Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,4,Mod(143,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.143");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 400.n (of order , degree , minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Relative dimension: | over |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 143.3 | ||
Root | of defining polynomial | ||
Character | 400.143 | ||
Dual form | 400.4.n.d.207.4 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | |||||||||
4.12311 | − | 4.12311i | 0.793492 | − | 0.793492i | −0.188568 | − | 0.982060i | ||
0.982060 | + | 0.188568i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.12311 | + | 4.12311i | 0.222627 | + | 0.222627i | 0.809604 | − | 0.586977i | ||
−0.586977 | + | 0.809604i | ||||||||
0 | 0 | |||||||||
− | 7.00000i | − | 0.259259i | |||||||
0 | 0 | |||||||||
− | 13.8564i | − | 0.379806i | −0.981803 | − | 0.189903i | ||||
0.981803 | − | 0.189903i | ||||||||
0 | 0 | |||||||||
−57.1314 | − | 57.1314i | −1.21888 | − | 1.21888i | −0.968025 | − | 0.250852i | ||
−0.250852 | − | 0.968025i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
57.1314 | − | 57.1314i | 0.815083 | − | 0.815083i | −0.170308 | − | 0.985391i | ||
0.985391 | + | 0.170308i | ||||||||
0 | 0 | |||||||||
−96.9948 | −1.17117 | −0.585583 | − | 0.810613i | ||||||
−0.585583 | + | 0.810613i | ||||||||
0 | 0 | |||||||||
34.0000 | 0.353305 | |||||||||
0 | 0 | |||||||||
86.5852 | − | 86.5852i | 0.784968 | − | 0.784968i | −0.195696 | − | 0.980665i | ||
0.980665 | + | 0.195696i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
82.4621 | + | 82.4621i | 0.587772 | + | 0.587772i | |||||
0 | 0 | |||||||||
− | 174.000i | − | 1.11417i | −0.830455 | − | 0.557086i | ||||
0.830455 | − | 0.557086i | ||||||||
0 | 0 | |||||||||
− | 193.990i | − | 1.12392i | −0.827164 | − | 0.561961i | ||||
0.827164 | − | 0.561961i | ||||||||
0 | 0 | |||||||||
−57.1314 | − | 57.1314i | −0.301373 | − | 0.301373i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | −0.707107 | − | 0.707107i | ||||||
0.707107 | + | 0.707107i | ||||||||
0 | 0 | |||||||||
−471.118 | −1.93434 | |||||||||
0 | 0 | |||||||||
252.000 | 0.959897 | 0.479949 | − | 0.877297i | ||||||
0.479949 | + | 0.877297i | ||||||||
0 | 0 | |||||||||
−202.032 | + | 202.032i | −0.716503 | + | 0.716503i | −0.967887 | − | 0.251385i | ||
0.251385 | + | 0.967887i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−284.494 | − | 284.494i | −0.882931 | − | 0.882931i | 0.110901 | − | 0.993832i | ||
−0.993832 | + | 0.110901i | ||||||||
0 | 0 | |||||||||
− | 309.000i | − | 0.900875i | |||||||
0 | 0 | |||||||||
− | 471.118i | − | 1.29352i | |||||||
0 | 0 | |||||||||
399.920 | + | 399.920i | 1.03648 | + | 1.03648i | 0.999309 | + | 0.0371671i | ||
0.0371671 | + | 0.999309i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−399.920 | + | 399.920i | −0.929310 | + | 0.929310i | |||||
0 | 0 | |||||||||
−872.954 | −1.92625 | −0.963126 | − | 0.269050i | ||||||
−0.963126 | + | 0.269050i | ||||||||
0 | 0 | |||||||||
56.0000 | 0.117542 | 0.0587710 | − | 0.998271i | ||||||
0.0587710 | + | 0.998271i | ||||||||
0 | 0 | |||||||||
28.8617 | − | 28.8617i | 0.0577181 | − | 0.0577181i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
317.479 | + | 317.479i | 0.578899 | + | 0.578899i | 0.934600 | − | 0.355701i | ||
−0.355701 | + | 0.934600i | ||||||||
0 | 0 | |||||||||
− | 714.000i | − | 1.24573i | |||||||
0 | 0 | |||||||||
− | 387.979i | − | 0.648517i | −0.945969 | − | 0.324258i | ||||
0.945969 | − | 0.324258i | ||||||||
0 | 0 | |||||||||
399.920 | + | 399.920i | 0.641193 | + | 0.641193i | 0.950849 | − | 0.309656i | ||
−0.309656 | + | 0.950849i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
57.1314 | − | 57.1314i | 0.0845549 | − | 0.0845549i | |||||
0 | 0 | |||||||||
−692.820 | −0.986688 | −0.493344 | − | 0.869834i | ||||||
−0.493344 | + | 0.869834i | ||||||||
0 | 0 | |||||||||
869.000 | 1.19204 | |||||||||
0 | 0 | |||||||||
−482.403 | + | 482.403i | −0.637960 | + | 0.637960i | −0.950052 | − | 0.312092i | ||
0.312092 | + | 0.950052i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−717.420 | − | 717.420i | −0.884087 | − | 0.884087i | |||||
0 | 0 | |||||||||
42.0000i | 0.0500224i | 0.999687 | + | 0.0250112i | ||||||
−0.999687 | + | 0.0250112i | ||||||||
0 | 0 | |||||||||
− | 471.118i | − | 0.542710i | |||||||
0 | 0 | |||||||||
−799.840 | − | 799.840i | −0.891823 | − | 0.891823i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
742.709 | − | 742.709i | 0.777429 | − | 0.777429i | −0.201964 | − | 0.979393i | ||
0.979393 | + | 0.201964i | ||||||||
0 | 0 | |||||||||
−96.9948 | −0.0984682 | |||||||||
0 | 0 | |||||||||
−1050.00 | −1.03444 | −0.517222 | − | 0.855851i | ||||||
−0.517222 | + | 0.855851i | ||||||||
0 | 0 | |||||||||
869.975 | − | 869.975i | 0.832245 | − | 0.832245i | −0.155579 | − | 0.987823i | ||
0.987823 | + | 0.155579i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1298.78 | + | 1298.78i | 1.17344 | + | 1.17344i | 0.981385 | + | 0.192051i | ||
0.192051 | + | 0.981385i | ||||||||
0 | 0 | |||||||||
− | 272.000i | − | 0.239017i | −0.992833 | − | 0.119509i | ||||
0.992833 | − | 0.119509i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−799.840 | − | 799.840i | −0.665864 | − | 0.665864i | 0.290892 | − | 0.956756i | ||
−0.956756 | + | 0.290892i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−399.920 | + | 399.920i | −0.316005 | + | 0.316005i | |||||
0 | 0 | |||||||||
471.118 | 0.362918 | |||||||||
0 | 0 | |||||||||
1139.00 | 0.855748 | |||||||||
0 | 0 | |||||||||
1039.02 | − | 1039.02i | 0.761671 | − | 0.761671i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−28.8617 | − | 28.8617i | −0.0201659 | − | 0.0201659i | 0.696952 | − | 0.717118i | ||
−0.717118 | + | 0.696952i | ||||||||
0 | 0 | |||||||||
1666.00i | 1.13708i | |||||||||
0 | 0 | |||||||||
1842.90i | 1.22912i | 0.788869 | + | 0.614561i | ||||||
−0.788869 | + | 0.614561i | ||||||||
0 | 0 | |||||||||
−399.920 | − | 399.920i | −0.260733 | − | 0.260733i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
799.840 | − | 799.840i | 0.498795 | − | 0.498795i | −0.412268 | − | 0.911063i | ||
0.911063 | + | 0.412268i | ||||||||
0 | 0 | |||||||||
2036.89 | 1.24293 | 0.621464 | − | 0.783443i | ||||||
0.621464 | + | 0.783443i | ||||||||
0 | 0 | |||||||||
−2346.00 | −1.40120 | |||||||||
0 | 0 | |||||||||
−791.636 | + | 791.636i | −0.462937 | + | 0.462937i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1274.04 | − | 1274.04i | −0.714837 | − | 0.714837i | |||||
0 | 0 | |||||||||
− | 744.000i | − | 0.409066i | −0.978860 | − | 0.204533i | ||||
0.978860 | − | 0.204533i | ||||||||
0 | 0 | |||||||||
859.097i | 0.462996i | 0.972835 | + | 0.231498i | ||||||
−0.972835 | + | 0.231498i | ||||||||
0 | 0 | |||||||||
−399.920 | − | 399.920i | −0.211318 | − | 0.211318i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
799.840 | − | 799.840i | 0.406587 | − | 0.406587i | −0.473960 | − | 0.880547i | ||
0.880547 | + | 0.473960i | ||||||||
0 | 0 | |||||||||
3297.82 | 1.64487 | |||||||||
0 | 0 | |||||||||
714.000 | 0.349510 | |||||||||
0 | 0 | |||||||||
−1356.50 | + | 1356.50i | −0.651837 | + | 0.651837i | −0.953435 | − | 0.301598i | ||
0.301598 | + | 0.953435i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1274.04 | + | 1274.04i | 0.590348 | + | 0.590348i | 0.937725 | − | 0.347377i | ||
−0.347377 | + | 0.937725i | ||||||||
0 | 0 | |||||||||
4331.00i | 1.97132i | |||||||||
0 | 0 | |||||||||
678.964i | 0.303635i | |||||||||
0 | 0 | |||||||||
2856.57 | + | 2856.57i | 1.25538 | + | 1.25538i | 0.953274 | + | 0.302109i | ||
0.302109 | + | 0.953274i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3599.28 | + | 3599.28i | −1.52847 | + | 1.52847i | |||||
0 | 0 | |||||||||
1842.90 | 0.769525 | 0.384762 | − | 0.923016i | ||||||
0.384762 | + | 0.923016i | ||||||||
0 | 0 | |||||||||
−3094.00 | −1.27058 | −0.635291 | − | 0.772273i | ||||||
−0.635291 | + | 0.772273i | ||||||||
0 | 0 | |||||||||
230.894 | − | 230.894i | 0.0932687 | − | 0.0932687i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−791.636 | − | 791.636i | −0.309573 | − | 0.309573i | |||||
0 | 0 | |||||||||
680.000i | 0.261708i | |||||||||
0 | 0 | |||||||||
3990.65i | 1.51180i | 0.654690 | + | 0.755898i | ||||||
−0.654690 | + | 0.755898i | ||||||||
0 | 0 | |||||||||
2799.44 | + | 2799.44i | 1.04408 | + | 1.04408i | 0.998982 | + | 0.0451010i | ||
0.0451010 | + | 0.998982i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
399.920 | − | 399.920i | 0.144635 | − | 0.144635i | −0.631081 | − | 0.775717i | ||
0.775717 | + | 0.631081i | ||||||||
0 | 0 | |||||||||
3103.84 | 1.10565 | 0.552827 | − | 0.833296i | ||||||
0.552827 | + | 0.833296i | ||||||||
0 | 0 | |||||||||
2618.00 | 0.918704 | |||||||||
0 | 0 | |||||||||
717.420 | − | 717.420i | 0.248045 | − | 0.248045i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−606.097 | − | 606.097i | −0.203510 | − | 0.203510i | |||||
0 | 0 | |||||||||
1344.00i | 0.444815i | |||||||||
0 | 0 | |||||||||
180.133i | 0.0587720i | 0.999568 | + | 0.0293860i | ||||||
−0.999568 | + | 0.0293860i | ||||||||
0 | 0 | |||||||||
−1599.68 | − | 1599.68i | −0.514593 | − | 0.514593i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
799.840 | − | 799.840i | 0.250215 | − | 0.250215i | |||||
0 | 0 | |||||||||
3297.82 | 1.01756 | |||||||||
0 | 0 | |||||||||
−6528.00 | −1.98697 | |||||||||
0 | 0 | |||||||||
−3756.15 | + | 3756.15i | −1.12794 | + | 1.12794i | −0.137427 | + | 0.990512i | ||
−0.990512 | + | 0.137427i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3401.56 | − | 3401.56i | −0.994580 | − | 0.994580i | 0.00540561 | − | 0.999985i | ||
−0.999985 | + | 0.00540561i | ||||||||
0 | 0 | |||||||||
− | 2170.00i | − | 0.626191i | −0.949722 | − | 0.313095i | ||||
0.949722 | − | 0.313095i | ||||||||
0 | 0 | |||||||||
− | 471.118i | − | 0.134187i | |||||||
0 | 0 | |||||||||
−1199.76 | − | 1199.76i | −0.337334 | − | 0.337334i | 0.518029 | − | 0.855363i | ||
−0.855363 | + | 0.518029i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2856.57 | + | 2856.57i | −0.782929 | + | 0.782929i | |||||
0 | 0 | |||||||||
−2798.99 | −0.757539 | −0.378770 | − | 0.925491i | ||||||
−0.378770 | + | 0.925491i | ||||||||
0 | 0 | |||||||||
5908.00 | 1.57912 | 0.789560 | − | 0.613674i | ||||||
0.789560 | + | 0.613674i | ||||||||
0 | 0 | |||||||||
1356.50 | − | 1356.50i | 0.358105 | − | 0.358105i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5541.45 | + | 5541.45i | 1.42751 | + | 1.42751i | |||||
0 | 0 | |||||||||
3978.00i | 1.01243i | |||||||||
0 | 0 | |||||||||
3588.81i | 0.902485i | 0.892401 | + | 0.451242i | ||||||
−0.892401 | + | 0.451242i | ||||||||
0 | 0 | |||||||||
−1199.76 | − | 1199.76i | −0.298135 | − | 0.298135i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4799.04 | − | 4799.04i | 1.16481 | − | 1.16481i | 0.181399 | − | 0.983410i | ||
0.983410 | − | 0.181399i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1218.00 | −0.288859 | |||||||||
0 | 0 | |||||||||
3723.16 | − | 3723.16i | 0.872928 | − | 0.872928i | −0.119862 | − | 0.992791i | ||
0.992791 | + | 0.119862i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
173.170 | + | 173.170i | 0.0396924 | + | 0.0396924i | |||||
0 | 0 | |||||||||
− | 2856.00i | − | 0.647336i | −0.946171 | − | 0.323668i | ||||
0.946171 | − | 0.323668i | ||||||||
0 | 0 | |||||||||
− | 6013.68i | − | 1.34799i | −0.738736 | − | 0.673995i | ||||
0.738736 | − | 0.673995i | ||||||||
0 | 0 | |||||||||
−1942.47 | − | 1942.47i | −0.430636 | − | 0.430636i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1599.68 | − | 1599.68i | 0.346987 | − | 0.346987i | −0.511999 | − | 0.858986i | ||
0.858986 | + | 0.511999i | ||||||||
0 | 0 | |||||||||
−1357.93 | −0.291387 | |||||||||
0 | 0 | |||||||||
636.000 | 0.135020 | 0.0675099 | − | 0.997719i | ||||||
0.0675099 | + | 0.997719i | ||||||||
0 | 0 | |||||||||
5661.02 | − | 5661.02i | 1.18909 | − | 1.18909i | 0.211773 | − | 0.977319i | ||
0.977319 | − | 0.211773i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1039.02 | + | 1039.02i | 0.213699 | + | 0.213699i | |||||
0 | 0 | |||||||||
− | 1615.00i | − | 0.328720i | |||||||
0 | 0 | |||||||||
− | 6124.53i | − | 1.23377i | |||||||
0 | 0 | |||||||||
−1942.47 | − | 1942.47i | −0.387305 | − | 0.387305i | 0.486420 | − | 0.873725i | ||
−0.873725 | + | 0.486420i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1142.63 | − | 1142.63i | 0.223239 | − | 0.223239i | |||||
0 | 0 | |||||||||
−9893.47 | −1.91356 | |||||||||
0 | 0 | |||||||||
−1666.00 | −0.319025 | |||||||||
0 | 0 | |||||||||
−4329.26 | + | 4329.26i | −0.820824 | + | 0.820824i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1331.76 | − | 1331.76i | −0.247582 | − | 0.247582i | 0.572395 | − | 0.819978i | ||
−0.819978 | + | 0.572395i | ||||||||
0 | 0 | |||||||||
− | 7174.00i | − | 1.32076i | |||||||
0 | 0 | |||||||||
4849.74i | 0.884256i | 0.896952 | + | 0.442128i | ||||||
−0.896952 | + | 0.442128i | ||||||||
0 | 0 | |||||||||
−2742.31 | − | 2742.31i | −0.495222 | − | 0.495222i | 0.414725 | − | 0.909947i | ||
−0.909947 | + | 0.414725i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1199.76 | − | 1199.76i | 0.212572 | − | 0.212572i | −0.592787 | − | 0.805359i | ||
0.805359 | + | 0.592787i | ||||||||
0 | 0 | |||||||||
−2411.01 | −0.423169 | |||||||||
0 | 0 | |||||||||
10710.0 | 1.86222 | |||||||||
0 | 0 | |||||||||
−5541.45 | + | 5541.45i | −0.954597 | + | 0.954597i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1121.48 | − | 1121.48i | −0.189658 | − | 0.189658i | |||||
0 | 0 | |||||||||
− | 2346.00i | − | 0.393128i | |||||||
0 | 0 | |||||||||
− | 5722.70i | − | 0.950296i | −0.879906 | − | 0.475148i | ||||
0.879906 | − | 0.475148i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4799.04 | + | 4799.04i | −0.775728 | + | 0.775728i | −0.979101 | − | 0.203373i | ||
0.203373 | + | 0.979101i | ||||||||
0 | 0 | |||||||||
−6595.65 | −1.05672 | |||||||||
0 | 0 | |||||||||
−2688.00 | −0.426872 | |||||||||
0 | 0 | |||||||||
2688.26 | − | 2688.26i | 0.423186 | − | 0.423186i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3203.65 | + | 3203.65i | 0.495623 | + | 0.495623i | 0.910072 | − | 0.414450i | ||
−0.414450 | + | 0.910072i | ||||||||
0 | 0 | |||||||||
− | 1778.00i | − | 0.272705i | −0.990660 | − | 0.136353i | ||||
0.990660 | − | 0.136353i | ||||||||
0 | 0 | |||||||||
− | 9422.36i | − | 1.43284i | |||||||
0 | 0 | |||||||||
3656.41 | + | 3656.41i | 0.551306 | + | 0.551306i | 0.926818 | − | 0.375511i | ||
−0.375511 | + | 0.926818i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1942.47 | − | 1942.47i | 0.287973 | − | 0.287973i | |||||
0 | 0 | |||||||||
−11445.4 | −1.68263 | −0.841316 | − | 0.540544i | ||||||
−0.841316 | + | 0.540544i | ||||||||
0 | 0 | |||||||||
2549.00 | 0.371629 | |||||||||
0 | 0 | |||||||||
4696.22 | − | 4696.22i | 0.679029 | − | 0.679029i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6930.94 | − | 6930.94i | −0.985810 | − | 0.985810i | 0.0140910 | − | 0.999901i | ||
−0.999901 | + | 0.0140910i | ||||||||
0 | 0 | |||||||||
− | 1764.00i | − | 0.248862i | |||||||
0 | 0 | |||||||||
3297.82i | 0.461495i | |||||||||
0 | 0 | |||||||||
8798.24 | + | 8798.24i | 1.22133 | + | 1.22133i | 0.967160 | + | 0.254169i | ||
0.254169 | + | 0.967160i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9940.87 | + | 9940.87i | −1.35804 | + | 1.35804i | |||||
0 | 0 | |||||||||
−872.954 | −0.118313 | −0.0591565 | − | 0.998249i | ||||||
−0.0591565 | + | 0.998249i | ||||||||
0 | 0 | |||||||||
−238.000 | −0.0320029 | |||||||||
0 | 0 | |||||||||
−1941.98 | + | 1941.98i | −0.259088 | + | 0.259088i | −0.824683 | − | 0.565595i | ||
0.565595 | + | 0.824683i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1414.23 | + | 1414.23i | 0.185760 | + | 0.185760i | |||||
0 | 0 | |||||||||
− | 11880.0i | − | 1.54843i | −0.632922 | − | 0.774216i | ||||
0.632922 | − | 0.774216i | ||||||||
0 | 0 | |||||||||
− | 9893.47i | − | 1.27963i | |||||||
0 | 0 | |||||||||
7598.48 | + | 7598.48i | 0.975299 | + | 0.975299i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−57.1314 | + | 57.1314i | −0.00722253 | + | 0.00722253i | −0.710709 | − | 0.703486i | ||
0.703486 | + | 0.710709i | ||||||||
0 | 0 | |||||||||
−3297.82 | −0.413779 | |||||||||
0 | 0 | |||||||||
−498.000 | −0.0620173 | −0.0310086 | − | 0.999519i | ||||||
−0.0310086 | + | 0.999519i | ||||||||
0 | 0 | |||||||||
−11082.9 | + | 11082.9i | −1.36992 | + | 1.36992i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7700.00i | 0.930906i | 0.885073 | + | 0.465453i | ||||||
−0.885073 | + | 0.465453i | ||||||||
0 | 0 | |||||||||
− | 6595.65i | − | 0.791580i | |||||||
0 | 0 | |||||||||
−3599.28 | − | 3599.28i | −0.428835 | − | 0.428835i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8398.32 | − | 8398.32i | 0.986253 | − | 0.986253i | |||||
0 | 0 | |||||||||
−3976.79 | −0.463673 | −0.231836 | − | 0.972755i | ||||||
−0.231836 | + | 0.972755i | ||||||||
0 | 0 | |||||||||
11768.0 | 1.36232 | 0.681161 | − | 0.732134i | ||||||
0.681161 | + | 0.732134i | ||||||||
0 | 0 | |||||||||
−1991.46 | + | 1991.46i | −0.228908 | + | 0.228908i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
230.894 | + | 230.894i | 0.0261680 | + | 0.0261680i | |||||
0 | 0 | |||||||||
6528.00i | 0.734673i | |||||||||
0 | 0 | |||||||||
17542.2i | 1.96051i | 0.197745 | + | 0.980254i | ||||||
−0.197745 | + | 0.980254i | ||||||||
0 | 0 | |||||||||
−7598.48 | − | 7598.48i | −0.843325 | − | 0.843325i | 0.145965 | − | 0.989290i | ||
−0.989290 | + | 0.145965i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8398.32 | + | 8398.32i | −0.919328 | + | 0.919328i | |||||
0 | 0 | |||||||||
1745.91 | 0.189812 | 0.0949062 | − | 0.995486i | ||||||
0.0949062 | + | 0.995486i | ||||||||
0 | 0 | |||||||||
−2163.00 | −0.233560 | |||||||||
0 | 0 | |||||||||
−1471.95 | + | 1471.95i | −0.157865 | + | 0.157865i | −0.781620 | − | 0.623755i | ||
0.623755 | + | 0.781620i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3067.59 | − | 3067.59i | −0.324591 | − | 0.324591i | |||||
0 | 0 | |||||||||
− | 15252.0i | − | 1.60309i | −0.597936 | − | 0.801544i | ||||
0.597936 | − | 0.801544i | ||||||||
0 | 0 | |||||||||
− | 3491.81i | − | 0.364575i | |||||||
0 | 0 | |||||||||
3542.15 | + | 3542.15i | 0.367383 | + | 0.367383i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6398.72 | − | 6398.72i | 0.654966 | − | 0.654966i | −0.299219 | − | 0.954185i | ||
0.954185 | + | 0.299219i | ||||||||
0 | 0 | |||||||||
9422.36 | 0.958165 | |||||||||
0 | 0 | |||||||||
−15582.0 | −1.57424 | −0.787122 | − | 0.616798i | ||||||
−0.787122 | + | 0.616798i | ||||||||
0 | 0 | |||||||||
11919.9 | − | 11919.9i | 1.19647 | − | 1.19647i | 0.221251 | − | 0.975217i | ||
0.975217 | − | 0.221251i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3005.74 | + | 3005.74i | 0.297836 | + | 0.297836i | 0.840166 | − | 0.542330i | ||
−0.542330 | + | 0.840166i | ||||||||
0 | 0 | |||||||||
2618.00i | 0.257757i | |||||||||
0 | 0 | |||||||||
− | 6595.65i | − | 0.645247i | |||||||
0 | 0 | |||||||||
2799.44 | + | 2799.44i | 0.272132 | + | 0.272132i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2799.44 | − | 2799.44i | 0.268716 | − | 0.268716i | |||||
0 | 0 | |||||||||
−387.979 | −0.0370088 | −0.0185044 | − | 0.999829i | ||||||
−0.0185044 | + | 0.999829i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2943.90 | − | 2943.90i | 0.277333 | − | 0.277333i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1356.50 | − | 1356.50i | −0.126220 | − | 0.126220i | 0.641175 | − | 0.767395i | ||
−0.767395 | + | 0.641175i | ||||||||
0 | 0 | |||||||||
11186.0i | 1.03445i | |||||||||
0 | 0 | |||||||||
14369.1i | 1.32071i | 0.750954 | + | 0.660354i | ||||||
−0.750954 | + | 0.660354i | ||||||||
0 | 0 | |||||||||
−9940.87 | − | 9940.87i | −0.908142 | − | 0.908142i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1599.68 | − | 1599.68i | 0.144377 | − | 0.144377i | |||||
0 | 0 | |||||||||
7357.75 | 0.660077 | 0.330038 | − | 0.943968i | ||||||
0.330038 | + | 0.943968i | ||||||||
0 | 0 | |||||||||
10506.0 | 0.936873 | |||||||||
0 | 0 | |||||||||
12579.6 | − | 12579.6i | 1.11510 | − | 1.11510i | 0.122653 | − | 0.992450i | ||
0.992450 | − | 0.122653i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
17857.2 | + | 17857.2i | 1.56423 | + | 1.56423i | |||||
0 | 0 | |||||||||
20370.0i | 1.77384i | 0.461923 | + | 0.886920i | ||||||
−0.461923 | + | 0.886920i | ||||||||
0 | 0 | |||||||||
3297.82i | 0.285493i | |||||||||
0 | 0 | |||||||||
−7998.40 | − | 7998.40i | −0.688378 | − | 0.688378i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3942.07 | + | 3942.07i | −0.335342 | + | 0.335342i | |||||
0 | 0 | |||||||||
23555.9 | 1.99227 | |||||||||
0 | 0 | |||||||||
−18438.0 | −1.55045 | −0.775224 | − | 0.631686i | ||||||
−0.775224 | + | 0.631686i | ||||||||
0 | 0 | |||||||||
−3904.58 | + | 3904.58i | −0.326454 | + | 0.326454i | −0.851236 | − | 0.524782i | ||
0.524782 | + | 0.851236i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−11082.9 | − | 11082.9i | −0.916089 | − | 0.916089i | |||||
0 | 0 | |||||||||
− | 2827.00i | − | 0.232350i | |||||||
0 | 0 | |||||||||
6110.68i | 0.499399i | |||||||||
0 | 0 | |||||||||
−14397.1 | − | 14397.1i | −1.17000 | − | 1.17000i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7598.48 | − | 7598.48i | 0.610612 | − | 0.610612i | |||||
0 | 0 | |||||||||
−4281.63 | −0.342157 | |||||||||
0 | 0 | |||||||||
6322.00 | 0.502410 | 0.251205 | − | 0.967934i | ||||||
0.251205 | + | 0.967934i | ||||||||
0 | 0 | |||||||||
−12756.9 | + | 12756.9i | −1.00820 | + | 1.00820i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1587.40 | − | 1587.40i | −0.124081 | − | 0.124081i | 0.642340 | − | 0.766420i | ||
−0.766420 | + | 0.642340i | ||||||||
0 | 0 | |||||||||
− | 392.000i | − | 0.0304739i | |||||||
0 | 0 | |||||||||
16877.1i | 1.30488i | |||||||||
0 | 0 | |||||||||
−2856.57 | − | 2856.57i | −0.219663 | − | 0.219663i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12797.4 | − | 12797.4i | 0.973510 | − | 0.973510i | −0.0261483 | − | 0.999658i | ||
0.999658 | + | 0.0261483i | ||||||||
0 | 0 | |||||||||
23084.8 | 1.74666 | |||||||||
0 | 0 | |||||||||
−6528.00 | −0.491288 | |||||||||
0 | 0 | |||||||||
729.790 | − | 729.790i | 0.0546305 | − | 0.0546305i | −0.679264 | − | 0.733894i | ||
0.733894 | + | 0.679264i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3582.98 | + | 3582.98i | 0.265381 | + | 0.265381i | |||||
0 | 0 | |||||||||
5196.00i | 0.382825i | 0.981510 | + | 0.191413i | ||||||
−0.981510 | + | 0.191413i | ||||||||
0 | 0 | |||||||||
− | 5528.71i | − | 0.405200i | −0.979262 | − | 0.202600i | ||||
0.979262 | − | 0.202600i | ||||||||
0 | 0 | |||||||||
16453.9 | + | 16453.9i | 1.19960 | + | 1.19960i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−17253.7 | + | 17253.7i | −1.24485 | + | 1.24485i | −0.286890 | + | 0.957963i | ||
−0.957963 | + | 0.286890i | ||||||||
0 | 0 | |||||||||
23084.8 | 1.65694 | |||||||||
0 | 0 | |||||||||
−3978.00 | −0.284054 | |||||||||
0 | 0 | |||||||||
5541.45 | − | 5541.45i | 0.393660 | − | 0.393660i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−13989.7 | − | 13989.7i | −0.983674 | − | 0.983674i | 0.0161949 | − | 0.999869i | ||
−0.999869 | + | 0.0161949i | ||||||||
0 | 0 | |||||||||
18816.0i | 1.31630i | |||||||||
0 | 0 | |||||||||
− | 3297.82i | − | 0.229534i | |||||||
0 | 0 | |||||||||
9255.29 | + | 9255.29i | 0.640926 | + | 0.640926i | 0.950783 | − | 0.309857i | ||
−0.309857 | + | 0.950783i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
12797.4 | − | 12797.4i | 0.877327 | − | 0.877327i | |||||
0 | 0 | |||||||||
−10586.3 | −0.722111 | −0.361055 | − | 0.932544i | ||||||
−0.361055 | + | 0.932544i | ||||||||
0 | 0 | |||||||||
−17612.0 | −1.19536 | −0.597678 | − | 0.801737i | ||||||
−0.597678 | + | 0.801737i | ||||||||
0 | 0 | |||||||||
2222.35 | − | 2222.35i | 0.150085 | − | 0.150085i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
13338.2 | + | 13338.2i | 0.891899 | + | 0.891899i | 0.994702 | − | 0.102803i | ||
−0.102803 | + | 0.994702i | ||||||||
0 | 0 | |||||||||
− | 5916.00i | − | 0.393643i | |||||||
0 | 0 | |||||||||
32507.1i | 2.15237i | |||||||||
0 | 0 | |||||||||
5198.96 | + | 5198.96i | 0.342551 | + | 0.342551i | 0.857326 | − | 0.514774i | ||
−0.514774 | + | 0.857326i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12397.5 | + | 12397.5i | −0.808923 | + | 0.808923i | −0.984471 | − | 0.175548i | ||
0.175548 | + | 0.984471i | ||||||||
0 | 0 | |||||||||
19108.0 | 1.24073 | 0.620367 | − | 0.784311i | ||||||
0.620367 | + | 0.784311i | ||||||||
0 | 0 | |||||||||
14280.0 | 0.922764 | |||||||||
0 | 0 | |||||||||
−173.170 | + | 173.170i | −0.0111363 | + | 0.0111363i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5541.45 | + | 5541.45i | 0.352958 | + | 0.352958i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4572.61i | 0.288483i | 0.989543 | + | 0.144242i | ||||||
−0.989543 | + | 0.144242i | ||||||||
0 | 0 | |||||||||
742.709 | + | 742.709i | 0.0466351 | + | 0.0466351i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−17653.6 | + | 17653.6i | −1.09806 | + | 1.09806i | |||||
0 | 0 | |||||||||
−2715.86 | −0.168134 | |||||||||
0 | 0 | |||||||||
−10404.0 | −0.641082 | −0.320541 | − | 0.947235i | ||||||
−0.320541 | + | 0.947235i | ||||||||
0 | 0 | |||||||||
−1034.90 | + | 1034.90i | −0.0634719 | + | 0.0634719i | −0.738130 | − | 0.674658i | ||
0.674658 | + | 0.738130i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3500.52 | − | 3500.52i | −0.212704 | − | 0.212704i | 0.592711 | − | 0.805415i | ||
−0.805415 | + | 0.592711i | ||||||||
0 | 0 | |||||||||
12096.0i | 0.731602i | |||||||||
0 | 0 | |||||||||
− | 6595.65i | − | 0.397087i | |||||||
0 | 0 | |||||||||
11597.7 | + | 11597.7i | 0.695026 | + | 0.695026i | 0.963333 | − | 0.268307i | ||
−0.268307 | + | 0.963333i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2799.44 | − | 2799.44i | 0.166235 | − | 0.166235i | |||||
0 | 0 | |||||||||
−762.102 | −0.0450490 | −0.0225245 | − | 0.999746i | ||||||
−0.0225245 | + | 0.999746i | ||||||||
0 | 0 | |||||||||
18592.0 | 1.09402 | 0.547008 | − | 0.837127i | ||||||
0.547008 | + | 0.837127i | ||||||||
0 | 0 | |||||||||
−26915.6 | + | 26915.6i | −1.57665 | + | 1.57665i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−15065.8 | − | 15065.8i | −0.874589 | − | 0.874589i | |||||
0 | 0 | |||||||||
30974.0i | 1.79002i | |||||||||
0 | 0 | |||||||||
− | 775.959i | − | 0.0446432i | |||||||
0 | 0 | |||||||||
9998.00 | + | 9998.00i | 0.572652 | + | 0.572652i | 0.932869 | − | 0.360217i | ||
−0.360217 | + | 0.932869i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−7141.43 | + | 7141.43i | −0.405417 | + | 0.405417i | −0.880137 | − | 0.474720i | ||
0.474720 | + | 0.880137i | ||||||||
0 | 0 | |||||||||
6124.53 | 0.346153 | |||||||||
0 | 0 | |||||||||
−28050.0 | −1.57838 | |||||||||
0 | 0 | |||||||||
−5974.38 | + | 5974.38i | −0.334705 | + | 0.334705i | −0.854370 | − | 0.519665i | ||
0.519665 | + | 0.854370i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8947.14 | − | 8947.14i | −0.496877 | − | 0.496877i | |||||
0 | 0 | |||||||||
− | 45696.0i | − | 2.52667i | |||||||
0 | 0 | |||||||||
− | 29001.5i | − | 1.59662i | −0.602244 | − | 0.798312i | ||||
0.602244 | − | 0.798312i | ||||||||
0 | 0 | |||||||||
−399.920 | − | 399.920i | −0.0219217 | − | 0.0219217i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
14397.1 | − | 14397.1i | 0.782396 | − | 0.782396i | |||||
0 | 0 | |||||||||
−9893.47 | −0.535344 | |||||||||
0 | 0 | |||||||||
3408.00 | 0.183621 | 0.0918105 | − | 0.995776i | ||||||
0.0918105 | + | 0.995776i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4329.26 | − | 4329.26i | −0.230295 | − | 0.230295i | |||||
0 | 0 | |||||||||
− | 16486.0i | − | 0.873265i | −0.899640 | − | 0.436632i | ||||
0.899640 | − | 0.436632i | ||||||||
0 | 0 | |||||||||
4849.74i | 0.255808i | |||||||||
0 | 0 | |||||||||
−16796.6 | − | 16796.6i | −0.882243 | − | 0.882243i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−11540.5 | + | 11540.5i | −0.601101 | + | 0.601101i | |||||
0 | 0 | |||||||||
2521.87 | 0.130806 | 0.0654032 | − | 0.997859i | ||||||
0.0654032 | + | 0.997859i | ||||||||
0 | 0 | |||||||||
7174.00 | 0.370560 | |||||||||
0 | 0 | |||||||||
24359.3 | − | 24359.3i | 1.25302 | − | 1.25302i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1653.37 | + | 1653.37i | 0.0843465 | + | 0.0843465i | 0.748021 | − | 0.663675i | ||
−0.663675 | + | 0.748021i | ||||||||
0 | 0 | |||||||||
12277.0i | 0.623736i | |||||||||
0 | 0 | |||||||||
23084.8i | 1.16802i | |||||||||
0 | 0 | |||||||||
−6055.93 | − | 6055.93i | −0.305158 | − | 0.305158i | 0.537870 | − | 0.843028i | ||
−0.843028 | + | 0.537870i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4399.12 | − | 4399.12i | 0.219869 | − | 0.219869i | |||||
0 | 0 | |||||||||
−25204.8 | −1.25463 | −0.627316 | − | 0.778764i | ||||||
−0.627316 | + | 0.778764i | ||||||||
0 | 0 | |||||||||
45696.0 | 2.26543 | |||||||||
0 | 0 | |||||||||
1125.61 | − | 1125.61i | 0.0555781 | − | 0.0555781i | −0.678771 | − | 0.734350i | ||
0.734350 | + | 0.678771i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3376.82 | + | 3376.82i | 0.165397 | + | 0.165397i | |||||
0 | 0 | |||||||||
10710.0i | 0.522476i | |||||||||
0 | 0 | |||||||||
− | 11140.6i | − | 0.541311i | −0.962676 | − | 0.270655i | ||||
0.962676 | − | 0.270655i | ||||||||
0 | 0 | |||||||||
14797.0 | + | 14797.0i | 0.716114 | + | 0.716114i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8798.24 | − | 8798.24i | 0.422427 | − | 0.422427i | −0.463611 | − | 0.886039i | ||
0.886039 | + | 0.463611i | ||||||||
0 | 0 | |||||||||
−9893.47 | −0.473136 | |||||||||
0 | 0 | |||||||||
−19110.0 | −0.910298 | −0.455149 | − | 0.890415i | ||||||
−0.455149 | + | 0.890415i | ||||||||
0 | 0 | |||||||||
1121.48 | − | 1121.48i | 0.0532116 | − | 0.0532116i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
49873.1 | + | 49873.1i | 2.34787 | + | 2.34787i | |||||
0 | 0 | |||||||||
− | 17458.0i | − | 0.818663i | −0.912386 | − | 0.409331i | ||||
0.912386 | − | 0.409331i | ||||||||
0 | 0 | |||||||||
− | 39573.9i | − | 1.84853i | |||||||
0 | 0 | |||||||||
−12054.7 | − | 12054.7i | −0.560904 | − | 0.560904i | 0.368660 | − | 0.929564i | ||
−0.929564 | + | 0.368660i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−24442.7 | −1.12420 | |||||||||
0 | 0 | |||||||||
−5376.00 | −0.246310 | |||||||||
0 | 0 | |||||||||
14348.4 | − | 14348.4i | 0.654879 | − | 0.654879i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−10443.8 | − | 10443.8i | −0.473040 | − | 0.473040i | 0.429857 | − | 0.902897i | ||
−0.902897 | + | 0.429857i | ||||||||
0 | 0 | |||||||||
− | 30702.0i | − | 1.38532i | |||||||
0 | 0 | |||||||||
− | 6595.65i | − | 0.296478i | |||||||
0 | 0 | |||||||||
−3199.36 | − | 3199.36i | −0.143269 | − | 0.143269i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3256.49 | − | 3256.49i | 0.144731 | − | 0.144731i | −0.631028 | − | 0.775760i | ||
0.775760 | + | 0.631028i | ||||||||
0 | 0 | |||||||||
−32507.1 | −1.43932 | |||||||||
0 | 0 | |||||||||
294.000 | 0.0129688 | |||||||||
0 | 0 | |||||||||
5541.45 | − | 5541.45i | 0.243529 | − | 0.243529i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−11775.6 | − | 11775.6i | −0.513656 | − | 0.513656i | |||||
0 | 0 | |||||||||
− | 12762.0i | − | 0.554621i | −0.960780 | − | 0.277310i | ||||
0.960780 | − | 0.277310i | ||||||||
0 | 0 | |||||||||
− | 1842.90i | − | 0.0797941i | −0.999204 | − | 0.0398971i | ||||
0.999204 | − | 0.0398971i | ||||||||
0 | 0 | |||||||||
−24795.0 | − | 24795.0i | −1.06962 | − | 1.06962i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
19596.1 | − | 19596.1i | 0.839143 | − | 0.839143i | |||||
0 | 0 | |||||||||
−3297.82 | −0.140702 | |||||||||
0 | 0 | |||||||||
18768.0 | 0.797817 | 0.398908 | − | 0.916991i | ||||||
0.398908 | + | 0.916991i | ||||||||
0 | 0 | |||||||||
−16306.9 | + | 16306.9i | −0.690671 | + | 0.690671i | −0.962380 | − | 0.271709i | ||
0.271709 | + | 0.962380i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−14113.4 | − | 14113.4i | −0.593435 | − | 0.593435i | 0.345123 | − | 0.938558i | ||
−0.938558 | + | 0.345123i | ||||||||
0 | 0 | |||||||||
19208.0i | 0.804730i | 0.915479 | + | 0.402365i | ||||||
−0.915479 | + | 0.402365i | ||||||||
0 | 0 | |||||||||
− | 13191.3i | − | 0.550663i | |||||||
0 | 0 | |||||||||
−17653.6 | − | 17653.6i | −0.734287 | − | 0.734287i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
15996.8 | − | 15996.8i | 0.660610 | − | 0.660610i | |||||
0 | 0 | |||||||||
−38216.0 | −1.57254 | −0.786270 | − | 0.617883i | ||||||
−0.786270 | + | 0.617883i | ||||||||
0 | 0 | |||||||||
−5887.00 | −0.241379 | |||||||||
0 | 0 | |||||||||
2622.30 | − | 2622.30i | 0.107137 | − | 0.107137i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4696.22 | + | 4696.22i | 0.190512 | + | 0.190512i | |||||
0 | 0 | |||||||||
− | 46682.0i | − | 1.88707i | |||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5198.96 | − | 5198.96i | −0.208686 | − | 0.208686i | 0.595023 | − | 0.803709i | ||
−0.803709 | + | 0.595023i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3999.20 | + | 3999.20i | −0.159405 | + | 0.159405i | −0.782303 | − | 0.622898i | ||
0.622898 | + | 0.782303i | ||||||||
0 | 0 | |||||||||
4946.74 | 0.196485 | 0.0982424 | − | 0.995163i | ||||||
0.0982424 | + | 0.995163i | ||||||||
0 | 0 | |||||||||
8568.00 | 0.339137 | |||||||||
0 | 0 | |||||||||
7013.40 | − | 7013.40i | 0.276638 | − | 0.276638i | −0.555127 | − | 0.831766i | ||
0.831766 | + | 0.555127i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6658.82 | − | 6658.82i | −0.260836 | − | 0.260836i | |||||
0 | 0 | |||||||||
9600.00i | 0.374750i | |||||||||
0 | 0 | |||||||||
− | 36276.1i | − | 1.41121i | |||||||
0 | 0 | |||||||||
−5198.96 | − | 5198.96i | −0.201556 | − | 0.201556i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
11997.6 | − | 11997.6i | 0.461950 | − | 0.461950i | −0.437344 | − | 0.899294i | ||
0.899294 | + | 0.437344i | ||||||||
0 | 0 | |||||||||
−16018.0 | −0.614646 | |||||||||
0 | 0 | |||||||||
13020.0 | 0.497906 | 0.248953 | − | 0.968516i | ||||||
0.248953 | + | 0.968516i | ||||||||
0 | 0 | |||||||||
9668.68 | − | 9668.68i | 0.368490 | − | 0.368490i | −0.498436 | − | 0.866926i | ||
0.866926 | + | 0.498436i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
13297.0 | + | 13297.0i | 0.503348 | + | 0.503348i | 0.912477 | − | 0.409128i | ||
−0.409128 | + | 0.912477i | ||||||||
0 | 0 | |||||||||
− | 238.000i | − | 0.00897892i | |||||||
0 | 0 | |||||||||
− | 12041.2i | − | 0.452745i | |||||||
0 | 0 | |||||||||
27594.5 | + | 27594.5i | 1.03406 | + | 1.03406i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−40791.8 | + | 40791.8i | −1.51839 | + | 1.51839i | |||||
0 | 0 | |||||||||
−33754.2 | −1.25224 | |||||||||
0 | 0 | |||||||||
45696.0 | 1.68963 | |||||||||
0 | 0 | |||||||||
−6869.09 | + | 6869.09i | −0.253144 | + | 0.253144i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9322.34 | + | 9322.34i | 0.341283 | + | 0.341283i | 0.856849 | − | 0.515567i | ||
−0.515567 | + | 0.856849i | ||||||||
0 | 0 | |||||||||
7350.00i | 0.268189i | |||||||||
0 | 0 | |||||||||
2133.89i | 0.0776057i | 0.999247 | + | 0.0388029i | ||||||
−0.999247 | + | 0.0388029i | ||||||||
0 | 0 | |||||||||
6684.38 | + | 6684.38i | 0.242301 | + | 0.242301i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−7598.48 | + | 7598.48i | −0.273636 | + | 0.273636i | |||||
0 | 0 | |||||||||
22613.7 | 0.811704 | 0.405852 | − | 0.913939i | ||||||
0.405852 | + | 0.913939i | ||||||||
0 | 0 | |||||||||
−10982.0 | −0.392909 | |||||||||
0 | 0 | |||||||||
−22165.8 | + | 22165.8i | −0.790462 | + | 0.790462i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6089.83 | − | 6089.83i | −0.215767 | − | 0.215767i | |||||
0 | 0 | |||||||||
− | 33684.0i | − | 1.18960i | −0.803875 | − | 0.594799i | ||||
0.803875 | − | 0.594799i | ||||||||
0 | 0 | |||||||||
29971.4i | 1.05507i | |||||||||
0 | 0 | |||||||||
19996.0 | + | 19996.0i | 0.701650 | + | 0.701650i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−20738.7 | + | 20738.7i | −0.723057 | + | 0.723057i | −0.969227 | − | 0.246170i | ||
0.246170 | + | 0.969227i | ||||||||
0 | 0 | |||||||||
−22613.7 | −0.785909 | |||||||||
0 | 0 | |||||||||
−33054.0 | −1.14509 | −0.572545 | − | 0.819873i | ||||||
−0.572545 | + | 0.819873i | ||||||||
0 | 0 | |||||||||
21819.5 | − | 21819.5i | 0.753489 | − | 0.753489i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
8398.77 | + | 8398.77i | 0.288198 | + | 0.288198i | 0.836367 | − | 0.548170i | ||
−0.548170 | + | 0.836367i | ||||||||
0 | 0 | |||||||||
− | 45696.0i | − | 1.56307i | |||||||
0 | 0 | |||||||||
− | 9893.47i | − | 0.337348i | |||||||
0 | 0 | |||||||||
15197.0 | + | 15197.0i | 0.516556 | + | 0.516556i | 0.916528 | − | 0.399972i | ||
−0.399972 | + | 0.916528i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9940.87 | + | 9940.87i | −0.335781 | + | 0.335781i | |||||
0 | 0 | |||||||||
6595.65 | 0.222090 | |||||||||
0 | 0 | |||||||||
−7841.00 | −0.263200 | |||||||||
0 | 0 | |||||||||
9091.45 | − | 9091.45i | 0.304224 | − | 0.304224i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−25484.9 | − | 25484.9i | −0.847507 | − | 0.847507i | 0.142314 | − | 0.989822i | ||
−0.989822 | + | 0.142314i | ||||||||
0 | 0 | |||||||||
45696.0i | 1.51493i | |||||||||
0 | 0 | |||||||||
− | 52668.2i | − | 1.74068i | −0.492449 | − | 0.870341i | ||||
0.492449 | − | 0.870341i | ||||||||
0 | 0 | |||||||||
8398.32 | + | 8398.32i | 0.276709 | + | 0.276709i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
40391.9 | − | 40391.9i | 1.32267 | − | 1.32267i | 0.411069 | − | 0.911604i | ||
0.911604 | − | 0.411069i | ||||||||
0 | 0 | |||||||||
581.969 | 0.0189988 | |||||||||
0 | 0 | |||||||||
−1904.00 | −0.0619674 | |||||||||
0 | 0 | |||||||||
−22104.0 | + | 22104.0i | −0.717200 | + | 0.717200i | −0.968031 | − | 0.250831i | ||
0.250831 | + | 0.968031i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−9672.81 | − | 9672.81i | −0.311944 | − | 0.311944i | |||||
0 | 0 | |||||||||
34986.0i | 1.12486i | |||||||||
0 | 0 | |||||||||
18235.0i | 0.584515i | 0.956340 | + | 0.292258i | ||||||
−0.956340 | + | 0.292258i | ||||||||
0 | 0 | |||||||||
−23595.3 | − | 23595.3i | −0.754052 | − | 0.754052i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−12854.6 | + | 12854.6i | −0.408333 | + | 0.408333i | −0.881157 | − | 0.472824i | ||
0.472824 | + | 0.881157i | ||||||||
0 | 0 | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 400.4.n.d.143.3 | yes | 8 | |
4.3 | odd | 2 | inner | 400.4.n.d.143.2 | yes | 8 | |
5.2 | odd | 4 | inner | 400.4.n.d.207.1 | yes | 8 | |
5.3 | odd | 4 | inner | 400.4.n.d.207.3 | yes | 8 | |
5.4 | even | 2 | inner | 400.4.n.d.143.1 | ✓ | 8 | |
20.3 | even | 4 | inner | 400.4.n.d.207.2 | yes | 8 | |
20.7 | even | 4 | inner | 400.4.n.d.207.4 | yes | 8 | |
20.19 | odd | 2 | inner | 400.4.n.d.143.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.4.n.d.143.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
400.4.n.d.143.2 | yes | 8 | 4.3 | odd | 2 | inner | |
400.4.n.d.143.3 | yes | 8 | 1.1 | even | 1 | trivial | |
400.4.n.d.143.4 | yes | 8 | 20.19 | odd | 2 | inner | |
400.4.n.d.207.1 | yes | 8 | 5.2 | odd | 4 | inner | |
400.4.n.d.207.2 | yes | 8 | 20.3 | even | 4 | inner | |
400.4.n.d.207.3 | yes | 8 | 5.3 | odd | 4 | inner | |
400.4.n.d.207.4 | yes | 8 | 20.7 | even | 4 | inner |