This page was generated from unit-3.1-parabolic/parabolic.ipynb.

3.1 Parabolic model problem

In this unit we want to turn to instationary problems. And we will start with a very basic setup: implicit Euler time stepping for the convection diffusion equation. After the main part of this tutorial we have supplementary material to extend the case in several regards.

We are solving the unsteady heat equation

\[\text{find } u:[0,T] \to H_{0,D}^1 \quad \int_{\Omega} \partial_t u v + \int_{\Omega} \nabla u \nabla v + b \cdot \nabla u v = \int f v \quad \forall v \in H_{0,D}^1, \quad u(t=0) = u_0\]

with a suitable advective field \(b\) (the wind).

#imports
from ngsolve import *
from netgen.geom2d import SplineGeometry
from ngsolve.webgui import Draw

• Geometry: \((-1,1)^2\)

• Dirichlet boundaries everywhere

• Mesh

from netgen.occ import *
from netgen.webgui import Draw as DrawGeo
shape = Rectangle(2,2).Face().Move((-1,-1,0))
shape.edges.Min(X).name="left"
shape.edges.Max(X).name="right"
shape.edges.Min(Y).name="bottom"
shape.edges.Max(Y).name="top"
mesh = Mesh(OCCGeometry(shape, dim=2).GenerateMesh(maxh=0.25))

fes = H1(mesh, order=3, dirichlet="bottom|right|left|top")
u,v = fes.TnT()
time = 0.0
dt = 0.001

We define the field \(b\) (the wind) as

\[b(x,y) := (2y(1-x^2),-2x(1-y^2)).\]

b = CoefficientFunction((2*y*(1-x*x),-2*x*(1-y*y)))
Draw(b,mesh,"wind", vectors={"grid_size": 32}, order=3)

BaseWebGuiScene

• bilinear forms for

• convection-diffusion stiffness and

• mass matrix separately.

• non-symmetric memory layout for the mass matrix so that a and m have the same sparsity pattern.

a = BilinearForm(fes, symmetric=False)
a += 0.01*grad(u)*grad(v)*dx + b*grad(u)*v*dx
a.Assemble()

m = BilinearForm(fes, symmetric=False)
m += u*v*dx
m.Assemble()

<ngsolve.comp.BilinearForm at 0x7ff09b4dd730>

Implicit Euler method

\[\underbrace{(M + \Delta t A)}_{M^\ast} u^{n+1} = M u^n + \Delta tf^{n+1}\]

or in an incremental form:

\[M^\ast (u^{n+1} - u^n) = - \Delta t A u^n + \Delta tf^{n+1}.\]

• Incremental form: \(u^{n+1} - u^n\) has homogeneous boundary conditions (unless boundary conditions are time-dependent).

• For the time stepping method: set up linear combinations of matrices.

• (Only) if the sparsity pattern of the matrices agree we can copy the pattern and sum up the entries.

First, we create a matrix of same format as m.mat and compare number of non-zero entries and sparsity pattern:

mstar = m.mat.CreateMatrix()
print(f"m.mat.nze = {m.mat.nze}, a.mat.nze={a.mat.nze}, mstar.nze={mstar.nze}")
from helper import ShowPattern
print("sparsity pattern a.mat:")
ShowPattern(a.mat,binarize=True)

m.mat.nze = 11104, a.mat.nze=11104, mstar.nze=11104
sparsity pattern a.mat:

print("sparsity pattern mstar:")
ShowPattern(mstar,binarize=True)

sparsity pattern mstar:

To access the entries we use the vector of nonzero-entries:

print(f"mstar.nze={mstar.nze}, len(mstar.AsVector())={len(mstar.AsVector())}")

mstar.nze=11104, len(mstar.AsVector())=11104

print(mstar.AsVector())

 0.00520833
 0.00260417
 0.00260417
 -0.000520833
 8.68056e-05
 -0.000520833
 8.68056e-05
 -0.000260417
 -1.32137e-19
 0.000173611
 0.00870064
 0.00221203
 0.00213829
 0.00435032
 -0.000442406
 7.37343e-05
 -0.000427658
 7.12763e-05
 -0.000870064
 0.000145011
 -0.000221203
 1.15196e-19
 -0.000213829
 -1.10114e-19
 0.000147469
 0.000142553
 0.00520833
 0.00260417
 0.00260417
 -0.000520833
 8.68056e-05
 -0.000520833
 8.68056e-05
 -0.000260417
 1.32137e-19
 0.000173611
 0.00811466
 0.00203707
 0.00202026
 0.00405733
 -0.000407414
 6.79023e-05
 -0.000404052
 6.73421e-05
 -0.000811466
 0.000135244
 -0.000203707
 1.04185e-19
 -0.000202026
 -1.01644e-19
 0.000135805
 0.000134684
 0.00260417
 0.019115
 0.00322599
 0.00633153
 0.00695335
 -0.000520833
 -8.68056e-05
 -0.000260417
 -1.42302e-19
 -0.000645197
 0.000107533
 -0.00126631
 0.000211051
 -0.00139067
 0.000231778
 -0.000322599
 -1.66018e-19
 -0.000372736
 1.91429e-19
 0.000173611
 0.000215066
 0.000248491
 0.00322599
 0.019175
 0.00276575
 0.00682174
 0.0063615
 -0.000645197
 -0.000107533
 -0.000322599
 -1.74489e-19
 -0.000553149
 9.21915e-05
 -0.00136435
 0.000227391
 -0.0012723
 0.00021205
 -0.000276575
 -1.42302e-19
 -0.000359576
 1.84653e-19
 0.000215066
 0.000184383
 0.000239717
 0.00276575
 0.0161661
 0.00254703
 0.005536
 0.00531728
 -0.000553149
 -9.21915e-05
 -0.000276575
 -1.49078e-19
 -0.000509407
 8.49011e-05
 -0.0011072
 0.000184533
 -0.00106346
 0.000177243
 -0.000254703
 -1.32137e-19
 -0.000277025
 1.42302e-19
 0.000184383
 0.000169802
 0.000184683
 0.00254703
 0.0144748
 0.00230512
 0.0049323
 0.00469039
 -0.000509407
 -8.49011e-05
 -0.000254703
 -1.40607e-19
 -0.000461025
 7.68375e-05
 -0.000986459
 0.00016441
 -0.000938077
 0.000156346
 -0.000230512
 -1.20279e-19
 -0.000238526
 1.18585e-19
 0.000169802
 0.000153675
 0.000159017
 0.00230512
 0.0128165
 0.00206284
 0.0043454
 0.00410312
 -0.000461025
 -7.68375e-05
 -0.000230512
 -1.23667e-19
 -0.000412568
 6.87613e-05
 -0.000869081
 0.000144847
 -0.000820623
 0.000136771
 -0.000206284
 -1.05032e-19
 -0.000204028
 1.06726e-19
 0.000153675
 0.000137523
 0.000136019
 0.00206284
 0.0122623
 0.00211946
 0.00401168
 0.00406831
 -0.000412568
 -6.87613e-05
 -0.000206284
 -1.10114e-19
 -0.000423892
 7.06487e-05
 -0.000802337
 0.000133723
 -0.000813661
 0.00013561
 -0.000211946
 -1.09267e-19
 -0.000194884
 9.74088e-20
 0.000137523
 0.000141297
 0.000129923
 0.00221203
 0.00211946
 0.0123988
 0.00398737
 0.00407994
 -0.000442406
 -7.37343e-05
 -0.000221203
 -5.0822e-21
 -0.000423892
 -7.06487e-05
 -0.000211946
 -1.15196e-19
 -0.000797474
 0.000132912
 -0.000815988
 0.000135998
 -0.000186791
 9.48677e-20
 0.000141297
 0.000147469
 0.000124527
 0.00213829
 0.010775
 0.00163783
 0.00374969
 0.00324924
 -0.000427658
 -7.12763e-05
 -0.000213829
 -1.16891e-19
 -0.000327566
 5.45944e-05
 -0.000749939
 0.00012499
 -0.000649847
 0.000108308
 -0.000163783
 -8.47033e-20
 -0.00016114
 8.30092e-20
 0.000142553
 0.000109189
 0.000107427
 0.00163783
 0.010437
 0.00201741
 0.00320108
 0.00358066
 -0.000327566
 -5.45944e-05
 -0.000163783
 -8.97855e-20
 -0.000403482
 6.7247e-05
 -0.000640216
 0.000106703
 -0.000716132
 0.000119355
 -0.000201741
 -1.04185e-19
 -0.000156325
 7.87741e-20
 0.000109189
 0.000134494
 0.000104217
 0.00201741
 0.012647
 0.0022013
 0.00412219
 0.00430608
 -0.000403482
 -6.7247e-05
 -0.000201741
 -1.10114e-19
 -0.00044026
 7.33767e-05
 -0.000824437
 0.000137406
 -0.000861216
 0.000143536
 -0.00022013
 -1.10114e-19
 -0.000210478
 1.0842e-19
 0.000134494
 0.000146753
 0.000140318
 0.0022013
 0.0137116
 0.00232766
 0.00452815
 0.00465451
 -0.00044026
 -7.33767e-05
 -0.00022013
 -1.18585e-19
 -0.000465532
 7.75887e-05
 -0.00090563
 0.000150938
 -0.000930902
 0.00015515
 -0.000232766
 -1.20279e-19
 -0.000232685
 1.18585e-19
 0.000146753
 0.000155177
 0.000155123
 0.00232766
 0.0142085
 0.00234657
 0.00475767
 0.00477658
 -0.000465532
 -7.75887e-05
 -0.000232766
 -1.25361e-19
 -0.000469313
 7.82189e-05
 -0.000951534
 0.000158589
 -0.000955315
 0.000159219
 -0.000234657
 -1.20279e-19
 -0.000243001
 1.25361e-19
 0.000155177
 0.000156438
 0.000162001
 0.00234657
 0.0139663
 0.00221218
 0.00477096
 0.00463658
 -0.000469313
 -7.82189e-05
 -0.000234657
 -1.27055e-19
 -0.000442437
 7.37395e-05
 -0.000954193
 0.000159032
 -0.000927316
 0.000154553
 -0.000221218
 -1.13502e-19
 -0.00024244
 1.25361e-19
 0.000156438
 0.000147479
 0.000161626
 0.00260417
 0.00221218
 0.0159643
 0.00576996
 0.00537798
 -0.000520833
 -8.68056e-05
 -0.000260417
 -8.47033e-21
 -0.000442437
 -7.37395e-05
 -0.000221218
 -1.20279e-19
 -0.00115399
 0.000192332
 -0.0010756
 0.000179266
 -0.000316579
 -1.59242e-19
 0.000147479
 0.000173611
 0.000211053
 0.00260417
 0.00576996
 0.020889
 0.00217575
 0.00566461
 0.00467456
 -0.000260417
 -1.40607e-19
 -0.000520833
 -8.68056e-05
 -0.00115399
 -0.000192332
 -0.000316579
 -1.71101e-19
 -0.000435149
 7.25248e-05
 -0.00113292
 0.00018882
 -0.000934911
 0.000155819
 -0.000217575
 -1.11808e-19
 -0.000249881
 1.28749e-19
 0.000173611
 0.00014505
 0.000211053
 0.000166587
 0.00217575
 0.0135856
 0.00255513
 0.00423766
 0.00461705
 -0.000435149
 -7.25248e-05
 -0.000217575
 -1.18585e-19
 -0.000511026
 8.5171e-05
 -0.000847533
 0.000141255
 -0.00092341
 0.000153902
 -0.000255513
 -1.33831e-19
 -0.000206192
 1.02491e-19
 0.00014505
 0.000170342
 0.000137461
 0.00255513
 0.0154444
 0.00263583
 0.00508638
 0.00516708
 -0.000511026
 -8.5171e-05
 -0.000255513
 -1.40607e-19
 -0.000527166
 8.78611e-05
 -0.00101728
 0.000169546
 -0.00103342
 0.000172236
 -0.000263583
 -1.35525e-19
 -0.000253125
 1.30443e-19
 0.000170342
 0.000175722
 0.00016875
 0.00263583
 0.0150836
 0.00241342
 0.00512838
 0.00490597
 -0.000527166
 -8.78611e-05
 -0.000263583
 -1.42302e-19
 -0.000482684
 8.04474e-05
 -0.00102568
 0.000170946
 -0.000981194
 0.000163532
 -0.000241342
 -1.21973e-19
 -0.000249255
 1.30443e-19
 0.000175722
 0.000160895
 0.00016617
 0.00241342
 0.0134244
 0.00213897
 0.00457325
 0.0042988
 -0.000482684
 -8.04474e-05
 -0.000241342
 -1.28749e-19
 -0.000427794
 7.1299e-05
 -0.00091465
 0.000152442
 -0.00085976
 0.000143293
 -0.000213897
 -1.09267e-19
 -0.000215983
 1.10961e-19
 0.000160895
 0.000142598
 0.000143989
 0.00213897
 0.0116778
 0.00188709
 0.00395182
 0.00369994
 -0.000427794
 -7.1299e-05
 -0.000213897
 -1.15196e-19
 -0.000377417
 6.29029e-05
 -0.000790364
 0.000131727
 -0.000739987
 0.000123331
 -0.000188709
 -9.48677e-20
 -0.000181285
 9.40207e-20
 0.000142598
 0.000125806
 0.000120857
 0.00203707
 0.00188709
 0.0114283
 0.00367708
 0.00382706
 -0.000407414
 -6.79023e-05
 -0.000203707
 -5.0822e-21
 -0.000377417
 -6.29029e-05
 -0.000188709
 -1.05032e-19
 -0.000735415
 0.000122569
 -0.000765412
 0.000127569
 -0.000178999
 9.14796e-20
 0.000125806
 0.000135805
 0.000119333
 0.00202026
 0.0112419
 0.00182934
 0.00379161
 0.00360069
 -0.000404052
 -6.73421e-05
 -0.000202026
 -1.10114e-19
 -0.000365868
 6.09781e-05
 -0.000758322
 0.000126387
 -0.000720138
 0.000120023
 -0.000182934
 -9.40207e-20
 -0.000177135
 9.06325e-20
 0.000134684
 0.000121956
 0.00011809
 0.00182934
 0.0111447
 0.00200449
 0.00356787
 0.00374302
 -0.000365868
 -6.09781e-05
 -0.000182934
 -1.01644e-19
 -0.000400898
 6.68164e-05
 -0.000713575
 0.000118929
 -0.000748605
 0.000124767
 -0.000200449
 -1.04185e-19
 -0.000173853
 8.97855e-20
 0.000121956
 0.000133633
 0.000115902
 0.00200449
 0.0122201
 0.00214151
 0.00396856
 0.00410558
 -0.000400898
 -6.68164e-05
 -0.000200449
 -1.0842e-19
 -0.000428302
 7.13837e-05
 -0.000793712
 0.000132285
 -0.000821116
 0.000136853
 -0.000214151
 -1.10961e-19
 -0.000196407
 1.01644e-19
 0.000133633
 0.000142767
 0.000130938
 0.00214151
 0.0127965
 0.0021674
 0.00423083
 0.00425672
 -0.000428302
 -7.13837e-05
 -0.000214151
 -1.18585e-19
 -0.00043348
 7.22467e-05
 -0.000846165
 0.000141028
 -0.000851343
 0.000141891
 -0.00021674
 -1.13502e-19
 -0.000208932
 1.06726e-19
 0.000142767
 0.000144493
 0.000139288
 0.0021674
 0.0138446
 0.00240048
 0.00452183
 0.00475491
 -0.00043348
 -7.22467e-05
 -0.00021674
 -1.20279e-19
 -0.000480096
 8.0016e-05
 -0.000904366
 0.000150728
 -0.000950981
 0.000158497
 -0.000240048
 -1.25361e-19
 -0.000235443
 1.21973e-19
 0.000144493
 0.000160032
 0.000156962
 0.00240048
 0.0174193
 0.00310554
 0.00630915
 0.00560409
 -0.000480096
 -8.0016e-05
 -0.000240048
 -1.32137e-19
 -0.000621108
 0.000103518
 -0.00126183
 0.000210305
 -0.00112082
 0.000186803
 -0.000310554
 -1.60936e-19
 -0.000320361
 -1.64324e-19
 0.000160032
 0.000207036
 0.000213574
 0.00260417
 0.00633153
 0.00310554
 0.0188741
 0.0068329
 -0.000260417
 -6.77626e-21
 -0.000520833
 -8.68056e-05
 -0.00126631
 -0.000211051
 -0.000372736
 -1.01644e-20
 -0.000621108
 -0.000103518
 -0.000310554
 -1.71101e-19
 -0.00136658
 0.000227763
 0.000173611
 0.000207036
 0.000248491
 0.00695335
 0.00682174
 0.00630915
 0.0068329
 0.046383
 0.00682739
 0.00630521
 0.00633322
 -0.000322599
 -6.77626e-21
 -0.000372736
 -2.06676e-19
 -0.00139067
 -0.000231778
 -0.00136435
 -0.000227391
 -0.000359576
 -1.35525e-20
 -0.000310554
 -6.77626e-21
 -0.00126183
 -0.000210305
 -0.000320361
 -1.72795e-19
 -0.00136658
 -0.000227763
 -0.00136548
 0.00022758
 -0.00126104
 0.000210174
 -0.00126664
 0.000211107
 -0.000323163
 -1.6263e-19
 -0.00031016
 1.60936e-19
 0.000215066
 0.000239717
 0.000207036
 0.000248491
 0.000213574
 0.000215442
 0.000206773
 0.0063615
 0.005536
 0.00682739
 0.03597
 0.00557911
 0.00562163
 0.00604439
 -0.000276575
 -8.47033e-21
 -0.000359576
 -1.93124e-19
 -0.0012723
 -0.00021205
 -0.0011072
 -0.000184533
 -0.000277025
 -8.47033e-21
 -0.00136548
 -0.00022758
 -0.000323163
 -1.74489e-19
 -0.00111582
 0.00018597
 -0.00112433
 0.000187388
 -0.00120888
 0.00020148
 -0.000280887
 -1.49078e-19
 -0.000281276
 -1.4569e-19
 0.000184383
 0.000239717
 0.000184683
 0.000187258
 0.000215442
 0.000187518
 0.00531728
 0.0049323
 0.00557911
 0.0311221
 0.00483155
 0.0054122
 0.00504963
 -0.000254703
 -6.77626e-21
 -0.000277025
 -1.49078e-19
 -0.00106346
 -0.000177243
 -0.000986459
 -0.00016441
 -0.000238526
 -8.47033e-21
 -0.00111582
 -0.00018597
 -0.000280887
 -1.5416e-19
 -0.000966311
 0.000161052
 -0.00108244
 0.000180407
 -0.00100993
 0.000168321
 -0.000244629
 -1.25361e-19
 -0.000260334
 1.30443e-19
 0.000169802
 0.000184683
 0.000159017
 0.000187258
 0.000163086
 0.000173556
 0.00469039
 0.0043454
 0.00483155
 0.0269776
 0.00414725
 0.00431187
 0.00465118
 -0.000230512
 -6.77626e-21
 -0.000238526
 -1.30443e-19
 -0.000938077
 -0.000156346
 -0.000869081
 -0.000144847
 -0.000204028
 -5.0822e-21
 -0.000966311
 -0.000161052
 -0.000244629
 -1.32137e-19
 -0.000829451
 0.000138242
 -0.000862373
 0.000143729
 -0.000930236
 0.000155039
 -0.000210697
 -1.0842e-19
 -0.000220489
 -1.13502e-19
 0.000153675
 0.000159017
 0.000136019
 0.000140465
 0.000163086
 0.000146993
 0.00410312
 0.00401168
 0.00414725
 0.0231507
 0.00365334
 0.00381889
 0.00341641
 -0.000206284
 -6.77626e-21
 -0.000204028
 -1.11808e-19
 -0.000820623
 -0.000136771
 -0.000802337
 -0.000133723
 -0.000194884
 -3.38813e-21
 -0.000829451
 -0.000138242
 -0.000210697
 -1.15196e-19
 -0.000730668
 0.000121778
 -0.000763778
 0.000127296
 -0.000683282
 0.00011388
 -0.00017045
 -8.63974e-20
 -0.000171191
 8.80914e-20
 0.000137523
 0.000136019
 0.000129923
 0.000140465
 0.000113633
 0.000114128
 0.00406831
 0.00398737
 0.00365334
 0.0233281
 0.0040747
 0.00352106
 0.00402335
 -0.000211946
 -3.38813e-21
 -0.000194884
 -1.05032e-19
 -0.000813661
 -0.00013561
 -0.000797474
 -0.000132912
 -0.000186791
 -6.77626e-21
 -0.000730668
 -0.000121778
 -0.00017045
 -9.31736e-20
 -0.00081494
 0.000135823
 -0.000704212
 0.000117369
 -0.000804671
 0.000134112
 -0.000220679
 -1.10114e-19
 -0.000181657
 9.06325e-20
 0.000141297
 0.000129923
 0.000124527
 0.000113633
 0.000147119
 0.000121104
 0.00435032
 0.00407994
 0.00374969
 0.0040747
 0.0236386
 0.00339428
 0.00398966
 -0.000221203
 -1.23667e-19
 -0.000213829
 -3.38813e-21
 -0.000870064
 -0.000145011
 -0.000186791
 -1.01644e-19
 -0.000815988
 -0.000135998
 -0.000749939
 -0.00012499
 -0.00016114
 -8.47033e-21
 -0.00081494
 -0.000135823
 -0.000220679
 -1.18585e-19
 -0.000678856
 0.000113143
 -0.000797933
 0.000132989
 -0.000178288
 -8.89385e-20
 0.000147469
 0.000124527
 0.000142553
 0.000107427
 0.000147119
 0.000118858
 0.00324924
 0.00320108
 0.00339428
 0.0167916
 0.0033637
 0.00358333
 -0.000163783
 -5.0822e-21
 -0.00016114
 -8.72444e-20
 -0.000649847
 -0.000108308
 -0.000640216
 -0.000106703
 -0.000156325
 -6.77626e-21
 -0.000678856
 -0.000113143
 -0.000178288
 -9.65618e-20
 -0.00067274
 0.000112123
 -0.000716666
 0.000119444
 -0.000180045
 -8.97855e-20
 0.000109189
 0.000107427
 0.000104217
 0.000118858
 0.00012003
 0.00358066
 0.00412219
 0.0033637
 0.0238428
 0.00424373
 0.00409703
 0.00443553
 -0.000201741
 -6.77626e-21
 -0.000156325
 -8.47033e-20
 -0.000716132
 -0.000119355
 -0.000824437
 -0.000137406
 -0.000210478
 -3.38813e-21
 -0.00067274
 -0.000112123
 -0.000180045
 -9.82558e-20
 -0.000848746
 0.000141458
 -0.000819406
 0.000136568
 -0.000887106
 0.000147851
 -0.000213896
 -1.10961e-19
 -0.000229658
 1.20279e-19
 0.000134494
 0.000104217
 0.000140318
 0.000142597
 0.00012003
 0.000153105
 0.00430608
 0.00452815
 0.00424373
 0.0269407
 0.00468238
 0.0044819
 0.00469848
 -0.00022013
 -6.77626e-21
 -0.000210478
 -1.15196e-19
 -0.000861216
 -0.000143536
 -0.00090563
 -0.000150938
 -0.000232685
 -3.38813e-21
 -0.000848746
 -0.000141458
 -0.000213896
 -1.18585e-19
 -0.000936476
 0.000156079
 -0.00089638
 0.000149397
 -0.000939696
 0.000156616
 -0.000235553
 -1.20279e-19
 -0.000234294
 1.20279e-19
 0.000146753
 0.000140318
 0.000155123
 0.000142597
 0.000157036
 0.000156196
 0.00465451
 0.00475767
 0.00468238
 0.029058
 0.00495599
 0.00491851
 0.00508895
 -0.000232766
 -6.77626e-21
 -0.000232685
 -1.23667e-19
 -0.000930902
 -0.00015515
 -0.000951534
 -0.000158589
 -0.000243001
 -3.38813e-21
 -0.000936476
 -0.000156079
 -0.000235553
 -1.25361e-19
 -0.000991198
 0.0001652
 -0.000983702
 0.00016395
 -0.00101779
 0.000169632
 -0.000252598
 -1.30443e-19
 -0.000256297
 1.32137e-19
 0.000155177
 0.000155123
 0.000162001
 0.000157036
 0.000168399
 0.000170865
 0.00477658
 0.00477096
 0.00495599
 0.0296174
 0.00492912
 0.005103
 0.00508175
 -0.000234657
 -5.0822e-21
 -0.000243001
 -1.30443e-19
 -0.000955315
 -0.000159219
 -0.000954193
 -0.000159032
 -0.00024244
 -1.18585e-20
 -0.000991198
 -0.0001652
 -0.000252598
 -1.37219e-19
 -0.000985824
 0.000164304
 -0.0010206
 0.0001701
 -0.00101635
 0.000169392
 -0.000250472
 -1.30443e-19
 -0.000257702
 1.30443e-19
 0.000156438
 0.000162001
 0.000161626
 0.000168399
 0.000166982
 0.000171801
 0.00463658
 0.00537798
 0.00566461
 0.00492912
 0.0299294
 0.00465762
 0.00466353
 -0.000221218
 -3.38813e-21
 -0.00024244
 -1.32137e-19
 -0.000927316
 -0.000154553
 -0.000316579
 -1.35525e-20
 -0.0010756
 -0.000179266
 -0.00113292
 -0.00018882
 -0.000249881
 -8.47033e-21
 -0.000985824
 -0.000164304
 -0.000250472
 -1.37219e-19
 -0.000931524
 0.000155254
 -0.000932707
 0.000155451
 -0.000215881
 -1.10961e-19
 0.000147479
 0.000161626
 0.000211053
 0.000166587
 0.000166982
 0.000143921
 0.00467456
 0.00423766
 0.00465762
 0.0221097
 0.0042215
 0.00431839
 -0.000217575
 -5.0822e-21
 -0.000249881
 -1.37219e-19
 -0.000934911
 -0.000155819
 -0.000847533
 -0.000141255
 -0.000206192
 -6.77626e-21
 -0.000931524
 -0.000155254
 -0.000215881
 -1.18585e-19
 -0.0008443
 0.000140717
 -0.000863679
 0.000143946
 -0.000215958
 -1.11808e-19
 0.00014505
 0.000137461
 0.000166587
 0.000143921
 0.000143972
 0.00461705
 0.00508638
 0.0042215
 0.0306934
 0.00556026
 0.0051694
 0.00603883
 -0.000255513
 -6.77626e-21
 -0.000206192
 -1.10114e-19
 -0.00092341
 -0.000153902
 -0.00101728
 -0.000169546
 -0.000253125
 -6.77626e-21
 -0.0008443
 -0.000140717
 -0.000215958
 -1.18585e-19
 -0.00111205
 0.000185342
 -0.00103388
 0.000172313
 -0.00120777
 0.000201294
 -0.000302901
 -1.52466e-19
 -0.000300982
 1.52466e-19
 0.000170342
 0.000137461
 0.00016875
 0.000201934
 0.000143972
 0.000200655
 0.00516708
 0.00512838
 0.00556026
 0.032842
 0.00508719
 0.00573237
 0.00616674
 -0.000263583
 -5.0822e-21
 -0.000253125
 -1.37219e-19
 -0.00103342
 -0.000172236
 -0.00102568
 -0.000170946
 -0.000249255
 -6.77626e-21
 -0.00111205
 -0.000185342
 -0.000302901
 -1.64324e-19
 -0.00101744
 0.000169573
 -0.00114647
 0.000191079
 -0.00123335
 0.000205558
 -0.000259464
 -1.33831e-19
 -0.000313773
 -1.59242e-19
 0.000175722
 0.00016875
 0.00016617
 0.000172976
 0.000201934
 0.000209182
 0.00490597
 0.00457325
 0.00508719
 0.0286919
 0.00440436
 0.0050356
 0.00468549
 -0.000241342
 -5.0822e-21
 -0.000249255
 -1.35525e-19
 -0.000981194
 -0.000163532
 -0.00091465
 -0.000152442
 -0.000215983
 -5.0822e-21
 -0.00101744
 -0.000169573
 -0.000259464
 -1.40607e-19
 -0.000880872
 0.000146812
 -0.00100712
 0.000167853
 -0.000937098
 0.000156183
 -0.000224453
 -1.13502e-19
 -0.000244096
 1.23667e-19
 0.000160895
 0.00016617
 0.000143989
 0.000172976
 0.000149635
 0.000162731
 0.0042988
 0.00395182
 0.00440436
 0.0244449
 0.00370928
 0.00421434
 0.00386625
 -0.000213897
 -1.69407e-21
 -0.000215983
 -1.18585e-19
 -0.00085976
 -0.000143293
 -0.000790364
 -0.000131727
 -0.000181285
 -5.0822e-21
 -0.000880872
 -0.000146812
 -0.000224453
 -1.20279e-19
 -0.000741857
 0.000123643
 -0.000842869
 0.000140478
 -0.000773249
 0.000128875
 -0.000189643
 -9.74088e-20
 -0.000196981
 1.01644e-19
 0.000142598
 0.000143989
 0.000120857
 0.000149635
 0.000126429
 0.000131321
 0.00369994
 0.00367708
 0.00370928
 0.0207168
 0.00328557
 0.00337292
 0.00297206
 -0.000188709
 -5.0822e-21
 -0.000181285
 -9.65618e-20
 -0.000739987
 -0.000123331
 -0.000735415
 -0.000122569
 -0.000178999
 -3.38813e-21
 -0.000741857
 -0.000123643
 -0.000189643
 -1.01644e-19
 -0.000657114
 0.000109519
 -0.000674584
 0.000112431
 -0.000594413
 9.90688e-05
 -0.000149558
 -7.708e-20
 -0.000147649
 7.28448e-20
 0.000125806
 0.000120857
 0.000119333
 0.000126429
 9.97053e-05
 9.84323e-05
 0.00405733
 0.00382706
 0.00379161
 0.00328557
 0.0211901
 0.00325213
 0.00297636
 -0.000203707
 -1.10114e-19
 -0.000202026
 -5.0822e-21
 -0.000811466
 -0.000135244
 -0.000178999
 -9.65618e-20
 -0.000765412
 -0.000127569
 -0.000758322
 -0.000126387
 -0.000177135
 -6.77626e-21
 -0.000657114
 -0.000109519
 -0.000149558
 -8.13152e-20
 -0.000650426
 0.000108404
 -0.000595272
 9.9212e-05
 -0.000148078
 -7.53859e-20
 0.000135805
 0.000119333
 0.000134684
 0.00011809
 9.97053e-05
 9.87187e-05
 0.00360069
 0.00356787
 0.00325213
 0.0202039
 0.0035649
 0.00293637
 0.00328196
 -0.000182934
 -3.38813e-21
 -0.000177135
 -9.74088e-20
 -0.000720138
 -0.000120023
 -0.000713575
 -0.000118929
 -0.000173853
 -5.0822e-21
 -0.000650426
 -0.000108404
 -0.000148078
 -7.96211e-20
 -0.000712981
 0.00011883
 -0.000587274
 9.7879e-05
 -0.000656392
 0.000109399
 -0.000182637
 -9.48677e-20
 -0.000145559
 7.36919e-20
 0.000121956
 0.00011809
 0.000115902
 9.87187e-05
 0.000121758
 9.70393e-05
 0.00374302
 0.00396856
 0.0035649
 0.0229321
 0.00402299
 0.00393257
 0.00370003
 -0.000200449
 -5.0822e-21
 -0.000173853
 -9.48677e-20
 -0.000748605
 -0.000124767
 -0.000793712
 -0.000132285
 -0.000196407
 -6.77626e-21
 -0.000712981
 -0.00011883
 -0.000182637
 -9.99499e-20
 -0.000804598
 0.0001341
 -0.000786515
 0.000131086
 -0.000740005
 0.000123334
 -0.000205892
 -1.07573e-19
 -0.000187365
 -9.65618e-20
 0.000133633
 0.000115902
 0.000130938
 0.000137261
 0.000121758
 0.00012491
 0.00410558
 0.00423083
 0.00402299
 0.0251482
 0.00428817
 0.00418036
 0.00432029
 -0.000214151
 -5.0822e-21
 -0.000196407
 -1.06726e-19
 -0.000821116
 -0.000136853
 -0.000846165
 -0.000141028
 -0.000208932
 -5.0822e-21
 -0.000804598
 -0.0001341
 -0.000205892
 -1.13502e-19
 -0.000857634
 0.000142939
 -0.000836071
 0.000139345
 -0.000864058
 0.00014401
 -0.000219886
 -1.13502e-19
 -0.000212144
 1.09267e-19
 0.000142767
 0.000130938
 0.000139288
 0.000137261
 0.00014659
 0.000141429
 0.00425672
 0.00452183
 0.00428817
 0.0256547
 0.00440429
 0.00416632
 0.00401733
 -0.00021674
 -3.38813e-21
 -0.000208932
 -1.15196e-19
 -0.000851343
 -0.000141891
 -0.000904366
 -0.000150728
 -0.000235443
 -6.77626e-21
 -0.000857634
 -0.000142939
 -0.000219886
 -1.18585e-19
 -0.000880858
 0.00014681
 -0.000833263
 0.000138877
 -0.000803465
 0.000133911
 -0.000204987
 -1.03338e-19
 -0.000196746
 9.99499e-20
 0.000144493
 0.000139288
 0.000156962
 0.00014659
 0.000136658
 0.000131164
 0.00475491
 0.00560409
 0.00630521
 0.00440429
 0.0306267
 0.00530496
 0.00425323
 -0.000240048
 -8.47033e-21
 -0.000235443
 -1.28749e-19
 -0.000950981
 -0.000158497
 -0.000320361
 -3.38813e-21
 -0.00112082
 -0.000186803
 -0.00126104
 -0.000210174
 -0.00031016
 -6.77626e-21
 -0.000880858
 -0.00014681
 -0.000204987
 -1.13502e-19
 -0.00106099
 0.000176832
 -0.000850645
 0.000141774
 -0.000220336
 -1.15196e-19
 0.000160032
 0.000156962
 0.000213574
 0.000136658
 0.000146891
 0.000206773
 0.00562163
 0.0054122
 0.0342579
 0.00596138
 0.00528001
 0.00622731
 0.00575537
 -0.000280887
 -3.38813e-21
 -0.00112433
 -0.000187388
 -0.000281276
 -1.52466e-19
 -0.00108244
 -0.000180407
 -0.000260334
 -8.47033e-21
 -0.00119228
 0.000198713
 -0.001056
 0.000176
 -0.00124546
 0.000207577
 -0.00115107
 0.000191846
 -0.000314861
 1.59242e-19
 -0.000267667
 -1.38913e-19
 -0.00030787
 1.55854e-19
 0.000187258
 0.000187518
 0.000173556
 0.000209908
 0.000205246
 0.000178445
 0.00633322
 0.00604439
 0.00530496
 0.00596138
 0.033982
 0.0046964
 0.00564166
 -0.000323163
 -1.35525e-20
 -0.00031016
 -1.67713e-19
 -0.00126664
 -0.000211107
 -0.000281276
       0
 -0.00120888
 -0.00020148
 -0.00106099
 -0.000176832
 -0.000220336
 -1.20279e-19
 -0.00119228
 -0.000198713
 -0.000314861
 -6.77626e-21
 -0.000939281
 0.000156547
 -0.00112833
 0.000188055
 -0.000249304
 1.23667e-19
 0.000215442
 0.000187518
 0.000146891
 0.000206773
 0.000166203
 0.000209908
 0.00431187
 0.00381889
 0.0245706
 0.00349111
 0.00447968
 0.00398674
 0.00448233
 -0.000210697
 -3.38813e-21
 -0.000862373
 -0.000143729
 -0.000220489
 -1.21973e-19
 -0.000763778
 -0.000127296
 -0.000171191
 -5.0822e-21
 -0.000698223
 0.00011637
 -0.000895935
 0.000149323
 -0.000797348
 0.000132891
 -0.000896466
 0.000149411
 -0.00017792
 -8.97855e-20
 -0.000227479
 1.15196e-19
 -0.000220754
 -1.13502e-19
 0.000140465
 0.000114128
 0.000146993
 0.000118613
 0.000147169
 0.000151652
 0.00341641
 0.00352106
 0.00349111
 0.0177034
 0.00365608
 0.00361871
 -0.00017045
 -3.38813e-21
 -0.000171191
 -9.48677e-20
 -0.000683282
 -0.00011388
 -0.000704212
 -0.000117369
 -0.000181657
 -6.77626e-21
 -0.000698223
 -0.00011637
 -0.00017792
 -9.57147e-20
 -0.000731215
 0.000121869
 -0.000723742
 0.000120624
 -0.000183951
 -9.31736e-20
 0.000113633
 0.000114128
 0.000121104
 0.000122634
 0.000118613
 0.00402335
 0.00398966
 0.00358333
 0.00409703
 0.00365608
 0.0282833
 0.00469546
 0.00423839
 -0.000220679
 -5.0822e-21
 -0.000181657
 -9.82558e-20
 -0.000804671
 -0.000134112
 -0.000178288
 -5.0822e-21
 -0.000797933
 -0.000132989
 -0.000180045
 -6.77626e-21
 -0.000716666
 -0.000119444
 -0.000819406
 -0.000136568
 -0.000229658
 -6.77626e-21
 -0.000731215
 -0.000121869
 -0.000183951
 -9.82558e-20
 -0.000939092
 0.000156515
 -0.000847678
 0.00014128
 -0.000239888
 -1.18585e-19
 0.000147119
 0.000121104
 0.000118858
 0.00012003
 0.000122634
 0.000153105
 0.000159925
 0.00443553
 0.0044819
 0.00469546
 0.0276011
 0.00475365
 0.00461134
 0.00462317
 -0.000213896
 -8.47033e-21
 -0.000229658
 -1.25361e-19
 -0.000887106
 -0.000147851
 -0.00089638
 -0.000149397
 -0.000234294
 -8.47033e-21
 -0.000939092
 -0.000156515
 -0.000239888
 -1.32137e-19
 -0.000950731
 0.000158455
 -0.000922269
 0.000153711
 -0.000924634
 0.000154106
 -0.000241071
 -1.23667e-19
 -0.000221246
 1.15196e-19
 0.000142597
 0.000156196
 0.000153105
 0.000160714
 0.000159925
 0.000147497
 0.00469848
 0.00491851
 0.00475365
 0.0297498
 0.0051953
 0.00498109
 0.00520272
 -0.000235553
 -8.47033e-21
 -0.000234294
 -1.23667e-19
 -0.000939696
 -0.000156616
 -0.000983702
 -0.00016395
 -0.000256297
 -5.0822e-21
 -0.000950731
 -0.000158455
 -0.000241071
 -1.32137e-19
 -0.00103906
 0.000173177
 -0.000996219
 0.000166036
 -0.00104054
 0.000173424
 -0.000263233
 -1.37219e-19
 -0.000257039
 1.32137e-19
 0.000157036
 0.000156196
 0.000170865
 0.000160714
 0.000175489
 0.000171359
 0.00508895
 0.005103
 0.0051953
 0.0330476
 0.0055772
 0.0062255
 0.00585766
 -0.000252598
 -8.47033e-21
 -0.000256297
 -1.40607e-19
 -0.00101779
 -0.000169632
 -0.0010206
 -0.0001701
 -0.000257702
 -6.77626e-21
 -0.00103906
 -0.000173177
 -0.000263233
 -1.43996e-19
 -0.00111544
 0.000185907
 -0.0012451
 0.000207517
 -0.00117153
 0.000195255
 -0.000300018
 -1.5416e-19
 -0.000322533
 -1.66018e-19
 0.000168399
 0.000170865
 0.000171801
 0.000200012
 0.000175489
 0.000215022
 0.00508175
 0.00466353
 0.00431839
 0.0051694
 0.0055772
 0.0308203
 0.00601
 -0.000250472
 -6.77626e-21
 -0.000257702
 -1.40607e-19
 -0.00101635
 -0.000169392
 -0.000215881
 -6.77626e-21
 -0.000932707
 -0.000155451
 -0.000215958
 -5.0822e-21
 -0.000863679
 -0.000143946
 -0.00103388
 -0.000172313
 -0.000300982
 -1.01644e-20
 -0.00111544
 -0.000185907
 -0.000300018
 -1.6263e-19
 -0.001202
 0.000200333
 0.000166982
 0.000171801
 0.000143921
 0.000143972
 0.000200655
 0.000200012
 0.00573237
 0.0050356
 0.0331324
 0.00631973
 0.00495384
 0.00521087
 0.00587998
 -0.000259464
 -6.77626e-21
 -0.00114647
 -0.000191079
 -0.000313773
 -1.67713e-19
 -0.00100712
 -0.000167853
 -0.000244096
 -6.77626e-21
 -0.00126395
 0.000210658
 -0.000990769
 0.000165128
 -0.00104217
 0.000173696
 -0.001176
 0.000195999
 -0.0003182
 1.60936e-19
 -0.000251289
 -1.33831e-19
 -0.000269798
 -1.38913e-19
 0.000172976
 0.000209182
 0.000162731
 0.000167526
 0.000212133
 0.000179866
 0.00603883
 0.00616674
 0.0062255
 0.00601
 0.00631973
 0.04365
 0.00642294
 0.00646627
 -0.000302901
 -1.01644e-20
 -0.000300982
 -1.64324e-19
 -0.00120777
 -0.000201294
 -0.000313773
 -3.38813e-21
 -0.00123335
 -0.000205558
 -0.000300018
 -6.77626e-21
 -0.0012451
 -0.000207517
 -0.000322533
 -1.77877e-19
 -0.001202
 -0.000200333
 -0.00126395
 -0.000210658
 -0.0003182
 -6.77626e-21
 -0.00128459
 0.000214098
 -0.00129325
 0.000215542
 -0.000324094
 -1.64324e-19
 0.000201934
 0.000209182
 0.000200655
 0.000200012
 0.000212133
 0.000215022
 0.000216063
 0.00468549
 0.00421434
 0.00495384
 0.0270099
 0.00400813
 0.00433674
 0.00481132
 -0.000224453
 -3.38813e-21
 -0.000244096
 -1.33831e-19
 -0.000937098
 -0.000156183
 -0.000842869
 -0.000140478
 -0.000196981
 -3.38813e-21
 -0.000990769
 -0.000165128
 -0.000251289
 -1.40607e-19
 -0.000801625
 0.000133604
 -0.000867349
 0.000144558
 -0.000962263
 0.000160377
 -0.000203831
 -1.06726e-19
 -0.000229843
 -1.16891e-19
 0.000149635
 0.000162731
 0.000131321
 0.000135887
 0.000167526
 0.000153229
 0.00386625
 0.00337292
 0.00400813
 0.0216273
 0.0029916
 0.00343263
 0.00395582
 -0.000189643
 -5.0822e-21
 -0.000196981
 -1.06726e-19
 -0.000773249
 -0.000128875
 -0.000674584
 -0.000112431
 -0.000147649
 -1.69407e-21
 -0.000801625
 -0.000133604
 -0.000203831
 -1.10114e-19
 -0.00059832
 9.97201e-05
 -0.000686525
 0.000114421
 -0.000791164
 0.000131861
 -0.000151512
 -7.7927e-20
 -0.000191751
 -9.74088e-20
 0.000126429
 0.000131321
 9.84323e-05
 0.000135887
 0.000101008
 0.000127834
 0.00297206
 0.00297636
 0.00293637
 0.0029916
 0.0148471
 0.00297071
 -0.000149558
 -5.0822e-21
 -0.000147649
 -8.13152e-20
 -0.000594413
 -9.90688e-05
 -0.000148078
 -5.0822e-21
 -0.000595272
 -9.9212e-05
 -0.000587274
 -9.7879e-05
 -0.000145559
 -3.38813e-21
 -0.00059832
 -9.97201e-05
 -0.000151512
 -8.21622e-20
 -0.000594141
 9.90236e-05
 9.97053e-05
 9.84323e-05
 9.87187e-05
 9.70393e-05
 0.000101008
 0.00393257
 0.00418036
 0.024983
 0.00383695
 0.00434242
 0.00421651
 0.0044742
 -0.000205892
 -6.77626e-21
 -0.000786515
 -0.000131086
 -0.000187365
 -1.05032e-19
 -0.000836071
 -0.000139345
 -0.000212144
 -3.38813e-21
 -0.00076739
 0.000127898
 -0.000868485
 0.000144747
 -0.000843302
 0.00014055
 -0.000894841
 0.00014914
 -0.00019633
 1.01644e-19
 -0.000222099
 -1.11808e-19
 -0.000225322
 1.13502e-19
 0.000137261
 0.00012491
 0.000141429
 0.000148066
 0.000130886
 0.000150214
 0.00328196
 0.00370003
 0.00343263
 0.00297071
 0.00383695
 0.0211031
 0.0038808
 -0.000182637
 -5.0822e-21
 -0.000145559
 -7.96211e-20
 -0.000656392
 -0.000109399
 -0.000187365
 -3.38813e-21
 -0.000740005
 -0.000123334
 -0.000151512
 -3.38813e-21
 -0.000686525
 -0.000114421
 -0.000191751
 -1.03338e-19
 -0.000594141
 -9.90236e-05
 -0.00076739
 -0.000127898
 -0.00019633
 -5.0822e-21
 -0.000776161
 0.00012936
 0.000121758
 9.70393e-05
 0.00012491
 0.000101008
 0.000127834
 0.000130886
 0.00432029
 0.00416632
 0.00434242
 0.0272024
 0.00426258
 0.00509244
 0.0050183
 -0.000219886
 -6.77626e-21
 -0.000212144
 -1.15196e-19
 -0.000864058
 -0.00014401
 -0.000833263
 -0.000138877
 -0.000196746
 -5.0822e-21
 -0.000868485
 -0.000144747
 -0.000222099
 -1.18585e-19
 -0.000852516
 0.000142086
 -0.00101849
 0.000169748
 -0.00100366
 0.000167277
 -0.000229512
 -1.18585e-19
 -0.000279732
 -1.42302e-19
 0.00014659
 0.000141429
 0.000131164
 0.000153008
 0.000148066
 0.000186488
 0.00401733
 0.00425323
 0.0046964
 0.00426258
 0.0220177
 0.00478816
 -0.000204987
 -3.38813e-21
 -0.000196746
 -1.06726e-19
 -0.000803465
 -0.000133911
 -0.000220336
 -6.77626e-21
 -0.000850645
 -0.000141774
 -0.000939281
 -0.000156547
 -0.000249304
 -5.0822e-21
 -0.000852516
 -0.000142086
 -0.000229512
 -1.25361e-19
 -0.000957633
 0.000159605
 0.000136658
 0.000131164
 0.000146891
 0.000166203
 0.000153008
 0.00504963
 0.00465118
 0.00528001
 0.00447968
 0.0295223
 0.00482997
 0.00523186
 -0.000244629
 -5.0822e-21
 -0.000260334
 -1.40607e-19
 -0.00100993
 -0.000168321
 -0.000220489
 -3.38813e-21
 -0.000930236
 -0.000155039
 -0.001056
 -0.000176
 -0.000267667
 -1.47384e-19
 -0.000895935
 -0.000149323
 -0.000227479
 -5.0822e-21
 -0.000965995
 0.000160999
 -0.00104637
 0.000174395
 -0.000255519
 -1.28749e-19
 0.000163086
 0.000173556
 0.000146993
 0.000178445
 0.000151652
 0.000170346
 0.00398674
 0.00361871
 0.00423839
 0.00461134
 0.0255308
 0.00454026
 0.00453535
 -0.00017792
 -5.0822e-21
 -0.000797348
 -0.000132891
 -0.000220754
 -1.21973e-19
 -0.000183951
 -5.0822e-21
 -0.000723742
 -0.000120624
 -0.000239888
 -3.38813e-21
 -0.000847678
 -0.00014128
 -0.000922269
 -0.000153711
 -0.000221246
 -5.0822e-21
 -0.000908053
 0.000151342
 -0.000907069
 0.000151178
 -0.00023278
 -1.21973e-19
 0.000122634
 0.000118613
 0.000159925
 0.000147169
 0.000147497
 0.000155187
 0.00462317
 0.00498109
 0.00454026
 0.0293148
 0.00521898
 0.00481523
 0.00513602
 -0.000241071
 -8.47033e-21
 -0.000221246
 -1.21973e-19
 -0.000924634
 -0.000154106
 -0.000996219
 -0.000166036
 -0.000257039
 -6.77626e-21
 -0.000908053
 -0.000151342
 -0.00023278
 -1.28749e-19
 -0.0010438
 0.000173966
 -0.000963046
 0.000160508
 -0.0010272
 0.000171201
 -0.00026486
 -1.35525e-19
 -0.000248743
 1.27055e-19
 0.000160714
 0.000171359
 0.000147497
 0.000155187
 0.000176573
 0.000165828
 0.00433674
 0.00395582
 0.00421651
 0.0038808
 0.0257018
 0.00467859
 0.00463337
 -0.000203831
 -6.77626e-21
 -0.000867349
 -0.000144558
 -0.000229843
 -1.23667e-19
 -0.000191751
 -3.38813e-21
 -0.000791164
 -0.000131861
 -0.00019633
 -1.05032e-19
 -0.000843302
 -0.00014055
 -0.000225322
 -6.77626e-21
 -0.000776161
 -0.00012936
 -0.000935717
 0.000155953
 -0.000926674
 0.000154446
 -0.000238015
 1.20279e-19
 0.000135887
 0.000153229
 0.000127834
 0.000130886
 0.000150214
 0.000158677
 0.00521087
 0.00481132
 0.00467859
 0.0304469
 0.00544325
 0.00496889
 0.005334
 -0.000251289
 -3.38813e-21
 -0.00104217
 -0.000173696
 -0.000269798
 -1.47384e-19
 -0.000229843
 -6.77626e-21
 -0.000962263
 -0.000160377
 -0.000935717
 -0.000155953
 -0.000238015
 -5.0822e-21
 -0.00108865
 0.000181442
 -0.000993778
 0.00016563
 -0.0010668
 0.0001778
 -0.000274526
 1.38913e-19
 -0.000258874
 -1.32137e-19
 0.000167526
 0.000153229
 0.000179866
 0.000158677
 0.000172582
 0.000183018
 0.00587998
 0.00642294
 0.00544325
 0.0348701
 0.00600737
 0.0055477
 0.00556886
 -0.0003182
 -1.74489e-19
 -0.000269798
 -6.77626e-21
 -0.001176
 -0.000195999
 -0.00128459
 -0.000214098
 -0.000324094
 -1.76183e-19
 -0.00108865
 -0.000181442
 -0.000274526
 -8.47033e-21
 -0.00120147
 0.000200246
 -0.00110954
 0.000184923
 -0.00111377
 0.000185629
 -0.000276642
 1.43996e-19
 -0.000280244
 -1.42302e-19
 0.000212133
 0.000179866
 0.000216063
 0.000184428
 0.000183018
 0.000186829
 0.00520272
 0.00585766
 0.00646627
 0.00521898
 0.00600737
 0.034168
 0.00541502
 -0.000263233
 -5.0822e-21
 -0.000257039
 -1.40607e-19
 -0.00104054
 -0.000173424
 -0.000322533
 -6.77626e-21
 -0.00117153
 -0.000195255
 -0.000324094
 -1.01644e-20
 -0.00129325
 -0.000215542
 -0.0010438
 -0.000173966
 -0.00026486
 -1.43996e-19
 -0.00120147
 -0.000200246
 -0.000276642
 -5.0822e-21
 -0.001083
 0.000180501
 0.000175489
 0.000171359
 0.000215022
 0.000216063
 0.000176573
 0.000184428
 0.00622731
 0.00564166
 0.00509244
 0.00478816
 0.039667
 0.00578108
 0.00611563
 0.0060207
 -0.000314861
 -1.71101e-19
 -0.00124546
 -0.000207577
 -0.00030787
 -6.77626e-21
 -0.000249304
 -1.35525e-19
 -0.00112833
 -0.000188055
 -0.000229512
 -3.38813e-21
 -0.00101849
 -0.000169748
 -0.000279732
 -1.50772e-19
 -0.000957633
 -0.000159605
 -0.00115622
 0.000192703
 -0.00122313
 0.000203854
 -0.00120414
 0.00020069
 -0.000298377
 1.52466e-19
 -0.000303693
 -1.59242e-19
 0.000202462
 0.000166203
 0.000209908
 0.000153008
 0.000205246
 0.000186488
 0.000198918
 0.0044742
 0.0050183
 0.00463337
 0.00496889
 0.00578108
 0.0304483
 0.0055725
 -0.000222099
 -5.0822e-21
 -0.000225322
 -1.23667e-19
 -0.000894841
 -0.00014914
 -0.000279732
 -1.01644e-20
 -0.00100366
 -0.000167277
 -0.000238015
 -1.28749e-19
 -0.000926674
 -0.000154446
 -0.000993778
 -0.00016563
 -0.000258874
 -1.40607e-19
 -0.00115622
 -0.000192703
 -0.000298377
 -6.77626e-21
 -0.0011145
 0.00018575
 0.000148066
 0.000186488
 0.000150214
 0.000158677
 0.000172582
 0.000198918
 0.00448233
 0.00482997
 0.00453535
 0.00481523
 0.0289636
 0.00518425
 0.00511649
 -0.000227479
 -1.21973e-19
 -0.000220754
 -6.77626e-21
 -0.000896466
 -0.000149411
 -0.000965995
 -0.000160999
 -0.000255519
 -1.35525e-19
 -0.00023278
 -3.38813e-21
 -0.000907069
 -0.000151178
 -0.000963046
 -0.000160508
 -0.000248743
 -1.01644e-20
 -0.00103685
 0.000172808
 -0.0010233
 0.00017055
 -0.000262906
 1.35525e-19
 0.000147169
 0.000151652
 0.000155187
 0.000165828
 0.000170346
 0.000175271
 0.00575537
 0.00523186
 0.00611563
 0.00518425
 0.0334242
 0.00577247
 0.0053646
 -0.000267667
 -8.47033e-21
 -0.00030787
 -1.67713e-19
 -0.00115107
 -0.000191846
 -0.000255519
 -3.38813e-21
 -0.00104637
 -0.000174395
 -0.00122313
 -0.000203854
 -0.000303693
 -1.67713e-19
 -0.00103685
 -0.000172808
 -0.000262906
 -5.0822e-21
 -0.00115449
 0.000192416
 -0.00107292
 0.00017882
 -0.000273554
 1.38913e-19
 0.000182369
 0.000202462
 0.000205246
 0.000178445
 0.000170346
 0.000175271
 0.005334
 0.0055477
 0.0060207
 0.0055725
 0.00577247
 0.0337853
 0.00553798
 -0.000274526
 -1.49078e-19
 -0.000258874
 -6.77626e-21
 -0.0010668
 -0.0001778
 -0.00110954
 -0.000184923
 -0.000280244
 -1.52466e-19
 -0.000298377
 -1.60936e-19
 -0.000303693
 -1.01644e-20
 -0.00120414
 -0.00020069
 -0.0011145
 -0.00018575
 -0.00115449
 -0.000192416
 -0.000273554
 -1.01644e-20
 -0.0011076
 0.000184599
 0.000182369
 0.000202462
 0.000172582
 0.000183018
 0.000198918
 0.000186829
 0.00513602
 0.00556886
 0.00541502
 0.00511649
 0.0053646
 0.00553798
 0.032139
 -0.00026486
 -5.0822e-21
 -0.000248743
 -1.37219e-19
 -0.0010272
 -0.000171201
 -0.000276642
 -1.52466e-19
 -0.000280244
 -1.01644e-20
 -0.00111377
 -0.000185629
 -0.001083
 -0.000180501
 -0.000262906
 -1.42302e-19
 -0.0010233
 -0.00017055
 -0.000273554
 -1.50772e-19
 -0.00107292
 -0.00017882
 -0.0011076
 -0.000184599
 0.000182369
 0.000176573
 0.000165828
 0.000184428
 0.000175271
 0.000186829
 -0.000520833
 -0.000520833
 -0.000260417
 8.68056e-05
       0
 4.34028e-05
 -6.2004e-06
 4.34028e-05
 -6.2004e-06
 -2.48016e-05
 8.68056e-05
 -8.68056e-05
 -6.77626e-21
       0
 9.3006e-06
 -6.2004e-06
 3.1002e-06
 6.2004e-06
 -3.1002e-06
 -8.47033e-22
 -0.000520833
 -0.000260417
 -0.000520833
 4.34028e-05
 -6.2004e-06
 8.68056e-05
 1.94818e-20
 4.34028e-05
 6.2004e-06
 -2.48016e-05
 8.68056e-05
 -1.42302e-19
 -8.68056e-05
 -6.2004e-06
 3.1002e-06
 1.94818e-20
 9.3006e-06
 6.2004e-06
 3.1002e-06
 -1.09055e-20
 -0.000442406
 -0.000442406
 -0.000221203
 7.37343e-05
 1.69407e-20
 3.68672e-05
 -5.26674e-06
 3.68672e-05
 -5.26674e-06
 -2.1067e-05
 7.37343e-05
 -7.37343e-05
 -1.23667e-19
 1.69407e-20
 7.90011e-06
 -5.26674e-06
 2.63337e-06
 5.26674e-06
 -2.63337e-06
 -9.74088e-21
 -0.000427658
 -0.000427658
 -0.000213829
 7.12763e-05
       0
 3.56382e-05
 -5.09116e-06
 3.56382e-05
 -5.09116e-06
 -2.03647e-05
 7.12763e-05
 -7.12763e-05
 -3.38813e-21
       0
 7.63675e-06
 -5.09116e-06
 2.54558e-06
 5.09116e-06
 -2.54558e-06
 -1.27055e-21
 -0.000870064
 -0.000221203
 -0.000213829
 -0.000870064
 3.68672e-05
 -5.26674e-06
 3.56382e-05
 -5.09116e-06
 0.000145011
 1.69407e-20
 3.68672e-05
 5.26674e-06
 3.56382e-05
 5.09116e-06
 -2.1067e-05
 -2.03647e-05
 0.000145011
 -5.0822e-21
 -1.16891e-19
 -0.000145011
 -5.26674e-06
 2.63337e-06
 -5.09116e-06
 2.54558e-06
 1.69407e-20
 1.55369e-05
 5.26674e-06
 2.63337e-06
 5.09116e-06
 2.54558e-06
 -1.27055e-21
 -9.31736e-21
 -0.000520833
 -0.000520833
 -0.000260417
 8.68056e-05
 1.94818e-20
 4.34028e-05
 -6.2004e-06
 4.34028e-05
 -6.2004e-06
 -2.48016e-05
 8.68056e-05
 -8.68056e-05
 -1.40607e-19
 1.94818e-20
 9.3006e-06
 -6.2004e-06
 3.1002e-06
 6.2004e-06
 -3.1002e-06
 -1.10114e-20
 -0.000520833
 -0.000260417
 -0.000520833
 4.34028e-05
 -6.2004e-06
 8.68056e-05
       0
 4.34028e-05
 6.2004e-06
 -2.48016e-05
 8.68056e-05
 -8.47033e-21
 -8.68056e-05
 -6.2004e-06
 3.1002e-06
       0
 9.3006e-06
 6.2004e-06
 3.1002e-06
 -1.27055e-21
 -0.000407414
 -0.000407414
 -0.000203707
 6.79023e-05
 1.52466e-20
 3.39512e-05
 -4.85016e-06
 3.39512e-05
 -4.85016e-06
 -1.94007e-05
 6.79023e-05
 -6.79023e-05
 -1.10114e-19
 1.52466e-20
 7.27525e-06
 -4.85016e-06
 2.42508e-06
 4.85016e-06
 -2.42508e-06
 -8.57621e-21
 -0.000404052
 -0.000404052
 -0.000202026
 6.73421e-05
 4.23516e-22
 3.3671e-05
 -4.81015e-06
 3.3671e-05
 -4.81015e-06
 -1.92406e-05
 6.73421e-05
 -6.73421e-05
 -5.0822e-21
 4.23516e-22
 7.21522e-06
 -4.81015e-06
 2.40507e-06
 4.81015e-06
 -2.40507e-06
 -8.47033e-22
 -0.000811466
 -0.000203707
 -0.000202026
 -0.000811466
 3.39512e-05
 -4.85016e-06
 3.3671e-05
 -4.81015e-06
 0.000135244
 1.60936e-20
 3.39512e-05
 4.85016e-06
 3.3671e-05
 4.81015e-06
 -1.94007e-05
 -1.92406e-05
 0.000135244
 -5.0822e-21
 -1.10114e-19
 -0.000135244
 -4.85016e-06
 2.42508e-06
 -4.81015e-06
 2.40507e-06
 1.60936e-20
 1.44905e-05
 4.85016e-06
 2.42508e-06
 4.81015e-06
 2.40507e-06
 -8.47033e-22
 -8.99973e-21
 -0.000645197
 -0.000645197
 -0.000322599
 0.000107533
       0
 5.37665e-05
 -7.68092e-06
 5.37665e-05
 -7.68092e-06
 -3.07237e-05
 0.000107533
 -0.000107533
 -6.77626e-21
       0
 1.15214e-05
 -7.68092e-06
 3.84046e-06
 7.68092e-06
 -3.84046e-06
 -1.27055e-21
 -0.000260417
 -0.00126631
 -0.00126631
 -0.000372736
 4.34028e-05
 6.2004e-06
 4.34028e-05
 6.2004e-06
 0.000211051
 4.74338e-20
 6.21227e-05
 -8.87466e-06
 6.21227e-05
 -8.87466e-06
 -2.48016e-05
 -3.54987e-05
 -1.32137e-19
 0.000211051
 -0.000211051
 -2.06676e-19
 -6.2004e-06
 -3.1002e-06
 6.2004e-06
 3.1002e-06
 4.74338e-20
 2.26126e-05
 -8.87466e-06
 4.43733e-06
 8.87466e-06
 -4.43733e-06
 -9.74088e-21
 -1.65171e-20
 -0.00139067
 -0.000322599
 -0.000372736
 -0.00139067
 5.37665e-05
 -7.68092e-06
 6.21227e-05
 -8.87466e-06
 0.000231778
 2.28699e-20
 5.37665e-05
 7.68092e-06
 6.21227e-05
 8.87466e-06
 -3.07237e-05
 -3.54987e-05
 0.000231778
 -1.74489e-19
 -1.01644e-20
 -0.000231778
 -7.68092e-06
 3.84046e-06
 -8.87466e-06
 4.43733e-06
 2.28699e-20
 2.48334e-05
 7.68092e-06
 3.84046e-06
 8.87466e-06
 4.43733e-06
 -1.37643e-20
 -1.69407e-21
 -0.000553149
 -0.000553149
 -0.000276575
 9.21915e-05
       0
 4.60958e-05
 -6.58511e-06
 4.60958e-05
 -6.58511e-06
 -2.63404e-05
 9.21915e-05
 -9.21915e-05
 -8.47033e-21
       0
 9.87766e-06
 -6.58511e-06
 3.29255e-06
 6.58511e-06
 -3.29255e-06
 -1.27055e-21
 -0.000322599
 -0.00136435
 -0.00136435
 -0.000359576
 5.37665e-05
 7.68092e-06
 5.37665e-05
 7.68092e-06
 0.000227391
 5.42101e-20
 5.99293e-05
 -8.56133e-06
 5.99293e-05
 -8.56133e-06
 -3.07237e-05
 -3.42453e-05
 -1.66018e-19
 0.000227391
 -0.000227391
 -1.93124e-19
 -7.68092e-06
 -3.84046e-06
 7.68092e-06
 3.84046e-06
 5.42101e-20
 2.43634e-05
 -8.56133e-06
 4.28066e-06
 8.56133e-06
 -4.28066e-06
 -1.27055e-20
 -1.54584e-20
 -0.0012723
 -0.000276575
 -0.000359576
 -0.0012723
 4.60958e-05
 -6.58511e-06
 5.99293e-05
 -8.56133e-06
 0.00021205
 2.03288e-20
 4.60958e-05
 6.58511e-06
 5.99293e-05
 8.56133e-06
 -2.63404e-05
 -3.42453e-05
 0.00021205
 -1.49078e-19
 -1.35525e-20
 -0.00021205
 -6.58511e-06
 3.29255e-06
 -8.56133e-06
 4.28066e-06
 2.03288e-20
 2.27197e-05
 6.58511e-06
 3.29255e-06
 8.56133e-06
 4.28066e-06
 -1.18585e-20
 -1.69407e-21
 -0.000509407
 -0.000509407
 -0.000254703
 8.49011e-05
       0
 4.24506e-05
 -6.06437e-06
 4.24506e-05
 -6.06437e-06
 -2.42575e-05
 8.49011e-05
 -8.49011e-05
 -6.77626e-21
       0
 9.09655e-06
 -6.06437e-06
 3.03218e-06
 6.06437e-06
 -3.03218e-06
 -1.27055e-21
 -0.000276575
 -0.0011072
 -0.0011072
 -0.000277025
 4.60958e-05
 6.58511e-06
 4.60958e-05
 6.58511e-06
 0.000184533
 4.15046e-20
 4.61708e-05
 -6.59583e-06
 4.61708e-05
 -6.59583e-06
 -2.63404e-05
 -2.63833e-05
 -1.42302e-19
 0.000184533
 -0.000184533
 -1.49078e-19
 -6.58511e-06
 -3.29255e-06
 6.58511e-06
 3.29255e-06
 4.15046e-20
 1.97714e-05
 -6.59583e-06
 3.29792e-06
 6.59583e-06
 -3.29792e-06
 -1.10114e-20
 -1.19643e-20
 -0.00106346
 -0.000254703
 -0.000277025
 -0.00106346
 4.24506e-05
 -6.06437e-06
 4.61708e-05
 -6.59583e-06
 0.000177243
 2.03288e-20
 4.24506e-05
 6.06437e-06
 4.61708e-05
 6.59583e-06
 -2.42575e-05
 -2.63833e-05
 0.000177243
 -1.40607e-19
 -8.47033e-21
 -0.000177243
 -6.06437e-06
 3.03218e-06
 -6.59583e-06
 3.29792e-06
 2.03288e-20
 1.89903e-05
 6.06437e-06
 3.03218e-06
 6.59583e-06
 3.29792e-06
 -1.09055e-20
 -1.27055e-21
 -0.000461025
 -0.000461025
 -0.000230512
 7.68375e-05
       0
 3.84187e-05
 -5.48839e-06
 3.84187e-05
 -5.48839e-06
 -2.19536e-05
 7.68375e-05
 -7.68375e-05
 -6.77626e-21
       0
 8.23259e-06
 -5.48839e-06
 2.7442e-06
 5.48839e-06
 -2.7442e-06
 -1.05879e-21
 -0.000254703
 -0.000986459
 -0.000986459
 -0.000238526
 4.24506e-05
 6.06437e-06
 4.24506e-05
 6.06437e-06
 0.00016441
 3.81165e-20
 3.97544e-05
 -5.6792e-06
 3.97544e-05
 -5.6792e-06
 -2.42575e-05
 -2.27168e-05
 -1.32137e-19
 0.00016441
 -0.00016441
 -1.30443e-19
 -6.06437e-06
 -3.03218e-06
 6.06437e-06
 3.03218e-06
 3.81165e-20
 1.76153e-05
 -5.6792e-06
 2.8396e-06
 5.6792e-06
 -2.8396e-06
 -9.95264e-21
 -1.0482e-20
 -0.000938077
 -0.000230512
 -0.000238526
 -0.000938077
 3.84187e-05
 -5.48839e-06
 3.97544e-05
 -5.6792e-06
 0.000156346
 1.77877e-20
 3.84187e-05
 5.48839e-06
 3.97544e-05
 5.6792e-06
 -2.19536e-05
 -2.27168e-05
 0.000156346
 -1.23667e-19
 -8.47033e-21
 -0.000156346
 -5.48839e-06
 2.7442e-06
 -5.6792e-06
 2.8396e-06
 1.77877e-20
 1.67514e-05
 5.48839e-06
 2.7442e-06
 5.6792e-06
 2.8396e-06
 -9.84676e-21
 -1.27055e-21
 -0.000412568
 -0.000412568
 -0.000206284
 6.87613e-05
       0
 3.43806e-05
 -4.91152e-06
 3.43806e-05
 -4.91152e-06
 -1.96461e-05
 6.87613e-05
 -6.87613e-05
 -6.77626e-21
       0
 7.36728e-06
 -4.91152e-06
 2.45576e-06
 4.91152e-06
 -2.45576e-06
 -8.47033e-22
 -0.000230512
 -0.000869081
 -0.000869081
 -0.000204028
 3.84187e-05
 5.48839e-06
 3.84187e-05
 5.48839e-06
 0.000144847
 3.47284e-20
 3.40046e-05
 -4.8578e-06
 3.40046e-05
 -4.8578e-06
 -2.19536e-05
 -1.94312e-05
 -1.20279e-19
 0.000144847
 -0.000144847
 -1.11808e-19
 -5.48839e-06
 -2.7442e-06
 5.48839e-06
 2.7442e-06
 3.47284e-20
 1.55193e-05
 -4.8578e-06
 2.4289e-06
 4.8578e-06
 -2.4289e-06
 -9.31736e-21
 -8.78797e-21
 -0.000820623
 -0.000206284
 -0.000204028
 -0.000820623
 3.43806e-05
 -4.91152e-06
 3.40046e-05
 -4.8578e-06
 0.000136771
 1.60936e-20
 3.43806e-05
 4.91152e-06
 3.40046e-05
 4.8578e-06
 -1.96461e-05
 -1.94312e-05
 0.000136771
 -1.10114e-19
 -5.0822e-21
 -0.000136771
 -4.91152e-06
 2.45576e-06
 -4.8578e-06
 2.4289e-06
 1.60936e-20
 1.4654e-05
 4.91152e-06
 2.45576e-06
 4.8578e-06
 2.4289e-06
 -8.68209e-21
 -1.05879e-21
 -0.000423892
 -0.000423892
 -0.000211946
 7.06487e-05
       0
 3.53244e-05
 -5.04634e-06
 3.53244e-05
 -5.04634e-06
 -2.01853e-05
 7.06487e-05
 -7.06487e-05
 -3.38813e-21
       0
 7.56951e-06
 -5.04634e-06
 2.52317e-06
 5.04634e-06
 -2.52317e-06
 -6.35275e-22
 -0.000206284
 -0.000802337
 -0.000802337
 -0.000194884
 3.43806e-05
 4.91152e-06
 3.43806e-05
 4.91152e-06
 0.000133723
 3.13402e-20
 3.24807e-05
 -4.64011e-06
 3.24807e-05
 -4.64011e-06
 -1.96461e-05
 -1.85604e-05
 -1.05032e-19
 0.000133723
 -0.000133723
 -1.05032e-19
 -4.91152e-06
 -2.45576e-06
 4.91152e-06
 2.45576e-06
 3.13402e-20
 1.43274e-05
 -4.64011e-06
 2.32005e-06
 4.64011e-06
 -2.32005e-06
 -7.6233e-21
 -8.57621e-21
 -0.000813661
 -0.000211946
 -0.000194884
 -0.000813661
 3.53244e-05
 -5.04634e-06
 3.24807e-05
 -4.64011e-06
 0.00013561
 1.65171e-20
 3.53244e-05
 5.04634e-06
 3.24807e-05
 4.64011e-06
 -2.01853e-05
 -1.85604e-05
 0.00013561
 -1.15196e-19
 -3.38813e-21
 -0.00013561
 -5.04634e-06
 2.52317e-06
 -4.64011e-06
 2.32005e-06
 1.65171e-20
 1.45297e-05
 5.04634e-06
 2.52317e-06
 4.64011e-06
 2.32005e-06
 -8.78797e-21
 -1.05879e-21
 -0.000211946
 -0.000797474
 -0.000797474
 -0.000186791
 3.53244e-05
 5.04634e-06
 3.53244e-05
 5.04634e-06
 0.000132912
 2.96462e-20
 3.11318e-05
 -4.4474e-06
 3.11318e-05
 -4.4474e-06
 -2.01853e-05
 -1.77896e-05
 -1.09267e-19
 0.000132912
 -0.000132912
 -1.01644e-19
 -5.04634e-06
 -2.52317e-06
 5.04634e-06
 2.52317e-06
 2.96462e-20
 1.42406e-05
 -4.4474e-06
 2.2237e-06
 4.4474e-06
 -2.2237e-06
 -8.47033e-21
 -8.15269e-21
 -0.000221203
 -0.000815988
 -0.000186791
 -0.000815988
 3.68672e-05
 5.26674e-06
 3.68672e-05
 5.26674e-06
 3.11318e-05
 -4.4474e-06
 0.000135998
 -1.86347e-20
 3.11318e-05
 4.4474e-06
 -2.1067e-05
 -1.77896e-05
 1.15196e-19
 0.000135998
 -6.77626e-21
 -0.000135998
 -5.26674e-06
 -2.63337e-06
 5.26674e-06
 2.63337e-06
 -4.4474e-06
 2.2237e-06
 -1.86347e-20
 1.45712e-05
 4.4474e-06
 2.2237e-06
 8.47033e-21
 -1.27055e-21
 -0.000327566
 -0.000327566
 -0.000163783
 5.45944e-05
       0
 2.72972e-05
 -3.8996e-06
 2.72972e-05
 -3.8996e-06
 -1.55984e-05
 5.45944e-05
 -5.45944e-05
 -5.0822e-21
       0
 5.8494e-06
 -3.8996e-06
 1.9498e-06
 3.8996e-06
 -1.9498e-06
 -8.47033e-22
 -0.000213829
 -0.000749939
 -0.000749939
 -0.00016114
 3.56382e-05
 5.09116e-06
 3.56382e-05
 5.09116e-06
 0.00012499
 2.92226e-20
 2.68567e-05
 -3.83668e-06
 2.68567e-05
 -3.83668e-06
 -2.03647e-05
 -1.53467e-05
 -1.10114e-19
 0.00012499
 -0.00012499
 -8.72444e-20
 -5.09116e-06
 -2.54558e-06
 5.09116e-06
 2.54558e-06
 2.92226e-20
 1.33918e-05
 -3.83668e-06
 1.91834e-06
 3.83668e-06
 -1.91834e-06
 -8.04681e-21
 -6.88214e-21
 -0.000649847
 -0.000163783
 -0.00016114
 -0.000649847
 2.72972e-05
 -3.8996e-06
 2.68567e-05
 -3.83668e-06
 0.000108308
 1.3129e-20
 2.72972e-05
 3.8996e-06
 2.68567e-05
 3.83668e-06
 -1.55984e-05
 -1.53467e-05
 0.000108308
 -8.97855e-20
 -8.47033e-21
 -0.000108308
 -3.8996e-06
 1.9498e-06
 -3.83668e-06
 1.91834e-06
 1.3129e-20
 1.16044e-05
 3.8996e-06
 1.9498e-06
 3.83668e-06
 1.91834e-06
 -7.19978e-21
 -8.47033e-22
 -0.000403482
 -0.000403482
 -0.000201741
 6.7247e-05
       0
 3.36235e-05
 -4.80336e-06
 3.36235e-05
 -4.80336e-06
 -1.92134e-05
 6.7247e-05
 -6.7247e-05
 -6.77626e-21
       0
 7.20504e-06
 -4.80336e-06
 2.40168e-06
 4.80336e-06
 -2.40168e-06
 -8.47033e-22
 -0.000163783
 -0.000640216
 -0.000640216
 -0.000156325
 2.72972e-05
 3.8996e-06
 2.72972e-05
 3.8996e-06
 0.000106703
 2.4564e-20
 2.60542e-05
 -3.72202e-06
 2.60542e-05
 -3.72202e-06
 -1.55984e-05
 -1.48881e-05
 -8.47033e-20
 0.000106703
 -0.000106703
 -8.47033e-20
 -3.8996e-06
 -1.9498e-06
 3.8996e-06
 1.9498e-06
 2.4564e-20
 1.14324e-05
 -3.72202e-06
 1.86101e-06
 3.72202e-06
 -1.86101e-06
 -6.67038e-21
 -6.77626e-21
 -0.000716132
 -0.000201741
 -0.000156325
 -0.000716132
 3.36235e-05
 -4.80336e-06
 2.60542e-05
 -3.72202e-06
 0.000119355
 1.56701e-20
 3.36235e-05
 4.80336e-06
 2.60542e-05
 3.72202e-06
 -1.92134e-05
 -1.48881e-05
 0.000119355
 -1.10114e-19
 -6.77626e-21
 -0.000119355
 -4.80336e-06
 2.40168e-06
 -3.72202e-06
 1.86101e-06
 1.56701e-20
 1.27881e-05
 4.80336e-06
 2.40168e-06
 3.72202e-06
 1.86101e-06
 -8.47033e-21
 -1.27055e-21
 -0.00044026
 -0.00044026
 -0.00022013
 7.33767e-05
       0
 3.66883e-05
 -5.24119e-06
 3.66883e-05
 -5.24119e-06
 -2.09648e-05
 7.33767e-05
 -7.33767e-05
 -6.77626e-21
       0
 7.86179e-06
 -5.24119e-06
 2.6206e-06
 5.24119e-06
 -2.6206e-06
 -1.05879e-21
 -0.000201741
 -0.000824437
 -0.000824437
 -0.000210478
 3.36235e-05
 4.80336e-06
 3.36235e-05
 4.80336e-06
 0.000137406
 3.04932e-20
 3.50796e-05
 -5.01137e-06
 3.50796e-05
 -5.01137e-06
 -1.92134e-05
 -2.00455e-05
 -1.04185e-19
 0.000137406
 -0.000137406
 -1.15196e-19
 -4.80336e-06
 -2.40168e-06
 4.80336e-06
 2.40168e-06
 3.04932e-20
 1.47221e-05
 -5.01137e-06
 2.50569e-06
 5.01137e-06
 -2.50569e-06
 -7.72918e-21
 -9.1056e-21
 -0.000861216
 -0.00022013
 -0.000210478
 -0.000861216
 3.66883e-05
 -5.24119e-06
 3.50796e-05
 -5.01137e-06
 0.000143536
 1.60936e-20
 3.66883e-05
 5.24119e-06
 3.50796e-05
 5.01137e-06
 -2.09648e-05
 -2.00455e-05
 0.000143536
 -1.18585e-19
 -3.38813e-21
 -0.000143536
 -5.24119e-06
 2.6206e-06
 -5.01137e-06
 2.50569e-06
 1.60936e-20
 1.53789e-05
 5.24119e-06
 2.6206e-06
 5.01137e-06
 2.50569e-06
 -9.42324e-21
 -1.27055e-21
 -0.000465532
 -0.000465532
 -0.000232766
 7.75887e-05
 4.23516e-22
 3.87944e-05
 -5.54205e-06
 3.87944e-05
 -5.54205e-06
 -2.21682e-05
 7.75887e-05
 -7.75887e-05
 -6.77626e-21
 4.23516e-22
 8.31308e-06
 -5.54205e-06
 2.77103e-06
 5.54205e-06
 -2.77103e-06
 -8.47033e-22
 -0.00022013
 -0.00090563
 -0.00090563
 -0.000232685
 3.66883e-05
 5.24119e-06
 3.66883e-05
 5.24119e-06
 0.000150938
 3.72694e-20
 3.87808e-05
 -5.54011e-06
 3.87808e-05
 -5.54011e-06
 -2.09648e-05
 -2.21605e-05
 -1.10114e-19
 0.000150938
 -0.000150938
 -1.23667e-19
 -5.24119e-06
 -2.6206e-06
 5.24119e-06
 2.6206e-06
 3.72694e-20
 1.6172e-05
 -5.54011e-06
 2.77006e-06
 5.54011e-06
 -2.77006e-06
 -8.68209e-21
 -9.95264e-21
 -0.000930902
 -0.000232766
 -0.000232685
 -0.000930902
 3.87944e-05
 -5.54205e-06
 3.87808e-05
 -5.54011e-06
 0.00015515
 1.65171e-20
 3.87944e-05
 5.54205e-06
 3.87808e-05
 5.54011e-06
 -2.21682e-05
 -2.21605e-05
 0.00015515
 -1.25361e-19
 -3.38813e-21
 -0.00015515
 -5.54205e-06
 2.77103e-06
 -5.54011e-06
 2.77006e-06
 1.65171e-20
 1.66232e-05
 5.54205e-06
 2.77103e-06
 5.54011e-06
 2.77006e-06
 -1.01644e-20
 -1.48231e-21
 -0.000469313
 -0.000469313
 -0.000234657
 7.82189e-05
       0
 3.91094e-05
 -5.58706e-06
 3.91094e-05
 -5.58706e-06
 -2.23483e-05
 7.82189e-05
 -7.82189e-05
 -5.0822e-21
       0
 8.38059e-06
 -5.58706e-06
 2.79353e-06
 5.58706e-06
 -2.79353e-06
 -1.05879e-21
 -0.000232766
 -0.000951534
 -0.000951534
 -0.000243001
 3.87944e-05
 5.54205e-06
 3.87944e-05
 5.54205e-06
 0.000158589
 3.64224e-20
 4.05002e-05
 -5.78574e-06
 4.05002e-05
 -5.78574e-06
 -2.21682e-05
 -2.3143e-05
 -1.20279e-19
 0.000158589
 -0.000158589
 -1.30443e-19
 -5.54205e-06
 -2.77103e-06
 5.54205e-06
 2.77103e-06
 3.64224e-20
 1.69917e-05
 -5.78574e-06
 2.89287e-06
 5.78574e-06
 -2.89287e-06
 -9.31736e-21
 -1.05879e-20
 -0.000955315
 -0.000234657
 -0.000243001
 -0.000955315
 3.91094e-05
 -5.58706e-06
 4.05002e-05
 -5.78574e-06
 0.000159219
 1.69407e-20
 3.91094e-05
 5.58706e-06
 4.05002e-05
 5.78574e-06
 -2.23483e-05
 -2.3143e-05
 0.000159219
 -1.27055e-19
 -3.38813e-21
 -0.000159219
 -5.58706e-06
 2.79353e-06
 -5.78574e-06
 2.89287e-06
 1.69407e-20
 1.70592e-05
 5.58706e-06
 2.79353e-06
 5.78574e-06
 2.89287e-06
 -9.95264e-21
 -1.48231e-21
 -0.000442437
 -0.000442437
 -0.000221218
 7.37395e-05
 4.23516e-22
 3.68697e-05
 -5.26711e-06
 3.68697e-05
 -5.26711e-06
 -2.10684e-05
 7.37395e-05
 -7.37395e-05
 -3.38813e-21
 4.23516e-22
 7.90066e-06
 -5.26711e-06
 2.63355e-06
 5.26711e-06
 -2.63355e-06
 -8.47033e-22
 -0.000234657
 -0.000954193
 -0.000954193
 -0.00024244
 3.91094e-05
 5.58706e-06
 3.91094e-05
 5.58706e-06
 0.000159032
 3.38813e-20
 4.04066e-05
 -5.77237e-06
 4.04066e-05
 -5.77237e-06
 -2.23483e-05
 -2.30895e-05
 -1.20279e-19
 0.000159032
 -0.000159032
 -1.32137e-19
 -5.58706e-06
 -2.79353e-06
 5.58706e-06
 2.79353e-06
 3.38813e-20
 1.70392e-05
 -5.77237e-06
 2.88619e-06
 5.77237e-06
 -2.88619e-06
 -8.89385e-21
 -1.03762e-20
 -0.000927316
 -0.000221218
 -0.00024244
 -0.000927316
 3.68697e-05
 -5.26711e-06
 4.04066e-05
 -5.77237e-06
 0.000154553
 1.69407e-20
 3.68697e-05
 5.26711e-06
 4.04066e-05
 5.77237e-06
 -2.10684e-05
 -2.30895e-05
 0.000154553
 -1.20279e-19
 -1.18585e-20
 -0.000154553
 -5.26711e-06
 2.63355e-06
 -5.77237e-06
 2.88619e-06
 1.69407e-20
 1.65592e-05
 5.26711e-06
 2.63355e-06
 5.77237e-06
 2.88619e-06
 -9.21148e-21
 -1.05879e-21
 -0.000260417
 -0.00115399
 -0.00115399
 -0.000316579
 4.34028e-05
 6.2004e-06
 4.34028e-05
 6.2004e-06
 0.000192332
 -1.86347e-20
 5.27632e-05
 -7.53761e-06
 5.27632e-05
 -7.53761e-06
 -2.48016e-05
 -3.01504e-05
 1.32137e-19
 0.000192332
 -0.000192332
 -1.35525e-20
 -6.2004e-06
 -3.1002e-06
 6.2004e-06
 3.1002e-06
 -1.86347e-20
 2.0607e-05
 -7.53761e-06
 3.7688e-06
 7.53761e-06
 -3.7688e-06
 1.05879e-20
 -8.47033e-22
 -0.000221218
 -0.0010756
 -0.000316579
 -0.0010756
 3.68697e-05
 5.26711e-06
 3.68697e-05
 5.26711e-06
 5.27632e-05
 -7.53761e-06
 0.000179266
 3.98105e-20
 5.27632e-05
 7.53761e-06
 -2.10684e-05
 -3.01504e-05
 -1.13502e-19
 0.000179266
 -1.71101e-19
 -0.000179266
 -5.26711e-06
 -2.63355e-06
 5.26711e-06
 2.63355e-06
 -7.53761e-06
 3.7688e-06
 3.98105e-20
 1.92071e-05
 7.53761e-06
 3.7688e-06
 -8.47033e-21
 -1.33408e-20
 -0.000435149
 -0.000435149
 -0.000217575
 7.25248e-05
 -4.23516e-22
 3.62624e-05
 -5.18035e-06
 3.62624e-05
 -5.18035e-06
 -2.07214e-05
 7.25248e-05
 -7.25248e-05
 -5.0822e-21
 -4.23516e-22
 7.77052e-06
 -5.18035e-06
 2.59017e-06
 5.18035e-06
 -2.59017e-06
 -1.05879e-21
 -0.000316579
 -0.00113292
 -0.00113292
 -0.000249881
 5.27632e-05
 7.53761e-06
 5.27632e-05
 7.53761e-06
 0.00018882
 4.31987e-20
 4.16469e-05
 -5.94955e-06
 4.16469e-05
 -5.94955e-06
 -3.01504e-05
 -2.37982e-05
 -1.59242e-19
 0.00018882
 -0.00018882
 -1.37219e-19
 -7.53761e-06
 -3.7688e-06
 7.53761e-06
 3.7688e-06
 4.31987e-20
 2.02307e-05
 -5.94955e-06
 2.97478e-06
 5.94955e-06
 -2.97478e-06
 -1.18585e-20
 -1.12232e-20
 -0.000934911
 -0.000217575
 -0.000249881
 -0.000934911
 3.62624e-05
 -5.18035e-06
 4.16469e-05
 -5.94955e-06
 0.000155819
 1.56701e-20
 3.62624e-05
 5.18035e-06
 4.16469e-05
 5.94955e-06
 -2.07214e-05
 -2.37982e-05
 0.000155819
 -1.18585e-19
 -8.47033e-21
 -0.000155819
 -5.18035e-06
 2.59017e-06
 -5.94955e-06
 2.97478e-06
 1.56701e-20
 1.66948e-05
 5.18035e-06
 2.59017e-06
 5.94955e-06
 2.97478e-06
 -9.31736e-21
 -1.48231e-21
 -0.000511026
 -0.000511026
 -0.000255513
 8.5171e-05
       0
 4.25855e-05
 -6.08364e-06
 4.25855e-05
 -6.08364e-06
 -2.43346e-05
 8.5171e-05
 -8.5171e-05
 -6.77626e-21
       0
 9.12546e-06
 -6.08364e-06
 3.04182e-06
 6.08364e-06
 -3.04182e-06
 -1.27055e-21
 -0.000217575
 -0.000847533
 -0.000847533
 -0.000206192
 3.62624e-05
 5.18035e-06
 3.62624e-05
 5.18035e-06
 0.000141255
 3.30343e-20
 3.43653e-05
 -4.90933e-06
 3.43653e-05
 -4.90933e-06
 -2.07214e-05
 -1.96373e-05
 -1.11808e-19
 0.000141255
 -0.000141255
 -1.10114e-19
 -5.18035e-06
 -2.59017e-06
 5.18035e-06
 2.59017e-06
 3.30343e-20
 1.51345e-05
 -4.90933e-06
 2.45466e-06
 4.90933e-06
 -2.45466e-06
 -8.47033e-21
 -8.89385e-21
 -0.00092341
 -0.000255513
 -0.000206192
 -0.00092341
 4.25855e-05
 -6.08364e-06
 3.43653e-05
 -4.90933e-06
 0.000153902
 1.99053e-20
 4.25855e-05
 6.08364e-06
 3.43653e-05
 4.90933e-06
 -2.43346e-05
 -1.96373e-05
 0.000153902
 -1.40607e-19
 -6.77626e-21
 -0.000153902
 -6.08364e-06
 3.04182e-06
 -4.90933e-06
 2.45466e-06
 1.99053e-20
 1.64895e-05
 6.08364e-06
 3.04182e-06
 4.90933e-06
 2.45466e-06
 -1.07997e-20
 -1.05879e-21
 -0.000527166
 -0.000527166
 -0.000263583
 8.78611e-05
       0
 4.39305e-05
 -6.27579e-06
 4.39305e-05
 -6.27579e-06
 -2.51032e-05
 8.78611e-05
 -8.78611e-05
 -5.0822e-21
       0
 9.41368e-06
 -6.27579e-06
 3.13789e-06
 6.27579e-06
 -3.13789e-06
 -1.27055e-21
 -0.000255513
 -0.00101728
 -0.00101728
 -0.000253125
 4.25855e-05
 6.08364e-06
 4.25855e-05
 6.08364e-06
 0.000169546
 3.89635e-20
 4.21875e-05
 -6.02679e-06
 4.21875e-05
 -6.02679e-06
 -2.43346e-05
 -2.41072e-05
 -1.33831e-19
 0.000169546
 -0.000169546
 -1.37219e-19
 -6.08364e-06
 -3.04182e-06
 6.08364e-06
 3.04182e-06
 3.89635e-20
 1.81656e-05
 -6.02679e-06
 3.01339e-06
 6.02679e-06
 -3.01339e-06
 -9.52912e-21
 -1.11173e-20
 -0.00103342
 -0.000263583
 -0.000253125
 -0.00103342
 4.39305e-05
 -6.27579e-06
 4.21875e-05
 -6.02679e-06
 0.000172236
 2.03288e-20
 4.39305e-05
 6.27579e-06
 4.21875e-05
 6.02679e-06
 -2.51032e-05
 -2.41072e-05
 0.000172236
 -1.42302e-19
 -6.77626e-21
 -0.000172236
 -6.27579e-06
 3.13789e-06
 -6.02679e-06
 3.01339e-06
 2.03288e-20
 1.84539e-05
 6.27579e-06
 3.13789e-06
 6.02679e-06
 3.01339e-06
 -1.12232e-20
 -1.27055e-21
 -0.000482684
 -0.000482684
 -0.000241342
 8.04474e-05
 -4.23516e-22
 4.02237e-05
 -5.74624e-06
 4.02237e-05
 -5.74624e-06
 -2.2985e-05
 8.04474e-05
 -8.04474e-05
 -5.0822e-21
 -4.23516e-22
 8.61936e-06
 -5.74624e-06
 2.87312e-06
 5.74624e-06
 -2.87312e-06
 -1.27055e-21
 -0.000263583
 -0.00102568
 -0.00102568
 -0.000249255
 4.39305e-05
 6.27579e-06
 4.39305e-05
 6.27579e-06
 0.000170946
 3.98105e-20
 4.15425e-05
 -5.93464e-06
 4.15425e-05
 -5.93464e-06
 -2.51032e-05
 -2.37386e-05
 -1.35525e-19
 0.000170946
 -0.000170946
 -1.35525e-19
 -6.27579e-06
 -3.13789e-06
 6.27579e-06
 3.13789e-06
 3.98105e-20
 1.83156e-05
 -5.93464e-06
 2.96732e-06
 5.93464e-06
 -2.96732e-06
 -1.01644e-20
 -1.09055e-20
 -0.000981194
 -0.000241342
 -0.000249255
 -0.000981194
 4.02237e-05
 -5.74624e-06
 4.15425e-05
 -5.93464e-06
 0.000163532
 1.90582e-20
 4.02237e-05
 5.74624e-06
 4.15425e-05
 5.93464e-06
 -2.2985e-05
 -2.37386e-05
 0.000163532
 -1.28749e-19
 -6.77626e-21
 -0.000163532
 -5.74624e-06
 2.87312e-06
 -5.93464e-06
 2.96732e-06
 1.90582e-20
 1.75213e-05
 5.74624e-06
 2.87312e-06
 5.93464e-06
 2.96732e-06
 -1.03762e-20
 -1.05879e-21
 -0.000427794
 -0.000427794
 -0.000213897
 7.1299e-05
       0
 3.56495e-05
 -5.09278e-06
 3.56495e-05
 -5.09278e-06
 -2.03711e-05
 7.1299e-05
 -7.1299e-05
 -1.69407e-21
       0
 7.63918e-06
 -5.09278e-06
 2.54639e-06
 5.09278e-06
 -2.54639e-06
 -1.27055e-21
 -0.000241342
 -0.00091465
 -0.00091465
 -0.000215983
 4.02237e-05
 5.74624e-06
 4.02237e-05
 5.74624e-06
 0.000152442
 3.47284e-20
 3.59972e-05
 -5.14245e-06
 3.59972e-05
 -5.14245e-06
 -2.2985e-05
 -2.05698e-05
 -1.21973e-19
 0.000152442
 -0.000152442
 -1.18585e-19
 -5.74624e-06
 -2.87312e-06
 5.74624e-06
 2.87312e-06
 3.47284e-20
 1.6333e-05
 -5.14245e-06
 2.57123e-06
 5.14245e-06
 -2.57123e-06
 -9.1056e-21
 -9.42324e-21
 -0.00085976
 -0.000213897
 -0.000215983
 -0.00085976
 3.56495e-05
 -5.09278e-06
 3.59972e-05
 -5.14245e-06
 0.000143293
 1.69407e-20
 3.56495e-05
 5.09278e-06
 3.59972e-05
 5.14245e-06
 -2.03711e-05
 -2.05698e-05
 0.000143293
 -1.15196e-19
 -5.0822e-21
 -0.000143293
 -5.09278e-06
 2.54639e-06
 -5.14245e-06
 2.57123e-06
 1.69407e-20
 1.53529e-05
 5.09278e-06
 2.54639e-06
 5.14245e-06
 2.57123e-06
 -9.31736e-21
 -1.48231e-21
 -0.000377417
 -0.000377417
 -0.000188709
 6.29029e-05
       0
 3.14514e-05
 -4.49306e-06
 3.14514e-05
 -4.49306e-06
 -1.79723e-05
 6.29029e-05
 -6.29029e-05
 -5.0822e-21
       0
 6.73959e-06
 -4.49306e-06
 2.24653e-06
 4.49306e-06
 -2.24653e-06
 -8.47033e-22
 -0.000213897
 -0.000790364
 -0.000790364
 -0.000181285
 3.56495e-05
 5.09278e-06
 3.56495e-05
 5.09278e-06
 0.000131727
 3.21873e-20
 3.02142e-05
 -4.31631e-06
 3.02142e-05
 -4.31631e-06
 -2.03711e-05
 -1.72652e-05
 -1.09267e-19
 0.000131727
 -0.000131727
 -9.65618e-20
 -5.09278e-06
 -2.54639e-06
 5.09278e-06
 2.54639e-06
 3.21873e-20
 1.41136e-05
 -4.31631e-06
 2.15815e-06
 4.31631e-06
 -2.15815e-06
 -8.68209e-21
 -7.94093e-21
 -0.000739987
 -0.000188709
 -0.000181285
 -0.000739987
 3.14514e-05
 -4.49306e-06
 3.02142e-05
 -4.31631e-06
 0.000123331
 1.43996e-20
 3.14514e-05
 4.49306e-06
 3.02142e-05
 4.31631e-06
 -1.79723e-05
 -1.72652e-05
 0.000123331
 -1.05032e-19
 -5.0822e-21
 -0.000123331
 -4.49306e-06
 2.24653e-06
 -4.31631e-06
 2.15815e-06
 1.43996e-20
 1.32141e-05
 4.49306e-06
 2.24653e-06
 4.31631e-06
 2.15815e-06
 -8.04681e-21
 -8.47033e-22
 -0.000188709
 -0.000735415
 -0.000735415
 -0.000178999
 3.14514e-05
 4.49306e-06
 3.14514e-05
 4.49306e-06
 0.000122569
 2.96462e-20
 2.98331e-05
 -4.26188e-06
 2.98331e-05
 -4.26188e-06
 -1.79723e-05
 -1.70475e-05
 -9.48677e-20
 0.000122569
 -0.000122569
 -9.65618e-20
 -4.49306e-06
 -2.24653e-06
 4.49306e-06
 2.24653e-06
 2.96462e-20
 1.31324e-05
 -4.26188e-06
 2.13094e-06
 4.26188e-06
 -2.13094e-06
 -7.6233e-21
 -7.83505e-21
 -0.000203707
 -0.000765412
 -0.000178999
 -0.000765412
 3.39512e-05
 4.85016e-06
 3.39512e-05
 4.85016e-06
 2.98331e-05
 -4.26188e-06
 0.000127569
 -1.60936e-20
 2.98331e-05
 4.26188e-06
 -1.94007e-05
 -1.70475e-05
 1.04185e-19
 0.000127569
 -3.38813e-21
 -0.000127569
 -4.85016e-06
 -2.42508e-06
 4.85016e-06
 2.42508e-06
 -4.26188e-06
 2.13094e-06
 -1.60936e-20
 1.36681e-05
 4.26188e-06
 2.13094e-06
 7.72918e-21
 -6.35275e-22
 -0.000365868
 -0.000365868
 -0.000182934
 6.09781e-05
       0
 3.0489e-05
 -4.35558e-06
 3.0489e-05
 -4.35558e-06
 -1.74223e-05
 6.09781e-05
 -6.09781e-05
 -3.38813e-21
       0
 6.53337e-06
 -4.35558e-06
 2.17779e-06
 4.35558e-06
 -2.17779e-06
 -8.47033e-22
 -0.000202026
 -0.000758322
 -0.000758322
 -0.000177135
 3.3671e-05
 4.81015e-06
 3.3671e-05
 4.81015e-06
 0.000126387
 3.04932e-20
 2.95225e-05
 -4.2175e-06
 2.95225e-05
 -4.2175e-06
 -1.92406e-05
 -1.687e-05
 -1.01644e-19
 0.000126387
 -0.000126387
 -9.74088e-20
 -4.81015e-06
 -2.40507e-06
 4.81015e-06
 2.40507e-06
 3.04932e-20
 1.35415e-05
 -4.2175e-06
 2.10875e-06
 4.2175e-06
 -2.10875e-06
 -8.25857e-21
 -7.94093e-21
 -0.000720138
 -0.000182934
 -0.000177135
 -0.000720138
 3.0489e-05
 -4.35558e-06
 2.95225e-05
 -4.2175e-06
 0.000120023
 1.43996e-20
 3.0489e-05
 4.35558e-06
 2.95225e-05
 4.2175e-06
 -1.74223e-05
 -1.687e-05
 0.000120023
 -1.01644e-19
 -6.77626e-21
 -0.000120023
 -4.35558e-06
 2.17779e-06
 -4.2175e-06
 2.10875e-06
 1.43996e-20
 1.28596e-05
 4.35558e-06
 2.17779e-06
 4.2175e-06
 2.10875e-06
 -7.72918e-21
 -6.35275e-22
 -0.000400898
 -0.000400898
 -0.000200449
 6.68164e-05
 -4.23516e-22
 3.34082e-05
 -4.7726e-06
 3.34082e-05
 -4.7726e-06
 -1.90904e-05
 6.68164e-05
 -6.68164e-05
 -5.0822e-21
 -4.23516e-22
 7.1589e-06
 -4.7726e-06
 2.3863e-06
 4.7726e-06
 -2.3863e-06
 -8.47033e-22
 -0.000182934
 -0.000713575
 -0.000713575
 -0.000173853
 3.0489e-05
 4.35558e-06
 3.0489e-05
 4.35558e-06
 0.000118929
 2.75286e-20
 2.89755e-05
 -4.13936e-06
 2.89755e-05
 -4.13936e-06
 -1.74223e-05
 -1.65574e-05
 -9.40207e-20
 0.000118929
 -0.000118929
 -9.48677e-20
 -4.35558e-06
 -2.17779e-06
 4.35558e-06
 2.17779e-06
 2.75286e-20
 1.27424e-05
 -4.13936e-06
 2.06968e-06
 4.13936e-06
 -2.06968e-06
 -7.19978e-21
 -7.41154e-21
 -0.000748605
 -0.000200449
 -0.000173853
 -0.000748605
 3.34082e-05
 -4.7726e-06
 2.89755e-05
 -4.13936e-06
 0.000124767
 1.60936e-20
 3.34082e-05
 4.7726e-06
 2.89755e-05
 4.13936e-06
 -1.90904e-05
 -1.65574e-05
 0.000124767
 -1.0842e-19
 -5.0822e-21
 -0.000124767
 -4.7726e-06
 2.3863e-06
 -4.13936e-06
 2.06968e-06
 1.60936e-20
 1.33679e-05
 4.7726e-06
 2.3863e-06
 4.13936e-06
 2.06968e-06
 -8.36445e-21
 -1.05879e-21
 -0.000428302
 -0.000428302
 -0.000214151
 7.13837e-05
       0
 3.56918e-05
 -5.09883e-06
 3.56918e-05
 -5.09883e-06
 -2.03953e-05
 7.13837e-05
 -7.13837e-05
 -5.0822e-21
       0
 7.64825e-06
 -5.09883e-06
 2.54942e-06
 5.09883e-06
 -2.54942e-06
 -1.05879e-21
 -0.000200449
 -0.000793712
 -0.000793712
 -0.000196407
 3.34082e-05
 4.7726e-06
 3.34082e-05
 4.7726e-06
 0.000132285
 3.21873e-20
 3.27345e-05
 -4.67635e-06
 3.27345e-05
 -4.67635e-06
 -1.90904e-05
 -1.87054e-05
 -1.04185e-19
 0.000132285
 -0.000132285
 -1.06726e-19
 -4.7726e-06
 -2.3863e-06
 4.7726e-06
 2.3863e-06
 3.21873e-20
 1.41734e-05
 -4.67635e-06
 2.33818e-06
 4.67635e-06
 -2.33818e-06
 -8.04681e-21
 -8.57621e-21
 -0.000821116
 -0.000214151
 -0.000196407
 -0.000821116
 3.56918e-05
 -5.09883e-06
 3.27345e-05
 -4.67635e-06
 0.000136853
 1.65171e-20
 3.56918e-05
 5.09883e-06
 3.27345e-05
 4.67635e-06
 -2.03953e-05
 -1.87054e-05
 0.000136853
 -1.18585e-19
 -6.77626e-21
 -0.000136853
 -5.09883e-06
 2.54942e-06
 -4.67635e-06
 2.33818e-06
 1.65171e-20
 1.46628e-05
 5.09883e-06
 2.54942e-06
 4.67635e-06
 2.33818e-06
 -9.1056e-21
 -1.05879e-21
 -0.00043348
 -0.00043348
 -0.00021674
 7.22467e-05
       0
 3.61234e-05
 -5.16048e-06
 3.61234e-05
 -5.16048e-06
 -2.06419e-05
 7.22467e-05
 -7.22467e-05
 -3.38813e-21
       0
 7.74072e-06
 -5.16048e-06
 2.58024e-06
 5.16048e-06
 -2.58024e-06
 -8.47033e-22
 -0.000214151
 -0.000846165
 -0.000846165
 -0.000208932
 3.56918e-05
 5.09883e-06
 3.56918e-05
 5.09883e-06
 0.000141028
 3.38813e-20
 3.48219e-05
 -4.97456e-06
 3.48219e-05
 -4.97456e-06
 -2.03953e-05
 -1.98982e-05
 -1.10961e-19
 0.000141028
 -0.000141028
 -1.15196e-19
 -5.09883e-06
 -2.54942e-06
 5.09883e-06
 2.54942e-06
 3.38813e-20
 1.51101e-05
 -4.97456e-06
 2.48728e-06
 4.97456e-06
 -2.48728e-06
 -8.25857e-21
 -9.21148e-21
 -0.000851343
 -0.00021674
 -0.000208932
 -0.000851343
 3.61234e-05
 -5.16048e-06
 3.48219e-05
 -4.97456e-06
 0.000141891
 1.60936e-20
 3.61234e-05
 5.16048e-06
 3.48219e-05
 4.97456e-06
 -2.06419e-05
 -1.98982e-05
 0.000141891
 -1.20279e-19
 -5.0822e-21
 -0.000141891
 -5.16048e-06
 2.58024e-06
 -4.97456e-06
 2.48728e-06
 1.60936e-20
 1.52026e-05
 5.16048e-06
 2.58024e-06
 4.97456e-06
 2.48728e-06
 -9.21148e-21
 -1.05879e-21
 -0.000480096
 -0.000480096
 -0.000240048
 8.0016e-05
 -4.23516e-22
 4.0008e-05
 -5.71543e-06
 4.0008e-05
 -5.71543e-06
 -2.28617e-05
 8.0016e-05
 -8.0016e-05
 -8.47033e-21
 -4.23516e-22
 8.57315e-06
 -5.71543e-06
 2.85772e-06
 5.71543e-06
 -2.85772e-06
 -1.05879e-21
 -0.00021674
 -0.000904366
 -0.000904366
 -0.000235443
 3.61234e-05
 5.16048e-06
 3.61234e-05
 5.16048e-06
 0.000150728
 3.55754e-20
 3.92404e-05
 -5.60578e-06
 3.92404e-05
 -5.60578e-06
 -2.06419e-05
 -2.24231e-05
 -1.13502e-19
 0.000150728
 -0.000150728
 -1.28749e-19
 -5.16048e-06
 -2.58024e-06
 5.16048e-06
 2.58024e-06
 3.55754e-20
 1.61494e-05
 -5.60578e-06
 2.80289e-06
 5.60578e-06
 -2.80289e-06
 -8.47033e-21
 -1.03762e-20
 -0.000950981
 -0.000240048
 -0.000235443
 -0.000950981
 4.0008e-05
 -5.71543e-06
 3.92404e-05
 -5.60578e-06
 0.000158497
 1.77877e-20
 4.0008e-05
 5.71543e-06
 3.92404e-05
 5.60578e-06
 -2.28617e-05
 -2.24231e-05
 0.000158497
 -1.32137e-19
 -6.77626e-21
 -0.000158497
 -5.71543e-06
 2.85772e-06
 -5.60578e-06
 2.80289e-06
 1.77877e-20
 1.69818e-05
 5.71543e-06
 2.85772e-06
 5.60578e-06
 2.80289e-06
 -1.03762e-20
 -1.48231e-21
 -0.000621108
 -0.000621108
 -0.000310554
 0.000103518
       0
 5.1759e-05
 -7.39414e-06
 5.1759e-05
 -7.39414e-06
 -2.95766e-05
 0.000103518
 -0.000103518
 -6.77626e-21
       0
 1.10912e-05
 -7.39414e-06
 3.69707e-06
 7.39414e-06
 -3.69707e-06
 -4.23516e-22
 -0.00126183
 -0.000310554
 -0.00126183
 -0.000320361
 5.1759e-05
 -7.39414e-06
 0.000210305
 2.37169e-20
 5.33935e-05
 -7.62765e-06
 5.1759e-05
 7.39414e-06
 5.33935e-05
 -7.62765e-06
 -2.95766e-05
 -3.05106e-05
 0.000210305
 -1.71101e-19
 -0.000210305
 -3.38813e-21
 -7.39414e-06
 3.69707e-06
 2.37169e-20
 2.25327e-05
 -7.62765e-06
 3.81382e-06
 7.39414e-06
 3.69707e-06
 7.62765e-06
 -3.81382e-06
 -1.3129e-20
 -1.27055e-21
 -0.000240048
 -0.00112082
 -0.000320361
 -0.00112082
 4.0008e-05
 5.71543e-06
 4.0008e-05
 5.71543e-06
 5.33935e-05
 -7.62765e-06
 0.000186803
 4.31987e-20
 5.33935e-05
 7.62765e-06
 -2.28617e-05
 -3.05106e-05
 -1.25361e-19
 0.000186803
 -1.72795e-19
 -0.000186803
 -5.71543e-06
 -2.85772e-06
 5.71543e-06
 2.85772e-06
 -7.62765e-06
 3.81382e-06
 4.31987e-20
 2.00146e-05
 7.62765e-06
 3.81382e-06
 -9.31736e-21
 -1.37643e-20
 -0.000372736
 -0.000310554
 -0.00136658
 -0.00136658
 6.21227e-05
 8.87466e-06
 6.21227e-05
 8.87466e-06
 5.1759e-05
 7.39414e-06
 5.1759e-05
 7.39414e-06
 0.000227763
 -3.38813e-21
 -2.95766e-05
 -3.54987e-05
 1.91429e-19
 -1.60936e-19
 0.000227763
 -0.000227763
 -8.87466e-06
 -4.43733e-06
 8.87466e-06
 4.43733e-06
 -7.39414e-06
 -3.69707e-06
 7.39414e-06
 3.69707e-06
 -3.38813e-21
 2.44032e-05
 -1.27055e-20
 1.48231e-20
 -0.000359576
 -0.00136548
 -0.00136548
 -0.000323163
 5.99293e-05
 8.56133e-06
 5.99293e-05
 8.56133e-06
 0.00022758
 -2.87991e-20
 5.38605e-05
 -7.69435e-06
 5.38605e-05
 -7.69435e-06
 -3.42453e-05
 -3.07774e-05
 1.84653e-19
 0.00022758
 -0.00022758
 -1.35525e-20
 -8.56133e-06
 -4.28066e-06
 8.56133e-06
 4.28066e-06
 -2.87991e-20
 2.43835e-05
 -7.69435e-06
 3.84718e-06
 7.69435e-06
 -3.84718e-06
 1.41878e-20
 -1.69407e-21
 -0.000320361
 -0.00126104
 -0.00126104
 -0.00031016
 5.33935e-05
 7.62765e-06
 5.33935e-05
 7.62765e-06
 0.000210174
 4.91279e-20
 5.16933e-05
 -7.38475e-06
 5.16933e-05
 -7.38475e-06
 -3.05106e-05
 -2.9539e-05
 -1.64324e-19
 0.000210174
 -0.000210174
 -1.67713e-19
 -7.62765e-06
 -3.81382e-06
 7.62765e-06
 3.81382e-06
 4.91279e-20
 2.25186e-05
 -7.38475e-06
 3.69238e-06
 7.38475e-06
 -3.69238e-06
 -1.3129e-20
 -1.33408e-20
 -0.00126664
 -0.000323163
 -0.00031016
 -0.00126664
 5.38605e-05
 -7.69435e-06
 5.16933e-05
 -7.38475e-06
 0.000211107
 2.4564e-20
 5.38605e-05
 7.69435e-06
 5.16933e-05
 7.38475e-06
 -3.07774e-05
 -2.9539e-05
 0.000211107
 -1.74489e-19
 -6.77626e-21
 -0.000211107
 -7.69435e-06
 3.84718e-06
 -7.38475e-06
 3.69238e-06
 2.4564e-20
 2.26187e-05
 7.69435e-06
 3.84718e-06
 7.38475e-06
 3.69238e-06
 -1.41878e-20
 -1.69407e-21
 -0.000277025
 -0.00111582
 -0.00111582
 -0.000280887
 4.61708e-05
 6.59583e-06
 4.61708e-05
 6.59583e-06
 0.00018597
 -2.03288e-20
 4.68144e-05
 -6.68777e-06
 4.68144e-05
 -6.68777e-06
 -2.63833e-05
 -2.67511e-05
 1.42302e-19
 0.00018597
 -0.00018597
 -3.38813e-21
 -6.59583e-06
 -3.29792e-06
 6.59583e-06
 3.29792e-06
 -2.03288e-20
 1.99254e-05
 -6.68777e-06
 3.34389e-06
 6.68777e-06
 -3.34389e-06
 1.07997e-20
 -8.47033e-22
 -0.00112433
 -0.000280887
 -0.00112433
 -0.000281276
 4.68144e-05
 -6.68777e-06
 0.000187388
 2.20229e-20
 4.68794e-05
 -6.69706e-06
 4.68144e-05
 6.68777e-06
 4.68794e-05
 -6.69706e-06
 -2.67511e-05
 -2.67882e-05
 0.000187388
 -1.5416e-19
 -0.000187388
       0
 -6.68777e-06
 3.34389e-06
 2.20229e-20
 2.00772e-05
 -6.69706e-06
 3.34853e-06
 6.68777e-06
 3.34389e-06
 6.69706e-06
 -3.34853e-06
 -1.17526e-20
 -8.47033e-22
 -0.000323163
 -0.00120888
 -0.000281276
 -0.00120888
 5.38605e-05
 7.69435e-06
 5.38605e-05
 7.69435e-06
 4.68794e-05
 -6.69706e-06
 0.00020148
 4.82809e-20
 4.68794e-05
 6.69706e-06
 -3.07774e-05
 -2.67882e-05
 -1.6263e-19
 0.00020148
 -1.52466e-19
 -0.00020148
 -7.69435e-06
 -3.84718e-06
 7.69435e-06
 3.84718e-06
 -6.69706e-06
 3.34853e-06
 4.82809e-20
 2.15871e-05
 6.69706e-06
 3.34853e-06
 -1.27055e-20
 -1.17526e-20
 -0.000238526
 -0.000966311
 -0.000966311
 -0.000244629
 3.97544e-05
 5.6792e-06
 3.97544e-05
 5.6792e-06
 0.000161052
 -1.90582e-20
 4.07715e-05
 -5.8245e-06
 4.07715e-05
 -5.8245e-06
 -2.27168e-05
 -2.3298e-05
 1.18585e-19
 0.000161052
 -0.000161052
 -5.0822e-21
 -5.6792e-06
 -2.8396e-06
 5.6792e-06
 2.8396e-06
 -1.90582e-20
 1.72555e-05
 -5.8245e-06
 2.91225e-06
 5.8245e-06
 -2.91225e-06
 9.31736e-21
 -1.27055e-21
 -0.000280887
 -0.00108244
 -0.00108244
 -0.000260334
 4.68144e-05
 6.68777e-06
 4.68144e-05
 6.68777e-06
 0.000180407
 3.98105e-20
 4.3389e-05
 -6.19842e-06
 4.3389e-05
 -6.19842e-06
 -2.67511e-05
 -2.47937e-05
 -1.49078e-19
 0.000180407
 -0.000180407
 -1.40607e-19
 -6.68777e-06
 -3.34389e-06
 6.68777e-06
 3.34389e-06
 3.98105e-20
 1.93293e-05
 -6.19842e-06
 3.09921e-06
 6.19842e-06
 -3.09921e-06
 -1.07997e-20
 -1.11173e-20
 -0.00100993
 -0.000244629
 -0.000260334
 -0.00100993
 4.07715e-05
 -5.8245e-06
 4.3389e-05
 -6.19842e-06
 0.000168321
 1.73642e-20
 4.07715e-05
 5.8245e-06
 4.3389e-05
 6.19842e-06
 -2.3298e-05
 -2.47937e-05
 0.000168321
 -1.32137e-19
 -8.47033e-21
 -0.000168321
 -5.8245e-06
 2.91225e-06
 -6.19842e-06
 3.09921e-06
 1.73642e-20
 1.80344e-05
 5.8245e-06
 2.91225e-06
 6.19842e-06
 3.09921e-06
 -1.03762e-20
 -1.27055e-21
 -0.000204028
 -0.000829451
 -0.000829451
 -0.000210697
 3.40046e-05
 4.8578e-06
 3.40046e-05
 4.8578e-06
 0.000138242
 -1.3976e-20
 3.51162e-05
 -5.01661e-06
 3.51162e-05
 -5.01661e-06
 -1.94312e-05
 -2.00664e-05
 1.06726e-19
 0.000138242
 -0.000138242
 -3.38813e-21
 -4.8578e-06
 -2.4289e-06
 4.8578e-06
 2.4289e-06
 -1.3976e-20
 1.48116e-05
 -5.01661e-06
 2.5083e-06
 5.01661e-06
 -2.5083e-06
 7.6233e-21
 -8.47033e-22
 -0.000862373
 -0.000210697
 -0.000862373
 -0.000220489
 3.51162e-05
 -5.01661e-06
 0.000143729
 1.60936e-20
 3.67482e-05
 -5.24974e-06
 3.51162e-05
 5.01661e-06
 3.67482e-05
 -5.24974e-06
 -2.00664e-05
 -2.0999e-05
 0.000143729
 -1.15196e-19
 -0.000143729
 -3.38813e-21
 -5.01661e-06
 2.5083e-06
 1.60936e-20
 1.53995e-05
 -5.24974e-06
 2.62487e-06
 5.01661e-06
 2.5083e-06
 5.24974e-06
 -2.62487e-06
 -8.78797e-21
 -6.35275e-22
 -0.000244629
 -0.000930236
 -0.000220489
 -0.000930236
 4.07715e-05
 5.8245e-06
 4.07715e-05
 5.8245e-06
 3.67482e-05
 -5.24974e-06
 0.000155039
 3.81165e-20
 3.67482e-05
 5.24974e-06
 -2.3298e-05
 -2.0999e-05
 -1.25361e-19
 0.000155039
 -1.21973e-19
 -0.000155039
 -5.8245e-06
 -2.91225e-06
 5.8245e-06
 2.91225e-06
 -5.24974e-06
 2.62487e-06
 3.81165e-20
 1.66114e-05
 5.24974e-06
 2.62487e-06
 -9.31736e-21
 -9.31736e-21
 -0.000194884
 -0.000730668
 -0.000730668
 -0.00017045
 3.24807e-05
 4.64011e-06
 3.24807e-05
 4.64011e-06
 0.000121778
 -1.69407e-20
 2.84083e-05
 -4.05832e-06
 2.84083e-05
 -4.05832e-06
 -1.85604e-05
 -1.62333e-05
 9.74088e-20
 0.000121778
 -0.000121778
 -3.38813e-21
 -4.64011e-06
 -2.32005e-06
 4.64011e-06
 2.32005e-06
 -1.69407e-20
 1.30476e-05
 -4.05832e-06
 2.02916e-06
 4.05832e-06
 -2.02916e-06
 7.72918e-21
 -4.23516e-22
 -0.000210697
 -0.000763778
 -0.000763778
 -0.000171191
 3.51162e-05
 5.01661e-06
 3.51162e-05
 5.01661e-06
 0.000127296
 2.96462e-20
 2.85319e-05
 -4.07599e-06
 2.85319e-05
 -4.07599e-06
 -2.00664e-05
 -1.63039e-05
 -1.0842e-19
 0.000127296
 -0.000127296
 -9.48677e-20
 -5.01661e-06
 -2.5083e-06
 5.01661e-06
 2.5083e-06
 2.96462e-20
 1.36389e-05
 -4.07599e-06
 2.03799e-06
 4.07599e-06
 -2.03799e-06
 -7.83505e-21
 -7.41154e-21
 -0.000683282
 -0.00017045
 -0.000171191
 -0.000683282
 2.84083e-05
 -4.05832e-06
 2.85319e-05
 -4.07599e-06
 0.00011388
 1.27055e-20
 2.84083e-05
 4.05832e-06
 2.85319e-05
 4.07599e-06
 -1.62333e-05
 -1.63039e-05
 0.00011388
 -9.31736e-20
 -5.0822e-21
 -0.00011388
 -4.05832e-06
 2.02916e-06
 -4.07599e-06
 2.03799e-06
 1.27055e-20
 1.22015e-05
 4.05832e-06
 2.02916e-06
 4.07599e-06
 2.03799e-06
 -7.41154e-21
 -8.47033e-22
 -0.000186791
 -0.00081494
 -0.00081494
 -0.000220679
 3.11318e-05
 4.4474e-06
 3.11318e-05
 4.4474e-06
 0.000135823
 -1.52466e-20
 3.67798e-05
 -5.25426e-06
 3.67798e-05
 -5.25426e-06
 -1.77896e-05
 -2.1017e-05
 9.48677e-20
 0.000135823
 -0.000135823
 -5.0822e-21
 -4.4474e-06
 -2.2237e-06
 4.4474e-06
 2.2237e-06
 -1.52466e-20
 1.45525e-05
 -5.25426e-06
 2.62713e-06
 5.25426e-06
 -2.62713e-06
 7.19978e-21
 -1.05879e-21
 -0.00017045
 -0.000704212
 -0.000704212
 -0.000181657
 2.84083e-05
 4.05832e-06
 2.84083e-05
 4.05832e-06
 0.000117369
 2.6258e-20
 3.02761e-05
 -4.32516e-06
 3.02761e-05
 -4.32516e-06
 -1.62333e-05
 -1.73006e-05
 -8.63974e-20
 0.000117369
 -0.000117369
 -9.82558e-20
 -4.05832e-06
 -2.02916e-06
 4.05832e-06
 2.02916e-06
 2.6258e-20
 1.25752e-05
 -4.32516e-06
 2.16258e-06
 4.32516e-06
 -2.16258e-06
 -6.98802e-21
 -8.04681e-21
 -0.000804671
 -0.000220679
 -0.000181657
 -0.000804671
 3.67798e-05
 -5.25426e-06
 3.02761e-05
 -4.32516e-06
 0.000134112
 1.69407e-20
 3.67798e-05
 5.25426e-06
 3.02761e-05
 4.32516e-06
 -2.1017e-05
 -1.73006e-05
 0.000134112
 -1.18585e-19
 -6.77626e-21
 -0.000134112
 -5.25426e-06
 2.62713e-06
 -4.32516e-06
 2.16258e-06
 1.69407e-20
 1.43691e-05
 5.25426e-06
 2.62713e-06
 4.32516e-06
 2.16258e-06
 -9.31736e-21
 -8.47033e-22
 -0.00016114
 -0.000678856
 -0.000678856
 -0.000178288
 2.68567e-05
 3.83668e-06
 2.68567e-05
 3.83668e-06
 0.000113143
 -1.27055e-20
 2.97146e-05
 -4.24494e-06
 2.97146e-05
 -4.24494e-06
 -1.53467e-05
 -1.69798e-05
 8.30092e-20
 0.000113143
 -0.000113143
 -5.0822e-21
 -3.83668e-06
 -1.91834e-06
 3.83668e-06
 1.91834e-06
 -1.27055e-20
 1.21224e-05
 -4.24494e-06
 2.12247e-06
 4.24494e-06
 -2.12247e-06
 6.56451e-21
 -8.47033e-22
 -0.000220679
 -0.000797933
 -0.000178288
 -0.000797933
 3.67798e-05
 5.25426e-06
 3.67798e-05
 5.25426e-06
 2.97146e-05
 -4.24494e-06
 0.000132989
 3.04932e-20
 2.97146e-05
 4.24494e-06
 -2.1017e-05
 -1.69798e-05
 -1.10114e-19
 0.000132989
 -9.65618e-20
 -0.000132989
 -5.25426e-06
 -2.62713e-06
 5.25426e-06
 2.62713e-06
 -4.24494e-06
 2.12247e-06
 3.04932e-20
 1.42488e-05
 4.24494e-06
 2.12247e-06
 -8.68209e-21
 -7.72918e-21
 -0.000156325
 -0.00067274
 -0.00067274
 -0.000180045
 2.60542e-05
 3.72202e-06
 2.60542e-05
 3.72202e-06
 0.000112123
 -1.2282e-20
 3.00075e-05
 -4.28679e-06
 3.00075e-05
 -4.28679e-06
 -1.48881e-05
 -1.71472e-05
 7.87741e-20
 0.000112123
 -0.000112123
 -6.77626e-21
 -3.72202e-06
 -1.86101e-06
 3.72202e-06
 1.86101e-06
 -1.2282e-20
 1.20132e-05
 -4.28679e-06
 2.1434e-06
 4.28679e-06
 -2.1434e-06
 5.92923e-21
 -4.23516e-22
 -0.000178288
 -0.000716666
 -0.000180045
 -0.000716666
 2.97146e-05
 4.24494e-06
 2.97146e-05
 4.24494e-06
 3.00075e-05
 -4.28679e-06
 0.000119444
 2.6258e-20
 3.00075e-05
 4.28679e-06
 -1.69798e-05
 -1.71472e-05
 -8.89385e-20
 0.000119444
 -9.82558e-20
 -0.000119444
 -4.24494e-06
 -2.12247e-06
 4.24494e-06
 2.12247e-06
 -4.28679e-06
 2.1434e-06
 2.6258e-20
 1.27976e-05
 4.28679e-06
 2.1434e-06
 -6.77626e-21
 -7.72918e-21
 -0.000210478
 -0.000848746
 -0.000848746
 -0.000213896
 3.50796e-05
 5.01137e-06
 3.50796e-05
 5.01137e-06
 0.000141458
 -1.52466e-20
 3.56493e-05
 -5.09275e-06
 3.56493e-05
 -5.09275e-06
 -2.00455e-05
 -2.0371e-05
 1.0842e-19
 0.000141458
 -0.000141458
 -8.47033e-21
 -5.01137e-06
 -2.50569e-06
 5.01137e-06
 2.50569e-06
 -1.52466e-20
 1.51562e-05
 -5.09275e-06
 2.54638e-06
 5.09275e-06
 -2.54638e-06
 7.94093e-21
 -8.47033e-22
 -0.000180045
 -0.000819406
 -0.000819406
 -0.000229658
 3.00075e-05
 4.28679e-06
 3.00075e-05
 4.28679e-06
 0.000136568
 3.30343e-20
 3.82763e-05
 -5.46804e-06
 3.82763e-05
 -5.46804e-06
 -1.71472e-05
 -2.18722e-05
 -8.97855e-20
 0.000136568
 -0.000136568
 -1.25361e-19
 -4.28679e-06
 -2.1434e-06
 4.28679e-06
 2.1434e-06
 3.30343e-20
 1.46322e-05
 -5.46804e-06
 2.73402e-06
 5.46804e-06
 -2.73402e-06
 -7.19978e-21
 -9.84676e-21
 -0.000887106
 -0.000213896
 -0.000229658
 -0.000887106
 3.56493e-05
 -5.09275e-06
 3.82763e-05
 -5.46804e-06
 0.000147851
 1.56701e-20
 3.56493e-05
 5.09275e-06
 3.82763e-05
 5.46804e-06
 -2.0371e-05
 -2.18722e-05
 0.000147851
 -1.18585e-19
 -6.77626e-21
 -0.000147851
 -5.09275e-06
 2.54638e-06
 -5.46804e-06
 2.73402e-06
 1.56701e-20
 1.58412e-05
 5.09275e-06
 2.54638e-06
 5.46804e-06
 2.73402e-06
 -9.21148e-21
 -1.05879e-21
 -0.000232685
 -0.000936476
 -0.000936476
 -0.000235553
 3.87808e-05
 5.54011e-06
 3.87808e-05
 5.54011e-06
 0.000156079
 -1.86347e-20
 3.92589e-05
 -5.60842e-06
 3.92589e-05
 -5.60842e-06
 -2.21605e-05
 -2.24337e-05
 1.18585e-19
 0.000156079
 -0.000156079
 -8.47033e-21
 -5.54011e-06
 -2.77006e-06
 5.54011e-06
 2.77006e-06
 -1.86347e-20
 1.67228e-05
 -5.60842e-06
 2.80421e-06
 5.60842e-06
 -2.80421e-06
 8.99973e-21
 -1.05879e-21
 -0.000213896
 -0.00089638
 -0.00089638
 -0.000234294
 3.56493e-05
 5.09275e-06
 3.56493e-05
 5.09275e-06
 0.000149397
 3.30343e-20
 3.90491e-05
 -5.57844e-06
 3.90491e-05
 -5.57844e-06
 -2.0371e-05
 -2.23138e-05
 -1.10961e-19
 0.000149397
 -0.000149397
 -1.23667e-19
 -5.09275e-06
 -2.54638e-06
 5.09275e-06
 2.54638e-06
 3.30343e-20
 1.60068e-05
 -5.57844e-06
 2.78922e-06
 5.57844e-06
 -2.78922e-06
 -8.47033e-21
 -1.03762e-20
 -0.000939696
 -0.000235553
 -0.000234294
 -0.000939696
 3.92589e-05
 -5.60842e-06
 3.90491e-05
 -5.57844e-06
 0.000156616
 1.82112e-20
 3.92589e-05
 5.60842e-06
 3.90491e-05
 5.57844e-06
 -2.24337e-05
 -2.23138e-05
 0.000156616
 -1.25361e-19
 -8.47033e-21
 -0.000156616
 -5.60842e-06
 2.80421e-06
 -5.57844e-06
 2.78922e-06
 1.82112e-20
 1.67803e-05
 5.60842e-06
 2.80421e-06
 5.57844e-06
 2.78922e-06
 -1.01644e-20
 -1.27055e-21
 -0.000243001
 -0.000991198
 -0.000991198
 -0.000252598
 4.05002e-05
 5.78574e-06
 4.05002e-05
 5.78574e-06
 0.0001652
 -1.65171e-20
 4.20997e-05
 -6.01424e-06
 4.20997e-05
 -6.01424e-06
 -2.3143e-05
 -2.40569e-05
 1.25361e-19
 0.0001652
 -0.0001652
 -8.47033e-21
 -5.78574e-06
 -2.89287e-06
 5.78574e-06
 2.89287e-06
 -1.65171e-20
 1.77e-05
 -6.01424e-06
 3.00712e-06
 6.01424e-06
 -3.00712e-06
 9.74088e-21
 -1.05879e-21
 -0.000235553
 -0.000983702
 -0.000983702
 -0.000256297
 3.92589e-05
 5.60842e-06
 3.92589e-05
 5.60842e-06
 0.00016395
 3.72694e-20
 4.27162e-05
 -6.10232e-06
 4.27162e-05
 -6.10232e-06
 -2.24337e-05
 -2.44093e-05
 -1.20279e-19
 0.00016395
 -0.00016395
 -1.40607e-19
 -5.60842e-06
 -2.80421e-06
 5.60842e-06
 2.80421e-06
 3.72694e-20
 1.75661e-05
 -6.10232e-06
 3.05116e-06
 6.10232e-06
 -3.05116e-06
 -8.99973e-21
 -1.13291e-20
 -0.00101779
 -0.000252598
 -0.000256297
 -0.00101779
 4.20997e-05
 -6.01424e-06
 4.27162e-05
 -6.10232e-06
 0.000169632
 1.90582e-20
 4.20997e-05
 6.01424e-06
 4.27162e-05
 6.10232e-06
 -2.40569e-05
 -2.44093e-05
 0.000169632
 -1.37219e-19
 -5.0822e-21
 -0.000169632
 -6.01424e-06
 3.00712e-06
 -6.10232e-06
 3.05116e-06
 1.90582e-20
 1.81748e-05
 6.01424e-06
 3.00712e-06
 6.10232e-06
 3.05116e-06
 -1.07997e-20
 -1.27055e-21
 -0.00024244
 -0.000985824
 -0.000985824
 -0.000250472
 4.04066e-05
 5.77237e-06
 4.04066e-05
 5.77237e-06
 0.000164304
 -1.90582e-20
 4.17454e-05
 -5.96363e-06
 4.17454e-05
 -5.96363e-06
 -2.30895e-05
 -2.38545e-05
 1.25361e-19
 0.000164304
 -0.000164304
 -6.77626e-21
 -5.77237e-06
 -2.88619e-06
 5.77237e-06
 2.88619e-06
 -1.90582e-20
 1.7604e-05
 -5.96363e-06
 2.98181e-06
 5.96363e-06
 -2.98181e-06
 9.52912e-21
 -1.27055e-21
 -0.000252598
 -0.0010206
 -0.0010206
 -0.000257702
 4.20997e-05
 6.01424e-06
 4.20997e-05
 6.01424e-06
 0.0001701
 4.06576e-20
 4.29503e-05
 -6.13576e-06
 4.29503e-05
 -6.13576e-06
 -2.40569e-05
 -2.45431e-05
 -1.30443e-19
 0.0001701
 -0.0001701
 -1.40607e-19
 -6.01424e-06
 -3.00712e-06
 6.01424e-06
 3.00712e-06
 4.06576e-20
 1.8225e-05
 -6.13576e-06
 3.06788e-06
 6.13576e-06
 -3.06788e-06
 -1.00585e-20
 -1.12232e-20
 -0.00101635
 -0.000250472
 -0.000257702
 -0.00101635
 4.17454e-05
 -5.96363e-06
 4.29503e-05
 -6.13576e-06
 0.000169392
 1.94818e-20
 4.17454e-05
 5.96363e-06
 4.29503e-05
 6.13576e-06
 -2.38545e-05
 -2.45431e-05
 0.000169392
 -1.37219e-19
 -6.77626e-21
 -0.000169392
 -5.96363e-06
 2.98181e-06
 -6.13576e-06
 3.06788e-06
 1.94818e-20
 1.81491e-05
 5.96363e-06
 2.98181e-06
 6.13576e-06
 3.06788e-06
 -1.10114e-20
 -1.27055e-21
 -0.000249881
 -0.000931524
 -0.000931524
 -0.000215881
 4.16469e-05
 5.94955e-06
 4.16469e-05
 5.94955e-06
 0.000155254
 -1.82112e-20
 3.59802e-05
 -5.14002e-06
 3.59802e-05
 -5.14002e-06
 -2.37982e-05
 -2.05601e-05
 1.28749e-19
 0.000155254
 -0.000155254
 -6.77626e-21
 -5.94955e-06
 -2.97478e-06
 5.94955e-06
 2.97478e-06
 -1.82112e-20
 1.66344e-05
 -5.14002e-06
 2.57001e-06
 5.14002e-06
 -2.57001e-06
 1.02703e-20
 -1.05879e-21
 -0.000250472
 -0.000932707
 -0.000215881
 -0.000932707
 4.17454e-05
 5.96363e-06
 4.17454e-05
 5.96363e-06
 3.59802e-05
 -5.14002e-06
 0.000155451
 3.47284e-20
 3.59802e-05
 5.14002e-06
 -2.38545e-05
 -2.05601e-05
 -1.30443e-19
 0.000155451
 -1.18585e-19
 -0.000155451
 -5.96363e-06
 -2.98181e-06
 5.96363e-06
 2.98181e-06
 -5.14002e-06
 2.57001e-06
 3.47284e-20
 1.66555e-05
 5.14002e-06
 2.57001e-06
 -1.00585e-20
 -9.1056e-21
 -0.000206192
 -0.0008443
 -0.0008443
 -0.000215958
 3.43653e-05
 4.90933e-06
 3.43653e-05
 4.90933e-06
 0.000140717
 -1.56701e-20
 3.59931e-05
 -5.14187e-06
 3.59931e-05
 -5.14187e-06
 -1.96373e-05
 -2.05675e-05
 1.02491e-19
 0.000140717
 -0.000140717
 -5.0822e-21
 -4.90933e-06
 -2.45466e-06
 4.90933e-06
 2.45466e-06
 -1.56701e-20
 1.50768e-05
 -5.14187e-06
 2.57093e-06
 5.14187e-06
 -2.57093e-06
 8.57621e-21
 -8.47033e-22
 -0.000215881
 -0.000863679
 -0.000215958
 -0.000863679
 3.59802e-05
 5.14002e-06
 3.59802e-05
 5.14002e-06
 3.59931e-05
 -5.14187e-06
 0.000143946
 3.30343e-20
 3.59931e-05
 5.14187e-06
 -2.05601e-05
 -2.05675e-05
 -1.10961e-19
 0.000143946
 -1.18585e-19
 -0.000143946
 -5.14002e-06
 -2.57001e-06
 5.14002e-06
 2.57001e-06
 -5.14187e-06
 2.57093e-06
 3.30343e-20
 1.54228e-05
 5.14187e-06
 2.57093e-06
 -8.25857e-21
 -9.52912e-21
 -0.000253125
 -0.00111205
 -0.00111205
 -0.000302901
 4.21875e-05
 6.02679e-06
 4.21875e-05
 6.02679e-06
 0.000185342
 -1.86347e-20
 5.04835e-05
 -7.21193e-06
 5.04835e-05
 -7.21193e-06
 -2.41072e-05
 -2.88477e-05
 1.30443e-19
 0.000185342
 -0.000185342
 -1.01644e-20
 -6.02679e-06
 -3.01339e-06
 6.02679e-06
 3.01339e-06
 -1.86347e-20
 1.98581e-05
 -7.21193e-06
 3.60597e-06
 7.21193e-06
 -3.60597e-06
 9.95264e-21
 -8.47033e-22
 -0.000215958
 -0.00103388
 -0.00103388
 -0.000300982
 3.59931e-05
 5.14187e-06
 3.59931e-05
 5.14187e-06
 0.000172313
 3.98105e-20
 5.01636e-05
 -7.16624e-06
 5.01636e-05
 -7.16624e-06
 -2.05675e-05
 -2.86649e-05
 -1.11808e-19
 0.000172313
 -0.000172313
 -1.64324e-19
 -5.14187e-06
 -2.57093e-06
 5.14187e-06
 2.57093e-06
 3.98105e-20
 1.84622e-05
 -7.16624e-06
 3.58312e-06
 7.16624e-06
 -3.58312e-06
 -8.57621e-21
 -1.33408e-20
 -0.00120777
 -0.000302901
 -0.000300982
 -0.00120777
 5.04835e-05
 -7.21193e-06
 5.01636e-05
 -7.16624e-06
 0.000201294
 2.28699e-20
 5.04835e-05
 7.21193e-06
 5.01636e-05
 7.16624e-06
 -2.88477e-05
 -2.86649e-05
 0.000201294
 -1.64324e-19
 -1.01644e-20
 -0.000201294
 -7.21193e-06
 3.60597e-06
 -7.16624e-06
 3.58312e-06
 2.28699e-20
 2.15672e-05
 7.21193e-06
 3.60597e-06
 7.16624e-06
 3.58312e-06
 -1.24937e-20
 -1.27055e-21
 -0.000249255
 -0.00101744
 -0.00101744
 -0.000259464
 4.15425e-05
 5.93464e-06
 4.15425e-05
 5.93464e-06
 0.000169573
 -2.03288e-20
 4.32439e-05
 -6.17771e-06
 4.32439e-05
 -6.17771e-06
 -2.37386e-05
 -2.47108e-05
 1.30443e-19
 0.000169573
 -0.000169573
 -6.77626e-21
 -5.93464e-06
 -2.96732e-06
 5.93464e-06
 2.96732e-06
 -2.03288e-20
 1.81685e-05
 -6.17771e-06
 3.08885e-06
 6.17771e-06
 -3.08885e-06
 1.03762e-20
 -8.47033e-22
 -0.00114647
 -0.000259464
 -0.00114647
 -0.000313773
 4.32439e-05
 -6.17771e-06
 0.000191079
 1.94818e-20
 5.22955e-05
 -7.47078e-06
 4.32439e-05
 6.17771e-06
 5.22955e-05
 -7.47078e-06
 -2.47108e-05
 -2.98831e-05
 0.000191079
 -1.40607e-19
 -0.000191079
 -3.38813e-21
 -6.17771e-06
 3.08885e-06
 1.94818e-20
 2.04727e-05
 -7.47078e-06
 3.73539e-06
 6.17771e-06
 3.08885e-06
 7.47078e-06
 -3.73539e-06
 -1.10114e-20
 -1.27055e-21
 -0.000302901
 -0.00123335
 -0.000313773
 -0.00123335
 5.04835e-05
 7.21193e-06
 5.04835e-05
 7.21193e-06
 5.22955e-05
 -7.47078e-06
 0.000205558
 4.74338e-20
 5.22955e-05
 7.47078e-06
 -2.88477e-05
 -2.98831e-05
 -1.52466e-19
 0.000205558
 -1.67713e-19
 -0.000205558
 -7.21193e-06
 -3.60597e-06
 7.21193e-06
 3.60597e-06
 -7.47078e-06
 3.73539e-06
 4.74338e-20
 2.20241e-05
 7.47078e-06
 3.73539e-06
 -1.16467e-20
 -1.29173e-20
 -0.000215983
 -0.000880872
 -0.000880872
 -0.000224453
 3.59972e-05
 5.14245e-06
 3.59972e-05
 5.14245e-06
 0.000146812
 -1.60936e-20
 3.74088e-05
 -5.34412e-06
 3.74088e-05
 -5.34412e-06
 -2.05698e-05
 -2.13765e-05
 1.10961e-19
 0.000146812
 -0.000146812
 -3.38813e-21
 -5.14245e-06
 -2.57123e-06
 5.14245e-06
 2.57123e-06
 -1.60936e-20
 1.57299e-05
 -5.34412e-06
 2.67206e-06
 5.34412e-06
 -2.67206e-06
 8.25857e-21
 -1.05879e-21
 -0.000259464
 -0.00100712
 -0.00100712
 -0.000244096
 4.32439e-05
 6.17771e-06
 4.32439e-05
 6.17771e-06
 0.000167853
 4.06576e-20
 4.06826e-05
 -5.81181e-06
 4.06826e-05
 -5.81181e-06
 -2.47108e-05
 -2.32472e-05
 -1.33831e-19
 0.000167853
 -0.000167853
 -1.33831e-19
 -6.17771e-06
 -3.08885e-06
 6.17771e-06
 3.08885e-06
 4.06576e-20
 1.79843e-05
 -5.81181e-06
 2.9059e-06
 5.81181e-06
 -2.9059e-06
 -1.01644e-20
 -1.06938e-20
 -0.000937098
 -0.000224453
 -0.000244096
 -0.000937098
 3.74088e-05
 -5.34412e-06
 4.06826e-05
 -5.81181e-06
 0.000156183
 1.73642e-20
 3.74088e-05
 5.34412e-06
 4.06826e-05
 5.81181e-06
 -2.13765e-05
 -2.32472e-05
 0.000156183
 -1.20279e-19
 -6.77626e-21
 -0.000156183
 -5.34412e-06
 2.67206e-06
 -5.81181e-06
 2.9059e-06
 1.73642e-20
 1.67339e-05
 5.34412e-06
 2.67206e-06
 5.81181e-06
 2.9059e-06
 -9.635e-21
 -1.05879e-21
 -0.000181285
 -0.000741857
 -0.000741857
 -0.000189643
 3.02142e-05
 4.31631e-06
 3.02142e-05
 4.31631e-06
 0.000123643
 -1.43996e-20
 3.16072e-05
 -4.51532e-06
 3.16072e-05
 -4.51532e-06
 -1.72652e-05
 -1.80613e-05
 9.40207e-20
 0.000123643
 -0.000123643
 -5.0822e-21
 -4.31631e-06
 -2.15815e-06
 4.31631e-06
 2.15815e-06
 -1.43996e-20
 1.32474e-05
 -4.51532e-06
 2.25766e-06
 4.51532e-06
 -2.25766e-06
 6.98802e-21
 -8.47033e-22
 -0.000224453
 -0.000842869
 -0.000842869
 -0.000196981
 3.74088e-05
 5.34412e-06
 3.74088e-05
 5.34412e-06
 0.000140478
 3.21873e-20
 3.28302e-05
 -4.69003e-06
 3.28302e-05
 -4.69003e-06
 -2.13765e-05
 -1.87601e-05
 -1.13502e-19
 0.000140478
 -0.000140478
 -1.06726e-19
 -5.34412e-06
 -2.67206e-06
 5.34412e-06
 2.67206e-06
 3.21873e-20
 1.50512e-05
 -4.69003e-06
 2.34502e-06
 4.69003e-06
 -2.34502e-06
 -8.68209e-21
 -8.78797e-21
 -0.000773249
 -0.000189643
 -0.000196981
 -0.000773249
 3.16072e-05
 -4.51532e-06
 3.28302e-05
 -4.69003e-06
 0.000128875
 1.52466e-20
 3.16072e-05
 4.51532e-06
 3.28302e-05
 4.69003e-06
 -1.80613e-05
 -1.87601e-05
 0.000128875
 -1.01644e-19
 -3.38813e-21
 -0.000128875
 -4.51532e-06
 2.25766e-06
 -4.69003e-06
 2.34502e-06
 1.52466e-20
 1.3808e-05
 4.51532e-06
 2.25766e-06
 4.69003e-06
 2.34502e-06
 -8.15269e-21
 -1.27055e-21
 -0.000178999
 -0.000657114
 -0.000657114
 -0.000149558
 2.98331e-05
 4.26188e-06
 2.98331e-05
 4.26188e-06
 0.000109519
 -1.35525e-20
 2.49263e-05
 -3.5609e-06
 2.49263e-05
 -3.5609e-06
 -1.70475e-05
 -1.42436e-05
 9.14796e-20
 0.000109519
 -0.000109519
 -5.0822e-21
 -4.26188e-06
 -2.13094e-06
 4.26188e-06
 2.13094e-06
 -1.35525e-20
 1.17342e-05
 -3.5609e-06
 1.78045e-06
 3.5609e-06
 -1.78045e-06
 7.41154e-21
 -6.35275e-22
 -0.000189643
 -0.000674584
 -0.000674584
 -0.000147649
 3.16072e-05
 4.51532e-06
 3.16072e-05
 4.51532e-06
 0.000112431
 2.5411e-20
 2.46081e-05
 -3.51544e-06
 2.46081e-05
 -3.51544e-06
 -1.80613e-05
 -1.40618e-05
 -9.74088e-20
 0.000112431
 -0.000112431
 -8.13152e-20
 -4.51532e-06
 -2.25766e-06
 4.51532e-06
 2.25766e-06
 2.5411e-20
 1.20461e-05
 -3.51544e-06
 1.75772e-06
 3.51544e-06
 -1.75772e-06
 -7.30566e-21
 -6.45863e-21
 -0.000594413
 -0.000149558
 -0.000147649
 -0.000594413
 2.49263e-05
 -3.5609e-06
 2.46081e-05
 -3.51544e-06
 9.90688e-05
 1.10114e-20
 2.49263e-05
 3.5609e-06
 2.46081e-05
 3.51544e-06
 -1.42436e-05
 -1.40618e-05
 9.90688e-05
 -8.13152e-20
 -1.69407e-21
 -9.90688e-05
 -3.5609e-06
 1.78045e-06
 -3.51544e-06
 1.75772e-06
 1.10114e-20
 1.06145e-05
 3.5609e-06
 1.78045e-06
 3.51544e-06
 1.75772e-06
 -6.35275e-21
 -6.35275e-22
 -0.000177135
 -0.000650426
 -0.000650426
 -0.000148078
 2.95225e-05
 4.2175e-06
 2.95225e-05
 4.2175e-06
 0.000108404
 -1.35525e-20
 2.46797e-05
 -3.52567e-06
 2.46797e-05
 -3.52567e-06
 -1.687e-05
 -1.41027e-05
 9.06325e-20
 0.000108404
 -0.000108404
 -5.0822e-21
 -4.2175e-06
 -2.10875e-06
 4.2175e-06
 2.10875e-06
 -1.35525e-20
 1.16147e-05
 -3.52567e-06
 1.76283e-06
 3.52567e-06
 -1.76283e-06
 6.98802e-21
 -8.47033e-22
 -0.000149558
 -0.000595272
 -0.000148078
 -0.000595272
 2.49263e-05
 3.5609e-06
 2.49263e-05
 3.5609e-06
 2.46797e-05
 -3.52567e-06
 9.9212e-05
 2.24464e-20
 2.46797e-05
 3.52567e-06
 -1.42436e-05
 -1.41027e-05
 -7.708e-20
 9.9212e-05
 -7.96211e-20
 -9.9212e-05
 -3.5609e-06
 -1.78045e-06
 3.5609e-06
 1.78045e-06
 -3.52567e-06
 1.76283e-06
 2.24464e-20
 1.06299e-05
 3.52567e-06
 1.76283e-06
 -5.82335e-21
 -6.35275e-21
 -0.000173853
 -0.000712981
 -0.000712981
 -0.000182637
 2.89755e-05
 4.13936e-06
 2.89755e-05
 4.13936e-06
 0.00011883
 -1.43996e-20
 3.04396e-05
 -4.34851e-06
 3.04396e-05
 -4.34851e-06
 -1.65574e-05
 -1.7394e-05
 8.97855e-20
 0.00011883
 -0.00011883
 -5.0822e-21
 -4.13936e-06
 -2.06968e-06
 4.13936e-06
 2.06968e-06
 -1.43996e-20
 1.27318e-05
 -4.34851e-06
 2.17425e-06
 4.34851e-06
 -2.17425e-06
 6.56451e-21
 -8.47033e-22
 -0.000148078
 -0.000587274
 -0.000587274
 -0.000145559
 2.46797e-05
 3.52567e-06
 2.46797e-05
 3.52567e-06
 9.7879e-05
 2.37169e-20
 2.42598e-05
 -3.46569e-06
 2.42598e-05
 -3.46569e-06
 -1.41027e-05
 -1.38628e-05
 -7.53859e-20
 9.7879e-05
 -9.7879e-05
 -7.96211e-20
 -3.52567e-06
 -1.76283e-06
 3.52567e-06
 1.76283e-06
 2.37169e-20
 1.0487e-05
 -3.46569e-06
 1.73284e-06
 3.46569e-06
 -1.73284e-06
 -5.71747e-21
 -6.14099e-21
 -0.000656392
 -0.000182637
 -0.000145559
 -0.000656392
 3.04396e-05
 -4.34851e-06
 2.42598e-05
 -3.46569e-06
 0.000109399
 1.43996e-20
 3.04396e-05
 4.34851e-06
 2.42598e-05
 3.46569e-06
 -1.7394e-05
 -1.38628e-05
 0.000109399
 -9.99499e-20
 -3.38813e-21
 -0.000109399
 -4.34851e-06
 2.17425e-06
 -3.46569e-06
 1.73284e-06
 1.43996e-20
 1.17213e-05
 4.34851e-06
 2.17425e-06
 3.46569e-06
 1.73284e-06
 -7.83505e-21
 -6.35275e-22
 -0.000196407
 -0.000804598
 -0.000804598
 -0.000205892
 3.27345e-05
 4.67635e-06
 3.27345e-05
 4.67635e-06
 0.0001341
 -1.52466e-20
 3.43153e-05
 -4.90219e-06
 3.43153e-05
 -4.90219e-06
 -1.87054e-05
 -1.96088e-05
 1.01644e-19
 0.0001341
 -0.0001341
 -6.77626e-21
 -4.67635e-06
 -2.33818e-06
 4.67635e-06
 2.33818e-06
 -1.52466e-20
 1.43678e-05
 -4.90219e-06
 2.4511e-06
 4.90219e-06
 -2.4511e-06
 8.04681e-21
 -8.47033e-22
 -0.000786515
 -0.000205892
 -0.000786515
 -0.000187365
 3.43153e-05
 -4.90219e-06
 0.000131086
 1.52466e-20
 3.12276e-05
 -4.46108e-06
 3.43153e-05
 4.90219e-06
 3.12276e-05
 -4.46108e-06
 -1.96088e-05
 -1.78443e-05
 0.000131086
 -1.13502e-19
 -0.000131086
 -3.38813e-21
 -4.90219e-06
 2.4511e-06
 1.52466e-20
 1.40449e-05
 -4.46108e-06
 2.23054e-06
 4.90219e-06
 2.4511e-06
 4.46108e-06
 -2.23054e-06
 -8.78797e-21
 -8.47033e-22
 -0.000182637
 -0.000740005
 -0.000187365
 -0.000740005
 3.04396e-05
 4.34851e-06
 3.04396e-05
 4.34851e-06
 3.12276e-05
 -4.46108e-06
 0.000123334
 2.79521e-20
 3.12276e-05
 4.46108e-06
 -1.7394e-05
 -1.78443e-05
 -9.48677e-20
 0.000123334
 -1.05032e-19
 -0.000123334
 -4.34851e-06
 -2.17425e-06
 4.34851e-06
 2.17425e-06
 -4.46108e-06
 2.23054e-06
 2.79521e-20
 1.32144e-05
 4.46108e-06
 2.23054e-06
 -6.88214e-21
 -7.94093e-21
 -0.000208932
 -0.000857634
 -0.000857634
 -0.000219886
 3.48219e-05
 4.97456e-06
 3.48219e-05
 4.97456e-06
 0.000142939
 -1.77877e-20
 3.66476e-05
 -5.23537e-06
 3.66476e-05
 -5.23537e-06
 -1.98982e-05
 -2.09415e-05
 1.06726e-19
 0.000142939
 -0.000142939
 -6.77626e-21
 -4.97456e-06
 -2.48728e-06
 4.97456e-06
 2.48728e-06
 -1.77877e-20
 1.53149e-05
 -5.23537e-06
 2.61768e-06
 5.23537e-06
 -2.61768e-06
 8.47033e-21
 -1.27055e-21
 -0.000205892
 -0.000836071
 -0.000836071
 -0.000212144
 3.43153e-05
 4.90219e-06
 3.43153e-05
 4.90219e-06
 0.000139345
 3.21873e-20
 3.53573e-05
 -5.05104e-06
 3.53573e-05
 -5.05104e-06
 -1.96088e-05
 -2.02041e-05
 -1.07573e-19
 0.000139345
 -0.000139345
 -1.15196e-19
 -4.90219e-06
 -2.4511e-06
 4.90219e-06
 2.4511e-06
 3.21873e-20
 1.49298e-05
 -5.05104e-06
 2.52552e-06
 5.05104e-06
 -2.52552e-06
 -8.04681e-21
 -9.21148e-21
 -0.000864058
 -0.000219886
 -0.000212144
 -0.000864058
 3.66476e-05
 -5.23537e-06
 3.53573e-05
 -5.05104e-06
 0.00014401
 1.60936e-20
 3.66476e-05
 5.23537e-06
 3.53573e-05
 5.05104e-06
 -2.09415e-05
 -2.02041e-05
 0.00014401
 -1.18585e-19
 -3.38813e-21
 -0.00014401
 -5.23537e-06
 2.61768e-06
 -5.05104e-06
 2.52552e-06
 1.60936e-20
 1.54296e-05
 5.23537e-06
 2.61768e-06
 5.05104e-06
 2.52552e-06
 -9.31736e-21
 -1.05879e-21
 -0.000235443
 -0.000880858
 -0.000880858
 -0.000204987
 3.92404e-05
 5.60578e-06
 3.92404e-05
 5.60578e-06
 0.00014681
 -1.69407e-20
 3.41644e-05
 -4.88063e-06
 3.41644e-05
 -4.88063e-06
 -2.24231e-05
 -1.95225e-05
 1.21973e-19
 0.00014681
 -0.00014681
 -3.38813e-21
 -5.60578e-06
 -2.80289e-06
 5.60578e-06
 2.80289e-06
 -1.69407e-20
 1.57296e-05
 -4.88063e-06
 2.44032e-06
 4.88063e-06
 -2.44032e-06
 8.99973e-21
 -8.47033e-22
 -0.000219886
 -0.000833263
 -0.000833263
 -0.000196746
 3.66476e-05
 5.23537e-06
 3.66476e-05
 5.23537e-06
 0.000138877
 3.21873e-20
 3.2791e-05
 -4.68443e-06
 3.2791e-05
 -4.68443e-06
 -2.09415e-05
 -1.87377e-05
 -1.13502e-19
 0.000138877
 -0.000138877
 -1.06726e-19
 -5.23537e-06
 -2.61768e-06
 5.23537e-06
 2.61768e-06
 3.21873e-20
 1.48797e-05
 -4.68443e-06
 2.34222e-06
 4.68443e-06
 -2.34222e-06
 -8.68209e-21
 -8.57621e-21
 -0.000803465
 -0.000204987
 -0.000196746
 -0.000803465
 3.41644e-05
 -4.88063e-06
 3.2791e-05
 -4.68443e-06
 0.000133911
 1.60936e-20
 3.41644e-05
 4.88063e-06
 3.2791e-05
 4.68443e-06
 -1.95225e-05
 -1.87377e-05
 0.000133911
 -1.13502e-19
 -5.0822e-21
 -0.000133911
 -4.88063e-06
 2.44032e-06
 -4.68443e-06
 2.34222e-06
 1.60936e-20
 1.43476e-05
 4.88063e-06
 2.44032e-06
 4.68443e-06
 2.34222e-06
 -8.78797e-21
 -8.47033e-22
 -0.00031016
 -0.00106099
 -0.00106099
 -0.000220336
 5.16933e-05
 7.38475e-06
 5.16933e-05
 7.38475e-06
 0.000176832
 -2.20229e-20
 3.67227e-05
 -5.24609e-06
 3.67227e-05
 -5.24609e-06
 -2.09844e-05
 -2.9539e-05
 1.60936e-19
 0.000176832
 -0.000176832
 -6.77626e-21
 -7.38475e-06
 -3.69238e-06
 7.38475e-06
 3.69238e-06
 -2.20229e-20
 1.89463e-05
 -5.24609e-06
 2.62305e-06
 5.24609e-06
 -2.62305e-06
 -8.47033e-22
 1.27055e-20
 -0.000204987
 -0.000850645
 -0.000220336
 -0.000850645
 3.41644e-05
 4.88063e-06
 3.41644e-05
 4.88063e-06
 3.67227e-05
 -5.24609e-06
 0.000141774
 3.30343e-20
 3.67227e-05
 5.24609e-06
 -1.95225e-05
 -2.09844e-05
 -1.03338e-19
 0.000141774
 -1.20279e-19
 -0.000141774
 -4.88063e-06
 -2.44032e-06
 4.88063e-06
 2.44032e-06
 -5.24609e-06
 2.62305e-06
 3.30343e-20
 1.51901e-05
 5.24609e-06
 2.62305e-06
 -7.94093e-21
 -9.52912e-21
 -0.000281276
 -0.00119228
 -0.00119228
 -0.000314861
 4.68794e-05
 6.69706e-06
 4.68794e-05
 6.69706e-06
 0.000198713
 4.74338e-20
 5.24769e-05
 -7.4967e-06
 5.24769e-05
 -7.4967e-06
 -2.67882e-05
 -2.99868e-05
 -1.4569e-19
 0.000198713
 -0.000198713
 -1.71101e-19
 -6.69706e-06
 -3.34853e-06
 6.69706e-06
 3.34853e-06
 4.74338e-20
 2.12906e-05
 -7.4967e-06
 3.74835e-06
 7.4967e-06
 -3.74835e-06
 -1.07997e-20
 -1.35525e-20
 -0.000260334
 -0.001056
 -0.001056
 -0.000267667
 4.3389e-05
 6.19842e-06
 4.3389e-05
 6.19842e-06
 0.000176
 -1.99053e-20
 4.46112e-05
 -6.37303e-06
 4.46112e-05
 -6.37303e-06
 -2.47937e-05
 -2.54921e-05
 1.30443e-19
 0.000176
 -0.000176
 -8.47033e-21
 -6.19842e-06
 -3.09921e-06
 6.19842e-06
 3.09921e-06
 -1.99053e-20
 1.88572e-05
 -6.37303e-06
 3.18651e-06
 6.37303e-06
 -3.18651e-06
 1.01644e-20
 -1.27055e-21
 -0.00124546
 -0.000314861
 -0.00124546
 -0.00030787
 5.24769e-05
 -7.4967e-06
 0.000207577
 2.28699e-20
 5.13116e-05
 -7.33023e-06
 5.24769e-05
 7.4967e-06
 5.13116e-05
 -7.33023e-06
 -2.99868e-05
 -2.93209e-05
 0.000207577
 -6.77626e-21
 -0.000207577
 -1.67713e-19
 -7.4967e-06
 3.74835e-06
 2.28699e-20
 2.22404e-05
 -7.33023e-06
 3.66511e-06
 7.4967e-06
 3.74835e-06
 7.33023e-06
 -3.66511e-06
 -1.27055e-21
 -1.35525e-20
 -0.00115107
 -0.000267667
 -0.00030787
 -0.00115107
 4.46112e-05
 -6.37303e-06
 5.13116e-05
 -7.33023e-06
 0.000191846
 2.11758e-20
 4.46112e-05
 6.37303e-06
 5.13116e-05
 7.33023e-06
 -2.93209e-05
 -2.54921e-05
 0.000191846
 -1.47384e-19
 -6.77626e-21
 -0.000191846
 -6.37303e-06
 3.18651e-06
 -7.33023e-06
 3.66511e-06
 2.11758e-20
 2.05549e-05
 6.37303e-06
 3.18651e-06
 7.33023e-06
 3.66511e-06
 -2.11758e-21
 -1.15408e-20
 -0.000220336
 -0.000939281
 -0.000939281
 -0.000249304
 3.67227e-05
 5.24609e-06
 3.67227e-05
 5.24609e-06
 0.000156547
 3.47284e-20
 4.15507e-05
 -5.93582e-06
 4.15507e-05
 -5.93582e-06
 -2.09844e-05
 -2.37433e-05
 -1.15196e-19
 0.000156547
 -0.000156547
 -1.35525e-19
 -5.24609e-06
 -2.62305e-06
 5.24609e-06
 2.62305e-06
 3.47284e-20
 1.67729e-05
 -5.93582e-06
 2.96791e-06
 5.93582e-06
 -2.96791e-06
 -8.68209e-21
 -1.09055e-20
 -0.000314861
 -0.00112833
 -0.000249304
 -0.00112833
 5.24769e-05
 7.4967e-06
 5.24769e-05
 7.4967e-06
 4.15507e-05
 -5.93582e-06
 0.000188055
 -2.75286e-20
 4.15507e-05
 5.93582e-06
 -2.37433e-05
 -2.99868e-05
 1.59242e-19
 0.000188055
 -5.0822e-21
 -0.000188055
 -7.4967e-06
 -3.74835e-06
 7.4967e-06
 3.74835e-06
 -5.93582e-06
 2.96791e-06
 -2.75286e-20
 2.01488e-05
 5.93582e-06
 2.96791e-06
 -1.27055e-21
 1.20702e-20
 -0.000171191
 -0.000698223
 -0.000698223
 -0.00017792
 2.85319e-05
 4.07599e-06
 2.85319e-05
 4.07599e-06
 0.00011637
 -1.3976e-20
 2.96533e-05
 -4.23619e-06
 2.96533e-05
 -4.23619e-06
 -1.63039e-05
 -1.69448e-05
 8.80914e-20
 0.00011637
 -0.00011637
 -5.0822e-21
 -4.07599e-06
 -2.03799e-06
 4.07599e-06
 2.03799e-06
 -1.3976e-20
 1.24683e-05
 -4.23619e-06
 2.11809e-06
 4.23619e-06
 -2.11809e-06
 6.67038e-21
 -6.35275e-22
 -0.000220489
 -0.000895935
 -0.000895935
 -0.000227479
 3.67482e-05
 5.24974e-06
 3.67482e-05
 5.24974e-06
 0.000149323
 3.21873e-20
 3.79131e-05
 -5.41616e-06
 3.79131e-05
 -5.41616e-06
 -2.0999e-05
 -2.16646e-05
 -1.13502e-19
 0.000149323
 -0.000149323
 -1.21973e-19
 -5.24974e-06
 -2.62487e-06
 5.24974e-06
 2.62487e-06
 3.21873e-20
 1.59988e-05
 -5.41616e-06
 2.70808e-06
 5.41616e-06
 -2.70808e-06
 -8.68209e-21
 -1.00585e-20
 -0.000797348
 -0.00017792
 -0.000797348
 -0.000220754
 2.96533e-05
 -4.23619e-06
 0.000132891
 1.35525e-20
 3.67924e-05
 -5.25605e-06
 2.96533e-05
 4.23619e-06
 3.67924e-05
 -5.25605e-06
 -1.69448e-05
 -2.10242e-05
 0.000132891
 -9.57147e-20
 -0.000132891
 -6.77626e-21
 -4.23619e-06
 2.11809e-06
 1.35525e-20
 1.42384e-05
 -5.25605e-06
 2.62803e-06
 4.23619e-06
 2.11809e-06
 5.25605e-06
 -2.62803e-06
 -7.41154e-21
 -8.47033e-22
 -0.000896466
 -0.000227479
 -0.000220754
 -0.000896466
 3.79131e-05
 -5.41616e-06
 3.67924e-05
 -5.25605e-06
 0.000149411
 1.73642e-20
 3.79131e-05
 5.41616e-06
 3.67924e-05
 5.25605e-06
 -2.10242e-05
 -2.16646e-05
 0.000149411
 -5.0822e-21
 -1.21973e-19
 -0.000149411
 -5.41616e-06
 2.70808e-06
 -5.25605e-06
 2.62803e-06
 1.73642e-20
 1.60083e-05
 5.41616e-06
 2.70808e-06
 5.25605e-06
 2.62803e-06
 -9.42324e-21
 -1.27055e-21
 -0.000181657
 -0.000731215
 -0.000731215
 -0.000183951
 3.02761e-05
 4.32516e-06
 3.02761e-05
 4.32516e-06
 0.000121869
 -1.35525e-20
 3.06585e-05
 -4.37979e-06
 3.06585e-05
 -4.37979e-06
 -1.73006e-05
 -1.75191e-05
 9.06325e-20
 0.000121869
 -0.000121869
 -5.0822e-21
 -4.32516e-06
 -2.16258e-06
 4.32516e-06
 2.16258e-06
 -1.35525e-20
 1.30574e-05
 -4.37979e-06
 2.18989e-06
 4.37979e-06
 -2.18989e-06
 7.51742e-21
 -8.47033e-22
 -0.00017792
 -0.000723742
 -0.000183951
 -0.000723742
 2.96533e-05
 4.23619e-06
 2.96533e-05
 4.23619e-06
 3.06585e-05
 -4.37979e-06
 0.000120624
 2.87991e-20
 3.06585e-05
 4.37979e-06
 -1.75191e-05
 -1.69448e-05
 -8.97855e-20
 0.000120624
 -9.82558e-20
 -0.000120624
 -4.23619e-06
 -2.11809e-06
 4.23619e-06
 2.11809e-06
 -4.37979e-06
 2.18989e-06
 2.87991e-20
 1.2924e-05
 4.37979e-06
 2.18989e-06
 -7.94093e-21
 -6.77626e-21
 -0.000229658
 -0.000939092
 -0.000939092
 -0.000239888
 3.82763e-05
 5.46804e-06
 3.82763e-05
 5.46804e-06
 0.000156515
 -1.69407e-20
 3.99814e-05
 -5.71162e-06
 3.99814e-05
 -5.71162e-06
 -2.18722e-05
 -2.28465e-05
 1.20279e-19
 0.000156515
 -0.000156515
 -3.38813e-21
 -5.46804e-06
 -2.73402e-06
 5.46804e-06
 2.73402e-06
 -1.69407e-20
 1.67695e-05
 -5.71162e-06
 2.85581e-06
 5.71162e-06
 -2.85581e-06
 8.89385e-21
 -1.05879e-21
 -0.000183951
 -0.000847678
 -0.000239888
 -0.000847678
 3.06585e-05
 4.37979e-06
 3.06585e-05
 4.37979e-06
 3.99814e-05
 -5.71162e-06
 0.00014128
 3.47284e-20
 3.99814e-05
 5.71162e-06
 -1.75191e-05
 -2.28465e-05
 -9.31736e-20
 0.00014128
 -1.32137e-19
 -0.00014128
 -4.37979e-06
 -2.18989e-06
 4.37979e-06
 2.18989e-06
 -5.71162e-06
 2.85581e-06
 3.47284e-20
 1.51371e-05
 5.71162e-06
 2.85581e-06
 -7.41154e-21
 -1.0482e-20
 -0.000234294
 -0.000950731
 -0.000950731
 -0.000241071
 3.90491e-05
 5.57844e-06
 3.90491e-05
 5.57844e-06
 0.000158455
 -1.73642e-20
 4.01785e-05
 -5.73978e-06
 4.01785e-05
 -5.73978e-06
 -2.23138e-05
 -2.29591e-05
 1.20279e-19
 0.000158455
 -0.000158455
 -8.47033e-21
 -5.57844e-06
 -2.78922e-06
 5.57844e-06
 2.78922e-06
 -1.73642e-20
 1.69773e-05
 -5.73978e-06
 2.86989e-06
 5.73978e-06
 -2.86989e-06
 9.42324e-21
 -1.27055e-21
 -0.000239888
 -0.000922269
 -0.000922269
 -0.000221246
 3.99814e-05
 5.71162e-06
 3.99814e-05
 5.71162e-06
 0.000153711
 3.55754e-20
 3.68744e-05
 -5.26777e-06
 3.68744e-05
 -5.26777e-06
 -2.28465e-05
 -2.10711e-05
 -1.18585e-19
 0.000153711
 -0.000153711
 -1.21973e-19
 -5.71162e-06
 -2.85581e-06
 5.71162e-06
 2.85581e-06
 3.55754e-20
 1.64691e-05
 -5.26777e-06
 2.63388e-06
 5.26777e-06
 -2.63388e-06
 -9.42324e-21
 -9.635e-21
 -0.000924634
 -0.000241071
 -0.000221246
 -0.000924634
 4.01785e-05
 -5.73978e-06
 3.68744e-05
 -5.26777e-06
 0.000154106
 1.82112e-20
 4.01785e-05
 5.73978e-06
 3.68744e-05
 5.26777e-06
 -2.29591e-05
 -2.10711e-05
 0.000154106
 -1.32137e-19
 -5.0822e-21
 -0.000154106
 -5.73978e-06
 2.86989e-06
 -5.26777e-06
 2.63388e-06
 1.82112e-20
 1.65113e-05
 5.73978e-06
 2.86989e-06
 5.26777e-06
 2.63388e-06
 -1.0482e-20
 -1.05879e-21
 -0.000256297
 -0.00103906
 -0.00103906
 -0.000263233
 4.27162e-05
 6.10232e-06
 4.27162e-05
 6.10232e-06
 0.000173177
 -2.03288e-20
 4.38722e-05
 -6.26746e-06
 4.38722e-05
 -6.26746e-06
 -2.44093e-05
 -2.50698e-05
 1.32137e-19
 0.000173177
 -0.000173177
 -5.0822e-21
 -6.10232e-06
 -3.05116e-06
 6.10232e-06
 3.05116e-06
 -2.03288e-20
 1.85547e-05
 -6.26746e-06
 3.13373e-06
 6.26746e-06
 -3.13373e-06
 1.01644e-20
 -1.27055e-21
 -0.000241071
 -0.000996219
 -0.000996219
 -0.000257039
 4.01785e-05
 5.73978e-06
 4.01785e-05
 5.73978e-06
 0.000166036
 4.06576e-20
 4.28398e-05
 -6.11997e-06
 4.28398e-05
 -6.11997e-06
 -2.29591e-05
 -2.44799e-05
 -1.23667e-19
 0.000166036
 -0.000166036
 -1.40607e-19
 -5.73978e-06
 -2.86989e-06
 5.73978e-06
 2.86989e-06
 4.06576e-20
 1.77896e-05
 -6.11997e-06
 3.05998e-06
 6.11997e-06
 -3.05998e-06
 -9.52912e-21
 -1.10114e-20
 -0.00104054
 -0.000263233
 -0.000257039
 -0.00104054
 4.38722e-05
 -6.26746e-06
 4.28398e-05
 -6.11997e-06
 0.000173424
 2.20229e-20
 4.38722e-05
 6.26746e-06
 4.28398e-05
 6.11997e-06
 -2.50698e-05
 -2.44799e-05
 0.000173424
 -1.43996e-19
 -6.77626e-21
 -0.000173424
 -6.26746e-06
 3.13373e-06
 -6.11997e-06
 3.05998e-06
 2.20229e-20
 1.85811e-05
 6.26746e-06
 3.13373e-06
 6.11997e-06
 3.05998e-06
 -1.12232e-20
 -1.27055e-21
 -0.000257702
 -0.00111544
 -0.00111544
 -0.000300018
 4.29503e-05
 6.13576e-06
 4.29503e-05
 6.13576e-06
 0.000185907
 -2.03288e-20
 5.00029e-05
 -7.14328e-06
 5.00029e-05
 -7.14328e-06
 -2.45431e-05
 -2.85731e-05
 1.30443e-19
 0.000185907
 -0.000185907
 -6.77626e-21
 -6.13576e-06
 -3.06788e-06
 6.13576e-06
 3.06788e-06
 -2.03288e-20
 1.99186e-05
 -7.14328e-06
 3.57164e-06
 7.14328e-06
 -3.57164e-06
 1.01644e-20
 -1.27055e-21
 -0.0012451
 -0.000300018
 -0.0012451
 -0.000322533
 5.00029e-05
 -7.14328e-06
 0.000207517
 2.28699e-20
 5.37554e-05
 -7.67935e-06
 5.00029e-05
 7.14328e-06
 5.37554e-05
 -7.67935e-06
 -2.85731e-05
 -3.07174e-05
 0.000207517
 -1.6263e-19
 -0.000207517
 -6.77626e-21
 -7.14328e-06
 3.57164e-06
 2.28699e-20
 2.22339e-05
 -7.67935e-06
 3.83967e-06
 7.14328e-06
 3.57164e-06
 7.67935e-06
 -3.83967e-06
 -1.27055e-20
 -8.47033e-22
 -0.000263233
 -0.00117153
 -0.000322533
 -0.00117153
 4.38722e-05
 6.26746e-06
 4.38722e-05
 6.26746e-06
 5.37554e-05
 -7.67935e-06
 0.000195255
 4.57398e-20
 5.37554e-05
 7.67935e-06
 -2.50698e-05
 -3.07174e-05
 -1.37219e-19
 0.000195255
 -1.77877e-19
 -0.000195255
 -6.26746e-06
 -3.13373e-06
 6.26746e-06
 3.13373e-06
 -7.67935e-06
 3.83967e-06
 4.57398e-20
 2.09202e-05
 7.67935e-06
 3.83967e-06
 -1.03762e-20
 -1.41878e-20
 -0.000300982
 -0.000300018
 -0.001202
 -0.001202
 5.01636e-05
 7.16624e-06
 5.01636e-05
 7.16624e-06
 5.00029e-05
 7.14328e-06
 5.00029e-05
 7.14328e-06
 0.000200333
 1.69407e-21
 -2.86649e-05
 -2.85731e-05
 1.52466e-19
 -1.5416e-19
 0.000200333
 -0.000200333
 -7.16624e-06
 -3.58312e-06
 7.16624e-06
 3.58312e-06
 -7.14328e-06
 -3.57164e-06
 7.14328e-06
 3.57164e-06
 1.69407e-21
 2.14643e-05
 1.20702e-20
 -1.18585e-20
 -0.000313773
 -0.00126395
 -0.00126395
 -0.0003182
 5.22955e-05
 7.47078e-06
 5.22955e-05
 7.47078e-06
 0.000210658
 5.0822e-20
 5.30333e-05
 -7.57619e-06
 5.30333e-05
 -7.57619e-06
 -2.98831e-05
 -3.03048e-05
 -1.59242e-19
 0.000210658
 -0.000210658
 -1.74489e-19
 -7.47078e-06
 -3.73539e-06
 7.47078e-06
 3.73539e-06
 5.0822e-20
 2.25705e-05
 -7.57619e-06
 3.78809e-06
 7.57619e-06
 -3.78809e-06
 -1.18585e-20
 -1.3976e-20
 -0.000244096
 -0.000990769
 -0.000990769
 -0.000251289
 4.06826e-05
 5.81181e-06
 4.06826e-05
 5.81181e-06
 0.000165128
 -2.07523e-20
 4.18814e-05
 -5.98306e-06
 4.18814e-05
 -5.98306e-06
 -2.32472e-05
 -2.39322e-05
 1.23667e-19
 0.000165128
 -0.000165128
 -3.38813e-21
 -5.81181e-06
 -2.9059e-06
 5.81181e-06
 2.9059e-06
 -2.07523e-20
 1.76923e-05
 -5.98306e-06
 2.99153e-06
 5.98306e-06
 -2.99153e-06
 9.74088e-21
 -1.05879e-21
 -0.00104217
 -0.000251289
 -0.00104217
 -0.000269798
 4.18814e-05
 -5.98306e-06
 0.000173696
 1.86347e-20
 4.49664e-05
 -6.42377e-06
 4.18814e-05
 5.98306e-06
 4.49664e-05
 -6.42377e-06
 -2.39322e-05
 -2.56951e-05
 0.000173696
 -1.40607e-19
 -0.000173696
 -6.77626e-21
 -5.98306e-06
 2.99153e-06
 1.86347e-20
 1.86102e-05
 -6.42377e-06
 3.21188e-06
 5.98306e-06
 2.99153e-06
 6.42377e-06
 -3.21188e-06
 -1.09055e-20
 -8.47033e-22
 -0.001176
 -0.0003182
 -0.000269798
 -0.001176
 5.30333e-05
 -7.57619e-06
 4.49664e-05
 -6.42377e-06
 0.000195999
 2.03288e-20
 5.30333e-05
 7.57619e-06
 4.49664e-05
 6.42377e-06
 -3.03048e-05
 -2.56951e-05
 0.000195999
 -6.77626e-21
 -1.47384e-19
 -0.000195999
 -7.57619e-06
 3.78809e-06
 -6.42377e-06
 3.21188e-06
 2.03288e-20
 2.09999e-05
 7.57619e-06
 3.78809e-06
 6.42377e-06
 3.21188e-06
 -1.27055e-21
 -1.17526e-20
 -0.0003182
 -0.00128459
 -0.00128459
 -0.000324094
 5.30333e-05
 7.57619e-06
 5.30333e-05
 7.57619e-06
 0.000214098
 -2.71051e-20
 5.40157e-05
 -7.71653e-06
 5.40157e-05
 -7.71653e-06
 -3.03048e-05
 -3.08661e-05
 1.60936e-19
 0.000214098
 -0.000214098
 -1.01644e-20
 -7.57619e-06
 -3.78809e-06
 7.57619e-06
 3.78809e-06
 -2.71051e-20
 2.29391e-05
 -7.71653e-06
 3.85827e-06
 7.71653e-06
 -3.85827e-06
 1.3129e-20
 -1.27055e-21
 -0.000322533
 -0.00129325
 -0.000324094
 -0.00129325
 5.37554e-05
 7.67935e-06
 5.37554e-05
 7.67935e-06
 5.40157e-05
 -7.71653e-06
 0.000215542
 4.91279e-20
 5.40157e-05
 7.71653e-06
 -3.07174e-05
 -3.08661e-05
 -1.66018e-19
 0.000215542
 -1.76183e-19
 -0.000215542
 -7.67935e-06
 -3.83967e-06
 7.67935e-06
 3.83967e-06
 -7.71653e-06
 3.85827e-06
 4.91279e-20
 2.30938e-05
 7.71653e-06
 3.85827e-06
 -1.27055e-20
 -1.43996e-20
 -0.000196981
 -0.000801625
 -0.000801625
 -0.000203831
 3.28302e-05
 4.69003e-06
 3.28302e-05
 4.69003e-06
 0.000133604
 -1.65171e-20
 3.39719e-05
 -4.85312e-06
 3.39719e-05
 -4.85312e-06
 -1.87601e-05
 -1.94125e-05
 1.01644e-19
 0.000133604
 -0.000133604
 -6.77626e-21
 -4.69003e-06
 -2.34502e-06
 4.69003e-06
 2.34502e-06
 -1.65171e-20
 1.43147e-05
 -4.85312e-06
 2.42656e-06
 4.85312e-06
 -2.42656e-06
 8.04681e-21
 -8.47033e-22
 -0.000867349
 -0.000203831
 -0.000867349
 -0.000229843
 3.39719e-05
 -4.85312e-06
 0.000144558
 1.48231e-20
 3.83072e-05
 -5.47246e-06
 3.39719e-05
 4.85312e-06
 3.83072e-05
 -5.47246e-06
 -1.94125e-05
 -2.18898e-05
 0.000144558
 -1.10114e-19
 -0.000144558
 -6.77626e-21
 -4.85312e-06
 2.42656e-06
 1.48231e-20
 1.54884e-05
 -5.47246e-06
 2.73623e-06
 4.85312e-06
 2.42656e-06
 5.47246e-06
 -2.73623e-06
 -8.68209e-21
 -1.05879e-21
 -0.000251289
 -0.000962263
 -0.000229843
 -0.000962263
 4.18814e-05
 5.98306e-06
 4.18814e-05
 5.98306e-06
 3.83072e-05
 -5.47246e-06
 0.000160377
 3.89635e-20
 3.83072e-05
 5.47246e-06
 -2.39322e-05
 -2.18898e-05
 -1.33831e-19
 0.000160377
 -1.23667e-19
 -0.000160377
 -5.98306e-06
 -2.99153e-06
 5.98306e-06
 2.99153e-06
 -5.47246e-06
 2.73623e-06
 3.89635e-20
 1.71833e-05
 5.47246e-06
 2.73623e-06
 -1.01644e-20
 -1.01644e-20
 -0.000147649
 -0.00059832
 -0.00059832
 -0.000151512
 2.46081e-05
 3.51544e-06
 2.46081e-05
 3.51544e-06
 9.97201e-05
 -1.27055e-20
 2.5252e-05
 -3.60742e-06
 2.5252e-05
 -3.60742e-06
 -1.40618e-05
 -1.44297e-05
 7.28448e-20
 9.97201e-05
 -9.97201e-05
 -3.38813e-21
 -3.51544e-06
 -1.75772e-06
 3.51544e-06
 1.75772e-06
 -1.27055e-20
 1.06843e-05
 -3.60742e-06
 1.80371e-06
 3.60742e-06
 -1.80371e-06
 5.50571e-21
 -8.47033e-22
 -0.000686525
 -0.000151512
 -0.000686525
 -0.000191751
 2.5252e-05
 -3.60742e-06
 0.000114421
 1.14349e-20
 3.19585e-05
 -4.5655e-06
 2.5252e-05
 3.60742e-06
 3.19585e-05
 -4.5655e-06
 -1.44297e-05
 -1.8262e-05
 0.000114421
 -8.21622e-20
 -0.000114421
 -3.38813e-21
 -3.60742e-06
 1.80371e-06
 1.14349e-20
 1.22594e-05
 -4.5655e-06
 2.28275e-06
 3.60742e-06
 1.80371e-06
 4.5655e-06
 -2.28275e-06
 -6.67038e-21
 -1.05879e-21
 -0.000203831
 -0.000791164
 -0.000191751
 -0.000791164
 3.39719e-05
 4.85312e-06
 3.39719e-05
 4.85312e-06
 3.19585e-05
 -4.5655e-06
 0.000131861
 2.96462e-20
 3.19585e-05
 4.5655e-06
 -1.94125e-05
 -1.8262e-05
 -1.06726e-19
 0.000131861
 -1.03338e-19
 -0.000131861
 -4.85312e-06
 -2.42656e-06
 4.85312e-06
 2.42656e-06
 -4.5655e-06
 2.28275e-06
 2.96462e-20
 1.41279e-05
 4.5655e-06
 2.28275e-06
 -8.36445e-21
 -8.25857e-21
 -0.000145559
 -0.000151512
 -0.000594141
 -0.000594141
 2.42598e-05
 3.46569e-06
 2.42598e-05
 3.46569e-06
 2.5252e-05
 3.60742e-06
 2.5252e-05
 3.60742e-06
 9.90236e-05
       0
 -1.38628e-05
 -1.44297e-05
 7.36919e-20
 -7.7927e-20
 9.90236e-05
 -9.90236e-05
 -3.46569e-06
 -1.73284e-06
 3.46569e-06
 1.73284e-06
 -3.60742e-06
 -1.80371e-06
 3.60742e-06
 1.80371e-06
       0
 1.06097e-05
 5.50571e-21
 -5.92923e-21
 -0.000187365
 -0.00076739
 -0.00076739
 -0.00019633
 3.12276e-05
 4.46108e-06
 3.12276e-05
 4.46108e-06
 0.000127898
 2.96462e-20
 3.27216e-05
 -4.67451e-06
 3.27216e-05
 -4.67451e-06
 -1.78443e-05
 -1.86981e-05
 -9.65618e-20
 0.000127898
 -0.000127898
 -1.05032e-19
 -4.46108e-06
 -2.23054e-06
 4.46108e-06
 2.23054e-06
 2.96462e-20
 1.37034e-05
 -4.67451e-06
 2.33726e-06
 4.67451e-06
 -2.33726e-06
 -7.19978e-21
 -8.47033e-21
 -0.000212144
 -0.000868485
 -0.000868485
 -0.000222099
 3.53573e-05
 5.05104e-06
 3.53573e-05
 5.05104e-06
 0.000144747
 -1.69407e-20
 3.70165e-05
 -5.28807e-06
 3.70165e-05
 -5.28807e-06
 -2.02041e-05
 -2.11523e-05
 1.09267e-19
 0.000144747
 -0.000144747
 -5.0822e-21
 -5.05104e-06
 -2.52552e-06
 5.05104e-06
 2.52552e-06
 -1.69407e-20
 1.55087e-05
 -5.28807e-06
 2.64403e-06
 5.28807e-06
 -2.64403e-06
 8.68209e-21
 -1.05879e-21
 -0.000843302
 -0.00019633
 -0.000843302
 -0.000225322
 3.27216e-05
 -4.67451e-06
 0.00014055
 1.73642e-20
 3.75536e-05
 -5.3648e-06
 3.27216e-05
 4.67451e-06
 3.75536e-05
 -5.3648e-06
 -1.86981e-05
 -2.14592e-05
 0.00014055
 -5.0822e-21
 -0.00014055
 -1.23667e-19
 -4.67451e-06
 2.33726e-06
 1.73642e-20
 1.5059e-05
 -5.3648e-06
 2.6824e-06
 4.67451e-06
 2.33726e-06
 5.3648e-06
 -2.6824e-06
 -1.05879e-21
 -9.84676e-21
 -0.000894841
 -0.000222099
 -0.000225322
 -0.000894841
 3.70165e-05
 -5.28807e-06
 3.75536e-05
 -5.3648e-06
 0.00014914
 1.69407e-20
 3.70165e-05
 5.28807e-06
 3.75536e-05
 5.3648e-06
 -2.11523e-05
 -2.14592e-05
 0.00014914
 -1.18585e-19
 -6.77626e-21
 -0.00014914
 -5.28807e-06
 2.64403e-06
 -5.3648e-06
 2.6824e-06
 1.69407e-20
 1.59793e-05
 5.28807e-06
 2.64403e-06
 5.3648e-06
 2.6824e-06
 -9.31736e-21
 -1.27055e-21
 -0.000191751
 -0.00019633
 -0.000776161
 -0.000776161
 3.19585e-05
 4.5655e-06
 3.19585e-05
 4.5655e-06
 3.27216e-05
 4.67451e-06
 3.27216e-05
 4.67451e-06
 0.00012936
       0
 -1.8262e-05
 -1.86981e-05
 -9.74088e-20
 1.01644e-19
 0.00012936
 -0.00012936
 -4.5655e-06
 -2.28275e-06
 4.5655e-06
 2.28275e-06
 -4.67451e-06
 -2.33726e-06
 4.67451e-06
 2.33726e-06
       0
 1.386e-05
 -7.83505e-21
 7.41154e-21
 -0.000196746
 -0.000852516
 -0.000852516
 -0.000229512
 3.2791e-05
 4.68443e-06
 3.2791e-05
 4.68443e-06
 0.000142086
 -1.43996e-20
 3.8252e-05
 -5.46457e-06
 3.8252e-05
 -5.46457e-06
 -1.87377e-05
 -2.18583e-05
 9.99499e-20
 0.000142086
 -0.000142086
 -3.38813e-21
 -4.68443e-06
 -2.34222e-06
 4.68443e-06
 2.34222e-06
 -1.43996e-20
 1.52235e-05
 -5.46457e-06
 2.73229e-06
 5.46457e-06
 -2.73229e-06
 7.83505e-21
 -6.35275e-22
 -0.00101849
 -0.000229512
 -0.00101849
 -0.000279732
 3.8252e-05
 -5.46457e-06
 0.000169748
 1.69407e-20
 4.66219e-05
 -6.66027e-06
 3.8252e-05
 5.46457e-06
 4.66219e-05
 -6.66027e-06
 -2.18583e-05
 -2.66411e-05
 0.000169748
 -1.25361e-19
 -0.000169748
 -1.01644e-20
 -5.46457e-06
 2.73229e-06
 1.69407e-20
 1.81873e-05
 -6.66027e-06
 3.33014e-06
 5.46457e-06
 2.73229e-06
 6.66027e-06
 -3.33014e-06
 -9.74088e-21
 -1.69407e-21
 -0.000222099
 -0.00100366
 -0.000279732
 -0.00100366
 3.70165e-05
 5.28807e-06
 3.70165e-05
 5.28807e-06
 4.66219e-05
 -6.66027e-06
 0.000167277
 4.06576e-20
 4.66219e-05
 6.66027e-06
 -2.11523e-05
 -2.66411e-05
 -1.11808e-19
 0.000167277
 -1.50772e-19
 -0.000167277
 -5.28807e-06
 -2.64403e-06
 5.28807e-06
 2.64403e-06
 -6.66027e-06
 3.33014e-06
 4.06576e-20
 1.79225e-05
 6.66027e-06
 3.33014e-06
 -8.47033e-21
 -1.19643e-20
 -0.000249304
 -0.000229512
 -0.000957633
 -0.000957633
 4.15507e-05
 5.93582e-06
 4.15507e-05
 5.93582e-06
 3.8252e-05
 5.46457e-06
 3.8252e-05
 5.46457e-06
 0.000159605
 -1.69407e-21
 -2.37433e-05
 -2.18583e-05
 1.23667e-19
 -1.18585e-19
 0.000159605
 -0.000159605
 -5.93582e-06
 -2.96791e-06
 5.93582e-06
 2.96791e-06
 -5.46457e-06
 -2.73229e-06
 5.46457e-06
 2.73229e-06
 -1.69407e-21
 1.71006e-05
 1.00585e-20
 -9.31736e-21
 -0.000227479
 -0.000965995
 -0.000965995
 -0.000255519
 3.79131e-05
 5.41616e-06
 3.79131e-05
 5.41616e-06
 0.000160999
 -1.73642e-20
 4.25865e-05
 -6.08378e-06
 4.25865e-05
 -6.08378e-06
 -2.16646e-05
 -2.43351e-05
 1.15196e-19
 0.000160999
 -0.000160999
 -3.38813e-21
 -5.41616e-06
 -2.70808e-06
 5.41616e-06
 2.70808e-06
 -1.73642e-20
 1.72499e-05
 -6.08378e-06
 3.04189e-06
 6.08378e-06
 -3.04189e-06
 8.78797e-21
 -1.05879e-21
 -0.000267667
 -0.00104637
 -0.000255519
 -0.00104637
 4.46112e-05
 6.37303e-06
 4.46112e-05
 6.37303e-06
 4.25865e-05
 -6.08378e-06
 0.000174395
 3.98105e-20
 4.25865e-05
 6.08378e-06
 -2.54921e-05
 -2.43351e-05
 -1.38913e-19
 0.000174395
 -1.35525e-19
 -0.000174395
 -6.37303e-06
 -3.18651e-06
 6.37303e-06
 3.18651e-06
 -6.08378e-06
 3.04189e-06
 3.98105e-20
 1.86852e-05
 6.08378e-06
 3.04189e-06
 -1.03762e-20
 -1.11173e-20
 -0.000221246
 -0.000908053
 -0.000908053
 -0.00023278
 3.68744e-05
 5.26777e-06
 3.68744e-05
 5.26777e-06
 0.000151342
 -1.90582e-20
 3.87967e-05
 -5.54239e-06
 3.87967e-05
 -5.54239e-06
 -2.10711e-05
 -2.21696e-05
 1.15196e-19
 0.000151342
 -0.000151342
 -3.38813e-21
 -5.26777e-06
 -2.63388e-06
 5.26777e-06
 2.63388e-06
 -1.90582e-20
 1.62152e-05
 -5.54239e-06
 2.77119e-06
 5.54239e-06
 -2.77119e-06
 9.1056e-21
 -8.47033e-22
 -0.000220754
 -0.000907069
 -0.00023278
 -0.000907069
 3.67924e-05
 5.25605e-06
 3.67924e-05
 5.25605e-06
 3.87967e-05
 -5.54239e-06
 0.000151178
 3.55754e-20
 3.87967e-05
 5.54239e-06
 -2.10242e-05
 -2.21696e-05
 -1.13502e-19
 0.000151178
 -1.28749e-19
 -0.000151178
 -5.25605e-06
 -2.62803e-06
 5.25605e-06
 2.62803e-06
 -5.54239e-06
 2.77119e-06
 3.55754e-20
 1.61977e-05
 5.54239e-06
 2.77119e-06
 -8.78797e-21
 -9.95264e-21
 -0.000257039
 -0.0010438
 -0.0010438
 -0.00026486
 4.28398e-05
 6.11997e-06
 4.28398e-05
 6.11997e-06
 0.000173966
 -2.07523e-20
 4.41433e-05
 -6.30618e-06
 4.41433e-05
 -6.30618e-06
 -2.44799e-05
 -2.52247e-05
 1.32137e-19
 0.000173966
 -0.000173966
 -5.0822e-21
 -6.11997e-06
 -3.05998e-06
 6.11997e-06
 3.05998e-06
 -2.07523e-20
 1.86392e-05
 -6.30618e-06
 3.15309e-06
 6.30618e-06
 -3.15309e-06
 1.03762e-20
 -8.47033e-22
 -0.00023278
 -0.000963046
 -0.000963046
 -0.000248743
 3.87967e-05
 5.54239e-06
 3.87967e-05
 5.54239e-06
 0.000160508
 3.55754e-20
 4.14571e-05
 -5.92245e-06
 4.14571e-05
 -5.92245e-06
 -2.21696e-05
 -2.36898e-05
 -1.21973e-19
 0.000160508
 -0.000160508
 -1.37219e-19
 -5.54239e-06
 -2.77119e-06
 5.54239e-06
 2.77119e-06
 3.55754e-20
 1.71972e-05
 -5.92245e-06
 2.96122e-06
 5.92245e-06
 -2.96122e-06
 -8.99973e-21
 -1.06938e-20
 -0.0010272
 -0.00026486
 -0.000248743
 -0.0010272
 4.41433e-05
 -6.30618e-06
 4.14571e-05
 -5.92245e-06
 0.000171201
 1.94818e-20
 4.41433e-05
 6.30618e-06
 4.14571e-05
 5.92245e-06
 -2.52247e-05
 -2.36898e-05
 0.000171201
 -1.43996e-19
 -1.01644e-20
 -0.000171201
 -6.30618e-06
 3.15309e-06
 -5.92245e-06
 2.96122e-06
 1.94818e-20
 1.83429e-05
 6.30618e-06
 3.15309e-06
 5.92245e-06
 2.96122e-06
 -1.15408e-20
 -1.27055e-21
 -0.000229843
 -0.000935717
 -0.000935717
 -0.000238015
 3.83072e-05
 5.47246e-06
 3.83072e-05
 5.47246e-06
 0.000155953
 3.72694e-20
 3.96692e-05
 -5.66703e-06
 3.96692e-05
 -5.66703e-06
 -2.18898e-05
 -2.26681e-05
 -1.16891e-19
 0.000155953
 -0.000155953
 -1.28749e-19
 -5.47246e-06
 -2.73623e-06
 5.47246e-06
 2.73623e-06
 3.72694e-20
 1.67092e-05
 -5.66703e-06
 2.83352e-06
 5.66703e-06
 -2.83352e-06
 -9.1056e-21
 -1.0482e-20
 -0.000225322
 -0.000926674
 -0.000238015
 -0.000926674
 3.75536e-05
 5.3648e-06
 3.75536e-05
 5.3648e-06
 3.96692e-05
 -5.66703e-06
 0.000154446
 -1.69407e-20
 3.96692e-05
 5.66703e-06
 -2.14592e-05
 -2.26681e-05
 1.13502e-19
 0.000154446
 -5.0822e-21
 -0.000154446
 -5.3648e-06
 -2.6824e-06
 5.3648e-06
 2.6824e-06
 -5.66703e-06
 2.83352e-06
 -1.69407e-20
 1.65478e-05
 5.66703e-06
 2.83352e-06
 8.68209e-21
 -1.48231e-21
 -0.000269798
 -0.00108865
 -0.00108865
 -0.000274526
 4.49664e-05
 6.42377e-06
 4.49664e-05
 6.42377e-06
 0.000181442
 4.06576e-20
 4.57544e-05
 -6.53634e-06
 4.57544e-05
 -6.53634e-06
 -2.56951e-05
 -2.61454e-05
 -1.38913e-19
 0.000181442
 -0.000181442
 -1.49078e-19
 -6.42377e-06
 -3.21188e-06
 6.42377e-06
 3.21188e-06
 4.06576e-20
 1.94402e-05
 -6.53634e-06
 3.26817e-06
 6.53634e-06
 -3.26817e-06
 -1.03762e-20
 -1.21761e-20
 -0.000238015
 -0.000993778
 -0.000993778
 -0.000258874
 3.96692e-05
 5.66703e-06
 3.96692e-05
 5.66703e-06
 0.00016563
 -1.86347e-20
 4.31456e-05
 -6.16366e-06
 4.31456e-05
 -6.16366e-06
 -2.26681e-05
 -2.46546e-05
 1.20279e-19
 0.00016563
 -0.00016563
 -6.77626e-21
 -5.66703e-06
 -2.83352e-06
 5.66703e-06
 2.83352e-06
 -1.86347e-20
 1.7746e-05
 -6.16366e-06
 3.08183e-06
 6.16366e-06
 -3.08183e-06
 9.635e-21
 -8.47033e-22
 -0.0010668
 -0.000274526
 -0.000258874
 -0.0010668
 4.57544e-05
 -6.53634e-06
 4.31456e-05
 -6.16366e-06
 0.0001778
 1.90582e-20
 4.57544e-05
 6.53634e-06
 4.31456e-05
 6.16366e-06
 -2.46546e-05
 -2.61454e-05
 0.0001778
 -8.47033e-21
 -1.40607e-19
 -0.0001778
 -6.53634e-06
 3.26817e-06
 -6.16366e-06
 3.08183e-06
 1.90582e-20
 1.905e-05
 6.53634e-06
 3.26817e-06
 6.16366e-06
 3.08183e-06
 -1.10114e-20
 -1.27055e-21
 -0.000324094
 -0.00120147
 -0.00120147
 -0.000276642
 5.40157e-05
 7.71653e-06
 5.40157e-05
 7.71653e-06
 0.000200246
 4.48927e-20
 4.61071e-05
 -6.58672e-06
 4.61071e-05
 -6.58672e-06
 -3.08661e-05
 -2.63469e-05
 -1.64324e-19
 0.000200246
 -0.000200246
 -1.52466e-19
 -7.71653e-06
 -3.85827e-06
 7.71653e-06
 3.85827e-06
 4.48927e-20
 2.14549e-05
 -6.58672e-06
 3.29336e-06
 6.58672e-06
 -3.29336e-06
 -1.27055e-20
 -1.2282e-20
 -0.000274526
 -0.00110954
 -0.00110954
 -0.000280244
 4.57544e-05
 6.53634e-06
 4.57544e-05
 6.53634e-06
 0.000184923
 -2.03288e-20
 4.67073e-05
 -6.67248e-06
 4.67073e-05
 -6.67248e-06
 -2.61454e-05
 -2.66899e-05
 1.38913e-19
 0.000184923
 -0.000184923
 -1.01644e-20
 -6.53634e-06
 -3.26817e-06
 6.53634e-06
 3.26817e-06
 -2.03288e-20
 1.98132e-05
 -6.67248e-06
 3.33624e-06
 6.67248e-06
 -3.33624e-06
 1.07997e-20
 -1.27055e-21
 -0.00111377
 -0.000276642
 -0.000280244
 -0.00111377
 4.61071e-05
 -6.58672e-06
 4.67073e-05
 -6.67248e-06
 0.000185629
 2.03288e-20
 4.61071e-05
 6.58672e-06
 4.67073e-05
 6.67248e-06
 -2.63469e-05
 -2.66899e-05
 0.000185629
 -5.0822e-21
 -1.52466e-19
 -0.000185629
 -6.58672e-06
 3.29336e-06
 -6.67248e-06
 3.33624e-06
 2.03288e-20
 1.98888e-05
 6.58672e-06
 3.29336e-06
 6.67248e-06
 3.33624e-06
 -1.27055e-21
 -1.24937e-20
 -0.00026486
 -0.000276642
 -0.001083
 -0.001083
 4.41433e-05
 6.30618e-06
 4.41433e-05
 6.30618e-06
 4.61071e-05
 6.58672e-06
 4.61071e-05
 6.58672e-06
 0.000180501
 1.69407e-21
 -2.52247e-05
 -2.63469e-05
 -1.35525e-19
 1.43996e-19
 0.000180501
 -0.000180501
 -6.30618e-06
 -3.15309e-06
 6.30618e-06
 3.15309e-06
 -6.58672e-06
 -3.29336e-06
 6.58672e-06
 3.29336e-06
 1.69407e-21
 1.93394e-05
 -1.05879e-20
 1.07997e-20
 -0.000279732
 -0.00115622
 -0.00115622
 -0.000298377
 4.66219e-05
 6.66027e-06
 4.66219e-05
 6.66027e-06
 0.000192703
 4.23516e-20
 4.97294e-05
 -7.1042e-06
 4.97294e-05
 -7.1042e-06
 -2.66411e-05
 -2.84168e-05
 -1.42302e-19
 0.000192703
 -0.000192703
 -1.60936e-19
 -6.66027e-06
 -3.33014e-06
 6.66027e-06
 3.33014e-06
 4.23516e-20
 2.06467e-05
 -7.1042e-06
 3.5521e-06
 7.1042e-06
 -3.5521e-06
 -1.05879e-20
 -1.29173e-20
 -0.00030787
 -0.00122313
 -0.00122313
 -0.000303693
 5.13116e-05
 7.33023e-06
 5.13116e-05
 7.33023e-06
 0.000203854
 -2.20229e-20
 5.06155e-05
 -7.23079e-06
 5.06155e-05
 -7.23079e-06
 -2.89232e-05
 -2.93209e-05
 1.55854e-19
 0.000203854
 -0.000203854
 -1.01644e-20
 -7.33023e-06
 -3.66511e-06
 7.33023e-06
 3.66511e-06
 -2.20229e-20
 2.18415e-05
 -7.23079e-06
 3.6154e-06
 7.23079e-06
 -3.6154e-06
 -1.27055e-21
 1.18585e-20
 -0.00120414
 -0.000298377
 -0.000303693
 -0.00120414
 4.97294e-05
 -7.1042e-06
 5.06155e-05
 -7.23079e-06
 0.00020069
 2.37169e-20
 4.97294e-05
 7.1042e-06
 5.06155e-05
 7.23079e-06
 -2.89232e-05
 -2.84168e-05
 0.00020069
 -6.77626e-21
 -1.67713e-19
 -0.00020069
 -7.1042e-06
 3.5521e-06
 -7.23079e-06
 3.6154e-06
 2.37169e-20
 2.15025e-05
 7.1042e-06
 3.5521e-06
 7.23079e-06
 3.6154e-06
 -1.29173e-20
 -1.27055e-21
 -0.000258874
 -0.000298377
 -0.0011145
 -0.0011145
 4.31456e-05
 6.16366e-06
 4.31456e-05
 6.16366e-06
 4.97294e-05
 7.1042e-06
 4.97294e-05
 7.1042e-06
 0.00018575
 -3.38813e-21
 -2.46546e-05
 -2.84168e-05
 -1.32137e-19
 1.52466e-19
 0.00018575
 -0.00018575
 -6.16366e-06
 -3.08183e-06
 6.16366e-06
 3.08183e-06
 -7.1042e-06
 -3.5521e-06
 7.1042e-06
 3.5521e-06
 -3.38813e-21
 1.99018e-05
 -1.01644e-20
 1.16467e-20
 -0.000255519
 -0.00103685
 -0.00103685
 -0.000262906
 4.25865e-05
 6.08378e-06
 4.25865e-05
 6.08378e-06
 0.000172808
 3.89635e-20
 4.38177e-05
 -6.25967e-06
 4.38177e-05
 -6.25967e-06
 -2.43351e-05
 -2.50387e-05
 -1.28749e-19
 0.000172808
 -0.000172808
 -1.42302e-19
 -6.08378e-06
 -3.04189e-06
 6.08378e-06
 3.04189e-06
 3.89635e-20
 1.85152e-05
 -6.25967e-06
 3.12983e-06
 6.25967e-06
 -3.12983e-06
 -1.05879e-20
 -1.15408e-20
 -0.000248743
 -0.0010233
 -0.000262906
 -0.0010233
 4.14571e-05
 5.92245e-06
 4.14571e-05
 5.92245e-06
 4.38177e-05
 -6.25967e-06
 0.00017055
 -1.86347e-20
 4.38177e-05
 6.25967e-06
 -2.36898e-05
 -2.50387e-05
 1.27055e-19
 0.00017055
 -5.0822e-21
 -0.00017055
 -5.92245e-06
 -2.96122e-06
 5.92245e-06
 2.96122e-06
 -6.25967e-06
 3.12983e-06
 -1.86347e-20
 1.82732e-05
 6.25967e-06
 3.12983e-06
 9.74088e-21
 -1.27055e-21
 -0.000303693
 -0.00115449
 -0.00115449
 -0.000273554
 5.06155e-05
 7.23079e-06
 5.06155e-05
 7.23079e-06
 0.000192416
 4.23516e-20
 4.55923e-05
 -6.51319e-06
 4.55923e-05
 -6.51319e-06
 -2.60527e-05
 -2.89232e-05
 -1.59242e-19
 0.000192416
 -0.000192416
 -1.50772e-19
 -7.23079e-06
 -3.6154e-06
 7.23079e-06
 3.6154e-06
 4.23516e-20
 2.0616e-05
 -6.51319e-06
 3.25659e-06
 6.51319e-06
 -3.25659e-06
 -1.19643e-20
 -1.14349e-20
 -0.000262906
 -0.00107292
 -0.000273554
 -0.00107292
 4.38177e-05
 6.25967e-06
 4.38177e-05
 6.25967e-06
 4.55923e-05
 -6.51319e-06
 0.00017882
 -2.20229e-20
 4.55923e-05
 6.51319e-06
 -2.60527e-05
 -2.50387e-05
 1.35525e-19
 0.00017882
 -1.01644e-20
 -0.00017882
 -6.25967e-06
 -3.12983e-06
 6.25967e-06
 3.12983e-06
 -6.51319e-06
 3.25659e-06
 -2.20229e-20
 1.91593e-05
 6.51319e-06
 3.25659e-06
 -1.69407e-21
 1.0482e-20
 -0.000280244
 -0.000273554
 -0.0011076
 -0.0011076
 4.67073e-05
 6.67248e-06
 4.67073e-05
 6.67248e-06
 4.55923e-05
 6.51319e-06
 4.55923e-05
 6.51319e-06
 0.000184599
       0
 -2.60527e-05
 -2.66899e-05
 -1.42302e-19
 1.38913e-19
 0.000184599
 -0.000184599
 -6.67248e-06
 -3.33624e-06
 6.67248e-06
 3.33624e-06
 -6.51319e-06
 -3.25659e-06
 6.51319e-06
 3.25659e-06
       0
 1.97785e-05
 1.05879e-20
 -1.14349e-20
 0.000173611
 0.000173611
 0.000173611
 -2.48016e-05
 -8.47033e-22
 -2.48016e-05
 -1.09055e-20
 -2.48016e-05
 -9.74088e-21
 1.24008e-05
 0.000215066
 0.000215066
 0.000215066
 -3.07237e-05
 -1.27055e-21
 -3.07237e-05
 -1.37643e-20
 -3.07237e-05
 -1.27055e-20
 1.53618e-05
 0.000184383
 0.000184383
 0.000184383
 -2.63404e-05
 -1.27055e-21
 -2.63404e-05
 -1.18585e-20
 -2.63404e-05
 -1.10114e-20
 1.31702e-05
 0.000239717
 0.000239717
 0.000239717
 -3.42453e-05
 -1.54584e-20
 -3.42453e-05
 -1.69407e-21
 -3.42453e-05
 1.41878e-20
 1.71227e-05
 0.000169802
 0.000169802
 0.000169802
 -2.42575e-05
 -1.27055e-21
 -2.42575e-05
 -1.09055e-20
 -2.42575e-05
 -9.95264e-21
 1.21287e-05
 0.000184683
 0.000184683
 0.000184683
 -2.63833e-05
 -1.19643e-20
 -2.63833e-05
 -1.27055e-21
 -2.63833e-05
 1.07997e-20
 1.31917e-05
 0.000153675
 0.000153675
 0.000153675
 -2.19536e-05
 -1.05879e-21
 -2.19536e-05
 -9.84676e-21
 -2.19536e-05
 -9.31736e-21
 1.09768e-05
 0.000159017
 0.000159017
 0.000159017
 -2.27168e-05
 -1.0482e-20
 -2.27168e-05
 -1.27055e-21
 -2.27168e-05
 9.31736e-21
 1.13584e-05
 0.000137523
 0.000137523
 0.000137523
 -1.96461e-05
 -8.47033e-22
 -1.96461e-05
 -8.68209e-21
 -1.96461e-05
 -7.6233e-21
 9.82304e-06
 0.000136019
 0.000136019
 0.000136019
 -1.94312e-05
 -8.78797e-21
 -1.94312e-05
 -1.05879e-21
 -1.94312e-05
 7.6233e-21
 9.71561e-06
 0.000141297
 0.000141297
 0.000141297
 -2.01853e-05
 -6.35275e-22
 -2.01853e-05
 -8.78797e-21
 -2.01853e-05
 -8.47033e-21
 1.00927e-05
 0.000129923
 0.000129923
 0.000129923
 -1.85604e-05
 -8.57621e-21
 -1.85604e-05
 -1.05879e-21
 -1.85604e-05
 7.72918e-21
 9.28021e-06
 0.000147469
 0.000147469
 0.000147469
 -2.1067e-05
 -9.74088e-21
 -2.1067e-05
 -1.27055e-21
 -2.1067e-05
 8.47033e-21
 1.05335e-05
 0.000124527
 0.000124527
 0.000124527
 -1.77896e-05
 -8.15269e-21
 -1.77896e-05
 -1.27055e-21
 -1.77896e-05
 7.19978e-21
 8.89481e-06
 0.000142553
 0.000142553
 0.000142553
 -2.03647e-05
 -1.27055e-21
 -2.03647e-05
 -9.31736e-21
 -2.03647e-05
 -8.04681e-21
 1.01823e-05
 0.000109189
 0.000109189
 0.000109189
 -1.55984e-05
 -8.47033e-22
 -1.55984e-05
 -7.19978e-21
 -1.55984e-05
 -6.67038e-21
 7.79919e-06
 0.000107427
 0.000107427
 0.000107427
 -1.53467e-05
 -6.88214e-21
 -1.53467e-05
 -8.47033e-22
 -1.53467e-05
 6.56451e-21
 7.67336e-06
 0.000134494
 0.000134494
 0.000134494
 -1.92134e-05
 -8.47033e-22
 -1.92134e-05
 -8.47033e-21
 -1.92134e-05
 -7.72918e-21
 9.60671e-06
 0.000104217
 0.000104217
 0.000104217
 -1.48881e-05
 -6.77626e-21
 -1.48881e-05
 -1.27055e-21
 -1.48881e-05
 5.92923e-21
 7.44405e-06
 0.000146753
 0.000146753
 0.000146753
 -2.09648e-05
 -1.05879e-21
 -2.09648e-05
 -9.42324e-21
 -2.09648e-05
 -8.68209e-21
 1.04824e-05
 0.000140318
 0.000140318
 0.000140318
 -2.00455e-05
 -9.1056e-21
 -2.00455e-05
 -1.27055e-21
 -2.00455e-05
 7.94093e-21
 1.00227e-05
 0.000155177
 0.000155177
 0.000155177
 -2.21682e-05
 -8.47033e-22
 -2.21682e-05
 -1.01644e-20
 -2.21682e-05
 -9.31736e-21
 1.10841e-05
 0.000155123
 0.000155123
 0.000155123
 -2.21605e-05
 -9.95264e-21
 -2.21605e-05
 -1.48231e-21
 -2.21605e-05
 8.99973e-21
 1.10802e-05
 0.000156438
 0.000156438
 0.000156438
 -2.23483e-05
 -1.05879e-21
 -2.23483e-05
 -9.95264e-21
 -2.23483e-05
 -8.89385e-21
 1.11741e-05
 0.000162001
 0.000162001
 0.000162001
 -2.3143e-05
 -1.05879e-20
 -2.3143e-05
 -1.48231e-21
 -2.3143e-05
 9.74088e-21
 1.15715e-05
 0.000147479
 0.000147479
 0.000147479
 -2.10684e-05
 -8.47033e-22
 -2.10684e-05
 -9.21148e-21
 -2.10684e-05
 -8.47033e-21
 1.05342e-05
 0.000161626
 0.000161626
 0.000161626
 -2.30895e-05
 -1.03762e-20
 -2.30895e-05
 -1.05879e-21
 -2.30895e-05
 9.52912e-21
 1.15447e-05
 0.000173611
 0.000173611
 0.000173611
 -2.48016e-05
 -1.10114e-20
 -2.48016e-05
 -1.27055e-21
 -2.48016e-05
 1.05879e-20
 1.24008e-05
 0.00014505
 0.00014505
 0.00014505
 -2.07214e-05
 -1.05879e-21
 -2.07214e-05
 -9.31736e-21
 -2.07214e-05
 -8.47033e-21
 1.03607e-05
 0.000170342
 0.000170342
 0.000170342
 -2.43346e-05
 -1.27055e-21
 -2.43346e-05
 -1.07997e-20
 -2.43346e-05
 -9.52912e-21
 1.21673e-05
 0.000137461
 0.000137461
 0.000137461
 -1.96373e-05
 -8.89385e-21
 -1.96373e-05
 -1.05879e-21
 -1.96373e-05
 8.57621e-21
 9.81866e-06
 0.000175722
 0.000175722
 0.000175722
 -2.51032e-05
 -1.27055e-21
 -2.51032e-05
 -1.12232e-20
 -2.51032e-05
 -1.01644e-20
 1.25516e-05
 0.00016875
 0.00016875
 0.00016875
 -2.41072e-05
 -1.11173e-20
 -2.41072e-05
 -1.27055e-21
 -2.41072e-05
 9.95264e-21
 1.20536e-05
 0.000160895
 0.000160895
 0.000160895
 -2.2985e-05
 -1.27055e-21
 -2.2985e-05
 -1.03762e-20
 -2.2985e-05
 -9.1056e-21
 1.14925e-05
 0.00016617
 0.00016617
 0.00016617
 -2.37386e-05
 -1.09055e-20
 -2.37386e-05
 -1.05879e-21
 -2.37386e-05
 1.03762e-20
 1.18693e-05
 0.000142598
 0.000142598
 0.000142598
 -2.03711e-05
 -1.27055e-21
 -2.03711e-05
 -9.31736e-21
 -2.03711e-05
 -8.68209e-21
 1.01856e-05
 0.000143989
 0.000143989
 0.000143989
 -2.05698e-05
 -9.42324e-21
 -2.05698e-05
 -1.48231e-21
 -2.05698e-05
 8.25857e-21
 1.02849e-05
 0.000125806
 0.000125806
 0.000125806
 -1.79723e-05
 -8.47033e-22
 -1.79723e-05
 -8.04681e-21
 -1.79723e-05
 -7.6233e-21
 8.98613e-06
 0.000120857
 0.000120857
 0.000120857
 -1.72652e-05
 -7.94093e-21
 -1.72652e-05
 -8.47033e-22
 -1.72652e-05
 6.98802e-21
 8.63262e-06
 0.000135805
 0.000135805
 0.000135805
 -1.94007e-05
 -8.57621e-21
 -1.94007e-05
 -8.47033e-22
 -1.94007e-05
 7.72918e-21
 9.70033e-06
 0.000119333
 0.000119333
 0.000119333
 -1.70475e-05
 -7.83505e-21
 -1.70475e-05
 -6.35275e-22
 -1.70475e-05
 7.41154e-21
 8.52376e-06
 0.000134684
 0.000134684
 0.000134684
 -1.92406e-05
 -8.47033e-22
 -1.92406e-05
 -8.99973e-21
 -1.92406e-05
 -8.25857e-21
 9.6203e-06
 0.000121956
 0.000121956
 0.000121956
 -1.74223e-05
 -8.47033e-22
 -1.74223e-05
 -7.72918e-21
 -1.74223e-05
 -7.19978e-21
 8.71115e-06
 0.00011809
 0.00011809
 0.00011809
 -1.687e-05
 -7.94093e-21
 -1.687e-05
 -6.35275e-22
 -1.687e-05
 6.98802e-21
 8.435e-06
 0.000133633
 0.000133633
 0.000133633
 -1.90904e-05
 -8.47033e-22
 -1.90904e-05
 -8.36445e-21
 -1.90904e-05
 -8.04681e-21
 9.5452e-06
 0.000115902
 0.000115902
 0.000115902
 -1.65574e-05
 -7.41154e-21
 -1.65574e-05
 -1.05879e-21
 -1.65574e-05
 6.56451e-21
 8.27872e-06
 0.000142767
 0.000142767
 0.000142767
 -2.03953e-05
 -1.05879e-21
 -2.03953e-05
 -9.1056e-21
 -2.03953e-05
 -8.25857e-21
 1.01977e-05
 0.000130938
 0.000130938
 0.000130938
 -1.87054e-05
 -8.57621e-21
 -1.87054e-05
 -1.05879e-21
 -1.87054e-05
 8.04681e-21
 9.35271e-06
 0.000144493
 0.000144493
 0.000144493
 -2.06419e-05
 -8.47033e-22
 -2.06419e-05
 -9.21148e-21
 -2.06419e-05
 -8.47033e-21
 1.0321e-05
 0.000139288
 0.000139288
 0.000139288
 -1.98982e-05
 -9.21148e-21
 -1.98982e-05
 -1.05879e-21
 -1.98982e-05
 8.47033e-21
 9.94912e-06
 0.000160032
 0.000160032
 0.000160032
 -2.28617e-05
 -1.05879e-21
 -2.28617e-05
 -1.03762e-20
 -2.28617e-05
 -9.31736e-21
 1.14309e-05
 0.000156962
 0.000156962
 0.000156962
 -2.24231e-05
 -1.03762e-20
 -2.24231e-05
 -1.48231e-21
 -2.24231e-05
 8.99973e-21
 1.12116e-05
 0.000207036
 0.000207036
 0.000207036
 -2.95766e-05
 -4.23516e-22
 -2.95766e-05
 -1.3129e-20
 -2.95766e-05
 -1.27055e-20
 1.47883e-05
 0.000248491
 0.000248491
 0.000248491
 -3.54987e-05
 -1.65171e-20
 -3.54987e-05
 -1.69407e-21
 -3.54987e-05
 1.48231e-20
 1.77493e-05
 0.000211053
 0.000211053
 0.000211053
 -3.01504e-05
 -8.47033e-22
 -3.01504e-05
 -1.33408e-20
 -3.01504e-05
 -1.18585e-20
 1.50752e-05
 0.000166587
 0.000166587
 0.000166587
 -2.37982e-05
 -1.12232e-20
 -2.37982e-05
 -1.48231e-21
 -2.37982e-05
 1.02703e-20
 1.18991e-05
 0.000213574
 0.000213574
 0.000213574
 -3.05106e-05
 -1.27055e-21
 -3.05106e-05
 -1.37643e-20
 -3.05106e-05
 -1.3129e-20
 1.52553e-05
 0.000187258
 0.000187258
 0.000187258
 -2.67511e-05
 -8.47033e-22
 -2.67511e-05
 -1.17526e-20
 -2.67511e-05
 -1.07997e-20
 1.33755e-05
 0.000215442
 0.000215442
 0.000215442
 -3.07774e-05
 -1.69407e-21
 -3.07774e-05
 -1.41878e-20
 -3.07774e-05
 -1.27055e-20
 1.53887e-05
 0.000187518
 0.000187518
 0.000187518
 -2.67882e-05
 -8.47033e-22
 -2.67882e-05
 -1.17526e-20
 -2.67882e-05
 -1.07997e-20
 1.33941e-05
 0.000140465
 0.000140465
 0.000140465
 -2.00664e-05
 -8.47033e-22
 -2.00664e-05
 -8.78797e-21
 -2.00664e-05
 -7.83505e-21
 1.00332e-05
 0.000113633
 0.000113633
 0.000113633
 -1.62333e-05
 -4.23516e-22
 -1.62333e-05
 -7.41154e-21
 -1.62333e-05
 -6.98802e-21
 8.11665e-06
 0.000114128
 0.000114128
 0.000114128
 -1.63039e-05
 -7.41154e-21
 -1.63039e-05
 -8.47033e-22
 -1.63039e-05
 6.67038e-21
 8.15197e-06
 0.000147119
 0.000147119
 0.000147119
 -2.1017e-05
 -1.05879e-21
 -2.1017e-05
 -9.31736e-21
 -2.1017e-05
 -8.68209e-21
 1.05085e-05
 0.000121104
 0.000121104
 0.000121104
 -1.73006e-05
 -8.04681e-21
 -1.73006e-05
 -8.47033e-22
 -1.73006e-05
 7.51742e-21
 8.65031e-06
 0.000118858
 0.000118858
 0.000118858
 -1.69798e-05
 -8.47033e-22
 -1.69798e-05
 -7.72918e-21
 -1.69798e-05
 -6.77626e-21
 8.48988e-06
 0.000142597
 0.000142597
 0.000142597
 -2.0371e-05
 -8.47033e-22
 -2.0371e-05
 -9.21148e-21
 -2.0371e-05
 -8.47033e-21
 1.01855e-05
 0.000182369
 0.000182369
 0.000182369
 -2.60527e-05
 -1.19643e-20
 -2.60527e-05
 -1.69407e-21
 -2.60527e-05
 1.05879e-20
 1.30264e-05
 0.00012003
 0.00012003
 0.00012003
 -1.71472e-05
 -4.23516e-22
 -1.71472e-05
 -7.72918e-21
 -1.71472e-05
 -7.19978e-21
 8.57358e-06
 0.000202462
 0.000202462
 0.000202462
 -2.89232e-05
 -1.27055e-21
 -2.89232e-05
 -1.29173e-20
 -2.89232e-05
 -1.14349e-20
 1.44616e-05
 0.000157036
 0.000157036
 0.000157036
 -2.24337e-05
 -1.05879e-21
 -2.24337e-05
 -1.01644e-20
 -2.24337e-05
 -8.99973e-21
 1.12168e-05
 0.000156196
 0.000156196
 0.000156196
 -2.23138e-05
 -1.03762e-20
 -2.23138e-05
 -1.27055e-21
 -2.23138e-05
 9.42324e-21
 1.11569e-05
 0.000168399
 0.000168399
 0.000168399
 -2.40569e-05
 -1.05879e-21
 -2.40569e-05
 -1.07997e-20
 -2.40569e-05
 -1.00585e-20
 1.20285e-05
 0.000170865
 0.000170865
 0.000170865
 -2.44093e-05
 -1.13291e-20
 -2.44093e-05
 -1.27055e-21
 -2.44093e-05
 1.01644e-20
 1.22046e-05
 0.000166982
 0.000166982
 0.000166982
 -2.38545e-05
 -1.27055e-21
 -2.38545e-05
 -1.10114e-20
 -2.38545e-05
 -1.00585e-20
 1.19273e-05
 0.000171801
 0.000171801
 0.000171801
 -2.45431e-05
 -1.12232e-20
 -2.45431e-05
 -1.27055e-21
 -2.45431e-05
 1.01644e-20
 1.22715e-05
 0.000143921
 0.000143921
 0.000143921
 -2.05601e-05
 -1.05879e-21
 -2.05601e-05
 -9.1056e-21
 -2.05601e-05
 -8.25857e-21
 1.028e-05
 0.000172976
 0.000172976
 0.000172976
 -2.47108e-05
 -8.47033e-22
 -2.47108e-05
 -1.10114e-20
 -2.47108e-05
 -1.01644e-20
 1.23554e-05
 0.000201934
 0.000201934
 0.000201934
 -2.88477e-05
 -8.47033e-22
 -2.88477e-05
 -1.24937e-20
 -2.88477e-05
 -1.16467e-20
 1.44239e-05
 0.000209182
 0.000209182
 0.000209182
 -2.98831e-05
 -1.27055e-21
 -2.98831e-05
 -1.29173e-20
 -2.98831e-05
 -1.18585e-20
 1.49416e-05
 0.000143972
 0.000143972
 0.000143972
 -2.05675e-05
 -8.47033e-22
 -2.05675e-05
 -9.52912e-21
 -2.05675e-05
 -8.57621e-21
 1.02837e-05
 0.000149635
 0.000149635
 0.000149635
 -2.13765e-05
 -1.05879e-21
 -2.13765e-05
 -9.635e-21
 -2.13765e-05
 -8.68209e-21
 1.06882e-05
 0.000162731
 0.000162731
 0.000162731
 -2.32472e-05
 -1.06938e-20
 -2.32472e-05
 -1.05879e-21
 -2.32472e-05
 9.74088e-21
 1.16236e-05
 0.000126429
 0.000126429
 0.000126429
 -1.80613e-05
 -8.47033e-22
 -1.80613e-05
 -8.15269e-21
 -1.80613e-05
 -7.30566e-21
 9.03063e-06
 0.000131321
 0.000131321
 0.000131321
 -1.87601e-05
 -8.78797e-21
 -1.87601e-05
 -1.27055e-21
 -1.87601e-05
 8.04681e-21
 9.38007e-06
 9.97053e-05
 9.97053e-05
 9.97053e-05
 -1.42436e-05
 -6.35275e-22
 -1.42436e-05
 -6.35275e-21
 -1.42436e-05
 -5.82335e-21
 7.12181e-06
 9.84323e-05
 9.84323e-05
 9.84323e-05
 -1.40618e-05
 -6.45863e-21
 -1.40618e-05
 -6.35275e-22
 -1.40618e-05
 5.50571e-21
 7.03088e-06
 9.87187e-05
 9.87187e-05
 9.87187e-05
 -1.41027e-05
 -8.47033e-22
 -1.41027e-05
 -6.35275e-21
 -1.41027e-05
 -5.71747e-21
 7.05133e-06
 0.000137261
 0.000137261
 0.000137261
 -1.96088e-05
 -8.47033e-22
 -1.96088e-05
 -8.78797e-21
 -1.96088e-05
 -8.04681e-21
 9.80438e-06
 0.000121758
 0.000121758
 0.000121758
 -1.7394e-05
 -8.47033e-22
 -1.7394e-05
 -7.83505e-21
 -1.7394e-05
 -6.88214e-21
 8.69701e-06
 9.70393e-05
 9.70393e-05
 9.70393e-05
 -1.38628e-05
 -6.14099e-21
 -1.38628e-05
 -6.35275e-22
 -1.38628e-05
 5.50571e-21
 6.93138e-06
 0.00012491
 0.00012491
 0.00012491
 -1.78443e-05
 -8.47033e-22
 -1.78443e-05
 -7.94093e-21
 -1.78443e-05
 -7.19978e-21
 8.92216e-06
 0.00014659
 0.00014659
 0.00014659
 -2.09415e-05
 -1.27055e-21
 -2.09415e-05
 -9.31736e-21
 -2.09415e-05
 -8.68209e-21
 1.04707e-05
 0.000141429
 0.000141429
 0.000141429
 -2.02041e-05
 -9.21148e-21
 -2.02041e-05
 -1.05879e-21
 -2.02041e-05
 8.68209e-21
 1.01021e-05
 0.000136658
 0.000136658
 0.000136658
 -1.95225e-05
 -8.47033e-22
 -1.95225e-05
 -8.78797e-21
 -1.95225e-05
 -7.94093e-21
 9.76127e-06
 0.000131164
 0.000131164
 0.000131164
 -1.87377e-05
 -8.57621e-21
 -1.87377e-05
 -8.47033e-22
 -1.87377e-05
 7.83505e-21
 9.36886e-06
 0.000163086
 0.000163086
 0.000163086
 -2.3298e-05
 -1.27055e-21
 -2.3298e-05
 -1.03762e-20
 -2.3298e-05
 -9.31736e-21
 1.1649e-05
 0.000173556
 0.000173556
 0.000173556
 -2.47937e-05
 -1.11173e-20
 -2.47937e-05
 -1.27055e-21
 -2.47937e-05
 1.01644e-20
 1.23968e-05
 0.000146993
 0.000146993
 0.000146993
 -2.0999e-05
 -6.35275e-22
 -2.0999e-05
 -9.31736e-21
 -2.0999e-05
 -8.68209e-21
 1.04995e-05
 0.000200655
 0.000200655
 0.000200655
 -2.86649e-05
 -1.33408e-20
 -2.86649e-05
 -1.27055e-21
 -2.86649e-05
 1.20702e-20
 1.43325e-05
 0.000146891
 0.000146891
 0.000146891
 -2.09844e-05
 -8.47033e-22
 -2.09844e-05
 -9.52912e-21
 -2.09844e-05
 -8.68209e-21
 1.04922e-05
 0.000206773
 0.000206773
 0.000206773
 -2.9539e-05
 -1.33408e-20
 -2.9539e-05
 -1.69407e-21
 -2.9539e-05
 1.27055e-20
 1.47695e-05
 0.000122634
 0.000122634
 0.000122634
 -1.75191e-05
 -8.47033e-22
 -1.75191e-05
 -7.94093e-21
 -1.75191e-05
 -7.41154e-21
 8.75957e-06
 0.000153105
 0.000153105
 0.000153105
 -2.18722e-05
 -9.84676e-21
 -2.18722e-05
 -1.05879e-21
 -2.18722e-05
 8.89385e-21
 1.09361e-05
 0.000118613
 0.000118613
 0.000118613
 -1.69448e-05
 -6.35275e-22
 -1.69448e-05
 -7.41154e-21
 -1.69448e-05
 -6.77626e-21
 8.47238e-06
 0.000200012
 0.000200012
 0.000200012
 -2.85731e-05
 -1.27055e-21
 -2.85731e-05
 -1.27055e-20
 -2.85731e-05
 -1.18585e-20
 1.42866e-05
 0.000160714
 0.000160714
 0.000160714
 -2.29591e-05
 -1.27055e-21
 -2.29591e-05
 -1.0482e-20
 -2.29591e-05
 -9.52912e-21
 1.14796e-05
 0.000135887
 0.000135887
 0.000135887
 -1.94125e-05
 -8.47033e-22
 -1.94125e-05
 -8.68209e-21
 -1.94125e-05
 -8.36445e-21
 9.70625e-06
 0.000167526
 0.000167526
 0.000167526
 -2.39322e-05
 -1.05879e-21
 -2.39322e-05
 -1.09055e-20
 -2.39322e-05
 -1.01644e-20
 1.19661e-05
 0.000153229
 0.000153229
 0.000153229
 -2.18898e-05
 -1.05879e-21
 -2.18898e-05
 -1.01644e-20
 -2.18898e-05
 -9.1056e-21
 1.09449e-05
 0.000212133
 0.000212133
 0.000212133
 -3.03048e-05
 -1.3976e-20
 -3.03048e-05
 -1.27055e-21
 -3.03048e-05
 1.3129e-20
 1.51524e-05
 0.000179866
 0.000179866
 0.000179866
 -2.56951e-05
 -8.47033e-22
 -2.56951e-05
 -1.17526e-20
 -2.56951e-05
 -1.03762e-20
 1.28475e-05
 0.000175489
 0.000175489
 0.000175489
 -2.50698e-05
 -1.27055e-21
 -2.50698e-05
 -1.12232e-20
 -2.50698e-05
 -1.03762e-20
 1.25349e-05
 0.000171359
 0.000171359
 0.000171359
 -2.44799e-05
 -1.10114e-20
 -2.44799e-05
 -1.27055e-21
 -2.44799e-05
 1.03762e-20
 1.22399e-05
 0.000215022
 0.000215022
 0.000215022
 -3.07174e-05
 -8.47033e-22
 -3.07174e-05
 -1.41878e-20
 -3.07174e-05
 -1.27055e-20
 1.53587e-05
 0.000166203
 0.000166203
 0.000166203
 -2.37433e-05
 -1.09055e-20
 -2.37433e-05
 -1.27055e-21
 -2.37433e-05
 1.00585e-20
 1.18716e-05
 0.000209908
 0.000209908
 0.000209908
 -2.99868e-05
 -1.35525e-20
 -2.99868e-05
 -1.27055e-21
 -2.99868e-05
 1.20702e-20
 1.49934e-05
 0.000101008
 0.000101008
 0.000101008
 -1.44297e-05
 -8.47033e-22
 -1.44297e-05
 -6.67038e-21
 -1.44297e-05
 -5.92923e-21
 7.21484e-06
 0.000153008
 0.000153008
 0.000153008
 -2.18583e-05
 -6.35275e-22
 -2.18583e-05
 -9.74088e-21
 -2.18583e-05
 -9.31736e-21
 1.09291e-05
 0.000148066
 0.000148066
 0.000148066
 -2.11523e-05
 -1.05879e-21
 -2.11523e-05
 -9.31736e-21
 -2.11523e-05
 -8.47033e-21
 1.05761e-05
 0.000127834
 0.000127834
 0.000127834
 -1.8262e-05
 -1.05879e-21
 -1.8262e-05
 -8.25857e-21
 -1.8262e-05
 -7.83505e-21
 9.13099e-06
 0.000216063
 0.000216063
 0.000216063
 -3.08661e-05
 -1.27055e-21
 -3.08661e-05
 -1.43996e-20
 -3.08661e-05
 -1.27055e-20
 1.54331e-05
 0.000159925
 0.000159925
 0.000159925
 -2.28465e-05
 -1.05879e-21
 -2.28465e-05
 -1.0482e-20
 -2.28465e-05
 -9.42324e-21
 1.14232e-05
 0.000147169
 0.000147169
 0.000147169
 -2.10242e-05
 -8.47033e-22
 -2.10242e-05
 -9.42324e-21
 -2.10242e-05
 -8.78797e-21
 1.05121e-05
 0.000147497
 0.000147497
 0.000147497
 -2.10711e-05
 -9.635e-21
 -2.10711e-05
 -1.05879e-21
 -2.10711e-05
 9.1056e-21
 1.05355e-05
 0.000205246
 0.000205246
 0.000205246
 -2.93209e-05
 -1.35525e-20
 -2.93209e-05
 -2.11758e-21
 -2.93209e-05
 1.18585e-20
 1.46605e-05
 0.000178445
 0.000178445
 0.000178445
 -2.54921e-05
 -1.27055e-21
 -2.54921e-05
 -1.15408e-20
 -2.54921e-05
 -1.03762e-20
 1.27461e-05
 0.000186488
 0.000186488
 0.000186488
 -2.66411e-05
 -1.69407e-21
 -2.66411e-05
 -1.19643e-20
 -2.66411e-05
 -1.05879e-20
 1.33205e-05
 0.000130886
 0.000130886
 0.000130886
 -1.86981e-05
 -8.47033e-21
 -1.86981e-05
 -1.05879e-21
 -1.86981e-05
 7.41154e-21
 9.34903e-06
 0.000150214
 0.000150214
 0.000150214
 -2.14592e-05
 -9.84676e-21
 -2.14592e-05
 -1.27055e-21
 -2.14592e-05
 8.68209e-21
 1.07296e-05
 0.000151652
 0.000151652
 0.000151652
 -2.16646e-05
 -1.00585e-20
 -2.16646e-05
 -1.27055e-21
 -2.16646e-05
 8.78797e-21
 1.08323e-05
 0.000158677
 0.000158677
 0.000158677
 -2.26681e-05
 -1.0482e-20
 -2.26681e-05
 -1.48231e-21
 -2.26681e-05
 9.635e-21
 1.13341e-05
 0.000172582
 0.000172582
 0.000172582
 -2.46546e-05
 -8.47033e-22
 -2.46546e-05
 -1.10114e-20
 -2.46546e-05
 -1.01644e-20
 1.23273e-05
 0.000155187
 0.000155187
 0.000155187
 -2.21696e-05
 -8.47033e-22
 -2.21696e-05
 -9.95264e-21
 -2.21696e-05
 -8.99973e-21
 1.10848e-05
 0.000176573
 0.000176573
 0.000176573
 -2.52247e-05
 -8.47033e-22
 -2.52247e-05
 -1.15408e-20
 -2.52247e-05
 -1.05879e-20
 1.26124e-05
 0.000165828
 0.000165828
 0.000165828
 -2.36898e-05
 -1.06938e-20
 -2.36898e-05
 -1.27055e-21
 -2.36898e-05
 9.74088e-21
 1.18449e-05
 0.000184428
 0.000184428
 0.000184428
 -2.63469e-05
 -1.2282e-20
 -2.63469e-05
 -1.27055e-21
 -2.63469e-05
 1.07997e-20
 1.31734e-05
 0.000183018
 0.000183018
 0.000183018
 -2.61454e-05
 -1.21761e-20
 -2.61454e-05
 -1.27055e-21
 -2.61454e-05
 1.07997e-20
 1.30727e-05
 0.000170346
 0.000170346
 0.000170346
 -2.43351e-05
 -1.05879e-21
 -2.43351e-05
 -1.11173e-20
 -2.43351e-05
 -1.05879e-20
 1.21676e-05
 0.000198918
 0.000198918
 0.000198918
 -2.84168e-05
 -1.29173e-20
 -2.84168e-05
 -1.27055e-21
 -2.84168e-05
 1.16467e-20
 1.42084e-05
 0.000175271
 0.000175271
 0.000175271
 -2.50387e-05
 -1.15408e-20
 -2.50387e-05
 -1.27055e-21
 -2.50387e-05
 1.0482e-20
 1.25193e-05
 0.000186829
 0.000186829
 0.000186829
 -2.66899e-05
 -1.27055e-21
 -2.66899e-05
 -1.24937e-20
 -2.66899e-05
 -1.14349e-20
 1.3345e-05

Using the vector we can build the linear combination of the a and the m matrix:

mstar.AsVector().data = m.mat.AsVector() + dt * a.mat.AsVector()
# corresponds to M* = M + dt * A
invmstar = mstar.Inverse(freedofs=fes.FreeDofs())

We set the r.h.s. \(f = exp(-6 ((x+\frac12)^2+y^2)) - exp(-6 ((x-\frac12)^2+y^2))\)

f = LinearForm(fes)
gaussp = exp(-6*((x+0.5)*(x+0.5)+y*y))-exp(-6*((x-0.5)*(x-0.5)+y*y))
Draw(gaussp,mesh,"f", deformation=True)
f += gaussp*v*dx
f.Assemble()

<ngsolve.comp.LinearForm at 0x7ff098ef55b0>

and the initial data: \(u_0 = (1-y^2)x\)

gfu = GridFunction(fes)
gfu.Set((1-y*y)*x) # note that boundary conditions remain
scene = Draw(gfu,mesh,"u")

we define a simple time loop including some visualization sampling:

def TimeStepping(invmstar, initial_cond = None, t0 = 0, tend = 2,
                 nsamples = 10):
    if initial_cond:
        gfu.Set(initial_cond)
    cnt = 0; time = t0
    sample_int = int(floor(tend / dt / nsamples)+1)
    gfut = GridFunction(gfu.space,multidim=0)
    gfut.AddMultiDimComponent(gfu.vec)
    while time < tend - 0.5 * dt:
        res = dt * f.vec - dt * a.mat * gfu.vec
        gfu.vec.data += invmstar * res
        print("\r",time,end="")
        scene.Redraw()
        if cnt % sample_int == 0:
            gfut.AddMultiDimComponent(gfu.vec)
        cnt += 1; time = cnt * dt
    return gfut

%%time
gfut = TimeStepping(invmstar, (1-y*y)*x)

 1.999CPU times: user 564 ms, sys: 16.1 ms, total: 580 ms
Wall time: 567 ms

Draw(gfut, mesh, interpolate_multidim=True, animate=True)

BaseWebGuiScene

Supplementary material:

The simple time stepping can be extended in several directions:

1. Instead of direct one could use iterative solvers

2. R.h.s. data time-dependent

3. boundary data time-dependent

4. Replace implicit Euler time stepping with (Singly diagonal) Runge-Kutta methods

Supplementary 1: Using iterative solvers

• For a factorization of \(M^\ast\) (and \({M^\ast}^{-1}\)) we required a sparse matrix \(M^\ast\)

• To store \(M^\ast\) as a sparse matrix requires new storage (and same memory layout of \(A\) and \(M\))

• For iterative solvers we only require the matrix (and preconditioner) applications and it suffices to have :math:`M^ast` available as a linear operator

• mstar_alt = m.mat + dt * a.mat has no storage but defines the operator action: sum of two matrix-vector multiplications

iterative solver version (with Jacobi preconditining):

mstar_alt = m.mat + dt * a.mat
premstar_alt = m.mat.CreateSmoother() + dt * a.mat.CreateSmoother()
print(premstar_alt)

Sum of
Scale a = 1
Print base-matrix
Scale b = 1
Scale with 0.001:
Print base-matrix

Now, replace the action of the inverse Matrix from the previous script with a solution of a conjugate gradient method:

from ngsolve.krylovspace import CGSolver
invmstar_alt = CGSolver(mstar_alt, premstar_alt, tol=1e-8, printrates="\r", maxiter=200)

Now, we can repeat the time stepping. As in 2D direct solvers are quite efficient, this simple preconditioned solver can hardly compete. We hence only do a few time steps:

%%time
gfut_a1 = TimeStepping(invmstar_alt, (1-y*y)*x, tend=25*dt, nsamples=5)

CG converged in 107 iterations to residual 3.4506237382489186e-11
CG converged in 107 iterations to residual 3.434400568946877e-11
CG converged in 107 iterations to residual 3.41904053343005e-11
CG converged in 107 iterations to residual 3.404224595837282e-11
CG converged in 107 iterations to residual 3.389722956134242e-11
CG converged in 107 iterations to residual 3.3753751774369674e-11
CG converged in 107 iterations to residual 3.3610733933076795e-11
CG converged in 107 iterations to residual 3.3467487850259067e-11
CG converged in 107 iterations to residual 3.332361060800224e-11
CG converged in 107 iterations to residual 3.3178904755819595e-11
CG converged in 107 iterations to residual 3.303331891114304e-11
CG converged in 107 iterations to residual 3.288690415261776e-11
CG converged in 107 iterations to residual 3.273978230993873e-11
CG converged in 107 iterations to residual 3.259212302910974e-11
CG converged in 107 iterations to residual 3.244412720384711e-11
CG converged in 107 iterations to residual 3.2296014963767106e-11
CG converged in 107 iterations to residual 3.2148016889930035e-11
CG converged in 107 iterations to residual 3.200036749909559e-11
CG converged in 107 iterations to residual 3.185330031735189e-11
CG converged in 107 iterations to residual 3.1707044070111576e-11
CG converged in 107 iterations to residual 3.156181966549319e-11
CG converged in 107 iterations to residual 3.1417837755470876e-11
CG converged in 107 iterations to residual 3.1275296734879405e-11
CG converged in 107 iterations to residual 3.113438109072801e-11
CG converged in 107 iterations to residual 3.0995260049605705e-11
 0.024CPU times: user 586 ms, sys: 0 ns, total: 586 ms
Wall time: 582 ms

Draw(gfut_a1, mesh, interpolate_multidim=True, animate=True)

BaseWebGuiScene

Supplementary 2: time-dependent r.h.s. data

Next: time-dependent r.h.s. data \(f=f(t)\):

• Use Parameter t representing the time.

• A Parameter is a constant CoefficientFunction the value of which can be changed with the Set-function.

t = Parameter(0.0)

An example of a time-dependent coefficient that we want to use as r.h.s. in the following is

omega=1
gausspt = exp(-6*((x+sin(omega*t))*(x+sin(omega*t))+y*y))-exp(-6*((x-sin(omega*t))*(x-sin(omega*t))+y*y))
gff = GridFunction(L2(mesh,order=gfu.space.globalorder+1))
gfft = GridFunction(gff.space,multidim=0)
time = 0.0
for i in range(7):
    t.Set(3*i/6)
    gff.Set(gausspt)
    gfft.AddMultiDimComponent(gff.vec)
Draw(gfft, mesh, interpolate_multidim=True, animate=True, autoscale=False, min=-1, max=1)

BaseWebGuiScene

Accordingly, we define a different linear form which then has to be assembled in every time step.

ft = LinearForm(fes)
ft += gausspt*v*dx

def TimeStepping_app2(invmstar, initial_cond = None, t0 = 0, tend = 2,
                      nsamples = 10):
    if initial_cond:
        gfu.Set(initial_cond)
    cnt = 0; time = t0
    sample_int = int(floor(tend / dt / nsamples)+1)
    gfut = GridFunction(gfu.space,multidim=0)
    gfut.AddMultiDimComponent(gfu.vec)
    while time < tend - 0.5 * dt:
        t.Set(time)
        ft.Assemble()
        res = dt * ft.vec - dt * a.mat * gfu.vec
        gfu.vec.data += invmstar * res
        print("\r",time,end="")
        if cnt % sample_int == 0:
            gfut.AddMultiDimComponent(gfu.vec)
        cnt += 1; time = cnt * dt
    return gfut

%%time
gfut_a2 = TimeStepping_app2(invmstar, initial_cond=CF(0),tend=2)
Draw(gfut_a2, mesh, interpolate_multidim=True, animate=True,
     min=-0.75,max=0.75,autoscale=False)

 1.999

CPU times: user 1.47 s, sys: 15.3 ms, total: 1.49 s
Wall time: 3.61 s

BaseWebGuiScene

Supplementary 3: Time dependent boundary conditions

• \(u|_{\partial \Omega} = u_D(t)\), \(f=0\)

• implicit Euler time stepping method, non-incremental form:

  \[M^\ast u^{n+1} = (M + \Delta t A) u^{n+1} = M u^n\]

• Homogenize w.r.t. to boundary conditions, i.e. we split

  \[u^{n+1} = u^{n+1}_0 + u^{n+1}_D\]

  where \(u^{n+1}_D\) is a (discrete) function with correct boundary condition:

\[{M^\ast} u^{n+1}_0 = M u^n - {M^\ast} u^{n+1}_D\]

uD = CoefficientFunction( [(1-x*x)*IfPos(sin(0.3*pi*t),sin(0.3*pi*t),0),0,0,0])
time = 0.0
t.Set(0.0)
gfu.Set(uD,BND)

def TimeStepping_app3(invmstar, initial_cond = None, t0 = 0, tend = 2,
                      nsamples = 10):
    if initial_cond:
        gfu.Set(initial_cond)
    cnt = 0; time = t0
    sample_int = int(floor(tend / dt / nsamples)+1)
    gfuD = GridFunction(gfu.space)
    gfut = GridFunction(gfu.space,multidim=0)
    gfut.AddMultiDimComponent(gfu.vec)
    while time < tend - 0.5 * dt:
        t.Set(time)
        gfuD.Set(uD,BND)
        res = m.mat * gfu.vec - mstar *gfuD.vec
        gfu.vec.data = gfuD.vec + invmstar * res
        print("\r",time,end="")
        if cnt % sample_int == 0:
            gfut.AddMultiDimComponent(gfu.vec)
        cnt += 1; time = cnt * dt
    return gfut

%%time
gfut_a3 = TimeStepping_app3(invmstar, initial_cond=CF(0),tend=10)
Draw(gfut_a3, mesh, interpolate_multidim=True, animate=True,
     #settings = {"subdivision" : 10},
     deformation = True, min = 0, max = 0.2, autoscale = False)

 9.999

CPU times: user 4.01 s, sys: 30.8 ms, total: 4.04 s
Wall time: 6.14 s

BaseWebGuiScene

Supplementary 4: Singly diagonally implicit Runge-Kutta methods

Let us consider more sophisticated time integration methods, SDIRK methods. To simplify presentation we set \(f=0\).

SDIRK methods for the semi-discrete problem \(\frac{d}{dt} u = M^{-1} F(u) = -M^{-1} \cdot A u\) are of the form:

\[u^{n+1} = u^n + \Delta t M^{-1} \sum_{i=0}^{s-1} b_i k_i\]

with

\[k_i = - A u_i \quad \text{ where $u_i$ is the solution to } \quad (M + a_{ii} \Delta t A) u_i = M u^n + \Delta t \sum_{j=0}^{i-1} a_{ij} k_j, \quad i=0,..,s-1.\]

The coefficients a,b and c are stored in the butcher tableau:

\[\begin{split}\begin{array}{c|cccc} c_0 & a_{00} & 0 & \ddots& \\ c_1 & a_{10} & a_{11} & 0 & \ddots \\ \vdots & \vdots & \vdots & \ddots & 0\\ c_{s-1} & a_{s-1,0} & a_{s-1,1} & \dots& a_{s-1,s-1} \\ \hline & b_{0} & b_1 & \dots& b_{s-1} \\ \end{array}\end{split}\]

For an SDIRK method we have \(a^\ast = a_{ii},~i=0,..,s-1\).

Simplest example: Implicit Euler

\[\begin{split}\begin{array}{c|c} 1 & 1 \\ \hline & 1 \\ \end{array}\end{split}\]

class sdirk1: #order 1 (implicit Euler)
    stages = 1
    a = [[1]]
    b = [1]
    c = [1]
    astar = 1

Midpoint rule:

class MR: #order 2 (midpoint rule)
    stages = 1
    a = [[0.5]]
    b = [1]
    c = [0.5]
    astar = 0.5

We can use for example the 2 stage SDIRK (order 3) method

\[\begin{split}\begin{array}{c|cc} p & p & 0 \\ 1-p & 1-2p & p \\ \hline & 1/2 & 1/2 \\ \end{array}\end{split}\]

with \(p = \frac{3 - \sqrt{3}}{6}\).

class sdirk2: #order 3
    p = (3 - sqrt(3))/6
    stages = 2
    a = [[p, 0],
         [1 - 2*p, p]]
    b = [1/2, 1/2]
    c = [p, 1 - p]
    astar = p

or the 5 stage SDIRK (order 4) method

\[\begin{split}\begin{array}{c|cccc} 1/4 & 1/4 \\ 3/4 & 1/2 & 1/4 & \\ 11/20 & 17/50 & -1/25 & 1/4 \\ 1/2 & 371/1360 & -137/2720 & 15/544 & 1/4 \\ 1 & 25/4 & -49/48 & 125/16 & -85/12 & 1/4 \\ \hline & 25/4 & -49/48 & 125/16 & -85/12 & 1/4 \\ \end{array}\end{split}\]

class sdirk5: #order 4
    stages = 5
    a = [[1/4, 0, 0, 0, 0],
         [1/2, 1/4, 0, 0, 0],
         [17/50,-1/25, 1/4, 0, 0],
         [371/1360, -137/2720, 15/544, 1/4,0],
         [25/24, -49/48, 125/16, -85/12, 1/4]]
    b = [25/24, -49/48, 125/16, -85/12, 1/4]
    c = [1/4, 3/4, 11/20, 1/2, 1]
    astar = 1/4

We have to update the \(M^\ast\) matrix due to the different diagonal in the butcher tableau. Further, we will also need the inverse mass matrix to compute the slope states \(k_i\).

In the next function, we put setup of the matrices, their inverses and the time stepping in one (larger) loop:

def TimeStepping_app4(m, a, butchertab, dt,
                      initial_cond = None, t0 = 0, tend = 2,
                      nsamples = 10):
    mstar.AsVector().data = m.mat.AsVector() + butchertab.astar * dt * a.mat.AsVector()
    invmstar = mstar.Inverse(freedofs=fes.FreeDofs())
    invmass = m.mat.Inverse(freedofs=fes.FreeDofs())

    rhsi, Mu0, ui = gfu.vec.CreateVector(),gfu.vec.CreateVector(),gfu.vec.CreateVector()
    k = [gfu.vec.CreateVector() for i in range(butchertab.stages)]

    if initial_cond:
        gfu.Set(initial_cond)
    cnt = 0; time = t0
    sample_int = int(floor(tend / dt / nsamples)+1)
    gfuD = GridFunction(gfu.space)
    gfut = GridFunction(gfu.space,multidim=0)
    gfut.AddMultiDimComponent(gfu.vec)
    while time < tend - 0.5 * dt:
        Mu0.data = m.mat * gfu.vec
        for i in range(butchertab.stages):
            rhsi.data = Mu0
            for j in range(0,i):
                rhsi.data += dt * butchertab.a[i][j] * k[j]
            t.Set(time+butchertab.c[i]*dt)
            gfu.Set(uD,BND)
            ui.data = gfu.vec; rhsi.data -= mstar * ui
            ui.data += invmstar * rhsi
            k[i].data = - a.mat * ui
        t.Set(time+dt)
        gfu.Set(uD,BND)
        Mu0.data -= m.mat * gfu.vec
        for i in range(0,butchertab.stages):
            Mu0.data += dt * butchertab.b[i] * k[i]
        gfu.vec.data += invmass * Mu0
        print("\r",time,end="")
        if cnt % sample_int == 0:
            gfut.AddMultiDimComponent(gfu.vec)
        cnt += 1; time = cnt * dt
    return gfut

Next, we simply apply the time stepping:

gfut_a4 = TimeStepping_app4(m, a, butchertab = sdirk5(),
                            dt = 0.25, initial_cond=CF(0),tend=10)
Draw(gfut_a4, mesh, interpolate_multidim=True, animate=True,
     order = 3,
     deformation = True, min = 0, max = 0.2, autoscale = False)

 9.75

BaseWebGuiScene

Tasks

If you want to play around and explore this tutorial unit, here are a few suggestions:

• Make a convergence study (for convergence in space, time and space and time)

• Re-introduce non-zero r.h.s. in the RK-script

• Generalize the RK script to fully implicit RK schemes (using product spaces, or block matrices, …)