Comparing discretization techniques

In Periodic problems and plane-wave discretizations we saw how simple 1D problems can be modelled using plane-wave basis sets. This example invites you to work out some details on these aspects yourself using a number of exercises. The solutions are given at the bottom of the page.

For this example we consider the discretization of

\[ H = - \frac12 Δ + V(x) \quad \text{with $V(x) = \cos(x)$}\]

on $[0, 2π]$ with periodic boundary conditions. The $\cos(x)$ takes the role of a lattice-periodic potential. We will be interested in the smallest eigenvalues of this discretized Hamiltonian. Of note the boundary condition matters: The spectrum we will get is different from e.g. the spectrum of $H$ on $\mathbb{R}$.

Finite differences

We approximate functions $ψ$ on $[0, 2\pi]$ by their values at grid points $x_k = 2\pi \frac{k}{N}$, $k=1, \dots, N$. The boundary conditions are imposed by $ψ(x_0) = ψ(x_N), ψ(x_{N+1}) = ψ(x_1)$. We then have

\[ \big(Hψ\big)(x_k) \approx \frac 1 2 \frac{-ψ_{k-1} + 2 ψ_k - ψ_{k+1}}{δx^2} + V(x_k) ψ(x_k)\]

with $δx = \frac{2π}{N}$.

This can be put in matrix form in the following way:

# Finite differences Hamiltonian -1/2 Delta + V on [0, 2pi] with periodic bc.
# Pass it a function V.
using LinearAlgebra

function build_finite_differences_matrix(Vfunction, N::Integer)
    δx = 2π/N

    # Finite-difference approximation to -½Δ
    T = 1/(2δx^2) * Tridiagonal(-ones(N-1), 2ones(N), -ones(N-1))
    # The type Tridiagonal is efficient, but to establish the periodic boundary conditions
    # we need to add elements not on the three diagonals, so convert to dense matrix
    T = Matrix(T)
    T[1, N] = T[N, 1] = -1 / (2δx^2)

    # Finite-difference approximation to potential: We collect all coordinates ...
    x_coords = [k * δx for k=1:N]
    V = Diagonal(Vfunction.(x_coords))  # ... and evaluate V on each of the x_coords

    T + V
end;

Exercise 1

Show that the finite-difference approximation of -½Δ is indeed an approximation of the second derivative. Obtain an estimate of the first eigenvalue of $H$. Hint: Take a look at the eigen function from LinearAlgebra.

Plane waves method

In this method, we expand states on the basis

\[ e_G(x) = \frac{1}{\sqrt{2\pi}} e^{iGx} \qquad \text{for $G=-N,\dots,N$}.\]

Exercise 2

Show that

\[ \langle e_G, e_{G'}\rangle = ∫_0^{2π} e_G^\ast(x) e_{G'}(x) d x = δ_{G, G'}\]

and (assuming $V(x) = \cos(x)$)

\[ \langle e_G, H e_{G'}\rangle = \frac 1 2 \left(|G|^2 \delta_{G,G'} + \delta_{G, G'+1} + \delta_{G, G'-1}\right).\]

What happens for a more general $V(x)$?

Exercise 3

Code this and check the first eigenvalue agrees with the finite-difference case. Compare accuracies at various basis set sizes $N$.

Using DFTK

We now use DFTK to do the same plane-wave discretization in this 1D system. To deal with a 1D case we use a 3D lattice with two lattice vectors set to zero.

using DFTK
a = 2π
lattice = a .* [[1 0 0.]; [0 0 0]; [0 0 0]];

Define Hamiltonian: Kinetic + Potential

terms = [Kinetic(),
         ExternalFromReal(r -> cos(r[1]))]  # r is a vector of size 3
model = Model(lattice; n_electrons=1, terms, spin_polarization=:spinless);  # One spinless electron

Ecut defines the number of plane waves by selecting all those $G$, which satisfy the relationship $½ |G|^2 ≤ \text{Ecut}$.

Ecut = 500
basis = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))

PlaneWaveBasis discretization:
    architecture         : DFTK.CPU()
    num. mpi processes   : 1
    num. julia threads   : 1
    num. DFTK  threads   : 1
    num. blas  threads   : 2
    num. fft   threads   : 1

    Ecut                 : 500.0 Ha
    fft_size             : (135, 1, 1), 135 total points
    kgrid                : MonkhorstPack([1, 1, 1])
    num.   red. kpoints  : 1
    num. irred. kpoints  : 1

    Estimated memory usage (per MPI process):
        single ψ             :   3.94KiB
        single ρ             :   1.05KiB
        peak memory (SCF)    :   44.2KiB
    
    Discretized Model(custom, 1D):
        lattice (in Bohr)    : [6.28319   , 0         , 0         ]
                               [0         , 0         , 0         ]
                               [0         , 0         , 0         ]
        unit cell volume     : 6.2832 Bohr
    
        num. electrons       : 1
        spin polarization    : spinless
        temperature          : 0 Ha
    
        terms                : Kinetic()
                               ExternalFromReal(Main.var"##363".var"#3#4"())

We now seek the ground state using the self-consistent field algorithm.

scfres = self_consistent_field(basis; tol=1e-4)
scfres.energies

Energy breakdown (in Ha):
    Kinetic             0.2090845 
    ExternalFromReal    -0.7441493

    total               -0.535064852288

On this simple linear (non-interacting) model, the SCF converges in one step. The ground state energy of is simply the lowest eigenvalue; it should match the smallest eigenvalue of $H$ computed above.

Plotting

We can also get the first eigenvector (in the plane wave basis) and plot it

using Plots

ψ_fourier = scfres.ψ[1][:, 1];    # first k-point, all G components, first eigenvector
# Transform the wave function to real space
ψ = ifft(basis, basis.kpoints[1], ψ_fourier)[:, 1, 1]
# Eigenvectors are only defined up to a phase. We fix it by imposing that psi(0) is real
ψ /= (ψ[1] / abs(ψ[1]))
plot(real(ψ); label="")

Again this should match with the result above.

Exercise 4

Look at the Fourier coefficients of ψ_fourier and compare with the result above.

The DFTK Hamiltonian

We can ask DFTK for the Hamiltonian

E, ham = energy_hamiltonian(basis, scfres.ψ, scfres.occupation; ρ=scfres.ρ)
H = ham.blocks[1]
typeof(H)

DFTK.DftHamiltonianBlock

This is an opaque data structure, which encodes the Hamiltonian. What can we do with it?

using InteractiveUtils
methodswith(typeof(H), supertypes=true)

9-element Vector{Method}:

Array(block::HamiltonianBlock) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/terms/Hamiltonian.jl:74
*(H::HamiltonianBlock, ψ) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/terms/Hamiltonian.jl:63
(Matrix)(block::HamiltonianBlock) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/terms/Hamiltonian.jl:75
eltype(block::HamiltonianBlock) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/terms/Hamiltonian.jl:64
size(block::HamiltonianBlock, i::Integer) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/terms/Hamiltonian.jl:65
size(block::HamiltonianBlock) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/terms/Hamiltonian.jl:66
mul!(Hψ::AbstractArray, H::DFTK.DftHamiltonianBlock, ψ::AbstractArray) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/terms/Hamiltonian.jl:137
PreconditionerNone(::HamiltonianBlock) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/eigen/preconditioners.jl:21
PreconditionerTPA(ham::HamiltonianBlock; kwargs...) in DFTK at /home/runner/work/DFTK.jl/DFTK.jl/src/eigen/preconditioners.jl:45

This defines a number of methods. For instance, it can be used as a linear operator:

H * DFTK.random_orbitals(basis, basis.kpoints[1], 1)

63×1 Matrix{ComplexF64}:
   0.03279797778742134 - 0.03382876807083241im
 -0.011535520759559144 - 0.06935799132595814im
   0.04958277077161584 - 0.004062145294638123im
  -0.13444237737284984 - 0.013343607128360663im
   -1.4272545285534992 - 0.7897317356552989im
    1.0092282038484899 + 0.344232244222421im
    0.6062681379451843 + 1.33575488695106im
    -2.621902359998899 + 0.5729017353725886im
 -0.051041706304620196 + 2.2749310458408987im
    -2.038201187300717 + 2.6035774899745388im
    4.1697923595439095 + 3.616544945054035im
   -2.8705888257116943 - 3.342491796115047im
     8.351365365320872 - 5.668167402059794im
   -2.3849963660153803 + 5.35779778450626im
    17.489318192055045 - 1.0988422599409458im
   -12.271625426344277 - 1.902947191704611im
     -9.64143619431847 - 4.751082098330021im
   -20.266824644373646 + 21.838040894568568im
    -2.489365306836505 + 14.770035421057527im
   -28.087974710722662 - 7.778476016729337im
   -15.963637685517966 + 23.999513529226107im
     12.37037746615114 + 39.51565953481619im
    -4.080767645341037 - 34.018115481543234im
    -7.761187158405147 + 0.17434241511160853im
     -8.72424573670233 + 8.559139804063085im
     -15.1189502109918 + 3.9362385238217734im
    13.473317552734093 - 5.354820620061567im
    28.271029524269103 + 3.0488376444526235im
     73.57163669171227 + 38.35628395492385im
     5.765527740617241 - 13.00610406618934im
     64.33247815241363 + 53.95310505241745im
    23.630149987665025 - 57.2804240697029im
    -54.62834227871139 + 0.45549744361904876im
   -26.398580453708917 - 4.999988834239707im
     57.02710965271096 - 7.374537333444185im
    32.110766806348884 - 33.07790231009826im
   0.30833627533048247 + 42.514192244737586im
   -23.606446063971525 + 5.010355969392575im
     70.20469585155772 - 39.049831890865875im
     -17.5477410296705 - 5.810092818563899im
    15.022806003336255 + 35.55472395832068im
    26.132929170996643 - 0.39031648834015575im
      32.8992403408153 + 23.353885568604802im
   -12.388187236902885 - 16.9464178533239im
    -6.238443568604663 - 19.95531001313456im
    16.298306826459136 - 5.66968453478318im
    -5.931087393476317 - 6.23692369307609im
     9.979520108295944 - 3.686135430267163im
   -18.648809690086736 - 8.210146970374176im
    18.835256134391944 - 2.8490260523786155im
     6.978926127012578 + 7.303291192483812im
   -0.7398434214371091 - 10.94397437394748im
     8.575229537971094 - 3.956662809201845im
   -2.5698960172795466 - 4.73861722931001im
   -6.4845226876264235 - 4.1495377089920815im
    3.5093152149293183 - 1.5066301050077087im
    0.8369340882455863 - 1.755812123285878im
    1.7042618530637434 + 2.092560083187027im
    2.0503325811095965 - 0.9622271867238238im
   0.30268474084997393 + 0.6040130773476969im
   0.45378927981088046 - 0.08718571397222352im
   0.26450474518461653 + 0.155957629104451im
   0.05960201663049063 + 0.015333282228326637im

We can also get its full matrix representation:

Array(H)

63×63 Matrix{ComplexF64}:
  3.21245e-19+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im
          0.5+9.98774e-18im           0.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im
  8.97271e-18+4.91711e-18im           0.5+9.98774e-18im           2.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im
 -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im           4.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im
 -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im           8.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im    9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im
   1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          12.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im
  1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          18.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im
 -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          24.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im
 -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          32.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im
  4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          40.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im
 -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          50.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im
  2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          60.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im
 -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          72.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im
 -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          84.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im
  2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          98.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im   -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im
  7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         112.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im
 -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         128.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im
          0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         144.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im
  6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         162.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im
 -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         180.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im
  3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         200.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im
 -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         220.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im
 -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         242.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im
  1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         264.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im
 -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         288.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im  -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im
 -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         312.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im   -6.4196e-18-3.9968e-18im   -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im
  9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         338.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   7.85256e-20-1.51998e-17im   -6.4196e-18-3.9968e-18im   -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im
  6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         364.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im   7.00086e-18-3.1146e-18im    7.85256e-20-1.51998e-17im   -6.4196e-18-3.9968e-18im   -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im
 -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         392.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -3.51205e-18+2.34442e-18im   7.00086e-18-3.1146e-18im    7.85256e-20-1.51998e-17im   -6.4196e-18-3.9968e-18im   -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im
  3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         420.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im   8.55835e-18+5.02783e-18im  -3.51205e-18+2.34442e-18im   7.00086e-18-3.1146e-18im    7.85256e-20-1.51998e-17im   -6.4196e-18-3.9968e-18im   -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im
  1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         450.0+0.0im                   0.5+1.16569e-17im  -2.68068e-18+8.11096e-18im   8.55835e-18+5.02783e-18im  -3.51205e-18+2.34442e-18im   7.00086e-18-3.1146e-18im    7.85256e-20-1.51998e-17im   -6.4196e-18-3.9968e-18im   -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im    3.0551e-18-4.69829e-18im
   3.0551e-18-4.69829e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         480.5+0.0im          -3.18704e-18-2.38796e-17im  -2.68068e-18+8.11096e-18im   8.55835e-18+5.02783e-18im  -3.51205e-18+2.34442e-18im   7.00086e-18-3.1146e-18im    7.85256e-20-1.51998e-17im   -6.4196e-18-3.9968e-18im   -1.96473e-17+2.10786e-17im  -1.21529e-17+1.03447e-17im           0.0+2.88705e-17im   8.50869e-18-3.40232e-18im  -4.10876e-18-1.59967e-17im  -4.53964e-18-4.47079e-18im  -2.33026e-17+1.55125e-17im   1.48727e-18-1.13135e-17im  -9.71381e-19+1.04378e-17im  -1.35822e-18+7.74245e-18im  -3.63007e-18-1.40327e-17im   2.63164e-17+2.78475e-17im   2.35457e-17+1.83632e-17im   1.13767e-17-3.75559e-17im  -1.96104e-17-1.42265e-17im  -8.08181e-18+2.00791e-17im   1.59347e-17+3.80377e-18im  -5.15297e-19-1.21159e-17im  -1.11563e-17+2.11254e-17im  -1.06426e-17+4.48441e-19im   9.97107e-18-1.10351e-17im   3.44846e-18+1.33684e-18im  -4.68096e-18+5.22695e-18im   4.39275e-18+8.91115e-18im
   3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im   -6.4196e-18+3.9968e-18im    7.85256e-20+1.51998e-17im   7.00086e-18+3.1146e-18im   -3.51205e-18-2.34442e-18im   8.55835e-18-5.02783e-18im  -2.68068e-18-8.11096e-18im   8.41322e-19+1.68969e-17im         480.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im
  1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im   -6.4196e-18+3.9968e-18im    7.85256e-20+1.51998e-17im   7.00086e-18+3.1146e-18im   -3.51205e-18-2.34442e-18im   8.55835e-18-5.02783e-18im  -2.68068e-18-8.11096e-18im           0.5+9.98774e-18im         450.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im
  3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im   -6.4196e-18+3.9968e-18im    7.85256e-20+1.51998e-17im   7.00086e-18+3.1146e-18im   -3.51205e-18-2.34442e-18im   8.55835e-18-5.02783e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         420.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im
 -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im   -6.4196e-18+3.9968e-18im    7.85256e-20+1.51998e-17im   7.00086e-18+3.1146e-18im   -3.51205e-18-2.34442e-18im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         392.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im
  6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im   -6.4196e-18+3.9968e-18im    7.85256e-20+1.51998e-17im   7.00086e-18+3.1146e-18im   -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         364.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im
  1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im   -6.4196e-18+3.9968e-18im    7.85256e-20+1.51998e-17im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         338.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im
 -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im   -6.4196e-18+3.9968e-18im    1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         312.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im
 -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -1.82858e-17-3.37562e-17im  -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         288.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im
  1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im  -1.21529e-17-1.03447e-17im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         264.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im
 -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im   1.96473e-17-2.89782e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         242.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im
 -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   8.50869e-18+3.40232e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         220.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im
  3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -4.10876e-18+1.59967e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         200.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im
 -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -4.53964e-18+4.47079e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         180.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im
  6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im  -2.33026e-17-1.55125e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         162.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im
 -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   1.48727e-18+1.13135e-17im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         144.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im
 -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -9.71381e-19-1.04378e-17im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         128.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im
  7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im   5.46006e-18+1.88734e-18im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im         112.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im
  2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im  -3.63007e-18+1.40327e-17im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          98.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im
 -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im   1.35822e-18-1.50482e-17im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          84.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im
 -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   2.35457e-17-1.83632e-17im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          72.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im
  2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im   1.13767e-17+3.75559e-17im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          60.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im
  1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -1.96104e-17+1.42265e-17im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          50.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im
  4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im  -8.08181e-18-2.00791e-17im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          40.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im
  3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im   1.59347e-17-3.80377e-18im   1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          32.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im
 -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -5.15297e-19+1.21159e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          24.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im
  1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im           0.0-1.67108e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          18.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im
   1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im  -1.06426e-17-4.48441e-19im   9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im          12.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im
 -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im   1.78543e-17-1.72668e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im           8.0+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im
 -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.44846e-18-1.33684e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im           4.5+0.0im                   0.5+1.16569e-17im   8.97271e-18-4.91711e-18im
  8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im  -4.68096e-18-5.22695e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im           2.0+0.0im                   0.5+1.16569e-17im
          0.5+1.16569e-17im   8.97271e-18-4.91711e-18im  -2.04669e-18-7.85756e-18im  -1.01526e-17+1.97211e-17im    1.0213e-17+1.52664e-17im   1.23204e-17+9.68665e-21im  -2.11585e-18-3.84134e-18im   3.64735e-18+1.55332e-17im   4.20171e-18-1.36319e-18im   1.04751e-17-1.37601e-17im   2.08131e-17+5.36003e-18im  -2.55944e-18-3.23188e-17im  -3.42569e-17+3.63887e-18im   2.40113e-18+2.87344e-17im   7.23023e-19-4.03029e-18im  -2.85334e-18+5.92892e-18im  -2.81457e-18+1.0037e-17im    6.26015e-18-6.40017e-20im  -4.02022e-18-1.83128e-17im   3.26871e-19-3.07798e-18im  -3.28243e-18+3.61775e-18im  -9.47944e-18-1.56453e-18im   1.81844e-17+2.83749e-18im  -5.03637e-18-1.0721e-18im   -2.25513e-17-1.21393e-17im   1.17651e-17+2.33973e-17im   6.59538e-18+2.3907e-18im   -2.63164e-17+7.46706e-18im   3.99783e-18-3.16376e-18im   1.17666e-17+6.83303e-18im    3.0551e-18+4.69829e-18im   4.39275e-18-8.91115e-18im   1.17666e-17-6.83303e-18im   3.99783e-18+3.16376e-18im  -1.17651e-17-7.53952e-18im   6.59538e-18-2.3907e-18im    9.02289e-18-1.67345e-17im  -2.25513e-17+1.21393e-17im  -5.03637e-18+1.0721e-18im    1.81844e-17-2.83749e-18im  -9.47944e-18+1.56453e-18im  -3.28243e-18-3.61775e-18im   3.26871e-19+3.07798e-18im  -8.02303e-18+9.48533e-18im   6.26015e-18+6.40017e-20im           0.0-1.14136e-17im  -2.85334e-18-5.92892e-18im   7.23023e-19+4.03029e-18im   2.40113e-18-2.87344e-17im  -3.42569e-17-3.63887e-18im  -2.55944e-18+3.23188e-17im   2.08131e-17-5.36003e-18im  -1.03454e-17-1.16715e-17im   4.20171e-18+1.36319e-18im  -8.22387e-18-4.9923e-19im   -2.11585e-18+3.84134e-18im   1.23204e-17-9.68665e-21im    1.0213e-17-1.52664e-17im  -1.01526e-17-1.97211e-17im  -2.04669e-18+7.85756e-18im   8.97271e-18+4.91711e-18im           0.5+9.98774e-18im           0.5+0.0im

Exercise 5

Compare this matrix Array(H) with the one you obtained in Exercise 3, get its eigenvectors and eigenvalues. Try to guess the ordering of $G$-vectors in DFTK.

Exercise 6

Increase the size of the problem, and compare the time spent by DFTK's internal diagonalization algorithms to a full diagonalization of Array(H). Hint: The @belapsed and @benchmark macros (from the BenchmarkTools package) are handy for this task. Note that there are some subtleties with global variables (see the BenchmarkTools docs for details). E.g. to use it to benchmark a function like eigen(H) run it as (note the $):

using BenchmarkTools
@benchmark eigen($H)

Solutions

Exercise 1

If we consider a function $f : [0, 2π] → \mathbb{R}$, to first order

\[f(x + δx) = f(x) + δx f'(x) + O(δx^2)\]

therefore after rearrangement

\[f'(x) = \frac{f(x + δx) - f(x)}{δx} + O(δx).\]

Similarly

\[f''(x) = \frac{f'(x + δx) - f'(x)}{δx} + O(δx),\]

such that overall

\[f''(x) \simeq \frac{f(x + 2δx) - f(x + δx) - f(x + δx) + f(x)}{δx^2} = \frac{f(x + 2δx) - 2f(x + δx) + f(x)}{δx^2}\]

In finite differences we consider a stick basis of vectors

\[\left\{ e_i = (0, …, 0, \underbrace{δx}_\text{$i$-th position}, 0, …, 0) \middle| i = 1, … N \right\}.\]

Keeping in mind the periodic boundary conditions (i.e. $e_0 = e_N$) projecting the Hamiltonian $H$ onto this basis thus yields the proposed structure.

We start off with $N = 100$ to obtain

Hfd = build_finite_differences_matrix(cos, 100)
L, V = eigen(Hfd)
L[1:5]

5-element Vector{Float64}:
 -0.5351640695081414
  0.3429576842587494
  0.8532206682511969
  2.053679933442362
  2.078512110605267

This is already pretty accurate (to about 4 digits) as can be estimated looking at the following convergence plot:

function fconv(N)
    L, V = eigen(build_finite_differences_matrix(cos, N))
    first(L)
end
Nrange = 10:10:100
plot(Nrange, abs.(fconv.(Nrange) .- fconv(200));
     yaxis=:log, legend=false, mark=:x, xlabel="N", ylabel="Absolute error")

Exercise 2

We note that
\[\langle e_G, e_{G'}\rangle = ∫_0^{2π} e_G^\ast(x) e_{G'}(x) d x = 1/2π ∫_0^{2π} e^{i(G'-G)x} d x\]
Since $e^{iy}$ is a periodic function with period $2\pi$, $\int_0^{2\pi} e^{i m y} = \delta_{0,m}$. Therefore if $G≠G'$ we have that $\langle e_G, e_{G'}\rangle = 0$, while $G=G'$ implies $\langle e_G, e_{G'}\rangle = 1$. In summary:
\[\langle e_G, e_{G'}\rangle = δ_{G, G'}\]
Next fo $V(x) = \cos(x)$ we obtain
\[\langle e_G, H e_{G'}\rangle = \frac 1 2 ∫_0^{2π} e_G^\ast(x) H e_{G'}(x) d x\]
We start by applying the Hamiltonian to a plane-wave:
\[H e_{G'}(x) = - \frac 1 2 (-|G|^2) \frac 1 {\sqrt{2π}} e^{iG'x) + cos(x) \frac 1 {\sqrt{2π}} e{iG'x}\]
Then, using the result of the first part of the exercise and the fact that $cos(x) = \frac 1 2 \left(e{ix} + e{-ix}\right)$, we get:
\[\begin{align*} ⟨ e_G, H e_{G'}⟩ &= \frac 1 2 G^2 δ_{G, G'} + \frac 1 {4π} \left(∫_0^{2π} e^{ix ⋅ (G'-G+1)} d x + ∫_0^{2π} e^{ix ⋅ (G'-G-1)} d x \right) \\ &= \frac 1 2 \left(|G|^2 \delta_{G,G'} + \delta_{G, G'+1} + \delta_{G, G'-1}\right) \end{align*}\]
In case a more general $V(x)$ was employed, this potential still has to be periodic over $[0, 2\pi]$ to fit our setting. Assuming sufficient regularity in $V$ we can employ a Fourier series:
\[V(x) = \sum_{G=- \infty}^{\infty} \hat{V}_G e_G(x)\]
where
\[\hat{V}_G = \frac{1}{\sqrt{2π}} ∫_0^{2π} V(x) e^{-iGx} dx = ∫_0^{2π} V(x) e_G^\ast dx .\]
Note that one can change of this as a change of basis from the position basis to the plane-wave basis.
Based on this expansion
\[\begin{align*} ⟨ e_G, V e_{G'} ⟩ &= \left\langle e_G, ∑_{G''} \hat{V}_{G''} \, e_{G'+G''} \right\rangle \\ &= \sum_{G''=-\infty}^\infty \hat{V}_{G''} ⟨ e_G, e_{G'+G''} ⟩ \\ &= \sum_{G''=-\infty}^\infty \hat{V}_{G''} \, δ_{G-G', G''} ⟩ \\ &= \hat{V}_{G-G'} \end{align*}\]
and therefore
\[⟨ e_G, H e_{G'} ⟩ = \frac 1 2 |G|^2 \delta_{G,G'} + \hat{V}_{G-G'},\]
i.e. essentially the Fourier transform of $V$ determines the contribution to the matrix elements of the Hamiltonian.

Exercise 3

The Hamiltonian matrix for the plane waves method can be found this way:

# Plane waves Hamiltonian -½Δ + cos on [0, 2pi].
function build_plane_waves_matrix_cos(N::Integer)
    # Plane wave approximation to -½Δ
    Gsq = [float(i)^2 for i in -N:N]
    # Hamiltonian as derived in Exercise 2:
    1/2 * Tridiagonal(ones(2N), Gsq, ones(2N))
end;

Then we check that the first eigenvalue agrees with the finite-difference case, using $N = 10$:

Hpw_cos = build_plane_waves_matrix_cos(10)
L, V = eigen(Hpw_cos)
L[1:5]

5-element Vector{Float64}:
 -0.5350648522878154
  0.34336012839908336
  0.8536343543207997
  2.0565044112660984
  2.081227363352144

We look at the convergence plot to compare the accuracy for various numbers of plane-waves $N$:

function fconv(N)
    L = eigvals(build_plane_waves_matrix_cos(N))
    first(L)
end

Nrange = 2:10
plot(Nrange, abs.(fconv.(Nrange) .- fconv(200)); yaxis=:log, legend=false,
     ylims=(1e-16,Inf), ylabel="Absolute error", xlabel="N", mark=:x)

Notice how compared to exercise 1 the considered basis size $N$ is much smaller, indicating that plane-wave methods more quickly lead to accurate solutions than finite-difference methods.

Exercise 4

For efficiency reasons the data in Fourier space is not ordered increasingly with $G$. Therefore to plot the Fourier space representation sensibly, we need to sort by ascending values of the $G$ vectors first. For this we extract the Fourier vector of each plane-wave basis function in the index order:

coords_G_vectors = G_vectors_cart(basis, basis.kpoints[1])  # Get coordinates of first and only k-point

# Only keep first component of each vector (because the others are zero for 1D problems):
coords_Gx = [G[1] for G in coords_G_vectors]

p = plot(coords_Gx, real(ψ_fourier); label="real part", xlims=(-10, 10))
plot!(p, coords_Gx, imag(ψ_fourier); label="imaginary part")

The plot is symmetric about the zero (confirming that the orbitals are real) and only takes peaked values, which corresponds to the expected result for a cosine potential.

Exercise 5

To figure out the ordering we consider a small basis and build the Hamiltonian:

basis_small  = PlaneWaveBasis(model; Ecut=5, kgrid=(1, 1, 1))
ham_small = Hamiltonian(basis_small)
H_small = Array(ham_small.blocks[1])
H_small[abs.(H_small) .< 1e-12] .= 0  # Drop numerically zero entries
H_small

7×7 Matrix{ComplexF64}:
 0.0+0.0im          0.5+1.00424e-16im  0.0+0.0im          0.0+0.0im          0.0+0.0im          0.0+0.0im          0.5-1.00424e-16im
 0.5-1.00424e-16im  0.5+0.0im          0.5+1.00424e-16im  0.0+0.0im          0.0+0.0im          0.0+0.0im          0.0+0.0im
 0.0+0.0im          0.5-1.00424e-16im  2.0+0.0im          0.5+1.00424e-16im  0.0+0.0im          0.0+0.0im          0.0+0.0im
 0.0+0.0im          0.0+0.0im          0.5-1.00424e-16im  4.5+0.0im          0.0+0.0im          0.0+0.0im          0.0+0.0im
 0.0+0.0im          0.0+0.0im          0.0+0.0im          0.0+0.0im          4.5+0.0im          0.5+1.00424e-16im  0.0+0.0im
 0.0+0.0im          0.0+0.0im          0.0+0.0im          0.0+0.0im          0.5-1.00424e-16im  2.0+0.0im          0.5+1.00424e-16im
 0.5+1.00424e-16im  0.0+0.0im          0.0+0.0im          0.0+0.0im          0.0+0.0im          0.5-1.00424e-16im  0.5+0.0im

The equivalent version using the build_plane_waves_matrix_cos function is N=3 (both give rice to a 7×7 matrix).

Hother = build_plane_waves_matrix_cos(3)

7×7 LinearAlgebra.Tridiagonal{Float64, Vector{Float64}}:
 4.5  0.5   ⋅    ⋅    ⋅    ⋅    ⋅ 
 0.5  2.0  0.5   ⋅    ⋅    ⋅    ⋅ 
  ⋅   0.5  0.5  0.5   ⋅    ⋅    ⋅ 
  ⋅    ⋅   0.5  0.0  0.5   ⋅    ⋅ 
  ⋅    ⋅    ⋅   0.5  0.5  0.5   ⋅ 
  ⋅    ⋅    ⋅    ⋅   0.5  2.0  0.5
  ⋅    ⋅    ⋅    ⋅    ⋅   0.5  4.5

By comparing the entries we find the ordering is 0,1,2,...,-2,-1, which can also be found by inspecting

first.(G_vectors(basis_small, basis_small.kpoints[1]))

7-element Vector{Int64}:
  0
  1
  2
  3
 -3
 -2
 -1

Both matrices have the same eigenvalues:

maximum(abs, eigvals(H_small) - eigvals(Hother))

1.7763568394002505e-15

and in the eigenvectors we find the same rearrangements in the entries of the eigenvectors of both matrices, matching the DFTK ordering of is 0,1,2,...,-2,-1.

eigvecs(Hother)[:, 1]

7-element Vector{Float64}:
 -0.008461095314567344
  0.08520425570524764
 -0.42353481192309905
  0.7915641575577494
 -0.42353481192310566
  0.08520425570524905
 -0.008461095314567471

eigvecs(H_small)[:, 1]

7-element Vector{ComplexF64}:
  -0.7915641575577493 + 1.5898485476322146e-16im
  0.42353481192310877 - 1.7013307112974292e-16im
 -0.08520425570525011 + 5.1339563909648e-17im
 0.008461095314567624 - 6.797609502050578e-18im
 0.008461095314567069 + 3.3988047510250303e-18im
 -0.08520425570524359 - 1.711318796988132e-17im
   0.4235348119230965 + 0.0im

Notice, that eigenvectors are only defined up to a phase, so the sign may globally be inverted between the two eigenvectors.

Exercise 6

We benchmark the time needed for a full diagonalization (instantiation of the Array plus call of eigen) versus the time needed for running the SCF (i.e. iterative diagonalization using plane waves).

using Printf

for Ecut in 200:200:1600
   basis_time = PlaneWaveBasis(model; Ecut, kgrid=(1, 1, 1))
   t_eigen = @elapsed eigen(Array(Hamiltonian(basis_time).blocks[1]))
   t_scf   = @elapsed self_consistent_field(basis_time; tol=1e-6, callback=identity);
   @printf "%4i  eigen=%8.4fms  scf=%8.4fms\n" Ecut 1000t_eigen 1000t_scf
end

 200  eigen=  2.2267ms  scf=  4.5533ms
 400  eigen=  4.0470ms  scf=  2.9989ms
 600  eigen=  6.0833ms  scf=  2.5595ms
 800  eigen=  9.3928ms  scf=  2.6227ms
1000  eigen= 11.6618ms  scf=  2.7617ms
1200  eigen= 14.1879ms  scf=  2.9341ms
1400  eigen= 16.4986ms  scf=  2.6922ms
1600  eigen= 24.1405ms  scf=  3.1197ms