Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,6,Mod(31,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.31");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 224.p (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 |
Twist minimal: | yes |
Sato-Tate group: |
Embedding invariants
Embedding label | 31.11 | ||
Character | 224.31 | ||
Dual form | 224.6.p.a.159.11 |
-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 | |||||||||
−8.16376 | + | 14.1401i | −0.523706 | + | 0.907085i | 0.475913 | + | 0.879492i | ||
−0.999619 | + | 0.0275929i | ||||||||
0 | 0 | |||||||||
19.2452 | − | 11.1112i | 0.344268 | − | 0.198763i | −0.317890 | − | 0.948128i | ||
0.662158 | + | 0.749364i | ||||||||
0 | 0 | |||||||||
103.004 | − | 78.7217i | 0.794530 | − | 0.607224i | |||||
0 | 0 | |||||||||
−11.7941 | − | 20.4280i | −0.0485354 | − | 0.0840658i | |||||
0 | 0 | |||||||||
−230.097 | − | 132.846i | −0.573362 | − | 0.331031i | 0.185129 | − | 0.982714i | ||
−0.758491 | + | 0.651684i | ||||||||
0 | 0 | |||||||||
− | 31.5899i | − | 0.0518430i | −0.999664 | − | 0.0259215i | ||||
0.999664 | − | 0.0259215i | ||||||||
0 | 0 | |||||||||
362.837i | 0.416374i | |||||||||
0 | 0 | |||||||||
110.876 | + | 64.0143i | 0.0930498 | + | 0.0537223i | 0.545803 | − | 0.837914i | ||
−0.452753 | + | 0.891636i | ||||||||
0 | 0 | |||||||||
−1375.26 | − | 2382.02i | −0.873979 | − | 1.51378i | −0.857847 | − | 0.513905i | ||
−0.0161318 | − | 0.999870i | ||||||||
0 | 0 | |||||||||
272.226 | + | 2099.15i | 0.134704 | + | 1.03871i | |||||
0 | 0 | |||||||||
−2222.74 | + | 1283.30i | −0.876130 | + | 0.505834i | −0.869381 | − | 0.494143i | ||
−0.00674965 | + | 0.999977i | ||||||||
0 | 0 | |||||||||
−1315.58 | + | 2278.66i | −0.420986 | + | 0.729170i | |||||
0 | 0 | |||||||||
−3582.45 | −0.945738 | |||||||||
0 | 0 | |||||||||
1603.73 | 0.354108 | 0.177054 | − | 0.984201i | ||||||
0.177054 | + | 0.984201i | ||||||||
0 | 0 | |||||||||
−349.938 | + | 606.110i | −0.0654014 | + | 0.113278i | −0.896872 | − | 0.442290i | ||
0.831471 | + | 0.555569i | ||||||||
0 | 0 | |||||||||
3756.91 | − | 2169.05i | 0.600546 | − | 0.346725i | |||||
0 | 0 | |||||||||
1107.64 | − | 2659.51i | 0.152838 | − | 0.366971i | |||||
0 | 0 | |||||||||
−2421.84 | − | 4194.76i | −0.290832 | − | 0.503735i | 0.683175 | − | 0.730255i | ||
−0.974007 | + | 0.226519i | ||||||||
0 | 0 | |||||||||
446.683 | + | 257.893i | 0.0470260 | + | 0.0271505i | |||||
0 | 0 | |||||||||
− | 5910.34i | − | 0.549101i | −0.961573 | − | 0.274551i | ||||
0.961573 | − | 0.274551i | ||||||||
0 | 0 | |||||||||
− | 15217.5i | − | 1.25508i | −0.778585 | − | 0.627540i | ||||
0.778585 | − | 0.627540i | ||||||||
0 | 0 | |||||||||
−453.959 | − | 262.093i | −0.0334184 | − | 0.0192941i | |||||
0 | 0 | |||||||||
−49.5838 | − | 85.8817i | −0.00327413 | − | 0.00567095i | 0.864384 | − | 0.502833i | ||
−0.867658 | + | 0.497162i | ||||||||
0 | 0 | |||||||||
4412.79 | − | 16217.4i | 0.262557 | − | 0.964916i | |||||
0 | 0 | |||||||||
−1810.33 | + | 1045.20i | −0.0974614 | + | 0.0562694i | |||||
0 | 0 | |||||||||
17857.4 | − | 30929.9i | 0.873228 | − | 1.51248i | 0.0145896 | − | 0.999894i | ||
0.858638 | − | 0.512582i | ||||||||
0 | 0 | |||||||||
−5904.34 | −0.263187 | |||||||||
0 | 0 | |||||||||
44909.2 | 1.83083 | |||||||||
0 | 0 | |||||||||
3443.80 | − | 5964.84i | 0.128798 | − | 0.223084i | −0.794413 | − | 0.607378i | ||
0.923211 | + | 0.384293i | ||||||||
0 | 0 | |||||||||
−3111.85 | + | 1796.62i | −0.107076 | + | 0.0618205i | −0.552582 | − | 0.833459i | ||
0.445505 | + | 0.895279i | ||||||||
0 | 0 | |||||||||
−2822.97 | − | 1175.72i | −0.0896097 | − | 0.0373209i | |||||
0 | 0 | |||||||||
−351.002 | − | 607.953i | −0.0103045 | − | 0.0178479i | |||||
0 | 0 | |||||||||
−42290.4 | − | 24416.4i | −1.15095 | − | 0.664499i | −0.201829 | − | 0.979421i | ||
−0.949118 | + | 0.314921i | ||||||||
0 | 0 | |||||||||
− | 41906.2i | − | 1.05963i | |||||||
0 | 0 | |||||||||
− | 31698.2i | − | 0.746257i | −0.927780 | − | 0.373128i | ||||
0.927780 | − | 0.373128i | ||||||||
0 | 0 | |||||||||
27063.6 | + | 15625.2i | 0.594399 | + | 0.343176i | 0.766835 | − | 0.641844i | ||
−0.172436 | + | 0.985021i | ||||||||
0 | 0 | |||||||||
−21480.2 | − | 37204.8i | −0.440946 | − | 0.763741i | |||||
0 | 0 | |||||||||
−34158.9 | + | 4429.84i | −0.656563 | + | 0.0851455i | |||||
0 | 0 | |||||||||
−20637.0 | + | 11914.8i | −0.372031 | + | 0.214792i | −0.674345 | − | 0.738416i | ||
0.302314 | + | 0.953208i | ||||||||
0 | 0 | |||||||||
32112.3 | − | 55620.1i | 0.543824 | − | 0.941931i | |||||
0 | 0 | |||||||||
18288.6 | 0.291398 | 0.145699 | − | 0.989329i | ||||||
0.145699 | + | 0.989329i | ||||||||
0 | 0 | |||||||||
2845.11 | 0.0427121 | |||||||||
0 | 0 | |||||||||
−13092.5 | + | 22676.8i | −0.185449 | + | 0.321206i | |||||
0 | 0 | |||||||||
60686.8 | − | 35037.5i | 0.812118 | − | 0.468876i | −0.0355730 | − | 0.999367i | ||
0.847691 | + | 0.530491i | ||||||||
0 | 0 | |||||||||
−2486.81 | − | 3253.90i | −0.0314803 | − | 0.0411908i | |||||
0 | 0 | |||||||||
−5713.62 | − | 9896.28i | −0.0685021 | − | 0.118649i | |||||
0 | 0 | |||||||||
−52934.2 | − | 30561.6i | −0.601766 | − | 0.347430i | |||||
0 | 0 | |||||||||
122256.i | 1.31929i | 0.751579 | + | 0.659644i | ||||||
−0.751579 | + | 0.659644i | ||||||||
0 | 0 | |||||||||
6267.22i | 0.0642668i | |||||||||
0 | 0 | |||||||||
−91505.7 | − | 52830.9i | −0.892575 | − | 0.515329i | −0.0177913 | − | 0.999842i | ||
−0.874784 | + | 0.484513i | ||||||||
0 | 0 | |||||||||
−90044.5 | − | 155962.i | −0.836304 | − | 1.44852i | −0.892964 | − | 0.450127i | ||
0.0566605 | − | 0.998394i | ||||||||
0 | 0 | |||||||||
28563.1 | + | 37373.8i | 0.252832 | + | 0.330822i | |||||
0 | 0 | |||||||||
−130537. | + | 75365.5i | −1.10223 | + | 0.636375i | −0.936807 | − | 0.349847i | ||
−0.165427 | + | 0.986222i | ||||||||
0 | 0 | |||||||||
−39532.1 | + | 68471.7i | −0.318701 | + | 0.552007i | −0.980217 | − | 0.197924i | ||
0.661516 | + | 0.749931i | ||||||||
0 | 0 | |||||||||
79085.5 | 0.609241 | |||||||||
0 | 0 | |||||||||
100179. | 0.738040 | 0.369020 | − | 0.929421i | ||||||
0.369020 | + | 0.929421i | ||||||||
0 | 0 | |||||||||
−28518.0 | + | 49394.6i | −0.201082 | + | 0.348285i | |||||
0 | 0 | |||||||||
−645.318 | + | 372.575i | −0.00435822 | + | 0.00251622i | |||||
0 | 0 | |||||||||
16460.0 | − | 2134.60i | 0.106552 | − | 0.0138181i | |||||
0 | 0 | |||||||||
−45229.2 | − | 78339.2i | −0.280837 | − | 0.486425i | |||||
0 | 0 | |||||||||
83572.5 | + | 48250.6i | 0.498082 | + | 0.287568i | |||||
0 | 0 | |||||||||
127916.i | 0.732233i | |||||||||
0 | 0 | |||||||||
− | 133657.i | − | 0.735329i | −0.929959 | − | 0.367664i | ||||
0.929959 | − | 0.367664i | ||||||||
0 | 0 | |||||||||
215176. | + | 124232.i | 1.13846 | + | 0.657292i | |||||
0 | 0 | |||||||||
64841.1 | + | 112308.i | 0.330120 | + | 0.571785i | 0.982535 | − | 0.186077i | ||
−0.652415 | + | 0.757862i | ||||||||
0 | 0 | |||||||||
−329174. | − | 137096.i | −1.61360 | − | 0.672039i | |||||
0 | 0 | |||||||||
−68944.9 | + | 39805.4i | −0.325588 | + | 0.187978i | |||||
0 | 0 | |||||||||
23507.7 | − | 40716.5i | 0.107006 | − | 0.185340i | −0.807550 | − | 0.589799i | ||
0.914556 | + | 0.404459i | ||||||||
0 | 0 | |||||||||
323808. | 1.42151 | 0.710756 | − | 0.703439i | ||||||
0.710756 | + | 0.703439i | ||||||||
0 | 0 | |||||||||
1619.16 | 0.00685871 | |||||||||
0 | 0 | |||||||||
−4196.61 | + | 7268.73i | −0.0171616 | + | 0.0297248i | |||||
0 | 0 | |||||||||
30864.0 | − | 17819.4i | 0.121908 | − | 0.0703837i | |||||
0 | 0 | |||||||||
193289. | + | 194792.i | 0.737759 | + | 0.743494i | |||||
0 | 0 | |||||||||
−88736.6 | − | 153696.i | −0.327444 | − | 0.567150i | 0.654560 | − | 0.756010i | ||
−0.982004 | + | 0.188860i | ||||||||
0 | 0 | |||||||||
132002. | + | 76211.4i | 0.471128 | + | 0.272006i | 0.716712 | − | 0.697370i | ||
−0.245584 | + | 0.969375i | ||||||||
0 | 0 | |||||||||
− | 3019.97i | − | 0.0104297i | |||||||
0 | 0 | |||||||||
15552.9i | 0.0519976i | |||||||||
0 | 0 | |||||||||
−269397. | − | 155536.i | −0.872254 | − | 0.503596i | −0.00415732 | − | 0.999991i | ||
−0.868097 | + | 0.496395i | ||||||||
0 | 0 | |||||||||
291567. | + | 505008.i | 0.914629 | + | 1.58418i | |||||
0 | 0 | |||||||||
−127928. | + | 307163.i | −0.388957 | + | 0.933908i | |||||
0 | 0 | |||||||||
152716. | − | 88170.5i | 0.450210 | − | 0.259929i | −0.257709 | − | 0.966223i | ||
0.707919 | + | 0.706294i | ||||||||
0 | 0 | |||||||||
48201.6 | − | 83487.6i | 0.137832 | − | 0.238733i | |||||
0 | 0 | |||||||||
469993. | 1.30407 | 0.652035 | − | 0.758189i | ||||||
0.652035 | + | 0.758189i | ||||||||
0 | 0 | |||||||||
370295. | 0.997312 | |||||||||
0 | 0 | |||||||||
−32439.9 | + | 56187.6i | −0.0848378 | + | 0.146943i | |||||
0 | 0 | |||||||||
−674698. | + | 389537.i | −1.71393 | + | 0.989540i | −0.784839 | + | 0.619700i | ||
−0.929095 | + | 0.369841i | ||||||||
0 | 0 | |||||||||
43868.9 | + | 338276.i | 0.108283 | + | 0.834981i | |||||
0 | 0 | |||||||||
56228.8 | + | 97391.1i | 0.134904 | + | 0.233661i | |||||
0 | 0 | |||||||||
−535593. | − | 309225.i | −1.24940 | − | 0.721343i | −0.278412 | − | 0.960462i | ||
−0.970990 | + | 0.239119i | ||||||||
0 | 0 | |||||||||
178785.i | 0.405635i | 0.979217 | + | 0.202818i | ||||||
−0.979217 | + | 0.202818i | ||||||||
0 | 0 | |||||||||
− | 58668.9i | − | 0.129503i | |||||||
0 | 0 | |||||||||
−93217.6 | − | 53819.2i | −0.200248 | − | 0.115613i | |||||
0 | 0 | |||||||||
−17008.1 | − | 29459.0i | −0.0355675 | − | 0.0616047i | |||||
0 | 0 | |||||||||
−369008. | + | 282017.i | −0.751418 | + | 0.574275i | |||||
0 | 0 | |||||||||
9396.44 | − | 5425.04i | 0.0186372 | − | 0.0107602i | −0.490652 | − | 0.871355i | ||
0.509290 | + | 0.860595i | ||||||||
0 | 0 | |||||||||
−473563. | + | 820235.i | −0.915133 | + | 1.58506i | −0.108427 | + | 0.994104i | ||
−0.806706 | + | 0.590953i | ||||||||
0 | 0 | |||||||||
11462.0 | 0.0215861 | |||||||||
0 | 0 | |||||||||
−81454.8 | −0.149538 | −0.0747689 | − | 0.997201i | ||||||
−0.0747689 | + | 0.997201i | ||||||||
0 | 0 | |||||||||
−491764. | + | 851761.i | −0.880287 | + | 1.52470i | −0.0292649 | + | 0.999572i | ||
−0.851022 | + | 0.525130i | ||||||||
0 | 0 | |||||||||
690498. | − | 398659.i | 1.20551 | − | 0.696004i | |||||
0 | 0 | |||||||||
165191. | − | 126248.i | 0.281350 | − | 0.215023i | |||||
0 | 0 | |||||||||
−65671.0 | − | 113745.i | −0.109141 | − | 0.189038i | |||||
0 | 0 | |||||||||
52430.4 | + | 30270.7i | 0.0850467 | + | 0.0491017i | |||||
0 | 0 | |||||||||
730793.i | 1.15725i | |||||||||
0 | 0 | |||||||||
− | 427608.i | − | 0.661210i | −0.943769 | − | 0.330605i | ||||
0.943769 | − | 0.330605i | ||||||||
0 | 0 | |||||||||
448214. | + | 258776.i | 0.676918 | + | 0.390819i | |||||
0 | 0 | |||||||||
−169084. | − | 292863.i | −0.249464 | − | 0.432084i | |||||
0 | 0 | |||||||||
11668.9 | + | 89979.7i | 0.0168221 | + | 0.129716i | |||||
0 | 0 | |||||||||
−441881. | + | 255120.i | −0.622580 | + | 0.359447i | |||||
0 | 0 | |||||||||
2022.21 | − | 3502.56i | 0.00278513 | − | 0.00482398i | |||||
0 | 0 | |||||||||
60238.8 | 0.0811174 | 0.0405587 | − | 0.999177i | ||||||
0.0405587 | + | 0.999177i | ||||||||
0 | 0 | |||||||||
62064.5 | 0.0817310 | |||||||||
0 | 0 | |||||||||
27615.1 | − | 47830.8i | 0.0355699 | − | 0.0616088i | −0.847692 | − | 0.530488i | ||
0.883262 | + | 0.468879i | ||||||||
0 | 0 | |||||||||
−3063.24 | + | 1768.56i | −0.00386004 | + | 0.00222859i | −0.501929 | − | 0.864909i | ||
0.498069 | + | 0.867138i | ||||||||
0 | 0 | |||||||||
216227. | − | 519172.i | 0.266612 | − | 0.640150i | |||||
0 | 0 | |||||||||
−599259. | − | 1.03795e6i | −0.723143 | − | 1.25252i | −0.959734 | − | 0.280912i | ||
0.236590 | − | 0.971610i | ||||||||
0 | 0 | |||||||||
−1908.50 | − | 1101.87i | −0.00225435 | − | 0.00130155i | |||||
0 | 0 | |||||||||
− | 389078.i | − | 0.449952i | |||||||
0 | 0 | |||||||||
− | 531464.i | − | 0.601837i | −0.953650 | − | 0.300918i | ||||
0.953650 | − | 0.300918i | ||||||||
0 | 0 | |||||||||
−487249. | − | 281313.i | −0.540391 | − | 0.311995i | 0.204846 | − | 0.978794i | ||
−0.745237 | + | 0.666799i | ||||||||
0 | 0 | |||||||||
89046.0 | + | 154232.i | 0.0967384 | + | 0.167556i | |||||
0 | 0 | |||||||||
−95269.3 | − | 361137.i | −0.101400 | − | 0.384377i | |||||
0 | 0 | |||||||||
−75247.8 | + | 43444.3i | −0.0784786 | + | 0.0453096i | |||||
0 | 0 | |||||||||
−149304. | + | 258602.i | −0.152607 | + | 0.264323i | |||||
0 | 0 | |||||||||
1.06837e6 | 1.07037 | 0.535187 | − | 0.844734i | ||||||
0.535187 | + | 0.844734i | ||||||||
0 | 0 | |||||||||
681926. | 0.669786 | |||||||||
0 | 0 | |||||||||
−23226.8 | + | 40229.9i | −0.0223686 | + | 0.0387435i | |||||
0 | 0 | |||||||||
1.16285e6 | − | 671372.i | 1.09822 | − | 0.634060i | 0.162470 | − | 0.986714i | ||
0.935754 | + | 0.352654i | ||||||||
0 | 0 | |||||||||
−579679. | − | 241427.i | −0.536955 | − | 0.223633i | |||||
0 | 0 | |||||||||
−18914.6 | − | 32761.0i | −0.0171868 | − | 0.0297684i | |||||
0 | 0 | |||||||||
−1.39724e6 | − | 806697.i | −1.24561 | − | 0.719153i | −0.275378 | − | 0.961336i | ||
−0.970231 | + | 0.242183i | ||||||||
0 | 0 | |||||||||
− | 793667.i | − | 0.694263i | |||||||
0 | 0 | |||||||||
1.14415e6i | 0.982213i | |||||||||
0 | 0 | |||||||||
1.89088e6 | + | 1.09170e6i | 1.59325 | + | 0.919864i | 0.992744 | + | 0.120245i | ||
0.600507 | + | 0.799619i | ||||||||
0 | 0 | |||||||||
203437. | + | 352363.i | 0.168270 | + | 0.291452i | 0.937812 | − | 0.347144i | ||
−0.769542 | + | 0.638597i | ||||||||
0 | 0 | |||||||||
66312.0 | − | 8599.58i | 0.0538500 | − | 0.00698346i | |||||
0 | 0 | |||||||||
605422. | − | 349541.i | 0.482755 | − | 0.278719i | |||||
0 | 0 | |||||||||
254717. | − | 441182.i | 0.199461 | − | 0.345477i | −0.748893 | − | 0.662691i | ||
0.948354 | + | 0.317215i | ||||||||
0 | 0 | |||||||||
16508.8 | 0.0126971 | |||||||||
0 | 0 | |||||||||
−1.11878e6 | −0.845240 | −0.422620 | − | 0.906307i | ||||||
−0.422620 | + | 0.906307i | ||||||||
0 | 0 | |||||||||
−134959. | + | 233755.i | −0.100169 | + | 0.173498i | −0.911754 | − | 0.410736i | ||
0.811585 | + | 0.584234i | ||||||||
0 | 0 | |||||||||
864285. | − | 498995.i | 0.630296 | − | 0.363902i | |||||
0 | 0 | |||||||||
−465272. | − | 608790.i | −0.333428 | − | 0.436278i | |||||
0 | 0 | |||||||||
−701733. | − | 1.21544e6i | −0.494228 | − | 0.856028i | |||||
0 | 0 | |||||||||
−1.72870e6 | − | 998066.i | −1.19671 | − | 0.690918i | |||||
0 | 0 | |||||||||
− | 1.92194e6i | − | 1.30789i | −0.756542 | − | 0.653945i | ||||
0.756542 | − | 0.653945i | ||||||||
0 | 0 | |||||||||
− | 153059.i | − | 0.102401i | |||||||
0 | 0 | |||||||||
824311. | + | 475916.i | 0.542250 | + | 0.313068i | |||||
0 | 0 | |||||||||
40539.3 | + | 70216.1i | 0.0262239 | + | 0.0454212i | |||||
0 | 0 | |||||||||
−1.19794e6 | − | 1.56747e6i | −0.762115 | − | 0.997199i | |||||
0 | 0 | |||||||||
1.49406e6 | − | 862597.i | 0.934894 | − | 0.539761i | |||||
0 | 0 | |||||||||
−39925.3 | + | 69152.7i | −0.0245753 | + | 0.0425657i | |||||
0 | 0 | |||||||||
−940708. | −0.569651 | −0.284825 | − | 0.958579i | ||||||
−0.284825 | + | 0.958579i | ||||||||
0 | 0 | |||||||||
2.94041e6 | 1.75191 | |||||||||
0 | 0 | |||||||||
365640. | − | 633306.i | 0.214364 | − | 0.371290i | −0.738712 | − | 0.674022i | ||
0.953076 | + | 0.302732i | ||||||||
0 | 0 | |||||||||
271139. | − | 156542.i | 0.156434 | − | 0.0903171i | −0.419740 | − | 0.907645i | ||
0.576173 | + | 0.817327i | ||||||||
0 | 0 | |||||||||
−67392.2 | + | 8739.66i | −0.0382678 | + | 0.00496270i | |||||
0 | 0 | |||||||||
1.65827e6 | + | 2.87221e6i | 0.926846 | + | 1.60534i | 0.788565 | + | 0.614951i | ||
0.138281 | + | 0.990393i | ||||||||
0 | 0 | |||||||||
−369013. | − | 213050.i | −0.203032 | − | 0.117221i | |||||
0 | 0 | |||||||||
− | 2.46107e6i | − | 1.33309i | |||||||
0 | 0 | |||||||||
− | 352145.i | − | 0.187809i | |||||||
0 | 0 | |||||||||
71982.5 | + | 41559.1i | 0.0378023 | + | 0.0218252i | |||||
0 | 0 | |||||||||
−645462. | − | 1.11797e6i | −0.333812 | − | 0.578179i | |||||
0 | 0 | |||||||||
−11868.1 | − | 4942.87i | −0.00604493 | − | 0.00251761i | |||||
0 | 0 | |||||||||
908606. | − | 524584.i | 0.455833 | − | 0.263175i | −0.254458 | − | 0.967084i | ||
0.710290 | + | 0.703909i | ||||||||
0 | 0 | |||||||||
−57127.0 | + | 98946.8i | −0.0282313 | + | 0.0488980i | |||||
0 | 0 | |||||||||
−1.08518e6 | −0.528312 | |||||||||
0 | 0 | |||||||||
−2.90507e6 | −1.39342 | −0.696710 | − | 0.717353i | ||||||
−0.696710 | + | 0.717353i | ||||||||
0 | 0 | |||||||||
−817837. | + | 1.41653e6i | −0.386516 | + | 0.669465i | |||||
0 | 0 | |||||||||
161039. | − | 92976.0i | 0.0749973 | − | 0.0432997i | |||||
0 | 0 | |||||||||
−822120. | − | 2.01784e6i | −0.377311 | − | 0.926086i | |||||
0 | 0 | |||||||||
−465628. | − | 806492.i | −0.210616 | − | 0.364798i | |||||
0 | 0 | |||||||||
−391122. | − | 225815.i | −0.174377 | − | 0.100677i | 0.410271 | − | 0.911964i | ||
−0.584648 | + | 0.811287i | ||||||||
0 | 0 | |||||||||
− | 1.27258e6i | − | 0.559269i | −0.960107 | − | 0.279634i | ||||
0.960107 | − | 0.279634i | ||||||||
0 | 0 | |||||||||
113169.i | 0.0490299i | |||||||||
0 | 0 | |||||||||
1.73409e6 | + | 1.00118e6i | 0.740686 | + | 0.427636i | 0.822319 | − | 0.569027i | ||
−0.0816324 | + | 0.996663i | ||||||||
0 | 0 | |||||||||
−352205. | − | 610037.i | −0.148328 | − | 0.256912i | |||||
0 | 0 | |||||||||
−104193. | + | 250172.i | −0.0432679 | + | 0.103889i | |||||
0 | 0 | |||||||||
−1.09761e6 | + | 633703.i | −0.449480 | + | 0.259507i | −0.707610 | − | 0.706603i | ||
0.258131 | + | 0.966110i | ||||||||
0 | 0 | |||||||||
−2.54463e6 | + | 4.40743e6i | −1.02768 | + | 1.77999i | |||||
0 | 0 | |||||||||
1.47696e6 | 0.588305 | |||||||||
0 | 0 | |||||||||
694457. | 0.272843 | |||||||||
0 | 0 | |||||||||
−2.18287e6 | + | 3.78084e6i | −0.845985 | + | 1.46529i | 0.0387779 | + | 0.999248i | ||
−0.884763 | + | 0.466041i | ||||||||
0 | 0 | |||||||||
−120736. | + | 69707.1i | −0.0461607 | + | 0.0266509i | |||||
0 | 0 | |||||||||
−595464. | − | 4.59167e6i | −0.224606 | − | 1.73195i | |||||
0 | 0 | |||||||||
1.74926e6 | + | 3.02980e6i | 0.651001 | + | 1.12757i | 0.982880 | + | 0.184245i | ||
−0.331879 | + | 0.943322i | ||||||||
0 | 0 | |||||||||
−1.80874e6 | − | 1.04427e6i | −0.664198 | − | 0.383475i | |||||
0 | 0 | |||||||||
− | 50661.7i | − | 0.0183580i | |||||||
0 | 0 | |||||||||
4.42455e6i | 1.58224i | 0.611663 | + | 0.791118i | ||||||
−0.611663 | + | 0.791118i | ||||||||
0 | 0 | |||||||||
1.88991e6 | + | 1.09114e6i | 0.667006 | + | 0.385096i | |||||
0 | 0 | |||||||||
2.38842e6 | + | 4.13686e6i | 0.831980 | + | 1.44103i | 0.896466 | + | 0.443113i | ||
−0.0644852 | + | 0.997919i | ||||||||
0 | 0 | |||||||||
−608172. | + | 464799.i | −0.209110 | + | 0.159814i | |||||
0 | 0 | |||||||||
−310862. | + | 179476.i | −0.105509 | + | 0.0609158i | |||||
0 | 0 | |||||||||
−1.27234e6 | + | 2.20375e6i | −0.426312 | + | 0.738395i | −0.996542 | − | 0.0830906i | ||
0.570230 | + | 0.821485i | ||||||||
0 | 0 | |||||||||
−328598. | −0.108698 | |||||||||
0 | 0 | |||||||||
−2.11739e6 | −0.691544 | |||||||||
0 | 0 | |||||||||
−264775. | + | 458604.i | −0.0853856 | + | 0.147892i | |||||
0 | 0 | |||||||||
−988211. | + | 570544.i | −0.314683 | + | 0.181682i | −0.649020 | − | 0.760771i | ||
0.334337 | + | 0.942454i | ||||||||
0 | 0 | |||||||||
4.62584e6 | − | 3.53533e6i | 1.45465 | − | 1.11173i | |||||
0 | 0 | |||||||||
−2.23541e6 | − | 3.87184e6i | −0.694217 | − | 1.20242i | −0.970444 | − | 0.241327i | ||
0.276227 | − | 0.961093i | ||||||||
0 | 0 | |||||||||
19147.0 | + | 11054.5i | 0.00587269 | + | 0.00339060i | |||||
0 | 0 | |||||||||
− | 1.42722e6i | − | 0.432369i | |||||||
0 | 0 | |||||||||
1.28693e6i | 0.385097i | |||||||||
0 | 0 | |||||||||
−497871. | − | 287446.i | −0.147167 | − | 0.0849666i | 0.424609 | − | 0.905377i | ||
−0.571775 | + | 0.820410i | ||||||||
0 | 0 | |||||||||
383823. | + | 664801.i | 0.112080 | + | 0.194127i | |||||
0 | 0 | |||||||||
−114836. | − | 885507.i | −0.0331285 | − | 0.255456i | |||||
0 | 0 | |||||||||
351968. | − | 203209.i | 0.100319 | − | 0.0579192i | |||||
0 | 0 | |||||||||
−2.64349e6 | + | 4.57866e6i | −0.744454 | + | 1.28943i | |||||
0 | 0 | |||||||||
2.06791e6 | 0.575434 | 0.287717 | − | 0.957715i | ||||||
0.287717 | + | 0.957715i | ||||||||
0 | 0 | |||||||||
−4.36685e6 | −1.20078 | −0.600390 | − | 0.799708i | ||||||
−0.600390 | + | 0.799708i | ||||||||
0 | 0 | |||||||||
−1169.59 | + | 2025.80i | −0.000317822 | + | 0.000550484i | |||||
0 | 0 | |||||||||
−291733. | + | 168432.i | −0.0783454 | + | 0.0452327i | |||||
0 | 0 | |||||||||
−179100. | + | 430030.i | −0.0475364 | + | 0.114138i | |||||
0 | 0 | |||||||||
−68520.2 | − | 118680.i | −0.0179753 | − | 0.0311341i | |||||
0 | 0 | |||||||||
5.19547e6 | + | 2.99961e6i | 1.34720 | + | 0.777806i | 0.987852 | − | 0.155398i | ||
0.359348 | + | 0.933204i | ||||||||
0 | 0 | |||||||||
− | 5.69706e6i | − | 1.46026i | −0.683307 | − | 0.730131i | ||||
0.683307 | − | 0.730131i | ||||||||
0 | 0 | |||||||||
581892.i | 0.147441i | |||||||||
0 | 0 | |||||||||
6.11368e6 | + | 3.52974e6i | 1.53144 | + | 0.884176i | |||||
0 | 0 | |||||||||
2.73386e6 | + | 4.73519e6i | 0.677042 | + | 1.17267i | 0.975867 | + | 0.218364i | ||
−0.298825 | + | 0.954308i | ||||||||
0 | 0 | |||||||||
−383333. | + | 101125.i | −0.0938598 | + | 0.0247606i | |||||
0 | 0 | |||||||||
5.51411e6 | − | 3.18357e6i | 1.33495 | − | 0.770735i | 0.348898 | − | 0.937161i | ||
0.986054 | + | 0.166426i | ||||||||
0 | 0 | |||||||||
778618. | − | 1.34861e6i | 0.186391 | − | 0.322838i | |||||
0 | 0 | |||||||||
2.89770e6 | 0.685938 | |||||||||
0 | 0 | |||||||||
4.50171e6 | 1.05381 | 0.526904 | − | 0.849925i | ||||||
0.526904 | + | 0.849925i | ||||||||
0 | 0 | |||||||||
−785167. | + | 1.35995e6i | −0.181769 | + | 0.314834i | |||||
0 | 0 | |||||||||
−2.15527e6 | + | 1.24434e6i | −0.493464 | + | 0.284902i | |||||
0 | 0 | |||||||||
−84013.8 | − | 34990.4i | −0.0190249 | − | 0.00792355i | |||||
0 | 0 | |||||||||
718680. | + | 1.24479e6i | 0.160970 | + | 0.278808i | 0.935217 | − | 0.354075i | ||
−0.774247 | + | 0.632884i | ||||||||
0 | 0 | |||||||||
−397208. | − | 229328.i | −0.0880008 | − | 0.0508073i | |||||
0 | 0 | |||||||||
− | 6.30635e6i | − | 1.38206i | −0.722828 | − | 0.691028i | ||||
0.722828 | − | 0.691028i | ||||||||
0 | 0 | |||||||||
9.12301e6i | 1.97782i | 0.148531 | + | 0.988908i | ||||||
−0.148531 | + | 0.988908i | ||||||||
0 | 0 | |||||||||
−219919. | − | 126970.i | −0.0471662 | − | 0.0272314i | |||||
0 | 0 | |||||||||
−664462. | − | 1.15088e6i | −0.140987 | − | 0.244196i | 0.786882 | − | 0.617104i | ||
−0.927868 | + | 0.372908i | ||||||||
0 | 0 | |||||||||
−6.27820e6 | + | 814179.i | −1.31796 | + | 0.170918i | |||||
0 | 0 | |||||||||
4.39858e6 | − | 2.53952e6i | 0.913609 | − | 0.527472i | |||||
0 | 0 | |||||||||
−2.02159e6 | + | 3.50149e6i | −0.415470 | + | 0.719615i | |||||
0 | 0 | |||||||||
7.23707e6 | 1.47173 | |||||||||
0 | 0 | |||||||||
−842447. | −0.169530 | |||||||||
0 | 0 | |||||||||
−2.00910e6 | + | 3.47987e6i | −0.400095 | + | 0.692985i | −0.993737 | − | 0.111744i | ||
0.593642 | + | 0.804729i | ||||||||
0 | 0 | |||||||||
−132512. | + | 76505.8i | −0.0261151 | + | 0.0150776i | |||||
0 | 0 | |||||||||
−3.29892e6 | − | 4.31652e6i | −0.643435 | − | 0.841910i | |||||
0 | 0 | |||||||||
1.35841e6 | + | 2.35283e6i | 0.262226 | + | 0.454188i | |||||
0 | 0 | |||||||||
−7.43986e6 | − | 4.29540e6i | −1.42148 | − | 0.820695i | −0.425059 | − | 0.905166i | ||
−0.996426 | + | 0.0844709i | ||||||||
0 | 0 | |||||||||
2.87921e6i | 0.544505i | |||||||||
0 | 0 | |||||||||
1.57232e6i | 0.294332i | 0.989112 | + | 0.147166i | ||||||
−0.989112 | + | 0.147166i | ||||||||
0 | 0 | |||||||||
177815. | + | 102662.i | 0.0329497 | + | 0.0190235i | |||||
0 | 0 | |||||||||
69636.4 | + | 120614.i | 0.0127739 | + | 0.0221250i | |||||
0 | 0 | |||||||||
−2.49533e6 | − | 3.26505e6i | −0.453145 | − | 0.592924i | |||||
0 | 0 | |||||||||
−1.25743e6 | + | 725978.i | −0.226065 | + | 0.130518i | −0.608755 | − | 0.793358i | ||
0.382691 | + | 0.923877i | ||||||||
0 | 0 | |||||||||
−3.83692e6 | + | 6.64573e6i | −0.682948 | + | 1.18290i | |||||
0 | 0 | |||||||||
−3.59897e6 | −0.634247 | −0.317123 | − | 0.948384i | ||||||
−0.317123 | + | 0.948384i | ||||||||
0 | 0 | |||||||||
−2.34806e6 | −0.409714 | |||||||||
0 | 0 | |||||||||
−3.02300e6 | + | 5.23599e6i | −0.522298 | + | 0.904647i | |||||
0 | 0 | |||||||||
−1.76938e6 | + | 1.02155e6i | −0.302711 | + | 0.174770i | −0.643660 | − | 0.765312i | ||
0.340949 | + | 0.940082i | ||||||||
0 | 0 | |||||||||
4.01770e6 | − | 521030.i | 0.680653 | − | 0.0882695i | |||||
0 | 0 | |||||||||
4.92680e6 | + | 8.53347e6i | 0.826555 | + | 1.43164i | |||||
0 | 0 | |||||||||
−3.46584e6 | − | 2.00101e6i | −0.575825 | − | 0.332453i | |||||
0 | 0 | |||||||||
26348.1i | 0.00433534i | |||||||||
0 | 0 | |||||||||
− | 1.27204e7i | − | 2.07291i | |||||||
0 | 0 | |||||||||
6.36726e6 | + | 3.67614e6i | 1.02768 | + | 0.593332i | 0.916320 | − | 0.400448i | ||
0.111362 | + | 0.993780i | ||||||||
0 | 0 | |||||||||
4.56417e6 | + | 7.90537e6i | 0.729638 | + | 1.26377i | 0.957036 | + | 0.289968i | ||
−0.227399 | + | 0.973802i | ||||||||
0 | 0 | |||||||||
−5.14138e6 | − | 2.14130e6i | −0.814107 | − | 0.339062i | |||||
0 | 0 | |||||||||
−77599.5 | + | 44802.1i | −0.0121712 | + | 0.00702703i | |||||
0 | 0 | |||||||||
75537.1 | − | 130834.i | 0.0117360 | − | 0.0203274i | |||||
0 | 0 | |||||||||
−162466. | −0.0250050 | |||||||||
0 | 0 | |||||||||
−186707. | −0.0284670 | |||||||||
0 | 0 | |||||||||
−1.67480e6 | + | 2.90085e6i | −0.252976 | + | 0.438167i | |||||
0 | 0 | |||||||||
8.74491e6 | − | 5.04887e6i | 1.30864 | − | 0.755542i | |||||
0 | 0 | |||||||||
−3.16979e6 | + | 3.14534e6i | −0.469957 | + | 0.466332i | |||||
0 | 0 | |||||||||
−5.66666e6 | − | 9.81493e6i | −0.832403 | − | 1.44176i | −0.896128 | − | 0.443797i | ||
0.0637246 | − | 0.997968i | ||||||||
0 | 0 | |||||||||
−2.52804e6 | − | 1.45956e6i | −0.367946 | − | 0.212433i | |||||
0 | 0 | |||||||||
1.75700e6i | 0.253385i | |||||||||
0 | 0 | |||||||||
9.79610e6i | 1.39986i | 0.714211 | + | 0.699930i | ||||||
−0.714211 | + | 0.699930i | ||||||||
0 | 0 | |||||||||
73402.9 | + | 42379.2i | 0.0103940 | + | 0.00600097i | |||||
0 | 0 | |||||||||
−2.20555e6 | − | 3.82012e6i | −0.309483 | − | 0.536040i | |||||
0 | 0 | |||||||||
−1.18775e6 | + | 2.85186e6i | −0.165163 | + | 0.396565i | |||||
0 | 0 | |||||||||
1.52201e6 | − | 878735.i | 0.209742 | − | 0.121095i | |||||
0 | 0 | |||||||||
−3.23228e6 | + | 5.59847e6i | −0.441439 | + | 0.764595i | −0.997797 | − | 0.0663481i | ||
0.556357 | + | 0.830943i | ||||||||
0 | 0 | |||||||||
−480718. | −0.0650670 | |||||||||
0 | 0 | |||||||||
555402. | 0.0745076 | |||||||||
0 | 0 | |||||||||
627220. | − | 1.08638e6i | 0.0833967 | − | 0.144447i | −0.821310 | − | 0.570482i | ||
0.904707 | + | 0.426035i | ||||||||
0 | 0 | |||||||||
1.92796e6 | − | 1.11311e6i | 0.254084 | − | 0.146695i | |||||
0 | 0 | |||||||||
−1.07080e6 | − | 8.25704e6i | −0.139879 | − | 1.07862i | |||||
0 | 0 | |||||||||
−2.77361e6 | − | 4.80403e6i | −0.359140 | − | 0.622050i | 0.628677 | − | 0.777667i | ||
−0.987817 | + | 0.155617i | ||||||||
0 | 0 | |||||||||
−5.57019e6 | − | 3.21595e6i | −0.714956 | − | 0.412780i | 0.0979373 | − | 0.995193i | ||
−0.812893 | + | 0.582412i | ||||||||
0 | 0 | |||||||||
177155.i | 0.0225407i | |||||||||
0 | 0 | |||||||||
− | 6.75314e6i | − | 0.851797i | |||||||
0 | 0 | |||||||||
9.92482e6 | + | 5.73010e6i | 1.24103 | + | 0.716510i | 0.969304 | − | 0.245864i | ||
0.271728 | + | 0.962374i | ||||||||
0 | 0 | |||||||||
−7.73211e6 | − | 1.33924e7i | −0.958521 | − | 1.66021i | |||||
0 | 0 | |||||||||
1.88381e6 | − | 1.43971e6i | 0.231524 | − | 0.176944i | |||||
0 | 0 | |||||||||
−8.21784e6 | + | 4.74457e6i | −1.00135 | + | 0.578130i | |||||
0 | 0 | |||||||||
−8279.51 | + | 14340.5i | −0.00100026 | + | 0.00173251i | |||||
0 | 0 | |||||||||
1.54952e7 | 1.85610 | 0.928052 | − | 0.372451i | ||||||
0.928052 | + | 0.372451i | ||||||||
0 | 0 | |||||||||
1.92502e6 | 0.228638 | |||||||||
0 | 0 | |||||||||
664978. | − | 1.15178e6i | 0.0783138 | − | 0.135644i | |||||
0 | 0 | |||||||||
7.54037e6 | − | 4.35344e6i | 0.880554 | − | 0.508388i | 0.00971325 | − | 0.999953i | ||
0.870841 | + | 0.491564i | ||||||||
0 | 0 | |||||||||
293058. | − | 223971.i | 0.0339361 | − | 0.0259358i | |||||
0 | 0 | |||||||||
−8.02929e6 | − | 1.39071e7i | −0.922023 | − | 1.59699i | |||||
0 | 0 | |||||||||
−9.92434e6 | − | 5.72982e6i | −1.13015 | − | 0.652490i | −0.186175 | − | 0.982517i | ||
−0.943972 | + | 0.330026i | ||||||||
0 | 0 | |||||||||
− | 9.83228e6i | − | 1.11037i | −0.831727 | − | 0.555185i | ||||
0.831727 | − | 0.555185i | ||||||||
0 | 0 | |||||||||
1.15188e6i | 0.129007i | |||||||||
0 | 0 | |||||||||
−1.74089e6 | − | 1.00510e6i | −0.193367 | − | 0.111640i | |||||
0 | 0 | |||||||||
6.70187e6 | + | 1.16080e7i | 0.738286 | + | 1.27875i | 0.953267 | + | 0.302130i | ||
−0.214981 | + | 0.976618i | ||||||||
0 | 0 | |||||||||
436576. | + | 3.36647e6i | 0.0476998 | + | 0.367817i | |||||
0 | 0 | |||||||||
−2712.99 | + | 1566.35i | −0.000293999 | + | 0.000169740i | |||||
0 | 0 | |||||||||
−838947. | + | 1.45310e6i | −0.0901744 | + | 0.156187i | −0.907584 | − | 0.419870i | ||
0.817410 | + | 0.576056i | ||||||||
0 | 0 | |||||||||
2.14449e6 | 0.228631 | |||||||||
0 | 0 | |||||||||
1.48745e7 | 1.57300 | 0.786499 | − | 0.617592i | ||||||
0.786499 | + | 0.617592i | ||||||||
0 | 0 | |||||||||
−3.56661e6 | + | 6.17755e6i | −0.374136 | + | 0.648022i | −0.990197 | − | 0.139676i | ||
0.616061 | + | 0.787698i | ||||||||
0 | 0 | |||||||||
7.96285e6 | − | 4.59735e6i | 0.828590 | − | 0.478387i | |||||
0 | 0 | |||||||||
3.49279e6 | − | 8.38638e6i | 0.360539 | − | 0.865674i | |||||
0 | 0 | |||||||||
−2.68990e6 | − | 4.65904e6i | −0.275445 | − | 0.477085i | |||||
0 | 0 | |||||||||
−1.03335e7 | − | 5.96603e6i | −1.04973 | − | 0.606061i | |||||
0 | 0 | |||||||||
− | 620131.i | − | 0.0624967i | |||||||
0 | 0 | |||||||||
− | 9.49875e6i | − | 0.949715i | −0.880063 | − | 0.474857i | ||||
0.880063 | − | 0.474857i | ||||||||
0 | 0 | |||||||||
6.04639e6 | + | 3.49089e6i | 0.599773 | + | 0.346279i | |||||
0 | 0 | |||||||||
−1.48509e6 | − | 2.57225e6i | −0.146156 | − | 0.253150i | |||||
0 | 0 | |||||||||
−512305. | − | 139400.i | −0.0500241 | − | 0.0136117i | |||||
0 | 0 | |||||||||
−647530. | + | 373852.i | −0.0627347 | + | 0.0362199i | |||||
0 | 0 | |||||||||
7.67359e6 | − | 1.32910e7i | 0.737655 | − | 1.27766i | −0.215894 | − | 0.976417i | ||
0.953549 | − | 0.301239i | ||||||||
0 | 0 | |||||||||
−988668. | −0.0943025 | −0.0471512 | − | 0.998888i | ||||||
−0.0471512 | + | 0.998888i | ||||||||
0 | 0 | |||||||||
5.52146e6 | 0.522582 | |||||||||
0 | 0 | |||||||||
−5.51747e6 | + | 9.55655e6i | −0.518179 | + | 0.897512i | 0.481598 | + | 0.876392i | ||
−0.999777 | + | 0.0211198i | ||||||||
0 | 0 | |||||||||
−1.58482e6 | + | 914994.i | −0.147695 | + | 0.0852720i | |||||
0 | 0 | |||||||||
−1.36758e6 | − | 569574.i | −0.126474 | − | 0.0526742i | |||||
0 | 0 | |||||||||
2.55762e6 | + | 4.42993e6i | 0.234722 | + | 0.406550i | 0.959192 | − | 0.282756i | ||
−0.724470 | + | 0.689306i | ||||||||
0 | 0 | |||||||||
2.49576e6 | + | 1.44093e6i | 0.227300 | + | 0.131232i | |||||
0 | 0 | |||||||||
− | 737139.i | − | 0.0666248i | |||||||
0 | 0 | |||||||||
− | 1.13694e7i | − | 1.01982i | −0.860227 | − | 0.509911i | ||||
0.860227 | − | 0.509911i | ||||||||
0 | 0 | |||||||||
−1.41836e7 | − | 8.18893e6i | −1.26265 | − | 0.728993i | −0.289066 | − | 0.957309i | ||
−0.973587 | + | 0.228316i | ||||||||
0 | 0 | |||||||||
33017.6 | + | 57188.2i | 0.00291717 | + | 0.00505269i | |||||
0 | 0 | |||||||||
−7.85832e6 | + | 1.01909e6i | −0.689089 | + | 0.0893635i | |||||
0 | 0 | |||||||||
−3.56467e6 | + | 2.05806e6i | −0.310245 | + | 0.179120i | |||||
0 | 0 | |||||||||
−491775. | + | 851779.i | −0.0424816 | + | 0.0735803i | |||||
0 | 0 | |||||||||
954701. | 0.0818580 | |||||||||
0 | 0 | |||||||||
9.53588e6 | 0.811564 | 0.405782 | − | 0.913970i | ||||||
0.405782 | + | 0.913970i | ||||||||
0 | 0 | |||||||||
4.71301e6 | − | 8.16317e6i | 0.398143 | − | 0.689604i | |||||
0 | 0 | |||||||||
1.06224e7 | − | 6.13284e6i | 0.890740 | − | 0.514269i | 0.0165554 | − | 0.999863i | ||
0.874184 | + | 0.485594i | ||||||||
0 | 0 | |||||||||
9.62416e6 | + | 1.25929e7i | 0.801103 | + | 1.04821i | |||||
0 | 0 | |||||||||
450887. | + | 780959.i | 0.0372563 | + | 0.0645298i | |||||
0 | 0 | |||||||||
−2.91586e6 | − | 1.68347e6i | −0.239175 | − | 0.138088i | 0.375623 | − | 0.926773i | ||
−0.614797 | + | 0.788685i | ||||||||
0 | 0 | |||||||||
− | 1.04480e6i | − | 0.0850756i | |||||||
0 | 0 | |||||||||
− | 57752.4i | − | 0.00466851i | |||||||
0 | 0 | |||||||||
−977071. | − | 564112.i | −0.0784112 | − | 0.0452707i | |||||
0 | 0 | |||||||||
−2.65246e6 | − | 4.59420e6i | −0.211327 | − | 0.366028i | 0.740803 | − | 0.671722i | ||
−0.952130 | + | 0.305694i | ||||||||
0 | 0 | |||||||||
493366. | + | 645551.i | 0.0390244 | + | 0.0510620i | |||||
0 | 0 | |||||||||
6.23174e6 | − | 3.59789e6i | 0.489381 | − | 0.282544i | |||||
0 | 0 | |||||||||
378346. | − | 655315.i | 0.0294990 | − | 0.0510938i | |||||
0 | 0 | |||||||||
1.95688e7 | 1.51486 | |||||||||
0 | 0 | |||||||||
3.03260e6 | 0.233088 | 0.116544 | − | 0.993186i | ||||||
0.116544 | + | 0.993186i | ||||||||
0 | 0 | |||||||||
−6.66133e6 | + | 1.15378e7i | −0.508362 | + | 0.880508i | |||||
0 | 0 | |||||||||
31161.1 | − | 17990.8i | 0.00236124 | − | 0.00136326i | |||||
0 | 0 | |||||||||
−1.35844e7 | + | 1.76168e6i | −1.02210 | + | 0.132549i | |||||
0 | 0 | |||||||||
−7.72319e6 | − | 1.33770e7i | −0.577007 | − | 0.999406i | −0.995820 | − | 0.0913332i | ||
0.418813 | − | 0.908072i | ||||||||
0 | 0 | |||||||||
486790. | + | 281049.i | 0.0361134 | + | 0.0208501i | |||||
0 | 0 | |||||||||
− | 1.79630e6i | − | 0.132329i | |||||||
0 | 0 | |||||||||
186517.i | 0.0136444i | |||||||||
0 | 0 | |||||||||
7.51492e6 | + | 4.33874e6i | 0.545917 | + | 0.315185i | |||||
0 | 0 | |||||||||
8.99286e6 | + | 1.55761e7i | 0.648748 | + | 1.12366i | 0.983422 | + | 0.181330i | ||
−0.334675 | + | 0.942334i | ||||||||
0 | 0 | |||||||||
−2.15525e7 | − | 8.97627e6i | −1.54405 | − | 0.643070i | |||||
0 | 0 | |||||||||
7.95557e6 | − | 4.59315e6i | 0.566012 | − | 0.326787i | |||||
0 | 0 | |||||||||
−2.10984e6 | + | 3.65435e6i | −0.149075 | + | 0.258205i | |||||
0 | 0 | |||||||||
−1.55969e7 | −1.09447 | −0.547234 | − | 0.836980i | ||||||
−0.547234 | + | 0.836980i | ||||||||
0 | 0 | |||||||||
1.26988e7 | 0.884998 | |||||||||
0 | 0 | |||||||||
974136. | − | 1.68725e6i | 0.0674258 | − | 0.116785i | |||||
0 | 0 | |||||||||
−1.11442e7 | + | 6.43409e6i | −0.766104 | + | 0.442310i | −0.831483 | − | 0.555550i | ||
0.0653790 | + | 0.997861i | ||||||||
0 | 0 | |||||||||
5.88426e6 | + | 1.60113e6i | 0.401766 | + | 0.109322i | |||||
0 | 0 | |||||||||
6.48726e6 | + | 1.12363e7i | 0.439939 | + | 0.761997i | |||||
0 | 0 | |||||||||
−1.72415e7 | − | 9.95440e6i | −1.16135 | − | 0.670508i | −0.209726 | − | 0.977760i | ||
−0.951628 | + | 0.307252i | ||||||||
0 | 0 | |||||||||
− | 1.41868e6i | − | 0.0949157i | |||||||
0 | 0 | |||||||||
− | 2.89554e7i | − | 1.92423i | −0.272640 | − | 0.962116i | ||||
0.272640 | − | 0.962116i | ||||||||
0 | 0 | |||||||||
−3.41550e6 | − | 1.97194e6i | −0.225457 | − | 0.130168i | |||||
0 | 0 | |||||||||
−215698. | − | 373600.i | −0.0141431 | − | 0.0244966i | |||||
0 | 0 | |||||||||
−7.51297e6 | + | 1.80391e7i | −0.489336 | + | 1.17492i | |||||
0 | 0 | |||||||||
56095.8 | − | 32386.9i | 0.00362936 | − | 0.00209541i | −0.498184 | − | 0.867071i | ||
0.501814 | + | 0.864976i | ||||||||
0 | 0 | |||||||||
−8.72188e6 | + | 1.51067e7i | −0.560561 | + | 0.970920i | |||||
0 | 0 | |||||||||
3.38720e6 | 0.216259 | |||||||||
0 | 0 | |||||||||
−1.28686e7 | −0.816190 | −0.408095 | − | 0.912940i | ||||||
−0.408095 | + | 0.912940i | ||||||||
0 | 0 | |||||||||
−5.56709e6 | + | 9.64248e6i | −0.350771 | + | 0.607553i | |||||
0 | 0 | |||||||||
−1.58510e7 | + | 9.15160e6i | −0.992193 | + | 0.572843i | −0.905929 | − | 0.423429i | ||
−0.0862641 | + | 0.996272i | ||||||||
0 | 0 | |||||||||
1.31822e6 | + | 1.01649e7i | 0.0819742 | + | 0.632110i | |||||
0 | 0 | |||||||||
−33555.5 | − | 58119.8i | −0.00207305 | − | 0.00359063i | |||||
0 | 0 | |||||||||
−188429. | − | 108789.i | −0.0115654 | − | 0.00667726i | |||||
0 | 0 | |||||||||
1.68118e7i | 1.02518i | 0.858634 | + | 0.512589i | ||||||
−0.858634 | + | 0.512589i | ||||||||
0 | 0 | |||||||||
2.19237e7i | 1.32824i | |||||||||
0 | 0 | |||||||||
2.16919e7 | + | 1.25238e7i | 1.30571 | + | 0.753854i | 0.981378 | − | 0.192088i | ||
0.324336 | + | 0.945942i | ||||||||
0 | 0 | |||||||||
−920744. | − | 1.59478e6i | −0.0550662 | − | 0.0953774i | |||||
0 | 0 | |||||||||
8.14615e6 | − | 6.22574e6i | 0.484061 | − | 0.369946i | |||||
0 | 0 | |||||||||
−1.40785e7 | + | 8.12825e6i | −0.831216 | + | 0.479903i | |||||
0 | 0 | |||||||||
−4.21099e6 | + | 7.29365e6i | −0.247034 | + | 0.427875i | |||||
0 | 0 | |||||||||
−5.74528e6 | −0.334894 | |||||||||
0 | 0 | |||||||||
−6.91278e6 | −0.400386 | |||||||||
0 | 0 | |||||||||
1.99502e6 | − | 3.45547e6i | 0.114818 | − | 0.198870i | −0.802889 | − | 0.596128i | ||
0.917707 | + | 0.397258i | ||||||||
0 | 0 | |||||||||
2.28135e7 | − | 1.31714e7i | 1.30467 | − | 0.753249i | |||||
0 | 0 | |||||||||
1.03189e7 | − | 7.88625e6i | 0.586395 | − | 0.448156i | |||||
0 | 0 | |||||||||
56755.2 | + | 98302.9i | 0.00320496 | + | 0.00555115i | |||||
0 | 0 | |||||||||
1.12225e7 | + | 6.47931e6i | 0.629755 | + | 0.363589i | |||||
0 | 0 | |||||||||
2.69992e7i | 1.50558i | 0.658259 | + | 0.752792i | ||||||
−0.658259 | + | 0.752792i | ||||||||
0 | 0 | |||||||||
− | 12696.3i | − | 0.000703575i | |||||||
0 | 0 | |||||||||
−1.43149e6 | − | 826473.i | −0.0788330 | − | 0.0455142i | |||||
0 | 0 | |||||||||
−4.15149e6 | − | 7.19060e6i | −0.227204 | − | 0.393528i | |||||
0 | 0 | |||||||||
950949. | + | 7.33284e6i | 0.0517211 | + | 0.398825i | |||||
0 | 0 | |||||||||
−3.08735e7 | + | 1.78248e7i | −1.66879 | + | 0.963476i | |||||
0 | 0 | |||||||||
8.61028e6 | − | 1.49134e7i | 0.462536 | − | 0.801136i | −0.536550 | − | 0.843868i | ||
0.999087 | + | 0.0427321i | ||||||||
0 | 0 | |||||||||
1.90148e7 | 1.01517 | 0.507587 | − | 0.861601i | ||||||
0.507587 | + | 0.861601i | ||||||||
0 | 0 | |||||||||
−6.64325e6 | −0.352496 | |||||||||
0 | 0 | |||||||||
1.95936e6 | − | 3.39371e6i | 0.103329 | − | 0.178970i | |||||
0 | 0 | |||||||||
−3.62483e7 | + | 2.09280e7i | −1.89991 | + | 1.09691i | |||||
0 | 0 | |||||||||
−37140.9 | + | 89177.3i | −0.00193483 | + | 0.00464563i | |||||
0 | 0 | |||||||||
−1.54355e6 | − | 2.67352e6i | −0.0799216 | − | 0.138428i | 0.823294 | − | 0.567615i | ||
−0.903216 | + | 0.429186i | ||||||||
0 | 0 | |||||||||
2.03659e7 | + | 1.17582e7i | 1.04810 | + | 0.605122i | 0.922117 | − | 0.386910i | ||
0.125984 | + | 0.992032i | ||||||||
0 | 0 | |||||||||
1.14143e7i | 0.583866i | |||||||||
0 | 0 | |||||||||
2.15389e7i | 1.09512i | 0.836767 | + | 0.547559i | ||||||
−0.836767 | + | 0.547559i | ||||||||
0 | 0 | |||||||||
−1.14533e7 | − | 6.61258e6i | −0.578823 | − | 0.334183i | 0.181843 | − | 0.983328i | ||
−0.760665 | + | 0.649144i | ||||||||
0 | 0 | |||||||||
4.15889e6 | + | 7.20342e6i | 0.208918 | + | 0.361856i | |||||
0 | 0 | |||||||||
1.52742e6 | − | 1.51563e6i | 0.0762684 | − | 0.0756801i | |||||
0 | 0 | |||||||||
9.04510e6 | − | 5.22219e6i | 0.448949 | − | 0.259201i | |||||
0 | 0 | |||||||||
1.25364e6 | − | 2.17136e6i | 0.0618526 | − | 0.107132i | |||||
0 | 0 | |||||||||
1.67107e7 | 0.819575 | 0.409788 | − | 0.912181i | ||||||
0.409788 | + | 0.912181i | ||||||||
0 | 0 | |||||||||
−1.79392e7 | −0.874607 | |||||||||
0 | 0 | |||||||||
9.13348e6 | − | 1.58196e7i | 0.442657 | − | 0.766704i | |||||
0 | 0 | |||||||||
7.12639e6 | − | 4.11442e6i | 0.343343 | − | 0.198229i | |||||
0 | 0 | |||||||||
−1.08258e7 | − | 4.50876e6i | −0.518503 | − | 0.215948i | |||||
0 | 0 | |||||||||
−2.20354e6 | − | 3.81664e6i | −0.104918 | − | 0.181724i | |||||
0 | 0 | |||||||||
1.07662e7 | + | 6.21590e6i | 0.509613 | + | 0.294225i | |||||
0 | 0 | |||||||||
484559.i | 0.0228020i | 0.999935 | + | 0.0114010i | ||||||
−0.999935 | + | 0.0114010i | ||||||||
0 | 0 | |||||||||
1.44179e6i | 0.0674506i | |||||||||
0 | 0 | |||||||||
−2.82629e7 | − | 1.63176e7i | −1.31451 | − | 0.758935i | −0.331674 | − | 0.943394i | ||
−0.982840 | + | 0.184459i | ||||||||
0 | 0 | |||||||||
−5.10980e6 | − | 8.85044e6i | −0.236277 | − | 0.409243i | 0.723366 | − | 0.690465i | ||
−0.959643 | + | 0.281221i | ||||||||
0 | 0 | |||||||||
1.24067e7 | − | 1.60894e6i | 0.570359 | − | 0.0739662i | |||||
0 | 0 | |||||||||
2.91512e7 | − | 1.68305e7i | 1.33239 | − | 0.769253i | 0.346721 | − | 0.937968i | ||
0.985665 | + | 0.168715i | ||||||||
0 | 0 | |||||||||
−8.65645e6 | + | 1.49934e7i | −0.393369 | + | 0.681334i | |||||
0 | 0 | |||||||||
2.29151e7 | 1.03532 | |||||||||
0 | 0 | |||||||||
6.33135e6 | 0.284411 | |||||||||
0 | 0 | |||||||||
−771312. | + | 1.33595e6i | −0.0344496 | + | 0.0596685i | |||||
0 | 0 | |||||||||
2.49744e6 | − | 1.44190e6i | 0.110907 | − | 0.0640322i | |||||
0 | 0 | |||||||||
1.00697e7 | + | 1.31759e7i | 0.444630 | + | 0.581781i | |||||
0 | 0 | |||||||||
3.88346e6 | + | 6.72635e6i | 0.170498 | + | 0.295311i | 0.938594 | − | 0.345023i | ||
−0.768096 | + | 0.640335i | ||||||||
0 | 0 | |||||||||
2.71764e7 | + | 1.56903e7i | 1.18637 | + | 0.684950i | |||||
0 | 0 | |||||||||
− | 3.44116e7i | − | 1.49370i | −0.664990 | − | 0.746852i | ||||
0.664990 | − | 0.746852i | ||||||||
0 | 0 | |||||||||
4.33214e7i | 1.86982i | 0.354880 | + | 0.934912i | ||||||
−0.354880 | + | 0.934912i | ||||||||
0 | 0 | |||||||||
2.16427e6 | + | 1.24954e6i | 0.0928865 | + | 0.0536280i | |||||
0 | 0 | |||||||||
−40392.9 | − | 69962.6i | −0.00172384 | − | 0.00298577i | 0.865162 | − | 0.501492i | ||
−0.866886 | + | 0.498506i | ||||||||
0 | 0 | |||||||||
−1.05217e7 | − | 1.37672e7i | −0.446510 | − | 0.584241i | |||||
0 | 0 | |||||||||
−1.47779e7 | + | 8.53200e6i | −0.623616 | + | 0.360045i | |||||
0 | 0 | |||||||||
−136381. | + | 236219.i | −0.00572303 | + | 0.00991258i | |||||
0 | 0 | |||||||||
−1.37434e7 | −0.573506 | |||||||||
0 | 0 | |||||||||
−1.32381e6 | −0.0549345 | |||||||||
0 | 0 | |||||||||
−561206. | + | 972037.i | −0.0231592 | + | 0.0401129i | |||||
0 | 0 | |||||||||
3.95991e6 | − | 2.28625e6i | 0.162507 | − | 0.0938237i | |||||
0 | 0 | |||||||||
3.19438e7 | − | 4.14258e6i | 1.30367 | − | 0.169064i | |||||
0 | 0 | |||||||||
1.98652e6 | + | 3.44076e6i | 0.0806254 | + | 0.139647i | |||||
0 | 0 | |||||||||
9.05859e6 | + | 5.22998e6i | 0.365630 | + | 0.211097i | 0.671548 | − | 0.740961i | ||
−0.305917 | + | 0.952058i | ||||||||
0 | 0 | |||||||||
2.49237e6i | 0.100047i | |||||||||
0 | 0 | |||||||||
− | 1.12503e7i | − | 0.449127i | −0.974459 | − | 0.224563i | ||||
0.974459 | − | 0.224563i | ||||||||
0 | 0 | |||||||||
−4.20816e6 | − | 2.42958e6i | −0.167076 | − | 0.0964616i | |||||
0 | 0 | |||||||||
−651882. | − | 1.12909e6i | −0.0257405 | − | 0.0445838i | |||||
0 | 0 | |||||||||
1.55200e7 | + | 6.46383e6i | 0.609493 | + | 0.253844i | |||||
0 | 0 | |||||||||
−4.64723e6 | + | 2.68308e6i | −0.181512 | + | 0.104796i | −0.588003 | − | 0.808859i | ||
0.406491 | + | 0.913655i | ||||||||
0 | 0 | |||||||||
7.67972e6 | − | 1.33017e7i | 0.298329 | − | 0.516722i | |||||
0 | 0 | |||||||||
−1.00134e6 | −0.0386882 | |||||||||
0 | 0 | |||||||||
1.27445e7 | 0.489745 | |||||||||
0 | 0 | |||||||||
−2.12399e6 | + | 3.67886e6i | −0.0811807 | + | 0.140609i | |||||
0 | 0 | |||||||||
−2.14406e7 | + | 1.23787e7i | −0.815074 | + | 0.470583i | −0.848715 | − | 0.528851i | ||
0.0336410 | + | 0.999434i | ||||||||
0 | 0 | |||||||||
−4.46988e7 | + | 1.17917e7i | −1.69014 | + | 0.445864i | |||||
0 | 0 | |||||||||
5.96999e6 | + | 1.03403e7i | 0.224527 | + | 0.388893i | |||||
0 | 0 | |||||||||
−654649. | − | 377962.i | −0.0244895 | − | 0.0141390i | |||||
0 | 0 | |||||||||
1.46850e6i | 0.0546419i | 0.999627 | + | 0.0273210i | ||||||
−0.999627 | + | 0.0273210i | ||||||||
0 | 0 | |||||||||
5.11189e6i | 0.189198i | |||||||||
0 | 0 | |||||||||
5.16498e6 | + | 2.98200e6i | 0.190149 | + | 0.109783i | 0.592052 | − | 0.805899i | ||
−0.401903 | + | 0.915682i | ||||||||
0 | 0 | |||||||||
7.58472e6 | + | 1.31371e7i | 0.277754 | + | 0.481084i | |||||
0 | 0 | |||||||||
−3.96808e6 | + | 9.52758e6i | −0.144544 | + | 0.347059i | |||||
0 | 0 | |||||||||
4.13119e7 | − | 2.38514e7i | 1.49692 | − | 0.864250i | 0.496931 | − | 0.867790i | ||
0.999994 | + | 0.00353991i | ||||||||
0 | 0 | |||||||||
493597. | − | 854935.i | 0.0177913 | − | 0.0308154i | |||||
0 | 0 | |||||||||
−5.41510e7 | −1.94158 | |||||||||
0 | 0 | |||||||||
−4.82889e7 | −1.72232 | −0.861162 | − | 0.508330i | ||||||
−0.861162 | + | 0.508330i | ||||||||
0 | 0 | |||||||||
120557. | − | 208812.i | 0.00427746 | − | 0.00740877i | |||||
0 | 0 | |||||||||
6.02507e6 | − | 3.47858e6i | 0.212658 | − | 0.122778i | |||||
0 | 0 | |||||||||
−783878. | − | 6.04455e6i | −0.0275234 | − | 0.212235i | |||||
0 | 0 | |||||||||
1.40697e7 | + | 2.43694e7i | 0.491445 | + | 0.851208i | |||||
0 | 0 | |||||||||
3.07913e6 | + | 1.77774e6i | 0.106995 | + | 0.0617735i | |||||
0 | 0 | |||||||||
2.10474e7i | 0.727580i | |||||||||
0 | 0 | |||||||||
− | 5.23912e7i | − | 1.80174i | −0.434089 | − | 0.900870i | ||||
0.434089 | − | 0.900870i | ||||||||
0 | 0 | |||||||||
4.97935e6 | + | 2.87483e6i | 0.170358 | + | 0.0983565i | |||||
0 | 0 | |||||||||
−1.39434e7 | − | 2.41507e7i | −0.474592 | − | 0.822017i | 0.524985 | − | 0.851112i | ||
−0.999577 | + | 0.0290944i | ||||||||
0 | 0 | |||||||||
3.33536e7 | − | 2.54907e7i | 1.12943 | − | 0.863176i | |||||
0 | 0 | |||||||||
−1.17530e6 | + | 678558.i | −0.0395946 | + | 0.0228599i | |||||
0 | 0 | |||||||||
2.87737e7 | − | 4.98375e7i | 0.964405 | − | 1.67040i | 0.253201 | − | 0.967414i | ||
0.711204 | − | 0.702985i | ||||||||
0 | 0 | |||||||||
−1.86184e7 | −0.620850 | |||||||||
0 | 0 | |||||||||
1.86499e6 | 0.0618732 | |||||||||
0 | 0 | |||||||||
5.32884e6 | − | 9.22981e6i | 0.175893 | − | 0.304656i | −0.764577 | − | 0.644532i | ||
0.940470 | + | 0.339877i | ||||||||
0 | 0 | |||||||||
−1.56761e6 | + | 905061.i | −0.0514811 | + | 0.0297226i | |||||
0 | 0 | |||||||||
166781. | − | 127463.i | 0.00544946 | − | 0.00416478i | |||||
0 | 0 | |||||||||
1.95285e7 | + | 3.38244e7i | 0.634862 | + | 1.09961i | |||||
0 | 0 | |||||||||
−5.15687e6 | − | 2.97732e6i | −0.166802 | − | 0.0963034i | 0.414275 | − | 0.910152i | ||
−0.581077 | + | 0.813848i | ||||||||
0 | 0 | |||||||||
1.71303e7i | 0.551306i | |||||||||
0 | 0 | |||||||||
2.18564e7i | 0.699875i | |||||||||
0 | 0 | |||||||||
−3.30824e7 | − | 1.91001e7i | −1.05404 | − | 0.608552i | −0.130265 | − | 0.991479i | ||
−0.923779 | + | 0.382927i | ||||||||
0 | 0 | |||||||||
8.67614e6 | + | 1.50275e7i | 0.275051 | + | 0.476402i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 224.6.p.a.31.11 | ✓ | 80 | |
4.3 | odd | 2 | inner | 224.6.p.a.31.30 | yes | 80 | |
7.5 | odd | 6 | inner | 224.6.p.a.159.30 | yes | 80 | |
28.19 | even | 6 | inner | 224.6.p.a.159.11 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.p.a.31.11 | ✓ | 80 | 1.1 | even | 1 | trivial | |
224.6.p.a.31.30 | yes | 80 | 4.3 | odd | 2 | inner | |
224.6.p.a.159.11 | yes | 80 | 28.19 | even | 6 | inner | |
224.6.p.a.159.30 | yes | 80 | 7.5 | odd | 6 | inner |