Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,8,Mod(67,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.67");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 294.e (of order , degree , not 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: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: |
Embedding invariants
Embedding label | 67.1 | ||
Root | of defining polynomial | ||
Character | 294.67 | ||
Dual form | 294.8.e.j.79.1 |
-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 .
4.00000 | + | 6.92820i | 0.353553 | + | 0.612372i | |||||
−13.5000 | + | 23.3827i | −0.288675 | + | 0.500000i | |||||
−32.0000 | + | 55.4256i | −0.250000 | + | 0.433013i | |||||
61.0000 | + | 105.655i | 0.218240 | + | 0.378003i | 0.954270 | − | 0.298946i | ||
−0.736030 | + | 0.676949i | ||||||||
−216.000 | −0.408248 | |||||||||
0 | 0 | |||||||||
−512.000 | −0.353553 | |||||||||
−364.500 | − | 631.333i | −0.166667 | − | 0.288675i | |||||
−488.000 | + | 845.241i | −0.154319 | + | 0.267289i | |||||
506.000 | − | 876.418i | 0.114624 | − | 0.198535i | −0.803005 | − | 0.595972i | ||
0.917629 | + | 0.397437i | ||||||||
−864.000 | − | 1496.49i | −0.144338 | − | 0.250000i | |||||
3126.00 | 0.394627 | 0.197314 | − | 0.980340i | ||||||
0.197314 | + | 0.980340i | ||||||||
0 | 0 | |||||||||
−3294.00 | −0.252002 | |||||||||
−2048.00 | − | 3547.24i | −0.125000 | − | 0.216506i | |||||
14147.0 | − | 24503.3i | 0.698382 | − | 1.20963i | −0.270645 | − | 0.962679i | ||
0.969027 | − | 0.246954i | ||||||||
2916.00 | − | 5050.66i | 0.117851 | − | 0.204124i | |||||
11114.0 | + | 19250.0i | 0.371734 | + | 0.643863i | 0.989832 | − | 0.142238i | ||
−0.618098 | + | 0.786101i | ||||||||
−7808.00 | −0.218240 | |||||||||
0 | 0 | |||||||||
8096.00 | 0.162103 | |||||||||
54320.0 | + | 94085.0i | 0.930920 | + | 1.61240i | 0.781753 | + | 0.623589i | ||
0.149167 | + | 0.988812i | ||||||||
6912.00 | − | 11971.9i | 0.102062 | − | 0.176777i | |||||
31620.5 | − | 54768.3i | 0.404742 | − | 0.701034i | |||||
12504.0 | + | 21657.6i | 0.139522 | + | 0.241659i | |||||
19683.0 | 0.192450 | |||||||||
0 | 0 | |||||||||
−41354.0 | −0.314865 | −0.157433 | − | 0.987530i | ||||||
−0.157433 | + | 0.987530i | ||||||||
−13176.0 | − | 22821.5i | −0.0890962 | − | 0.154319i | |||||
−23328.0 | + | 40405.3i | −0.140641 | + | 0.243597i | −0.927738 | − | 0.373232i | ||
0.787097 | + | 0.616829i | ||||||||
16384.0 | − | 28377.9i | 0.0883883 | − | 0.153093i | |||||
13662.0 | + | 23663.3i | 0.0661783 | + | 0.114624i | |||||
226352. | 0.987662 | |||||||||
0 | 0 | |||||||||
46656.0 | 0.166667 | |||||||||
42857.0 | + | 74230.5i | 0.139096 | + | 0.240922i | 0.927155 | − | 0.374678i | ||
−0.788058 | + | 0.615600i | ||||||||
−88912.0 | + | 154000.i | −0.262856 | + | 0.455280i | |||||
−42201.0 | + | 73094.3i | −0.113919 | + | 0.197314i | |||||
−31232.0 | − | 54095.4i | −0.0771596 | − | 0.133644i | |||||
−155694. | −0.352800 | −0.176400 | − | 0.984319i | ||||||
−0.176400 | + | 0.984319i | ||||||||
0 | 0 | |||||||||
926804. | 1.77766 | 0.888829 | − | 0.458239i | ||||||
0.888829 | + | 0.458239i | ||||||||
32384.0 | + | 56090.7i | 0.0573121 | + | 0.0992674i | |||||
44469.0 | − | 77022.6i | 0.0727467 | − | 0.126001i | |||||
−434560. | + | 752680.i | −0.658260 | + | 1.14014i | |||||
264576. | + | 458259.i | 0.371713 | + | 0.643826i | 0.989829 | − | 0.142261i | ||
−0.618116 | + | 0.786087i | ||||||||
110592. | 0.144338 | |||||||||
0 | 0 | |||||||||
505928. | 0.572392 | |||||||||
381969. | + | 661590.i | 0.403211 | + | 0.698382i | |||||
−100032. | + | 173261.i | −0.0986569 | + | 0.170879i | |||||
147033. | − | 254669.i | 0.135659 | − | 0.234969i | −0.790190 | − | 0.612862i | ||
0.925849 | + | 0.377893i | ||||||||
78732.0 | + | 136368.i | 0.0680414 | + | 0.117851i | |||||
123464. | 0.100062 | |||||||||
0 | 0 | |||||||||
−600156. | −0.429242 | |||||||||
−165416. | − | 286509.i | −0.111322 | − | 0.192815i | |||||
333646. | − | 577892.i | 0.211497 | − | 0.366323i | −0.740686 | − | 0.671851i | ||
0.952183 | + | 0.305528i | ||||||||
105408. | − | 182572.i | 0.0630005 | − | 0.109120i | |||||
−416715. | − | 721772.i | −0.235063 | − | 0.407141i | 0.724228 | − | 0.689561i | ||
−0.959291 | + | 0.282419i | ||||||||
−373248. | −0.198896 | |||||||||
0 | 0 | |||||||||
262144. | 0.125000 | |||||||||
190686. | + | 330278.i | 0.0861236 | + | 0.149170i | |||||
−109296. | + | 189306.i | −0.0467951 | + | 0.0810515i | |||||
−576998. | + | 999390.i | −0.234376 | + | 0.405951i | −0.959091 | − | 0.283098i | ||
0.724715 | + | 0.689048i | ||||||||
905408. | + | 1.56821e6i | 0.349191 | + | 0.604817i | |||||
−2.93328e6 | −1.07493 | |||||||||
0 | 0 | |||||||||
3.84234e6 | 1.27406 | 0.637032 | − | 0.770838i | ||||||
0.637032 | + | 0.770838i | ||||||||
186624. | + | 323242.i | 0.0589256 | + | 0.102062i | |||||
−741845. | + | 1.28491e6i | −0.223194 | + | 0.386584i | −0.955776 | − | 0.294095i | ||
0.732582 | + | 0.680679i | ||||||||
−342856. | + | 593844.i | −0.0983560 | + | 0.170358i | |||||
853754. | + | 1.47874e6i | 0.233678 | + | 0.404742i | |||||
−1.42259e6 | −0.371734 | |||||||||
0 | 0 | |||||||||
−675216. | −0.161106 | |||||||||
1.88191e6 | + | 3.25957e6i | 0.429442 | + | 0.743815i | 0.996824 | − | 0.0796396i | ||
−0.567382 | + | 0.823455i | ||||||||
249856. | − | 432763.i | 0.0545601 | − | 0.0945008i | |||||
−265720. | + | 460241.i | −0.0555556 | + | 0.0962250i | |||||
−622776. | − | 1.07868e6i | −0.124734 | − | 0.216045i | |||||
−5.39309e6 | −1.03530 | −0.517648 | − | 0.855594i | ||||||
−0.517648 | + | 0.855594i | ||||||||
0 | 0 | |||||||||
3.45187e6 | 0.609660 | |||||||||
3.70722e6 | + | 6.42109e6i | 0.628497 | + | 1.08859i | |||||
558279. | − | 966968.i | 0.0908937 | − | 0.157433i | |||||
−259072. | + | 448726.i | −0.0405258 | + | 0.0701927i | |||||
−1.25134e6 | − | 2.16739e6i | −0.188153 | − | 0.325891i | 0.756481 | − | 0.654015i | ||
−0.944635 | + | 0.328124i | ||||||||
711504. | 0.102879 | |||||||||
0 | 0 | |||||||||
−6.95296e6 | −0.930920 | |||||||||
−629856. | − | 1.09094e6i | −0.0811991 | − | 0.140641i | |||||
−2.11661e6 | + | 3.66607e6i | −0.262841 | + | 0.455254i | |||||
−1.35591e6 | + | 2.34850e6i | −0.162255 | + | 0.281034i | |||||
442368. | + | 766204.i | 0.0510310 | + | 0.0883883i | |||||
−4.59755e6 | −0.511476 | −0.255738 | − | 0.966746i | ||||||
−0.255738 | + | 0.966746i | ||||||||
0 | 0 | |||||||||
−737748. | −0.0764161 | |||||||||
2.02371e6 | + | 3.50517e6i | 0.202371 | + | 0.350517i | |||||
−1.02642e7 | + | 1.77782e7i | −0.991292 | + | 1.71697i | −0.381609 | + | 0.924324i | ||
−0.609684 | + | 0.792645i | ||||||||
−3.05575e6 | + | 5.29272e6i | −0.285113 | + | 0.493831i | |||||
−7.11670e6 | − | 1.23265e7i | −0.641724 | − | 1.11150i | −0.985048 | − | 0.172282i | ||
0.343324 | − | 0.939217i | ||||||||
−1.60051e6 | −0.139522 | |||||||||
0 | 0 | |||||||||
2.35253e6 | 0.191851 | |||||||||
4.66012e6 | + | 8.07157e6i | 0.367751 | + | 0.636964i | 0.989214 | − | 0.146480i | ||
−0.621462 | + | 0.783444i | ||||||||
−629856. | + | 1.09094e6i | −0.0481125 | + | 0.0833333i | |||||
−2.15312e6 | + | 3.72932e6i | −0.159249 | + | 0.275827i | −0.934598 | − | 0.355706i | ||
0.775349 | + | 0.631533i | ||||||||
493856. | + | 855384.i | 0.0353774 | + | 0.0612755i | |||||
−2.31428e6 | −0.160615 | |||||||||
0 | 0 | |||||||||
6.93570e6 | 0.452184 | 0.226092 | − | 0.974106i | ||||||
0.226092 | + | 0.974106i | ||||||||
−2.40062e6 | − | 4.15800e6i | −0.151760 | − | 0.262856i | |||||
−6.62704e6 | + | 1.14784e7i | −0.406328 | + | 0.703781i | |||||
1.32333e6 | − | 2.29207e6i | 0.0787163 | − | 0.136341i | |||||
−1.13943e6 | − | 1.97355e6i | −0.0657712 | − | 0.113919i | |||||
5.33834e6 | 0.299102 | |||||||||
0 | 0 | |||||||||
1.68653e6 | 0.0890962 | |||||||||
9.23151e6 | + | 1.59895e7i | 0.473723 | + | 0.820512i | |||||
3.33372e6 | − | 5.77417e6i | 0.166215 | − | 0.287892i | |||||
2.10187e6 | − | 3.64054e6i | 0.101845 | − | 0.176400i | |||||
−1.49299e6 | − | 2.58594e6i | −0.0703204 | − | 0.121799i | |||||
1.72467e7 | 0.789805 | |||||||||
0 | 0 | |||||||||
−3.14502e7 | −1.36242 | −0.681209 | − | 0.732089i | ||||||
−0.681209 | + | 0.732089i | ||||||||
1.04858e6 | + | 1.81619e6i | 0.0441942 | + | 0.0765466i | |||||
−1.25119e7 | + | 2.16712e7i | −0.513166 | + | 0.888829i | |||||
−1.52549e6 | + | 2.64222e6i | −0.0608986 | + | 0.105479i | |||||
2.24401e6 | + | 3.88674e6i | 0.0872118 | + | 0.151055i | 0.906332 | − | 0.422567i | ||
−0.819120 | + | 0.573623i | ||||||||
−1.74874e6 | −0.0661783 | |||||||||
0 | 0 | |||||||||
−9.23197e6 | −0.331457 | |||||||||
1.20066e6 | + | 2.07961e6i | 0.0420004 | + | 0.0727467i | |||||
−7.24326e6 | + | 1.25457e7i | −0.246915 | + | 0.427670i | |||||
−7.81282e6 | + | 1.35322e7i | −0.259589 | + | 0.449621i | −0.966132 | − | 0.258049i | ||
0.706543 | + | 0.707670i | ||||||||
−1.17331e7 | − | 2.03224e7i | −0.380046 | − | 0.658260i | |||||
−5.42435e7 | −1.71315 | −0.856577 | − | 0.516020i | ||||||
−0.856577 | + | 0.516020i | ||||||||
0 | 0 | |||||||||
−1.42871e7 | −0.429217 | |||||||||
1.53693e7 | + | 2.66205e7i | 0.450450 | + | 0.780201i | |||||
1.58176e6 | − | 2.73968e6i | 0.0452338 | − | 0.0783473i | |||||
−1.49299e6 | + | 2.58594e6i | −0.0416667 | + | 0.0721688i | |||||
−2.52259e6 | − | 4.36926e6i | −0.0687162 | − | 0.119020i | |||||
−1.18695e7 | −0.315644 | |||||||||
0 | 0 | |||||||||
−5.48570e6 | −0.139096 | |||||||||
1.62475e7 | + | 2.81415e7i | 0.402378 | + | 0.696939i | 0.994012 | − | 0.109267i | ||
−0.591635 | + | 0.806206i | ||||||||
−6.83003e6 | + | 1.18300e7i | −0.165235 | + | 0.286196i | |||||
3.81669e7 | − | 6.61070e7i | 0.902127 | − | 1.56253i | 0.0773993 | − | 0.997000i | ||
0.824728 | − | 0.565530i | ||||||||
−5.69037e6 | − | 9.85601e6i | −0.131428 | − | 0.227640i | |||||
−2.06263e7 | −0.465588 | |||||||||
0 | 0 | |||||||||
−5.69203e6 | −0.122774 | |||||||||
−2.70086e6 | − | 4.67803e6i | −0.0569596 | − | 0.0986569i | |||||
1.46210e7 | − | 2.53244e7i | 0.301529 | − | 0.522264i | −0.674953 | − | 0.737861i | ||
0.976483 | + | 0.215596i | ||||||||
−1.50553e7 | + | 2.60765e7i | −0.303661 | + | 0.525957i | |||||
3.96989e6 | + | 6.87605e6i | 0.0783229 | + | 0.135659i | |||||
3.99770e6 | 0.0771596 | |||||||||
0 | 0 | |||||||||
−4.25153e6 | −0.0785674 | |||||||||
4.75449e7 | + | 8.23502e7i | 0.859899 | + | 1.48939i | 0.872025 | + | 0.489462i | ||
−0.0121263 | + | 0.999926i | ||||||||
4.98221e6 | − | 8.62944e6i | 0.0882000 | − | 0.152767i | |||||
−1.66676e6 | + | 2.88692e6i | −0.0288855 | + | 0.0500312i | |||||
−2.15724e7 | − | 3.73644e7i | −0.366032 | − | 0.633987i | |||||
−2.29949e7 | −0.382054 | −0.191027 | − | 0.981585i | ||||||
−0.191027 | + | 0.981585i | ||||||||
0 | 0 | |||||||||
−5.29766e7 | −0.844269 | |||||||||
1.38075e7 | + | 2.39152e7i | 0.215547 | + | 0.373339i | |||||
8.10211e6 | − | 1.40333e7i | 0.123911 | − | 0.214621i | |||||
−2.96577e7 | + | 5.13687e7i | −0.444415 | + | 0.769749i | |||||
−5.97430e7 | − | 1.03478e8i | −0.877255 | − | 1.51945i | −0.854341 | − | 0.519713i | ||
−0.0229141 | − | 0.999737i | ||||||||
8.93246e6 | 0.128543 | |||||||||
0 | 0 | |||||||||
−4.14515e6 | −0.0573121 | |||||||||
9.00844e6 | + | 1.56031e7i | 0.122108 | + | 0.211497i | |||||
1.00108e7 | − | 1.73391e7i | 0.133045 | − | 0.230440i | |||||
−4.69127e7 | + | 8.12553e7i | −0.611372 | + | 1.05893i | 0.379638 | + | 0.925135i | ||
−0.991010 | + | 0.133791i | ||||||||
2.84602e6 | + | 4.92944e6i | 0.0363734 | + | 0.0630005i | |||||
1.48834e8 | 1.86564 | 0.932819 | − | 0.360346i | ||||||
0.932819 | + | 0.360346i | ||||||||
0 | 0 | |||||||||
2.25026e7 | 0.271428 | |||||||||
−2.78118e7 | − | 4.81715e7i | −0.329130 | − | 0.570070i | |||||
−5.22855e6 | + | 9.05612e6i | −0.0607128 | + | 0.105158i | |||||
5.03885e6 | − | 8.72754e6i | 0.0574164 | − | 0.0994481i | |||||
−1.43168e7 | − | 2.47974e7i | −0.160103 | − | 0.277306i | |||||
−3.38657e7 | −0.371713 | |||||||||
0 | 0 | |||||||||
−2.16945e7 | −0.229463 | |||||||||
5.07030e7 | + | 8.78202e7i | 0.526522 | + | 0.911963i | 0.999522 | + | 0.0309010i | ||
−0.473000 | + | 0.881062i | ||||||||
−3.53894e6 | + | 6.12963e6i | −0.0360844 | + | 0.0625000i | |||||
−3.52948e7 | + | 6.11324e7i | −0.353395 | + | 0.612097i | −0.986842 | − | 0.161688i | ||
0.633447 | + | 0.773786i | ||||||||
−1.83902e7 | − | 3.18528e7i | −0.180834 | − | 0.313214i | |||||
−1.02970e7 | −0.0994469 | |||||||||
0 | 0 | |||||||||
5.02307e7 | 0.468099 | 0.234049 | − | 0.972225i | ||||||
0.234049 | + | 0.972225i | ||||||||
−2.95099e6 | − | 5.11127e6i | −0.0270172 | − | 0.0467951i | |||||
−1.04449e8 | + | 1.80910e8i | −0.939544 | + | 1.62734i | −0.173220 | + | 0.984883i | ||
−0.766324 | + | 0.642454i | ||||||||
−1.61897e7 | + | 2.80414e7i | −0.143098 | + | 0.247853i | |||||
−1.55789e7 | − | 2.69835e7i | −0.135317 | − | 0.234376i | |||||
−1.64228e8 | −1.40190 | |||||||||
0 | 0 | |||||||||
−4.88920e7 | −0.403211 | |||||||||
−9.49733e6 | − | 1.64499e7i | −0.0769951 | − | 0.133359i | |||||
5.69336e7 | − | 9.86119e7i | 0.453767 | − | 0.785948i | |||||
3.95993e7 | − | 6.85880e7i | 0.310307 | − | 0.537467i | |||||
−6.40205e6 | − | 1.10887e7i | −0.0493284 | − | 0.0854393i | |||||
2.24947e7 | 0.170439 | |||||||||
0 | 0 | |||||||||
−8.44931e7 | −0.619202 | −0.309601 | − | 0.950866i | ||||||
−0.309601 | + | 0.950866i | ||||||||
9.41011e6 | + | 1.62988e7i | 0.0678296 | + | 0.117484i | |||||
−5.18715e7 | + | 8.98441e7i | −0.367790 | + | 0.637032i | |||||
−3.72810e7 | + | 6.45725e7i | −0.260039 | + | 0.450401i | |||||
5.65350e7 | + | 9.79216e7i | 0.387957 | + | 0.671961i | |||||
−1.00777e7 | −0.0680414 | |||||||||
0 | 0 | |||||||||
−3.44500e7 | −0.225212 | |||||||||
−2.00298e7 | − | 3.46927e7i | −0.128861 | − | 0.223194i | |||||
−3.95085e6 | + | 6.84307e6i | −0.0250156 | + | 0.0433283i | |||||
4.42235e7 | − | 7.65974e7i | 0.275601 | − | 0.477354i | |||||
−9.25711e6 | − | 1.60338e7i | −0.0567858 | − | 0.0983560i | |||||
1.50175e8 | 0.906837 | 0.453418 | − | 0.891298i | ||||||
0.453418 | + | 0.891298i | ||||||||
0 | 0 | |||||||||
−4.61027e7 | −0.269828 | |||||||||
2.77428e7 | + | 4.80519e7i | 0.159871 | + | 0.276905i | |||||
1.51437e8 | − | 2.62296e8i | 0.859293 | − | 1.48834i | −0.0133116 | − | 0.999911i | ||
0.872604 | − | 0.488428i | ||||||||
1.92050e7 | − | 3.32640e7i | 0.107310 | − | 0.185867i | |||||
2.65687e7 | + | 4.60183e7i | 0.146199 | + | 0.253225i | 0.929820 | − | 0.368015i | ||
−0.783620 | + | 0.621240i | ||||||||
−1.06033e8 | −0.574635 | |||||||||
0 | 0 | |||||||||
2.11732e7 | 0.111322 | |||||||||
6.81754e7 | + | 1.18083e8i | 0.353087 | + | 0.611565i | 0.986789 | − | 0.162013i | ||
−0.633702 | + | 0.773578i | ||||||||
9.11542e6 | − | 1.57884e7i | 0.0465073 | − | 0.0805530i | |||||
−3.22783e7 | + | 5.59076e7i | −0.162246 | + | 0.281018i | |||||
2.13533e7 | + | 3.69851e7i | 0.105748 | + | 0.183162i | |||||
−1.01623e8 | −0.495877 | |||||||||
0 | 0 | |||||||||
2.26802e8 | 1.07462 | 0.537309 | − | 0.843385i | ||||||
0.537309 | + | 0.843385i | ||||||||
6.74611e6 | + | 1.16846e7i | 0.0315003 | + | 0.0545601i | |||||
−2.02527e8 | + | 3.50786e8i | −0.932014 | + | 1.61430i | −0.152139 | + | 0.988359i | ||
−0.779874 | + | 0.625936i | ||||||||
−7.38521e7 | + | 1.27916e8i | −0.334972 | + | 0.580189i | |||||
−7.17445e6 | − | 1.24265e7i | −0.0320750 | − | 0.0555556i | |||||
5.33395e7 | 0.235063 | |||||||||
0 | 0 | |||||||||
3.36299e7 | 0.144030 | |||||||||
3.47424e7 | + | 6.01755e7i | 0.146697 | + | 0.254086i | |||||
1.19439e7 | − | 2.06875e7i | 0.0497241 | − | 0.0861246i | |||||
7.28067e7 | − | 1.26105e8i | 0.298864 | − | 0.517648i | |||||
6.89866e7 | + | 1.19488e8i | 0.279238 | + | 0.483655i | |||||
−3.08065e7 | −0.122966 | −0.0614828 | − | 0.998108i | ||||||
−0.0614828 | + | 0.998108i | ||||||||
0 | 0 | |||||||||
1.09944e8 | 0.426824 | |||||||||
−1.25801e8 | − | 2.17893e8i | −0.481687 | − | 0.834307i | |||||
−4.66002e7 | + | 8.07139e7i | −0.175994 | + | 0.304830i | |||||
−8.38861e6 | + | 1.45295e7i | −0.0312500 | + | 0.0541266i | |||||
1.37566e8 | + | 2.38271e8i | 0.505527 | + | 0.875599i | 0.999980 | + | 0.00639407i | ||
−0.494452 | + | 0.869205i | ||||||||
−2.00190e8 | −0.725726 | |||||||||
0 | 0 | |||||||||
−2.44078e7 | −0.0861236 | |||||||||
1.50735e7 | + | 2.61081e7i | 0.0524775 | + | 0.0908937i | |||||
−1.79521e7 | + | 3.10939e7i | −0.0616681 | + | 0.106812i | |||||
2.41998e8 | − | 4.19153e8i | 0.820288 | − | 1.42078i | −0.0851790 | − | 0.996366i | ||
0.905467 | − | 0.424416i | ||||||||
−6.99494e6 | − | 1.21156e7i | −0.0233976 | − | 0.0405258i | |||||
3.58761e7 | 0.118425 | |||||||||
0 | 0 | |||||||||
6.75726e7 | 0.217261 | |||||||||
−3.69279e7 | − | 6.39610e7i | −0.117188 | − | 0.202975i | |||||
−1.23687e8 | + | 2.14233e8i | −0.387429 | + | 0.671047i | −0.992103 | − | 0.125427i | ||
0.604674 | + | 0.796473i | ||||||||
−9.60530e6 | + | 1.66369e7i | −0.0296987 | + | 0.0514397i | |||||
1.14143e8 | + | 1.97702e8i | 0.348384 | + | 0.603418i | 0.985963 | − | 0.166967i | ||
−0.637579 | + | 0.770385i | ||||||||
−1.15892e8 | −0.349191 | |||||||||
0 | 0 | |||||||||
−1.25005e8 | −0.367114 | |||||||||
−3.19999e7 | − | 5.54255e7i | −0.0927865 | − | 0.160711i | |||||
9.38650e7 | − | 1.62579e8i | 0.268733 | − | 0.465460i | |||||
1.77558e8 | − | 3.07539e8i | 0.501950 | − | 0.869403i | −0.498047 | − | 0.867150i | ||
0.999997 | − | 0.00225351i | ||||||||
−2.16974e8 | − | 3.75810e8i | −0.605691 | − | 1.04909i | |||||
3.40122e7 | 0.0937606 | |||||||||
0 | 0 | |||||||||
2.28167e8 | 0.613453 | 0.306726 | − | 0.951798i | ||||||
0.306726 | + | 0.951798i | ||||||||
−5.71484e7 | − | 9.89840e7i | −0.151751 | − | 0.262841i | |||||
1.06896e8 | − | 1.85149e8i | 0.280354 | − | 0.485588i | −0.691118 | − | 0.722742i | ||
0.971472 | + | 0.237154i | ||||||||
−1.22955e8 | + | 2.12964e8i | −0.318516 | + | 0.551686i | |||||
−3.66095e7 | − | 6.34095e7i | −0.0936779 | − | 0.162255i | |||||
2.53081e7 | 0.0639703 | |||||||||
0 | 0 | |||||||||
−2.38879e7 | −0.0589256 | |||||||||
−1.95106e8 | − | 3.37933e8i | −0.475475 | − | 0.823547i | |||||
2.01808e7 | − | 3.49541e7i | 0.0485897 | − | 0.0841599i | |||||
6.20669e7 | − | 1.07503e8i | 0.147650 | − | 0.255738i | |||||
−4.74781e7 | − | 8.22344e7i | −0.111597 | − | 0.193292i | |||||
3.78816e8 | 0.879816 | 0.439908 | − | 0.898043i | ||||||
0.439908 | + | 0.898043i | ||||||||
0 | 0 | |||||||||
8.14096e7 | 0.184628 | |||||||||
−2.19428e7 | − | 3.80060e7i | −0.0491780 | − | 0.0851788i | |||||
9.95960e6 | − | 1.72505e7i | 0.0220594 | − | 0.0382080i | |||||
−1.29980e8 | + | 2.25132e8i | −0.284524 | + | 0.492810i | |||||
1.69804e8 | + | 2.94110e8i | 0.367367 | + | 0.636297i | |||||
−1.09280e8 | −0.233678 | |||||||||
0 | 0 | |||||||||
6.10671e8 | 1.27580 | |||||||||
−2.77134e8 | − | 4.80011e8i | −0.572323 | − | 0.991292i | |||||
4.55229e7 | − | 7.88481e7i | 0.0929336 | − | 0.160966i | |||||
5.08392e7 | − | 8.80561e7i | 0.102601 | − | 0.177709i | |||||
−8.25053e7 | − | 1.42903e8i | −0.164610 | − | 0.285113i | |||||
6.33814e8 | 1.25019 | 0.625097 | − | 0.780547i | ||||||
0.625097 | + | 0.780547i | ||||||||
0 | 0 | |||||||||
3.84302e8 | 0.740999 | |||||||||
−2.27681e7 | − | 3.94356e7i | −0.0434072 | − | 0.0751834i | |||||
1.95098e8 | − | 3.37919e8i | 0.367782 | − | 0.637018i | −0.621436 | − | 0.783465i | ||
0.989218 | + | 0.146447i | ||||||||
2.16069e7 | − | 3.74243e7i | 0.0402765 | − | 0.0697609i | |||||
5.02221e8 | + | 8.69872e8i | 0.925741 | + | 1.60343i | 0.790365 | + | 0.612636i | ||
0.135376 | + | 0.990794i | ||||||||
2.33937e8 | 0.426427 | |||||||||
0 | 0 | |||||||||
−2.40885e8 | −0.429442 | |||||||||
−1.21487e8 | − | 2.10422e8i | −0.214202 | − | 0.371009i | 0.738823 | − | 0.673899i | ||
−0.953025 | + | 0.302890i | ||||||||
−3.17591e7 | + | 5.50084e7i | −0.0553826 | + | 0.0959255i | |||||
−2.09251e7 | + | 3.62434e7i | −0.0360911 | + | 0.0625117i | |||||
1.59908e7 | + | 2.76969e7i | 0.0272800 | + | 0.0472504i | |||||
−2.51647e8 | −0.424642 | |||||||||
0 | 0 | |||||||||
6.28919e8 | 1.03845 | |||||||||
−1.70061e7 | − | 2.94555e7i | −0.0277778 | − | 0.0481125i | |||||
9.88457e7 | − | 1.71206e8i | 0.159722 | − | 0.276647i | |||||
−3.80359e8 | + | 6.58801e8i | −0.608040 | + | 1.05316i | |||||
−5.81343e7 | − | 1.00692e8i | −0.0919423 | − | 0.159249i | |||||
7.97153e7 | 0.124734 | |||||||||
0 | 0 | |||||||||
−2.66682e7 | −0.0408503 | |||||||||
1.41758e7 | + | 2.45533e7i | 0.0214858 | + | 0.0372144i | 0.876568 | − | 0.481277i | ||
−0.855083 | + | 0.518492i | ||||||||
1.72579e8 | − | 2.98915e8i | 0.258824 | − | 0.448296i | |||||
3.12428e7 | − | 5.41140e7i | 0.0463654 | − | 0.0803073i | |||||
−9.19797e7 | − | 1.59314e8i | −0.135076 | − | 0.233959i | |||||
−1.40788e8 | −0.204601 | |||||||||
0 | 0 | |||||||||
−1.01675e9 | −1.44714 | −0.723572 | − | 0.690249i | ||||||
−0.723572 | + | 0.690249i | ||||||||
−2.11907e8 | − | 3.67033e8i | −0.298494 | − | 0.517007i | |||||
−9.36319e7 | + | 1.62175e8i | −0.130534 | + | 0.226092i | |||||
−1.10460e8 | + | 1.91322e8i | −0.152415 | + | 0.263991i | |||||
2.36079e7 | + | 4.08901e7i | 0.0322417 | + | 0.0558442i | |||||
1.29634e8 | 0.175237 | |||||||||
0 | 0 | |||||||||
−4.74524e8 | −0.628497 | |||||||||
−1.78930e8 | − | 3.09916e8i | −0.234594 | − | 0.406328i | |||||
4.77944e8 | − | 8.27824e8i | 0.620313 | − | 1.07441i | |||||
4.85247e8 | − | 8.40472e8i | 0.623461 | − | 1.07987i | −0.365375 | − | 0.930860i | ||
0.988836 | − | 0.149006i | ||||||||
3.57299e7 | + | 6.18859e7i | 0.0454469 | + | 0.0787163i | |||||
8.84145e8 | 1.11336 | 0.556678 | − | 0.830728i | ||||||
0.556678 | + | 0.830728i | ||||||||
0 | 0 | |||||||||
6.15291e7 | 0.0759461 | |||||||||
−1.65806e7 | − | 2.87185e7i | −0.0202629 | − | 0.0350963i | |||||
5.45231e8 | − | 9.44367e8i | 0.659734 | − | 1.14269i | −0.320951 | − | 0.947096i | ||
0.980684 | − | 0.195597i | ||||||||
−7.20675e7 | + | 1.24825e8i | −0.0863432 | + | 0.149551i | |||||
2.34382e8 | + | 4.05962e8i | 0.278052 | + | 0.481600i | |||||
1.60172e8 | 0.188153 | |||||||||
0 | 0 | |||||||||
−7.50604e8 | −0.864610 | |||||||||
−5.16865e8 | − | 8.95236e8i | −0.589585 | − | 1.02119i | −0.994287 | − | 0.106742i | ||
0.404702 | − | 0.914449i | ||||||||
−2.27681e7 | + | 3.94356e7i | −0.0257199 | + | 0.0445481i | |||||
1.99894e8 | − | 3.46226e8i | 0.223627 | − | 0.387333i | |||||
5.95336e8 | + | 1.03115e9i | 0.659603 | + | 1.14247i | |||||
−4.98502e8 | −0.547008 | |||||||||
0 | 0 | |||||||||
−1.81010e8 | −0.194840 | |||||||||
9.00104e7 | + | 1.55903e8i | 0.0959642 | + | 0.166215i | |||||
1.21092e8 | − | 2.09737e8i | 0.127874 | − | 0.221484i | −0.794979 | − | 0.606637i | ||
0.922853 | + | 0.385153i | ||||||||
2.22495e8 | − | 3.85372e8i | 0.232730 | − | 0.403100i | |||||
5.67505e7 | + | 9.82947e7i | 0.0588000 | + | 0.101845i | |||||
−8.36569e7 | −0.0858609 | |||||||||
0 | 0 | |||||||||
8.06216e7 | 0.0811991 | |||||||||
7.18844e8 | + | 1.24507e9i | 0.717222 | + | 1.24226i | 0.962096 | + | 0.272710i | ||
−0.244874 | + | 0.969555i | ||||||||
1.14534e8 | − | 1.98379e8i | 0.113210 | − | 0.196085i | |||||
−2.32830e8 | + | 4.03273e8i | −0.227997 | + | 0.394902i | |||||
−1.35463e8 | − | 2.34629e8i | −0.131420 | − | 0.227627i | |||||
−1.29273e8 | −0.124254 | |||||||||
0 | 0 | |||||||||
1.20169e9 | 1.13385 | 0.566924 | − | 0.823770i | ||||||
0.566924 | + | 0.823770i | ||||||||
−8.67781e7 | − | 1.50304e8i | −0.0811274 | − | 0.140517i | |||||
4.24577e8 | − | 7.35390e8i | 0.393296 | − | 0.681209i | |||||
−4.05624e8 | + | 7.02561e8i | −0.372307 | + | 0.644855i | |||||
−3.15429e8 | − | 5.46340e8i | −0.286884 | − | 0.496898i | 0.686180 | − | 0.727431i | ||
−0.973064 | + | 0.230534i | ||||||||
−5.66231e7 | −0.0510310 | |||||||||
0 | 0 | |||||||||
−5.64717e8 | −0.499775 | |||||||||
−3.37820e8 | − | 5.85122e8i | −0.296276 | − | 0.513166i | |||||
1.47122e8 | − | 2.54822e8i | 0.127869 | − | 0.221476i | |||||
7.10929e8 | − | 1.23137e9i | 0.612354 | − | 1.06063i | −0.378488 | − | 0.925606i | ||
0.990843 | − | 0.135022i | ||||||||
−4.11882e7 | − | 7.13400e7i | −0.0351598 | − | 0.0608986i | |||||
3.07386e9 | 2.60055 | |||||||||
0 | 0 | |||||||||
−1.21177e8 | −0.100704 | |||||||||
2.00923e8 | + | 3.48009e8i | 0.165498 | + | 0.286651i | |||||
−2.29593e8 | + | 3.97667e8i | −0.187443 | + | 0.324661i | |||||
2.36079e7 | − | 4.08901e7i | 0.0191040 | − | 0.0330891i | |||||
−3.52485e7 | − | 6.10521e7i | −0.0282731 | − | 0.0489704i | 0.851543 | − | 0.524285i | ||
−0.879816 | + | 0.475315i | ||||||||
−1.67118e9 | −1.32872 | |||||||||
0 | 0 | |||||||||
−2.59035e8 | −0.202371 | |||||||||
−1.01161e9 | − | 1.75216e9i | −0.783444 | − | 1.35697i | −0.929924 | − | 0.367752i | ||
0.146480 | − | 0.989214i | ||||||||
1.24632e8 | − | 2.15868e8i | 0.0956835 | − | 0.165729i | |||||
−7.29233e7 | + | 1.26307e8i | −0.0555007 | + | 0.0961301i | |||||
−6.56911e8 | − | 1.13780e9i | −0.495646 | − | 0.858484i | |||||
−6.48358e7 | −0.0484978 | |||||||||
0 | 0 | |||||||||
8.67426e7 | 0.0637752 | |||||||||
−1.95568e8 | − | 3.38734e8i | −0.142557 | − | 0.246915i | |||||
−7.18632e8 | + | 1.24471e9i | −0.519368 | + | 0.899571i | 0.480379 | + | 0.877061i | ||
−0.999747 | + | 0.0225102i | ||||||||
7.59787e7 | − | 1.31599e8i | 0.0544438 | − | 0.0942994i | |||||
−2.10946e8 | − | 3.65369e8i | −0.149874 | − | 0.259589i | |||||
9.10938e8 | 0.641724 | |||||||||
0 | 0 | |||||||||
6.33588e8 | 0.438840 | |||||||||
−3.28979e8 | − | 5.69808e8i | −0.225943 | − | 0.391345i | |||||
5.12164e7 | − | 8.87094e7i | 0.0348805 | − | 0.0604147i | |||||
7.32288e8 | − | 1.26836e9i | 0.494545 | − | 0.856577i | |||||
8.99789e7 | + | 1.55848e8i | 0.0602593 | + | 0.104372i | |||||
8.62098e7 | 0.0572542 | 0.0286271 | − | 0.999590i | ||||||
0.0286271 | + | 0.999590i | ||||||||
0 | 0 | |||||||||
−1.18254e9 | −0.772378 | −0.386189 | − | 0.922420i | ||||||
−0.386189 | + | 0.922420i | ||||||||
−3.37972e8 | − | 5.85385e8i | −0.218921 | − | 0.379183i | |||||
1.92876e8 | − | 3.34071e8i | 0.123904 | − | 0.214609i | |||||
−7.52809e7 | + | 1.30390e8i | −0.0479628 | + | 0.0830740i | |||||
−8.94670e8 | − | 1.54961e9i | −0.565330 | − | 0.979180i | |||||
−8.29945e8 | −0.520134 | |||||||||
0 | 0 | |||||||||
−5.96496e8 | −0.367751 | |||||||||
4.27074e7 | + | 7.39714e7i | 0.0261158 | + | 0.0452338i | |||||
−4.52280e8 | + | 7.83373e8i | −0.274327 | + | 0.475148i | |||||
−3.02329e8 | + | 5.23649e8i | −0.181890 | + | 0.315043i | −0.942524 | − | 0.334138i | ||
0.760634 | + | 0.649181i | ||||||||
−4.03108e7 | − | 6.98203e7i | −0.0240563 | − | 0.0416667i | |||||
7.16394e7 | 0.0424076 | 0.0212038 | − | 0.999775i | ||||||
0.0212038 | + | 0.999775i | ||||||||
0 | 0 | |||||||||
1.36220e8 | 0.0793467 | |||||||||
−1.37800e8 | − | 2.38676e8i | −0.0796244 | − | 0.137913i | |||||
−1.20742e9 | + | 2.09132e9i | −0.692110 | + | 1.19877i | |||||
1.60239e8 | − | 2.77541e8i | 0.0911187 | − | 0.157822i | |||||
−9.74587e7 | − | 1.68803e8i | −0.0549788 | − | 0.0952260i | 0.837226 | − | 0.546857i | ||
−0.892205 | + | 0.451631i | ||||||||
−6.32136e7 | −0.0353774 | |||||||||
0 | 0 | |||||||||
7.07576e8 | 0.389758 | |||||||||
1.04009e9 | + | 1.80149e9i | 0.568405 | + | 0.984507i | 0.996724 | + | 0.0808791i | ||
−0.428319 | + | 0.903628i | ||||||||
7.40569e7 | − | 1.28270e8i | 0.0401537 | − | 0.0695482i | |||||
1.52664e8 | − | 2.64422e8i | 0.0821253 | − | 0.142245i | |||||
6.00698e8 | + | 1.04044e9i | 0.320615 | + | 0.555322i | |||||
−8.77364e8 | −0.464626 | |||||||||
0 | 0 | |||||||||
1.78606e9 | 0.931180 | 0.465590 | − | 0.885000i | ||||||
0.465590 | + | 0.885000i | ||||||||
−1.84411e8 | − | 3.19409e8i | −0.0953987 | − | 0.165235i | |||||
−7.87812e7 | + | 1.36453e8i | −0.0404394 | + | 0.0700431i | |||||
−2.21942e8 | + | 3.84415e8i | −0.113046 | + | 0.195802i | |||||
1.03051e9 | + | 1.78489e9i | 0.520843 | + | 0.902127i | |||||
2.42299e9 | 1.21522 | |||||||||
0 | 0 | |||||||||
3.07280e8 | 0.151760 | |||||||||
1.12154e9 | + | 1.94256e9i | 0.549678 | + | 0.952069i | 0.998296 | + | 0.0583463i | ||
−0.448619 | + | 0.893723i | ||||||||
−2.12549e8 | + | 3.68146e8i | −0.103379 | + | 0.179057i | |||||
2.78455e8 | − | 4.82299e8i | 0.134404 | − | 0.232794i | |||||
−4.24131e8 | − | 7.34616e8i | −0.203164 | − | 0.351891i | |||||
−2.60254e9 | −1.23721 | −0.618607 | − | 0.785701i | ||||||
−0.618607 | + | 0.785701i | ||||||||
0 | 0 | |||||||||
−7.12557e8 | −0.333646 | −0.166823 | − | 0.985987i | ||||||
−0.166823 | + | 0.985987i | ||||||||
8.46930e7 | + | 1.46693e8i | 0.0393581 | + | 0.0681703i | |||||
7.68424e7 | − | 1.33095e8i | 0.0354418 | − | 0.0613870i | |||||
−5.45403e8 | + | 9.44666e8i | −0.249670 | + | 0.432442i | |||||
3.16734e8 | + | 5.48600e8i | 0.143908 | + | 0.249257i | 0.928965 | − | 0.370167i | ||
−0.785057 | + | 0.619424i | ||||||||
1.45847e8 | 0.0657712 | |||||||||
0 | 0 | |||||||||
−5.16452e8 | −0.229450 | |||||||||
3.94768e8 | + | 6.83759e8i | 0.174088 | + | 0.301529i | |||||
−1.70827e8 | + | 2.95881e8i | −0.0747754 | + | 0.129515i | |||||
4.68963e8 | − | 8.12267e8i | 0.203763 | − | 0.352927i | |||||
−4.06493e8 | − | 7.04067e8i | −0.175319 | − | 0.303661i | |||||
1.40572e9 | 0.601827 | |||||||||
0 | 0 | |||||||||
−2.14374e8 | −0.0904395 | |||||||||
9.07208e8 | + | 1.57133e9i | 0.379935 | + | 0.658067i | |||||
1.10276e8 | − | 1.91004e8i | 0.0458466 | − | 0.0794086i | −0.842191 | − | 0.539179i | ||
0.888038 | + | 0.459770i | ||||||||
−5.39689e7 | + | 9.34769e7i | −0.0222741 | + | 0.0385798i | |||||
1.33971e8 | + | 2.32045e8i | 0.0548912 | + | 0.0950744i | |||||
−3.24042e9 | −1.31807 | |||||||||
0 | 0 | |||||||||
−1.18163e9 | −0.473723 | |||||||||
−2.80451e8 | − | 4.85755e8i | −0.111625 | − | 0.193340i | |||||
5.73956e7 | − | 9.94121e7i | 0.0226805 | − | 0.0392837i | |||||
−1.96466e9 | + | 3.40289e9i | −0.770791 | + | 1.33505i | 0.166339 | + | 0.986069i | ||
−0.937130 | + | 0.348980i | ||||||||
2.13358e8 | + | 3.69547e8i | 0.0831074 | + | 0.143946i | |||||
−2.56742e9 | −0.992925 | |||||||||
0 | 0 | |||||||||
−3.28904e9 | −1.25396 | −0.626980 | − | 0.779036i | ||||||
−0.626980 | + | 0.779036i | ||||||||
1.34520e8 | + | 2.32995e8i | 0.0509223 | + | 0.0882000i | |||||
−5.85035e8 | + | 1.01331e9i | −0.219896 | + | 0.380871i | |||||
−2.77939e8 | + | 4.81404e8i | −0.103730 | + | 0.179666i | |||||
−4.50026e7 | − | 7.79468e7i | −0.0166771 | − | 0.0288855i | |||||
1.91103e8 | 0.0703204 | |||||||||
0 | 0 | |||||||||
1.16491e9 | 0.422658 | |||||||||
2.15315e9 | + | 3.72937e9i | 0.775752 | + | 1.34364i | 0.934371 | + | 0.356302i | ||
−0.158619 | + | 0.987340i | ||||||||
−5.51893e8 | + | 9.55906e8i | −0.197451 | + | 0.341995i | |||||
3.10432e8 | − | 5.37683e8i | 0.110289 | − | 0.191027i | |||||
−1.23226e8 | − | 2.13433e8i | −0.0434749 | − | 0.0753008i | |||||
−2.56392e9 | −0.898291 | −0.449145 | − | 0.893459i | ||||||
−0.449145 | + | 0.893459i | ||||||||
0 | 0 | |||||||||
−2.50447e9 | −0.865360 | |||||||||
4.39775e8 | + | 7.61712e8i | 0.150905 | + | 0.261375i | |||||
7.15185e8 | − | 1.23874e9i | 0.243720 | − | 0.422135i | |||||
1.00641e9 | − | 1.74315e9i | 0.340604 | − | 0.589944i | |||||
−2.10193e9 | − | 3.64065e9i | −0.706490 | − | 1.22368i | −0.966151 | − | 0.257977i | ||
0.259661 | − | 0.965700i | ||||||||
−7.45603e8 | −0.248893 | |||||||||
0 | 0 | |||||||||
−1.34218e8 | −0.0441942 | |||||||||
2.18757e8 | + | 3.78898e8i | 0.0715403 | + | 0.123911i | |||||
−1.10053e9 | + | 1.90617e9i | −0.357462 | + | 0.619142i | |||||
8.68237e8 | − | 1.50383e9i | 0.280100 | − | 0.485148i | |||||
−8.00759e8 | − | 1.38695e9i | −0.256583 | − | 0.444415i | |||||
5.35502e8 | 0.170429 | |||||||||
0 | 0 | |||||||||
3.22612e9 | 1.01297 | |||||||||
−9.76312e7 | − | 1.69102e8i | −0.0304493 | − | 0.0527397i | |||||
−2.25385e9 | + | 3.90378e9i | −0.698220 | + | 1.20935i | 0.270862 | + | 0.962618i | ||
−0.969083 | + | 0.246735i | ||||||||
−1.20588e8 | + | 2.08865e8i | −0.0371072 | + | 0.0642716i | |||||
2.73176e9 | + | 4.73154e9i | 0.835000 | + | 1.44626i | 0.894031 | + | 0.448006i | ||
−0.0590308 | + | 0.998256i | ||||||||
−2.87233e8 | −0.0872118 | |||||||||
0 | 0 | |||||||||
3.87197e9 | 1.16006 | |||||||||
6.60042e8 | + | 1.14323e9i | 0.196442 | + | 0.340248i | |||||
5.59596e7 | − | 9.69248e7i | 0.0165446 | − | 0.0286560i | |||||
−4.19891e9 | + | 7.27273e9i | −1.23322 | + | 2.13601i | |||||
1.43504e8 | + | 2.48557e8i | 0.0418696 | + | 0.0725203i | |||||
−4.86456e8 | −0.140998 | |||||||||
0 | 0 | |||||||||
−4.86699e8 | −0.139224 | |||||||||
2.70291e8 | + | 4.68157e8i | 0.0768133 | + | 0.133045i | |||||
−5.68535e8 | + | 9.84731e8i | −0.160516 | + | 0.278022i | |||||
2.95423e8 | − | 5.11688e8i | 0.0828643 | − | 0.143525i | |||||
−1.26664e9 | − | 2.19389e9i | −0.352976 | − | 0.611372i | |||||
−1.97900e9 | −0.547907 | |||||||||
0 | 0 | |||||||||
−1.53685e8 | −0.0420004 | |||||||||
3.29315e9 | + | 5.70390e9i | 0.894171 | + | 1.54875i | 0.834827 | + | 0.550512i | ||
0.0593443 | + | 0.998238i | ||||||||
−9.13146e8 | + | 1.58162e9i | −0.246345 | + | 0.426681i | |||||
−2.00926e9 | + | 3.48014e9i | −0.538563 | + | 0.932819i | |||||
−4.63569e8 | − | 8.02925e8i | −0.123458 | − | 0.213835i | |||||
−5.25362e8 | −0.139018 | |||||||||
0 | 0 | |||||||||
−1.71749e9 | −0.448681 | −0.224340 | − | 0.974511i | ||||||
−0.224340 | + | 0.974511i | ||||||||
−5.00021e8 | − | 8.66061e8i | −0.129794 | − | 0.224810i | |||||
−3.03785e8 | + | 5.26171e8i | −0.0783544 | + | 0.135714i | |||||
2.56000e8 | − | 4.43404e8i | 0.0656100 | − | 0.113640i | |||||
−4.59608e8 | − | 7.96065e8i | −0.117046 | − | 0.202730i | |||||
1.50184e9 | 0.380046 | |||||||||
0 | 0 | |||||||||
2.84093e9 | 0.709865 | |||||||||
−1.41171e8 | − | 2.44515e8i | −0.0350526 | − | 0.0607128i | |||||
1.73579e9 | − | 3.00648e9i | 0.428288 | − | 0.741817i | |||||
−2.47132e9 | + | 4.28045e9i | −0.605949 | + | 1.04953i | 0.385952 | + | 0.922519i | ||
−0.991901 | + | 0.127015i | ||||||||
1.36049e8 | + | 2.35644e8i | 0.0331494 | + | 0.0574164i | |||||
2.89719e9 | 0.701513 | |||||||||
0 | 0 | |||||||||
7.73105e8 | 0.184871 | |||||||||
9.12669e8 | + | 1.58079e9i | 0.216888 | + | 0.375661i | |||||
1.69154e9 | − | 2.92983e9i | 0.399487 | − | 0.691932i | −0.594176 | − | 0.804335i | ||
0.993663 | + | 0.112404i | ||||||||
4.57187e8 | − | 7.91872e8i | 0.107304 | − | 0.185857i | |||||
4.23078e8 | + | 7.32792e8i | 0.0986848 | + | 0.170927i | |||||
1.71033e9 | 0.396481 | |||||||||
0 | 0 | |||||||||
−1.96728e9 | −0.450450 | |||||||||
1.12318e9 | + | 1.94540e9i | 0.255596 | + | 0.442706i | 0.965057 | − | 0.262039i | ||
−0.709461 | + | 0.704745i | ||||||||
2.92876e8 | − | 5.07276e8i | 0.0662403 | − | 0.114731i | |||||
3.40547e8 | − | 5.89845e8i | 0.0765509 | − | 0.132590i | −0.825209 | − | 0.564828i | ||
0.901760 | + | 0.432238i | ||||||||
1.01232e8 | + | 1.75340e8i | 0.0226169 | + | 0.0391736i | |||||
−2.73796e9 | −0.607976 | |||||||||
0 | 0 | |||||||||
6.87050e9 | 1.50713 | |||||||||
−9.55515e7 | − | 1.65500e8i | −0.0208333 | − | 0.0360844i | |||||
3.74148e8 | − | 6.48043e8i | 0.0810827 | − | 0.140439i | −0.822633 | − | 0.568573i | ||
0.903715 | + | 0.428134i | ||||||||
1.56085e9 | − | 2.70347e9i | 0.336212 | − | 0.582336i | |||||
−9.52959e8 | − | 1.65057e9i | −0.204032 | − | 0.353395i | |||||
3.22892e8 | 0.0687162 | |||||||||
0 | 0 | |||||||||
9.93071e8 | 0.208809 | |||||||||
−1.48797e8 | − | 2.57725e8i | −0.0310996 | − | 0.0538662i | |||||
3.79825e8 | − | 6.57876e8i | 0.0789111 | − | 0.136678i | |||||
1.39010e8 | − | 2.40773e8i | 0.0287079 | − | 0.0497235i | |||||
1.51527e9 | + | 2.62452e9i | 0.311062 | + | 0.538775i | |||||
−6.17294e9 | −1.25968 | −0.629838 | − | 0.776727i | ||||||
−0.629838 | + | 0.776727i | ||||||||
0 | 0 | |||||||||
−1.03707e9 | −0.209124 | |||||||||
3.25638e8 | + | 5.64022e8i | 0.0652760 | + | 0.113061i | |||||
−6.78115e8 | + | 1.17453e9i | −0.135129 | + | 0.234049i | |||||
1.75542e8 | − | 3.04048e8i | 0.0347741 | − | 0.0602305i | |||||
−5.02125e9 | − | 8.69705e9i | −0.988826 | − | 1.71270i | −0.623513 | − | 0.781813i | ||
−0.365314 | − | 0.930885i | ||||||||
1.59354e8 | 0.0311967 | |||||||||
0 | 0 | |||||||||
−2.07968e9 | −0.402378 | |||||||||
−2.82011e9 | − | 4.88458e9i | −0.542446 | − | 0.939544i | |||||
−1.35843e9 | + | 2.35288e9i | −0.259767 | + | 0.449930i | |||||
6.61221e8 | − | 1.14527e9i | 0.125705 | − | 0.217728i | −0.796303 | − | 0.604898i | ||
0.922008 | + | 0.387170i | ||||||||
−4.37122e8 | − | 7.57117e8i | −0.0826177 | − | 0.143098i | |||||
−4.48600e8 | −0.0842944 | −0.0421472 | − | 0.999111i | ||||||
−0.0421472 | + | 0.999111i | ||||||||
0 | 0 | |||||||||
8.41263e8 | 0.156250 | |||||||||
2.44268e9 | + | 4.23085e9i | 0.451064 | + | 0.781265i | |||||
−1.12624e9 | + | 1.95071e9i | −0.206771 | + | 0.358137i | |||||
2.21707e9 | − | 3.84009e9i | 0.404693 | − | 0.700950i | |||||
−4.45750e8 | − | 7.72061e8i | −0.0808967 | − | 0.140117i | 0.822739 | − | 0.568420i | ||
−0.903635 | + | 0.428303i | ||||||||
7.28367e8 | 0.131428 | |||||||||
0 | 0 | |||||||||
8.13428e8 | 0.145099 | |||||||||
8.27065e8 | + | 1.43252e9i | 0.146688 | + | 0.254071i | |||||
6.60042e8 | − | 1.14323e9i | 0.116397 | − | 0.201606i | |||||
−1.75709e9 | + | 3.04336e9i | −0.308092 | + | 0.533632i | −0.977945 | − | 0.208862i | ||
0.669853 | + | 0.742494i | ||||||||
2.53525e9 | + | 4.39119e9i | 0.442010 | + | 0.765584i | |||||
5.12856e8 | 0.0889063 | |||||||||
0 | 0 | |||||||||
3.78067e9 | 0.647993 | 0.323996 | − | 0.946058i | ||||||
0.323996 | + | 0.946058i | ||||||||
1.53721e9 | + | 2.66252e9i | 0.261983 | + | 0.453767i | |||||
−1.34483e9 | + | 2.32932e9i | −0.227903 | + | 0.394740i | −0.957187 | − | 0.289472i | ||
0.729283 | + | 0.684212i | ||||||||
1.82145e8 | − | 3.15484e8i | 0.0306935 | − | 0.0531627i | |||||
1.06918e9 | + | 1.85188e9i | 0.179156 | + | 0.310307i | |||||
3.12156e9 | 0.520123 | |||||||||
0 | 0 | |||||||||
3.45711e8 | 0.0569596 | |||||||||
−1.41831e9 | − | 2.45658e9i | −0.232375 | − | 0.402486i | |||||
−4.01777e9 | + | 6.95898e9i | −0.654598 | + | 1.13380i | |||||
−3.03679e8 | + | 5.25987e8i | −0.0492015 | + | 0.0852195i | |||||
9.35747e8 | + | 1.62076e9i | 0.150765 | + | 0.261132i | |||||
2.42519e9 | 0.388570 | |||||||||
0 | 0 | |||||||||
−6.91824e9 | −1.09621 | −0.548104 | − | 0.836410i | ||||||
−0.548104 | + | 0.836410i | ||||||||
−9.63539e8 | − | 1.66890e9i | −0.151831 | − | 0.262978i | |||||
1.14066e9 | − | 1.97568e9i | 0.178748 | − | 0.309601i | |||||
9.71898e8 | − | 1.68338e9i | 0.151464 | − | 0.262343i | |||||
−1.91846e9 | − | 3.32287e9i | −0.297334 | − | 0.514998i | |||||
−5.08146e8 | −0.0783229 | |||||||||
0 | 0 | |||||||||
−3.34802e8 | −0.0510406 | |||||||||
−1.40053e9 | − | 2.42579e9i | −0.212344 | − | 0.367790i | |||||
−1.27926e8 | + | 2.21575e8i | −0.0192899 | + | 0.0334111i | |||||
2.74979e9 | − | 4.76278e9i | 0.412379 | − | 0.714262i | −0.582770 | − | 0.812637i | ||
0.995149 | + | 0.0983750i | ||||||||
−1.00659e9 | − | 1.74346e9i | −0.150134 | − | 0.260039i | |||||
−1.35931e9 | −0.201641 | −0.100821 | − | 0.994905i | ||||||
−0.100821 | + | 0.994905i | ||||||||
0 | 0 | |||||||||
−3.05289e9 | −0.447974 | |||||||||
2.51568e9 | + | 4.35728e9i | 0.367148 | + | 0.635919i | |||||
3.64592e9 | − | 6.31492e9i | 0.529228 | − | 0.916649i | −0.470191 | − | 0.882565i | ||
0.999419 | − | 0.0340847i | ||||||||
1.36049e8 | − | 2.35644e8i | 0.0196419 | − | 0.0340207i | |||||
−3.37650e8 | − | 5.84827e8i | −0.0484853 | − | 0.0839790i | |||||
1.58153e9 | 0.225882 | |||||||||
0 | 0 | |||||||||
−6.08575e9 | −0.859899 | |||||||||
4.98442e8 | + | 8.63327e8i | 0.0700517 | + | 0.121333i | 0.898924 | − | 0.438105i | ||
−0.828872 | + | 0.559438i | ||||||||
4.65075e8 | − | 8.05533e8i | 0.0650130 | − | 0.112606i | |||||
−2.73769e8 | + | 4.74182e8i | −0.0380662 | + | 0.0659327i | |||||
3.18861e8 | + | 5.52284e8i | 0.0441000 | + | 0.0763834i | |||||
1.08161e9 | 0.148796 | |||||||||
0 | 0 | |||||||||
−1.35118e10 | −1.83914 | −0.919568 | − | 0.392932i | ||||||
−0.919568 | + | 0.392932i | ||||||||
−1.06673e8 | − | 1.84763e8i | −0.0144428 | − | 0.0250156i | |||||
3.89968e9 | − | 6.75444e9i | 0.525199 | − | 0.909671i | −0.474370 | − | 0.880325i | ||
0.999569 | − | 0.0293460i | ||||||||
−1.13407e8 | + | 1.96426e8i | −0.0151927 | + | 0.0263146i | |||||
1.19404e9 | + | 2.06813e9i | 0.159118 | + | 0.275601i | |||||
2.76126e9 | 0.366032 | |||||||||
0 | 0 | |||||||||
4.99884e8 | 0.0655706 | |||||||||
−2.24635e9 | − | 3.89079e9i | −0.293114 | − | 0.507689i | |||||
7.35838e8 | − | 1.27451e9i | 0.0955135 | − | 0.165434i | |||||
−2.02736e9 | + | 3.51148e9i | −0.261781 | + | 0.453418i | |||||
−5.63150e8 | − | 9.75404e8i | −0.0723373 | − | 0.125292i | |||||
−8.43431e8 | −0.107776 | |||||||||
0 | 0 | |||||||||
−6.85231e9 | −0.866531 | −0.433265 | − | 0.901266i | ||||||
−0.433265 | + | 0.901266i | ||||||||
−4.06702e9 | − | 7.04428e9i | −0.511642 | − | 0.886191i | |||||
6.22386e8 | − | 1.07800e9i | 0.0778927 | − | 0.134914i | |||||
1.69525e9 | − | 2.93626e9i | 0.211067 | − | 0.365579i | |||||
3.82852e9 | + | 6.63119e9i | 0.474210 | + | 0.821355i | 0.999564 | − | 0.0295283i | ||
−0.525354 | + | 0.850884i | ||||||||
−1.49811e9 | −0.184604 | |||||||||
0 | 0 | |||||||||
−1.76736e9 | −0.215547 | |||||||||
4.08880e9 | + | 7.08200e9i | 0.496113 | + | 0.859293i | |||||
−1.88863e8 | + | 3.27121e8i | −0.0227983 | + | 0.0394878i | |||||
2.76338e9 | − | 4.78631e9i | 0.331870 | − | 0.574815i | −0.651009 | − | 0.759070i | ||
0.982878 | + | 0.184255i | ||||||||
5.18535e8 | + | 8.98129e8i | 0.0619557 | + | 0.107310i | |||||
−1.90633e9 | −0.226611 | |||||||||
0 | 0 | |||||||||
−1.43471e9 | −0.168817 | |||||||||
−1.89809e9 | − | 3.28760e9i | −0.222207 | − | 0.384874i | |||||
4.59625e8 | − | 7.96094e8i | 0.0535348 | − | 0.0927251i | |||||
1.43144e9 | − | 2.47933e9i | 0.165883 | − | 0.287318i | |||||
−7.59635e8 | − | 1.31573e9i | −0.0875854 | − | 0.151702i | 0.818905 | − | 0.573930i | ||
−0.906490 | + | 0.422227i | ||||||||
7.64711e9 | 0.877255 | |||||||||
0 | 0 | |||||||||
7.76395e9 | 0.881708 | |||||||||
−3.30886e9 | − | 5.73111e9i | −0.373879 | − | 0.647577i | |||||
−2.85839e8 | + | 4.95087e8i | −0.0321358 | + | 0.0556608i | |||||
−2.20260e9 | + | 3.81502e9i | −0.246389 | + | 0.426758i | |||||
3.53658e9 | + | 6.12553e9i | 0.393631 | + | 0.681789i | |||||
−3.68147e9 | −0.407710 | |||||||||
0 | 0 | |||||||||
6.81967e9 | 0.747739 | 0.373869 | − | 0.927481i | ||||||
0.373869 | + | 0.927481i | ||||||||
2.46116e8 | + | 4.26286e8i | 0.0268510 | + | 0.0465073i | |||||
−9.52625e8 | + | 1.65000e9i | −0.103414 | + | 0.179118i | |||||
1.32645e8 | − | 2.29748e8i | 0.0143280 | − | 0.0248169i | |||||
−8.71513e8 | − | 1.50951e9i | −0.0936725 | − | 0.162246i | |||||
8.72369e9 | 0.933005 | |||||||||
0 | 0 | |||||||||
−1.15308e9 | −0.122108 | |||||||||
−6.08497e9 | − | 1.05395e10i | −0.641205 | − | 1.11060i | −0.985164 | − | 0.171615i | ||
0.343959 | − | 0.938984i | ||||||||
−1.87506e9 | + | 3.24770e9i | −0.196612 | + | 0.340543i | |||||
1.37191e9 | − | 2.37622e9i | 0.143147 | − | 0.247938i | |||||
6.40689e8 | + | 1.10971e9i | 0.0665223 | + | 0.115220i | |||||
−5.06871e9 | −0.523702 | |||||||||
0 | 0 | |||||||||
3.85948e8 | 0.0394874 | |||||||||
−3.00242e9 | − | 5.20034e9i | −0.305686 | − | 0.529463i | |||||
−3.06183e9 | + | 5.30324e9i | −0.310216 | + | 0.537309i | |||||
4.13492e9 | − | 7.16189e9i | 0.416899 | − | 0.722091i | |||||
−1.00013e9 | − | 1.73227e9i | −0.100347 | − | 0.173806i | 0.811481 | − | 0.584379i | ||
−0.911828 | + | 0.410573i | ||||||||
−3.64290e8 | −0.0363734 | |||||||||
0 | 0 | |||||||||
3.19830e9 | 0.316256 | |||||||||
−5.46822e9 | − | 9.47123e9i | −0.538098 | − | 0.932014i | |||||
−4.76269e9 | + | 8.24922e9i | −0.466409 | + | 0.807845i | |||||
−1.30763e9 | + | 2.26489e9i | −0.127439 | + | 0.220731i | |||||
−1.99401e9 | − | 3.45372e9i | −0.193396 | − | 0.334972i | |||||
1.21193e10 | 1.16979 | 0.584895 | − | 0.811109i | ||||||
0.584895 | + | 0.811109i | ||||||||
0 | 0 | |||||||||
3.87420e8 | 0.0370370 | |||||||||
−7.24041e8 | − | 1.25408e9i | −0.0688863 | − | 0.119315i | |||||
1.31115e10 | − | 2.27098e10i | 1.24148 | − | 2.15031i | |||||
−7.20084e8 | + | 1.24722e9i | −0.0678569 | + | 0.117532i | |||||
−6.52266e9 | − | 1.12976e10i | −0.611732 | − | 1.05955i | −0.990948 | − | 0.134243i | ||
0.379217 | − | 0.925308i | ||||||||
1.93746e9 | 0.180841 | |||||||||
0 | 0 | |||||||||
3.55992e9 | 0.329130 | |||||||||
5.83922e8 | + | 1.01138e9i | 0.0537302 | + | 0.0930635i | |||||
−4.54004e8 | + | 7.86357e8i | −0.0415779 | + | 0.0720150i | |||||
−1.13794e9 | + | 1.97096e9i | −0.103720 | + | 0.179648i | −0.913214 | − | 0.407479i | ||
0.809495 | + | 0.587127i | ||||||||
−3.34627e8 | − | 5.79592e8i | −0.0303564 | − | 0.0525789i | |||||
−1.87609e9 | −0.169391 | |||||||||
0 | 0 | |||||||||
2.13411e9 | 0.190878 | 0.0954390 | − | 0.995435i | ||||||
0.0954390 | + | 0.995435i | ||||||||
3.22486e8 | + | 5.58563e8i | 0.0287082 | + | 0.0497241i | |||||
−1.98219e9 | + | 3.43326e9i | −0.175630 | + | 0.304200i | |||||
−5.75075e9 | + | 9.96059e9i | −0.507152 | + | 0.878414i | |||||
1.96578e9 | + | 3.40483e9i | 0.172549 | + | 0.298864i | |||||
1.83255e9 | 0.160103 | |||||||||
0 | 0 | |||||||||
−3.72528e9 | −0.322436 | |||||||||
−1.02089e10 | − | 1.76823e10i | −0.879503 | − | 1.52334i | −0.851887 | − | 0.523725i | ||
−0.0276155 | − | 0.999619i | ||||||||
1.08370e9 | − | 1.87703e9i | 0.0929283 | − | 0.160957i | |||||
4.15887e8 | − | 7.20338e8i | 0.0354971 | − | 0.0614828i | |||||
−5.17090e8 | − | 8.95627e8i | −0.0439306 | − | 0.0760900i | |||||
9.31273e9 | 0.787522 | |||||||||
0 | 0 | |||||||||
8.04759e9 | 0.674265 | 0.337132 | − | 0.941457i | ||||||
0.337132 | + | 0.941457i | ||||||||
4.80676e9 | + | 8.32555e9i | 0.400876 | + | 0.694337i | |||||
−1.48424e9 | + | 2.57078e9i | −0.123213 | + | 0.213412i | |||||
6.94225e8 | − | 1.20243e9i | 0.0573657 | − | 0.0993604i | |||||
−2.80867e9 | − | 4.86476e9i | −0.231023 | − | 0.400143i | 0.727087 | − | 0.686546i | ||
−0.958109 | + | 0.286403i | ||||||||
6.79324e9 | 0.556204 | |||||||||
0 | 0 | |||||||||
−6.48998e9 | −0.526522 | |||||||||
−1.25821e9 | − | 2.17928e9i | −0.101610 | − | 0.175994i | |||||
2.52343e9 | − | 4.37072e9i | 0.202858 | − | 0.351360i | |||||
1.04298e9 | − | 1.80649e9i | 0.0834624 | − | 0.144561i | |||||
−2.26492e8 | − | 3.92296e8i | −0.0180422 | − | 0.0312500i | |||||
−8.92653e9 | −0.707849 | −0.353924 | − | 0.935274i | ||||||
−0.353924 | + | 0.935274i | ||||||||
0 | 0 | |||||||||
−7.42855e9 | −0.583733 | |||||||||
−2.25887e9 | − | 3.91247e9i | −0.176697 | − | 0.306049i | |||||
8.99328e9 | − | 1.55768e10i | 0.700310 | − | 1.21297i | −0.268048 | − | 0.963406i | ||
0.968358 | − | 0.249566i | ||||||||
2.70256e9 | − | 4.68097e9i | 0.209499 | − | 0.362863i | |||||
1.47529e9 | + | 2.55527e9i | 0.113847 | + | 0.197188i | |||||
2.35395e9 | 0.180834 | |||||||||
0 | 0 | |||||||||
1.13749e10 | 0.866000 | |||||||||
−1.73038e9 | − | 2.99711e9i | −0.131148 | − | 0.227155i | |||||
3.29505e8 | − | 5.70720e8i | 0.0248617 | − | 0.0430618i | |||||
1.94422e9 | − | 3.36749e9i | 0.146038 | − | 0.252946i | |||||
1.22954e10 | + | 2.12963e10i | 0.919434 | + | 1.59251i | |||||
−8.13971e8 | −0.0605958 | |||||||||
0 | 0 | |||||||||
3.56753e9 | 0.263223 | |||||||||
−4.84706e8 | − | 8.39536e8i | −0.0356041 | − | 0.0616681i | |||||
6.57941e9 | − | 1.13959e10i | 0.481144 | − | 0.833366i | −0.518622 | − | 0.855004i | ||
0.999766 | + | 0.0216375i | ||||||||
−1.60738e9 | + | 2.78407e9i | −0.117025 | + | 0.202693i | |||||
6.53395e9 | + | 1.13171e10i | 0.473594 | + | 0.820288i | |||||
−3.67349e9 | −0.265084 | |||||||||
0 | 0 | |||||||||
3.77727e8 | 0.0270172 | |||||||||
−1.30265e9 | − | 2.25626e9i | −0.0927624 | − | 0.160669i | |||||
2.81988e8 | − | 4.88417e8i | 0.0199921 | − | 0.0346273i | |||||
−4.84327e8 | + | 8.38878e8i | −0.0341864 | + | 0.0592126i | |||||
−6.68471e9 | − | 1.15783e10i | −0.469772 | − | 0.813669i | |||||
2.50099e9 | 0.174988 | 0.0874939 | − | 0.996165i | ||||||
0.0874939 | + | 0.996165i | ||||||||
0 | 0 | |||||||||
1.49718e10 | 1.03839 | |||||||||
−1.03614e9 | − | 1.79465e9i | −0.0715490 | − | 0.123927i | |||||
−9.12231e8 | + | 1.58003e9i | −0.0627178 | + | 0.108630i | |||||
8.09289e9 | − | 1.40173e10i | 0.553979 | − | 0.959519i | |||||
7.50747e8 | + | 1.30033e9i | 0.0511669 | + | 0.0886237i | |||||
1.99411e9 | 0.135317 | |||||||||
0 | 0 | |||||||||
−1.16677e9 | −0.0784899 | |||||||||
−3.33956e9 | − | 5.78428e9i | −0.223682 | − | 0.387429i | |||||
5.25529e9 | − | 9.10243e9i | 0.350475 | − | 0.607040i | |||||
−5.60593e9 | + | 9.70975e9i | −0.372244 | + | 0.644746i | −0.989910 | − | 0.141695i | ||
0.617666 | + | 0.786440i | ||||||||
−2.59343e8 | − | 4.49196e8i | −0.0171466 | − | 0.0296987i | |||||
−2.38194e10 | −1.56804 | −0.784020 | − | 0.620736i | ||||||
−0.784020 | + | 0.620736i | ||||||||
0 | 0 | |||||||||
−6.16374e9 | −0.402279 | |||||||||
3.46970e8 | + | 6.00970e8i | 0.0225479 | + | 0.0390542i | |||||
−5.80048e9 | + | 1.00467e10i | −0.375329 | + | 0.650089i | |||||
1.56455e9 | − | 2.70987e9i | 0.100803 | − | 0.174596i | |||||
1.03005e10 | + | 1.78410e10i | 0.660817 | + | 1.14457i | |||||
−1.14981e10 | −0.734497 | |||||||||
0 | 0 | |||||||||
1.21566e9 | 0.0769951 | |||||||||
1.01461e10 | + | 1.75735e10i | 0.639877 | + | 1.10830i | 0.985459 | + | 0.169912i | ||
−0.345582 | + | 0.938389i | ||||||||
1.68757e9 | − | 2.92296e9i | 0.105977 | − | 0.183557i | |||||
2.77965e9 | − | 4.81449e9i | 0.173816 | − | 0.301059i | −0.765935 | − | 0.642918i | ||
0.939751 | + | 0.341860i | ||||||||
3.64375e9 | + | 6.31116e9i | 0.226884 | + | 0.392974i | |||||
1.72800e9 | 0.107141 | |||||||||
0 | 0 | |||||||||
2.02195e10 | 1.24308 | 0.621542 | − | 0.783381i | ||||||
0.621542 | + | 0.783381i | ||||||||
2.53435e9 | + | 4.38963e9i | 0.155153 | + | 0.268733i | |||||
−1.87400e9 | + | 3.24586e9i | −0.114243 | + | 0.197874i | −0.917477 | − | 0.397789i | ||
0.803234 | + | 0.595663i | ||||||||
2.63183e9 | − | 4.55846e9i | 0.159766 | − | 0.276723i | |||||
4.79406e9 | + | 8.30356e9i | 0.289801 | + | 0.501950i | |||||
8.19462e8 | 0.0493284 | |||||||||
0 | 0 | |||||||||
1.17166e10 | 0.699392 | |||||||||
−1.40269e9 | − | 2.42953e9i | −0.0833795 | − | 0.144418i | |||||
−7.19832e8 | + | 1.24678e9i | −0.0426097 | + | 0.0738022i | |||||
−4.59165e8 | + | 7.95297e8i | −0.0270664 | + | 0.0468803i | |||||
3.44839e8 | + | 5.97279e8i | 0.0202424 | + | 0.0350609i | |||||
2.03224e10 | 1.18798 | 0.593988 | − | 0.804474i | ||||||
0.593988 | + | 0.804474i | ||||||||
0 | 0 | |||||||||
−1.55397e10 | −0.900860 | |||||||||
−4.73017e9 | − | 8.19290e9i | −0.273077 | − | 0.472983i | |||||
−3.08026e9 | + | 5.33516e9i | −0.177089 | + | 0.306726i | |||||
2.70378e9 | − | 4.68308e9i | 0.154801 | − | 0.268123i | |||||
−3.23158e9 | − | 5.59725e9i | −0.184254 | − | 0.319136i | |||||
3.08601e9 | 0.175227 | |||||||||
0 | 0 | |||||||||
−1.20449e9 | −0.0678296 | |||||||||
2.88618e9 | + | 4.99901e9i | 0.161863 | + | 0.280354i | |||||
7.15736e9 | − | 1.23969e10i | 0.399748 | − | 0.692385i | |||||
−4.65598e9 | + | 8.06440e9i | −0.258975 | + | 0.448558i | |||||
−3.31978e9 | − | 5.75002e9i | −0.183895 | − | 0.318516i | |||||
3.86410e8 | 0.0213170 | 0.0106585 | − | 0.999943i | ||||||
0.0106585 | + | 0.999943i | ||||||||
0 | 0 | |||||||||
1.97691e9 | 0.108170 | |||||||||
−2.38598e9 | − | 4.13264e9i | −0.130020 | − | 0.225201i | |||||
2.32122e9 | − | 4.02047e9i | 0.125975 | − | 0.218195i | −0.796139 | − | 0.605114i | ||
0.922114 | + | 0.386919i | ||||||||
−3.41659e8 | + | 5.91771e8i | −0.0184666 | + | 0.0319851i | |||||
1.36654e10 | + | 2.36691e10i | 0.735606 | + | 1.27411i | 0.954457 | + | 0.298349i | ||
−0.218851 | + | 0.975758i | ||||||||
−7.23649e9 | −0.387957 | |||||||||
0 | 0 | |||||||||
−4.83726e9 | −0.257231 | |||||||||
−9.21669e9 | − | 1.59638e10i | −0.488132 | − | 0.845469i | 0.511775 | − | 0.859120i | ||
−0.999907 | + | 0.0136503i | ||||||||
3.22486e8 | − | 5.58563e8i | 0.0170103 | − | 0.0294628i | |||||
7.28865e9 | − | 1.26243e10i | 0.382905 | − | 0.663210i | |||||
2.86558e8 | + | 4.96332e8i | 0.0149934 | + | 0.0259693i | |||||
1.05357e10 | 0.549032 | |||||||||
0 | 0 | |||||||||
3.80899e9 | 0.196898 | |||||||||
5.44880e8 | + | 9.43760e8i | 0.0280533 | + | 0.0485897i | |||||
−1.80370e9 | + | 3.12409e9i | −0.0924911 | + | 0.160199i | |||||
1.10240e9 | − | 1.90941e9i | 0.0563029 | − | 0.0975196i | |||||
1.67581e9 | + | 2.90258e9i | 0.0852460 | + | 0.147650i | |||||
−1.93188e10 | −0.978791 | |||||||||
0 | 0 | |||||||||
2.56382e9 | 0.128861 | |||||||||
6.51437e9 | + | 1.12832e10i | 0.326117 | + | 0.564852i | 0.981738 | − | 0.190239i | ||
−0.655620 | + | 0.755091i | ||||||||
7.79670e8 | − | 1.35043e9i | 0.0388759 | − | 0.0673350i | |||||
−5.11402e9 | + | 8.85774e9i | −0.253981 | + | 0.439908i | |||||
−2.52854e8 | − | 4.37956e8i | −0.0125078 | − | 0.0216641i | |||||
3.46348e10 | 1.70646 | 0.853232 | − | 0.521531i | ||||||
0.853232 | + | 0.521531i | ||||||||
0 | 0 | |||||||||
3.40346e10 | 1.66363 | 0.831817 | − | 0.555049i | ||||||
0.831817 | + | 0.555049i | ||||||||
2.83031e9 | + | 4.90223e9i | 0.137800 | + | 0.238677i | |||||
−1.09903e9 | + | 1.90358e9i | −0.0532977 | + | 0.0923142i | |||||
−8.32073e9 | + | 1.44119e10i | −0.401923 | + | 0.696152i | |||||
2.39074e9 | + | 4.14089e9i | 0.115027 | + | 0.199233i | 0.917791 | − | 0.397065i | ||
−0.802764 | + | 0.596298i | ||||||||
1.18491e9 | 0.0567858 | |||||||||
0 | 0 | |||||||||
2.44263e9 | 0.116143 | |||||||||
2.68909e8 | + | 4.65764e8i | 0.0127360 | + | 0.0220594i | |||||
−4.80558e9 | + | 8.32352e9i | −0.226709 | + | 0.392672i | |||||
−5.88100e9 | + | 1.01862e10i | −0.276357 | + | 0.478665i | |||||
−3.50946e9 | − | 6.07856e9i | −0.164270 | − | 0.284524i | |||||
−1.14467e10 | −0.533704 | |||||||||
0 | 0 | |||||||||
−9.16943e9 | −0.424198 | |||||||||
7.14424e9 | + | 1.23742e10i | 0.329222 | + | 0.570229i | |||||
9.64706e8 | − | 1.67092e9i | 0.0442829 | − | 0.0767002i | |||||
1.47529e9 | − | 2.55527e9i | 0.0674571 | − | 0.116839i | |||||
−4.16015e9 | − | 7.20559e9i | −0.189484 | − | 0.328196i | |||||
−1.26050e9 | −0.0571899 | |||||||||
0 | 0 | |||||||||
−3.55108e9 | −0.159871 | |||||||||
9.07888e9 | + | 1.57251e10i | 0.407157 | + | 0.705217i | |||||
−8.24405e9 | + | 1.42791e10i | −0.368292 | + | 0.637900i | |||||
1.39320e10 | − | 2.41309e10i | 0.619993 | − | 1.07386i | −0.369494 | − | 0.929233i | ||
0.989486 | − | 0.144626i | ||||||||
9.69196e9 | + | 1.67870e10i | 0.429646 | + | 0.744169i | |||||
1.49653e10 | 0.660862 | |||||||||
0 | 0 | |||||||||
3.21050e10 | 1.40689 | 0.703443 | − | 0.710752i | ||||||
0.703443 | + | 0.710752i | ||||||||
1.22912e9 | + | 2.12890e9i | 0.0536552 | + | 0.0929336i | |||||
−2.72890e9 | + | 4.72660e9i | −0.118670 | + | 0.205542i | |||||
−8.97232e9 | + | 1.55405e10i | −0.388681 | + | 0.673215i | |||||
1.37266e9 | + | 2.37752e9i | 0.0592364 | + | 0.102601i | |||||
−3.40079e9 | −0.146199 | |||||||||
0 | 0 | |||||||||
4.45529e9 | 0.190076 | |||||||||
−1.41227e10 | − | 2.44612e10i | −0.600224 | − | 1.03962i | −0.992787 | − | 0.119893i | ||
0.392563 | − | 0.919725i | ||||||||
3.39304e9 | − | 5.87693e9i | 0.143659 | − | 0.248824i | |||||
−8.55648e9 | + | 1.48203e10i | −0.360900 | + | 0.625097i | |||||
−1.04102e10 | − | 1.80309e10i | −0.437421 | − | 0.757636i | |||||
1.20111e10 | 0.502780 | |||||||||
0 | 0 | |||||||||
5.42064e9 | 0.225193 | |||||||||
−2.85023e9 | − | 4.93674e9i | −0.117962 | − | 0.204316i | |||||
−5.18807e9 | + | 8.98601e9i | −0.213908 | + | 0.370500i | |||||
−6.77544e8 | + | 1.17354e9i | −0.0278304 | + | 0.0482037i | |||||
−5.14871e9 | − | 8.91783e9i | −0.210690 | − | 0.364925i | 0.741241 | − | 0.671239i | ||
−0.951931 | + | 0.306314i | ||||||||
1.22948e9 | 0.0501223 | |||||||||
0 | 0 | |||||||||
−8.72645e9 | −0.353087 | |||||||||
5.26764e9 | + | 9.12382e9i | 0.212339 | + | 0.367782i | |||||
−2.53388e9 | + | 4.38880e9i | −0.101759 | + | 0.176251i | |||||
1.74665e9 | − | 3.02528e9i | 0.0698818 | − | 0.121039i | |||||
5.83387e8 | + | 1.01046e9i | 0.0232536 | + | 0.0402765i | |||||
−3.96648e10 | −1.57513 | −0.787565 | − | 0.616231i | ||||||
−0.787565 | + | 0.616231i | ||||||||
0 | 0 | |||||||||
−2.71199e10 | −1.06895 | |||||||||
−2.06581e9 | − | 3.57809e9i | −0.0811228 | − | 0.140509i | |||||
−1.43147e9 | + | 2.47938e9i | −0.0560040 | + | 0.0970017i | −0.892668 | − | 0.450714i | ||
0.836664 | + | 0.547716i | ||||||||
−3.15815e9 | + | 5.47007e9i | −0.123099 | + | 0.213213i | |||||
−8.45730e9 | − | 1.46485e10i | −0.328428 | − | 0.568855i | |||||
−2.73323e9 | −0.105748 | |||||||||
0 | 0 | |||||||||
7.50341e9 | 0.288164 | |||||||||
−3.42124e9 | − | 5.92575e9i | −0.130906 | − | 0.226735i | 0.793120 | − | 0.609065i | ||
−0.924026 | + | 0.382330i | ||||||||
3.25194e9 | − | 5.63253e9i | 0.123969 | − | 0.214721i | |||||
−2.31901e9 | + | 4.01664e9i | −0.0880786 | + | 0.152557i | |||||
5.62288e9 | + | 9.73912e9i | 0.212778 | + | 0.368542i | |||||
6.56031e9 | 0.247339 | |||||||||
0 | 0 | |||||||||
−2.50283e10 | −0.936711 | −0.468356 | − | 0.883540i | ||||||
−0.468356 | + | 0.883540i | ||||||||
−8.57496e8 | − | 1.48523e9i | −0.0319752 | − | 0.0553826i | |||||
−6.18576e9 | + | 1.07141e10i | −0.229817 | + | 0.398054i | |||||
−7.25766e9 | + | 1.25706e10i | −0.268655 | + | 0.465323i | |||||
−5.64978e8 | − | 9.78571e8i | −0.0208372 | − | 0.0360911i | |||||
1.76442e9 | 0.0648368 | |||||||||
0 | 0 | |||||||||
−8.63502e8 | −0.0315003 | |||||||||
1.26679e10 | + | 2.19415e10i | 0.460440 | + | 0.797506i | |||||
−1.07177e9 | + | 1.85636e9i | −0.0388140 | + | 0.0672278i | |||||
3.39723e9 | − | 5.88417e9i | 0.122584 | − | 0.212321i | |||||
−1.29617e10 | − | 2.24503e10i | −0.466007 | − | 0.807148i | |||||
−8.61193e9 | −0.308500 | |||||||||
0 | 0 | |||||||||
−5.13292e10 | −1.82546 | −0.912730 | − | 0.408564i | ||||||
−0.912730 | + | 0.408564i | ||||||||
−4.72653e9 | − | 8.18660e9i | −0.167486 | − | 0.290095i | |||||
−8.49041e9 | + | 1.47058e10i | −0.299775 | + | 0.519225i | |||||
2.24360e9 | − | 3.88604e9i | 0.0789306 | − | 0.136712i | |||||
−1.81266e10 | − | 3.13962e10i | −0.635403 | − | 1.10055i | −0.986430 | − | 0.164184i | ||
0.351027 | − | 0.936365i | ||||||||
9.18330e8 | 0.0320750 | |||||||||
0 | 0 | |||||||||
−3.14346e10 | −1.09006 | |||||||||
2.66883e9 | + | 4.62256e9i | 0.0922158 | + | 0.159722i | |||||
−1.70686e9 | + | 2.95638e9i | −0.0587658 | + | 0.101785i | |||||
1.78987e10 | − | 3.10014e10i | 0.614031 | − | 1.06353i | −0.376523 | − | 0.926407i | ||
0.990554 | − | 0.137125i | ||||||||
−1.02697e10 | − | 1.77876e10i | −0.351052 | − | 0.608040i | |||||
−2.53272e9 | −0.0862677 | |||||||||
0 | 0 | |||||||||
3.13925e9 | 0.106166 | |||||||||
−1.31561e10 | − | 2.27871e10i | −0.443342 | − | 0.767890i | |||||
−2.44510e10 | + | 4.23504e10i | −0.821030 | + | 1.42207i | 0.0838854 | + | 0.996475i | ||
−0.904916 | + | 0.425591i | ||||||||
−1.07616e9 | + | 1.86396e9i | −0.0360075 | + | 0.0623668i | |||||
3.06407e9 | + | 5.30713e9i | 0.102158 | + | 0.176943i | |||||
−9.36056e9 | −0.310980 | |||||||||
0 | 0 | |||||||||
−4.44702e9 | −0.146697 | |||||||||
5.03440e10 | + | 8.71984e10i | 1.65486 | + | 2.86630i | |||||
3.60021e8 | − | 6.23575e8i | 0.0117925 | − | 0.0204252i | |||||
3.44941e9 | − | 5.97455e9i | 0.112587 | − | 0.195006i | −0.804226 | − | 0.594324i | ||
0.916812 | + | 0.399318i | ||||||||
7.64412e8 | + | 1.32400e9i | 0.0248620 | + | 0.0430623i | |||||
−7.65495e8 | −0.0248096 | |||||||||
0 | 0 | |||||||||
−2.54855e10 | −0.820185 | |||||||||
4.65963e9 | + | 8.07072e9i | 0.149432 | + | 0.258824i | |||||
2.76515e9 | − | 4.78939e9i | 0.0883662 | − | 0.153055i | −0.818454 | − | 0.574571i | ||
0.906821 | + | 0.421517i | ||||||||
−1.72252e10 | + | 2.98349e10i | −0.548539 | + | 0.950098i | |||||
8.43554e8 | + | 1.46108e9i | 0.0267691 | + | 0.0463654i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 294.8.e.j.67.1 | 2 | ||
7.2 | even | 3 | inner | 294.8.e.j.79.1 | 2 | ||
7.3 | odd | 6 | 294.8.a.c.1.1 | 1 | |||
7.4 | even | 3 | 42.8.a.c.1.1 | ✓ | 1 | ||
7.5 | odd | 6 | 294.8.e.n.79.1 | 2 | |||
7.6 | odd | 2 | 294.8.e.n.67.1 | 2 | |||
21.11 | odd | 6 | 126.8.a.g.1.1 | 1 | |||
28.11 | odd | 6 | 336.8.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.8.a.c.1.1 | ✓ | 1 | 7.4 | even | 3 | ||
126.8.a.g.1.1 | 1 | 21.11 | odd | 6 | |||
294.8.a.c.1.1 | 1 | 7.3 | odd | 6 | |||
294.8.e.j.67.1 | 2 | 1.1 | even | 1 | trivial | ||
294.8.e.j.79.1 | 2 | 7.2 | even | 3 | inner | ||
294.8.e.n.67.1 | 2 | 7.6 | odd | 2 | |||
294.8.e.n.79.1 | 2 | 7.5 | odd | 6 | |||
336.8.a.d.1.1 | 1 | 28.11 | odd | 6 |