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 0x7fa0a37609b0>

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 = 11257, a.mat.nze=11257, mstar.nze=11257

/usr/lib/python3/dist-packages/scipy/__init__.py:146: UserWarning: A NumPy version >=1.17.3 and <1.25.0 is required for this version of SciPy (detected version 1.26.4
  warnings.warn(f"A NumPy version >={np_minversion} and <{np_maxversion}"

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=11257, len(mstar.AsVector())=11257

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
 0.00823929
 0.00207589
 0.00204376
 0.00411964
 -0.000415177
 6.91962e-05
 -0.000408752
 6.81253e-05
 -0.000823929
 0.000137321
 -0.000207589
 1.05879e-19
 -0.000204376
 -1.05032e-19
 0.000138392
 0.000136251
 0.00520833
 0.00260417
 0.00260417
 -0.000520833
 8.68056e-05
 -0.000520833
 8.68056e-05
 -0.000260417
 1.32137e-19
 0.000173611
 0.00827496
 0.00209025
 0.00204723
 0.00413748
 -0.000418049
 6.96749e-05
 -0.000409446
 6.82411e-05
 -0.000827496
 0.000137916
 -0.000209025
 1.05032e-19
 -0.000204723
 -1.04185e-19
 0.00013935
 0.000136482
 0.00260417
 0.0195488
 0.00333868
 0.00643574
 0.00717025
 -0.000520833
 -8.68056e-05
 -0.000260417
 -1.42302e-19
 -0.000667736
 0.000111289
 -0.00128715
 0.000214525
 -0.00143405
 0.000239008
 -0.000333868
 -1.72795e-19
 -0.000383157
 1.96512e-19
 0.000173611
 0.000222579
 0.000255438
 0.00333868
 0.0199715
 0.00282601
 0.00715975
 0.00664708
 -0.000667736
 -0.000111289
 -0.000333868
 -1.86347e-19
 -0.000565201
 9.42002e-05
 -0.00143195
 0.000238658
 -0.00132942
 0.000221569
 -0.000282601
 -1.40607e-19
 -0.000382107
 1.89735e-19
 0.000222579
 0.0001884
 0.000254738
 0.00282601
 0.0165345
 0.0025482
 0.00571903
 0.00544123
 -0.000565201
 -9.42002e-05
 -0.000282601
 -1.5416e-19
 -0.00050964
 8.494e-05
 -0.00114381
 0.000190634
 -0.00108825
 0.000181374
 -0.00025482
 -1.28749e-19
 -0.000289303
 1.49078e-19
 0.0001884
 0.00016988
 0.000192868
 0.0025482
 0.0146259
 0.00229409
 0.00501886
 0.00476475
 -0.00050964
 -8.494e-05
 -0.00025482
 -1.38913e-19
 -0.000458819
 7.64698e-05
 -0.00100377
 0.000167295
 -0.000952951
 0.000158825
 -0.000229409
 -1.16891e-19
 -0.000247066
 1.23667e-19
 0.00016988
 0.00015294
 0.000164711
 0.00229409
 0.0128843
 0.00205426
 0.00438791
 0.00414808
 -0.000458819
 -7.64698e-05
 -0.000229409
 -1.23667e-19
 -0.000410852
 6.84754e-05
 -0.000877582
 0.000146264
 -0.000829615
 0.000138269
 -0.000205426
 -1.05879e-19
 -0.000209382
 1.05032e-19
 0.00015294
 0.000136951
 0.000139588
 0.00205426
 0.0113433
 0.00188867
 0.00378299
 0.00361739
 -0.000410852
 -6.84754e-05
 -0.000205426
 -1.11808e-19
 -0.000377733
 6.29555e-05
 -0.000756598
 0.0001261
 -0.000723479
 0.00012058
 -0.000188867
 -9.74088e-20
 -0.000172873
 8.72444e-20
 0.000136951
 0.000125911
 0.000115249
 0.00207589
 0.00188867
 0.0112674
 0.0035578
 0.00374502
 -0.000415177
 -6.91962e-05
 -0.000207589
 -6.77626e-21
 -0.000377733
 -6.29555e-05
 -0.000188867
 -1.01644e-19
 -0.00071156
 0.000118593
 -0.000749004
 0.000124834
 -0.000166913
 8.63974e-20
 0.000125911
 0.000138392
 0.000111275
 0.00204376
 0.011037
 0.00182396
 0.00369454
 0.00347474
 -0.000408752
 -6.81253e-05
 -0.000204376
 -1.11808e-19
 -0.000364791
 6.07985e-05
 -0.000738909
 0.000123151
 -0.000694948
 0.000115825
 -0.000182396
 -9.31736e-20
 -0.000165078
 8.38563e-20
 0.000136251
 0.000121597
 0.000110052
 0.00182396
 0.0108765
 0.00194398
 0.00349425
 0.00361428
 -0.000364791
 -6.07985e-05
 -0.000182396
 -9.82558e-20
 -0.000388797
 6.47995e-05
 -0.00069885
 0.000116475
 -0.000722856
 0.000120476
 -0.000194398
 -9.91029e-20
 -0.00016703
 8.63974e-20
 0.000121597
 0.000129599
 0.000111353
 0.00194398
 0.0120504
 0.00210766
 0.00391754
 0.00408122
 -0.000388797
 -6.47995e-05
 -0.000194398
 -1.06726e-19
 -0.000421533
 7.02554e-05
 -0.000783508
 0.000130585
 -0.000816244
 0.000136041
 -0.000210766
 -1.06726e-19
 -0.000197356
 9.91029e-20
 0.000129599
 0.000140511
 0.000131571
 0.00210766
 0.013149
 0.00223556
 0.00433894
 0.00446684
 -0.000421533
 -7.02554e-05
 -0.000210766
 -1.15196e-19
 -0.000447112
 7.45186e-05
 -0.000867788
 0.000144631
 -0.000893368
 0.000148895
 -0.000223556
 -1.15196e-19
 -0.000223128
 1.13502e-19
 0.000140511
 0.000149037
 0.000148752
 0.00223556
 0.0137898
 0.00227834
 0.00461655
 0.00465933
 -0.000447112
 -7.45186e-05
 -0.000223556
 -1.21973e-19
 -0.000455667
 7.59445e-05
 -0.00092331
 0.000153885
 -0.000931866
 0.000155311
 -0.000227834
 -1.16891e-19
 -0.000238099
 1.20279e-19
 0.000149037
 0.000151889
 0.000158733
 0.00227834
 0.0137701
 0.00222092
 0.00466414
 0.00460672
 -0.000455667
 -7.59445e-05
 -0.000227834
 -1.23667e-19
 -0.000444183
 7.40305e-05
 -0.000932829
 0.000155471
 -0.000921345
 0.000153557
 -0.000222092
 -1.10114e-19
 -0.000238581
 1.21973e-19
 0.000151889
 0.000148061
 0.000159054
 0.00260417
 0.00222092
 0.0159979
 0.00577804
 0.00539478
 -0.000520833
 -8.68056e-05
 -0.000260417
 -8.47033e-21
 -0.000444183
 -7.40305e-05
 -0.000222092
 -1.20279e-19
 -0.00115561
 0.000192601
 -0.00107896
 0.000179826
 -0.000317387
 -1.66018e-19
 0.000148061
 0.000173611
 0.000211591
 0.00260417
 0.00577804
 0.0208155
 0.00213338
 0.00567023
 0.00462974
 -0.000260417
 -1.40607e-19
 -0.000520833
 -8.68056e-05
 -0.00115561
 -0.000192601
 -0.000317387
 -1.74489e-19
 -0.000426676
 7.11127e-05
 -0.00113405
 0.000189008
 -0.000925948
 0.000154325
 -0.000213338
 -1.07573e-19
 -0.000249636
 1.28749e-19
 0.000173611
 0.000142225
 0.000211591
 0.000166424
 0.00213338
 0.0130808
 0.00245703
 0.00408339
 0.00440703
 -0.000426676
 -7.11127e-05
 -0.000213338
 -1.15196e-19
 -0.000491405
 8.19009e-05
 -0.000816677
 0.000136113
 -0.000881406
 0.000146901
 -0.000245703
 -1.27055e-19
 -0.000195001
 9.65618e-20
 0.000142225
 0.000163802
 0.00013
 0.00245703
 0.0151149
 0.00253105
 0.00502639
 0.0051004
 -0.000491405
 -8.19009e-05
 -0.000245703
 -1.35525e-19
 -0.000506209
 8.43682e-05
 -0.00100528
 0.000167546
 -0.00102008
 0.000170013
 -0.000253105
 -1.28749e-19
 -0.000256936
 1.30443e-19
 0.000163802
 0.000168736
 0.000171291
 0.00253105
 0.0147573
 0.00233337
 0.00504528
 0.0048476
 -0.000506209
 -8.43682e-05
 -0.000253105
 -1.38913e-19
 -0.000466674
 7.7779e-05
 -0.00100906
 0.000168176
 -0.00096952
 0.000161587
 -0.000233337
 -1.18585e-19
 -0.000251423
 1.30443e-19
 0.000168736
 0.000155558
 0.000167615
 0.00233337
 0.0131456
 0.00208849
 0.00448428
 0.00423941
 -0.000466674
 -7.7779e-05
 -0.000233337
 -1.25361e-19
 -0.000417699
 6.96165e-05
 -0.000896857
 0.000149476
 -0.000847882
 0.000141314
 -0.000208849
 -1.09267e-19
 -0.000215091
 1.10114e-19
 0.000155558
 0.000139233
 0.000143394
 0.00208849
 0.0115252
 0.00191176
 0.00385083
 0.00367409
 -0.000417699
 -6.96165e-05
 -0.000208849
 -1.15196e-19
 -0.000382351
 6.37252e-05
 -0.000770166
 0.000128361
 -0.000734818
 0.00012247
 -0.000191176
 -9.65618e-20
 -0.000176233
 8.97855e-20
 0.000139233
 0.00012745
 0.000117489
 0.00209025
 0.00191176
 0.0113796
 0.00359955
 0.00377804
 -0.000418049
 -6.96749e-05
 -0.000209025
 -5.0822e-21
 -0.000382351
 -6.37252e-05
 -0.000191176
 -1.01644e-19
 -0.00071991
 0.000119985
 -0.000755608
 0.000125935
 -0.000168779
 8.47033e-20
 0.00012745
 0.00013935
 0.000112519
 0.00204723
 0.0110568
 0.0018212
 0.00370721
 0.00348118
 -0.000409446
 -6.82411e-05
 -0.000204723
 -1.11808e-19
 -0.00036424
 6.07067e-05
 -0.000741441
 0.000123574
 -0.000696235
 0.000116039
 -0.00018212
 -9.31736e-20
 -0.000165997
 8.30092e-20
 0.000136482
 0.000121413
 0.000110665
 0.0018212
 0.010812
 0.00192355
 0.00348244
 0.00358479
 -0.00036424
 -6.07067e-05
 -0.00018212
 -9.82558e-20
 -0.000384711
 6.41185e-05
 -0.000696488
 0.000116081
 -0.000716959
 0.000119493
 -0.000192355
 -9.82558e-20
 -0.000166124
 8.47033e-20
 0.000121413
 0.000128237
 0.000110749
 0.00192355
 0.0117603
 0.00204529
 0.00383488
 0.00395662
 -0.000384711
 -6.41185e-05
 -0.000192355
 -1.05032e-19
 -0.000409058
 6.81764e-05
 -0.000766976
 0.000127829
 -0.000791323
 0.000131887
 -0.000204529
 -1.03338e-19
 -0.000191133
 9.91029e-20
 0.000128237
 0.000136353
 0.000127422
 0.00204529
 0.0123838
 0.00211338
 0.00407853
 0.00414662
 -0.000409058
 -6.81764e-05
 -0.000204529
 -1.11808e-19
 -0.000422677
 7.04461e-05
 -0.000815705
 0.000135951
 -0.000829324
 0.000138221
 -0.000211338
 -1.10961e-19
 -0.000203324
 1.04185e-19
 0.000136353
 0.000140892
 0.000135549
 0.00211338
 0.0134801
 0.00237036
 0.00436969
 0.00462666
 -0.000422677
 -7.04461e-05
 -0.000211338
 -1.15196e-19
 -0.000474071
 7.90119e-05
 -0.000873938
 0.000145656
 -0.000925333
 0.000154222
 -0.000237036
 -1.21973e-19
 -0.000225631
 1.15196e-19
 0.000140892
 0.000158024
 0.00015042
 0.00237036
 0.0176168
 0.00309706
 0.00643805
 0.00571135
 -0.000474071
 -7.90119e-05
 -0.000237036
 -1.32137e-19
 -0.000619411
 0.000103235
 -0.00128761
 0.000214602
 -0.00114227
 0.000190378
 -0.000309706
 -1.57548e-19
 -0.0003341
 -1.72795e-19
 0.000158024
 0.00020647
 0.000222733
 0.00260417
 0.00643574
 0.00309706
 0.0190656
 0.00692863
 -0.000260417
 -6.77626e-21
 -0.000520833
 -8.68056e-05
 -0.00128715
 -0.000214525
 -0.000383157
 -1.01644e-20
 -0.000619411
 -0.000103235
 -0.000309706
 -1.69407e-19
 -0.00138573
 0.000230954
 0.000173611
 0.00020647
 0.000255438
 0.00717025
 0.00715975
 0.00643805
 0.00692863
 0.0482623
 0.00732708
 0.00653677
 0.00670178
 -0.000333868
 -6.77626e-21
 -0.000383157
 -2.10064e-19
 -0.00143405
 -0.000239008
 -0.00143195
 -0.000238658
 -0.000382107
 -1.01644e-20
 -0.000309706
 -1.01644e-20
 -0.00128761
 -0.000214602
 -0.0003341
 -1.81265e-19
 -0.00138573
 -0.000230954
 -0.00146542
 0.000244236
 -0.00130735
 0.000217892
 -0.00134036
 0.000223393
 -0.0003506
 -1.79571e-19
 -0.000319578
 1.64324e-19
 0.000222579
 0.000254738
 0.00020647
 0.000255438
 0.000222733
 0.000233734
 0.000213052
 0.00664708
 0.00571903
 0.00732708
 0.0380433
 0.00579165
 0.00597555
 0.00658292
 -0.000282601
 -6.77626e-21
 -0.000382107
 -2.06676e-19
 -0.00132942
 -0.000221569
 -0.00114381
 -0.000190634
 -0.000289303
 -3.38813e-21
 -0.00146542
 -0.000244236
 -0.0003506
 -1.89735e-19
 -0.00115833
 0.000193055
 -0.00119511
 0.000199185
 -0.00131658
 0.000219431
 -0.000289863
 -1.47384e-19
 -0.000307692
 -1.57548e-19
 0.0001884
 0.000254738
 0.000192868
 0.000193242
 0.000233734
 0.000205128
 0.00544123
 0.00501886
 0.00579165
 0.0321184
 0.00495698
 0.005661
 0.0052487
 -0.00025482
 -5.0822e-21
 -0.000289303
 -1.57548e-19
 -0.00108825
 -0.000181374
 -0.00100377
 -0.000167295
 -0.000247066
 -6.77626e-21
 -0.00115833
 -0.000193055
 -0.000289863
 -1.57548e-19
 -0.000991396
 0.000165233
 -0.0011322
 0.0001887
 -0.00104974
 0.000174957
 -0.000248632
 -1.27055e-19
 -0.000276238
 1.42302e-19
 0.00016988
 0.000192868
 0.000164711
 0.000193242
 0.000165755
 0.000184158
 0.00476475
 0.00438791
 0.00495698
 0.0274883
 0.00419246
 0.00439926
 0.00478694
 -0.000229409
 -3.38813e-21
 -0.000247066
 -1.33831e-19
 -0.000952951
 -0.000158825
 -0.000877582
 -0.000146264
 -0.000209382
 -6.77626e-21
 -0.000991396
 -0.000165233
 -0.000248632
 -1.35525e-19
 -0.000838491
 0.000139749
 -0.000879852
 0.000146642
 -0.000957388
 0.000159565
 -0.000209864
 -1.06726e-19
 -0.000230062
 -1.16891e-19
 0.00015294
 0.000164711
 0.000139588
 0.000139909
 0.000165755
 0.000153374
 0.00414808
 0.00378299
 0.00419246
 0.0229244
 0.00339801
 0.00391612
 0.00348676
 -0.000205426
 -5.0822e-21
 -0.000209382
 -1.15196e-19
 -0.000829615
 -0.000138269
 -0.000756598
 -0.0001261
 -0.000172873
 -1.69407e-21
 -0.000838491
 -0.000139749
 -0.000209864
 -1.15196e-19
 -0.000679602
 0.000113267
 -0.000783224
 0.000130537
 -0.000697353
 0.000116225
 -0.000166928
 -8.89385e-20
 -0.000181748
 9.31736e-20
 0.000136951
 0.000139588
 0.000115249
 0.000139909
 0.000111286
 0.000121165
 0.00361739
 0.0035578
 0.00339801
 0.0188525
 0.00292067
 0.00288818
 0.00247044
 -0.000188867
 -5.0822e-21
 -0.000172873
 -9.40207e-20
 -0.000723479
 -0.00012058
 -0.00071156
 -0.000118593
 -0.000166913
 -5.0822e-21
 -0.000679602
 -0.000113267
 -0.000166928
 -9.23266e-20
 -0.000584135
 9.73558e-05
 -0.000577636
 9.62727e-05
 -0.000494088
 8.2348e-05
 -0.000125154
 -6.35275e-20
 -0.00012189
 6.09864e-20
 0.000125911
 0.000115249
 0.000111275
 0.000111286
 8.34361e-05
 8.12599e-05
 0.00411964
 0.00374502
 0.00369454
 0.00292067
 0.019862
 0.0028907
 0.00249146
 -0.000207589
 -1.13502e-19
 -0.000204376
 -3.38813e-21
 -0.000823929
 -0.000137321
 -0.000166913
 -9.06325e-20
 -0.000749004
 -0.000124834
 -0.000738909
 -0.000123151
 -0.000165078
 -6.77626e-21
 -0.000584135
 -9.73558e-05
 -0.000125154
 -6.69156e-20
 -0.00057814
 9.63567e-05
 -0.000498292
 8.30486e-05
 -0.000123992
 -6.35275e-20
 0.000138392
 0.000111275
 0.000136251
 0.000110052
 8.34361e-05
 8.26611e-05
 0.00347474
 0.00349425
 0.0028907
 0.0184461
 0.00330099
 0.00244731
 0.00283809
 -0.000182396
 -3.38813e-21
 -0.000165078
 -9.06325e-20
 -0.000694948
 -0.000115825
 -0.00069885
 -0.000116475
 -0.00016703
 -3.38813e-21
 -0.00057814
 -9.63567e-05
 -0.000123992
 -6.77626e-20
 -0.000660198
 0.000110033
 -0.000489463
 8.15771e-05
 -0.000567619
 9.46032e-05
 -0.00016307
 -8.47033e-20
 -0.00012074
 6.18334e-20
 0.000121597
 0.000110052
 0.000111353
 8.26611e-05
 0.000108713
 8.04932e-05
 0.00361428
 0.00391754
 0.00330099
 0.0220011
 0.00398018
 0.003782
 0.00340607
 -0.000194398
 -5.0822e-21
 -0.00016703
 -8.97855e-20
 -0.000722856
 -0.000120476
 -0.000783508
 -0.000130585
 -0.000197356
 -3.38813e-21
 -0.000660198
 -0.000110033
 -0.00016307
 -8.89385e-20
 -0.000796036
 0.000132673
 -0.0007564
 0.000126067
 -0.000681215
 0.000113536
 -0.000200662
 -1.04185e-19
 -0.000177538
 -9.23266e-20
 0.000129599
 0.000111353
 0.000131571
 0.000133775
 0.000108713
 0.000118358
 0.00408122
 0.00433894
 0.00398018
 0.0256174
 0.00452959
 0.0041979
 0.00448959
 -0.000210766
 -3.38813e-21
 -0.000197356
 -1.06726e-19
 -0.000816244
 -0.000136041
 -0.000867788
 -0.000144631
 -0.000223128
 -5.0822e-21
 -0.000796036
 -0.000132673
 -0.000200662
 -1.0842e-19
 -0.000905917
 0.000150986
 -0.00083958
 0.00013993
 -0.000897917
 0.000149653
 -0.000229831
 -1.18585e-19
 -0.000219128
 1.11808e-19
 0.000140511
 0.000131571
 0.000148752
 0.000133775
 0.000153221
 0.000146085
 0.00446684
 0.00461655
 0.00452959
 0.0284055
 0.00489079
 0.0048451
 0.0050566
 -0.000223556
 -6.77626e-21
 -0.000223128
 -1.21973e-19
 -0.000893368
 -0.000148895
 -0.00092331
 -0.000153885
 -0.000238099
 -3.38813e-21
 -0.000905917
 -0.000150986
 -0.000229831
 -1.25361e-19
 -0.000978159
 0.000163026
 -0.000969021
 0.000161503
 -0.00101132
 0.000168553
 -0.00025098
 -1.30443e-19
 -0.00025468
 1.33831e-19
 0.000149037
 0.000148752
 0.000158733
 0.000153221
 0.00016732
 0.000169786
 0.00465933
 0.00466414
 0.00489079
 0.0293038
 0.00483702
 0.00515554
 0.00509695
 -0.000227834
 -1.01644e-20
 -0.000238099
 -1.30443e-19
 -0.000931866
 -0.000155311
 -0.000932829
 -0.000155471
 -0.000238581
 -3.38813e-21
 -0.000978159
 -0.000163026
 -0.00025098
 -1.35525e-19
 -0.000967404
 0.000161234
 -0.00103111
 0.000171851
 -0.00101939
 0.000169898
 -0.000245121
 -1.25361e-19
 -0.000264574
 1.37219e-19
 0.000151889
 0.000158733
 0.000159054
 0.00016732
 0.000163414
 0.000176383
 0.00460672
 0.00539478
 0.00567023
 0.00483702
 0.0296137
 0.00457507
 0.00452992
 -0.000222092
 -3.38813e-21
 -0.000238581
 -1.28749e-19
 -0.000921345
 -0.000153557
 -0.000317387
 -1.01644e-20
 -0.00107896
 -0.000179826
 -0.00113405
 -0.000189008
 -0.000249636
 -6.77626e-21
 -0.000967404
 -0.000161234
 -0.000245121
 -1.33831e-19
 -0.000915014
 0.000152502
 -0.000905984
 0.000150997
 -0.000207871
 -1.09267e-19
 0.000148061
 0.000159054
 0.000211591
 0.000166424
 0.000163414
 0.000138581
 0.00462974
 0.00408339
 0.00457507
 0.0214627
 0.00402288
 0.00415159
 -0.000213338
 -3.38813e-21
 -0.000249636
 -1.35525e-19
 -0.000925948
 -0.000154325
 -0.000816677
 -0.000136113
 -0.000195001
 -5.0822e-21
 -0.000915014
 -0.000152502
 -0.000207871
 -1.13502e-19
 -0.000804577
 0.000134096
 -0.000830317
 0.000138386
 -0.000207288
 -1.05879e-19
 0.000142225
 0.00013
 0.000166424
 0.000138581
 0.000138192
 0.00440703
 0.00502639
 0.00402288
 0.0307427
 0.00578985
 0.00517445
 0.00632206
 -0.000245703
 -5.0822e-21
 -0.000195001
 -1.05032e-19
 -0.000881406
 -0.000146901
 -0.00100528
 -0.000167546
 -0.000256936
 -8.47033e-21
 -0.000804577
 -0.000134096
 -0.000207288
 -1.13502e-19
 -0.00115797
 0.000192995
 -0.00103489
 0.000172482
 -0.00126441
 0.000210735
 -0.000322049
 -1.67713e-19
 -0.000310157
 1.60936e-19
 0.000163802
 0.00013
 0.000171291
 0.000214699
 0.000138192
 0.000206772
 0.0051004
 0.00504528
 0.00578985
 0.0337514
 0.0051692
 0.00604057
 0.00660608
 -0.000253105
 -1.01644e-20
 -0.000256936
 -1.38913e-19
 -0.00102008
 -0.000170013
 -0.00100906
 -0.000168176
 -0.000251423
 -6.77626e-21
 -0.00115797
 -0.000192995
 -0.000322049
 -1.76183e-19
 -0.00103384
 0.000172307
 -0.00120811
 0.000201352
 -0.00132122
 0.000220203
 -0.000265497
 -1.35525e-19
 -0.000338559
 -1.72795e-19
 0.000168736
 0.000171291
 0.000167615
 0.000176998
 0.000214699
 0.000225706
 0.0048476
 0.00448428
 0.0051692
 0.0285982
 0.00432996
 0.00512151
 0.00464559
 -0.000233337
 -5.0822e-21
 -0.000251423
 -1.38913e-19
 -0.00096952
 -0.000161587
 -0.000896857
 -0.000149476
 -0.000215091
 -6.77626e-21
 -0.00103384
 -0.000172307
 -0.000265497
 -1.43996e-19
 -0.000865993
 0.000144332
 -0.0010243
 0.000170717
 -0.000929118
 0.000154853
 -0.000217905
 -1.13502e-19
 -0.000246654
 1.23667e-19
 0.000155558
 0.000167615
 0.000143394
 0.000176998
 0.00014527
 0.000164436
 0.00423941
 0.00385083
 0.00432996
 0.0235276
 0.00346737
 0.00405703
 0.00358302
 -0.000208849
 -5.0822e-21
 -0.000215091
 -1.16891e-19
 -0.000847882
 -0.000141314
 -0.000770166
 -0.000128361
 -0.000176233
 -8.47033e-21
 -0.000865993
 -0.000144332
 -0.000217905
 -1.16891e-19
 -0.000693475
 0.000115579
 -0.000811407
 0.000135234
 -0.000716605
 0.000119434
 -0.000170504
 -8.55503e-20
 -0.000187798
 9.40207e-20
 0.000139233
 0.000143394
 0.000117489
 0.00014527
 0.000113669
 0.000125199
 0.00367409
 0.00359955
 0.00346737
 0.0191475
 0.00295431
 0.00294536
 0.00250683
 -0.000191176
 -3.38813e-21
 -0.000176233
 -9.48677e-20
 -0.000734818
 -0.00012247
 -0.00071991
 -0.000119985
 -0.000168779
 -5.0822e-21
 -0.000693475
 -0.000115579
 -0.000170504
 -9.23266e-20
 -0.000590861
 9.84769e-05
 -0.000589072
 9.81786e-05
 -0.000501367
 8.35611e-05
 -0.000126651
 -6.43745e-20
 -0.000124032
 6.35275e-20
 0.00012745
 0.000117489
 0.000112519
 0.000113669
 8.44343e-05
 8.2688e-05
 0.00413748
 0.00377804
 0.00370721
 0.00295431
 0.0200032
 0.00290982
 0.00251636
 -0.000209025
 -1.13502e-19
 -0.000204723
 -3.38813e-21
 -0.000827496
 -0.000137916
 -0.000168779
 -9.23266e-20
 -0.000755608
 -0.000125935
 -0.000741441
 -0.000123574
 -0.000165997
 -5.0822e-21
 -0.000590861
 -9.84769e-05
 -0.000126651
 -6.86097e-20
 -0.000581964
 9.6994e-05
 -0.000503272
 8.38786e-05
 -0.000124984
 -6.35275e-20
 0.00013935
 0.000112519
 0.000136482
 0.000110665
 8.44343e-05
 8.3323e-05
 0.00348118
 0.00348244
 0.00290982
 0.0184768
 0.00329119
 0.00246604
 0.00284615
 -0.00018212
 -6.77626e-21
 -0.000165997
 -8.97855e-20
 -0.000696235
 -0.000116039
 -0.000696488
 -0.000116081
 -0.000166124
 -5.0822e-21
 -0.000581964
 -9.6994e-05
 -0.000124984
 -6.77626e-20
 -0.000658239
 0.000109706
 -0.000493208
 8.22013e-05
 -0.00056923
 9.48717e-05
 -0.000162995
 -8.21622e-20
 -0.00012162
 6.09864e-20
 0.000121413
 0.000110665
 0.000110749
 8.3323e-05
 0.000108664
 8.10797e-05
 0.00358479
 0.00383488
 0.00329119
 0.0217142
 0.00387442
 0.00373103
 0.00339789
 -0.000192355
 -3.38813e-21
 -0.000166124
 -9.23266e-20
 -0.000716959
 -0.000119493
 -0.000766976
 -0.000127829
 -0.000191133
 -5.0822e-21
 -0.000658239
 -0.000109706
 -0.000162995
 -8.80914e-20
 -0.000774883
 0.000129147
 -0.000746206
 0.000124368
 -0.000679579
 0.000113263
 -0.000196309
 -1.00797e-19
 -0.000176794
 -9.14796e-20
 0.000128237
 0.000110749
 0.000127422
 0.000130873
 0.000108664
 0.000117863
 0.00395662
 0.00407853
 0.00387442
 0.0242183
 0.00412017
 0.00403235
 0.0041562
 -0.000204529
 -6.77626e-21
 -0.000191133
 -1.05032e-19
 -0.000791323
 -0.000131887
 -0.000815705
 -0.000135951
 -0.000203324
 -3.38813e-21
 -0.000774883
 -0.000129147
 -0.000196309
 -1.0842e-19
 -0.000824034
 0.000137339
 -0.00080647
 0.000134412
 -0.000831239
 0.00013854
 -0.000208694
 -1.0842e-19
 -0.000206926
 1.02491e-19
 0.000136353
 0.000127422
 0.000135549
 0.000130873
 0.000139129
 0.000137951
 0.00414662
 0.00436969
 0.00412017
 0.0244604
 0.00415141
 0.0039322
 0.00374036
 -0.000211338
 -3.38813e-21
 -0.000203324
 -1.11808e-19
 -0.000829324
 -0.000138221
 -0.000873938
 -0.000145656
 -0.000225631
 -1.69407e-21
 -0.000824034
 -0.000137339
 -0.000208694
 -1.13502e-19
 -0.000830281
 0.00013838
 -0.00078644
 0.000131073
 -0.000748073
 0.000124679
 -0.00018951
 -9.65618e-20
 -0.000184526
 9.48677e-20
 0.000140892
 0.000135549
 0.00015042
 0.000139129
 0.00012634
 0.000123018
 0.00462666
 0.00571135
 0.00653677
 0.00415141
 0.0304277
 0.0053511
 0.00405043
 -0.000237036
 -5.0822e-21
 -0.000225631
 -1.25361e-19
 -0.000925333
 -0.000154222
 -0.0003341
 -6.77626e-21
 -0.00114227
 -0.000190378
 -0.00130735
 -0.000217892
 -0.000319578
 -1.01644e-20
 -0.000830281
 -0.00013838
 -0.00018951
 -1.03338e-19
 -0.00107022
 0.00017837
 -0.000810085
 0.000135014
 -0.000215533
 -1.11808e-19
 0.000158024
 0.00015042
 0.000222733
 0.00012634
 0.000143689
 0.000213052
 0.00597555
 0.005661
 0.036801
 0.00646794
 0.00560492
 0.00682002
 0.00627154
 -0.000289863
 -6.77626e-21
 -0.00119511
 -0.000199185
 -0.000307692
 -1.69407e-19
 -0.0011322
 -0.0001887
 -0.000276238
 -5.0822e-21
 -0.00129359
 0.000215598
 -0.00112098
 0.000186831
 -0.001364
 0.000227334
 -0.00125431
 0.000209051
 -0.000339102
 1.71101e-19
 -0.000284254
 -1.47384e-19
 -0.0003429
 1.77877e-19
 0.000193242
 0.000205128
 0.000184158
 0.000226068
 0.0002286
 0.000189503
 0.00670178
 0.00658292
 0.0053511
 0.00646794
 0.0356228
 0.00464169
 0.00587739
 -0.0003506
 -6.77626e-21
 -0.000319578
 -1.72795e-19
 -0.00134036
 -0.000223393
 -0.000307692
 -1.35525e-20
 -0.00131658
 -0.000219431
 -0.00107022
 -0.00017837
 -0.000215533
 -1.15196e-19
 -0.00129359
 -0.000215598
 -0.000339102
 -1.35525e-20
 -0.000928338
 0.000154723
 -0.00117548
 0.000195913
 -0.000248636
 1.27055e-19
 0.000233734
 0.000205128
 0.000143689
 0.000213052
 0.000165758
 0.000226068
 0.00439926
 0.00391612
 0.0252273
 0.0036879
 0.0046604
 0.00403713
 0.00452649
 -0.000209864
 -3.38813e-21
 -0.000879852
 -0.000146642
 -0.000230062
 -1.25361e-19
 -0.000783224
 -0.000130537
 -0.000181748
 -5.0822e-21
 -0.000737581
 0.00012293
 -0.000932079
 0.000155347
 -0.000807427
 0.000134571
 -0.000905298
 0.000150883
 -0.000187043
 -9.57147e-20
 -0.000235978
 1.20279e-19
 -0.000216671
 -1.10114e-19
 0.000139909
 0.000121165
 0.000153374
 0.000124695
 0.000144447
 0.000157319
 0.00348676
 0.00288818
 0.0036879
 0.0189902
 0.00245699
 0.00291903
 0.00355137
 -0.000166928
 -1.69407e-21
 -0.000181748
 -9.82558e-20
 -0.000697353
 -0.000116225
 -0.000577636
 -9.62727e-05
 -0.00012189
 -3.38813e-21
 -0.000737581
 -0.00012293
 -0.000187043
 -9.99499e-20
 -0.000491397
 8.18995e-05
 -0.000583806
 9.7301e-05
 -0.000710274
 0.000118379
 -0.000123809
 -6.26804e-20
 -0.000168094
 -8.63974e-20
 0.000111286
 0.000121165
 8.12599e-05
 8.25392e-05
 0.000112063
 0.000124695
 0.00247044
 0.00249146
 0.00244731
 0.00245699
 0.0123117
 0.00244549
 -0.000125154
 -2.5411e-21
 -0.00012189
 -6.60686e-20
 -0.000494088
 -8.2348e-05
 -0.000123992
 -5.0822e-21
 -0.000498292
 -8.30486e-05
 -0.000489463
 -8.15771e-05
 -0.00012074
 -1.69407e-21
 -0.000491397
 -8.18995e-05
 -0.000123809
 -6.86097e-20
 -0.000489097
 8.15162e-05
 8.34361e-05
 8.12599e-05
 8.26611e-05
 8.04932e-05
 8.25392e-05
 0.003782
 0.0041979
 0.0245023
 0.00362452
 0.00448278
 0.00398638
 0.00442873
 -0.000200662
 -3.38813e-21
 -0.0007564
 -0.000126067
 -0.000177538
 -9.74088e-20
 -0.00083958
 -0.00013993
 -0.000219128
 -3.38813e-21
 -0.000724903
 0.000120817
 -0.000896555
 0.000149426
 -0.000797275
 0.000132879
 -0.000885746
 0.000147624
 -0.000184914
 9.23266e-20
 -0.00022915
 -1.20279e-19
 -0.000213723
 1.06726e-19
 0.000133775
 0.000118358
 0.000146085
 0.000152767
 0.000123276
 0.000142482
 0.00283809
 0.00340607
 0.00291903
 0.00244549
 0.00362452
 0.0187633
 0.00353008
 -0.00016307
 -6.77626e-21
 -0.00012074
 -6.52215e-20
 -0.000567619
 -9.46032e-05
 -0.000177538
 -6.77626e-21
 -0.000681215
 -0.000113536
 -0.000123809
 -1.69407e-21
 -0.000583806
 -9.7301e-05
 -0.000168094
 -8.97855e-20
 -0.000489097
 -8.15162e-05
 -0.000724903
 -0.000120817
 -0.000184914
 -6.77626e-21
 -0.000706017
 0.000117669
 0.000108713
 8.04932e-05
 0.000118358
 8.25392e-05
 0.000112063
 0.000123276
 0.00448959
 0.0048451
 0.00448278
 0.0292834
 0.00526624
 0.00488587
 0.00531382
 -0.000229831
 -5.0822e-21
 -0.000219128
 -1.18585e-19
 -0.000897917
 -0.000149653
 -0.000969021
 -0.000161503
 -0.00025468
 -6.77626e-21
 -0.000896555
 -0.000149426
 -0.00022915
 -1.25361e-19
 -0.00105325
 0.000175541
 -0.000977174
 0.000162862
 -0.00106276
 0.000177127
 -0.000271945
 -1.37219e-19
 -0.000259437
 1.32137e-19
 0.000153221
 0.000146085
 0.000169786
 0.000152767
 0.000181296
 0.000172958
 0.0050566
 0.00515554
 0.00526624
 0.034294
 0.00589549
 0.00672523
 0.00619493
 -0.00025098
 -6.77626e-21
 -0.00025468
 -1.40607e-19
 -0.00101132
 -0.000168553
 -0.00103111
 -0.000171851
 -0.000264574
 -6.77626e-21
 -0.00105325
 -0.000175541
 -0.000271945
 -1.47384e-19
 -0.0011791
 0.000196516
 -0.00134505
 0.000224174
 -0.00123899
 0.000206498
 -0.000324975
 -1.69407e-19
 -0.000347549
 -1.79571e-19
 0.00016732
 0.000169786
 0.000176383
 0.00021665
 0.000181296
 0.000231699
 0.00509695
 0.00452992
 0.00415159
 0.00517445
 0.00589549
 0.0311997
 0.00635132
 -0.000245121
 -6.77626e-21
 -0.000264574
 -1.4569e-19
 -0.00101939
 -0.000169898
 -0.000207871
 -3.38813e-21
 -0.000905984
 -0.000150997
 -0.000207288
 -3.38813e-21
 -0.000830317
 -0.000138386
 -0.00103489
 -0.000172482
 -0.000310157
 -3.38813e-21
 -0.0011791
 -0.000196516
 -0.000324975
 -1.76183e-19
 -0.00127026
 0.000211711
 0.000163414
 0.000176383
 0.000138581
 0.000138192
 0.000206772
 0.00021665
 0.00604057
 0.00512151
 0.0348624
 0.0068771
 0.00501892
 0.00543259
 0.00637171
 -0.000265497
 -6.77626e-21
 -0.00120811
 -0.000201352
 -0.000338559
 -1.84653e-19
 -0.0010243
 -0.000170717
 -0.000246654
 -6.77626e-21
 -0.00137542
 0.000229237
 -0.00100378
 0.000167297
 -0.00108652
 0.000181086
 -0.00127434
 0.00021239
 -0.00034915
 1.76183e-19
 -0.000255238
 -1.30443e-19
 -0.000288021
 -1.49078e-19
 0.000176998
 0.000225706
 0.000164436
 0.000170159
 0.000232767
 0.000192014
 0.00632206
 0.00660608
 0.00672523
 0.00635132
 0.0068771
 0.0470308
 0.00708252
 0.0070665
 -0.000322049
 -1.01644e-20
 -0.000310157
 -1.69407e-19
 -0.00126441
 -0.000210735
 -0.000338559
 -1.35525e-20
 -0.00132122
 -0.000220203
 -0.000324975
 -1.01644e-20
 -0.00134505
 -0.000224174
 -0.000347549
 -1.88041e-19
 -0.00127026
 -0.000211711
 -0.00137542
 -0.000229237
 -0.00034915
 -1.35525e-20
 -0.0014165
 0.000236084
 -0.0014133
 0.00023555
 -0.000359102
 -1.82959e-19
 0.000214699
 0.000225706
 0.000206772
 0.00021665
 0.000232767
 0.000231699
 0.000239401
 0.00464559
 0.00405703
 0.00501892
 0.0265767
 0.00381334
 0.00421241
 0.00482944
 -0.000217905
 -5.0822e-21
 -0.000246654
 -1.32137e-19
 -0.000929118
 -0.000154853
 -0.000811407
 -0.000135234
 -0.000187798
 -3.38813e-21
 -0.00100378
 -0.000167297
 -0.000255238
 -1.37219e-19
 -0.000762667
 0.000127111
 -0.000842482
 0.000140414
 -0.000965889
 0.000160981
 -0.000193535
 -9.99499e-20
 -0.000227706
 -1.16891e-19
 0.00014527
 0.000164436
 0.000125199
 0.000129024
 0.000170159
 0.000151804
 0.00358302
 0.00294536
 0.00381334
 0.0194656
 0.00249606
 0.00297409
 0.0036537
 -0.000170504
 -5.0822e-21
 -0.000187798
 -9.99499e-20
 -0.000716605
 -0.000119434
 -0.000589072
 -9.81786e-05
 -0.000124032
 -3.38813e-21
 -0.000762667
 -0.000127111
 -0.000193535
 -1.03338e-19
 -0.000499211
 8.32019e-05
 -0.000594818
 9.91363e-05
 -0.000730741
 0.00012179
 -0.000125574
 -6.52215e-20
 -0.000171835
 -8.89385e-20
 0.000113669
 0.000125199
 8.2688e-05
 0.000129024
 8.37158e-05
 0.000114557
 0.00250683
 0.00251636
 0.00246604
 0.00249606
 0.0124572
 0.00247193
 -0.000126651
 -2.5411e-21
 -0.000124032
 -6.77626e-20
 -0.000501367
 -8.35611e-05
 -0.000124984
 -5.0822e-21
 -0.000503272
 -8.38786e-05
 -0.000493208
 -8.22013e-05
 -0.00012162
 -3.38813e-21
 -0.000499211
 -8.32019e-05
 -0.000125574
 -6.86097e-20
 -0.000494387
 8.23978e-05
 8.44343e-05
 8.2688e-05
 8.3323e-05
 8.10797e-05
 8.37158e-05
 0.00373103
 0.00403235
 0.024226
 0.00363982
 0.00431845
 0.00406353
 0.00444084
 -0.000196309
 -5.0822e-21
 -0.000746206
 -0.000124368
 -0.000176794
 -9.65618e-20
 -0.00080647
 -0.000134412
 -0.000206926
 -1.69407e-21
 -0.000727963
 0.000121327
 -0.000863691
 0.000143948
 -0.000812706
 0.000135451
 -0.000888169
 0.000148028
 -0.000187188
 9.74088e-20
 -0.000224919
 -1.16891e-19
 -0.000219165
 1.13502e-19
 0.000130873
 0.000117863
 0.000137951
 0.000149946
 0.000124792
 0.00014611
 0.00284615
 0.00339789
 0.00297409
 0.00247193
 0.00363982
 0.0189201
 0.00359023
 -0.000162995
 -6.77626e-21
 -0.00012162
 -6.77626e-20
 -0.00056923
 -9.48717e-05
 -0.000176794
 -5.0822e-21
 -0.000679579
 -0.000113263
 -0.000125574
 -2.5411e-21
 -0.000594818
 -9.91363e-05
 -0.000171835
 -9.23266e-20
 -0.000494387
 -8.23978e-05
 -0.000727963
 -0.000121327
 -0.000187188
 -1.69407e-21
 -0.000718046
 0.000119674
 0.000108664
 8.10797e-05
 0.000117863
 8.37158e-05
 0.000114557
 0.000124792
 0.0041562
 0.0039322
 0.00431845
 0.0268652
 0.00413787
 0.00518194
 0.00513853
 -0.000208694
 -6.77626e-21
 -0.000206926
 -1.10114e-19
 -0.000831239
 -0.00013854
 -0.00078644
 -0.000131073
 -0.000184526
 -3.38813e-21
 -0.000863691
 -0.000143948
 -0.000224919
 -1.25361e-19
 -0.000827574
 0.000137929
 -0.00103639
 0.000172731
 -0.00102771
 0.000171284
 -0.000229261
 -1.15196e-19
 -0.000288933
 -1.4569e-19
 0.000139129
 0.000137951
 0.000123018
 0.00015284
 0.000149946
 0.000192622
 0.00374036
 0.00405043
 0.00464169
 0.00413787
 0.0213493
 0.00477897
 -0.00018951
 -5.0822e-21
 -0.000184526
 -1.01644e-19
 -0.000748073
 -0.000124679
 -0.000215533
 -6.77626e-21
 -0.000810085
 -0.000135014
 -0.000928338
 -0.000154723
 -0.000248636
 -3.38813e-21
 -0.000827574
 -0.000137929
 -0.000229261
 -1.21973e-19
 -0.000955794
 0.000159299
 0.00012634
 0.000123018
 0.000143689
 0.000165758
 0.00015284
 0.0052487
 0.00478694
 0.00560492
 0.0046604
 0.0308418
 0.00502904
 0.0055118
 -0.000248632
 -3.38813e-21
 -0.000276238
 -1.49078e-19
 -0.00104974
 -0.000174957
 -0.000230062
 -5.0822e-21
 -0.000957388
 -0.000159565
 -0.00112098
 -0.000186831
 -0.000284254
 -1.52466e-19
 -0.000932079
 -0.000155347
 -0.000235978
 -5.0822e-21
 -0.00100581
 0.000167635
 -0.00110236
 0.000183727
 -0.000266926
 -1.35525e-19
 0.000165755
 0.000184158
 0.000153374
 0.000189503
 0.000157319
 0.000177951
 0.00403713
 0.00355137
 0.00398638
 0.00353008
 0.0239716
 0.00441856
 0.00444803
 -0.000187043
 -6.77626e-21
 -0.000807427
 -0.000134571
 -0.000216671
 -1.18585e-19
 -0.000168094
 -5.0822e-21
 -0.000710274
 -0.000118379
 -0.000184914
 -1.01644e-19
 -0.000797275
 -0.000132879
 -0.000213723
 -5.0822e-21
 -0.000706017
 -0.000117669
 -0.000883712
 0.000147285
 -0.000889607
 0.000148268
 -0.000228133
 -1.15196e-19
 0.000112063
 0.000124695
 0.000123276
 0.000144447
 0.000142482
 0.000152088
 0.00442873
 0.00488587
 0.00441856
 0.029176
 0.00531511
 0.00484415
 0.00528356
 -0.00022915
 -6.77626e-21
 -0.000213723
 -1.15196e-19
 -0.000885746
 -0.000147624
 -0.000977174
 -0.000162862
 -0.000259437
 -8.47033e-21
 -0.000883712
 -0.000147285
 -0.000228133
 -1.25361e-19
 -0.00106302
 0.00017717
 -0.00096883
 0.000161472
 -0.00105671
 0.000176119
 -0.000272073
 -1.38913e-19
 -0.000256283
 1.27055e-19
 0.000152767
 0.000172958
 0.000142482
 0.000152088
 0.000181382
 0.000170855
 0.00421241
 0.0036537
 0.00406353
 0.00359023
 0.0247841
 0.00467484
 0.00458943
 -0.000193535
 -3.38813e-21
 -0.000842482
 -0.000140414
 -0.000227706
 -1.21973e-19
 -0.000171835
 -3.38813e-21
 -0.000730741
 -0.00012179
 -0.000187188
 -1.03338e-19
 -0.000812706
 -0.000135451
 -0.000219165
 -3.38813e-21
 -0.000718046
 -0.000119674
 -0.000934968
 0.000155828
 -0.000917886
 0.000152981
 -0.000239778
 1.23667e-19
 0.000129024
 0.000151804
 0.000114557
 0.000124792
 0.00014611
 0.000159852
 0.00543259
 0.00482944
 0.00467484
 0.0315322
 0.00580245
 0.00513419
 0.00565866
 -0.000255238
 -5.0822e-21
 -0.00108652
 -0.000181086
 -0.000288021
 -1.57548e-19
 -0.000227706
 -3.38813e-21
 -0.000965889
 -0.000160981
 -0.000934968
 -0.000155828
 -0.000239778
 -6.77626e-21
 -0.00116049
 0.000193415
 -0.00102684
 0.00017114
 -0.00113173
 0.000188622
 -0.000292224
 1.5416e-19
 -0.000273641
 -1.38913e-19
 0.000170159
 0.000151804
 0.000192014
 0.000159852
 0.000182428
 0.000194816
 0.00637171
 0.00708252
 0.00580245
 0.03776
 0.00657054
 0.00593778
 0.00599505
 -0.00034915
 -1.89735e-19
 -0.000288021
       0
 -0.00127434
 -0.00021239
 -0.0014165
 -0.000236084
 -0.000359102
 -1.96512e-19
 -0.00116049
 -0.000193415
 -0.000292224
 -3.38813e-21
 -0.00131411
 0.000219018
 -0.00118756
 0.000197926
 -0.00119901
 0.000199835
 -0.000297952
 1.50772e-19
 -0.000301553
 -1.55854e-19
 0.000232767
 0.000192014
 0.000239401
 0.000198635
 0.000194816
 0.000201035
 0.00531382
 0.00619493
 0.0070665
 0.00531511
 0.00657054
 0.0361611
 0.00570025
 -0.000271945
 -6.77626e-21
 -0.000259437
 -1.40607e-19
 -0.00106276
 -0.000177127
 -0.000347549
 -1.01644e-20
 -0.00123899
 -0.000206498
 -0.000359102
 -1.01644e-20
 -0.0014133
 -0.00023555
 -0.00106302
 -0.00017717
 -0.000272073
 -1.49078e-19
 -0.00131411
 -0.000219018
 -0.000297952
 -1.35525e-20
 -0.00114005
 0.000190008
 0.000181296
 0.000172958
 0.000231699
 0.000239401
 0.000181382
 0.000198635
 0.00682002
 0.00587739
 0.00518194
 0.00477897
 0.0422237
 0.00611276
 0.0068291
 0.00662353
 -0.000339102
 -1.86347e-19
 -0.001364
 -0.000227334
 -0.0003429
 -3.38813e-21
 -0.000248636
 -1.35525e-19
 -0.00117548
 -0.000195913
 -0.000229261
 -3.38813e-21
 -0.00103639
 -0.000172731
 -0.000288933
 -1.59242e-19
 -0.000955794
 -0.000159299
 -0.00122255
 0.000203759
 -0.00136582
 0.000227637
 -0.00132471
 0.000220784
 -0.000322343
 1.6263e-19
 -0.000340011
 -1.76183e-19
 0.000165758
 0.000226068
 0.00015284
 0.0002286
 0.000192622
 0.000214895
 0.000226674
 0.00444084
 0.00513853
 0.00458943
 0.00513419
 0.00611276
 0.0313756
 0.00595984
 -0.000224919
 -6.77626e-21
 -0.000219165
 -1.18585e-19
 -0.000888169
 -0.000148028
 -0.000288933
 -6.77626e-21
 -0.00102771
 -0.000171284
 -0.000239778
 -1.30443e-19
 -0.000917886
 -0.000152981
 -0.00102684
 -0.00017114
 -0.000273641
 -1.47384e-19
 -0.00122255
 -0.000203759
 -0.000322343
 -1.01644e-20
 -0.00119197
 0.000198661
 0.000149946
 0.000192622
 0.00014611
 0.000159852
 0.000182428
 0.000214895
 0.00452649
 0.00502904
 0.00444803
 0.00484415
 0.0295762
 0.00541744
 0.005311
 -0.000235978
 -1.30443e-19
 -0.000216671
 -6.77626e-21
 -0.000905298
 -0.000150883
 -0.00100581
 -0.000167635
 -0.000266926
 -1.4569e-19
 -0.000228133
 -6.77626e-21
 -0.000889607
 -0.000148268
 -0.00096883
 -0.000161472
 -0.000256283
 -1.18585e-20
 -0.00108349
 0.000180581
 -0.0010622
 0.000177033
 -0.000274818
 1.37219e-19
 0.000144447
 0.000157319
 0.000152088
 0.000170855
 0.000177951
 0.000183212
 0.00627154
 0.0055118
 0.0068291
 0.00541744
 0.0361049
 0.00636346
 0.00571154
 -0.000284254
 -6.77626e-21
 -0.0003429
 -1.89735e-19
 -0.00125431
 -0.000209051
 -0.000266926
 -5.0822e-21
 -0.00110236
 -0.000183727
 -0.00136582
 -0.000227637
 -0.000340011
 -1.84653e-19
 -0.00108349
 -0.000180581
 -0.000274818
 -5.0822e-21
 -0.00127269
 0.000212115
 -0.00114231
 0.000190385
 -0.000296336
 1.52466e-19
 0.0002286
 0.000189503
 0.000177951
 0.000183212
 0.000226674
 0.000197557
 0.00565866
 0.00593778
 0.00662353
 0.00595984
 0.00636346
 0.0365222
 0.00597889
 -0.000292224
 -1.60936e-19
 -0.000273641
 -8.47033e-21
 -0.00113173
 -0.000188622
 -0.00118756
 -0.000197926
 -0.000301553
 -1.64324e-19
 -0.000322343
 -1.74489e-19
 -0.000340011
 -6.77626e-21
 -0.00132471
 -0.000220784
 -0.00119197
 -0.000198661
 -0.00127269
 -0.000212115
 -0.000296336
 -1.01644e-20
 -0.00119578
 0.000199296
 0.000182428
 0.000194816
 0.000214895
 0.000201035
 0.000226674
 0.000197557
 0.00528356
 0.00599505
 0.00570025
 0.005311
 0.00571154
 0.00597889
 0.0339803
 -0.000272073
 -1.01644e-20
 -0.000256283
 -1.38913e-19
 -0.00105671
 -0.000176119
 -0.000297952
 -1.59242e-19
 -0.000301553
       0
 -0.00119901
 -0.000199835
 -0.00114005
 -0.000190008
 -0.000274818
 -1.52466e-19
 -0.0010622
 -0.000177033
 -0.000296336
 -1.6263e-19
 -0.00114231
 -0.000190385
 -0.00119578
 -0.000199296
 0.000181382
 0.000170855
 0.000198635
 0.000183212
 0.000201035
 0.000197557
 -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
 -0.000415177
 -0.000415177
 -0.000207589
 6.91962e-05
 1.52466e-20
 3.45981e-05
 -4.94259e-06
 3.45981e-05
 -4.94259e-06
 -1.97703e-05
 6.91962e-05
 -6.91962e-05
 -1.13502e-19
 1.52466e-20
 7.41388e-06
 -4.94259e-06
 2.47129e-06
 4.94259e-06
 -2.47129e-06
 -9.1056e-21
 -0.000408752
 -0.000408752
 -0.000204376
 6.81253e-05
       0
 3.40626e-05
 -4.86609e-06
 3.40626e-05
 -4.86609e-06
 -1.94644e-05
 6.81253e-05
 -6.81253e-05
 -3.38813e-21
       0
 7.29914e-06
 -4.86609e-06
 2.43305e-06
 4.86609e-06
 -2.43305e-06
 -6.35275e-22
 -0.000823929
 -0.000207589
 -0.000204376
 -0.000823929
 3.45981e-05
 -4.94259e-06
 3.40626e-05
 -4.86609e-06
 0.000137321
 1.60936e-20
 3.45981e-05
 4.94259e-06
 3.40626e-05
 4.86609e-06
 -1.97703e-05
 -1.94644e-05
 0.000137321
 -6.77626e-21
 -1.11808e-19
 -0.000137321
 -4.94259e-06
 2.47129e-06
 -4.86609e-06
 2.43305e-06
 1.60936e-20
 1.4713e-05
 4.94259e-06
 2.47129e-06
 4.86609e-06
 2.43305e-06
 -8.47033e-22
 -8.89385e-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
 -0.000418049
 -0.000418049
 -0.000209025
 6.96749e-05
 1.60936e-20
 3.48374e-05
 -4.97678e-06
 3.48374e-05
 -4.97678e-06
 -1.99071e-05
 6.96749e-05
 -6.96749e-05
 -1.13502e-19
 1.60936e-20
 7.46516e-06
 -4.97678e-06
 2.48839e-06
 4.97678e-06
 -2.48839e-06
 -8.99973e-21
 -0.000409446
 -0.000409446
 -0.000204723
 6.82411e-05
 4.23516e-22
 3.41205e-05
 -4.87436e-06
 3.41205e-05
 -4.87436e-06
 -1.94974e-05
 6.82411e-05
 -6.82411e-05
 -3.38813e-21
 4.23516e-22
 7.31154e-06
 -4.87436e-06
 2.43718e-06
 4.87436e-06
 -2.43718e-06
 -8.47033e-22
 -0.000827496
 -0.000209025
 -0.000204723
 -0.000827496
 3.48374e-05
 -4.97678e-06
 3.41205e-05
 -4.87436e-06
 0.000137916
 1.60936e-20
 3.48374e-05
 4.97678e-06
 3.41205e-05
 4.87436e-06
 -1.99071e-05
 -1.94974e-05
 0.000137916
 -5.0822e-21
 -1.11808e-19
 -0.000137916
 -4.97678e-06
 2.48839e-06
 -4.87436e-06
 2.43718e-06
 1.60936e-20
 1.47767e-05
 4.97678e-06
 2.48839e-06
 4.87436e-06
 2.43718e-06
 -1.05879e-21
 -8.68209e-21
 -0.000667736
 -0.000667736
 -0.000333868
 0.000111289
       0
 5.56447e-05
 -7.94924e-06
 5.56447e-05
 -7.94924e-06
 -3.1797e-05
 0.000111289
 -0.000111289
 -6.77626e-21
       0
 1.19239e-05
 -7.94924e-06
 3.97462e-06
 7.94924e-06
 -3.97462e-06
 -1.69407e-21
 -0.000260417
 -0.00128715
 -0.00128715
 -0.000383157
 4.34028e-05
 6.2004e-06
 4.34028e-05
 6.2004e-06
 0.000214525
 4.91279e-20
 6.38595e-05
 -9.12279e-06
 6.38595e-05
 -9.12279e-06
 -2.48016e-05
 -3.64911e-05
 -1.32137e-19
 0.000214525
 -0.000214525
 -2.10064e-19
 -6.2004e-06
 -3.1002e-06
 6.2004e-06
 3.1002e-06
 4.91279e-20
 2.29848e-05
 -9.12279e-06
 4.56139e-06
 9.12279e-06
 -4.56139e-06
 -9.74088e-21
 -1.65171e-20
 -0.00143405
 -0.000333868
 -0.000383157
 -0.00143405
 5.56447e-05
 -7.94924e-06
 6.38595e-05
 -9.12279e-06
 0.000239008
 2.6258e-20
 5.56447e-05
 7.94924e-06
 6.38595e-05
 9.12279e-06
 -3.1797e-05
 -3.64911e-05
 0.000239008
 -1.86347e-19
 -1.01644e-20
 -0.000239008
 -7.94924e-06
 3.97462e-06
 -9.12279e-06
 4.56139e-06
 2.6258e-20
 2.5608e-05
 7.94924e-06
 3.97462e-06
 9.12279e-06
 4.56139e-06
 -1.43996e-20
 -1.69407e-21
 -0.000565201
 -0.000565201
 -0.000282601
 9.42002e-05
       0
 4.71001e-05
 -6.72859e-06
 4.71001e-05
 -6.72859e-06
 -2.69143e-05
 9.42002e-05
 -9.42002e-05
 -6.77626e-21
       0
 1.00929e-05
 -6.72859e-06
 3.36429e-06
 6.72859e-06
 -3.36429e-06
 -8.47033e-22
 -0.000333868
 -0.00143195
 -0.00143195
 -0.000382107
 5.56447e-05
 7.94924e-06
 5.56447e-05
 7.94924e-06
 0.000238658
 5.59042e-20
 6.36845e-05
 -9.09779e-06
 6.36845e-05
 -9.09779e-06
 -3.1797e-05
 -3.63912e-05
 -1.72795e-19
 0.000238658
 -0.000238658
 -2.06676e-19
 -7.94924e-06
 -3.97462e-06
 7.94924e-06
 3.97462e-06
 5.59042e-20
 2.55705e-05
 -9.09779e-06
 4.5489e-06
 9.09779e-06
 -4.5489e-06
 -1.3129e-20
 -1.63054e-20
 -0.00132942
 -0.000282601
 -0.000382107
 -0.00132942
 4.71001e-05
 -6.72859e-06
 6.36845e-05
 -9.09779e-06
 0.000221569
 2.11758e-20
 4.71001e-05
 6.72859e-06
 6.36845e-05
 9.09779e-06
 -2.69143e-05
 -3.63912e-05
 0.000221569
 -1.5416e-19
 -1.01644e-20
 -0.000221569
 -6.72859e-06
 3.36429e-06
 -9.09779e-06
 4.5489e-06
 2.11758e-20
 2.37396e-05
 6.72859e-06
 3.36429e-06
 9.09779e-06
 4.5489e-06
 -1.20702e-20
 -1.69407e-21
 -0.00050964
 -0.00050964
 -0.00025482
 8.494e-05
       0
 4.247e-05
 -6.06714e-06
 4.247e-05
 -6.06714e-06
 -2.42686e-05
 8.494e-05
 -8.494e-05
 -5.0822e-21
       0
 9.10072e-06
 -6.06714e-06
 3.03357e-06
 6.06714e-06
 -3.03357e-06
 -1.27055e-21
 -0.000282601
 -0.00114381
 -0.00114381
 -0.000289303
 4.71001e-05
 6.72859e-06
 4.71001e-05
 6.72859e-06
 0.000190634
 4.82809e-20
 4.82171e-05
 -6.88816e-06
 4.82171e-05
 -6.88816e-06
 -2.69143e-05
 -2.75526e-05
 -1.40607e-19
 0.000190634
 -0.000190634
 -1.57548e-19
 -6.72859e-06
 -3.36429e-06
 6.72859e-06
 3.36429e-06
 4.82809e-20
 2.04251e-05
 -6.88816e-06
 3.44408e-06
 6.88816e-06
 -3.44408e-06
 -1.12232e-20
 -1.28114e-20
 -0.00108825
 -0.00025482
 -0.000289303
 -0.00108825
 4.247e-05
 -6.06714e-06
 4.82171e-05
 -6.88816e-06
 0.000181374
 1.86347e-20
 4.247e-05
 6.06714e-06
 4.82171e-05
 6.88816e-06
 -2.42686e-05
 -2.75526e-05
 0.000181374
 -1.38913e-19
 -3.38813e-21
 -0.000181374
 -6.06714e-06
 3.03357e-06
 -6.88816e-06
 3.44408e-06
 1.86347e-20
 1.9433e-05
 6.06714e-06
 3.03357e-06
 6.88816e-06
 3.44408e-06
 -1.10114e-20
 -1.27055e-21
 -0.000458819
 -0.000458819
 -0.000229409
 7.64698e-05
       0
 3.82349e-05
 -5.46213e-06
 3.82349e-05
 -5.46213e-06
 -2.18485e-05
 7.64698e-05
 -7.64698e-05
 -3.38813e-21
       0
 8.19319e-06
 -5.46213e-06
 2.73106e-06
 5.46213e-06
 -2.73106e-06
 -8.47033e-22
 -0.00025482
 -0.00100377
 -0.00100377
 -0.000247066
 4.247e-05
 6.06714e-06
 4.247e-05
 6.06714e-06
 0.000167295
 3.81165e-20
 4.11777e-05
 -5.88252e-06
 4.11777e-05
 -5.88252e-06
 -2.42686e-05
 -2.35301e-05
 -1.28749e-19
 0.000167295
 -0.000167295
 -1.33831e-19
 -6.06714e-06
 -3.03357e-06
 6.06714e-06
 3.03357e-06
 3.81165e-20
 1.79245e-05
 -5.88252e-06
 2.94126e-06
 5.88252e-06
 -2.94126e-06
 -1.05879e-20
 -1.06938e-20
 -0.000952951
 -0.000229409
 -0.000247066
 -0.000952951
 3.82349e-05
 -5.46213e-06
 4.11777e-05
 -5.88252e-06
 0.000158825
 1.69407e-20
 3.82349e-05
 5.46213e-06
 4.11777e-05
 5.88252e-06
 -2.18485e-05
 -2.35301e-05
 0.000158825
 -1.23667e-19
 -6.77626e-21
 -0.000158825
 -5.46213e-06
 2.73106e-06
 -5.88252e-06
 2.94126e-06
 1.69407e-20
 1.7017e-05
 5.46213e-06
 2.73106e-06
 5.88252e-06
 2.94126e-06
 -9.84676e-21
 -1.27055e-21
 -0.000410852
 -0.000410852
 -0.000205426
 6.84754e-05
 -4.23516e-22
 3.42377e-05
 -4.8911e-06
 3.42377e-05
 -4.8911e-06
 -1.95644e-05
 6.84754e-05
 -6.84754e-05
 -5.0822e-21
 -4.23516e-22
 7.33665e-06
 -4.8911e-06
 2.44555e-06
 4.8911e-06
 -2.44555e-06
 -8.47033e-22
 -0.000229409
 -0.000877582
 -0.000877582
 -0.000209382
 3.82349e-05
 5.46213e-06
 3.82349e-05
 5.46213e-06
 0.000146264
 3.13402e-20
 3.48969e-05
 -4.98528e-06
 3.48969e-05
 -4.98528e-06
 -2.18485e-05
 -1.99411e-05
 -1.16891e-19
 0.000146264
 -0.000146264
 -1.15196e-19
 -5.46213e-06
 -2.73106e-06
 5.46213e-06
 2.73106e-06
 3.13402e-20
 1.56711e-05
 -4.98528e-06
 2.49264e-06
 4.98528e-06
 -2.49264e-06
 -9.42324e-21
 -9.21148e-21
 -0.000829615
 -0.000205426
 -0.000209382
 -0.000829615
 3.42377e-05
 -4.8911e-06
 3.48969e-05
 -4.98528e-06
 0.000138269
 1.60936e-20
 3.42377e-05
 4.8911e-06
 3.48969e-05
 4.98528e-06
 -1.95644e-05
 -1.99411e-05
 0.000138269
 -1.11808e-19
 -6.77626e-21
 -0.000138269
 -4.8911e-06
 2.44555e-06
 -4.98528e-06
 2.49264e-06
 1.60936e-20
 1.48146e-05
 4.8911e-06
 2.44555e-06
 4.98528e-06
 2.49264e-06
 -8.89385e-21
 -1.27055e-21
 -0.000377733
 -0.000377733
 -0.000188867
 6.29555e-05
 4.23516e-22
 3.14778e-05
 -4.49682e-06
 3.14778e-05
 -4.49682e-06
 -1.79873e-05
 6.29555e-05
 -6.29555e-05
 -5.0822e-21
 4.23516e-22
 6.74524e-06
 -4.49682e-06
 2.24841e-06
 4.49682e-06
 -2.24841e-06
 -8.47033e-22
 -0.000205426
 -0.000756598
 -0.000756598
 -0.000172873
 3.42377e-05
 4.8911e-06
 3.42377e-05
 4.8911e-06
 0.0001261
 2.79521e-20
 2.88121e-05
 -4.11602e-06
 2.88121e-05
 -4.11602e-06
 -1.95644e-05
 -1.64641e-05
 -1.05879e-19
 0.0001261
 -0.0001261
 -9.40207e-20
 -4.8911e-06
 -2.44555e-06
 4.8911e-06
 2.44555e-06
 2.79521e-20
 1.35107e-05
 -4.11602e-06
 2.05801e-06
 4.11602e-06
 -2.05801e-06
 -8.04681e-21
 -7.30566e-21
 -0.000723479
 -0.000188867
 -0.000172873
 -0.000723479
 3.14778e-05
 -4.49682e-06
 2.88121e-05
 -4.11602e-06
 0.00012058
 1.43996e-20
 3.14778e-05
 4.49682e-06
 2.88121e-05
 4.11602e-06
 -1.79873e-05
 -1.64641e-05
 0.00012058
 -1.01644e-19
 -1.69407e-21
 -0.00012058
 -4.49682e-06
 2.24841e-06
 -4.11602e-06
 2.05801e-06
 1.43996e-20
 1.29193e-05
 4.49682e-06
 2.24841e-06
 4.11602e-06
 2.05801e-06
 -8.15269e-21
 -8.47033e-22
 -0.000188867
 -0.00071156
 -0.00071156
 -0.000166913
 3.14778e-05
 4.49682e-06
 3.14778e-05
 4.49682e-06
 0.000118593
 2.75286e-20
 2.78189e-05
 -3.97412e-06
 2.78189e-05
 -3.97412e-06
 -1.79873e-05
 -1.58965e-05
 -9.74088e-20
 0.000118593
 -0.000118593
 -9.06325e-20
 -4.49682e-06
 -2.24841e-06
 4.49682e-06
 2.24841e-06
 2.75286e-20
 1.27064e-05
 -3.97412e-06
 1.98706e-06
 3.97412e-06
 -1.98706e-06
 -7.6233e-21
 -7.51742e-21
 -0.000207589
 -0.000749004
 -0.000166913
 -0.000749004
 3.45981e-05
 4.94259e-06
 3.45981e-05
 4.94259e-06
 2.78189e-05
 -3.97412e-06
 0.000124834
 -1.65171e-20
 2.78189e-05
 3.97412e-06
 -1.97703e-05
 -1.58965e-05
 1.05879e-19
 0.000124834
 -5.0822e-21
 -0.000124834
 -4.94259e-06
 -2.47129e-06
 4.94259e-06
 2.47129e-06
 -3.97412e-06
 1.98706e-06
 -1.65171e-20
 1.33751e-05
 3.97412e-06
 1.98706e-06
 8.89385e-21
 -8.47033e-22
 -0.000364791
 -0.000364791
 -0.000182396
 6.07985e-05
       0
 3.03993e-05
 -4.34275e-06
 3.03993e-05
 -4.34275e-06
 -1.7371e-05
 6.07985e-05
 -6.07985e-05
 -3.38813e-21
       0
 6.51413e-06
 -4.34275e-06
 2.17138e-06
 4.34275e-06
 -2.17138e-06
 -6.35275e-22
 -0.000204376
 -0.000738909
 -0.000738909
 -0.000165078
 3.40626e-05
 4.86609e-06
 3.40626e-05
 4.86609e-06
 0.000123151
 2.83756e-20
 2.75131e-05
 -3.93044e-06
 2.75131e-05
 -3.93044e-06
 -1.94644e-05
 -1.57218e-05
 -1.05032e-19
 0.000123151
 -0.000123151
 -9.06325e-20
 -4.86609e-06
 -2.43305e-06
 4.86609e-06
 2.43305e-06
 2.83756e-20
 1.31948e-05
 -3.93044e-06
 1.96522e-06
 3.93044e-06
 -1.96522e-06
 -8.04681e-21
 -7.30566e-21
 -0.000694948
 -0.000182396
 -0.000165078
 -0.000694948
 3.03993e-05
 -4.34275e-06
 2.75131e-05
 -3.93044e-06
 0.000115825
 1.43996e-20
 3.03993e-05
 4.34275e-06
 2.75131e-05
 3.93044e-06
 -1.7371e-05
 -1.57218e-05
 0.000115825
 -9.82558e-20
 -6.77626e-21
 -0.000115825
 -4.34275e-06
 2.17138e-06
 -3.93044e-06
 1.96522e-06
 1.43996e-20
 1.24098e-05
 4.34275e-06
 2.17138e-06
 3.93044e-06
 1.96522e-06
 -7.6233e-21
 -1.05879e-21
 -0.000388797
 -0.000388797
 -0.000194398
 6.47995e-05
 4.23516e-22
 3.23997e-05
 -4.62853e-06
 3.23997e-05
 -4.62853e-06
 -1.85141e-05
 6.47995e-05
 -6.47995e-05
 -5.0822e-21
 4.23516e-22
 6.9428e-06
 -4.62853e-06
 2.31427e-06
 4.62853e-06
 -2.31427e-06
 -6.35275e-22
 -0.000182396
 -0.00069885
 -0.00069885
 -0.00016703
 3.03993e-05
 4.34275e-06
 3.03993e-05
 4.34275e-06
 0.000116475
 2.6258e-20
 2.78383e-05
 -3.97689e-06
 2.78383e-05
 -3.97689e-06
 -1.7371e-05
 -1.59076e-05
 -9.31736e-20
 0.000116475
 -0.000116475
 -8.97855e-20
 -4.34275e-06
 -2.17138e-06
 4.34275e-06
 2.17138e-06
 2.6258e-20
 1.24795e-05
 -3.97689e-06
 1.98845e-06
 3.97689e-06
 -1.98845e-06
 -6.88214e-21
 -7.30566e-21
 -0.000722856
 -0.000194398
 -0.00016703
 -0.000722856
 3.23997e-05
 -4.62853e-06
 2.78383e-05
 -3.97689e-06
 0.000120476
 1.52466e-20
 3.23997e-05
 4.62853e-06
 2.78383e-05
 3.97689e-06
 -1.85141e-05
 -1.59076e-05
 0.000120476
 -1.06726e-19
 -3.38813e-21
 -0.000120476
 -4.62853e-06
 2.31427e-06
 -3.97689e-06
 1.98845e-06
 1.52466e-20
 1.29081e-05
 4.62853e-06
 2.31427e-06
 3.97689e-06
 1.98845e-06
 -8.15269e-21
 -1.05879e-21
 -0.000421533
 -0.000421533
 -0.000210766
 7.02554e-05
       0
 3.51277e-05
 -5.01824e-06
 3.51277e-05
 -5.01824e-06
 -2.0073e-05
 7.02554e-05
 -7.02554e-05
 -3.38813e-21
       0
 7.52737e-06
 -5.01824e-06
 2.50912e-06
 5.01824e-06
 -2.50912e-06
 -1.05879e-21
 -0.000194398
 -0.000783508
 -0.000783508
 -0.000197356
 3.23997e-05
 4.62853e-06
 3.23997e-05
 4.62853e-06
 0.000130585
 2.87991e-20
 3.28926e-05
 -4.69895e-06
 3.28926e-05
 -4.69895e-06
 -1.85141e-05
 -1.87958e-05
 -9.91029e-20
 0.000130585
 -0.000130585
 -1.06726e-19
 -4.62853e-06
 -2.31427e-06
 4.62853e-06
 2.31427e-06
 2.87991e-20
 1.39912e-05
 -4.69895e-06
 2.34947e-06
 4.69895e-06
 -2.34947e-06
 -7.83505e-21
 -8.57621e-21
 -0.000816244
 -0.000210766
 -0.000197356
 -0.000816244
 3.51277e-05
 -5.01824e-06
 3.28926e-05
 -4.69895e-06
 0.000136041
 1.60936e-20
 3.51277e-05
 5.01824e-06
 3.28926e-05
 4.69895e-06
 -2.0073e-05
 -1.87958e-05
 0.000136041
 -1.15196e-19
 -3.38813e-21
 -0.000136041
 -5.01824e-06
 2.50912e-06
 -4.69895e-06
 2.34947e-06
 1.60936e-20
 1.45758e-05
 5.01824e-06
 2.50912e-06
 4.69895e-06
 2.34947e-06
 -9.1056e-21
 -1.05879e-21
 -0.000447112
 -0.000447112
 -0.000223556
 7.45186e-05
       0
 3.72593e-05
 -5.32276e-06
 3.72593e-05
 -5.32276e-06
 -2.1291e-05
 7.45186e-05
 -7.45186e-05
 -6.77626e-21
       0
 7.98414e-06
 -5.32276e-06
 2.66138e-06
 5.32276e-06
 -2.66138e-06
 -1.05879e-21
 -0.000210766
 -0.000867788
 -0.000867788
 -0.000223128
 3.51277e-05
 5.01824e-06
 3.51277e-05
 5.01824e-06
 0.000144631
 3.30343e-20
 3.7188e-05
 -5.31257e-06
 3.7188e-05
 -5.31257e-06
 -2.0073e-05
 -2.12503e-05
 -1.06726e-19
 0.000144631
 -0.000144631
 -1.21973e-19
 -5.01824e-06
 -2.50912e-06
 5.01824e-06
 2.50912e-06
 3.30343e-20
 1.54962e-05
 -5.31257e-06
 2.65629e-06
 5.31257e-06
 -2.65629e-06
 -8.47033e-21
 -9.74088e-21
 -0.000893368
 -0.000223556
 -0.000223128
 -0.000893368
 3.72593e-05
 -5.32276e-06
 3.7188e-05
 -5.31257e-06
 0.000148895
 1.77877e-20
 3.72593e-05
 5.32276e-06
 3.7188e-05
 5.31257e-06
 -2.1291e-05
 -2.12503e-05
 0.000148895
 -1.21973e-19
 -5.0822e-21
 -0.000148895
 -5.32276e-06
 2.66138e-06
 -5.31257e-06
 2.65629e-06
 1.77877e-20
 1.5953e-05
 5.32276e-06
 2.66138e-06
 5.31257e-06
 2.65629e-06
 -9.52912e-21
 -1.05879e-21
 -0.000455667
 -0.000455667
 -0.000227834
 7.59445e-05
       0
 3.79723e-05
 -5.42461e-06
 3.79723e-05
 -5.42461e-06
 -2.16984e-05
 7.59445e-05
 -7.59445e-05
 -1.01644e-20
       0
 8.13692e-06
 -5.42461e-06
 2.71231e-06
 5.42461e-06
 -2.71231e-06
 -1.05879e-21
 -0.000223556
 -0.00092331
 -0.00092331
 -0.000238099
 3.72593e-05
 5.32276e-06
 3.72593e-05
 5.32276e-06
 0.000153885
 3.47284e-20
 3.96832e-05
 -5.66903e-06
 3.96832e-05
 -5.66903e-06
 -2.1291e-05
 -2.26761e-05
 -1.15196e-19
 0.000153885
 -0.000153885
 -1.30443e-19
 -5.32276e-06
 -2.66138e-06
 5.32276e-06
 2.66138e-06
 3.47284e-20
 1.64877e-05
 -5.66903e-06
 2.83452e-06
 5.66903e-06
 -2.83452e-06
 -8.89385e-21
 -1.05879e-20
 -0.000931866
 -0.000227834
 -0.000238099
 -0.000931866
 3.79723e-05
 -5.42461e-06
 3.96832e-05
 -5.66903e-06
 0.000155311
 1.69407e-20
 3.79723e-05
 5.42461e-06
 3.96832e-05
 5.66903e-06
 -2.16984e-05
 -2.26761e-05
 0.000155311
 -1.23667e-19
 -3.38813e-21
 -0.000155311
 -5.42461e-06
 2.71231e-06
 -5.66903e-06
 2.83452e-06
 1.69407e-20
 1.66405e-05
 5.42461e-06
 2.71231e-06
 5.66903e-06
 2.83452e-06
 -9.31736e-21
 -1.48231e-21
 -0.000444183
 -0.000444183
 -0.000222092
 7.40305e-05
 -4.23516e-22
 3.70153e-05
 -5.28789e-06
 3.70153e-05
 -5.28789e-06
 -2.11516e-05
 7.40305e-05
 -7.40305e-05
 -3.38813e-21
 -4.23516e-22
 7.93184e-06
 -5.28789e-06
 2.64395e-06
 5.28789e-06
 -2.64395e-06
 -1.27055e-21
 -0.000227834
 -0.000932829
 -0.000932829
 -0.000238581
 3.79723e-05
 5.42461e-06
 3.79723e-05
 5.42461e-06
 0.000155471
 3.72694e-20
 3.97635e-05
 -5.68049e-06
 3.97635e-05
 -5.68049e-06
 -2.16984e-05
 -2.2722e-05
 -1.16891e-19
 0.000155471
 -0.000155471
 -1.28749e-19
 -5.42461e-06
 -2.71231e-06
 5.42461e-06
 2.71231e-06
 3.72694e-20
 1.66577e-05
 -5.68049e-06
 2.84025e-06
 5.68049e-06
 -2.84025e-06
 -8.47033e-21
 -1.0482e-20
 -0.000921345
 -0.000222092
 -0.000238581
 -0.000921345
 3.70153e-05
 -5.28789e-06
 3.97635e-05
 -5.68049e-06
 0.000153557
 1.77877e-20
 3.70153e-05
 5.28789e-06
 3.97635e-05
 5.68049e-06
 -2.11516e-05
 -2.2722e-05
 0.000153557
 -1.20279e-19
 -3.38813e-21
 -0.000153557
 -5.28789e-06
 2.64395e-06
 -5.68049e-06
 2.84025e-06
 1.77877e-20
 1.64526e-05
 5.28789e-06
 2.64395e-06
 5.68049e-06
 2.84025e-06
 -9.52912e-21
 -1.27055e-21
 -0.000260417
 -0.00115561
 -0.00115561
 -0.000317387
 4.34028e-05
 6.2004e-06
 4.34028e-05
 6.2004e-06
 0.000192601
 -1.86347e-20
 5.28978e-05
 -7.55683e-06
 5.28978e-05
 -7.55683e-06
 -2.48016e-05
 -3.02273e-05
 1.32137e-19
 0.000192601
 -0.000192601
 -1.01644e-20
 -6.2004e-06
 -3.1002e-06
 6.2004e-06
 3.1002e-06
 -1.86347e-20
 2.06358e-05
 -7.55683e-06
 3.77841e-06
 7.55683e-06
 -3.77841e-06
 1.05879e-20
 -1.69407e-21
 -0.000222092
 -0.00107896
 -0.000317387
 -0.00107896
 3.70153e-05
 5.28789e-06
 3.70153e-05
 5.28789e-06
 5.28978e-05
 -7.55683e-06
 0.000179826
 4.15046e-20
 5.28978e-05
 7.55683e-06
 -2.11516e-05
 -3.02273e-05
 -1.10114e-19
 0.000179826
 -1.74489e-19
 -0.000179826
 -5.28789e-06
 -2.64395e-06
 5.28789e-06
 2.64395e-06
 -7.55683e-06
 3.77841e-06
 4.15046e-20
 1.92671e-05
 7.55683e-06
 3.77841e-06
 -8.47033e-21
 -1.35525e-20
 -0.000426676
 -0.000426676
 -0.000213338
 7.11127e-05
       0
 3.55563e-05
 -5.07948e-06
 3.55563e-05
 -5.07948e-06
 -2.03179e-05
 7.11127e-05
 -7.11127e-05
 -3.38813e-21
       0
 7.61921e-06
 -5.07948e-06
 2.53974e-06
 5.07948e-06
 -2.53974e-06
 -1.27055e-21
 -0.000317387
 -0.00113405
 -0.00113405
 -0.000249636
 5.28978e-05
 7.55683e-06
 5.28978e-05
 7.55683e-06
 0.000189008
 4.06576e-20
 4.1606e-05
 -5.94371e-06
 4.1606e-05
 -5.94371e-06
 -3.02273e-05
 -2.37749e-05
 -1.66018e-19
 0.000189008
 -0.000189008
 -1.35525e-19
 -7.55683e-06
 -3.77841e-06
 7.55683e-06
 3.77841e-06
 4.06576e-20
 2.02508e-05
 -5.94371e-06
 2.97186e-06
 5.94371e-06
 -2.97186e-06
 -1.2282e-20
 -1.07997e-20
 -0.000925948
 -0.000213338
 -0.000249636
 -0.000925948
 3.55563e-05
 -5.07948e-06
 4.1606e-05
 -5.94371e-06
 0.000154325
 1.60936e-20
 3.55563e-05
 5.07948e-06
 4.1606e-05
 5.94371e-06
 -2.03179e-05
 -2.37749e-05
 0.000154325
 -1.15196e-19
 -6.77626e-21
 -0.000154325
 -5.07948e-06
 2.53974e-06
 -5.94371e-06
 2.97186e-06
 1.60936e-20
 1.65348e-05
 5.07948e-06
 2.53974e-06
 5.94371e-06
 2.97186e-06
 -8.99973e-21
 -1.05879e-21
 -0.000491405
 -0.000491405
 -0.000245703
 8.19009e-05
       0
 4.09505e-05
 -5.85006e-06
 4.09505e-05
 -5.85006e-06
 -2.34003e-05
 8.19009e-05
 -8.19009e-05
 -5.0822e-21
       0
 8.7751e-06
 -5.85006e-06
 2.92503e-06
 5.85006e-06
 -2.92503e-06
 -8.47033e-22
 -0.000213338
 -0.000816677
 -0.000816677
 -0.000195001
 3.55563e-05
 5.07948e-06
 3.55563e-05
 5.07948e-06
 0.000136113
 3.13402e-20
 3.25001e-05
 -4.64287e-06
 3.25001e-05
 -4.64287e-06
 -2.03179e-05
 -1.85715e-05
 -1.07573e-19
 0.000136113
 -0.000136113
 -1.05032e-19
 -5.07948e-06
 -2.53974e-06
 5.07948e-06
 2.53974e-06
 3.13402e-20
 1.45835e-05
 -4.64287e-06
 2.32143e-06
 4.64287e-06
 -2.32143e-06
 -8.47033e-21
 -8.57621e-21
 -0.000881406
 -0.000245703
 -0.000195001
 -0.000881406
 4.09505e-05
 -5.85006e-06
 3.25001e-05
 -4.64287e-06
 0.000146901
 1.99053e-20
 4.09505e-05
 5.85006e-06
 3.25001e-05
 4.64287e-06
 -2.34003e-05
 -1.85715e-05
 0.000146901
 -1.35525e-19
 -5.0822e-21
 -0.000146901
 -5.85006e-06
 2.92503e-06
 -4.64287e-06
 2.32143e-06
 1.99053e-20
 1.57394e-05
 5.85006e-06
 2.92503e-06
 4.64287e-06
 2.32143e-06
 -1.02703e-20
 -1.05879e-21
 -0.000506209
 -0.000506209
 -0.000253105
 8.43682e-05
 4.23516e-22
 4.21841e-05
 -6.0263e-06
 4.21841e-05
 -6.0263e-06
 -2.41052e-05
 8.43682e-05
 -8.43682e-05
 -1.01644e-20
 4.23516e-22
 9.03945e-06
 -6.0263e-06
 3.01315e-06
 6.0263e-06
 -3.01315e-06
 -1.27055e-21
 -0.000245703
 -0.00100528
 -0.00100528
 -0.000256936
 4.09505e-05
 5.85006e-06
 4.09505e-05
 5.85006e-06
 0.000167546
 4.06576e-20
 4.28227e-05
 -6.11752e-06
 4.28227e-05
 -6.11752e-06
 -2.34003e-05
 -2.44701e-05
 -1.27055e-19
 0.000167546
 -0.000167546
 -1.38913e-19
 -5.85006e-06
 -2.92503e-06
 5.85006e-06
 2.92503e-06
 4.06576e-20
 1.79514e-05
 -6.11752e-06
 3.05876e-06
 6.11752e-06
 -3.05876e-06
 -9.42324e-21
 -1.12232e-20
 -0.00102008
 -0.000253105
 -0.000256936
 -0.00102008
 4.21841e-05
 -6.0263e-06
 4.28227e-05
 -6.11752e-06
 0.000170013
 1.86347e-20
 4.21841e-05
 6.0263e-06
 4.28227e-05
 6.11752e-06
 -2.41052e-05
 -2.44701e-05
 0.000170013
 -1.38913e-19
 -8.47033e-21
 -0.000170013
 -6.0263e-06
 3.01315e-06
 -6.11752e-06
 3.05876e-06
 1.86347e-20
 1.82157e-05
 6.0263e-06
 3.01315e-06
 6.11752e-06
 3.05876e-06
 -1.09055e-20
 -1.27055e-21
 -0.000466674
 -0.000466674
 -0.000233337
 7.7779e-05
       0
 3.88895e-05
 -5.55564e-06
 3.88895e-05
 -5.55564e-06
 -2.22226e-05
 7.7779e-05
 -7.7779e-05
 -5.0822e-21
       0
 8.33346e-06
 -5.55564e-06
 2.77782e-06
 5.55564e-06
 -2.77782e-06
 -8.47033e-22
 -0.000253105
 -0.00100906
 -0.00100906
 -0.000251423
 4.21841e-05
 6.0263e-06
 4.21841e-05
 6.0263e-06
 0.000168176
 4.06576e-20
 4.19039e-05
 -5.98627e-06
 4.19039e-05
 -5.98627e-06
 -2.41052e-05
 -2.39451e-05
 -1.28749e-19
 0.000168176
 -0.000168176
 -1.38913e-19
 -6.0263e-06
 -3.01315e-06
 6.0263e-06
 3.01315e-06
 4.06576e-20
 1.80188e-05
 -5.98627e-06
 2.99313e-06
 5.98627e-06
 -2.99313e-06
 -9.95264e-21
 -1.10114e-20
 -0.00096952
 -0.000233337
 -0.000251423
 -0.00096952
 3.88895e-05
 -5.55564e-06
 4.19039e-05
 -5.98627e-06
 0.000161587
 1.77877e-20
 3.88895e-05
 5.55564e-06
 4.19039e-05
 5.98627e-06
 -2.22226e-05
 -2.39451e-05
 0.000161587
 -1.25361e-19
 -6.77626e-21
 -0.000161587
 -5.55564e-06
 2.77782e-06
 -5.98627e-06
 2.99313e-06
 1.77877e-20
 1.73129e-05
 5.55564e-06
 2.77782e-06
 5.98627e-06
 2.99313e-06
 -9.84676e-21
 -1.48231e-21
 -0.000417699
 -0.000417699
 -0.000208849
 6.96165e-05
       0
 3.48082e-05
 -4.97261e-06
 3.48082e-05
 -4.97261e-06
 -1.98904e-05
 6.96165e-05
 -6.96165e-05
 -5.0822e-21
       0
 7.45891e-06
 -4.97261e-06
 2.4863e-06
 4.97261e-06
 -2.4863e-06
 -1.27055e-21
 -0.000233337
 -0.000896857
 -0.000896857
 -0.000215091
 3.88895e-05
 5.55564e-06
 3.88895e-05
 5.55564e-06
 0.000149476
 3.30343e-20
 3.58486e-05
 -5.12123e-06
 3.58486e-05
 -5.12123e-06
 -2.22226e-05
 -2.04849e-05
 -1.18585e-19
 0.000149476
 -0.000149476
 -1.16891e-19
 -5.55564e-06
 -2.77782e-06
 5.55564e-06
 2.77782e-06
 3.30343e-20
 1.60153e-05
 -5.12123e-06
 2.56061e-06
 5.12123e-06
 -2.56061e-06
 -8.99973e-21
 -9.42324e-21
 -0.000847882
 -0.000208849
 -0.000215091
 -0.000847882
 3.48082e-05
 -4.97261e-06
 3.58486e-05
 -5.12123e-06
 0.000141314
 1.60936e-20
 3.48082e-05
 4.97261e-06
 3.58486e-05
 5.12123e-06
 -1.98904e-05
 -2.04849e-05
 0.000141314
 -1.15196e-19
 -6.77626e-21
 -0.000141314
 -4.97261e-06
 2.4863e-06
 -5.12123e-06
 2.56061e-06
 1.60936e-20
 1.51407e-05
 4.97261e-06
 2.4863e-06
 5.12123e-06
 2.56061e-06
 -8.99973e-21
 -1.27055e-21
 -0.000382351
 -0.000382351
 -0.000191176
 6.37252e-05
       0
 3.18626e-05
 -4.5518e-06
 3.18626e-05
 -4.5518e-06
 -1.82072e-05
 6.37252e-05
 -6.37252e-05
 -3.38813e-21
       0
 6.8277e-06
 -4.5518e-06
 2.2759e-06
 4.5518e-06
 -2.2759e-06
 -1.05879e-21
 -0.000208849
 -0.000770166
 -0.000770166
 -0.000176233
 3.48082e-05
 4.97261e-06
 3.48082e-05
 4.97261e-06
 0.000128361
 2.83756e-20
 2.93722e-05
 -4.19603e-06
 2.93722e-05
 -4.19603e-06
 -1.98904e-05
 -1.67841e-05
 -1.09267e-19
 0.000128361
 -0.000128361
 -9.48677e-20
 -4.97261e-06
 -2.4863e-06
 4.97261e-06
 2.4863e-06
 2.83756e-20
 1.3753e-05
 -4.19603e-06
 2.09802e-06
 4.19603e-06
 -2.09802e-06
 -7.83505e-21
 -7.41154e-21
 -0.000734818
 -0.000191176
 -0.000176233
 -0.000734818
 3.18626e-05
 -4.5518e-06
 2.93722e-05
 -4.19603e-06
 0.00012247
 1.52466e-20
 3.18626e-05
 4.5518e-06
 2.93722e-05
 4.19603e-06
 -1.82072e-05
 -1.67841e-05
 0.00012247
 -1.01644e-19
 -8.47033e-21
 -0.00012247
 -4.5518e-06
 2.2759e-06
 -4.19603e-06
 2.09802e-06
 1.52466e-20
 1.31218e-05
 4.5518e-06
 2.2759e-06
 4.19603e-06
 2.09802e-06
 -8.15269e-21
 -1.05879e-21
 -0.000191176
 -0.00071991
 -0.00071991
 -0.000168779
 3.18626e-05
 4.5518e-06
 3.18626e-05
 4.5518e-06
 0.000119985
 2.5411e-20
 2.81299e-05
 -4.01855e-06
 2.81299e-05
 -4.01855e-06
 -1.82072e-05
 -1.60742e-05
 -9.65618e-20
 0.000119985
 -0.000119985
 -9.23266e-20
 -4.5518e-06
 -2.2759e-06
 4.5518e-06
 2.2759e-06
 2.5411e-20
 1.28555e-05
 -4.01855e-06
 2.00928e-06
 4.01855e-06
 -2.00928e-06
 -7.41154e-21
 -7.30566e-21
 -0.000209025
 -0.000755608
 -0.000168779
 -0.000755608
 3.48374e-05
 4.97678e-06
 3.48374e-05
 4.97678e-06
 2.81299e-05
 -4.01855e-06
 0.000125935
 -1.43996e-20
 2.81299e-05
 4.01855e-06
 -1.99071e-05
 -1.60742e-05
 1.05032e-19
 0.000125935
 -5.0822e-21
 -0.000125935
 -4.97678e-06
 -2.48839e-06
 4.97678e-06
 2.48839e-06
 -4.01855e-06
 2.00928e-06
 -1.43996e-20
 1.3493e-05
 4.01855e-06
 2.00928e-06
 7.83505e-21
 -4.23516e-22
 -0.00036424
 -0.00036424
 -0.00018212
 6.07067e-05
       0
 3.03534e-05
 -4.33619e-06
 3.03534e-05
 -4.33619e-06
 -1.73448e-05
 6.07067e-05
 -6.07067e-05
 -6.77626e-21
       0
 6.50429e-06
 -4.33619e-06
 2.1681e-06
 4.33619e-06
 -2.1681e-06
 -8.47033e-22
 -0.000204723
 -0.000741441
 -0.000741441
 -0.000165997
 3.41205e-05
 4.87436e-06
 3.41205e-05
 4.87436e-06
 0.000123574
 2.87991e-20
 2.76662e-05
 -3.95232e-06
 2.76662e-05
 -3.95232e-06
 -1.94974e-05
 -1.58093e-05
 -1.04185e-19
 0.000123574
 -0.000123574
 -8.97855e-20
 -4.87436e-06
 -2.43718e-06
 4.87436e-06
 2.43718e-06
 2.87991e-20
 1.324e-05
 -3.95232e-06
 1.97616e-06
 3.95232e-06
 -1.97616e-06
 -7.51742e-21
 -7.30566e-21
 -0.000696235
 -0.00018212
 -0.000165997
 -0.000696235
 3.03534e-05
 -4.33619e-06
 2.76662e-05
 -3.95232e-06
 0.000116039
 1.35525e-20
 3.03534e-05
 4.33619e-06
 2.76662e-05
 3.95232e-06
 -1.73448e-05
 -1.58093e-05
 0.000116039
 -9.82558e-20
 -5.0822e-21
 -0.000116039
 -4.33619e-06
 2.1681e-06
 -3.95232e-06
 1.97616e-06
 1.35525e-20
 1.24328e-05
 4.33619e-06
 2.1681e-06
 3.95232e-06
 1.97616e-06
 -7.72918e-21
 -6.35275e-22
 -0.000384711
 -0.000384711
 -0.000192355
 6.41185e-05
       0
 3.20592e-05
 -4.57989e-06
 3.20592e-05
 -4.57989e-06
 -1.83196e-05
 6.41185e-05
 -6.41185e-05
 -3.38813e-21
       0
 6.86984e-06
 -4.57989e-06
 2.28995e-06
 4.57989e-06
 -2.28995e-06
 -8.47033e-22
 -0.00018212
 -0.000696488
 -0.000696488
 -0.000166124
 3.03534e-05
 4.33619e-06
 3.03534e-05
 4.33619e-06
 0.000116081
 2.79521e-20
 2.76873e-05
 -3.95533e-06
 2.76873e-05
 -3.95533e-06
 -1.73448e-05
 -1.58213e-05
 -9.31736e-20
 0.000116081
 -0.000116081
 -9.23266e-20
 -4.33619e-06
 -2.1681e-06
 4.33619e-06
 2.1681e-06
 2.79521e-20
 1.24373e-05
 -3.95533e-06
 1.97767e-06
 3.95533e-06
 -1.97767e-06
 -6.98802e-21
 -7.19978e-21
 -0.000716959
 -0.000192355
 -0.000166124
 -0.000716959
 3.20592e-05
 -4.57989e-06
 2.76873e-05
 -3.95533e-06
 0.000119493
 1.52466e-20
 3.20592e-05
 4.57989e-06
 2.76873e-05
 3.95533e-06
 -1.83196e-05
 -1.58213e-05
 0.000119493
 -1.05032e-19
 -5.0822e-21
 -0.000119493
 -4.57989e-06
 2.28995e-06
 -3.95533e-06
 1.97767e-06
 1.52466e-20
 1.28028e-05
 4.57989e-06
 2.28995e-06
 3.95533e-06
 1.97767e-06
 -8.36445e-21
 -6.35275e-22
 -0.000409058
 -0.000409058
 -0.000204529
 6.81764e-05
       0
 3.40882e-05
 -4.86974e-06
 3.40882e-05
 -4.86974e-06
 -1.9479e-05
 6.81764e-05
 -6.81764e-05
 -6.77626e-21
       0
 7.30461e-06
 -4.86974e-06
 2.43487e-06
 4.86974e-06
 -2.43487e-06
 -8.47033e-22
 -0.000192355
 -0.000766976
 -0.000766976
 -0.000191133
 3.20592e-05
 4.57989e-06
 3.20592e-05
 4.57989e-06
 0.000127829
 3.04932e-20
 3.18554e-05
 -4.55078e-06
 3.18554e-05
 -4.55078e-06
 -1.83196e-05
 -1.82031e-05
 -9.82558e-20
 0.000127829
 -0.000127829
 -1.05032e-19
 -4.57989e-06
 -2.28995e-06
 4.57989e-06
 2.28995e-06
 3.04932e-20
 1.3696e-05
 -4.55078e-06
 2.27539e-06
 4.55078e-06
 -2.27539e-06
 -7.41154e-21
 -8.25857e-21
 -0.000791323
 -0.000204529
 -0.000191133
 -0.000791323
 3.40882e-05
 -4.86974e-06
 3.18554e-05
 -4.55078e-06
 0.000131887
 1.52466e-20
 3.40882e-05
 4.86974e-06
 3.18554e-05
 4.55078e-06
 -1.9479e-05
 -1.82031e-05
 0.000131887
 -1.11808e-19
 -5.0822e-21
 -0.000131887
 -4.86974e-06
 2.43487e-06
 -4.55078e-06
 2.27539e-06
 1.52466e-20
 1.41308e-05
 4.86974e-06
 2.43487e-06
 4.55078e-06
 2.27539e-06
 -8.68209e-21
 -8.47033e-22
 -0.000422677
 -0.000422677
 -0.000211338
 7.04461e-05
       0
 3.5223e-05
 -5.03186e-06
 3.5223e-05
 -5.03186e-06
 -2.01275e-05
 7.04461e-05
 -7.04461e-05
 -3.38813e-21
       0
 7.5478e-06
 -5.03186e-06
 2.51593e-06
 5.03186e-06
 -2.51593e-06
 -1.27055e-21
 -0.000204529
 -0.000815705
 -0.000815705
 -0.000203324
 3.40882e-05
 4.86974e-06
 3.40882e-05
 4.86974e-06
 0.000135951
 3.13402e-20
 3.38873e-05
 -4.84104e-06
 3.38873e-05
 -4.84104e-06
 -1.9479e-05
 -1.93641e-05
 -1.03338e-19
 0.000135951
 -0.000135951
 -1.11808e-19
 -4.86974e-06
 -2.43487e-06
 4.86974e-06
 2.43487e-06
 3.13402e-20
 1.45662e-05
 -4.84104e-06
 2.42052e-06
 4.84104e-06
 -2.42052e-06
 -7.94093e-21
 -8.89385e-21
 -0.000829324
 -0.000211338
 -0.000203324
 -0.000829324
 3.5223e-05
 -5.03186e-06
 3.38873e-05
 -4.84104e-06
 0.000138221
 1.52466e-20
 3.5223e-05
 5.03186e-06
 3.38873e-05
 4.84104e-06
 -2.01275e-05
 -1.93641e-05
 0.000138221
 -1.15196e-19
 -3.38813e-21
 -0.000138221
 -5.03186e-06
 2.51593e-06
 -4.84104e-06
 2.42052e-06
 1.52466e-20
 1.48094e-05
 5.03186e-06
 2.51593e-06
 4.84104e-06
 2.42052e-06
 -8.99973e-21
 -1.05879e-21
 -0.000474071
 -0.000474071
 -0.000237036
 7.90119e-05
       0
 3.95059e-05
 -5.64371e-06
 3.95059e-05
 -5.64371e-06
 -2.25748e-05
 7.90119e-05
 -7.90119e-05
 -5.0822e-21
       0
 8.46556e-06
 -5.64371e-06
 2.82185e-06
 5.64371e-06
 -2.82185e-06
 -1.05879e-21
 -0.000211338
 -0.000873938
 -0.000873938
 -0.000225631
 3.5223e-05
 5.03186e-06
 3.5223e-05
 5.03186e-06
 0.000145656
 3.47284e-20
 3.76051e-05
 -5.37216e-06
 3.76051e-05
 -5.37216e-06
 -2.01275e-05
 -2.14886e-05
 -1.10961e-19
 0.000145656
 -0.000145656
 -1.25361e-19
 -5.03186e-06
 -2.51593e-06
 5.03186e-06
 2.51593e-06
 3.47284e-20
 1.5606e-05
 -5.37216e-06
 2.68608e-06
 5.37216e-06
 -2.68608e-06
 -8.04681e-21
 -1.00585e-20
 -0.000925333
 -0.000237036
 -0.000225631
 -0.000925333
 3.95059e-05
 -5.64371e-06
 3.76051e-05
 -5.37216e-06
 0.000154222
 1.77877e-20
 3.95059e-05
 5.64371e-06
 3.76051e-05
 5.37216e-06
 -2.25748e-05
 -2.14886e-05
 0.000154222
 -1.32137e-19
 -1.69407e-21
 -0.000154222
 -5.64371e-06
 2.82185e-06
 -5.37216e-06
 2.68608e-06
 1.77877e-20
 1.65238e-05
 5.64371e-06
 2.82185e-06
 5.37216e-06
 2.68608e-06
 -9.95264e-21
 -1.48231e-21
 -0.000619411
 -0.000619411
 -0.000309706
 0.000103235
       0
 5.16176e-05
 -7.37394e-06
 5.16176e-05
 -7.37394e-06
 -2.94958e-05
 0.000103235
 -0.000103235
 -1.01644e-20
       0
 1.10609e-05
 -7.37394e-06
 3.68697e-06
 7.37394e-06
 -3.68697e-06
 -1.69407e-21
 -0.00128761
 -0.000309706
 -0.00128761
 -0.0003341
 5.16176e-05
 -7.37394e-06
 0.000214602
 2.37169e-20
 5.56833e-05
 -7.95475e-06
 5.16176e-05
 7.37394e-06
 5.56833e-05
 -7.95475e-06
 -2.94958e-05
 -3.1819e-05
 0.000214602
 -1.69407e-19
 -0.000214602
 -6.77626e-21
 -7.37394e-06
 3.68697e-06
 2.37169e-20
 2.2993e-05
 -7.95475e-06
 3.97738e-06
 7.37394e-06
 3.68697e-06
 7.95475e-06
 -3.97738e-06
 -1.37643e-20
 -1.27055e-21
 -0.000237036
 -0.00114227
 -0.0003341
 -0.00114227
 3.95059e-05
 5.64371e-06
 3.95059e-05
 5.64371e-06
 5.56833e-05
 -7.95475e-06
 0.000190378
 4.40457e-20
 5.56833e-05
 7.95475e-06
 -2.25748e-05
 -3.1819e-05
 -1.21973e-19
 0.000190378
 -1.81265e-19
 -0.000190378
 -5.64371e-06
 -2.82185e-06
 5.64371e-06
 2.82185e-06
 -7.95475e-06
 3.97738e-06
 4.40457e-20
 2.03977e-05
 7.95475e-06
 3.97738e-06
 -9.1056e-21
 -1.46113e-20
 -0.000383157
 -0.000309706
 -0.00138573
 -0.00138573
 6.38595e-05
 9.12279e-06
 6.38595e-05
 9.12279e-06
 5.16176e-05
 7.37394e-06
 5.16176e-05
 7.37394e-06
 0.000230954
 -3.38813e-21
 -2.94958e-05
 -3.64911e-05
 1.96512e-19
 -1.57548e-19
 0.000230954
 -0.000230954
 -9.12279e-06
 -4.56139e-06
 9.12279e-06
 4.56139e-06
 -7.37394e-06
 -3.68697e-06
 7.37394e-06
 3.68697e-06
 -3.38813e-21
 2.47451e-05
 -1.2282e-20
 1.50348e-20
 -0.000382107
 -0.00146542
 -0.00146542
 -0.0003506
 6.36845e-05
 9.09779e-06
 6.36845e-05
 9.09779e-06
 0.000244236
 -3.04932e-20
 5.84334e-05
 -8.34763e-06
 5.84334e-05
 -8.34763e-06
 -3.63912e-05
 -3.33905e-05
 1.89735e-19
 0.000244236
 -0.000244236
 -6.77626e-21
 -9.09779e-06
 -4.5489e-06
 9.09779e-06
 4.5489e-06
 -3.04932e-20
 2.61681e-05
 -8.34763e-06
 4.17381e-06
 8.34763e-06
 -4.17381e-06
 1.43996e-20
 -1.69407e-21
 -0.0003341
 -0.00130735
 -0.00130735
 -0.000319578
 5.56833e-05
 7.95475e-06
 5.56833e-05
 7.95475e-06
 0.000217892
 4.99749e-20
 5.32629e-05
 -7.60899e-06
 5.32629e-05
 -7.60899e-06
 -3.1819e-05
 -3.0436e-05
 -1.72795e-19
 0.000217892
 -0.000217892
 -1.72795e-19
 -7.95475e-06
 -3.97738e-06
 7.95475e-06
 3.97738e-06
 4.99749e-20
 2.33456e-05
 -7.60899e-06
 3.8045e-06
 7.60899e-06
 -3.8045e-06
 -1.29173e-20
 -1.3976e-20
 -0.00134036
 -0.0003506
 -0.000319578
 -0.00134036
 5.84334e-05
 -8.34763e-06
 5.32629e-05
 -7.60899e-06
 0.000223393
 2.6258e-20
 5.84334e-05
 8.34763e-06
 5.32629e-05
 7.60899e-06
 -3.33905e-05
 -3.0436e-05
 0.000223393
 -1.89735e-19
 -1.01644e-20
 -0.000223393
 -8.34763e-06
 4.17381e-06
 -7.60899e-06
 3.8045e-06
 2.6258e-20
 2.39349e-05
 8.34763e-06
 4.17381e-06
 7.60899e-06
 3.8045e-06
 -1.50348e-20
 -2.11758e-21
 -0.000289303
 -0.00115833
 -0.00115833
 -0.000289863
 4.82171e-05
 6.88816e-06
 4.82171e-05
 6.88816e-06
 0.000193055
 -2.20229e-20
 4.83105e-05
 -6.9015e-06
 4.83105e-05
 -6.9015e-06
 -2.75526e-05
 -2.7606e-05
 1.49078e-19
 0.000193055
 -0.000193055
 -6.77626e-21
 -6.88816e-06
 -3.44408e-06
 6.88816e-06
 3.44408e-06
 -2.20229e-20
 2.06845e-05
 -6.9015e-06
 3.45075e-06
 6.9015e-06
 -3.45075e-06
 1.18585e-20
 -8.47033e-22
 -0.00119511
 -0.000289863
 -0.00119511
 -0.000307692
 4.83105e-05
 -6.9015e-06
 0.000199185
 2.28699e-20
 5.1282e-05
 -7.326e-06
 4.83105e-05
 6.9015e-06
 5.1282e-05
 -7.326e-06
 -2.7606e-05
 -2.9304e-05
 0.000199185
 -1.57548e-19
 -0.000199185
 -1.35525e-20
 -6.9015e-06
 3.45075e-06
 2.28699e-20
 2.13412e-05
 -7.326e-06
 3.663e-06
 6.9015e-06
 3.45075e-06
 7.326e-06
 -3.663e-06
 -1.2282e-20
 -1.27055e-21
 -0.0003506
 -0.00131658
 -0.000307692
 -0.00131658
 5.84334e-05
 8.34763e-06
 5.84334e-05
 8.34763e-06
 5.1282e-05
 -7.326e-06
 0.000219431
 5.2516e-20
 5.1282e-05
 7.326e-06
 -3.33905e-05
 -2.9304e-05
 -1.79571e-19
 0.000219431
 -1.69407e-19
 -0.000219431
 -8.34763e-06
 -4.17381e-06
 8.34763e-06
 4.17381e-06
 -7.326e-06
 3.663e-06
 5.2516e-20
 2.35104e-05
 7.326e-06
 3.663e-06
 -1.35525e-20
 -1.33408e-20
 -0.000247066
 -0.000991396
 -0.000991396
 -0.000248632
 4.11777e-05
 5.88252e-06
 4.11777e-05
 5.88252e-06
 0.000165233
 -1.86347e-20
 4.14387e-05
 -5.91982e-06
 4.14387e-05
 -5.91982e-06
 -2.35301e-05
 -2.36793e-05
 1.23667e-19
 0.000165233
 -0.000165233
 -3.38813e-21
 -5.88252e-06
 -2.94126e-06
 5.88252e-06
 2.94126e-06
 -1.86347e-20
 1.77035e-05
 -5.91982e-06
 2.95991e-06
 5.91982e-06
 -2.95991e-06
 1.00585e-20
 -1.05879e-21
 -0.000289863
 -0.0011322
 -0.0011322
 -0.000276238
 4.83105e-05
 6.9015e-06
 4.83105e-05
 6.9015e-06
 0.0001887
 4.40457e-20
 4.60396e-05
 -6.57709e-06
 4.60396e-05
 -6.57709e-06
 -2.7606e-05
 -2.63083e-05
 -1.47384e-19
 0.0001887
 -0.0001887
 -1.49078e-19
 -6.9015e-06
 -3.45075e-06
 6.9015e-06
 3.45075e-06
 4.40457e-20
 2.02179e-05
 -6.57709e-06
 3.28854e-06
 6.57709e-06
 -3.28854e-06
 -1.14349e-20
 -1.21761e-20
 -0.00104974
 -0.000248632
 -0.000276238
 -0.00104974
 4.14387e-05
 -5.91982e-06
 4.60396e-05
 -6.57709e-06
 0.000174957
 1.99053e-20
 4.14387e-05
 5.91982e-06
 4.60396e-05
 6.57709e-06
 -2.36793e-05
 -2.63083e-05
 0.000174957
 -1.35525e-19
 -5.0822e-21
 -0.000174957
 -5.91982e-06
 2.95991e-06
 -6.57709e-06
 3.28854e-06
 1.99053e-20
 1.87454e-05
 5.91982e-06
 2.95991e-06
 6.57709e-06
 3.28854e-06
 -1.0482e-20
 -1.27055e-21
 -0.000209382
 -0.000838491
 -0.000838491
 -0.000209864
 3.48969e-05
 4.98528e-06
 3.48969e-05
 4.98528e-06
 0.000139749
 -1.69407e-20
 3.49774e-05
 -4.99677e-06
 3.49774e-05
 -4.99677e-06
 -1.99411e-05
 -1.99871e-05
 1.05032e-19
 0.000139749
 -0.000139749
 -3.38813e-21
 -4.98528e-06
 -2.49264e-06
 4.98528e-06
 2.49264e-06
 -1.69407e-20
 1.49731e-05
 -4.99677e-06
 2.49838e-06
 4.99677e-06
 -2.49838e-06
 8.47033e-21
 -1.05879e-21
 -0.000879852
 -0.000209864
 -0.000879852
 -0.000230062
 3.49774e-05
 -4.99677e-06
 0.000146642
 1.60936e-20
 3.83436e-05
 -5.47766e-06
 3.49774e-05
 4.99677e-06
 3.83436e-05
 -5.47766e-06
 -1.99871e-05
 -2.19106e-05
 0.000146642
 -1.15196e-19
 -0.000146642
 -5.0822e-21
 -4.99677e-06
 2.49838e-06
 1.60936e-20
 1.57116e-05
 -5.47766e-06
 2.73883e-06
 4.99677e-06
 2.49838e-06
 5.47766e-06
 -2.73883e-06
 -8.99973e-21
 -1.05879e-21
 -0.000248632
 -0.000957388
 -0.000230062
 -0.000957388
 4.14387e-05
 5.91982e-06
 4.14387e-05
 5.91982e-06
 3.83436e-05
 -5.47766e-06
 0.000159565
 3.81165e-20
 3.83436e-05
 5.47766e-06
 -2.36793e-05
 -2.19106e-05
 -1.27055e-19
 0.000159565
 -1.25361e-19
 -0.000159565
 -5.91982e-06
 -2.95991e-06
 5.91982e-06
 2.95991e-06
 -5.47766e-06
 2.73883e-06
 3.81165e-20
 1.70962e-05
 5.47766e-06
 2.73883e-06
 -9.52912e-21
 -1.00585e-20
 -0.000172873
 -0.000679602
 -0.000679602
 -0.000166928
 2.88121e-05
 4.11602e-06
 2.88121e-05
 4.11602e-06
 0.000113267
 -1.35525e-20
 2.78214e-05
 -3.97449e-06
 2.78214e-05
 -3.97449e-06
 -1.64641e-05
 -1.58979e-05
 8.72444e-20
 0.000113267
 -0.000113267
 -1.69407e-21
 -4.11602e-06
 -2.05801e-06
 4.11602e-06
 2.05801e-06
 -1.35525e-20
 1.21358e-05
 -3.97449e-06
 1.98724e-06
 3.97449e-06
 -1.98724e-06
 6.98802e-21
 -8.47033e-22
 -0.000209864
 -0.000783224
 -0.000783224
 -0.000181748
 3.49774e-05
 4.99677e-06
 3.49774e-05
 4.99677e-06
 0.000130537
 3.21873e-20
 3.02913e-05
 -4.32733e-06
 3.02913e-05
 -4.32733e-06
 -1.99871e-05
 -1.73093e-05
 -1.06726e-19
 0.000130537
 -0.000130537
 -9.82558e-20
 -4.99677e-06
 -2.49838e-06
 4.99677e-06
 2.49838e-06
 3.21873e-20
 1.39861e-05
 -4.32733e-06
 2.16366e-06
 4.32733e-06
 -2.16366e-06
 -8.15269e-21
 -7.94093e-21
 -0.000697353
 -0.000166928
 -0.000181748
 -0.000697353
 2.78214e-05
 -3.97449e-06
 3.02913e-05
 -4.32733e-06
 0.000116225
 1.27055e-20
 2.78214e-05
 3.97449e-06
 3.02913e-05
 4.32733e-06
 -1.58979e-05
 -1.73093e-05
 0.000116225
 -9.23266e-20
 -5.0822e-21
 -0.000116225
 -3.97449e-06
 1.98724e-06
 -4.32733e-06
 2.16366e-06
 1.27055e-20
 1.24527e-05
 3.97449e-06
 1.98724e-06
 4.32733e-06
 2.16366e-06
 -7.19978e-21
 -1.05879e-21
 -0.000166913
 -0.000584135
 -0.000584135
 -0.000125154
 2.78189e-05
 3.97412e-06
 2.78189e-05
 3.97412e-06
 9.73558e-05
 -1.27055e-20
 2.0859e-05
 -2.97986e-06
 2.0859e-05
 -2.97986e-06
 -1.58965e-05
 -1.19194e-05
 8.63974e-20
 9.73558e-05
 -9.73558e-05
 -2.5411e-21
 -3.97412e-06
 -1.98706e-06
 3.97412e-06
 1.98706e-06
 -1.27055e-20
 1.0431e-05
 -2.97986e-06
 1.48993e-06
 2.97986e-06
 -1.48993e-06
 6.77626e-21
 -5.29396e-22
 -0.000166928
 -0.000577636
 -0.000577636
 -0.00012189
 2.78214e-05
 3.97449e-06
 2.78214e-05
 3.97449e-06
 9.62727e-05
 2.15993e-20
 2.0315e-05
 -2.90214e-06
 2.0315e-05
 -2.90214e-06
 -1.58979e-05
 -1.16086e-05
 -8.89385e-20
 9.62727e-05
 -9.62727e-05
 -6.60686e-20
 -3.97449e-06
 -1.98724e-06
 3.97449e-06
 1.98724e-06
 2.15993e-20
 1.03149e-05
 -2.90214e-06
 1.45107e-06
 2.90214e-06
 -1.45107e-06
 -6.67038e-21
 -5.24102e-21
 -0.000494088
 -0.000125154
 -0.00012189
 -0.000494088
 2.0859e-05
 -2.97986e-06
 2.0315e-05
 -2.90214e-06
 8.2348e-05
 9.74088e-21
 2.0859e-05
 2.97986e-06
 2.0315e-05
 2.90214e-06
 -1.19194e-05
 -1.16086e-05
 8.2348e-05
 -6.69156e-20
 -3.38813e-21
 -8.2348e-05
 -2.97986e-06
 1.48993e-06
 -2.90214e-06
 1.45107e-06
 9.74088e-21
 8.823e-06
 2.97986e-06
 1.48993e-06
 2.90214e-06
 1.45107e-06
 -5.29396e-21
 -6.35275e-22
 -0.000165078
 -0.00057814
 -0.00057814
 -0.000123992
 2.75131e-05
 3.93044e-06
 2.75131e-05
 3.93044e-06
 9.63567e-05
 -1.18585e-20
 2.06653e-05
 -2.95218e-06
 2.06653e-05
 -2.95218e-06
 -1.57218e-05
 -1.18087e-05
 8.38563e-20
 9.63567e-05
 -9.63567e-05
 -5.0822e-21
 -3.93044e-06
 -1.96522e-06
 3.93044e-06
 1.96522e-06
 -1.18585e-20
 1.03239e-05
 -2.95218e-06
 1.47609e-06
 2.95218e-06
 -1.47609e-06
 6.45863e-21
 -6.35275e-22
 -0.000125154
 -0.000498292
 -0.000123992
 -0.000498292
 2.0859e-05
 2.97986e-06
 2.0859e-05
 2.97986e-06
 2.06653e-05
 -2.95218e-06
 8.30486e-05
 2.03288e-20
 2.06653e-05
 2.95218e-06
 -1.19194e-05
 -1.18087e-05
 -6.35275e-20
 8.30486e-05
 -6.77626e-20
 -8.30486e-05
 -2.97986e-06
 -1.48993e-06
 2.97986e-06
 1.48993e-06
 -2.95218e-06
 1.47609e-06
 2.03288e-20
 8.89806e-06
 2.95218e-06
 1.47609e-06
 -5.0822e-21
 -5.3469e-21
 -0.00016703
 -0.000660198
 -0.000660198
 -0.00016307
 2.78383e-05
 3.97689e-06
 2.78383e-05
 3.97689e-06
 0.000110033
 -1.35525e-20
 2.71783e-05
 -3.88261e-06
 2.71783e-05
 -3.88261e-06
 -1.59076e-05
 -1.55304e-05
 8.63974e-20
 0.000110033
 -0.000110033
 -6.77626e-21
 -3.97689e-06
 -1.98845e-06
 3.97689e-06
 1.98845e-06
 -1.35525e-20
 1.17893e-05
 -3.88261e-06
 1.94131e-06
 3.88261e-06
 -1.94131e-06
 6.45863e-21
 -8.47033e-22
 -0.000123992
 -0.000489463
 -0.000489463
 -0.00012074
 2.06653e-05
 2.95218e-06
 2.06653e-05
 2.95218e-06
 8.15771e-05
 1.94818e-20
 2.01233e-05
 -2.87476e-06
 2.01233e-05
 -2.87476e-06
 -1.18087e-05
 -1.1499e-05
 -6.35275e-20
 8.15771e-05
 -8.15771e-05
 -6.52215e-20
 -2.95218e-06
 -1.47609e-06
 2.95218e-06
 1.47609e-06
 1.94818e-20
 8.74041e-06
 -2.87476e-06
 1.43738e-06
 2.87476e-06
 -1.43738e-06
 -4.87044e-21
 -5.18808e-21
 -0.000567619
 -0.00016307
 -0.00012074
 -0.000567619
 2.71783e-05
 -3.88261e-06
 2.01233e-05
 -2.87476e-06
 9.46032e-05
 1.2282e-20
 2.71783e-05
 3.88261e-06
 2.01233e-05
 2.87476e-06
 -1.55304e-05
 -1.1499e-05
 9.46032e-05
 -8.89385e-20
 -1.69407e-21
 -9.46032e-05
 -3.88261e-06
 1.94131e-06
 -2.87476e-06
 1.43738e-06
 1.2282e-20
 1.01361e-05
 3.88261e-06
 1.94131e-06
 2.87476e-06
 1.43738e-06
 -6.88214e-21
 -6.35275e-22
 -0.000197356
 -0.000796036
 -0.000796036
 -0.000200662
 3.28926e-05
 4.69895e-06
 3.28926e-05
 4.69895e-06
 0.000132673
 -1.69407e-20
 3.34437e-05
 -4.77768e-06
 3.34437e-05
 -4.77768e-06
 -1.87958e-05
 -1.91107e-05
 9.91029e-20
 0.000132673
 -0.000132673
 -3.38813e-21
 -4.69895e-06
 -2.34947e-06
 4.69895e-06
 2.34947e-06
 -1.69407e-20
 1.42149e-05
 -4.77768e-06
 2.38884e-06
 4.77768e-06
 -2.38884e-06
 7.6233e-21
 -1.05879e-21
 -0.0007564
 -0.000200662
 -0.0007564
 -0.000177538
 3.34437e-05
 -4.77768e-06
 0.000126067
 1.60936e-20
 2.95896e-05
 -4.22708e-06
 3.34437e-05
 4.77768e-06
 2.95896e-05
 -4.22708e-06
 -1.91107e-05
 -1.69083e-05
 0.000126067
 -1.0842e-19
 -0.000126067
 -6.77626e-21
 -4.77768e-06
 2.38884e-06
 1.60936e-20
 1.35071e-05
 -4.22708e-06
 2.11354e-06
 4.77768e-06
 2.38884e-06
 4.22708e-06
 -2.11354e-06
 -8.36445e-21
 -6.35275e-22
 -0.00016307
 -0.000681215
 -0.000177538
 -0.000681215
 2.71783e-05
 3.88261e-06
 2.71783e-05
 3.88261e-06
 2.95896e-05
 -4.22708e-06
 0.000113536
 2.66815e-20
 2.95896e-05
 4.22708e-06
 -1.55304e-05
 -1.69083e-05
 -8.47033e-20
 0.000113536
 -9.74088e-20
 -0.000113536
 -3.88261e-06
 -1.94131e-06
 3.88261e-06
 1.94131e-06
 -4.22708e-06
 2.11354e-06
 2.66815e-20
 1.21645e-05
 4.22708e-06
 2.11354e-06
 -6.24687e-21
 -7.51742e-21
 -0.000223128
 -0.000905917
 -0.000905917
 -0.000229831
 3.7188e-05
 5.31257e-06
 3.7188e-05
 5.31257e-06
 0.000150986
 -1.69407e-20
 3.83051e-05
 -5.47216e-06
 3.83051e-05
 -5.47216e-06
 -2.12503e-05
 -2.18886e-05
 1.13502e-19
 0.000150986
 -0.000150986
 -5.0822e-21
 -5.31257e-06
 -2.65629e-06
 5.31257e-06
 2.65629e-06
 -1.69407e-20
 1.61771e-05
 -5.47216e-06
 2.73608e-06
 5.47216e-06
 -2.73608e-06
 8.78797e-21
 -8.47033e-22
 -0.000200662
 -0.00083958
 -0.00083958
 -0.000219128
 3.34437e-05
 4.77768e-06
 3.34437e-05
 4.77768e-06
 0.00013993
 3.13402e-20
 3.65213e-05
 -5.21733e-06
 3.65213e-05
 -5.21733e-06
 -1.91107e-05
 -2.08693e-05
 -1.04185e-19
 0.00013993
 -0.00013993
 -1.18585e-19
 -4.77768e-06
 -2.38884e-06
 4.77768e-06
 2.38884e-06
 3.13402e-20
 1.49925e-05
 -5.21733e-06
 2.60866e-06
 5.21733e-06
 -2.60866e-06
 -7.6233e-21
 -9.52912e-21
 -0.000897917
 -0.000229831
 -0.000219128
 -0.000897917
 3.83051e-05
 -5.47216e-06
 3.65213e-05
 -5.21733e-06
 0.000149653
 1.69407e-20
 3.83051e-05
 5.47216e-06
 3.65213e-05
 5.21733e-06
 -2.18886e-05
 -2.08693e-05
 0.000149653
 -1.25361e-19
 -3.38813e-21
 -0.000149653
 -5.47216e-06
 2.73608e-06
 -5.21733e-06
 2.60866e-06
 1.69407e-20
 1.60342e-05
 5.47216e-06
 2.73608e-06
 5.21733e-06
 2.60866e-06
 -9.95264e-21
 -1.48231e-21
 -0.000238099
 -0.000978159
 -0.000978159
 -0.00025098
 3.96832e-05
 5.66903e-06
 3.96832e-05
 5.66903e-06
 0.000163026
 -1.86347e-20
 4.183e-05
 -5.97572e-06
 4.183e-05
 -5.97572e-06
 -2.26761e-05
 -2.39029e-05
 1.20279e-19
 0.000163026
 -0.000163026
 -6.77626e-21
 -5.66903e-06
 -2.83452e-06
 5.66903e-06
 2.83452e-06
 -1.86347e-20
 1.74671e-05
 -5.97572e-06
 2.98786e-06
 5.97572e-06
 -2.98786e-06
 9.52912e-21
 -1.27055e-21
 -0.000229831
 -0.000969021
 -0.000969021
 -0.00025468
 3.83051e-05
 5.47216e-06
 3.83051e-05
 5.47216e-06
 0.000161503
 3.89635e-20
 4.24466e-05
 -6.0638e-06
 4.24466e-05
 -6.0638e-06
 -2.18886e-05
 -2.42552e-05
 -1.18585e-19
 0.000161503
 -0.000161503
 -1.40607e-19
 -5.47216e-06
 -2.73608e-06
 5.47216e-06
 2.73608e-06
 3.89635e-20
 1.73039e-05
 -6.0638e-06
 3.0319e-06
 6.0638e-06
 -3.0319e-06
 -9.31736e-21
 -1.09055e-20
 -0.00101132
 -0.00025098
 -0.00025468
 -0.00101132
 4.183e-05
 -5.97572e-06
 4.24466e-05
 -6.0638e-06
 0.000168553
 2.07523e-20
 4.183e-05
 5.97572e-06
 4.24466e-05
 6.0638e-06
 -2.39029e-05
 -2.42552e-05
 0.000168553
 -1.35525e-19
 -6.77626e-21
 -0.000168553
 -5.97572e-06
 2.98786e-06
 -6.0638e-06
 3.0319e-06
 2.07523e-20
 1.80593e-05
 5.97572e-06
 2.98786e-06
 6.0638e-06
 3.0319e-06
 -1.05879e-20
 -1.27055e-21
 -0.000238581
 -0.000967404
 -0.000967404
 -0.000245121
 3.97635e-05
 5.68049e-06
 3.97635e-05
 5.68049e-06
 0.000161234
 -1.86347e-20
 4.08535e-05
 -5.83622e-06
 4.08535e-05
 -5.83622e-06
 -2.2722e-05
 -2.33449e-05
 1.21973e-19
 0.000161234
 -0.000161234
 -6.77626e-21
 -5.68049e-06
 -2.84025e-06
 5.68049e-06
 2.84025e-06
 -1.86347e-20
 1.72751e-05
 -5.83622e-06
 2.91811e-06
 5.83622e-06
 -2.91811e-06
 9.21148e-21
 -8.47033e-22
 -0.00025098
 -0.00103111
 -0.00103111
 -0.000264574
 4.183e-05
 5.97572e-06
 4.183e-05
 5.97572e-06
 0.000171851
 3.89635e-20
 4.40956e-05
 -6.29938e-06
 4.40956e-05
 -6.29938e-06
 -2.39029e-05
 -2.51975e-05
 -1.30443e-19
 0.000171851
 -0.000171851
 -1.4569e-19
 -5.97572e-06
 -2.98786e-06
 5.97572e-06
 2.98786e-06
 3.89635e-20
 1.84126e-05
 -6.29938e-06
 3.14969e-06
 6.29938e-06
 -3.14969e-06
 -9.74088e-21
 -1.17526e-20
 -0.00101939
 -0.000245121
 -0.000264574
 -0.00101939
 4.08535e-05
 -5.83622e-06
 4.40956e-05
 -6.29938e-06
 0.000169898
 1.77877e-20
 4.08535e-05
 5.83622e-06
 4.40956e-05
 6.29938e-06
 -2.33449e-05
 -2.51975e-05
 0.000169898
 -1.33831e-19
 -6.77626e-21
 -0.000169898
 -5.83622e-06
 2.91811e-06
 -6.29938e-06
 3.14969e-06
 1.77877e-20
 1.82034e-05
 5.83622e-06
 2.91811e-06
 6.29938e-06
 3.14969e-06
 -1.05879e-20
 -1.27055e-21
 -0.000249636
 -0.000915014
 -0.000915014
 -0.000207871
 4.1606e-05
 5.94371e-06
 4.1606e-05
 5.94371e-06
 0.000152502
 -1.73642e-20
 3.46451e-05
 -4.94931e-06
 3.46451e-05
 -4.94931e-06
 -2.37749e-05
 -1.97972e-05
 1.28749e-19
 0.000152502
 -0.000152502
 -3.38813e-21
 -5.94371e-06
 -2.97186e-06
 5.94371e-06
 2.97186e-06
 -1.73642e-20
 1.63395e-05
 -4.94931e-06
 2.47465e-06
 4.94931e-06
 -2.47465e-06
 9.635e-21
 -6.35275e-22
 -0.000245121
 -0.000905984
 -0.000207871
 -0.000905984
 4.08535e-05
 5.83622e-06
 4.08535e-05
 5.83622e-06
 3.46451e-05
 -4.94931e-06
 0.000150997
 3.81165e-20
 3.46451e-05
 4.94931e-06
 -2.33449e-05
 -1.97972e-05
 -1.25361e-19
 0.000150997
 -1.13502e-19
 -0.000150997
 -5.83622e-06
 -2.91811e-06
 5.83622e-06
 2.91811e-06
 -4.94931e-06
 2.47465e-06
 3.81165e-20
 1.61783e-05
 4.94931e-06
 2.47465e-06
 -9.74088e-21
 -8.89385e-21
 -0.000195001
 -0.000804577
 -0.000804577
 -0.000207288
 3.25001e-05
 4.64287e-06
 3.25001e-05
 4.64287e-06
 0.000134096
 -1.43996e-20
 3.4548e-05
 -4.93543e-06
 3.4548e-05
 -4.93543e-06
 -1.85715e-05
 -1.97417e-05
 9.65618e-20
 0.000134096
 -0.000134096
 -3.38813e-21
 -4.64287e-06
 -2.32143e-06
 4.64287e-06
 2.32143e-06
 -1.43996e-20
 1.43674e-05
 -4.93543e-06
 2.46771e-06
 4.93543e-06
 -2.46771e-06
 7.72918e-21
 -8.47033e-22
 -0.000207871
 -0.000830317
 -0.000207288
 -0.000830317
 3.46451e-05
 4.94931e-06
 3.46451e-05
 4.94931e-06
 3.4548e-05
 -4.93543e-06
 0.000138386
 3.21873e-20
 3.4548e-05
 4.93543e-06
 -1.97972e-05
 -1.97417e-05
 -1.09267e-19
 0.000138386
 -1.13502e-19
 -0.000138386
 -4.94931e-06
 -2.47465e-06
 4.94931e-06
 2.47465e-06
 -4.93543e-06
 2.46771e-06
 3.21873e-20
 1.48271e-05
 4.93543e-06
 2.46771e-06
 -8.47033e-21
 -8.89385e-21
 -0.000256936
 -0.00115797
 -0.00115797
 -0.000322049
 4.28227e-05
 6.11752e-06
 4.28227e-05
 6.11752e-06
 0.000192995
 -2.03288e-20
 5.36748e-05
 -7.66783e-06
 5.36748e-05
 -7.66783e-06
 -2.44701e-05
 -3.06713e-05
 1.30443e-19
 0.000192995
 -0.000192995
 -1.01644e-20
 -6.11752e-06
 -3.05876e-06
 6.11752e-06
 3.05876e-06
 -2.03288e-20
 2.0678e-05
 -7.66783e-06
 3.83392e-06
 7.66783e-06
 -3.83392e-06
 1.01644e-20
 -8.47033e-22
 -0.000207288
 -0.00103489
 -0.00103489
 -0.000310157
 3.4548e-05
 4.93543e-06
 3.4548e-05
 4.93543e-06
 0.000172482
 3.89635e-20
 5.16929e-05
 -7.3847e-06
 5.16929e-05
 -7.3847e-06
 -1.97417e-05
 -2.95388e-05
 -1.05879e-19
 0.000172482
 -0.000172482
 -1.69407e-19
 -4.93543e-06
 -2.46771e-06
 4.93543e-06
 2.46771e-06
 3.89635e-20
 1.84802e-05
 -7.3847e-06
 3.69235e-06
 7.3847e-06
 -3.69235e-06
 -8.04681e-21
 -1.33408e-20
 -0.00126441
 -0.000322049
 -0.000310157
 -0.00126441
 5.36748e-05
 -7.66783e-06
 5.16929e-05
 -7.3847e-06
 0.000210735
 2.5411e-20
 5.36748e-05
 7.66783e-06
 5.16929e-05
 7.3847e-06
 -3.06713e-05
 -2.95388e-05
 0.000210735
 -1.76183e-19
 -3.38813e-21
 -0.000210735
 -7.66783e-06
 3.83392e-06
 -7.3847e-06
 3.69235e-06
 2.5411e-20
 2.25788e-05
 7.66783e-06
 3.83392e-06
 7.3847e-06
 3.69235e-06
 -1.35525e-20
 -1.69407e-21
 -0.000251423
 -0.00103384
 -0.00103384
 -0.000265497
 4.19039e-05
 5.98627e-06
 4.19039e-05
 5.98627e-06
 0.000172307
 -2.03288e-20
 4.42495e-05
 -6.32136e-06
 4.42495e-05
 -6.32136e-06
 -2.39451e-05
 -2.52855e-05
 1.30443e-19
 0.000172307
 -0.000172307
 -6.77626e-21
 -5.98627e-06
 -2.99313e-06
 5.98627e-06
 2.99313e-06
 -2.03288e-20
 1.84614e-05
 -6.32136e-06
 3.16068e-06
 6.32136e-06
 -3.16068e-06
 9.95264e-21
 -1.27055e-21
 -0.00120811
 -0.000265497
 -0.00120811
 -0.000338559
 4.42495e-05
 -6.32136e-06
 0.000201352
 1.86347e-20
 5.64265e-05
 -8.06093e-06
 4.42495e-05
 6.32136e-06
 5.64265e-05
 -8.06093e-06
 -2.52855e-05
 -3.22437e-05
 0.000201352
 -1.43996e-19
 -0.000201352
 -1.35525e-20
 -6.32136e-06
 3.16068e-06
 1.86347e-20
 2.15734e-05
 -8.06093e-06
 4.03047e-06
 6.32136e-06
 3.16068e-06
 8.06093e-06
 -4.03047e-06
 -1.10114e-20
 -2.11758e-21
 -0.000322049
 -0.00132122
 -0.000338559
 -0.00132122
 5.36748e-05
 7.66783e-06
 5.36748e-05
 7.66783e-06
 5.64265e-05
 -8.06093e-06
 0.000220203
 5.33631e-20
 5.64265e-05
 8.06093e-06
 -3.06713e-05
 -3.22437e-05
 -1.67713e-19
 0.000220203
 -1.84653e-19
 -0.000220203
 -7.66783e-06
 -3.83392e-06
 7.66783e-06
 3.83392e-06
 -8.06093e-06
 4.03047e-06
 5.33631e-20
 2.35932e-05
 8.06093e-06
 4.03047e-06
 -1.24937e-20
 -1.46113e-20
 -0.000215091
 -0.000865993
 -0.000865993
 -0.000217905
 3.58486e-05
 5.12123e-06
 3.58486e-05
 5.12123e-06
 0.000144332
 -1.69407e-20
 3.63175e-05
 -5.18821e-06
 3.63175e-05
 -5.18821e-06
 -2.04849e-05
 -2.07529e-05
 1.10114e-19
 0.000144332
 -0.000144332
 -5.0822e-21
 -5.12123e-06
 -2.56061e-06
 5.12123e-06
 2.56061e-06
 -1.69407e-20
 1.54642e-05
 -5.18821e-06
 2.59411e-06
 5.18821e-06
 -2.59411e-06
 8.57621e-21
 -8.47033e-22
 -0.000265497
 -0.0010243
 -0.0010243
 -0.000246654
 4.42495e-05
 6.32136e-06
 4.42495e-05
 6.32136e-06
 0.000170717
 4.15046e-20
 4.1109e-05
 -5.87271e-06
 4.1109e-05
 -5.87271e-06
 -2.52855e-05
 -2.34909e-05
 -1.35525e-19
 0.000170717
 -0.000170717
 -1.32137e-19
 -6.32136e-06
 -3.16068e-06
 6.32136e-06
 3.16068e-06
 4.15046e-20
 1.82911e-05
 -5.87271e-06
 2.93636e-06
 5.87271e-06
 -2.93636e-06
 -9.74088e-21
 -1.05879e-20
 -0.000929118
 -0.000217905
 -0.000246654
 -0.000929118
 3.63175e-05
 -5.18821e-06
 4.1109e-05
 -5.87271e-06
 0.000154853
 1.60936e-20
 3.63175e-05
 5.18821e-06
 4.1109e-05
 5.87271e-06
 -2.07529e-05
 -2.34909e-05
 0.000154853
 -1.16891e-19
 -6.77626e-21
 -0.000154853
 -5.18821e-06
 2.59411e-06
 -5.87271e-06
 2.93636e-06
 1.60936e-20
 1.65914e-05
 5.18821e-06
 2.59411e-06
 5.87271e-06
 2.93636e-06
 -9.31736e-21
 -1.05879e-21
 -0.000176233
 -0.000693475
 -0.000693475
 -0.000170504
 2.93722e-05
 4.19603e-06
 2.93722e-05
 4.19603e-06
 0.000115579
 -1.52466e-20
 2.84173e-05
 -4.05962e-06
 2.84173e-05
 -4.05962e-06
 -1.67841e-05
 -1.62385e-05
 8.97855e-20
 0.000115579
 -0.000115579
 -5.0822e-21
 -4.19603e-06
 -2.09802e-06
 4.19603e-06
 2.09802e-06
 -1.52466e-20
 1.23835e-05
 -4.05962e-06
 2.02981e-06
 4.05962e-06
 -2.02981e-06
 6.77626e-21
 -8.47033e-22
 -0.000217905
 -0.000811407
 -0.000811407
 -0.000187798
 3.63175e-05
 5.18821e-06
 3.63175e-05
 5.18821e-06
 0.000135234
 3.04932e-20
 3.12997e-05
 -4.47139e-06
 3.12997e-05
 -4.47139e-06
 -2.07529e-05
 -1.78856e-05
 -1.13502e-19
 0.000135234
 -0.000135234
 -9.99499e-20
 -5.18821e-06
 -2.59411e-06
 5.18821e-06
 2.59411e-06
 3.04932e-20
 1.44894e-05
 -4.47139e-06
 2.2357e-06
 4.47139e-06
 -2.2357e-06
 -8.47033e-21
 -8.15269e-21
 -0.000716605
 -0.000170504
 -0.000187798
 -0.000716605
 2.84173e-05
 -4.05962e-06
 3.12997e-05
 -4.47139e-06
 0.000119434
 1.3129e-20
 2.84173e-05
 4.05962e-06
 3.12997e-05
 4.47139e-06
 -1.62385e-05
 -1.78856e-05
 0.000119434
 -9.23266e-20
 -3.38813e-21
 -0.000119434
 -4.05962e-06
 2.02981e-06
 -4.47139e-06
 2.2357e-06
 1.3129e-20
 1.27965e-05
 4.05962e-06
 2.02981e-06
 4.47139e-06
 2.2357e-06
 -7.19978e-21
 -1.05879e-21
 -0.000168779
 -0.000590861
 -0.000590861
 -0.000126651
 2.81299e-05
 4.01855e-06
 2.81299e-05
 4.01855e-06
 9.84769e-05
 -1.27055e-20
 2.11086e-05
 -3.01551e-06
 2.11086e-05
 -3.01551e-06
 -1.60742e-05
 -1.2062e-05
 8.47033e-20
 9.84769e-05
 -9.84769e-05
 -2.5411e-21
 -4.01855e-06
 -2.00928e-06
 4.01855e-06
 2.00928e-06
 -1.27055e-20
 1.05511e-05
 -3.01551e-06
 1.50776e-06
 3.01551e-06
 -1.50776e-06
 6.45863e-21
 -5.29396e-22
 -0.000170504
 -0.000589072
 -0.000589072
 -0.000124032
 2.84173e-05
 4.05962e-06
 2.84173e-05
 4.05962e-06
 9.81786e-05
 2.24464e-20
 2.0672e-05
 -2.95314e-06
 2.0672e-05
 -2.95314e-06
 -1.62385e-05
 -1.18126e-05
 -8.55503e-20
 9.81786e-05
 -9.81786e-05
 -6.77626e-20
 -4.05962e-06
 -2.02981e-06
 4.05962e-06
 2.02981e-06
 2.24464e-20
 1.05191e-05
 -2.95314e-06
 1.47657e-06
 2.95314e-06
 -1.47657e-06
 -6.56451e-21
 -5.3469e-21
 -0.000501367
 -0.000126651
 -0.000124032
 -0.000501367
 2.11086e-05
 -3.01551e-06
 2.0672e-05
 -2.95314e-06
 8.35611e-05
 9.74088e-21
 2.11086e-05
 3.01551e-06
 2.0672e-05
 2.95314e-06
 -1.2062e-05
 -1.18126e-05
 8.35611e-05
 -6.86097e-20
 -3.38813e-21
 -8.35611e-05
 -3.01551e-06
 1.50776e-06
 -2.95314e-06
 1.47657e-06
 9.74088e-21
 8.95298e-06
 3.01551e-06
 1.50776e-06
 2.95314e-06
 1.47657e-06
 -5.39984e-21
 -7.41154e-22
 -0.000165997
 -0.000581964
 -0.000581964
 -0.000124984
 2.76662e-05
 3.95232e-06
 2.76662e-05
 3.95232e-06
 9.6994e-05
 -1.27055e-20
 2.08307e-05
 -2.97582e-06
 2.08307e-05
 -2.97582e-06
 -1.58093e-05
 -1.19033e-05
 8.30092e-20
 9.6994e-05
 -9.6994e-05
 -5.0822e-21
 -3.95232e-06
 -1.97616e-06
 3.95232e-06
 1.97616e-06
 -1.27055e-20
 1.03922e-05
 -2.97582e-06
 1.48791e-06
 2.97582e-06
 -1.48791e-06
 6.77626e-21
 -5.29396e-22
 -0.000126651
 -0.000503272
 -0.000124984
 -0.000503272
 2.11086e-05
 3.01551e-06
 2.11086e-05
 3.01551e-06
 2.08307e-05
 -2.97582e-06
 8.38786e-05
 1.99053e-20
 2.08307e-05
 2.97582e-06
 -1.2062e-05
 -1.19033e-05
 -6.43745e-20
 8.38786e-05
 -6.77626e-20
 -8.38786e-05
 -3.01551e-06
 -1.50776e-06
 3.01551e-06
 1.50776e-06
 -2.97582e-06
 1.48791e-06
 1.99053e-20
 8.987e-06
 2.97582e-06
 1.48791e-06
 -4.92338e-21
 -5.24102e-21
 -0.000166124
 -0.000658239
 -0.000658239
 -0.000162995
 2.76873e-05
 3.95533e-06
 2.76873e-05
 3.95533e-06
 0.000109706
 -1.35525e-20
 2.71659e-05
 -3.88084e-06
 2.71659e-05
 -3.88084e-06
 -1.58213e-05
 -1.55234e-05
 8.47033e-20
 0.000109706
 -0.000109706
 -6.77626e-21
 -3.95533e-06
 -1.97767e-06
 3.95533e-06
 1.97767e-06
 -1.35525e-20
 1.17543e-05
 -3.88084e-06
 1.94042e-06
 3.88084e-06
 -1.94042e-06
 6.67038e-21
 -6.35275e-22
 -0.000124984
 -0.000493208
 -0.000493208
 -0.00012162
 2.08307e-05
 2.97582e-06
 2.08307e-05
 2.97582e-06
 8.22013e-05
 1.90582e-20
 2.02699e-05
 -2.89571e-06
 2.02699e-05
 -2.89571e-06
 -1.19033e-05
 -1.15828e-05
 -6.35275e-20
 8.22013e-05
 -8.22013e-05
 -6.77626e-20
 -2.97582e-06
 -1.48791e-06
 2.97582e-06
 1.48791e-06
 1.90582e-20
 8.80729e-06
 -2.89571e-06
 1.44785e-06
 2.89571e-06
 -1.44785e-06
 -4.87044e-21
 -5.29396e-21
 -0.00056923
 -0.000162995
 -0.00012162
 -0.00056923
 2.71659e-05
 -3.88084e-06
 2.02699e-05
 -2.89571e-06
 9.48717e-05
 1.2282e-20
 2.71659e-05
 3.88084e-06
 2.02699e-05
 2.89571e-06
 -1.55234e-05
 -1.15828e-05
 9.48717e-05
 -8.80914e-20
 -3.38813e-21
 -9.48717e-05
 -3.88084e-06
 1.94042e-06
 -2.89571e-06
 1.44785e-06
 1.2282e-20
 1.01648e-05
 3.88084e-06
 1.94042e-06
 2.89571e-06
 1.44785e-06
 -6.88214e-21
 -7.41154e-22
 -0.000191133
 -0.000774883
 -0.000774883
 -0.000196309
 3.18554e-05
 4.55078e-06
 3.18554e-05
 4.55078e-06
 0.000129147
 -1.56701e-20
 3.27182e-05
 -4.67402e-06
 3.27182e-05
 -4.67402e-06
 -1.82031e-05
 -1.86961e-05
 9.91029e-20
 0.000129147
 -0.000129147
 -5.0822e-21
 -4.55078e-06
 -2.27539e-06
 4.55078e-06
 2.27539e-06
 -1.56701e-20
 1.38372e-05
 -4.67402e-06
 2.33701e-06
 4.67402e-06
 -2.33701e-06
 7.51742e-21
 -8.47033e-22
 -0.000746206
 -0.000196309
 -0.000746206
 -0.000176794
 3.27182e-05
 -4.67402e-06
 0.000124368
 1.56701e-20
 2.94656e-05
 -4.20938e-06
 3.27182e-05
 4.67402e-06
 2.94656e-05
 -4.20938e-06
 -1.86961e-05
 -1.68375e-05
 0.000124368
 -1.0842e-19
 -0.000124368
 -5.0822e-21
 -4.67402e-06
 2.33701e-06
 1.56701e-20
 1.33251e-05
 -4.20938e-06
 2.10469e-06
 4.67402e-06
 2.33701e-06
 4.20938e-06
 -2.10469e-06
 -8.36445e-21
 -8.47033e-22
 -0.000162995
 -0.000679579
 -0.000176794
 -0.000679579
 2.71659e-05
 3.88084e-06
 2.71659e-05
 3.88084e-06
 2.94656e-05
 -4.20938e-06
 0.000113263
 2.71051e-20
 2.94656e-05
 4.20938e-06
 -1.55234e-05
 -1.68375e-05
 -8.21622e-20
 0.000113263
 -9.65618e-20
 -0.000113263
 -3.88084e-06
 -1.94042e-06
 3.88084e-06
 1.94042e-06
 -4.20938e-06
 2.10469e-06
 2.71051e-20
 1.21353e-05
 4.20938e-06
 2.10469e-06
 -6.56451e-21
 -7.51742e-21
 -0.000203324
 -0.000824034
 -0.000824034
 -0.000208694
 3.38873e-05
 4.84104e-06
 3.38873e-05
 4.84104e-06
 0.000137339
 -1.52466e-20
 3.47823e-05
 -4.9689e-06
 3.47823e-05
 -4.9689e-06
 -1.93641e-05
 -1.98756e-05
 1.04185e-19
 0.000137339
 -0.000137339
 -6.77626e-21
 -4.84104e-06
 -2.42052e-06
 4.84104e-06
 2.42052e-06
 -1.52466e-20
 1.47149e-05
 -4.9689e-06
 2.48445e-06
 4.9689e-06
 -2.48445e-06
 8.04681e-21
 -1.05879e-21
 -0.000196309
 -0.00080647
 -0.00080647
 -0.000206926
 3.27182e-05
 4.67402e-06
 3.27182e-05
 4.67402e-06
 0.000134412
 2.96462e-20
 3.44877e-05
 -4.92681e-06
 3.44877e-05
 -4.92681e-06
 -1.86961e-05
 -1.97072e-05
 -1.00797e-19
 0.000134412
 -0.000134412
 -1.10114e-19
 -4.67402e-06
 -2.33701e-06
 4.67402e-06
 2.33701e-06
 2.96462e-20
 1.44012e-05
 -4.92681e-06
 2.4634e-06
 4.92681e-06
 -2.4634e-06
 -7.6233e-21
 -8.99973e-21
 -0.000831239
 -0.000208694
 -0.000206926
 -0.000831239
 3.47823e-05
 -4.9689e-06
 3.44877e-05
 -4.92681e-06
 0.00013854
 1.52466e-20
 3.47823e-05
 4.9689e-06
 3.44877e-05
 4.92681e-06
 -1.98756e-05
 -1.97072e-05
 0.00013854
 -1.13502e-19
 -1.69407e-21
 -0.00013854
 -4.9689e-06
 2.48445e-06
 -4.92681e-06
 2.4634e-06
 1.52466e-20
 1.48436e-05
 4.9689e-06
 2.48445e-06
 4.92681e-06
 2.4634e-06
 -8.99973e-21
 -1.05879e-21
 -0.000225631
 -0.000830281
 -0.000830281
 -0.00018951
 3.76051e-05
 5.37216e-06
 3.76051e-05
 5.37216e-06
 0.00013838
 -1.69407e-20
 3.1585e-05
 -4.51214e-06
 3.1585e-05
 -4.51214e-06
 -2.14886e-05
 -1.80486e-05
 1.15196e-19
 0.00013838
 -0.00013838
 -5.0822e-21
 -5.37216e-06
 -2.68608e-06
 5.37216e-06
 2.68608e-06
 -1.69407e-20
 1.48265e-05
 -4.51214e-06
 2.25607e-06
 4.51214e-06
 -2.25607e-06
 9.1056e-21
 -8.47033e-22
 -0.000208694
 -0.00078644
 -0.00078644
 -0.000184526
 3.47823e-05
 4.9689e-06
 3.47823e-05
 4.9689e-06
 0.000131073
 3.04932e-20
 3.07544e-05
 -4.39349e-06
 3.07544e-05
 -4.39349e-06
 -1.98756e-05
 -1.75739e-05
 -1.0842e-19
 0.000131073
 -0.000131073
 -1.01644e-19
 -4.9689e-06
 -2.48445e-06
 4.9689e-06
 2.48445e-06
 3.04932e-20
 1.40436e-05
 -4.39349e-06
 2.19674e-06
 4.39349e-06
 -2.19674e-06
 -8.15269e-21
 -7.94093e-21
 -0.000748073
 -0.00018951
 -0.000184526
 -0.000748073
 3.1585e-05
 -4.51214e-06
 3.07544e-05
 -4.39349e-06
 0.000124679
 1.43996e-20
 3.1585e-05
 4.51214e-06
 3.07544e-05
 4.39349e-06
 -1.80486e-05
 -1.75739e-05
 0.000124679
 -1.03338e-19
 -3.38813e-21
 -0.000124679
 -4.51214e-06
 2.25607e-06
 -4.39349e-06
 2.19674e-06
 1.43996e-20
 1.33584e-05
 4.51214e-06
 2.25607e-06
 4.39349e-06
 2.19674e-06
 -8.04681e-21
 -8.47033e-22
 -0.000319578
 -0.00107022
 -0.00107022
 -0.000215533
 5.32629e-05
 7.60899e-06
 5.32629e-05
 7.60899e-06
 0.00017837
 -2.49875e-20
 3.59221e-05
 -5.13173e-06
 3.59221e-05
 -5.13173e-06
 -2.05269e-05
 -3.0436e-05
 1.64324e-19
 0.00017837
 -0.00017837
 -6.77626e-21
 -7.60899e-06
 -3.8045e-06
 7.60899e-06
 3.8045e-06
 -2.49875e-20
 1.91111e-05
 -5.13173e-06
 2.56587e-06
 5.13173e-06
 -2.56587e-06
 -1.27055e-21
 1.24937e-20
 -0.00018951
 -0.000810085
 -0.000215533
 -0.000810085
 3.1585e-05
 4.51214e-06
 3.1585e-05
 4.51214e-06
 3.59221e-05
 -5.13173e-06
 0.000135014
 3.21873e-20
 3.59221e-05
 5.13173e-06
 -1.80486e-05
 -2.05269e-05
 -9.65618e-20
 0.000135014
 -1.15196e-19
 -0.000135014
 -4.51214e-06
 -2.25607e-06
 4.51214e-06
 2.25607e-06
 -5.13173e-06
 2.56587e-06
 3.21873e-20
 1.44658e-05
 5.13173e-06
 2.56587e-06
 -7.30566e-21
 -9.31736e-21
 -0.000307692
 -0.00129359
 -0.00129359
 -0.000339102
 5.1282e-05
 7.326e-06
 5.1282e-05
 7.326e-06
 0.000215598
 4.74338e-20
 5.65171e-05
 -8.07387e-06
 5.65171e-05
 -8.07387e-06
 -2.9304e-05
 -3.22955e-05
 -1.57548e-19
 0.000215598
 -0.000215598
 -1.86347e-19
 -7.326e-06
 -3.663e-06
 7.326e-06
 3.663e-06
 4.74338e-20
 2.30998e-05
 -8.07387e-06
 4.03693e-06
 8.07387e-06
 -4.03693e-06
 -1.20702e-20
 -1.48231e-20
 -0.000276238
 -0.00112098
 -0.00112098
 -0.000284254
 4.60396e-05
 6.57709e-06
 4.60396e-05
 6.57709e-06
 0.000186831
 -2.37169e-20
 4.73757e-05
 -6.76796e-06
 4.73757e-05
 -6.76796e-06
 -2.63083e-05
 -2.70718e-05
 1.42302e-19
 0.000186831
 -0.000186831
 -6.77626e-21
 -6.57709e-06
 -3.28854e-06
 6.57709e-06
 3.28854e-06
 -2.37169e-20
 2.00176e-05
 -6.76796e-06
 3.38398e-06
 6.76796e-06
 -3.38398e-06
 1.12232e-20
 -1.27055e-21
 -0.001364
 -0.000339102
 -0.001364
 -0.0003429
 5.65171e-05
 -8.07387e-06
 0.000227334
 2.5411e-20
 5.71499e-05
 -8.16428e-06
 5.65171e-05
 8.07387e-06
 5.71499e-05
 -8.16428e-06
 -3.22955e-05
 -3.26571e-05
 0.000227334
 -1.35525e-20
 -0.000227334
 -1.89735e-19
 -8.07387e-06
 4.03693e-06
 2.5411e-20
 2.43572e-05
 -8.16428e-06
 4.08214e-06
 8.07387e-06
 4.03693e-06
 8.16428e-06
 -4.08214e-06
 -2.11758e-21
 -1.52466e-20
 -0.00125431
 -0.000284254
 -0.0003429
 -0.00125431
 4.73757e-05
 -6.76796e-06
 5.71499e-05
 -8.16428e-06
 0.000209051
 2.28699e-20
 4.73757e-05
 6.76796e-06
 5.71499e-05
 8.16428e-06
 -3.26571e-05
 -2.70718e-05
 0.000209051
 -1.52466e-19
 -3.38813e-21
 -0.000209051
 -6.76796e-06
 3.38398e-06
 -8.16428e-06
 4.08214e-06
 2.28699e-20
 2.23984e-05
 6.76796e-06
 3.38398e-06
 8.16428e-06
 4.08214e-06
 -2.11758e-21
 -1.20702e-20
 -0.000215533
 -0.000928338
 -0.000928338
 -0.000248636
 3.59221e-05
 5.13173e-06
 3.59221e-05
 5.13173e-06
 0.000154723
 3.47284e-20
 4.14394e-05
 -5.91991e-06
 4.14394e-05
 -5.91991e-06
 -2.05269e-05
 -2.36796e-05
 -1.11808e-19
 0.000154723
 -0.000154723
 -1.35525e-19
 -5.13173e-06
 -2.56587e-06
 5.13173e-06
 2.56587e-06
 3.47284e-20
 1.65775e-05
 -5.91991e-06
 2.95996e-06
 5.91991e-06
 -2.95996e-06
 -8.57621e-21
 -1.06938e-20
 -0.000339102
 -0.00117548
 -0.000248636
 -0.00117548
 5.65171e-05
 8.07387e-06
 5.65171e-05
 8.07387e-06
 4.14394e-05
 -5.91991e-06
 0.000195913
 -2.49875e-20
 4.14394e-05
 5.91991e-06
 -2.36796e-05
 -3.22955e-05
 1.71101e-19
 0.000195913
 -3.38813e-21
 -0.000195913
 -8.07387e-06
 -4.03693e-06
 8.07387e-06
 4.03693e-06
 -5.91991e-06
 2.95996e-06
 -2.49875e-20
 2.09907e-05
 5.91991e-06
 2.95996e-06
 -1.05879e-21
 1.3129e-20
 -0.000181748
 -0.000737581
 -0.000737581
 -0.000187043
 3.02913e-05
 4.32733e-06
 3.02913e-05
 4.32733e-06
 0.00012293
 -1.35525e-20
 3.11738e-05
 -4.45339e-06
 3.11738e-05
 -4.45339e-06
 -1.73093e-05
 -1.78136e-05
 9.31736e-20
 0.00012293
 -0.00012293
 -6.77626e-21
 -4.32733e-06
 -2.16366e-06
 4.32733e-06
 2.16366e-06
 -1.35525e-20
 1.31711e-05
 -4.45339e-06
 2.2267e-06
 4.45339e-06
 -2.2267e-06
 6.98802e-21
 -6.35275e-22
 -0.000230062
 -0.000932079
 -0.000932079
 -0.000235978
 3.83436e-05
 5.47766e-06
 3.83436e-05
 5.47766e-06
 0.000155347
 3.55754e-20
 3.93297e-05
 -5.61852e-06
 3.93297e-05
 -5.61852e-06
 -2.19106e-05
 -2.24741e-05
 -1.16891e-19
 0.000155347
 -0.000155347
 -1.30443e-19
 -5.47766e-06
 -2.73883e-06
 5.47766e-06
 2.73883e-06
 3.55754e-20
 1.66443e-05
 -5.61852e-06
 2.80926e-06
 5.61852e-06
 -2.80926e-06
 -9.21148e-21
 -1.01644e-20
 -0.000807427
 -0.000187043
 -0.000807427
 -0.000216671
 3.11738e-05
 -4.45339e-06
 0.000134571
 1.3976e-20
 3.61118e-05
 -5.15883e-06
 3.11738e-05
 4.45339e-06
 3.61118e-05
 -5.15883e-06
 -1.78136e-05
 -2.06353e-05
 0.000134571
 -9.99499e-20
 -0.000134571
 -6.77626e-21
 -4.45339e-06
 2.2267e-06
 1.3976e-20
 1.44183e-05
 -5.15883e-06
 2.57941e-06
 4.45339e-06
 2.2267e-06
 5.15883e-06
 -2.57941e-06
 -8.15269e-21
 -8.47033e-22
 -0.000905298
 -0.000235978
 -0.000216671
 -0.000905298
 3.93297e-05
 -5.61852e-06
 3.61118e-05
 -5.15883e-06
 0.000150883
 1.60936e-20
 3.93297e-05
 5.61852e-06
 3.61118e-05
 5.15883e-06
 -2.06353e-05
 -2.24741e-05
 0.000150883
 -5.0822e-21
 -1.18585e-19
 -0.000150883
 -5.61852e-06
 2.80926e-06
 -5.15883e-06
 2.57941e-06
 1.60936e-20
 1.6166e-05
 5.61852e-06
 2.80926e-06
 5.15883e-06
 2.57941e-06
 -9.21148e-21
 -1.48231e-21
 -0.00012189
 -0.000491397
 -0.000491397
 -0.000123809
 2.0315e-05
 2.90214e-06
 2.0315e-05
 2.90214e-06
 8.18995e-05
 -1.01644e-20
 2.06348e-05
 -2.94783e-06
 2.06348e-05
 -2.94783e-06
 -1.16086e-05
 -1.17913e-05
 6.09864e-20
 8.18995e-05
 -8.18995e-05
 -1.69407e-21
 -2.90214e-06
 -1.45107e-06
 2.90214e-06
 1.45107e-06
 -1.01644e-20
 8.77495e-06
 -2.94783e-06
 1.47391e-06
 2.94783e-06
 -1.47391e-06
 4.87044e-21
 -5.29396e-22
 -0.000583806
 -0.000123809
 -0.000583806
 -0.000168094
 2.06348e-05
 -2.94783e-06
 9.7301e-05
 8.89385e-21
 2.80157e-05
 -4.00224e-06
 2.06348e-05
 2.94783e-06
 2.80157e-05
 -4.00224e-06
 -1.17913e-05
 -1.6009e-05
 9.7301e-05
 -6.86097e-20
 -9.7301e-05
 -5.0822e-21
 -2.94783e-06
 1.47391e-06
 8.89385e-21
 1.04251e-05
 -4.00224e-06
 2.00112e-06
 2.94783e-06
 1.47391e-06
 4.00224e-06
 -2.00112e-06
 -5.24102e-21
 -4.23516e-22
 -0.000187043
 -0.000710274
 -0.000168094
 -0.000710274
 3.11738e-05
 4.45339e-06
 3.11738e-05
 4.45339e-06
 2.80157e-05
 -4.00224e-06
 0.000118379
 2.6258e-20
 2.80157e-05
 4.00224e-06
 -1.6009e-05
 -1.78136e-05
 -9.57147e-20
 0.000118379
 -8.97855e-20
 -0.000118379
 -4.45339e-06
 -2.2267e-06
 4.45339e-06
 2.2267e-06
 -4.00224e-06
 2.00112e-06
 2.6258e-20
 1.26835e-05
 4.00224e-06
 2.00112e-06
 -6.98802e-21
 -7.30566e-21
 -0.00012074
 -0.000123809
 -0.000489097
 -0.000489097
 2.01233e-05
 2.87476e-06
 2.01233e-05
 2.87476e-06
 2.06348e-05
 2.94783e-06
 2.06348e-05
 2.94783e-06
 8.15162e-05
 -1.69407e-21
 -1.1499e-05
 -1.17913e-05
 6.18334e-20
 -6.26804e-20
 8.15162e-05
 -8.15162e-05
 -2.87476e-06
 -1.43738e-06
 2.87476e-06
 1.43738e-06
 -2.94783e-06
 -1.47391e-06
 2.94783e-06
 1.47391e-06
 -1.69407e-21
 8.73388e-06
 4.71162e-21
 -4.76456e-21
 -0.000177538
 -0.000724903
 -0.000724903
 -0.000184914
 2.95896e-05
 4.22708e-06
 2.95896e-05
 4.22708e-06
 0.000120817
 2.71051e-20
 3.0819e-05
 -4.40272e-06
 3.0819e-05
 -4.40272e-06
 -1.69083e-05
 -1.76109e-05
 -9.23266e-20
 0.000120817
 -0.000120817
 -1.01644e-19
 -4.22708e-06
 -2.11354e-06
 4.22708e-06
 2.11354e-06
 2.71051e-20
 1.29447e-05
 -4.40272e-06
 2.20136e-06
 4.40272e-06
 -2.20136e-06
 -6.77626e-21
 -8.15269e-21
 -0.000219128
 -0.000896555
 -0.000896555
 -0.00022915
 3.65213e-05
 5.21733e-06
 3.65213e-05
 5.21733e-06
 0.000149426
 -1.65171e-20
 3.81916e-05
 -5.45595e-06
 3.81916e-05
 -5.45595e-06
 -2.08693e-05
 -2.18238e-05
 1.11808e-19
 0.000149426
 -0.000149426
 -6.77626e-21
 -5.21733e-06
 -2.60866e-06
 5.21733e-06
 2.60866e-06
 -1.65171e-20
 1.60099e-05
 -5.45595e-06
 2.72797e-06
 5.45595e-06
 -2.72797e-06
 8.57621e-21
 -1.05879e-21
 -0.000797275
 -0.000184914
 -0.000797275
 -0.000213723
 3.0819e-05
 -4.40272e-06
 0.000132879
 1.60936e-20
 3.56206e-05
 -5.08865e-06
 3.0819e-05
 4.40272e-06
 3.56206e-05
 -5.08865e-06
 -1.76109e-05
 -2.03546e-05
 0.000132879
 -6.77626e-21
 -0.000132879
 -1.15196e-19
 -4.40272e-06
 2.20136e-06
 1.60936e-20
 1.42371e-05
 -5.08865e-06
 2.54433e-06
 4.40272e-06
 2.20136e-06
 5.08865e-06
 -2.54433e-06
 -1.05879e-21
 -9.1056e-21
 -0.000885746
 -0.00022915
 -0.000213723
 -0.000885746
 3.81916e-05
 -5.45595e-06
 3.56206e-05
 -5.08865e-06
 0.000147624
 1.69407e-20
 3.81916e-05
 5.45595e-06
 3.56206e-05
 5.08865e-06
 -2.18238e-05
 -2.03546e-05
 0.000147624
 -1.25361e-19
 -5.0822e-21
 -0.000147624
 -5.45595e-06
 2.72797e-06
 -5.08865e-06
 2.54433e-06
 1.69407e-20
 1.58169e-05
 5.45595e-06
 2.72797e-06
 5.08865e-06
 2.54433e-06
 -9.84676e-21
 -8.47033e-22
 -0.000168094
 -0.000184914
 -0.000706017
 -0.000706017
 2.80157e-05
 4.00224e-06
 2.80157e-05
 4.00224e-06
 3.0819e-05
 4.40272e-06
 3.0819e-05
 4.40272e-06
 0.000117669
 -1.69407e-21
 -1.6009e-05
 -1.76109e-05
 -8.63974e-20
 9.23266e-20
 0.000117669
 -0.000117669
 -4.00224e-06
 -2.00112e-06
 4.00224e-06
 2.00112e-06
 -4.40272e-06
 -2.20136e-06
 4.40272e-06
 2.20136e-06
 -1.69407e-21
 1.26074e-05
 -6.56451e-21
 6.98802e-21
 -0.00025468
 -0.00105325
 -0.00105325
 -0.000271945
 4.24466e-05
 6.0638e-06
 4.24466e-05
 6.0638e-06
 0.000175541
 -2.03288e-20
 4.53241e-05
 -6.47487e-06
 4.53241e-05
 -6.47487e-06
 -2.42552e-05
 -2.58995e-05
 1.33831e-19
 0.000175541
 -0.000175541
 -6.77626e-21
 -6.0638e-06
 -3.0319e-06
 6.0638e-06
 3.0319e-06
 -2.03288e-20
 1.8808e-05
 -6.47487e-06
 3.23744e-06
 6.47487e-06
 -3.23744e-06
 1.01644e-20
 -8.47033e-22
 -0.00022915
 -0.000977174
 -0.000977174
 -0.000259437
 3.81916e-05
 5.45595e-06
 3.81916e-05
 5.45595e-06
 0.000162862
 3.55754e-20
 4.32396e-05
 -6.17708e-06
 4.32396e-05
 -6.17708e-06
 -2.18238e-05
 -2.47083e-05
 -1.20279e-19
 0.000162862
 -0.000162862
 -1.40607e-19
 -5.45595e-06
 -2.72797e-06
 5.45595e-06
 2.72797e-06
 3.55754e-20
 1.74495e-05
 -6.17708e-06
 3.08854e-06
 6.17708e-06
 -3.08854e-06
 -9.21148e-21
 -1.13291e-20
 -0.00106276
 -0.000271945
 -0.000259437
 -0.00106276
 4.53241e-05
 -6.47487e-06
 4.32396e-05
 -6.17708e-06
 0.000177127
 2.03288e-20
 4.53241e-05
 6.47487e-06
 4.32396e-05
 6.17708e-06
 -2.58995e-05
 -2.47083e-05
 0.000177127
 -1.47384e-19
 -8.47033e-21
 -0.000177127
 -6.47487e-06
 3.23744e-06
 -6.17708e-06
 3.08854e-06
 2.03288e-20
 1.89779e-05
 6.47487e-06
 3.23744e-06
 6.17708e-06
 3.08854e-06
 -1.14349e-20
 -1.27055e-21
 -0.000264574
 -0.0011791
 -0.0011791
 -0.000324975
 4.40956e-05
 6.29938e-06
 4.40956e-05
 6.29938e-06
 0.000196516
 -1.86347e-20
 5.41625e-05
 -7.7375e-06
 5.41625e-05
 -7.7375e-06
 -2.51975e-05
 -3.095e-05
 1.37219e-19
 0.000196516
 -0.000196516
 -1.01644e-20
 -6.29938e-06
 -3.14969e-06
 6.29938e-06
 3.14969e-06
 -1.86347e-20
 2.10553e-05
 -7.7375e-06
 3.86875e-06
 7.7375e-06
 -3.86875e-06
 1.07997e-20
 -1.69407e-21
 -0.00134505
 -0.000324975
 -0.00134505
 -0.000347549
 5.41625e-05
 -7.7375e-06
 0.000224174
 2.5411e-20
 5.79248e-05
 -8.27497e-06
 5.41625e-05
 7.7375e-06
 5.79248e-05
 -8.27497e-06
 -3.095e-05
 -3.30999e-05
 0.000224174
 -1.76183e-19
 -0.000224174
 -1.01644e-20
 -7.7375e-06
 3.86875e-06
 2.5411e-20
 2.40187e-05
 -8.27497e-06
 4.13748e-06
 7.7375e-06
 3.86875e-06
 8.27497e-06
 -4.13748e-06
 -1.37643e-20
 -8.47033e-22
 -0.000271945
 -0.00123899
 -0.000347549
 -0.00123899
 4.53241e-05
 6.47487e-06
 4.53241e-05
 6.47487e-06
 5.79248e-05
 -8.27497e-06
 0.000206498
 5.0822e-20
 5.79248e-05
 8.27497e-06
 -2.58995e-05
 -3.30999e-05
 -1.37219e-19
 0.000206498
 -1.88041e-19
 -0.000206498
 -6.47487e-06
 -3.23744e-06
 6.47487e-06
 3.23744e-06
 -8.27497e-06
 4.13748e-06
 5.0822e-20
 2.21248e-05
 8.27497e-06
 4.13748e-06
 -1.05879e-20
 -1.48231e-20
 -0.000310157
 -0.000324975
 -0.00127026
 -0.00127026
 5.16929e-05
 7.3847e-06
 5.16929e-05
 7.3847e-06
 5.41625e-05
 7.7375e-06
 5.41625e-05
 7.7375e-06
 0.000211711
       0
 -2.95388e-05
 -3.095e-05
 1.60936e-19
 -1.69407e-19
 0.000211711
 -0.000211711
 -7.3847e-06
 -3.69235e-06
 7.3847e-06
 3.69235e-06
 -7.7375e-06
 -3.86875e-06
 7.7375e-06
 3.86875e-06
       0
 2.26833e-05
 1.2282e-20
 -1.24937e-20
 -0.000338559
 -0.00137542
 -0.00137542
 -0.00034915
 5.64265e-05
 8.06093e-06
 5.64265e-05
 8.06093e-06
 0.000229237
 5.2516e-20
 5.81917e-05
 -8.3131e-06
 5.81917e-05
 -8.3131e-06
 -3.22437e-05
 -3.32524e-05
 -1.72795e-19
 0.000229237
 -0.000229237
 -1.89735e-19
 -8.06093e-06
 -4.03047e-06
 8.06093e-06
 4.03047e-06
 5.2516e-20
 2.45611e-05
 -8.3131e-06
 4.15655e-06
 8.3131e-06
 -4.15655e-06
 -1.3129e-20
 -1.46113e-20
 -0.000246654
 -0.00100378
 -0.00100378
 -0.000255238
 4.1109e-05
 5.87271e-06
 4.1109e-05
 5.87271e-06
 0.000167297
 -1.86347e-20
 4.25397e-05
 -6.07711e-06
 4.25397e-05
 -6.07711e-06
 -2.34909e-05
 -2.43084e-05
 1.23667e-19
 0.000167297
 -0.000167297
 -5.0822e-21
 -5.87271e-06
 -2.93636e-06
 5.87271e-06
 2.93636e-06
 -1.86347e-20
 1.79247e-05
 -6.07711e-06
 3.03855e-06
 6.07711e-06
 -3.03855e-06
 9.84676e-21
 -8.47033e-22
 -0.00108652
 -0.000255238
 -0.00108652
 -0.000288021
 4.25397e-05
 -6.07711e-06
 0.000181086
 1.94818e-20
 4.80035e-05
 -6.85764e-06
 4.25397e-05
 6.07711e-06
 4.80035e-05
 -6.85764e-06
 -2.43084e-05
 -2.74305e-05
 0.000181086
 -1.37219e-19
 -0.000181086
       0
 -6.07711e-06
 3.03855e-06
 1.94818e-20
 1.94021e-05
 -6.85764e-06
 3.42882e-06
 6.07711e-06
 3.03855e-06
 6.85764e-06
 -3.42882e-06
 -1.11173e-20
 -1.69407e-21
 -0.00127434
 -0.00034915
 -0.000288021
 -0.00127434
 5.81917e-05
 -8.3131e-06
 4.80035e-05
 -6.85764e-06
 0.00021239
 2.28699e-20
 5.81917e-05
 8.3131e-06
 4.80035e-05
 6.85764e-06
 -3.32524e-05
 -2.74305e-05
 0.00021239
 -1.35525e-20
 -1.57548e-19
 -0.00021239
 -8.3131e-06
 4.15655e-06
 -6.85764e-06
 3.42882e-06
 2.28699e-20
 2.27561e-05
 8.3131e-06
 4.15655e-06
 6.85764e-06
 3.42882e-06
 -2.11758e-21
 -1.17526e-20
 -0.00034915
 -0.0014165
 -0.0014165
 -0.000359102
 5.81917e-05
 8.3131e-06
 5.81917e-05
 8.3131e-06
 0.000236084
 -2.5411e-20
 5.98503e-05
 -8.55004e-06
 5.98503e-05
 -8.55004e-06
 -3.32524e-05
 -3.42001e-05
 1.76183e-19
 0.000236084
 -0.000236084
 -1.01644e-20
 -8.3131e-06
 -4.15655e-06
 8.3131e-06
 4.15655e-06
 -2.5411e-20
 2.52947e-05
 -8.55004e-06
 4.27502e-06
 8.55004e-06
 -4.27502e-06
 1.27055e-20
 -1.27055e-21
 -0.000347549
 -0.0014133
 -0.000359102
 -0.0014133
 5.79248e-05
 8.27497e-06
 5.79248e-05
 8.27497e-06
 5.98503e-05
 -8.55004e-06
 0.00023555
 5.42101e-20
 5.98503e-05
 8.55004e-06
 -3.30999e-05
 -3.42001e-05
 -1.79571e-19
 0.00023555
 -1.96512e-19
 -0.00023555
 -8.27497e-06
 -4.13748e-06
 8.27497e-06
 4.13748e-06
 -8.55004e-06
 4.27502e-06
 5.42101e-20
 2.52375e-05
 8.55004e-06
 4.27502e-06
 -1.35525e-20
 -1.50348e-20
 -0.000187798
 -0.000762667
 -0.000762667
 -0.000193535
 3.12997e-05
 4.47139e-06
 3.12997e-05
 4.47139e-06
 0.000127111
 -1.3129e-20
 3.22559e-05
 -4.60798e-06
 3.22559e-05
 -4.60798e-06
 -1.78856e-05
 -1.84319e-05
 9.40207e-20
 0.000127111
 -0.000127111
 -3.38813e-21
 -4.47139e-06
 -2.2357e-06
 4.47139e-06
 2.2357e-06
 -1.3129e-20
 1.36191e-05
 -4.60798e-06
 2.30399e-06
 4.60798e-06
 -2.30399e-06
 6.98802e-21
 -1.05879e-21
 -0.000842482
 -0.000193535
 -0.000842482
 -0.000227706
 3.22559e-05
 -4.60798e-06
 0.000140414
 1.52466e-20
 3.7951e-05
 -5.42157e-06
 3.22559e-05
 4.60798e-06
 3.7951e-05
 -5.42157e-06
 -1.84319e-05
 -2.16863e-05
 0.000140414
 -1.03338e-19
 -0.000140414
 -3.38813e-21
 -4.60798e-06
 2.30399e-06
 1.52466e-20
 1.50443e-05
 -5.42157e-06
 2.71078e-06
 4.60798e-06
 2.30399e-06
 5.42157e-06
 -2.71078e-06
 -8.47033e-21
 -8.47033e-22
 -0.000255238
 -0.000965889
 -0.000227706
 -0.000965889
 4.25397e-05
 6.07711e-06
 4.25397e-05
 6.07711e-06
 3.7951e-05
 -5.42157e-06
 0.000160981
 3.72694e-20
 3.7951e-05
 5.42157e-06
 -2.43084e-05
 -2.16863e-05
 -1.30443e-19
 0.000160981
 -1.21973e-19
 -0.000160981
 -6.07711e-06
 -3.03855e-06
 6.07711e-06
 3.03855e-06
 -5.42157e-06
 2.71078e-06
 3.72694e-20
 1.7248e-05
 5.42157e-06
 2.71078e-06
 -1.01644e-20
 -9.74088e-21
 -0.000124032
 -0.000499211
 -0.000499211
 -0.000125574
 2.0672e-05
 2.95314e-06
 2.0672e-05
 2.95314e-06
 8.32019e-05
 -1.03762e-20
 2.09289e-05
 -2.98985e-06
 2.09289e-05
 -2.98985e-06
 -1.18126e-05
 -1.19594e-05
 6.35275e-20
 8.32019e-05
 -8.32019e-05
 -2.5411e-21
 -2.95314e-06
 -1.47657e-06
 2.95314e-06
 1.47657e-06
 -1.03762e-20
 8.91449e-06
 -2.98985e-06
 1.49492e-06
 2.98985e-06
 -1.49492e-06
 4.76456e-21
 -5.29396e-22
 -0.000594818
 -0.000125574
 -0.000594818
 -0.000171835
 2.09289e-05
 -2.98985e-06
 9.91363e-05
 9.74088e-21
 2.86392e-05
 -4.09131e-06
 2.09289e-05
 2.98985e-06
 2.86392e-05
 -4.09131e-06
 -1.19594e-05
 -1.63653e-05
 9.91363e-05
 -6.86097e-20
 -9.91363e-05
 -3.38813e-21
 -2.98985e-06
 1.49492e-06
 9.74088e-21
 1.06217e-05
 -4.09131e-06
 2.04566e-06
 2.98985e-06
 1.49492e-06
 4.09131e-06
 -2.04566e-06
 -5.24102e-21
 -4.23516e-22
 -0.000193535
 -0.000730741
 -0.000171835
 -0.000730741
 3.22559e-05
 4.60798e-06
 3.22559e-05
 4.60798e-06
 2.86392e-05
 -4.09131e-06
 0.00012179
 2.71051e-20
 2.86392e-05
 4.09131e-06
 -1.84319e-05
 -1.63653e-05
 -9.99499e-20
 0.00012179
 -9.23266e-20
 -0.00012179
 -4.60798e-06
 -2.30399e-06
 4.60798e-06
 2.30399e-06
 -4.09131e-06
 2.04566e-06
 2.71051e-20
 1.30489e-05
 4.09131e-06
 2.04566e-06
 -7.51742e-21
 -7.51742e-21
 -0.00012162
 -0.000125574
 -0.000494387
 -0.000494387
 2.02699e-05
 2.89571e-06
 2.02699e-05
 2.89571e-06
 2.09289e-05
 2.98985e-06
 2.09289e-05
 2.98985e-06
 8.23978e-05
 1.69407e-21
 -1.15828e-05
 -1.19594e-05
 6.09864e-20
 -6.52215e-20
 8.23978e-05
 -8.23978e-05
 -2.89571e-06
 -1.44785e-06
 2.89571e-06
 1.44785e-06
 -2.98985e-06
 -1.49492e-06
 2.98985e-06
 1.49492e-06
 1.69407e-21
 8.82833e-06
 4.76456e-21
 -4.87044e-21
 -0.000176794
 -0.000727963
 -0.000727963
 -0.000187188
 2.94656e-05
 4.20938e-06
 2.94656e-05
 4.20938e-06
 0.000121327
 2.87991e-20
 3.1198e-05
 -4.45685e-06
 3.1198e-05
 -4.45685e-06
 -1.68375e-05
 -1.78274e-05
 -9.14796e-20
 0.000121327
 -0.000121327
 -1.03338e-19
 -4.20938e-06
 -2.10469e-06
 4.20938e-06
 2.10469e-06
 2.87991e-20
 1.29993e-05
 -4.45685e-06
 2.22843e-06
 4.45685e-06
 -2.22843e-06
 -6.77626e-21
 -7.94093e-21
 -0.000206926
 -0.000863691
 -0.000863691
 -0.000224919
 3.44877e-05
 4.92681e-06
 3.44877e-05
 4.92681e-06
 0.000143948
 -1.52466e-20
 3.74866e-05
 -5.35522e-06
 3.74866e-05
 -5.35522e-06
 -1.97072e-05
 -2.14209e-05
 1.02491e-19
 0.000143948
 -0.000143948
 -6.77626e-21
 -4.92681e-06
 -2.4634e-06
 4.92681e-06
 2.4634e-06
 -1.52466e-20
 1.5423e-05
 -5.35522e-06
 2.67761e-06
 5.35522e-06
 -2.67761e-06
 8.25857e-21
 -1.05879e-21
 -0.000812706
 -0.000187188
 -0.000812706
 -0.000219165
 3.1198e-05
 -4.45685e-06
 0.000135451
 1.60936e-20
 3.65275e-05
 -5.21822e-06
 3.1198e-05
 4.45685e-06
 3.65275e-05
 -5.21822e-06
 -1.78274e-05
 -2.08729e-05
 0.000135451
 -1.69407e-21
 -0.000135451
 -1.18585e-19
 -4.45685e-06
 2.22843e-06
 1.60936e-20
 1.45126e-05
 -5.21822e-06
 2.60911e-06
 4.45685e-06
 2.22843e-06
 5.21822e-06
 -2.60911e-06
 -1.27055e-21
 -9.52912e-21
 -0.000888169
 -0.000224919
 -0.000219165
 -0.000888169
 3.74866e-05
 -5.35522e-06
 3.65275e-05
 -5.21822e-06
 0.000148028
 1.69407e-20
 3.74866e-05
 5.35522e-06
 3.65275e-05
 5.21822e-06
 -2.14209e-05
 -2.08729e-05
 0.000148028
 -1.25361e-19
 -3.38813e-21
 -0.000148028
 -5.35522e-06
 2.67761e-06
 -5.21822e-06
 2.60911e-06
 1.69407e-20
 1.58602e-05
 5.35522e-06
 2.67761e-06
 5.21822e-06
 2.60911e-06
 -9.84676e-21
 -8.47033e-22
 -0.000171835
 -0.000187188
 -0.000718046
 -0.000718046
 2.86392e-05
 4.09131e-06
 2.86392e-05
 4.09131e-06
 3.1198e-05
 4.45685e-06
 3.1198e-05
 4.45685e-06
 0.000119674
 -8.47033e-22
 -1.63653e-05
 -1.78274e-05
 -8.89385e-20
 9.74088e-20
 0.000119674
 -0.000119674
 -4.09131e-06
 -2.04566e-06
 4.09131e-06
 2.04566e-06
 -4.45685e-06
 -2.22843e-06
 4.45685e-06
 2.22843e-06
 -8.47033e-22
 1.28223e-05
 -7.19978e-21
 7.30566e-21
 -0.000184526
 -0.000827574
 -0.000827574
 -0.000229261
 3.07544e-05
 4.39349e-06
 3.07544e-05
 4.39349e-06
 0.000137929
 -1.43996e-20
 3.82101e-05
 -5.45859e-06
 3.82101e-05
 -5.45859e-06
 -1.75739e-05
 -2.18344e-05
 9.48677e-20
 0.000137929
 -0.000137929
 -3.38813e-21
 -4.39349e-06
 -2.19674e-06
 4.39349e-06
 2.19674e-06
 -1.43996e-20
 1.47781e-05
 -5.45859e-06
 2.72929e-06
 5.45859e-06
 -2.72929e-06
 7.41154e-21
 -1.05879e-21
 -0.00103639
 -0.000229261
 -0.00103639
 -0.000288933
 3.82101e-05
 -5.45859e-06
 0.000172731
 1.69407e-20
 4.81555e-05
 -6.87936e-06
 3.82101e-05
 5.45859e-06
 4.81555e-05
 -6.87936e-06
 -2.18344e-05
 -2.75175e-05
 0.000172731
 -1.21973e-19
 -0.000172731
 -6.77626e-21
 -5.45859e-06
 2.72929e-06
 1.69407e-20
 1.85069e-05
 -6.87936e-06
 3.43968e-06
 5.45859e-06
 2.72929e-06
 6.87936e-06
 -3.43968e-06
 -9.95264e-21
 -1.69407e-21
 -0.000224919
 -0.00102771
 -0.000288933
 -0.00102771
 3.74866e-05
 5.35522e-06
 3.74866e-05
 5.35522e-06
 4.81555e-05
 -6.87936e-06
 0.000171284
 3.89635e-20
 4.81555e-05
 6.87936e-06
 -2.14209e-05
 -2.75175e-05
 -1.16891e-19
 0.000171284
 -1.59242e-19
 -0.000171284
 -5.35522e-06
 -2.67761e-06
 5.35522e-06
 2.67761e-06
 -6.87936e-06
 3.43968e-06
 3.89635e-20
 1.83519e-05
 6.87936e-06
 3.43968e-06
 -8.89385e-21
 -1.24937e-20
 -0.000248636
 -0.000229261
 -0.000955794
 -0.000955794
 4.14394e-05
 5.91991e-06
 4.14394e-05
 5.91991e-06
 3.82101e-05
 5.45859e-06
 3.82101e-05
 5.45859e-06
 0.000159299
 -3.38813e-21
 -2.36796e-05
 -2.18344e-05
 1.27055e-19
 -1.15196e-19
 0.000159299
 -0.000159299
 -5.91991e-06
 -2.95996e-06
 5.91991e-06
 2.95996e-06
 -5.45859e-06
 -2.72929e-06
 5.45859e-06
 2.72929e-06
 -3.38813e-21
 1.70677e-05
 9.52912e-21
 -9.31736e-21
 -0.000235978
 -0.00100581
 -0.00100581
 -0.000266926
 3.93297e-05
 5.61852e-06
 3.93297e-05
 5.61852e-06
 0.000167635
 -1.69407e-20
 4.44877e-05
 -6.35538e-06
 4.44877e-05
 -6.35538e-06
 -2.24741e-05
 -2.54215e-05
 1.20279e-19
 0.000167635
 -0.000167635
 -5.0822e-21
 -5.61852e-06
 -2.80926e-06
 5.61852e-06
 2.80926e-06
 -1.69407e-20
 1.79609e-05
 -6.35538e-06
 3.17769e-06
 6.35538e-06
 -3.17769e-06
 8.89385e-21
 -1.27055e-21
 -0.000284254
 -0.00110236
 -0.000266926
 -0.00110236
 4.73757e-05
 6.76796e-06
 4.73757e-05
 6.76796e-06
 4.44877e-05
 -6.35538e-06
 0.000183727
 4.23516e-20
 4.44877e-05
 6.35538e-06
 -2.70718e-05
 -2.54215e-05
 -1.47384e-19
 0.000183727
 -1.4569e-19
 -0.000183727
 -6.76796e-06
 -3.38398e-06
 6.76796e-06
 3.38398e-06
 -6.35538e-06
 3.17769e-06
 4.23516e-20
 1.9685e-05
 6.35538e-06
 3.17769e-06
 -1.10114e-20
 -1.15408e-20
 -0.000213723
 -0.000883712
 -0.000883712
 -0.000228133
 3.56206e-05
 5.08865e-06
 3.56206e-05
 5.08865e-06
 0.000147285
 -1.77877e-20
 3.80221e-05
 -5.43173e-06
 3.80221e-05
 -5.43173e-06
 -2.03546e-05
 -2.17269e-05
 1.06726e-19
 0.000147285
 -0.000147285
 -6.77626e-21
 -5.08865e-06
 -2.54433e-06
 5.08865e-06
 2.54433e-06
 -1.77877e-20
 1.57806e-05
 -5.43173e-06
 2.71586e-06
 5.43173e-06
 -2.71586e-06
 8.47033e-21
 -1.27055e-21
 -0.000216671
 -0.000889607
 -0.000228133
 -0.000889607
 3.61118e-05
 5.15883e-06
 3.61118e-05
 5.15883e-06
 3.80221e-05
 -5.43173e-06
 0.000148268
 3.38813e-20
 3.80221e-05
 5.43173e-06
 -2.06353e-05
 -2.17269e-05
 -1.10114e-19
 0.000148268
 -1.25361e-19
 -0.000148268
 -5.15883e-06
 -2.57941e-06
 5.15883e-06
 2.57941e-06
 -5.43173e-06
 2.71586e-06
 3.38813e-20
 1.58858e-05
 5.43173e-06
 2.71586e-06
 -8.36445e-21
 -9.52912e-21
 -0.000259437
 -0.00106302
 -0.00106302
 -0.000272073
 4.32396e-05
 6.17708e-06
 4.32396e-05
 6.17708e-06
 0.00017717
 -2.20229e-20
 4.53455e-05
 -6.47793e-06
 4.53455e-05
 -6.47793e-06
 -2.47083e-05
 -2.59117e-05
 1.32137e-19
 0.00017717
 -0.00017717
 -1.01644e-20
 -6.17708e-06
 -3.08854e-06
 6.17708e-06
 3.08854e-06
 -2.20229e-20
 1.89825e-05
 -6.47793e-06
 3.23897e-06
 6.47793e-06
 -3.23897e-06
 9.84676e-21
 -1.27055e-21
 -0.000228133
 -0.00096883
 -0.00096883
 -0.000256283
 3.80221e-05
 5.43173e-06
 3.80221e-05
 5.43173e-06
 0.000161472
 3.72694e-20
 4.27138e-05
 -6.10197e-06
 4.27138e-05
 -6.10197e-06
 -2.17269e-05
 -2.44079e-05
 -1.15196e-19
 0.000161472
 -0.000161472
 -1.38913e-19
 -5.43173e-06
 -2.71586e-06
 5.43173e-06
 2.71586e-06
 3.72694e-20
 1.73005e-05
 -6.10197e-06
 3.05098e-06
 6.10197e-06
 -3.05098e-06
 -8.57621e-21
 -1.10114e-20
 -0.00105671
 -0.000272073
 -0.000256283
 -0.00105671
 4.53455e-05
 -6.47793e-06
 4.27138e-05
 -6.10197e-06
 0.000176119
 1.94818e-20
 4.53455e-05
 6.47793e-06
 4.27138e-05
 6.10197e-06
 -2.59117e-05
 -2.44079e-05
 0.000176119
 -1.49078e-19
 -1.18585e-20
 -0.000176119
 -6.47793e-06
 3.23897e-06
 -6.10197e-06
 3.05098e-06
 1.94818e-20
 1.88698e-05
 6.47793e-06
 3.23897e-06
 6.10197e-06
 3.05098e-06
 -1.18585e-20
 -1.27055e-21
 -0.000227706
 -0.000934968
 -0.000934968
 -0.000239778
 3.7951e-05
 5.42157e-06
 3.7951e-05
 5.42157e-06
 0.000155828
 3.64224e-20
 3.9963e-05
 -5.709e-06
 3.9963e-05
 -5.709e-06
 -2.16863e-05
 -2.2836e-05
 -1.16891e-19
 0.000155828
 -0.000155828
 -1.30443e-19
 -5.42157e-06
 -2.71078e-06
 5.42157e-06
 2.71078e-06
 3.64224e-20
 1.66959e-05
 -5.709e-06
 2.8545e-06
 5.709e-06
 -2.8545e-06
 -8.99973e-21
 -1.0482e-20
 -0.000219165
 -0.000917886
 -0.000239778
 -0.000917886
 3.65275e-05
 5.21822e-06
 3.65275e-05
 5.21822e-06
 3.9963e-05
 -5.709e-06
 0.000152981
 -1.73642e-20
 3.9963e-05
 5.709e-06
 -2.08729e-05
 -2.2836e-05
 1.13502e-19
 0.000152981
 -6.77626e-21
 -0.000152981
 -5.21822e-06
 -2.60911e-06
 5.21822e-06
 2.60911e-06
 -5.709e-06
 2.8545e-06
 -1.73642e-20
 1.63908e-05
 5.709e-06
 2.8545e-06
 8.57621e-21
 -1.27055e-21
 -0.000288021
 -0.00116049
 -0.00116049
 -0.000292224
 4.80035e-05
 6.85764e-06
 4.80035e-05
 6.85764e-06
 0.000193415
 4.23516e-20
 4.87041e-05
 -6.95773e-06
 4.87041e-05
 -6.95773e-06
 -2.74305e-05
 -2.78309e-05
 -1.49078e-19
 0.000193415
 -0.000193415
 -1.60936e-19
 -6.85764e-06
 -3.42882e-06
 6.85764e-06
 3.42882e-06
 4.23516e-20
 2.0723e-05
 -6.95773e-06
 3.47886e-06
 6.95773e-06
 -3.47886e-06
 -1.14349e-20
 -1.27055e-20
 -0.000239778
 -0.00102684
 -0.00102684
 -0.000273641
 3.9963e-05
 5.709e-06
 3.9963e-05
 5.709e-06
 0.00017114
 -1.82112e-20
 4.56069e-05
 -6.51527e-06
 4.56069e-05
 -6.51527e-06
 -2.2836e-05
 -2.60611e-05
 1.23667e-19
 0.00017114
 -0.00017114
 -8.47033e-21
 -5.709e-06
 -2.8545e-06
 5.709e-06
 2.8545e-06
 -1.82112e-20
 1.83364e-05
 -6.51527e-06
 3.25763e-06
 6.51527e-06
 -3.25763e-06
 9.635e-21
 -1.27055e-21
 -0.00113173
 -0.000292224
 -0.000273641
 -0.00113173
 4.87041e-05
 -6.95773e-06
 4.56069e-05
 -6.51527e-06
 0.000188622
 2.11758e-20
 4.87041e-05
 6.95773e-06
 4.56069e-05
 6.51527e-06
 -2.60611e-05
 -2.78309e-05
 0.000188622
 -3.38813e-21
 -1.47384e-19
 -0.000188622
 -6.95773e-06
 3.47886e-06
 -6.51527e-06
 3.25763e-06
 2.11758e-20
 2.02095e-05
 6.95773e-06
 3.47886e-06
 6.51527e-06
 3.25763e-06
 -1.16467e-20
 -2.11758e-21
 -0.000359102
 -0.00131411
 -0.00131411
 -0.000297952
 5.98503e-05
 8.55004e-06
 5.98503e-05
 8.55004e-06
 0.000219018
 5.2516e-20
 4.96587e-05
 -7.0941e-06
 4.96587e-05
 -7.0941e-06
 -3.42001e-05
 -2.83764e-05
 -1.82959e-19
 0.000219018
 -0.000219018
 -1.59242e-19
 -8.55004e-06
 -4.27502e-06
 8.55004e-06
 4.27502e-06
 5.2516e-20
 2.34662e-05
 -7.0941e-06
 3.54705e-06
 7.0941e-06
 -3.54705e-06
 -1.35525e-20
 -1.3129e-20
 -0.000292224
 -0.00118756
 -0.00118756
 -0.000301553
 4.87041e-05
 6.95773e-06
 4.87041e-05
 6.95773e-06
 0.000197926
 -2.5411e-20
 5.02589e-05
 -7.17984e-06
 5.02589e-05
 -7.17984e-06
 -2.78309e-05
 -2.87193e-05
 1.5416e-19
 0.000197926
 -0.000197926
       0
 -6.95773e-06
 -3.47886e-06
 6.95773e-06
 3.47886e-06
 -2.5411e-20
 2.12063e-05
 -7.17984e-06
 3.58992e-06
 7.17984e-06
 -3.58992e-06
 1.12232e-20
 -1.69407e-21
 -0.00119901
 -0.000297952
 -0.000301553
 -0.00119901
 4.96587e-05
 -7.0941e-06
 5.02589e-05
 -7.17984e-06
 0.000199835
 2.4564e-20
 4.96587e-05
 7.0941e-06
 5.02589e-05
 7.17984e-06
 -2.83764e-05
 -2.87193e-05
 0.000199835
 -1.35525e-20
 -1.64324e-19
 -0.000199835
 -7.0941e-06
 3.54705e-06
 -7.17984e-06
 3.58992e-06
 2.4564e-20
 2.14109e-05
 7.0941e-06
 3.54705e-06
 7.17984e-06
 3.58992e-06
 -2.11758e-21
 -1.35525e-20
 -0.000272073
 -0.000297952
 -0.00114005
 -0.00114005
 4.53455e-05
 6.47793e-06
 4.53455e-05
 6.47793e-06
 4.96587e-05
 7.0941e-06
 4.96587e-05
 7.0941e-06
 0.000190008
 -1.69407e-21
 -2.59117e-05
 -2.83764e-05
 -1.38913e-19
 1.50772e-19
 0.000190008
 -0.000190008
 -6.47793e-06
 -3.23897e-06
 6.47793e-06
 3.23897e-06
 -7.0941e-06
 -3.54705e-06
 7.0941e-06
 3.54705e-06
 -1.69407e-21
 2.0358e-05
 -1.05879e-20
 1.16467e-20
 -0.000288933
 -0.00122255
 -0.00122255
 -0.000322343
 4.81555e-05
 6.87936e-06
 4.81555e-05
 6.87936e-06
 0.000203759
 4.40457e-20
 5.37238e-05
 -7.67483e-06
 5.37238e-05
 -7.67483e-06
 -2.75175e-05
 -3.06993e-05
 -1.4569e-19
 0.000203759
 -0.000203759
 -1.74489e-19
 -6.87936e-06
 -3.43968e-06
 6.87936e-06
 3.43968e-06
 4.40457e-20
 2.18313e-05
 -7.67483e-06
 3.83741e-06
 7.67483e-06
 -3.83741e-06
 -1.14349e-20
 -1.3976e-20
 -0.0003429
 -0.00136582
 -0.00136582
 -0.000340011
 5.71499e-05
 8.16428e-06
 5.71499e-05
 8.16428e-06
 0.000227637
 -2.71051e-20
 5.66684e-05
 -8.09549e-06
 5.66684e-05
 -8.09549e-06
 -3.26571e-05
 -3.2382e-05
 1.77877e-19
 0.000227637
 -0.000227637
 -6.77626e-21
 -8.16428e-06
 -4.08214e-06
 8.16428e-06
 4.08214e-06
 -2.71051e-20
 2.43897e-05
 -8.09549e-06
 4.04775e-06
 8.09549e-06
 -4.04775e-06
 1.3129e-20
 -2.11758e-21
 -0.00132471
 -0.000322343
 -0.000340011
 -0.00132471
 5.37238e-05
 -7.67483e-06
 5.66684e-05
 -8.09549e-06
 0.000220784
 2.6258e-20
 5.37238e-05
 7.67483e-06
 5.66684e-05
 8.09549e-06
 -3.06993e-05
 -3.2382e-05
 0.000220784
 -1.01644e-20
 -1.84653e-19
 -0.000220784
 -7.67483e-06
 3.83741e-06
 -8.09549e-06
 4.04775e-06
 2.6258e-20
 2.36555e-05
 7.67483e-06
 3.83741e-06
 8.09549e-06
 4.04775e-06
 -1.27055e-21
 -1.43996e-20
 -0.000273641
 -0.000322343
 -0.00119197
 -0.00119197
 4.56069e-05
 6.51527e-06
 4.56069e-05
 6.51527e-06
 5.37238e-05
 7.67483e-06
 5.37238e-05
 7.67483e-06
 0.000198661
 -5.0822e-21
 -2.60611e-05
 -3.06993e-05
 -1.38913e-19
 1.6263e-19
 0.000198661
 -0.000198661
 -6.51527e-06
 -3.25763e-06
 6.51527e-06
 3.25763e-06
 -7.67483e-06
 -3.83741e-06
 7.67483e-06
 3.83741e-06
 -5.0822e-21
 2.12851e-05
 -1.07997e-20
 1.29173e-20
 -0.000266926
 -0.00108349
 -0.00108349
 -0.000274818
 4.44877e-05
 6.35538e-06
 4.44877e-05
 6.35538e-06
 0.000180581
 4.23516e-20
 4.5803e-05
 -6.54328e-06
 4.5803e-05
 -6.54328e-06
 -2.54215e-05
 -2.61731e-05
 -1.35525e-19
 0.000180581
 -0.000180581
 -1.52466e-19
 -6.35538e-06
 -3.17769e-06
 6.35538e-06
 3.17769e-06
 4.23516e-20
 1.9348e-05
 -6.54328e-06
 3.27164e-06
 6.54328e-06
 -3.27164e-06
 -1.03762e-20
 -1.16467e-20
 -0.000256283
 -0.0010622
 -0.000274818
 -0.0010622
 4.27138e-05
 6.10197e-06
 4.27138e-05
 6.10197e-06
 4.5803e-05
 -6.54328e-06
 0.000177033
 -2.24464e-20
 4.5803e-05
 6.54328e-06
 -2.44079e-05
 -2.61731e-05
 1.27055e-19
 0.000177033
 -5.0822e-21
 -0.000177033
 -6.10197e-06
 -3.05098e-06
 6.10197e-06
 3.05098e-06
 -6.54328e-06
 3.27164e-06
 -2.24464e-20
 1.89679e-05
 6.54328e-06
 3.27164e-06
 1.01644e-20
 -1.69407e-21
 -0.000340011
 -0.00127269
 -0.00127269
 -0.000296336
 5.66684e-05
 8.09549e-06
 5.66684e-05
 8.09549e-06
 0.000212115
 4.65868e-20
 4.93893e-05
 -7.05561e-06
 4.93893e-05
 -7.05561e-06
 -3.2382e-05
 -2.82225e-05
 -1.76183e-19
 0.000212115
 -0.000212115
 -1.6263e-19
 -8.09549e-06
 -4.04775e-06
 8.09549e-06
 4.04775e-06
 4.65868e-20
 2.27267e-05
 -7.05561e-06
 3.52781e-06
 7.05561e-06
 -3.52781e-06
 -1.29173e-20
 -1.3129e-20
 -0.000274818
 -0.00114231
 -0.000296336
 -0.00114231
 4.5803e-05
 6.54328e-06
 4.5803e-05
 6.54328e-06
 4.93893e-05
 -7.05561e-06
 0.000190385
 -2.20229e-20
 4.93893e-05
 7.05561e-06
 -2.61731e-05
 -2.82225e-05
 1.37219e-19
 0.000190385
 -1.01644e-20
 -0.000190385
 -6.54328e-06
 -3.27164e-06
 6.54328e-06
 3.27164e-06
 -7.05561e-06
 3.52781e-06
 -2.20229e-20
 2.03983e-05
 7.05561e-06
 3.52781e-06
 1.07997e-20
 -1.27055e-21
 -0.000301553
 -0.000296336
 -0.00119578
 -0.00119578
 5.02589e-05
 7.17984e-06
 5.02589e-05
 7.17984e-06
 4.93893e-05
 7.05561e-06
 4.93893e-05
 7.05561e-06
 0.000199296
       0
 -2.87193e-05
 -2.82225e-05
 -1.55854e-19
 1.52466e-19
 0.000199296
 -0.000199296
 -7.17984e-06
 -3.58992e-06
 7.17984e-06
 3.58992e-06
 -7.05561e-06
 -3.52781e-06
 7.05561e-06
 3.52781e-06
       0
 2.13532e-05
 -1.18585e-20
 1.18585e-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
 0.000222579
 0.000222579
 0.000222579
 -3.1797e-05
 -1.69407e-21
 -3.1797e-05
 -1.43996e-20
 -3.1797e-05
 -1.3129e-20
 1.58985e-05
 0.0001884
 0.0001884
 0.0001884
 -2.69143e-05
 -8.47033e-22
 -2.69143e-05
 -1.20702e-20
 -2.69143e-05
 -1.12232e-20
 1.34572e-05
 0.000254738
 0.000254738
 0.000254738
 -3.63912e-05
 -1.63054e-20
 -3.63912e-05
 -1.69407e-21
 -3.63912e-05
 1.43996e-20
 1.81956e-05
 0.00016988
 0.00016988
 0.00016988
 -2.42686e-05
 -1.27055e-21
 -2.42686e-05
 -1.10114e-20
 -2.42686e-05
 -1.05879e-20
 1.21343e-05
 0.000192868
 0.000192868
 0.000192868
 -2.75526e-05
 -1.28114e-20
 -2.75526e-05
 -1.27055e-21
 -2.75526e-05
 1.18585e-20
 1.37763e-05
 0.00015294
 0.00015294
 0.00015294
 -2.18485e-05
 -8.47033e-22
 -2.18485e-05
 -9.84676e-21
 -2.18485e-05
 -9.42324e-21
 1.09243e-05
 0.000164711
 0.000164711
 0.000164711
 -2.35301e-05
 -1.06938e-20
 -2.35301e-05
 -1.27055e-21
 -2.35301e-05
 1.00585e-20
 1.1765e-05
 0.000136951
 0.000136951
 0.000136951
 -1.95644e-05
 -8.47033e-22
 -1.95644e-05
 -8.89385e-21
 -1.95644e-05
 -8.04681e-21
 9.7822e-06
 0.000139588
 0.000139588
 0.000139588
 -1.99411e-05
 -9.21148e-21
 -1.99411e-05
 -1.27055e-21
 -1.99411e-05
 8.47033e-21
 9.97055e-06
 0.000125911
 0.000125911
 0.000125911
 -1.79873e-05
 -8.47033e-22
 -1.79873e-05
 -8.15269e-21
 -1.79873e-05
 -7.6233e-21
 8.99365e-06
 0.000115249
 0.000115249
 0.000115249
 -1.64641e-05
 -7.30566e-21
 -1.64641e-05
 -8.47033e-22
 -1.64641e-05
 6.98802e-21
 8.23204e-06
 0.000138392
 0.000138392
 0.000138392
 -1.97703e-05
 -9.1056e-21
 -1.97703e-05
 -8.47033e-22
 -1.97703e-05
 8.89385e-21
 9.88517e-06
 0.000111275
 0.000111275
 0.000111275
 -1.58965e-05
 -7.51742e-21
 -1.58965e-05
 -8.47033e-22
 -1.58965e-05
 6.77626e-21
 7.94825e-06
 0.000136251
 0.000136251
 0.000136251
 -1.94644e-05
 -6.35275e-22
 -1.94644e-05
 -8.89385e-21
 -1.94644e-05
 -8.04681e-21
 9.73218e-06
 0.000121597
 0.000121597
 0.000121597
 -1.7371e-05
 -6.35275e-22
 -1.7371e-05
 -7.6233e-21
 -1.7371e-05
 -6.88214e-21
 8.6855e-06
 0.000110052
 0.000110052
 0.000110052
 -1.57218e-05
 -7.30566e-21
 -1.57218e-05
 -1.05879e-21
 -1.57218e-05
 6.45863e-21
 7.86088e-06
 0.000129599
 0.000129599
 0.000129599
 -1.85141e-05
 -6.35275e-22
 -1.85141e-05
 -8.15269e-21
 -1.85141e-05
 -7.83505e-21
 9.25706e-06
 0.000111353
 0.000111353
 0.000111353
 -1.59076e-05
 -7.30566e-21
 -1.59076e-05
 -1.05879e-21
 -1.59076e-05
 6.45863e-21
 7.95379e-06
 0.000140511
 0.000140511
 0.000140511
 -2.0073e-05
 -1.05879e-21
 -2.0073e-05
 -9.1056e-21
 -2.0073e-05
 -8.47033e-21
 1.00365e-05
 0.000131571
 0.000131571
 0.000131571
 -1.87958e-05
 -8.57621e-21
 -1.87958e-05
 -1.05879e-21
 -1.87958e-05
 7.6233e-21
 9.39789e-06
 0.000149037
 0.000149037
 0.000149037
 -2.1291e-05
 -1.05879e-21
 -2.1291e-05
 -9.52912e-21
 -2.1291e-05
 -8.89385e-21
 1.06455e-05
 0.000148752
 0.000148752
 0.000148752
 -2.12503e-05
 -9.74088e-21
 -2.12503e-05
 -1.05879e-21
 -2.12503e-05
 8.78797e-21
 1.06251e-05
 0.000151889
 0.000151889
 0.000151889
 -2.16984e-05
 -1.05879e-21
 -2.16984e-05
 -9.31736e-21
 -2.16984e-05
 -8.47033e-21
 1.08492e-05
 0.000158733
 0.000158733
 0.000158733
 -2.26761e-05
 -1.05879e-20
 -2.26761e-05
 -1.48231e-21
 -2.26761e-05
 9.52912e-21
 1.13381e-05
 0.000148061
 0.000148061
 0.000148061
 -2.11516e-05
 -1.27055e-21
 -2.11516e-05
 -9.52912e-21
 -2.11516e-05
 -8.47033e-21
 1.05758e-05
 0.000159054
 0.000159054
 0.000159054
 -2.2722e-05
 -1.0482e-20
 -2.2722e-05
 -1.27055e-21
 -2.2722e-05
 9.21148e-21
 1.1361e-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
 0.000142225
 0.000142225
 0.000142225
 -2.03179e-05
 -1.27055e-21
 -2.03179e-05
 -8.99973e-21
 -2.03179e-05
 -8.47033e-21
 1.0159e-05
 0.000163802
 0.000163802
 0.000163802
 -2.34003e-05
 -8.47033e-22
 -2.34003e-05
 -1.02703e-20
 -2.34003e-05
 -9.42324e-21
 1.17001e-05
 0.00013
 0.00013
 0.00013
 -1.85715e-05
 -8.57621e-21
 -1.85715e-05
 -1.05879e-21
 -1.85715e-05
 7.72918e-21
 9.28574e-06
 0.000168736
 0.000168736
 0.000168736
 -2.41052e-05
 -1.27055e-21
 -2.41052e-05
 -1.09055e-20
 -2.41052e-05
 -9.95264e-21
 1.20526e-05
 0.000171291
 0.000171291
 0.000171291
 -2.44701e-05
 -1.12232e-20
 -2.44701e-05
 -1.27055e-21
 -2.44701e-05
 1.01644e-20
 1.2235e-05
 0.000155558
 0.000155558
 0.000155558
 -2.22226e-05
 -8.47033e-22
 -2.22226e-05
 -9.84676e-21
 -2.22226e-05
 -8.99973e-21
 1.11113e-05
 0.000167615
 0.000167615
 0.000167615
 -2.39451e-05
 -1.10114e-20
 -2.39451e-05
 -1.48231e-21
 -2.39451e-05
 9.95264e-21
 1.19725e-05
 0.000139233
 0.000139233
 0.000139233
 -1.98904e-05
 -1.27055e-21
 -1.98904e-05
 -8.99973e-21
 -1.98904e-05
 -7.83505e-21
 9.94521e-06
 0.000143394
 0.000143394
 0.000143394
 -2.04849e-05
 -9.42324e-21
 -2.04849e-05
 -1.27055e-21
 -2.04849e-05
 8.57621e-21
 1.02425e-05
 0.00012745
 0.00012745
 0.00012745
 -1.82072e-05
 -1.05879e-21
 -1.82072e-05
 -8.15269e-21
 -1.82072e-05
 -7.41154e-21
 9.1036e-06
 0.000117489
 0.000117489
 0.000117489
 -1.67841e-05
 -7.41154e-21
 -1.67841e-05
 -1.05879e-21
 -1.67841e-05
 6.77626e-21
 8.39206e-06
 0.00013935
 0.00013935
 0.00013935
 -1.99071e-05
 -8.99973e-21
 -1.99071e-05
 -1.05879e-21
 -1.99071e-05
 7.83505e-21
 9.95355e-06
 0.000112519
 0.000112519
 0.000112519
 -1.60742e-05
 -7.30566e-21
 -1.60742e-05
 -4.23516e-22
 -1.60742e-05
 6.45863e-21
 8.03711e-06
 0.000136482
 0.000136482
 0.000136482
 -1.94974e-05
 -8.47033e-22
 -1.94974e-05
 -8.68209e-21
 -1.94974e-05
 -7.51742e-21
 9.74872e-06
 0.000121413
 0.000121413
 0.000121413
 -1.73448e-05
 -8.47033e-22
 -1.73448e-05
 -7.72918e-21
 -1.73448e-05
 -6.98802e-21
 8.67239e-06
 0.000110665
 0.000110665
 0.000110665
 -1.58093e-05
 -7.30566e-21
 -1.58093e-05
 -6.35275e-22
 -1.58093e-05
 6.77626e-21
 7.90464e-06
 0.000128237
 0.000128237
 0.000128237
 -1.83196e-05
 -8.47033e-22
 -1.83196e-05
 -8.36445e-21
 -1.83196e-05
 -7.41154e-21
 9.15978e-06
 0.000110749
 0.000110749
 0.000110749
 -1.58213e-05
 -7.19978e-21
 -1.58213e-05
 -6.35275e-22
 -1.58213e-05
 6.67038e-21
 7.91067e-06
 0.000136353
 0.000136353
 0.000136353
 -1.9479e-05
 -8.47033e-22
 -1.9479e-05
 -8.68209e-21
 -1.9479e-05
 -7.94093e-21
 9.73948e-06
 0.000127422
 0.000127422
 0.000127422
 -1.82031e-05
 -8.25857e-21
 -1.82031e-05
 -8.47033e-22
 -1.82031e-05
 7.51742e-21
 9.10155e-06
 0.000140892
 0.000140892
 0.000140892
 -2.01275e-05
 -1.27055e-21
 -2.01275e-05
 -8.99973e-21
 -2.01275e-05
 -8.04681e-21
 1.00637e-05
 0.000135549
 0.000135549
 0.000135549
 -1.93641e-05
 -8.89385e-21
 -1.93641e-05
 -1.05879e-21
 -1.93641e-05
 8.04681e-21
 9.68207e-06
 0.000158024
 0.000158024
 0.000158024
 -2.25748e-05
 -1.05879e-21
 -2.25748e-05
 -9.95264e-21
 -2.25748e-05
 -9.1056e-21
 1.12874e-05
 0.00015042
 0.00015042
 0.00015042
 -2.14886e-05
 -1.00585e-20
 -2.14886e-05
 -1.48231e-21
 -2.14886e-05
 9.1056e-21
 1.07443e-05
 0.00020647
 0.00020647
 0.00020647
 -2.94958e-05
 -1.69407e-21
 -2.94958e-05
 -1.37643e-20
 -2.94958e-05
 -1.2282e-20
 1.47479e-05
 0.000255438
 0.000255438
 0.000255438
 -3.64911e-05
 -1.65171e-20
 -3.64911e-05
 -1.69407e-21
 -3.64911e-05
 1.50348e-20
 1.82456e-05
 0.000211591
 0.000211591
 0.000211591
 -3.02273e-05
 -1.69407e-21
 -3.02273e-05
 -1.35525e-20
 -3.02273e-05
 -1.2282e-20
 1.51137e-05
 0.000166424
 0.000166424
 0.000166424
 -2.37749e-05
 -1.07997e-20
 -2.37749e-05
 -1.05879e-21
 -2.37749e-05
 9.635e-21
 1.18874e-05
 0.000222733
 0.000222733
 0.000222733
 -3.1819e-05
 -1.27055e-21
 -3.1819e-05
 -1.46113e-20
 -3.1819e-05
 -1.29173e-20
 1.59095e-05
 0.000193242
 0.000193242
 0.000193242
 -2.7606e-05
 -8.47033e-22
 -2.7606e-05
 -1.2282e-20
 -2.7606e-05
 -1.14349e-20
 1.3803e-05
 0.000233734
 0.000233734
 0.000233734
 -3.33905e-05
 -1.69407e-21
 -3.33905e-05
 -1.50348e-20
 -3.33905e-05
 -1.35525e-20
 1.66953e-05
 0.000205128
 0.000205128
 0.000205128
 -2.9304e-05
 -1.27055e-21
 -2.9304e-05
 -1.33408e-20
 -2.9304e-05
 -1.20702e-20
 1.4652e-05
 0.000139909
 0.000139909
 0.000139909
 -1.99871e-05
 -1.05879e-21
 -1.99871e-05
 -8.99973e-21
 -1.99871e-05
 -8.15269e-21
 9.99353e-06
 0.000111286
 0.000111286
 0.000111286
 -1.58979e-05
 -8.47033e-22
 -1.58979e-05
 -7.19978e-21
 -1.58979e-05
 -6.67038e-21
 7.94897e-06
 0.000121165
 0.000121165
 0.000121165
 -1.73093e-05
 -7.94093e-21
 -1.73093e-05
 -1.05879e-21
 -1.73093e-05
 6.98802e-21
 8.65466e-06
 8.34361e-05
 8.34361e-05
 8.34361e-05
 -1.19194e-05
 -5.29396e-22
 -1.19194e-05
 -5.29396e-21
 -1.19194e-05
 -5.0822e-21
 5.95972e-06
 8.12599e-05
 8.12599e-05
 8.12599e-05
 -1.16086e-05
 -5.24102e-21
 -1.16086e-05
 -6.35275e-22
 -1.16086e-05
 4.87044e-21
 5.80428e-06
 8.26611e-05
 8.26611e-05
 8.26611e-05
 -1.18087e-05
 -6.35275e-22
 -1.18087e-05
 -5.3469e-21
 -1.18087e-05
 -4.87044e-21
 5.90436e-06
 0.000133775
 0.000133775
 0.000133775
 -1.91107e-05
 -1.05879e-21
 -1.91107e-05
 -8.36445e-21
 -1.91107e-05
 -7.6233e-21
 9.55535e-06
 0.000108713
 0.000108713
 0.000108713
 -1.55304e-05
 -8.47033e-22
 -1.55304e-05
 -6.88214e-21
 -1.55304e-05
 -6.24687e-21
 7.76522e-06
 8.04932e-05
 8.04932e-05
 8.04932e-05
 -1.1499e-05
 -5.18808e-21
 -1.1499e-05
 -6.35275e-22
 -1.1499e-05
 4.71162e-21
 5.74951e-06
 0.000118358
 0.000118358
 0.000118358
 -1.69083e-05
 -6.35275e-22
 -1.69083e-05
 -7.51742e-21
 -1.69083e-05
 -6.77626e-21
 8.45417e-06
 0.000153221
 0.000153221
 0.000153221
 -2.18886e-05
 -8.47033e-22
 -2.18886e-05
 -9.95264e-21
 -2.18886e-05
 -9.31736e-21
 1.09443e-05
 0.000146085
 0.000146085
 0.000146085
 -2.08693e-05
 -9.52912e-21
 -2.08693e-05
 -1.48231e-21
 -2.08693e-05
 8.57621e-21
 1.04347e-05
 0.00016732
 0.00016732
 0.00016732
 -2.39029e-05
 -1.27055e-21
 -2.39029e-05
 -1.05879e-20
 -2.39029e-05
 -9.74088e-21
 1.19514e-05
 0.000169786
 0.000169786
 0.000169786
 -2.42552e-05
 -1.09055e-20
 -2.42552e-05
 -1.27055e-21
 -2.42552e-05
 1.01644e-20
 1.21276e-05
 0.000163414
 0.000163414
 0.000163414
 -2.33449e-05
 -8.47033e-22
 -2.33449e-05
 -1.05879e-20
 -2.33449e-05
 -9.74088e-21
 1.16724e-05
 0.000176383
 0.000176383
 0.000176383
 -2.51975e-05
 -1.17526e-20
 -2.51975e-05
 -1.27055e-21
 -2.51975e-05
 1.07997e-20
 1.25988e-05
 0.000138581
 0.000138581
 0.000138581
 -1.97972e-05
 -6.35275e-22
 -1.97972e-05
 -8.89385e-21
 -1.97972e-05
 -8.47033e-21
 9.89861e-06
 0.000176998
 0.000176998
 0.000176998
 -2.52855e-05
 -1.27055e-21
 -2.52855e-05
 -1.10114e-20
 -2.52855e-05
 -9.74088e-21
 1.26427e-05
 0.000214699
 0.000214699
 0.000214699
 -3.06713e-05
 -8.47033e-22
 -3.06713e-05
 -1.35525e-20
 -3.06713e-05
 -1.24937e-20
 1.53357e-05
 0.000225706
 0.000225706
 0.000225706
 -3.22437e-05
 -2.11758e-21
 -3.22437e-05
 -1.46113e-20
 -3.22437e-05
 -1.3129e-20
 1.61219e-05
 0.000138192
 0.000138192
 0.000138192
 -1.97417e-05
 -8.47033e-22
 -1.97417e-05
 -8.89385e-21
 -1.97417e-05
 -8.04681e-21
 9.87085e-06
 0.00014527
 0.00014527
 0.00014527
 -2.07529e-05
 -8.47033e-22
 -2.07529e-05
 -9.31736e-21
 -2.07529e-05
 -8.47033e-21
 1.03764e-05
 0.000164436
 0.000164436
 0.000164436
 -2.34909e-05
 -1.05879e-20
 -2.34909e-05
 -1.05879e-21
 -2.34909e-05
 9.84676e-21
 1.17454e-05
 0.000113669
 0.000113669
 0.000113669
 -1.62385e-05
 -8.47033e-22
 -1.62385e-05
 -7.19978e-21
 -1.62385e-05
 -6.56451e-21
 8.11923e-06
 0.000125199
 0.000125199
 0.000125199
 -1.78856e-05
 -8.15269e-21
 -1.78856e-05
 -1.05879e-21
 -1.78856e-05
 6.98802e-21
 8.94278e-06
 8.44343e-05
 8.44343e-05
 8.44343e-05
 -1.2062e-05
 -5.29396e-22
 -1.2062e-05
 -5.39984e-21
 -1.2062e-05
 -4.92338e-21
 6.03102e-06
 8.2688e-05
 8.2688e-05
 8.2688e-05
 -1.18126e-05
 -5.3469e-21
 -1.18126e-05
 -7.41154e-22
 -1.18126e-05
 4.76456e-21
 5.90628e-06
 8.3323e-05
 8.3323e-05
 8.3323e-05
 -1.19033e-05
 -5.29396e-22
 -1.19033e-05
 -5.24102e-21
 -1.19033e-05
 -4.87044e-21
 5.95164e-06
 0.000130873
 0.000130873
 0.000130873
 -1.86961e-05
 -8.47033e-22
 -1.86961e-05
 -8.36445e-21
 -1.86961e-05
 -7.6233e-21
 9.34805e-06
 0.000108664
 0.000108664
 0.000108664
 -1.55234e-05
 -6.35275e-22
 -1.55234e-05
 -6.88214e-21
 -1.55234e-05
 -6.56451e-21
 7.76169e-06
 8.10797e-05
 8.10797e-05
 8.10797e-05
 -1.15828e-05
 -5.29396e-21
 -1.15828e-05
 -7.41154e-22
 -1.15828e-05
 4.76456e-21
 5.79141e-06
 0.000117863
 0.000117863
 0.000117863
 -1.68375e-05
 -8.47033e-22
 -1.68375e-05
 -7.51742e-21
 -1.68375e-05
 -6.77626e-21
 8.41875e-06
 0.000139129
 0.000139129
 0.000139129
 -1.98756e-05
 -1.05879e-21
 -1.98756e-05
 -8.99973e-21
 -1.98756e-05
 -8.15269e-21
 9.93779e-06
 0.000137951
 0.000137951
 0.000137951
 -1.97072e-05
 -8.99973e-21
 -1.97072e-05
 -1.05879e-21
 -1.97072e-05
 8.25857e-21
 9.85362e-06
 0.00012634
 0.00012634
 0.00012634
 -1.80486e-05
 -8.47033e-22
 -1.80486e-05
 -8.04681e-21
 -1.80486e-05
 -7.30566e-21
 9.02428e-06
 0.000123018
 0.000123018
 0.000123018
 -1.75739e-05
 -7.94093e-21
 -1.75739e-05
 -8.47033e-22
 -1.75739e-05
 7.41154e-21
 8.78697e-06
 0.000165755
 0.000165755
 0.000165755
 -2.36793e-05
 -1.05879e-21
 -2.36793e-05
 -1.0482e-20
 -2.36793e-05
 -9.52912e-21
 1.18396e-05
 0.000184158
 0.000184158
 0.000184158
 -2.63083e-05
 -1.21761e-20
 -2.63083e-05
 -1.27055e-21
 -2.63083e-05
 1.12232e-20
 1.31542e-05
 0.000153374
 0.000153374
 0.000153374
 -2.19106e-05
 -1.05879e-21
 -2.19106e-05
 -1.00585e-20
 -2.19106e-05
 -9.21148e-21
 1.09553e-05
 0.000206772
 0.000206772
 0.000206772
 -2.95388e-05
 -1.33408e-20
 -2.95388e-05
 -1.69407e-21
 -2.95388e-05
 1.2282e-20
 1.47694e-05
 0.000143689
 0.000143689
 0.000143689
 -2.05269e-05
 -1.27055e-21
 -2.05269e-05
 -9.31736e-21
 -2.05269e-05
 -8.57621e-21
 1.02635e-05
 0.000213052
 0.000213052
 0.000213052
 -3.0436e-05
 -1.3976e-20
 -3.0436e-05
 -2.11758e-21
 -3.0436e-05
 1.24937e-20
 1.5218e-05
 8.25392e-05
 8.25392e-05
 8.25392e-05
 -1.17913e-05
 -5.29396e-22
 -1.17913e-05
 -5.24102e-21
 -1.17913e-05
 -4.76456e-21
 5.89566e-06
 0.000112063
 0.000112063
 0.000112063
 -1.6009e-05
 -4.23516e-22
 -1.6009e-05
 -6.98802e-21
 -1.6009e-05
 -6.56451e-21
 8.00449e-06
 0.000124695
 0.000124695
 0.000124695
 -1.78136e-05
 -6.35275e-22
 -1.78136e-05
 -8.15269e-21
 -1.78136e-05
 -7.30566e-21
 8.90679e-06
 0.00021665
 0.00021665
 0.00021665
 -3.095e-05
 -1.69407e-21
 -3.095e-05
 -1.37643e-20
 -3.095e-05
 -1.24937e-20
 1.5475e-05
 0.000152767
 0.000152767
 0.000152767
 -2.18238e-05
 -1.05879e-21
 -2.18238e-05
 -9.84676e-21
 -2.18238e-05
 -9.21148e-21
 1.09119e-05
 0.000129024
 0.000129024
 0.000129024
 -1.84319e-05
 -1.05879e-21
 -1.84319e-05
 -8.47033e-21
 -1.84319e-05
 -7.51742e-21
 9.21597e-06
 0.000170159
 0.000170159
 0.000170159
 -2.43084e-05
 -8.47033e-22
 -2.43084e-05
 -1.11173e-20
 -2.43084e-05
 -1.01644e-20
 1.21542e-05
 0.000151804
 0.000151804
 0.000151804
 -2.16863e-05
 -8.47033e-22
 -2.16863e-05
 -9.74088e-21
 -2.16863e-05
 -8.99973e-21
 1.08431e-05
 0.000232767
 0.000232767
 0.000232767
 -3.32524e-05
 -1.46113e-20
 -3.32524e-05
 -2.11758e-21
 -3.32524e-05
 1.27055e-20
 1.66262e-05
 0.000192014
 0.000192014
 0.000192014
 -2.74305e-05
 -1.69407e-21
 -2.74305e-05
 -1.17526e-20
 -2.74305e-05
 -1.14349e-20
 1.37153e-05
 0.000181296
 0.000181296
 0.000181296
 -2.58995e-05
 -8.47033e-22
 -2.58995e-05
 -1.14349e-20
 -2.58995e-05
 -1.05879e-20
 1.29497e-05
 0.000172958
 0.000172958
 0.000172958
 -2.47083e-05
 -1.13291e-20
 -2.47083e-05
 -1.27055e-21
 -2.47083e-05
 9.84676e-21
 1.23542e-05
 0.000231699
 0.000231699
 0.000231699
 -3.30999e-05
 -8.47033e-22
 -3.30999e-05
 -1.48231e-20
 -3.30999e-05
 -1.35525e-20
 1.65499e-05
 0.000165758
 0.000165758
 0.000165758
 -2.36796e-05
 -1.06938e-20
 -2.36796e-05
 -1.05879e-21
 -2.36796e-05
 9.52912e-21
 1.18398e-05
 0.000226068
 0.000226068
 0.000226068
 -3.22955e-05
 -1.48231e-20
 -3.22955e-05
 -2.11758e-21
 -3.22955e-05
 1.3129e-20
 1.61477e-05
 8.37158e-05
 8.37158e-05
 8.37158e-05
 -1.19594e-05
 -5.29396e-22
 -1.19594e-05
 -5.24102e-21
 -1.19594e-05
 -4.87044e-21
 5.9797e-06
 0.00015284
 0.00015284
 0.00015284
 -2.18344e-05
 -1.05879e-21
 -2.18344e-05
 -9.95264e-21
 -2.18344e-05
 -9.31736e-21
 1.09172e-05
 0.000149946
 0.000149946
 0.000149946
 -2.14209e-05
 -1.05879e-21
 -2.14209e-05
 -9.84676e-21
 -2.14209e-05
 -8.89385e-21
 1.07104e-05
 0.000114557
 0.000114557
 0.000114557
 -1.63653e-05
 -4.23516e-22
 -1.63653e-05
 -7.51742e-21
 -1.63653e-05
 -7.19978e-21
 8.18263e-06
 0.000239401
 0.000239401
 0.000239401
 -3.42001e-05
 -1.27055e-21
 -3.42001e-05
 -1.50348e-20
 -3.42001e-05
 -1.35525e-20
 1.71001e-05
 0.000123276
 0.000123276
 0.000123276
 -1.76109e-05
 -8.15269e-21
 -1.76109e-05
 -1.05879e-21
 -1.76109e-05
 6.98802e-21
 8.80544e-06
 0.000144447
 0.000144447
 0.000144447
 -2.06353e-05
 -8.47033e-22
 -2.06353e-05
 -9.21148e-21
 -2.06353e-05
 -8.36445e-21
 1.03177e-05
 0.000142482
 0.000142482
 0.000142482
 -2.03546e-05
 -9.1056e-21
 -2.03546e-05
 -8.47033e-22
 -2.03546e-05
 8.47033e-21
 1.01773e-05
 0.0002286
 0.0002286
 0.0002286
 -3.26571e-05
 -1.52466e-20
 -3.26571e-05
 -2.11758e-21
 -3.26571e-05
 1.3129e-20
 1.63286e-05
 0.000189503
 0.000189503
 0.000189503
 -2.70718e-05
 -1.27055e-21
 -2.70718e-05
 -1.20702e-20
 -2.70718e-05
 -1.10114e-20
 1.35359e-05
 0.000192622
 0.000192622
 0.000192622
 -2.75175e-05
 -1.69407e-21
 -2.75175e-05
 -1.24937e-20
 -2.75175e-05
 -1.14349e-20
 1.37587e-05
 0.000124792
 0.000124792
 0.000124792
 -1.78274e-05
 -7.94093e-21
 -1.78274e-05
 -1.27055e-21
 -1.78274e-05
 7.30566e-21
 8.91371e-06
 0.00014611
 0.00014611
 0.00014611
 -2.08729e-05
 -9.52912e-21
 -2.08729e-05
 -8.47033e-22
 -2.08729e-05
 8.57621e-21
 1.04364e-05
 0.000157319
 0.000157319
 0.000157319
 -2.24741e-05
 -1.01644e-20
 -2.24741e-05
 -1.48231e-21
 -2.24741e-05
 8.89385e-21
 1.1237e-05
 0.000159852
 0.000159852
 0.000159852
 -2.2836e-05
 -1.0482e-20
 -2.2836e-05
 -1.27055e-21
 -2.2836e-05
 9.635e-21
 1.1418e-05
 0.000182428
 0.000182428
 0.000182428
 -2.60611e-05
 -1.27055e-21
 -2.60611e-05
 -1.16467e-20
 -2.60611e-05
 -1.07997e-20
 1.30305e-05
 0.000152088
 0.000152088
 0.000152088
 -2.17269e-05
 -1.27055e-21
 -2.17269e-05
 -9.52912e-21
 -2.17269e-05
 -8.57621e-21
 1.08635e-05
 0.000181382
 0.000181382
 0.000181382
 -2.59117e-05
 -1.27055e-21
 -2.59117e-05
 -1.18585e-20
 -2.59117e-05
 -1.05879e-20
 1.29559e-05
 0.000170855
 0.000170855
 0.000170855
 -2.44079e-05
 -1.10114e-20
 -2.44079e-05
 -1.27055e-21
 -2.44079e-05
 1.01644e-20
 1.22039e-05
 0.000198635
 0.000198635
 0.000198635
 -2.83764e-05
 -1.3129e-20
 -2.83764e-05
 -2.11758e-21
 -2.83764e-05
 1.16467e-20
 1.41882e-05
 0.000194816
 0.000194816
 0.000194816
 -2.78309e-05
 -1.27055e-20
 -2.78309e-05
 -2.11758e-21
 -2.78309e-05
 1.12232e-20
 1.39155e-05
 0.000177951
 0.000177951
 0.000177951
 -2.54215e-05
 -1.27055e-21
 -2.54215e-05
 -1.15408e-20
 -2.54215e-05
 -1.03762e-20
 1.27108e-05
 0.000214895
 0.000214895
 0.000214895
 -3.06993e-05
 -1.3976e-20
 -3.06993e-05
 -1.27055e-21
 -3.06993e-05
 1.29173e-20
 1.53497e-05
 0.000183212
 0.000183212
 0.000183212
 -2.61731e-05
 -1.16467e-20
 -2.61731e-05
 -1.69407e-21
 -2.61731e-05
 1.07997e-20
 1.30866e-05
 0.000201035
 0.000201035
 0.000201035
 -2.87193e-05
 -1.69407e-21
 -2.87193e-05
 -1.35525e-20
 -2.87193e-05
 -1.18585e-20
 1.43597e-05
 0.000226674
 0.000226674
 0.000226674
 -3.2382e-05
 -2.11758e-21
 -3.2382e-05
 -1.43996e-20
 -3.2382e-05
 -1.29173e-20
 1.6191e-05
 0.000197557
 0.000197557
 0.000197557
 -2.82225e-05
 -1.3129e-20
 -2.82225e-05
 -1.27055e-21
 -2.82225e-05
 1.18585e-20
 1.41112e-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 0x7fa01dc83c30>

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 589 ms, sys: 27.3 ms, total: 617 ms
Wall time: 598 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 106 iterations to residual 3.179997173468708e-11
CG converged in 106 iterations to residual 3.172974283068946e-11
CG converged in 106 iterations to residual 3.1666528830867264e-11
CG converged in 105 iterations to residual 3.502507154825672e-11
CG converged in 105 iterations to residual 3.4933147424173465e-11
CG converged in 105 iterations to residual 3.484797624395548e-11
CG converged in 105 iterations to residual 3.476771620809102e-11
CG converged in 105 iterations to residual 3.4691128105411784e-11
CG converged in 105 iterations to residual 3.461741248001953e-11
CG converged in 105 iterations to residual 3.454608343928488e-11
CG converged in 105 iterations to residual 3.4476873407271355e-11
CG converged in 105 iterations to residual 3.440966273646705e-11
CG converged in 105 iterations to residual 3.4344428616270596e-11
CG converged in 105 iterations to residual 3.428120859428714e-11
CG converged in 105 iterations to residual 3.4220074951956934e-11
CG converged in 105 iterations to residual 3.416111700780233e-11
CG converged in 105 iterations to residual 3.410442911028546e-11
CG converged in 105 iterations to residual 3.405010262573133e-11
CG converged in 105 iterations to residual 3.399822064357001e-11
CG converged in 105 iterations to residual 3.3948854436133415e-11
CG converged in 105 iterations to residual 3.3902060947529143e-11
CG converged in 105 iterations to residual 3.3857880766492275e-11
CG converged in 105 iterations to residual 3.381633617744213e-11
CG converged in 105 iterations to residual 3.377742899478914e-11
CG converged in 105 iterations to residual 3.3741137976274976e-11
 0.024CPU times: user 626 ms, sys: 6.88 ms, total: 633 ms
Wall time: 628 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 1.57 s, sys: 16.4 ms, total: 1.59 s
Wall time: 5.42 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 4.03 s, sys: 30.5 ms, total: 4.06 s
Wall time: 7.94 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, …)