681609366543925, 0.0008242541858354435, 0.00040461219229506696, 0.00012482222523039425, 0.0009524408243044265, -9.847939418251977e-5, 0.0005248159375944854, 0.0003164512784967741, -0.0004521531742241765, 0.0006129087423163233, 0.00024441922605609876, -0.0011954139594116337, -0.0006485299745064867, -0.00035426973241946106, 6.94462536180663e-5, -0.00026651455012431186, 2.5015002417615272e-5, -4.030410248622521e-5, -0.0004803600908878763, 5.1093725578433484e-5, -5.2609927094456574e-5, -0.00016902676198888688, 0.00016836392087269634, 0.0007345194516237593, -5.432735813678635e-5, -0.0004758760628387823, 0.0003497331945283481, 3.924215325985245e-5, 6.442637689765357e-5, 0.000370500183118343, 6.062107040676904e-5, -0.00017691809606195722, 0.00015198851835822135, -0.00034344827710784806, -0.0006153557164338718, -0.0010022916943383262, -0.0005707925864721616, -0.0011316417596287064, -0.002800997962021801, -0.0015940386243241812, -0.001839626427839133, -0.0031620641866191013, -0.0003596088982313183, -0.0014874557595997069, -0.002081101772858081, 0.00046381788500592623, 0.00022577751006966237, -0.001370486753996174, -0.0012763093467863887, 0.0038986917203467477, 0.0007666057596772304, -0.00445621847697341, 0.00498268049907102, 0.00153285486518453, -0.00716545071092517, 0.0024075991697654034, 0.002311565930482796, -0.006683501729951258, -0.00505065734578903, 0.0024398341756029502, 0.00510253435230094, -0.008977549818293603, 0.002111096216753628, 0.010999604668559313, 0.0015603766329213135, 0.0009000320155813896, 0.006201615784828898, 0.01108233212074764, -0.001400435293551732, 0.003985425006362817, 0.012364554634116742, -0.0048477273726468826, 0.007309101263279787, 0.009210536837450723, -0.0071738135002436315, 0.008104564594481369, 0.0030522356531546813, -0.010590607674956615, 0.002122428085145947, -0.0013013846212116924, -0.005891195639254991, -0.007048908329717867, -0.0011286857105764479, -0.004862008635682336, -0.006809928512203825, -0.0009394131373824333, -0.0011161024496728008, 0.002236071739946809, -0.007899979355708476, 0.0017305244149718232, 0.000773340588656107, -0.00551489040460925, 0.0023735662455341626, -0.0010441638316805416, -0.0028926891529452202, 0.0021340466303758337, -0.0012558825257282652, 3.2509034012404814e-5, 0.0014152056798168364, 0.0003476260256117564, 0.0019088719499879847, 0.0002580189207740866, 0.0015427889492972383, 0.0013986967177381294, -3.211176382456019e-5, 0.0008038860016758649, 8.151852089981695e-5, 8.811242735053072e-5, 0.00022733485357786214, -0.0001528850485451226, 0.00019279994229903406, -0.0003110581702041414, 0.0001390378576828033, -0.00037346332190088885, -0.00042128495826735697, 0.0002585161854554265, -9.835433711740426e-5, -0.00022554876176398786, 0.0001322901254144768, 0.0004368592638347322, -0.0002159813367574704, 7.864344416303807e-5, 0.00043490609740757483, -0.00013392800093253384, 7.774661592968471e-5, 0.0005958792219124799, 7.621747959750886e-5, -0.0003588140667245129, 0.0004076804614621579, 0.00021528632133908896, -0.0008686824961072908, -0.0017165254432195578, 0.0008514443739021184, -0.0026726982061956975, -0.0043279448580413864, 0.00046618645109263834, -0.0016903301436664547, -0.00857770138266668, -0.0004079367030599643, 0.0010932781232545197, -0.005817698786838377, -0.0027150073207575297, 0.004403196777197988, -0.0011424482709396888, -0.0056671204070675996, 0.006938454565559433, 0.0025169204537053413, -0.008708762477343363, 0.005772247627696832, 0.00367555550398721, -0.011368223165104425, -0.000666056447254839, 0.0029567117513057475, -0.007523288669345815, -0.010601783780845928, 0.001960014452862257, 0.0037090647946665437, -0.014799631692752004, 0.0017137813861516507, 0.01642307771570583, -0.0038560251063366907, 0.0012914816477455182, 0.012506125722908809, 0.015501406112991585, -0.0008715370973018195, 0.004347102613439011, 0.021668518252646044, -0.0048322640810962965, 0.006769969793676139, 0.018980361690230554, -0.009771477415152751, 0.009833034222594916, 0.01213731949405954, -0.013222463798213907, 0.005179894994656039, 0.005528524658656189, -0.011740628085985774, -0.00046879645510688507, 0.005647563870401651, -0.009465571450967608, 0.002962542126692248, 0.005508712748070657, -0.005120885241557159, 0.0065175188740251196, -0.004316984126007546, 0.0007177919106104997, 0.0008402368970510872, -0.01098306597640152, 0.002701694777754915, -0.0021784685490950826, -0.006653711250256358, 0.0031477241016045605, -0.003295851926666622, -0.001349001341732552, 0.000978966227727242, -1.5583524099770933e-5, 0.00281607444664075, 0.0001856005045115284, 0.0015119682661831025, 0.001294707722362241, 0.0003493412727237302, 0.0011887702424638344, -5.317554722600681e-5, 0.0008403764909749159, 0.0003096223665656167, -0.0003525654484336035, 0.00028307227346943497, -0.00040266096817764564, 0.0002087331193868251, 0.00012112312627832625, 6.664325026515438e-5, 0.000207027518100163, 7.362971372971488e-5, -0.00021587823195279028, 0.0002360749441189178, 0.0005074185591180748, -0.0003795480319978435, -0.0001526169981230063, 0.0006370021818684939, -0.0007392122056667848, -3.9071355966945914e-5, 0.0006794550049156313, -0.00023019982072548472, -0.000317041356113746, 0.0013430289405966763, 0.00039059309080104844, -0.001735462859361049, -0.00046231761376514674, 0.0018442368962390556, -0.00228112512579844, -0.004082738439210713, 0.0033209590358301943, -0.0017214143523346325, -0.007850893533159773, 0.0019691705405185302, 0.002606277620011648, -0.006470787611160863, -0.0032780520423864225, 0.008686837857440462, -0.0011016771896570977, -0.008830691043739845, 0.010704689055259684, 0.003547462414924759, -0.013961951907702807, 0.007643202404788269, 0.005194873022199328, -0.016965396775063705, -0.004481167592785383, 0.00252027219536405, -0.009749303206122122, -0.017189552625602397, 3.821605951219226e-6, 0.0034446308585722855, -0.02108149860370763, -0.00012698172485939513, 0.02086693191827488, -0.013619818143938268, 0.004824291848277904, 0.025653281467743518, 0.012279688243749325, 0.0033728895094241977, 0.004752414392970327, 0.031550796594227576, -0.0033614139374210394, 0.0032379689222256395, 0.03029670269525383, -0.012246440027825801, 0.004973845584495897, 0.023093953445194968, -0.019533091129869454, 0.0025439305903094483, 0.013071528162813857, -0.015413803238213557, 0.004419789632568215, 0.011681023499135133, -0.0102301633591731, 0.008425176579633799, 0.009756148614041248, -0.007803083178630117, 0.010791001091433427, 0.0002218985310202945, -0.0004300532225452748, 0.0009654949547112198, -0.015166712061593767, 0.0019370093837513514, -0.003470975299395539, -0.00966937303267681, 0.0011527884258744545, -0.00660592261081279, -0.0029404842055978497, -0.0021333419110344232, 0.00028727663885906606, 0.005257668120399781, -0.000608458817565362, 0.0030270337212985614, 0.0019004714551485184, 0.0013012965997515576, 0.0015387417125851755, -0.0009682854150648262, 0.0009850764288799243, 0.0002247094558345933, -0.0005088124636505592, 0.0007128323157045711, -1.0429530580769409e-6, -3.624340332200516e-5, 0.0003313820227946806, -5.4268212381203786e-5, 0.00038888134798292946, 0.00010595380342028789, -7.946495380118244e-5, 0.0005596509721708449, 0.0005217947464505711, -0.000645643474205106, -0.00026962941117158806, 0.00037362465407805346, -0.0004986161115175388, -6.680066151585078e-5, 0.00274561347695436, -0.0018764102839473186, -0.000994106461089378, 0.0026500398896782493, -0.0006084617103323375, -0.003156541828558392, -0.00022938882211295943, 0.0029900326518546255, -0.004703317640389988, -0.004278344864050055, 0.0059102733531955255, -0.003752120581932858, -0.009086840781964202, 0.0063365213794499015, 0.0019053338730529931, -0.008747961534032954, -0.0015513744033730248, 0.013131202898086653, -0.002084204379378016, -0.010990360419342177, 0.01641586321461035, 0.003054196136823837, -0.019008913121417264, 0.01152383428490595, 0.004754741138806756, -0.023181569168043238, -0.006282828556361398, 0.0005145879122032891, -0.012686491094450001, -0.02340955225128157, -0.004215763284204397, 0.00213227418501899, -0.029778724427609444, -0.0028104174688029903, 0.02368793628037183, -0.022992744606345168, 0.020169463003715953, 0.02561336903150342, -0.01744841370325305, 0.030545144234934388, 0.008541446741686512, 0.018066061413898542, -0.001446851160538004, -0.0021049020725092717, 0.03692402343696542, -0.015142126640170376, -0.0116231572026063, 0.02555096597209971, -0.025477047795610528, -0.015308517578373445, 0.013520759510562887, -0.02451710469942544, 0.005397339302458867, 0.017475321147416338, -0.013858484836790868, 0.01548281198169432, 0.01530021437400866, -0.009617160321504272, 0.016368357367796176, 0.006268927748217012, -3.513951648052477e-5, 0.0013338495499734544, -0.015967038048298278, 0.001957301013882094, -0.006948518838529021, -0.010982955288362501, -0.007103747343623005, -0.007735341503634863, -0.0007017657044137362, -0.005826296267731796, 0.003395700772342833, 0.004045112494741929, -0.002142273007045989, 0.004340685972083022, 0.00021300871472389296, 0.0015203034994330019, 0.001600574937840354, -0.0020647074272837147, 0.0018017298586901023, 0.00042505732253528256, -0.0013962478777747819, 0.0008415263559042745, 0.00010632644889093163, -0.00018661413839078254, 0.000588744036250596, 0.00033203810401190884, 0.0003692233212395169, -1.596072972579756e-5, 0.0001597073141013834, 0.0003891618393564373, 0.0005768635425446547, -0.00027336765855224675, -0.00010600971865181141, 0.0009317718494075507, -0.0006563260916402214, -0.0001145156002163569, 0.0031006460671937804, -0.00251187403892942, -0.0009696991770616627, 0.0030882887808226594, -0.003026206625642062, -0.0038015481359457708, -0.0003501814343034679, 0.0015257331100353322, -0.011229361227130792, -0.005179602509021102, 0.007223232791172426, -0.007620837481726532, -0.011693753239516366, 0.011421126591892346, -0.002122382666927394, -0.013526034561909553, 0.0027672246080917506, 0.017338991826712627, -0.003968613883188843, -0.012829427171124865, 0.023371123113844466, 0.0016622788525837407, -0.023533081549776954, 0.016289709283174334, 0.0031592606230122053, -0.029454799992126933, -0.0064576562671939475, -0.0014967015568527109, -0.015492318099245318, -0.02777020754787506, -0.01017274997496256, -0.0009079149380608722, -0.034305006822733485, 0.01717120553883403, 0.011138419497648011, 0.03462307541034364, 0.030277367274806885, -0.013318398222906617, -0.023256602803075458, 0.022817956723057795, 0.0028455524139968124, -0.03133860620634573, -0.005746013318300835, 0.014011316656351833, 0.02633243609857542, -0.015952878942136726, -0.02838610643180135, 0.012223591669814057, -0.020297682309059158, -0.033914000002890424, 0.0026313319457710975, -0.03898412872936835, -0.006093522195371836, 0.014398711693768135, -0.02050900624075563, 0.02494364140353954, 0.017618440119255858, -0.011029603541954616, 0.02493832911927606, 0.010267578773775644, 0.013250050789341185, -0.011008917899816494, -0.01589024867669282, 0.007337035198996171, -0.014939150145365447, -0.005832557085192835, -0.009847557780258805, 0.002929634090725423, 0.00834623927127842, -0.006417193634907105, 0.006769707660022624, 0.0025421002788326916, -0.0032805319440434417, 0.005606846594713889, -0.0012151527880403697, 0.0011577326622416665, 0.0030199155452337732, -0.004282938041484572, 0.0026328795460372773, 9.789828641556397e-8, -0.0024569485770480383, 0.001299380390557599, -0.00013397314978223527, -0.00021213637694921046, 0.00023635891441575686, 0.00016063695170833844, 0.000690294231351504, -0.00015700306092450504, 0.00017710572702789686, 0.0002881262813703126, 0.0008201129217572701, 0.00017424026043004457, -2.594635266855185e-5, 0.0011595390642304359, -0.00019155265704571043, -0.00011694112291525593, 0.0028692575597708456, -0.0019880114191235376, -0.0008292757942109219, 0.0027198910244467783, -0.004532126867559037, -0.0032512256999096155, -0.0007968099066993027, -0.004268530584670553, -0.01048963072609593, -0.007129121874445823, 0.004062627572162345, -0.014187239568809658, -0.014398596437965927, 0.013487038125872746, -0.010327399847531107, -0.019918576490316076, 0.010255735850190205, 0.017012030024073917, -0.005356907481463481, -0.013878097044131886, 0.0289925354451346, 0.0011714879011041333, -0.0284391271543033, 0.019395959464188553, 0.003108953276192527, -0.03512990619117269, -0.0081896122440368, 1.231032403709798e-6, -0.016998308630018066, -0.03182536195261833, -0.01301669466402539, 0.0011874635185642986, -0.036033642751609585, 0.004944390188794461, -0.01873515942908352, 0.037829996481513105, 0.017806588445292662, -0.03894889381685508, 0.0015876259209222782, 0.009445750956901913, -0.0002970217099437845, -0.037965849366011196, -0.015211300099860752, 0.013532621378796718, -0.027549392218491266, -0.01538072188530931, -0.03296111842145289, 0.0027320761941091102, -0.014521233194733486, -0.03856712114757535, -0.0017546334669519925, -0.037892130170948744, -0.021897651823718164, -0.001754748302464783, -0.031229570735841723, 0.031515224356349215, 0.001754246748364996, -0.013005754166255223, 0.03265198402503394, -0.014056467940263778, 0.021258041882884365, -0.021636193686936714, -0.011053051544923835, 0.01567706659000367, -0.01741109286284739, 0.004899519485297614, -0.005177167175201373, 0.010428605711854633, 0.013635843857220036, -0.0068197360887665755, 0.010064918892290775, 0.0014351947454269947, -0.004569385275486476, 0.006915356738417748, -0.0026117008900272158, -0.0021198055385118694, 0.002488412152959845, -0.008447439326220373, 0.001297013337551192, -0.003647890224243296, -0.0020606889336019472, 0.0006163680995494849, -0.0028203638025421345, 0.000722040479499273, -0.0006592828720841506, -0.0002994881302940212, 0.0009618964470298857, -0.0004978363489890029, 0.00039421397920900487, 0.0005071496903894843, 0.0008129403890951933, 0.0007185554470882682, -3.811764479810522e-5, 0.0035129595688382967, 0.0017523177128446399, -0.000654144876227951, 0.005030058045027579, -0.0004873982684144551, -0.001660875520472145, 0.004129568305926786, -0.0063110676250808075, -0.0035127173742779782, -0.0005769836656554498, -0.011495964749359733, -0.008426335863114575, -0.008678802747983322, -0.008558150987963207, -0.018887474896125137, -0.017392975945848578, 0.007446042386675212, -0.022807131369148432, -0.02607307737447, 0.02001141369649609, 0.006497773786466045, -0.002902707388271618, -0.015169202984327324, 0.031817247299702374, 0.004415126336571117, -0.03413568863828539, 0.01652175821212197, 0.006558704316104198, -0.03696689481144123, -0.01336877885646075, 0.005979004986453275, -0.016578492517525266, -0.036210636304851294, 0.0027746917024946433, 0.040937238439798296, -0.012431395575031768, 0.00318248549469288, -0.01392759281586255, 0.04120855166534313, 0.0034086262424118403, -0.03905266546938485, 0.016176324404789656, -0.005265725349118099, -0.008146811642329015, -0.038497211727859956, -0.017062146044075303, 0.020696611436425618, -0.021624566606533894, -0.014285505377144753, -0.03407801427291671, 0.003222251172334478, -0.011346299670221566, -0.03863171251600723, 0.0025209561408544028, -0.03547461979456693, -0.02360239177708395, -0.004916113938668514, -0.031164481219416645, 0.021770841039685046, -0.021559401498142502, -0.008537241620858001, 0.009342558932819798, -0.04417216399821901, 0.023243772938140738, -0.02649013466794064, -0.02192501526706037, 0.02352647233964708, -0.02011859629300953, 0.007710660280268118, 0.0016875912553417022, 0.014381539675014165, 0.017348298628790775, -0.0073395359763776015, 0.014025845711533287, -0.00017584872208959343, -0.006157821927191371, 0.007741980838775333, -0.005149911649433888, -0.004667115739590083, -0.0006621029480138086, -0.0065629093114488776, -0.0006819537570028994, -0.004096248215586213, -0.0003628741816377583, -0.0004692533770176403, -0.0027094361422480714, 0.0015298598925281193, -0.001161365673781317, -0.0010085865203574825, 0.0020266035853263886, -0.00034604232883734854, 0.0007157979079336312, 0.00031298231221513114, 0.0010903836833116554, 0.0014870938439247308, -0.0003134395301096181, 0.0037957958735634592, 0.0028769479103039246, -0.0011680006220054367, 0.005624331473073932, 0.0030977029940112777, -0.001983747509849258, 0.009277393923290056, -0.002301391378212345, -0.0034126089272398675, 0.0033864794603279454, -0.017587252742244406, -0.0034671662252447584, -0.0063608047771070925, -0.027330921519472817, -0.010685946480259011, -0.019397651423459256, -0.016153544441371664, -0.029521176138998358, -0.020501567808214844, 0.02535164108454406, -0.017405172670964388, 0.014281625266014241, -0.01921906254165471, 0.02541296215298787, 0.012663286899860456, -0.03724020926451927, 0.0033206479764510918, 0.010789661031618021, -0.03426465487158789, -0.019089463963518644, 0.012203901585875873, -0.017091978182793715, -0.04067106419124173, 0.0071117236298551, 0.04602349492628065, -0.0038604513085030508, -0.0003672113757176928, -0.003993547253939488, 0.05118634217079869, -0.004781753690359617, -0.0449952889960981, 0.02567705520678331, -0.0208460090058074, -0.022859498396236435, -0.023736386200272203, -0.019686481101834543, 0.031642553368165266, -0.01797401464328027, -0.013478200233978844, -0.03815205770207403, 0.007501266464439735, -0.009438599296827893, -0.03774442205076179, 0.013680187380567685, -0.037610715297357426, -0.01795389455581912, 0.005952877307829385, -0.027862278087640018, 0.015110182582624225, -0.025329847802025157, -0.008729236100926154, 0.0033687453746123436, -0.045946249036222804, 0.01932565077590611, -0.023785673192478807, -0.03230414107265876, 0.027380879508380848, -0.02101216051367996, 0.008385669426337714, 0.007239640695547379, 0.012617424109400432, 0.019974199887436702, -0.006896269506793811, 0.017474393167911603, -0.0026127482225883373, -0.006431894491259607, 0.007558011537370224, -0.009718959344169536, -0.0041070039153801845, -0.002985751472900608, -0.008156649757187367, -0.0008498763180321046, -0.005554352483699047, -0.0009256151785405515, -8.98837417695994e-5, -0.003445986921541583, 0.001375601922776478, -0.0003983232076083193, -0.0028189507720964404, 0.002609124316014467, -0.00024412965056966232, 0.0009279483551025201, 0.00024556129133069003, 0.0019708535160439175, 0.0015336203266735928, -0.0013694016469106242, 0.004022196550418915, 0.0027548909212651985, -0.0018488479386216446, 0.006409048124201293, 0.004688434086540297, -0.0026732255586840556, 0.010276262781327077, 0.006763740347991356, -0.0025128568080018394, 0.018522997296536902, 0.0018770322547836129, 0.0075544882541644705, 0.0019215357196627856, -0.021799914873123463, 0.022881537918402143, -0.0162696555883825, -0.029260410988676478, 0.02558987975295563, -0.017250376634260878, 0.021464434991101764, 0.025313706477752305, 0.032433462355757725, -0.013801145964606963, -0.0036437373081630617, 0.017750052630002535, -0.02994845323587238, -0.012358627788164002, 0.012980932929262935, -0.033089988674767264, -0.02383417995694475, 0.015161732928762151, -0.025441774387322248, -0.047263259497310285, 0.03166969732867443, 0.08935314743804358, 0.021546120683504606, 0.017684083131563236, 0.047077550269349656, 0.08943600616807039, 0.10506587136716665, -0.02367171253897079, -0.07290597156061172, -0.05004203548353756, -0.08469133365074916, -0.017920887894058393, -0.04976026050034461, 0.016351399714102998, 0.04567722015079379, -0.04798696600154084, -0.010346547125724132, -0.03117449690714146, -0.0062711472082332305, -0.0355202122043046, 0.02878256065669058, -0.03229419134822283, -0.009882385568057348, 0.021979647784003787, -0.029842465294133588, 0.01440989300286954, -0.02394247804255528, -0.00941235961298517, 0.003399982372927464, -0.04383191101779745, 0.014258159458586352, -0.016198722986940656, -0.03485485547630954, 0.02508350478606589, -0.014776313820084387, 0.016205850555780856, 0.007151877267096867, 0.009767629462660247, 0.022427583211919688, -0.002756593211424255, 0.02007635236128259, -0.004207717851397886, -0.0019124574246527056, 0.006605340430117525, -0.014613754223061198, 0.00010109234864523485, -0.002090084738833084, -0.011270906705285747, 0.0014070795423991966, -0.005692715106340547, -0.004741595000668938, 0.0017468933196922508, -0.0038606226292675536, -0.0009587771064543502, 0.002216949442598363, -0.002851142937223718, -0.0009446960005439119, -0.0005712201734230797, 0.0005710738388219785, -0.0012877020453960465, 0.0016776705963551938, -0.0009213412066054687, -0.0015055960673087043, 0.004147281001985332, 0.00011399235705221129, -0.002228327682422874, 0.0069307012714338, 0.0029984063954537955, -0.0032675701116749644, 0.009282486267737845, 0.008735681463525954, -0.0034120361306986887, 0.010757707359213262, 0.01744529600572863, 0.0019236141324365662, 0.0030162925523713165, 0.020870333323749265, 0.022872899703755667, -0.010899242350182702, 0.009890672910591357, 0.03913037983021599, -0.006047930228770204, 0.006841347516101931, 0.04128355946432153, 0.03369368818219085, -0.012236851839618135, -0.006047769435274543, 0.018807954154942488, -0.023818711990634605, -0.021900581337981142, 0.012582466096828632, -0.03571382582777132, -0.029174003776848013, 0.015538467319884185, -0.06341644100042033, -0.0569614232853959, 0.09796934091437161, 0.11657342212327072, 0.08592579625301225, -0.07294327956229568, -0.08723194358094516, -0.14379128543305011, -0.17624776010844093, -0.03408606243699421, 0.05829246224265559, 0.07887082576859192, 0.07060657487549254, -0.0471921260614004, -0.09091574136207099, -0.07634982693134157, 0.09558503552726881, -0.03785616444285509, -0.01196719251570667, -0.08309226951830023, -0.01739266662327674, -0.04892374396078274, 0.03254854219167547, -0.020064742240257845, -0.0055413127097166445, 0.03694121871634376, -0.03178619960332716, 0.011832014107265603, -0.016677830738620992, -0.00808220732385184, 0.003972918151949107, -0.042023671621848294, 0.016328419622012345, -0.004510103367147515, -0.03812750694836941, 0.014086532151591825, 0.003558855879737825, 0.031549475869014854, 0.004030949854743796, 0.011963060306014869, 0.02403747858583394, 0.005679394091515508, 0.02190569727482886, -0.00011604669954875949, 0.006263623475226766, 0.00829154951707806, -0.01529732639830628, 0.005970263449625058, 0.0024678650625601715, -0.012951765355821624, 0.00483983857872464, 0.0002946929222467977, -0.008300582509017008, 0.0026799303656077963, 1.7474611240077507e-5, -0.004406376338410785, 0.0010223207911279966, -0.0002721113857641695, -0.002310603463316975, -0.0002984677161201699, -0.0011369214622942271, -0.0012062952487883957, 0.0014142233881818025, -0.0017053353445052035, -0.000977816983207805, 0.0029876244630320735, -0.0020021193212222906, -0.0012805113676649384, 0.006445932564938406, -0.0002820608096476101, -0.0034446458980848054, 0.009663899077888524, 0.007194880034727939, -0.006148797145740694, 0.008401206665747918, 0.018614955672207324, -0.004276322056214329, -0.0001589188748612059, 0.028458773220618818, 0.007638158566644641, -0.012167360899472384, 0.020281485341390067, 0.025360299964313052, -0.01108758296710229, 0.008844211833969055, 0.034045377591613336, 0.022061276902512257, -0.006280575468868485, 0.02349829045102455, 0.01858454096746212, -0.018214444243893815, -0.0310752262668726, 0.008194323367403564, -0.044047343380072775, -0.044352470386182806, 0.015567341136885916, -0.11563701755399929, -0.0031656099924267534, -0.06427475504216694, -0.07327848926350045, 0.18720507912010434, 0.13474211963088906, -0.07971442106728752, -0.1372700852717132, 0.06737705544188757, 0.027631605449291465, -0.024048442436880212, 0.058429131441343284, 0.031960484113072674, -0.0040629771667651205, 0.0755308759781415, 0.04863594718867305, 0.01996983182253459, 0.021614324950408808, 0.0942813115804973, -0.09444447176672707, 0.05040398344130144, -0.029206214399386952, -0.0002658700667502879, -0.00035005413235234217, 5.041363152556337e-5, 0.050577956475148886, -0.032184791720019826, -0.016780499663295527, 0.019807676652376788, -0.0010231139750104263, -2.6423335549373112e-5, -0.04704234009222254, 0.02661485078349058, 0.029352801436882195, -0.013085702273289772, 0.0043530927327822, 0.017293780250442804, 0.03271178350864419, 0.0017155932757068099, 0.01844857748541405, 0.025542929123175385, 0.00962846920588304, 0.02402950786127754, 0.006681843253515884, 0.013286546513674625, 0.013514232749038414, -0.010779049131522899, 0.010662854437754702, 0.008280422305185949, -0.009837309790552815, 0.006471232470081897, 0.006304891893905773, -0.00722557270065842, 0.0022321257182203367, 0.003432326679873077, -0.0060318134621790654, 4.94643089685654e-5, 2.427157875808962e-5, -0.0016896578316689867, -0.00029790188503709785, -0.0011179319342449192, -0.001796654759734859, 0.0027891642995650535, -0.0014744230532303443, -0.0014001630764991268, 0.0030340494950609827, -0.0034931502086966576, -0.0010140135178756556, 0.005747443395488282, -0.005095553701540028, -0.0036574054849720663, 0.009763625830941215, -0.0013905052889515769, -0.009949394533269216, 0.009738744421796609, 0.010953433031300362, -0.014909044231609839, -0.00016533397719956946, 0.02725860862524893, -0.009254648075798007, -0.013817948088182107, 0.02463848930595338, 0.013909540713719162, -0.010344025191568702, 0.01184402160505183, 0.030749886767279702, 0.009195272609033106, 0.01245044582345602, 0.03332498967471722, 0.01099005278993161, 0.012470799238295693, -0.03881970527859531, -0.011343818248439004, -0.031048953254673356, -0.055982283137837506, 0.24007128380046877, 0.04260922492540359, -0.021974263646113715, 0.12489489068829555, -0.053215978738219406, -0.027658263621047327, 0.05339453311429651, 0.013416375802077307, -0.04903164566869432, 0.026884818816121953, 0.025678392064819183, -0.022796102606078, 0.026934158868438432, 0.033085076704236924, -0.0014205125308825734, -0.001807478492032822, 0.045329757164786294, 0.05152050301977879, -0.020385289933095723, 0.03190505620983257, -0.09796396550349953, 0.06818805260009078, 0.04738336631155245, -0.031487449519376494, 0.019379152545307202, 0.025904445231085163, 0.04837601678039195, -0.003685185037909236, -0.051470204597761075, 0.0079698203041265, 0.010366804941820225, -0.021978024807816424, -0.044723609539827985, 0.031671927048038485, 0.03668652434960464, 0.008871176221383305, 0.0026314055318753925, 0.025952427011067015, 0.032105819533309994, 0.0004119506649062982, 0.02530711626082027, 0.024892137009142112, 0.008060987757566206, 0.028235331960259794, 0.011477900419245837, 0.01734589043941376, 0.020334884408714386, -0.0020582898488236525, 0.015122024583981097, 0.012900232108489897, -0.0013713734430260594, 0.008136492619471015, 0.01025419429773392, 0.0001910952222346998, 0.001506805160472452, 0.007733433057842445, -0.0029699672455664452, -0.0009573344476212197, 0.000916981992787706, -0.006166122025029457, -0.00022205177133413515, -0.0008299012151109196, -0.0019481350858738106, 7.981251172772226e-5, 0.00191684532742601, -0.0004034259057640306, -0.0010894159008000893, 0.006669546947995224, -0.001789140782365166, 0.001370089741581014, -0.007751619145348209, -0.001058602081245092, 0.00485007819864443, -0.013112755758429835, -0.0038043471612650287, 0.009744891268104095, -0.017223554571651454, -0.010716131196731232, 0.012259548209729076, -0.01578081325335905, -0.02269917767068727, 0.008827120105814885, 0.009618049838321605, -0.03433684591667474, 0.012577857994332205, 0.029686675788985026, 0.019582671326638237, 0.013472732537127984, 0.029791688258940068, 0.022933708504504907, 0.003350180344666414, 0.05200812325294378, 0.002247682801088593, -0.015953650175661974, -0.03847962030096892, 0.08444683259339825, -0.1491782894193996, 0.15190940926315885, -0.07607945219935765, 0.09029661830725541, -0.05632097291499109, -0.014500715981383982, 0.008604346059337123, 0.01816075579278527, -0.03940579598887954, 0.005019174683795399, 0.024362130782746492, -0.02658620251325547, 0.005735491298988287, 0.03362120874393045, -0.009503140619938889, -0.030271426202920514, 0.013823683615037217, 0.0638396253705046, -0.07670241761519145, 0.012685127074644096, 0.03343495020823256, 0.004918794721512322, -0.11612779368297979, -0.06414361170701524, 0.03764044240109359, 0.10299353298423157, 0.056901752278506565, -0.04130567358984521, 0.040008388673233045, -0.0006653051335784503, -0.009960960800234708, -0.041885543373149176, -0.05507505413459974, 0.053748387648703266, -0.0067584734608213915, -0.025497692080789048, 0.005812835920210904, 0.038698348821624345, 0.02991573764448432, -0.0002981158462522174, 0.03251275240993605, 0.023050876184271197, 0.0026827210311612744, 0.03224918853099513, 0.015202950533208037, 0.015064273158688362, 0.024339151341485163, 0.013171414178959796, 0.016062217114488717, 0.009160912347429622, 0.015670871387941227, 0.008221073924547058, 0.004348257210250171, 0.011798644826552159, 0.003269716746174415, 0.005017620719821034, 0.006378404505427304, -0.0001106764620216169, 0.005259104688689122, -0.001888533182127194, 0.0001540617345154659, 0.0006027632578876848, -0.0018390973929190522, -0.0008055004153172218, 0.0026171942719528485, -0.0006618589594434117, -0.0021937289357634748, 0.003999452868856196, -0.0004331382047754382, 0.00023929560207271755, -0.007707441201710081, 0.0034084977579770183, 0.0051397412101863, -0.012286387214900043, 0.0028097265250597633, 0.010143336809028992, -0.0197186744727318, 0.001879250695606862, 0.017271623854999158, -0.028453853981741023, -0.004328487560701246, 0.02867783102449159, -0.020607548218931158, -0.022897402065251815, 0.035297974093116656, 0.024686151962576626, -0.019863177116008345, 0.019429618100439458, 0.045923229353689254, 0.008125036676989564, -0.009711690936769777, 0.04925619271276796, 0.021830132612730747, 0.0824517484105647, -0.01619543388341417, 0.0627414223001167, 0.2238260339968045, -0.07567499589191304, 0.09422331538833424, 0.05313433460473567, -0.023993825981789424, -0.07551667004677269, -0.01357293070563864, 0.02090199918687203, -0.035936203685596795, -0.011691177206708104, 0.01879940253693709, -0.028792632528429733, -0.015575930939034666, 0.01802207504780828, -0.030790796984051412, -0.06113140293930419, -0.01587266805904851, 0.06126660860999221, 0.10898636672068324, 0.03354837622927381, 0.015536778095712746, 0.1604086481880874, 0.0012207812243033285, 0.11828038763635335, -0.02005675089371645, 0.07103526422879046, 0.033895819700464826, -0.056880627699454275, 0.01506720806350113, 0.0012852006438745284, -0.025125321950004453, -0.02952598725915903, -0.03962939240631568, 0.005948993551235754, -0.04917651916759144, -0.08695246187363852, 0.014308020016891753, 0.06269306740360564, -0.00013973833718911467, -0.0015013585993535659, 0.04329554161419665, 0.02074914907926443, -0.009197429364589468, 0.03209611291888999, 0.02001230690266506, -0.002243275675485607, 0.011574611322063914, 0.0339731948413448, 0.011691607110983243, -0.004989721471298243, 0.02431706481717071, 0.009646835644359066, -0.0018081027129273031, 0.014386604856576196, 0.005576075706121074, 0.001496156388299862, 0.007768388673035052, 0.0023979711337712784, 0.004044534376547356, 0.0024207711023020093, 0.0006582911075100041, 0.0024601436187732906, -0.001840992206705598, -0.0009287505981264685, 0.0016787131914600632, -0.0006642485282199477, -0.0014371603393663148, 0.003572212093707957, -0.0007763954053830195, 0.005950017921658592, 0.0023975433280133468, 0.004597385550656044, 0.008927289240248923, -0.005876007229529172, 0.006271122690144639, 0.01283031908641601, -0.012319089671787582, 0.009660629000186898, 0.01828050685917577, -0.022149537981528928, 0.013081419633836749, 0.032854005910958925, -0.02844976966761851, -0.008630874928712874, 0.029446687169938677, 0.020582524476403467, -0.036857631429963116, 0.004163006673186436, 0.05598325821598925, -0.011087666748607249, -0.04878814251715382, -0.00868212843965659, 0.022397098547767655, 0.026283594610594024, -0.07324820701104878, -0.005232743504877927, 0.10675147962330071, -0.033070919858898186, 0.017627212971212163, 0.0019050008946787712, -0.08228638530643068, 0.030400378489925738, -0.03839511368968044, 0.02784250638537133, -0.03688710403119882, -0.025675908712655855, 0.013983317205130267, -0.03522261579817697, -0.022939837541761023, -0.001657796385500437, -0.047139929712732336, 0.025535481845050903, -0.03469725950089616, -0.07643950616019096, 0.023277685100590636, 0.10539327765252918, -0.027069240031012066, -0.04174666645111468, 0.04110946236488308, -0.010078006214551473, -0.03522599744024587, 0.02270493275812539, 0.011349515906974864, -0.04033769773696842, -0.010259546658146245, 0.010149080540655582, -0.028178569588470093, -0.03343105936613875, -0.018344475618257586, -0.024439710253522245, -0.052288638983286055, -0.06915793965899013, -0.01488418281294217, -0.019584079329438148, -0.0686370020250387, -0.01862821691041226, 0.02619038150812971, 0.03857325960063823, -0.027179524017881464, 0.005229841226520946, 0.029859075584264285, -0.023636101621949585, -0.020486121171690536, 0.015193151855864602, 0.00932610674743095, -0.021026689916825898, 0.014654961831729095, 0.014537081811584479, -0.005804151142246797, 0.010352578467536684, 0.008387639444025478, 0.0001158512127162306, 0.00619116804020545, 0.0037633614682651894, 0.0023310915638451437, 0.00300609183145504, 0.001001222860620858, 0.0027362297765032018, 0.0002357483673929188, -0.001548311822995051, 0.0015615005179501686, -0.0010944755334097466, 4.976693856326415e-5, 0.0029061954521336295, -0.0011190399367798976, 0.005364938449701249, 0.003352231485181179, 0.0011156424334818021, 0.009412117680874127, 0.0025503364365862726, 0.005060720967045948, 0.01113241483249077, 0.0024790601106768856, 0.012330606881577076, 0.002462107629887597, 0.002519954205135521, 0.025861013849552448, -0.02516474995419726, -0.006736167938376042, 0.02353368943246845, -0.018682312966499692, -0.040739309898730265, 0.008135942552863413, -0.010839822353113341, -0.04011898914175247, 0.019900809520325278, -0.035613458263274146, -0.02928514332430995, 0.017586928803453934, -0.02570513157597025, -0.03276023894105853, -0.04188844904368926, -0.06190457588336894, 0.010006079126225151, -0.13987515162085568, -0.15766478108797427, 0.04074378451757675, -0.059250512054855264, -0.08551533961309803, 0.03745694292150961, -0.02626423740615683, -0.0506084509748139, 0.004304834347708207, -0.0534077855795772, 0.008952433107696264, -0.06656346904834097, -0.11565093305706536, 0.09614008350628714, -0.061905607475016416, -0.09260517095507123, -0.04103751447141024, 0.002592054649837756, -0.05281217751745251, -0.05128037795979786, -0.015556713484722647, -0.03447265543098885, -0.03627939296611699, -0.021068625376336733, 0.007121718341421649, -0.01691058353820034, -0.021347738073978256, 0.023060552109058243, -0.020634548618366905, -0.033603023730345315, 0.015066936365609436, -0.04197259549185601, -0.042558764928815905, -0.027076626785944642, -0.04198587437404102, -0.03245665944092878, -0.0407185679847889, -0.010635186967038768, -0.04112761604392183, 0.026941147508666472, 0.0008837224193472915, -0.017228718448647224, 0.04180509481242516, -0.023584486425204384, -0.029633734433317044, 0.006599468403771477, -0.0012278259903827223, -0.023891903837117475, -0.0203873188241491, 0.017974931120363406, -0.008312166541662348, -0.005282980949844129, 0.011901111781568772, -0.0010371750410224786, 0.0014397833872117696, 0.004739009804505587, 0.0004873573154609403, 0.002100923012002015, 0.0013700324934816622, 0.0014579538195156046, 0.0013075678576099652, -0.0022675143120347093, 0.0005431741046280786, -0.0017658894365107376, 0.0022989883242887565, 0.0024174431665148688, -0.0018343169317392566, 0.004520208686661472, 0.003362246940299619, -0.00030744326177744826, 0.006402984167066481, 0.00659660904762771, 0.0019173422305874884, 0.0032979908407571347, 0.01180706022532189, 0.0074148691622303795, -0.01139341167620793, 0.010801642120327911, 0.013262040652433194, -0.022410991815892786, -0.00947235234138771, 0.013599944357082392, -0.004970691522511684, -0.03076041887708703, 0.014313711929368582, 0.004718115746182664, -0.02795814555958126, 0.024490370232870345, -0.018817760891438207, -0.0014038546244975534, 0.03538032307455289, -0.01747698818975895, 0.03416739760663178, -0.04012402235565402, -0.039608023267921226, 0.06554226008914753, -0.07324176764475461, 0.03342629656695987, 0.08941559185340751, 0.07850601199495265, -0.10465837070089878, -0.06989242350172548, 0.1129057628046006, -0.08108366820387984, -0.05991462693602026, -0.06617145063727936, 0.06067638109494641, -0.1055254338175146, -0.1272505376994354, -0.02105194038842626, -0.07251759314508016, 0.09084856312582158, -0.05362718690513198, 0.004759891698534357, -0.0711406117525679, -0.037384561312960536, -0.05041788289410072, -0.04472409907951028, -0.008152025265338656, -0.0407490316870342, -0.0003549471873787393, 0.0026502500829145535, -0.017733767916460304, 0.03109070667600928, -0.003205254844539245, -0.011511230081435817, 0.03558178716718001, -0.03242106517874677, -0.021099139117747148, 0.019583820058574626, -0.04828592405745458, -0.022143820411076095, -0.004386230647767277, 0.00690382040719961, -0.014249293547075157, 0.04486807461128017, 0.026644161276946014, 0.004611804860665801, 0.03588139635738172, 0.007067847645427701, -0.0024605981733300487, 0.05077901922374946, -0.03396994280496866, -0.012424623361450476, -0.012008345655535243, -0.0031374879746154283, -0.008462773271940387, -0.020189182450430877, 0.006703322163545213, -0.005583202040192947, -0.007733822466520711, 0.0054978213528554115, -0.0030018226938076775, -0.0012685174392154048, 0.002549864874941494, -0.00117544201167441, 0.0008474658327077202, -0.001580748427779086, -0.0010837371084074425, -0.0006371516615228922, 0.0033068880955763064, 0.0026999463124883975, -0.0021807768373297344, 0.003599854545080124, 0.00414194772801387, -0.001497849082200624, 0.0026028418132880825, 0.007607399492243947, -0.0005079415760364042, -0.0031262433014600244, 0.011191127351924977, 0.002389026336465482, -0.014323740121676892, 0.005518531092358693, 0.006912783570302646, -0.00908959274758953, -0.018797614808806425, 0.0092826716628439, 0.007844112179606835, -0.023774946450858335, 0.013137438750242893, 0.013836024157050398, -0.013043488064624142, 0.02610350152185987, 0.0002971279874419948, 0.03337107793320072, 0.01964133743691746, -0.009100541494658382, 0.03523157728452419, -0.0319401225952844, -0.005947011062668363, 0.031166361460798025, -0.05280318071993923, -0.06989259482195972, 0.027692403607015217, 0.016435828614184095, -0.0362012406621305, -0.06307387014002641, 0.06679041480846536, -0.021289097597233686, -0.06582921795085128, -0.009241484995144813, -0.04783468294727395, 0.016780863324146945, -0.03286185504169769, -0.022570448970796974, 0.07755465361802315, 0.04542831745923827, -0.03881176010184203, 0.05954042235972476, 0.02155914536904403, -0.010611419658823297, -0.05597483684010395, -0.03856599643382261, 0.003743384464746071, -0.04531596998438829, -0.004132569403212636, 0.010276221930083724, -0.003859154633288899, 0.041316778184385415, 5.1038849816546325e-5, 1.330459760406379e-5, 0.038478854489201464, -0.021840111985695916, -0.0158090897278338, 0.0352564704194324, -0.0347869250332255, -0.018666487533763886, 0.012023681342716537, -0.0073257750619750185, 0.03996221928965317, -0.011890066468938776, 0.031122610322669747, 0.01598769043507641, 0.025304946525488935, 0.01700704062580241, 0.0017842177752249349, 0.05444990310163044, -0.021215852558266985, -0.0125829941528107, 0.03740806911868121, -0.02059744963190442, -0.01047125055678257, 0.0038060259663410707, -0.006240209184657397, -0.0063206864906211, -0.006163819912644895, 0.0008496623766009883, -0.004111049595948717, -0.004314113091430759, 0.002109593449241216, -0.002124608104773071, -0.0017311723011690068, -0.0007979257308133916, 0.00017072667530542451, 0.0003876076478056144, 0.0007139186818752209, 0.002370887968910306, -0.0013019442616542403, 0.0008259252612443314, 0.0040183051266800204, -0.0019115067821129034, -0.0012463219008843295, 0.005693713812223747, -0.001129487455475081, -0.006745163998290723, 0.007469201525137984, 0.0010232927828849872, -0.011005385751767977, -0.006542565572093059, 0.006196811537705529, 0.008552152440824674, -0.01731436362101456, 0.004559782956229715, 0.01762984293506795, -0.014991048650022572, 0.010485569882787866, 0.016360433185752494, 0.0033191730627490567, 0.026603154435064995, -0.0057860961673596315, 0.034927411987466635, 0.012490156482345718, -0.009434785035046698, 0.028941422321467705, -0.027771074359270873, -0.002459964633887784, 0.015327183892591753, -0.03972686992414668, -0.005408908720614794, 0.01514317678137937, -0.03994396456378266, -0.017386214411501063, -0.00745077289808311, 0.036786522531204735, 0.007868951398250395, -0.04623199345216491, -0.015297088973766894, -0.040946028231296554, -0.011743858193332861, -0.03305899842816779, -0.010969282091387223, 0.04687922585892518, 0.036289029358785994, 0.010930847295001763, 0.05120194608914346, 0.04474607820092326, 0.02358105446981844, -0.0475706504990419, -0.026094114321825547, 0.0382128198103425, 0.02374162983556916, -0.04817896961137085, -0.0034275498544592063, 0.035695884579083334, 0.038200927911137, -0.008650129414002346, 0.009161002453798922, 0.05054770793150052, -0.017120680860738414, -0.025168260898627344, 0.04058831118094468, -0.023113127850213376, -0.030014810504809433, 0.01879308297314618, 0.0016748823272673633, 0.017952709479673524, -0.03554963609322844, 0.03231701863866595, 0.020707625919119652, 0.005362866161138221, 0.012439820157536093, -0.008376892749848146, 0.04248697456927658, -0.007254257089030084, -0.014824887955404445, 0.03320581217738802, -0.01068948572392097, -0.00915507673038653, 0.013855255490186708, -0.007582935552966583, -0.004393613953488093, 0.0015042576742891926, -0.0018096488818350853, -0.0015690577587833953, -0.0040473125543988705, 0.001016628605341181, -8.461056420733651e-5, -0.0015647306551946805, -0.00036954180864091717, 0.00025239148566548843, 0.0001512502149144026, -0.0009132779939712174, 0.0013998765675635036, -0.0004913491839056575, -0.001770164409138312, 0.0028268915676030715, -0.0008291614549583158, -0.00418953255801056, 0.004041173251753638, 0.0006774521148375328, -0.007019153544233076, 0.0025096553198816233, 0.005041855629385739, 0.0068008420098484, -0.008466664340548668, 0.005929200479340421, 0.015253079566253786, -0.008278590979893845, 0.0019147063303464184, 0.021896294695257362, -0.0032857932144626325, 0.005538155819184025, 0.006318554259691997, 0.023202907440483294, 0.01952928063083982, -0.019480897691887555, 0.03002209498104409, 0.00716306926383521, -0.017660960387209722, 0.021704858037222205, -0.027288511303840725, 0.0002874770222181594, 0.005915166400651746, -0.037973661461543434, -0.004060874989331956, 0.013596567534878999, -0.03330512885349722, -0.008866943169439378, 0.009352880596629467, -0.03284765022057492, 0.00758518979837205, -0.023793113332104102, -0.032411895285373, 0.011932584289810163, -0.03372379814781082, -0.022224986280828543, -0.0010698241562846307, 0.031982574828607765, 0.027909146950120336, 0.027828478535802875, 0.044435812761362464, 0.020230597878838165, 0.05691973656137766, 0.004128640740507024, -0.0131617762699805, -0.018859100829264914, 0.07562266454934476, 0.016808386734446616, -0.03389075053994892, 0.07144904178837291, 0.02568140716138434, -0.06318368736124962, 0.04566744617347049, 0.06717448303231151, -0.0091534269620881, -0.038343347705554164, 0.03781476834702476, 0.0015236797791728122, -0.033166912016115054, 0.02636005760312978, 0.018530223719090844, 0.017345493883037376, -0.028558360427127463, 0.015136098334738363, 0.017608054077731604, -0.025585507920004056, 0.005635798201350607, -0.017016670179457672, 0.02498857591351842, -0.0016423116630360055, -0.013014778757158897, 0.02024978274771952, -0.003399175178663932, -0.007415323583278554, 0.011662709137042182, -0.003933025316615891, -0.003282424125665508, 0.004787582124312233, -0.002374204470583038, 0.0003830100824929491, -0.0017151117956729295, 0.00010869699379123347, 0.00026121101326371035, -0.0009484326002798674, -0.000816120883190395, 0.0003345803311826961, 0.0001214018019912727, -0.0010497750711700225, 0.0008563371075031863, 0.00027319635722049094, -0.002037326820057126, 0.0012661792339871884, 0.0009894512007668991, -0.0032022528189115523, 0.0014808626738141884, 0.0028492131689576918, -0.0023864980833733585, 0.0012807764027034587, 0.007823036328877271, 0.00841023998068427, -0.001808598353964663, 0.006074987072218836, 0.017206611380033623, -0.0013076592875880368, 0.001242722749917118, 0.01931600087200119, 0.007658973608826233, -0.0009046359328354356, -0.011788796449639613, 0.02505694505222661, 0.0007830335379998425, -0.03227070613652904, 0.022284769362283543, -0.0013260629521586263, -0.04004094146766619, 0.00491281746950386, -0.02270425809053199, 0.017055063754303403, -0.01658933619229, -0.03595432335203207, -0.005446247190436671, 0.025106857203393746, -0.022891544290515486, -0.013038092679437056, 0.016957869005901887, -0.02736346129615999, 0.012337663557801986, -0.014123327898952478, -0.039080555981878616, 0.03560434961110703, -0.029808919467011523, -0.013650788972552806, 0.04158289808111228, -0.019511754598064097, -0.015797261402945056, -0.005116230130375822, -0.004795836225135437, -0.048443402514608436, 0.003916802445598766, -0.033296790087009136, -0.02746750279872466, -0.026204675481539083, -0.006445486146527036, 0.025833062563228773, -0.02412665810911117, 0.03956573826962873, 0.00550370568601876, -0.006483924699657576, -0.000320827142692034, 0.05527051631076505, 0.0041670065123571055, -0.044137783019267074, 0.028621940196456183, 0.021575805052494557, -0.013718882418658379, 0.036466364991237996, 0.02541855692993206, 0.026374985763511695, -0.0016495181026923845, 0.001360441702772267, 0.014370251416703806, -0.02764892758574755, -0.005622945134229507, -0.022636532027795538, 0.0028587757727637627, -0.00045126425596518394, -0.011275845787220627, 0.011124297883624106, -0.00018084306060763862, -0.006160753236582457, 0.008156654812966908, -0.0008647665427183947, -0.0030834683615138057, 0.005333229845193992, -0.0029062014305757554, 0.0021115308550890863, 0.000844666544913431, -0.0001488858907565251, 0.0007108829978379524, -0.0005987219899159387, -0.0004711940176464402, -0.0005903552856187571, 3.6266879440677204e-5, 8.227709367487315e-6, -0.00045953143952406043, 0.0001932189401509959, -0.0012771763553836202, 0.0003076367346473785, 0.0015449585366568458, -0.00144171022388103, 0.0008379034828643561, 0.0020441812580455146, -0.001243777382059447, 0.001405936479374413, 0.004270182966249749, 0.005322394814105636, 0.0009546677514178724, 0.006153022332814486, 0.013943103423625683, 0.0006300011159109164, 0.002080629656016957, 0.010532354273620082, 0.012376178874423542, -0.005197895518084563, -0.016533622633480374, 0.017363674789472094, -0.007497664669165638, -0.03389326484963435, 0.01786180282688334, -0.009970274506858506, -0.05430057894941826, 0.002880177607347383, -0.016912762969069402, 0.0425106270102102, -0.03268754207977675, 0.030738221394081413, -0.0018220676365742741, 0.043063370068754346, 0.011677875599254458, -0.017791986191902753, 0.02478504889274104, -0.028028064586910657, 0.0321084764961233, 0.0013404369330988048, -0.026195180660283382, 0.04645816788973875, -0.006148309448072752, 0.021740336716392833, 0.030288921618654038, -0.0011247368917453166, 0.036302444501959096, -0.02248022644033502, -0.01620814817628652, -0.03531082779055162, -0.008555314339293744, -0.03018798557322347, -0.02188697750329452, 0.017127560841808477, -0.02679882425183302, 0.0052787825467679374, 0.030632271591540368, -0.01719311586365021, -0.003275864289894556, 0.010665683927634399, -0.012609125101729403, -0.0404802273895883, 0.037101852697364934, 0.014338389375874068, -0.022772466459510015, 0.018467091826299395, 0.017029734933003134, 0.033932123599387076, 0.016722302928082352, 0.024933460052433108, 0.013847784266159726, -0.0030875569504769623, 0.01621946896881511, -0.018203704793632803, -0.011764148374424578, -0.010927239545759542, -0.007240615496476136, -0.001800479502865765, -0.009361335056737594, 0.005223165025880964, 0.0008079541801513596, -0.005278962124608955, 0.005252809139101534, 0.001326224578954472, -0.003917682625637499, 0.005445407730914633, 0.00013955327274803482, 0.00017796980026728735, 0.00198048542894525, -0.00011711099695349135, 0.00031433845367401003, -0.0002366813810341008, -1.1745994556039863e-5, -0.0009832698970345093, 0.00010081060186577744, 0.00021358774820715495, -0.0006279536331491565, -4.606710911927872e-5, -0.0008857915793601168, 0.0001247830889556191, 0.0008844059861615782, -0.0017404241270364469, 0.0010408446887429656, 0.001707730735541166, -0.0013515170536600564, 0.0010157009061758553, 0.0026618375054129283, 0.002413518548833485, 3.3913136817595744e-5, 0.0051717912138581346, 0.00827926038282449, -0.0013923028271765057, 0.0036971255624894546, 0.006995388285301835, 0.01068980195270761, -0.003992555050122302, -0.013638604310374931, 0.012164076301003766, -0.007202585771377776, -0.023818440617930838, 0.017099939785737227, -0.01224480970268263, -0.027647313184960276, 0.02906212834310117, -0.02225468872449929, 0.04873927912954454, -0.007063278509305329, 0.026139656799258035, -0.01153910543444279, -0.025600752123565954, -0.03790187504523567, -0.018454508403946676, 0.01958491346750806, -0.03425450681315856, 0.01800432576211338, 0.04216715117602089, 0.001988695634182815, 0.02255426703988466, 0.018174859680411732, 0.04362259232709124, -0.00508156139414581, 0.013278376776928337, 0.055095229434045566, -0.036259244438128384, -0.015563230212763792, -0.013289913341521558, -0.011843639196242907, -0.02551230759262266, -0.015226829579755904, 0.01990776628799839, -0.01951613974360726, 0.001532340182366839, 0.02680046026767538, -0.010960889709315087, -0.0006271712107744153, 0.02369164827138509, -0.006635150621683827, -0.020174846231026177, -0.0070940124594820065, 0.02272111895923869, -0.025762322231171843, -0.0015193033994639444, 0.02982446015773675, 0.014800450749283173, 0.008301328312030044, 0.017690780465827467, 0.014681299648023782, -0.000644884792715606, 0.016219171017945226, 0.007410646665008582, -0.009899307420061652, -0.00624811789172736, -0.0017718333415980407, -0.003936726298464653, -0.0056969554957218985, 0.0018434028526455718, 0.00012965229341317525, -0.003452464913291659, 0.002536700618614963, 0.0016814841921077427, -0.0024406139809391744, 0.0026744106740071616, 0.0004580396159256522, -0.00020243340737414705, 0.0005421140934616536, 0.0004729931699037687, 0.00040180844921135586, 0.0004973028209403188, 0.00022062223304336864, -0.00039383785517029543, -7.247771948650506e-5, 0.00010397019460424453, -0.00043597967045379607, -0.0001633491945657991, -0.0016539368108570386, -7.185818775597743e-5, 2.1244206773480976e-5, -0.0016928301831706928, 0.0005826867155752153, 0.0007134138460330646, -0.001959360977665827, 0.00020006679601379017, 0.0023107160532755047, 0.0011016963279689464, -0.0018915561122803248, 0.0031817028694825123, 0.0041400064639392576, -0.003482394509511791, 0.0035163289532298097, 0.004738602206511972, -0.0019565784950475516, 0.008094978934702226, -0.009668561443093573, 0.009593707444551854, -0.003308316749297507, -0.012377935741959377, 0.014814336776406279, -0.008181397222602922, -0.005754131122542916, 0.024636202958152817, -0.01587114623452312, 0.03259146286983688, 0.010401798189281225, -0.015024677901609948, 0.000915560394531162, -0.0030512515251250602, -0.04059697499376729, -0.014587952533470143, 0.011244564988382688, -0.033890093964640544, -0.008834140329936957, 0.03802642092148069, -0.0031044347361940342, 0.0006300038183187831, 0.0235553799518911, 0.036183128278941164, -0.013332161072816913, 0.009507296534118683, 0.039547429291929684, -0.03141455423112758, -0.011418075936478787, 0.007680903142559915, -0.012554435039912317, -0.0207978289223707, -0.008331105654986355, 0.020823115218273288, -0.01087262693422386, 0.00045328985704378745, 0.021634914117903734, -0.0044216036939060035, 0.0005006900988098604, 0.020801808472902583, -0.0012617231703063265, -0.008111234673112632, -0.008514087686557691, 0.013916261916260369, -0.014519733062254169, -0.01029125237482504, 0.01581014167243096, -0.0012286452892565178, 0.003234182705840271, 0.011721892802143247, 0.009537715235543975, 0.0036157959882828494, -0.0037666096980114834, 0.010849032147483487, -0.004744931039155395, -0.00594952331817645, 0.0036177965316159006, -0.0037744009234778383, -0.0030347831053930997, 0.0016824183385066895, -0.0010984157339730377, -0.0018103158440825455, 0.0010319723352384227, 0.0005902299027732962, -0.0010301059151279592, 0.000708309459435429, 0.0006847045513522667, -0.0002813513559910586, 0.0002347490757598234, 0.0004675429408156638, 0.0003923392859155699, -0.00013043936812162765, 7.470987917784288e-5, -0.00011890377812039759, -0.00013424165240071633, -4.507421095594486e-5, -0.00011638382419835144, -0.00040345013280215607, -0.000519766351635186, 7.731897017687842e-5, -0.0001333524035543829, -0.0009651698249556131, 2.694573783647724e-5, 5.4279891316975955e-5, -0.0020184553174818058, -0.0014106755926498126, 0.0019099679020353221, 0.0010700917994641203, -0.0024335853009078232, 0.0015389861732369608, 0.0020769631025248534, -0.002743852454307084, 0.0021123297032516245, 0.0012292320946746152, -0.002430309109759527, 0.005406382162916027, -0.00614130490527683, 0.00658635302868453, 0.0015581716924004214, -0.006119808022563855, 0.010766367001198625, -0.003476841076856127, 0.0007296286175992061, 0.0141836732464256, -0.008760656287834505, 0.011576671267520175, 0.005265389090062797, -0.01633243017808432, -0.0010599490491054876, 0.00013419739440806102, -0.02587198935646634, -0.009723726864702168, 0.0077248970918107115, -0.02286593650668758, -0.01282052323455892, 0.021217324571991693, -0.008501157264437662, -0.009753464019094299, 0.017314603338373435, 0.018829456598925747, -0.013652459221131034, 0.0030886179655321335, 0.023071804833575734, -0.019328026634364413, -0.009226374710871307, 0.009669177525461627, -0.011793812815459047, -0.014696649734412561, -0.0034138302730515194, 0.01907801934270831, -0.0009128733557310401, -2.372795681677029e-5, 0.019913068992543873, 0.00022378264322051218, 0.0010457463416079034, 0.014716658873358907, 0.0014033932465923717, -0.0007349196543946671, -0.006840612785296012, 0.008666855789341265, -0.00707970175065639, -0.008178868618539397, 0.006245933053790038, -0.004545852821217631, -0.0008456208621579398, 0.00737612376318532, -0.005080674311463509, 0.00306996091800717, -0.005288072938336241, 0.0035797762058334156, -0.0010364698320545545, -0.0049147977613206275, 0.003901331789243621, -0.0028348945778584084, -0.0023221789337313807, 0.0025184223503828635, -0.001940516518976952, -0.0012096893295772179, 0.0012266071251979154, -5.912947439667706e-5, -0.00025810995232310364, 0.0002371300614098254, 0.0004721085209257282, -0.00017052187709866855, 4.789355050746568e-5, 0.0003162881985888973, -2.775699560629704e-5, -0.0001014169355307775, 0.0001762227661108718, 0.00011354974905286301, -5.3228103850621e-5, -0.0001789679623303009, 8.379319531057998e-5, -0.00029418763506700247, -0.00045788846259860633, 3.490265058788336e-5, -0.00015240629127851135, -0.0006394066571218462, -0.00015921473456774663, -2.4909313142317477e-5, -0.00011951092212351288, -0.000774542719362885, 0.000246676358657586, 0.0008608029756937469, -0.0016575273648733759, 0.0004781568019449393, 0.001696045494138623, -0.002425468747029947, 0.0015950021394165329, -9.222207902801594e-5, -0.0017969381365311283, 0.004088613748304538, -0.0033808129486671353, 0.0024018682482845914, 0.0035033086878861683, -0.0032267170386984104, 0.006885157964254791, 0.000754289862203608, 0.005455798149339235, 0.0067941053520189695, -0.004226732937396456, 0.007245554351604706, 0.0016713082075311856, -0.008866381197382074, -0.0009276568407349285, 0.0011795622000989262, -0.017001063507960632, -0.005849204542509046, 0.005729954501908178, -0.0127046384604016, -0.008780823489556971, 0.010775940413258647, -0.007082233536055794, -0.011424962552241407, 0.009606740065131535, 0.0055634972392548405, -0.011775633325414104, -0.00182535918970748, 0.009882779048278582, -0.01141919345710024, -0.0076922793665060215, 0.003986435492786968, -0.010061263267966485, -0.007272764652075618, -0.0033966252024601224, 0.010555751483858643, 0.004821041730846681, -0.0011469604224462484, 0.01152483181662828, 0.0031518804366735577, 0.0012199908388892942, 0.009998057424800809, 0.002722410952561127, 0.0025569704466723692, -0.003991526266336513, 0.006379373516620666, -0.0004452385428445654, -0.004529651517245413, 0.002916056124186103, -0.0034243397020886257, -0.0004122382537653633, 0.000308227856261743, -0.0038582418517081685, 0.0019777772682785274, -0.0027926863254574097, 0.0003587530240687358, 0.00021869547846762964, -0.002654923819968927, 0.0027144311144257573, -0.001115493425181801, -0.001087457782525426, 0.0016457974282161358, -0.0005805363760720154, -0.00047620499805006147, 0.0004227449619043671, -0.0005405376872249178, -0.00019451024642265475, 0.0001220900066669329, 2.8802669843614827e-5, 0.0003926891274957561, -0.00021686060777422736, 0.00032731972545831377, -2.0592133209803596e-5, 0.000412806902291478, 1.9072860906791327e-5, 0.0001683926737542849, -3.4909455089685866e-6, -0.0003488678188514661, 0.00043713450983500667, -0.00023249929555035242, -0.0002570137449351924, 5.193902414087003e-5, -1.778022533863038e-5, -0.000277670960397721, -0.0001280088298538828, -9.738576905174296e-5, 0.0003146319622121653, -0.00048495976274036233, -5.881939538187327e-5, 0.0003505185671567661, -0.00041165456055189116, -3.17770758656107e-5, 0.0006693024772747401, -0.0014012507271036088, 0.0005065493285708498, -0.001850669382378787, -0.001848413492710154, 0.003470904113120633, -0.00245310208279005, -0.0002518412324584235, 0.003202750655618005, 0.00037643802772626, -0.0003652914679546254, 0.005067909943179544, 0.0044063855501822406, -0.0008147439165255267, 0.0007534339115090945, 0.005181516630497496, 0.00014289819255423054, -0.002244872270432769, -0.00046632692451899216, 0.0032669544853625473, -0.007626943228721783, -0.0035275485404659655, 0.00490590149662813, -0.006353003913076433, -0.004988125477560059, 0.005942277957962605, -0.004136123606947495, -0.008575264957371733, 0.003563818487965461, -0.0008962243152358398, -0.008391652901286352, -0.003772375854451252, 0.0008187460652042736, -0.006261344250360117, -0.005243579005329043, -0.0008445246147396296, -0.005842157459121559, -0.0020661492124299905, -0.004716339653092639, 0.003891023257944706, 0.004914652551848932, -0.0020048289840645358, 0.00489826708227789, 0.003642457845101949, 0.0005863677361465501, 0.004240268002414932, 0.0030226521072251613, 0.0029399504920393053, -0.0006599948867812909, 0.004283027327479305, 0.0030067744975019704, -0.0024434503236411297, 0.0037470419203829873, -0.0017001422182001428, -0.00025999887345786967, 0.0004945486060799533, -0.0019316963956916894, 0.0014015326469189796, -0.0018592719352166337, -0.0012734719863058074, 0.00022752604591477616, -0.0008325209776629083, 0.0006518972291357669, -0.0002209680088458665, -0.0005844381978040241, 0.0006374504964404263, -0.00030042086851128386, -0.0003180272425871931, 0.0003200036372991237, -0.0003208251794789606, -0.00017938739608229935, 0.00020115090688488453, -0.0004278007807151667, 0.0008980933901507176, -0.00093974013699267, -2.7631143589819885e-5, 0.0003705962178759673, -0.0002235993759496778, 8.581380884434842e-5, -1.0589056125158736e-5, 0.00012781475087996367, -5.149788444528732e-5, 6.735381575231207e-5, -6.980169283087346e-5, 0.0008549004010196457, -0.0002896350773146033, -0.00045639612879548044, 0.00014433339612713933, 7.438414283406539e-5, -0.0001462889562334815, 0.0008962046370550658, -0.0004491999354411937, -0.0001358439303968773, 0.0002567723536874162, -0.00017456165110240926, -0.00013211760762490125, 5.154707583231821e-5, -0.0021842997980774746, 0.00020423859641678426, -0.0009323951145042024, -0.00027410037452760765, 0.00036660083681395084, -0.0017717165364799687, -0.0009889645061435819, 0.001967052485219031, 0.0012009955946495725, -0.002131903072140317, 0.002116497386715458, 0.0029504747442344113, -0.0018703980652161481, 0.001276718310714233, 0.0021259411869414572, -0.00011529339912164583, 0.0004616210707140103, -4.8110739394234836e-5, 0.0032274744244031855, -0.0017411664005025302, -0.0018106018938169452, 0.0036789011236225727, -0.0019759713448787306, -0.0027589639529380905, 0.0038304272188982836, -0.0016759625836861324, -0.00598509214257093, 0.000594668612545961, -0.0022630158489036134, -0.004787771140472798, -0.003484082900968667, -0.002324357537373124, -0.0038070667862865584, -0.0032554866029256588, -0.002542745312509413, -0.0027592869454837517, -0.0004558065487428717, -0.003768088779687184, 0.0009543963623660244, 0.002532265884845586, -0.0020945845216664366, 0.0018746550739031928, 0.0021527736234791595, -0.0003480483561401199, 0.001487068404218091, 0.001742418952433109, 0.0015902510847306463, 0.00011347454077632074, 0.002441709290866115, 0.0029138318965964464, -0.00035445245569196355, 0.001068255540614595, 0.0001112134261241416, 1.9839070663845676e-5, 0.0007330614521734104, -0.0008567626776148304, 0.00020065614759897757, -6.666667230547972e-5, -0.0007130253927398629, 0.0006725864352563189, -0.001353164480187536, 0.0010002303625923482, 7.0680511095689e-5, -0.00044100642593638526, 0.00037864316998856935, -0.0002183762311663193, -0.0002983978074009783, 0.0003585514605662062, -0.0003036410651982877, -8.070987518439697e-7, 6.941117930794801e-5, -2.992911622236709e-5, -7.402081183160249e-6, -0.0001321253618196528, 2.2799440018698467e-6, -3.741796475578213e-7, -0.0001356503621078061, 7.821990533270799e-5, 1.084861652171913e-5, 4.6464773734985364e-5, -0.0001664592242747621, 0.0003059684833095625, 0.00010971801770890643, -0.00012570335947511378, 0.00012127343790639659, 2.410158458287476e-5, 0.0002275813856283744, 0.00015904076210810915, 0.00010614634050301082, 0.00018989134217286876, 3.532532642815507e-5, -2.8817283086439075e-5, 0.0001966183522169241, 0.0002352676465310342, -0.00014350390681891243, -0.00033096530447796537, -3.169237203877814e-5, -0.00032416449160339346, -0.0005326110733232359, -0.00011514499383106136, -1.6327508693523084e-6, -0.0005192848533754159, -0.0007485019640352898, 0.0002437465984378839, 0.00036682564101518287, -0.0005826700046300241, 0.0002464608811585777, 0.0013538328490401495, -0.0008591301153472691, 0.0005672756472275329, 0.0011641307385705524, -0.0002599234294600801, 0.0005958199614809318, -9.08652380041424e-6, 0.0012246707850920118, 0.00040949283817204443, -0.0003817131862232187, 0.0013308474125837658, 0.0006385514882180452, -0.00020237498356237058, 0.0015870557723673304, 0.0013669986689095282, -0.0026913104908060587, -0.0016841984911645188, -0.00026982903494541025, -0.0023514041251430483, -0.0021783086903424675, -0.0020049433834278753, -0.0029573016475834698, -0.0022861213061646257, -0.003047202938188654, -0.0019435514646578206, -0.0002736703433588217, -0.0026296896020856515, 0.00043480955299381044, 0.0014594130869672753, -0.0020460318504711824, 0.000891442608272253, 0.0009917315550983013, -0.001150526638822271, 0.00021658070314920273, 0.000955169383503071, 0.0004151454265862082, -3.466693148061745e-5, 0.00022333896621834577, 0.0005007305134544424, 0.00010158561723786084, 0.0008770453345158246, 0.0003170773462852869, 9.645822968684504e-5, 0.0005231463164375129, -0.0002625018735430571, 5.811704781894167e-5, 0.00015411755787419655, -0.0005943673084048015, -0.00042006486954656403, -0.001069531932086781, -0.00016964791878725855, -0.00014522101936285627, -0.0009883434416747602, 0.0008560808379524285, 7.062584826224038e-5, -0.00018739479839661858, 0.00017485171678150731, -0.00018896266975880632, -2.5010204380245336e-5, 0.000177248522290165, -6.855996742321184e-5, -0.00020041597059828115, -3.9155519519723546e-5, -7.150825770943099e-5, 3.78534396262591e-5, -0.00013885999587317298, 0.05755100129562894, 0.057551001296848654, -0.010242835890749497, 0.11458860749126752, 0.10442311515907059, 0.041169849800993315, 0.02503688391783294, 0.0663021557100921, 0.05652896110417649, -0.010109454904140256, 0.046496065002990465, 0.039241634732247066, 0.017195501510771986, 0.05650411387359346, 0.02808671617185623, 0.01549607344102931, 0.04365162268338308, 0.03782628865198354, -0.033539035009513905, 0.006710466123679542, 0.015753932297547818, 0.08800186060171834, 0.03462920653773137, -0.052403403893253146, -0.10937815173453733, -0.031173831014268988, 0.08350658381099997, 0.12597340714342087, -0.04641809281094043, -0.06347117387315218, 0.01460886756092407, 0.013728808466115303, 0.002099939769347984, -0.19642505543529912, 0.024337656421894102, 0.01494734341573567, -0.0045500208006439375, -0.008657022333915267, -0.12750074249750268, 0.01495413363248006, -0.0041704105743546336, 0.023379290117620202, -0.011444100733469444, 0.07765026850662347, 0.01555109860674823, 0.0032106711800736817, -0.004578880080126947, 0.002071353478066523, 0.11646129786134037, 0.03061943453308166, 0.006910402120673847, 0.012510396195244376, -0.29982800301919615, 0.22250923172847012, 0.14249873161381438, 0.017739843743807396, -0.009803029268563888, 0.046156408229023685, -0.18883682829220844, 0.20746057094868003, 0.1563150092983598, 0.03657108688647759, 0.07032899925718697, 0.05930256815665265, 0.15956566623931911, -0.017078570969223238, 0.19373924908357473, 0.029327941081879444, 0.04106662270969433, 0.02736654970961926, 0.07433902769045496, 0.27007290689171526, -0.08365864926956201, 0.18546911732883384, -0.00728195098400652, 0.04135923628228456, 0.010448546789663848, 0.13890346505968185, 0.18311047976749034, 0.07819861678617064, 0.03667601329038399, 0.040671941655151506, 0.012680183660143922, 0.17572052292273693, 0.11372237304634528, -0.6933412140911193, 0.057715647880650846, 0.05655458685035344, 0.015082691913656516, 0.14793992432919895, 0.08085629500340144, 0.11677097128648235, -0.04282948724485162, 0.06629457461767821, -0.019921874295802416, 0.106013039241812, 0.10222480753984034, 0.20144700449456826, -0.042627687137497136, 0.03892354687890946, 0.1147260471305238, 0.13864051074928613, 0.003384066361115371, -0.054683532879402114, 0.006765321030876906, 0.02351901694368394, -0.0012284061034834332, 0.018757755122287334, 0.015252735582814012, 0.02048132373473891, -0.006641792153497067, -0.027481559181263507, -0.007317508619410595, -0.003842718664508582, 0.019373033694858082, -0.02349771634894664, -0.006968157443751509, 0.027244417942488483, 0.012424167560532079, -0.06509123581934576, 0.006483032966963868, 0.00647987076210725, 0.0245278442058414, -0.015290678102251187, -0.006108084622062229, 0.0120892231738265, 0.01576475479548388, -0.037038247697757556, -0.010331777307181739, 0.013282616967582577, -0.0014721788496030567, -0.03357901379644784, 0.0041168419127466105, -0.001954158378898559, 0.023091762232173928, 0.010869438971812122, -0.0010502638256723415, 0.0002327725373105698, 0.02429216803746726, -0.0030554715883844854, -0.017034024680428472, 0.020188873603441897, 9.489762916038983e-5, 0.010147837212767715, 0.06313668809748343, 0.016616486993414267, -0.005543567149698572, 0.032890826205690914, 0.030265153199348808, -0.02724065309903161, 0.03392205109305394, 0.011761197208664849, -0.008044391041465718, 0.018088783238261037, -0.03316931101591848, 0.021913101028841985, -0.0749431021517506, -0.010917583699509827, 0.011380693760135376, 0.0298904070237073, 0.01310917829293641, 0.021894449338853216, -0.04719290809576986, -0.006731305676418794, 0.008709765750130313, 0.03246424447306024, -0.06987796056229417, 0.02296572938901381, 0.03989466182285997, -0.004244432422867889, -0.0074435953344573385, -0.023657672293521875, 0.022951741155414228, 0.016618375198047482, 0.010935233208738973, 0.06751507653549779, 0.04076105807079613, -0.0028246494255363577, 0.03935881071836712, 0.042628105410730484, 0.007317490232046432, -0.01779115010786911, 0.04575979073543525, -7.125554199045213e-5, 0.025872261176459674, 0.016348931119619704, -0.05079385420922906, -0.022126376757180464, 0.028409206205560866, 0.017743421949481916, -0.07265201580177451, 0.007745443193471236, 0.0372859567288081, 0.002026617194474211, 0.020195730944684295, 0.0032477826987762017, -0.045076251444856295, -0.0013492324768315169, -0.023807816709302255, 0.01450160915499094, 0.025533775085076732, 0.008715262935125092, 0.015645415558978595, 0.02011702789582915, 5.564128881792872e-5, 0.03463309095575714, -0.02595504900706331, 0.008378347464659083, 0.9342506611870772, 0.10037703163285057, 0.5788514179499369, 0.7398843593674533, 0.9222231444372957, 0.18067196596897667, 0.45815670707906414, 0.8201181873590115, 0.9039928412564735, 0.25711186611246367, 0.37230256795055294, 0.8624920122482538, 0.8290466529889333, 0.4425331644934683, 0.3870355875496936, 0.8559811367822242, 0.769745913627382, 0.5388681042614432, 0.3979779938931314, 0.8509493764637057, 0.6399986222215361, 0.6876206224049686, 0.33474875414452127, 0.877749790929863, 0.8813767386282672, 0.3250705406983584, 0.5558018212976559, 0.7571512833199081, 0.31162770002421425, 0.8862222636213346, 0.7747500468122256, 0.5312123117496287, 0.93885016245718, -0.03207173655083746, 0.34707766669636597, 0.872625171697682, 0.24555044341706714, 0.9067543585431324, 0.7647899896588352, 0.5454458468089096, 0.9384711571181824, -0.0422745061519243, 0.23849309087482523, 0.9086390021641901, 0.5992465888990961, 0.7235122365231315, 0.9379626885608358, -0.05180882286723354, -0.017697667284362225, 0.9392856971906308, 0.14592680129111657, 0.9280118878089326, 0.556055198323438, 0.7572244017956093, 0.9394087211820743, -0.005704144099310573, 0.2367689780716783, 0.9090882732866861, 0.41714404685250833, 0.8417767836056904, 0.9353673492637458, 0.08726830081841497, -0.4340521353528723, 0.8334866932473114, 0.18956825336097158, 0.9200903181191733, 0.3200873733052253, 0.8832471175359102, 0.9292235322541118, 0.138180814451513, -0.5122361022285661, 0.7877789707409335, 0.23078134648709545, 0.9106280064081852, 0.03650633938616474, 0.9387034287015841, 0.7072020505517751, 0.6183222732479662, 0.8946035981608308, 0.28694182042999566, -0.7759203596360525, 0.529230937166809, 0.19464230293310092, 0.9190308691278294, -0.011126610964376005, 0.9393443356249398, 0.6260553247131383, 0.700413681118761, 0.8598849300341903, 0.37852048749950856, -0.8484029755534657, 0.4028152358580999, 0.20711425459332922, 0.9162993792230996, -0.25618755347225786, 0.9038460211989083, 0.2659450556377684, 0.9011389642410619, 0.7320262088865461, 0.5888440329808386, -0.9353957171900739, 0.08610353317815857, -0.8104340587444302, -0.4747582875784401, 0.23785126689475086, 0.9088054374853178, -0.3768316266565599, 0.8605666814330738, 0.12926793625512137, 0.9305890000691603, 0.6658850831344271, 0.6626700411163511, -0.9385185510657542, -0.04206748756721242, -0.7714733374807935, -0.5358542271255402, 0.27367018910380914, 0.8986701728808237, -0.7685872510778933, 0.5401478206651251, -0.2451580674514454, 0.9067854073845738, -0.28700369957767813, 0.8946863642745463, -0.932990129365485, 0.10973487122301254, 0.36381158035362576, 0.8661042614379897, -0.9393211855930776, 0.014953354332003392, -0.3779938895150968, 0.8599858329450083, -0.9389667076970603, 0.029603100111616036, -0.6603131918926098, 0.6681984074964923, 0.48456919392879094, 0.8047895524253966, -0.7610630375213097, -0.5507038520950519, -0.4314915794061707, 0.8344703533513427, -0.7000232885895054, -0.6265121563045186, 0.03475351226567363, 0.9387641099054032, 0.5785633759245725, 0.7401093176880682, -0.4683546532704446, -0.8143972002321529, -0.4874542042683437, 0.8030753356558247, -0.38494741507759256, -0.8569414467032564, 0.27879472998824834, 0.897046199941687, -0.33424494948064193, -0.8779790922088764, -0.44265731522158325, 0.8286003740923761, -0.2829241979002093, -0.8958212070456916, 0.4685188267932182, 0.8142062889899527, -0.003251735775027521, 0.9394109595864576, -0.08552626645981555, 0.9355107968150782, -0.0006881314795699517, 0.9394154731124953, 0.046036267186115504, 0.9382867984788863, 0.0045562725171556535, 0.9394037431886615, 0.053015546177318344, 0.9379183137059603, -0.010050494213250064, 0.9393642802569822, 0.03623445682279284, 0.9387101817209532, 0.015687604280922314, 0.9392726137970584, -0.06256518608545959, 0.9373262732700102, -0.011789262370866353, 0.9393483268466964, -0.043962353353769176, 0.9383858241517264, -0.019077331229733728, 0.93922804234628, 0.010223023565151966, 0.9393492008993906, 0.023362369690022644, 0.9391249094016065, 0.048681807053248684, 0.9381459045401932, 0.003284628853707706, 0.9394007170616288, 0.005481759587730582, 0.9393945997222624, -0.010491255352753021, 0.9393533474262776, -0.007142914373945228, 0.9393896874814753, -0.0067167830990306305, 0.9393930605948855, -0.04757144779793346, 0.938203120721751, 0.03666815070531503, 0.9386931514831355, -0.03591705990216437, 0.9387141959937361, 0.011661924669408949, 0.9393421852418637, 0.016288852608887898, 0.9392793967845297, 0.005538504282633292, 0.9394020684051282, -0.007054202681064953, 0.9393835882394478, -0.0596663539589821, 0.9375101241999784, -0.0356326994973478, 0.9387339138961664, 0.006136914353318095, 0.9394068459799426, 0.020169239709991408, 0.9391864021287223, 0.031039614742188464, 0.9389095666174658, -0.02064701613819146, 0.9391837841051798, 0.0066436518963205494, 0.9393997912510439, -0.004497051573703323, 0.9394070808701006, -0.04065591526046585, 0.9385265612931556, -0.011784310521580625, 0.9393405189223384, 0.0007100498072502281, 0.9394127738949801, 0.0007805849941391754, 0.9394019844325305, -0.0063299243275887086, 0.9393865892036948, -0.01141692906977718, 0.939336283860125, -0.044730544770918666, 0.9383452137937008, 0.0006140047361404702, 0.9394104022915953, 0.03928110638698058, 0.9385952501284714, 0.012637141455062525, 0.9393394178316118, -0.008342124923829214, 0.9393839399658317, -0.0832132907492936, 0.9357218142390737, 0.00015794398927444366, 0.9394143825388853, 0.04158572326665399, 0.9384957299256834, -0.013402208805517674, 0.9393034006852677, -0.21386839155995335, 0.9147853928857044, 0.03252383077708152, 0.9388569775206135, -0.04999592395837545, 0.9380835204351815, -1.6314650408347853e-5, 0.9394018828928516, 0.027849991526362187, 0.9390078255373949, -0.024147571738946508, 0.9390997146330554, 0.05131334295052001, 0.9380151937096163, -0.01927522149075469, 0.9392088687253748, -0.07093782103796543, 0.9367318379486976, -0.0003157519456872851, 0.9394132464896405, -0.041085546966674026, 0.938519303369092, 0.1749532249162381, 0.9230471436020997, 0.027257726666367794, 0.9390076779822462, 0.03861018893821863, 0.9386196000695913, -0.00040617505025039975, 0.9394092510309853, -0.020032564937748045, 0.9392040509702182, 0.07699126845733946, 0.9362972014810318, 0.039879491778626076, 0.938548084445912, 0.12706449030798037, 0.9307870560069462, -0.00042966566036986624, 0.939409236591249, -0.026314934122514098, 0.9390529319295395, -0.13877776040923445, 0.929097189973093, 0.04634833297584042, 0.9382785029897316, 0.12535144789317798, 0.9310133380431266, -0.0004759632827978163, 0.9394105431904718, -0.04802573117648456, 0.9382101301880871, 0.04212123720959499, 0.9384652203045247, 0.09599547875727057, 0.9345000776357316, -0.000438492441856673, 0.9394116486843506, -0.04183356190013501, 0.938469265478956, -0.020863795971687634, 0.9391802940896367, 0.009160134164017005, -0.09292868484373124, 0.03510119342272539, -2.132277528697243e-8, 0.019302508280167628, -0.1934891415751766, -0.0032793528481479717, -0.07810732476837963, 0.022737469581011492, 0.06531813014825595, 1.348784643296338e-14, 0.046701844054095304, -0.022462901329703196, 0.10737022437436909, 0.013269797082087042, 0.047713909407851925, -0.04433746387879824, 0.0574190368044134, 0.0028309853758902545, 0.11663341613763815, 0.07221420103669189, -0.06348921783257913, 0.04555973072826318, 0.08759133608370355, 0.027173265367954846, 0.016189939466356953, -0.058063635350449054, 0.05154141771874011]
Final objective value:     -2477.441488207146
)

Now let's evaluate our fits by plotting the residuals

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

These look reasonable, although there may be some minor overfitting. Let's 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 │ 1.007  missing  missing  missing  missing    1.024  missing
 0.73 hr │ 227.070703125 GHz │ 0.999    1.019  missing  missing  missing    1.015  missing
 0.88 hr │ 227.070703125 GHz │ 1.021    0.993  missing  missing  missing    0.973  missing
  1.3 hr │ 227.070703125 GHz │ 0.993    0.996  missing  missing  missing     1.02  missing
 1.45 hr │ 227.070703125 GHz │ 0.977    0.993  missing  missing  missing    1.028  missing
 1.89 hr │ 227.070703125 GHz │ 1.013    0.937  missing  missing  missing    1.007  missing
 2.04 hr │ 227.070703125 GHz │ 1.007    1.025    0.985  missing  missing    0.994  missing
 2.46 hr │ 227.070703125 GHz │ 1.012    1.016    0.964  missing     0.99    1.013  missing
 2.61 hr │ 227.070703125 GHz │ 0.999    0.967    1.004  missing    0.998  missing  missing
 3.06 hr │ 227.070703125 GHz │ 1.023    1.011    0.999  missing      1.0    1.025  missing
 3.21 hr │ 227.070703125 GHz │ 0.997    0.983     1.02  missing      1.0  missing  missing
 3.62 hr │ 227.070703125 GHz │  1.01    1.065    1.017  missing    0.994    1.033  missing
 3.78 hr │ 227.070703125 GHz │ 1.031    0.973    1.035  missing    1.012    0.992  missing
 4.23 hr │ 227.070703125 GHz │ 1.018    0.967    1.022    0.928    0.989    1.011  missing
 4.37 hr │ 227.070703125 GHz │  1.03    1.013    1.022    0.954    0.993    1.009  missing
 4.79 hr │ 227.070703125 GHz │ 1.033    0.933    1.023    1.041    0.996    0.993    0.977
 4.95 hr │ 227.070703125 GHz │ 1.023    1.017    1.011     1.07    1.042    0.997     1.04
 5.63 hr │ 227.070703125 GHz │ 1.044    1.007    0.982    1.047      1.0  missing    1.026
 6.15 hr │ 227.070703125 GHz │ 1.016     0.95    0.978    1.029    1.018  missing     0.93
 6.72 hr │ 227.070703125 GHz │ 1.008    1.038    1.002     1.02    1.003  missing    0.956
 7.23 hr │ 227.070703125 GHz │ 0.999    0.976    1.015    1.026    1.009  missing    1.016
 7.44 hr │ 227.070703125 GHz │  1.02  missing      1.0    1.035    0.974  missing    1.008
─────────┴───────────────────┴─────────────────────────────────────────────────────────────

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.


  1. Hamaker J.P, Bregman J.D., Sault R.J. (1996) [https://articles.adsabs.harvard.edu/pdf/1996A%26AS..117..137H] ↩︎

  2. Pesce D. (2021) [https://ui.adsabs.harvard.edu/abs/2021AJ....161..178P/abstract] ↩︎