Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,9,Mod(8,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.8");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 81.f (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: | |
Relative dimension: | over |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: |
Embedding invariants
Embedding label | 71.19 | ||
Character | 81.71 | ||
Dual form | 81.9.f.a.8.19 |
-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 .
21.5826 | − | 3.80559i | 1.34891 | − | 0.237850i | 0.547923 | − | 0.836529i | ||
0.800989 | + | 0.598679i | ||||||||
0 | 0 | |||||||||
210.764 | − | 76.7119i | 0.823297 | − | 0.299656i | |||||
−129.757 | + | 154.639i | −0.207612 | + | 0.247422i | −0.859795 | − | 0.510639i | ||
0.652183 | + | 0.758061i | ||||||||
0 | 0 | |||||||||
1479.28 | + | 538.412i | 0.616108 | + | 0.224245i | 0.631174 | − | 0.775641i | ||
−0.0150656 | + | 0.999887i | ||||||||
−601.827 | + | 347.465i | −0.146930 | + | 0.0848304i | |||||
0 | 0 | |||||||||
−2212.01 | + | 3831.31i | −0.221201 | + | 0.383131i | |||||
5647.40 | + | 6730.30i | 0.385725 | + | 0.459689i | 0.923612 | − | 0.383328i | ||
−0.537888 | + | 0.843017i | ||||||||
0 | 0 | |||||||||
−2496.75 | + | 14159.8i | −0.0874182 | + | 0.495773i | 0.909390 | + | 0.415944i | ||
−0.996809 | + | 0.0798295i | ||||||||
33975.6 | + | 5990.81i | 0.884412 | + | 0.155946i | |||||
0 | 0 | |||||||||
−55651.7 | + | 46697.3i | −0.849178 | + | 0.712545i | |||||
48327.4 | + | 27901.8i | 0.578626 | + | 0.334070i | 0.760587 | − | 0.649236i | ||
−0.181961 | + | 0.983306i | ||||||||
0 | 0 | |||||||||
24124.8 | + | 41785.3i | 0.185118 | + | 0.320634i | 0.943616 | − | 0.331041i | ||
−0.758498 | + | 0.651675i | ||||||||
−15485.6 | + | 42546.2i | −0.0967847 | + | 0.265914i | |||||
0 | 0 | |||||||||
147498. | + | 123766.i | 0.629645 | + | 0.528335i | |||||
57310.9 | + | 157460.i | 0.204798 | + | 0.562678i | 0.998987 | − | 0.0449922i | ||
−0.794189 | + | 0.607671i | ||||||||
0 | 0 | |||||||||
60755.1 | + | 344560.i | 0.155533 | + | 0.882072i | |||||
315106.i | 0.689547i | |||||||||
0 | 0 | |||||||||
353081. | 0.574437 | |||||||||
52796.6 | − | 9309.47i | 0.0746473 | − | 0.0131623i | −0.136200 | − | 0.990681i | ||
0.210847 | + | 0.977519i | ||||||||
0 | 0 | |||||||||
971027. | − | 353425.i | 1.05144 | − | 0.382693i | 0.242234 | − | 0.970218i | ||
0.809206 | + | 0.587525i | ||||||||
−909043. | + | 1.08336e6i | −0.866931 | + | 1.03317i | |||||
0 | 0 | |||||||||
1.14921e6 | + | 418280.i | 0.859974 | + | 0.313005i | |||||
−275206. | + | 158890.i | −0.183394 | + | 0.105883i | |||||
0 | 0 | |||||||||
−932654. | + | 1.61540e6i | −0.497638 | + | 0.861935i | −0.999996 | − | 0.00272492i | ||
0.502358 | + | 0.864660i | ||||||||
679693. | + | 810026.i | 0.325970 | + | 0.388476i | |||||
0 | 0 | |||||||||
24359.9 | − | 138152.i | 0.00951559 | − | 0.0539656i | |||||
4.40599e6 | + | 776896.i | 1.55922 | + | 0.274933i | 0.885709 | − | 0.464241i | ||
0.673515 | + | 0.739174i | ||||||||
0 | 0 | |||||||||
−3.96290e6 | + | 3.32527e6i | −1.15915 | + | 0.972641i | −0.999893 | − | 0.0145968i | ||
−0.159255 | + | 0.987238i | ||||||||
1.70656e6 | + | 985285.i | 0.455315 | + | 0.262876i | |||||
0 | 0 | |||||||||
1.83615e6 | + | 3.18030e6i | 0.410087 | + | 0.710292i | |||||
1.82983e6 | − | 5.02741e6i | 0.374990 | − | 1.03028i | −0.598416 | − | 0.801186i | ||
0.973405 | − | 0.229090i | ||||||||
0 | 0 | |||||||||
−2.51772e6 | − | 2.11262e6i | −0.436741 | − | 0.366469i | |||||
2.62251e6 | + | 7.20528e6i | 0.419601 | + | 1.15284i | |||||
0 | 0 | |||||||||
559998. | + | 3.17591e6i | 0.0765901 | + | 0.434364i | |||||
− | 1.03085e7i | − | 1.30645i | −0.757163 | − | 0.653226i | ||||
0.757163 | − | 0.653226i | ||||||||
0 | 0 | |||||||||
−1.77356e6 | −0.193818 | |||||||||
−1.07735e6 | + | 189966.i | −0.109548 | + | 0.0193162i | |||||
0 | 0 | |||||||||
1.10406e6 | − | 401845.i | 0.0975620 | − | 0.0355097i | |||||
555817. | − | 662397.i | 0.0458695 | − | 0.0546651i | −0.742622 | − | 0.669711i | ||
0.788491 | + | 0.615046i | ||||||||
0 | 0 | |||||||||
−1.53716e7 | − | 5.59480e6i | −1.11020 | − | 0.404078i | −0.279130 | − | 0.960253i | ||
−0.831065 | + | 0.556175i | ||||||||
1.96123e7 | − | 1.13232e7i | 1.32728 | − | 0.766303i | |||||
0 | 0 | |||||||||
−6.19773e6 | + | 1.07348e7i | −0.369414 | + | 0.639843i | |||||
−1.86568e6 | − | 2.22343e6i | −0.104516 | − | 0.124558i | |||||
0 | 0 | |||||||||
1.38317e6 | − | 7.84434e6i | 0.0686398 | − | 0.389276i | −0.931062 | − | 0.364861i | ||
0.999702 | − | 0.0244149i | ||||||||
1.23261e7 | + | 2.17342e6i | 0.576487 | + | 0.101650i | |||||
0 | 0 | |||||||||
−5.33499e6 | + | 4.47659e6i | −0.222199 | + | 0.186447i | |||||
1.63960e7 | + | 9.46623e6i | 0.645215 | + | 0.372515i | 0.786620 | − | 0.617437i | ||
−0.141406 | + | 0.989952i | ||||||||
0 | 0 | |||||||||
2.49290e7 | + | 4.31782e7i | 0.877835 | + | 1.52045i | 0.853712 | + | 0.520745i | ||
0.0241223 | + | 0.999709i | ||||||||
−1.39815e7 | + | 3.84139e7i | −0.466259 | + | 1.28104i | |||||
0 | 0 | |||||||||
8.29006e6 | + | 6.95619e6i | 0.248487 | + | 0.208505i | |||||
4.73038e6 | + | 1.29966e7i | 0.134565 | + | 0.369715i | |||||
0 | 0 | |||||||||
−2.63044e6 | − | 1.49180e7i | −0.0675336 | − | 0.383002i | −0.999776 | − | 0.0211675i | ||
0.932242 | − | 0.361834i | ||||||||
− | 1.46652e7i | − | 0.358038i | |||||||
0 | 0 | |||||||||
9.80493e7 | 2.16865 | |||||||||
−8.67787e7 | + | 1.53014e7i | −1.82852 | + | 0.322418i | −0.978802 | − | 0.204811i | ||
−0.849723 | + | 0.527229i | ||||||||
0 | 0 | |||||||||
−1.05855e7 | + | 3.85282e6i | −0.202786 | + | 0.0738080i | |||||
−7.28750e7 | + | 8.68490e7i | −1.33225 | + | 1.58771i | |||||
0 | 0 | |||||||||
−5.73730e6 | − | 2.08821e6i | −0.0956703 | − | 0.0348211i | |||||
6.02765e7 | − | 3.48007e7i | 0.960701 | − | 0.554661i | 0.0643121 | − | 0.997930i | ||
0.896389 | + | 0.443269i | ||||||||
0 | 0 | |||||||||
−1.13172e7 | + | 1.96019e7i | −0.165034 | + | 0.285847i | |||||
2.41582e7 | + | 2.87906e7i | 0.337220 | + | 0.401883i | |||||
0 | 0 | |||||||||
2.03602e7 | − | 1.15468e8i | 0.260777 | − | 1.47894i | |||||
−9.59199e6 | − | 1.69133e6i | −0.117765 | − | 0.0207651i | |||||
0 | 0 | |||||||||
−2.85952e7 | + | 2.39942e7i | −0.323003 | + | 0.271032i | −0.789842 | − | 0.613311i | ||
0.466839 | + | 0.884343i | ||||||||
−6.23788e7 | − | 3.60144e7i | −0.676289 | − | 0.390456i | |||||
0 | 0 | |||||||||
3.92368e7 | + | 6.79601e7i | 0.392368 | + | 0.679601i | |||||
4.94931e7 | − | 1.35981e8i | 0.475619 | − | 1.30675i | −0.437558 | − | 0.899190i | ||
0.913177 | − | 0.407563i | ||||||||
0 | 0 | |||||||||
−9.02900e7 | − | 7.57623e7i | −0.802215 | − | 0.673138i | 0.146521 | − | 0.989208i | ||
−0.948736 | + | 0.316069i | ||||||||
−3.41742e6 | − | 9.38928e6i | −0.0292122 | − | 0.0802599i | |||||
0 | 0 | |||||||||
−3.92301e7 | − | 2.22485e8i | −0.310739 | − | 1.76229i | |||||
− | 1.92244e8i | − | 1.46662i | −0.679894 | − | 0.733311i | ||||
0.679894 | − | 0.733311i | ||||||||
0 | 0 | |||||||||
−8.87094e7 | −0.628440 | −0.314220 | − | 0.949350i | ||||||
−0.314220 | + | 0.949350i | ||||||||
−3.82779e7 | + | 6.74943e6i | −0.261443 | + | 0.0460995i | |||||
0 | 0 | |||||||||
−1.07467e8 | + | 3.91147e7i | −0.682970 | + | 0.248581i | |||||
1.98236e7 | − | 2.36248e7i | 0.121582 | − | 0.144895i | −0.701820 | − | 0.712354i | ||
0.823402 | + | 0.567459i | ||||||||
0 | 0 | |||||||||
−3.17860e7 | − | 1.15692e7i | −0.181738 | − | 0.0661470i | |||||
1.04135e7 | − | 6.01223e6i | 0.0575128 | − | 0.0332050i | |||||
0 | 0 | |||||||||
9.47516e6 | − | 1.64115e7i | 0.0488718 | − | 0.0846485i | |||||
5.64669e7 | + | 6.72946e7i | 0.281583 | + | 0.335577i | |||||
0 | 0 | |||||||||
2.38191e7 | − | 1.35085e8i | 0.111118 | − | 0.630181i | |||||
−3.53050e8 | − | 6.22523e7i | −1.59366 | − | 0.281006i | |||||
0 | 0 | |||||||||
1.77546e8 | − | 1.48979e8i | 0.750972 | − | 0.630140i | |||||
−1.29455e8 | − | 7.47411e7i | −0.530249 | − | 0.306139i | |||||
0 | 0 | |||||||||
−3.00728e7 | − | 5.20876e7i | −0.115600 | − | 0.200225i | 0.802419 | − | 0.596761i | ||
−0.918020 | + | 0.396535i | ||||||||
3.09142e7 | − | 8.49361e7i | 0.115164 | − | 0.316412i | |||||
0 | 0 | |||||||||
−4.87276e7 | − | 4.08874e7i | −0.170609 | − | 0.143158i | |||||
3.55348e7 | + | 9.76311e7i | 0.120662 | + | 0.331515i | 0.985288 | − | 0.170900i | ||
−0.864627 | + | 0.502415i | ||||||||
0 | 0 | |||||||||
1.31894e7 | + | 7.48011e7i | 0.0421522 | + | 0.239057i | |||||
− | 1.74565e8i | − | 0.541424i | |||||||
0 | 0 | |||||||||
−3.87797e7 | −0.113357 | |||||||||
1.72397e8 | − | 3.03983e7i | 0.489383 | − | 0.0862913i | 0.0764886 | − | 0.997070i | ||
0.412894 | + | 0.910779i | ||||||||
0 | 0 | |||||||||
−3.82714e8 | + | 1.39297e8i | −1.02522 | + | 0.373148i | −0.799257 | − | 0.600989i | ||
−0.225959 | + | 0.974137i | ||||||||
−4.58148e7 | + | 5.46000e7i | −0.119260 | + | 0.142128i | |||||
0 | 0 | |||||||||
3.89892e8 | + | 1.41909e8i | 0.958940 | + | 0.349026i | |||||
−1.09400e8 | + | 6.31620e7i | −0.261621 | + | 0.151047i | |||||
0 | 0 | |||||||||
−5.41114e6 | + | 9.37238e6i | −0.0122410 | + | 0.0212020i | |||||
7.02350e8 | + | 8.37028e8i | 1.54576 | + | 1.84217i | |||||
0 | 0 | |||||||||
−7.26494e7 | + | 4.12015e8i | −0.151421 | + | 0.858749i | |||||
−2.83527e8 | − | 4.99934e7i | −0.575240 | − | 0.101430i | −0.121543 | − | 0.992586i | ||
−0.453697 | + | 0.891156i | ||||||||
0 | 0 | |||||||||
5.12960e8 | − | 4.30425e8i | 0.986680 | − | 0.827922i | 0.00159590 | − | 0.999999i | ||
0.985084 | + | 0.172076i | ||||||||
−2.90379e7 | − | 1.67650e7i | −0.0543990 | − | 0.0314073i | |||||
0 | 0 | |||||||||
1.51554e8 | + | 2.62498e8i | 0.269453 | + | 0.466706i | |||||
−7.13446e7 | + | 1.96018e8i | −0.123605 | + | 0.339601i | |||||
0 | 0 | |||||||||
6.50076e8 | + | 5.45478e8i | 1.06995 | + | 0.897798i | 0.995048 | − | 0.0993922i | ||
0.0749061 | + | 0.997191i | ||||||||
−1.13543e8 | − | 3.11958e8i | −0.182194 | − | 0.500573i | |||||
0 | 0 | |||||||||
−4.95737e7 | − | 2.81147e8i | −0.0756435 | − | 0.428996i | |||||
2.63784e8i | 0.392596i | |||||||||
0 | 0 | |||||||||
4.59051e8 | 0.650296 | 0.325148 | − | 0.945663i | ||||||
0.325148 | + | 0.945663i | ||||||||
9.88223e8 | − | 1.74250e8i | 1.36609 | − | 0.240879i | |||||
0 | 0 | |||||||||
−1.81468e9 | + | 6.60489e8i | −2.38983 | + | 0.869827i | |||||
−1.44585e8 | + | 1.72310e8i | −0.185890 | + | 0.221536i | −0.850939 | − | 0.525265i | ||
0.665049 | + | 0.746800i | ||||||||
0 | 0 | |||||||||
5.72270e8 | + | 2.08289e8i | 0.701543 | + | 0.255341i | |||||
−2.13801e8 | + | 1.23438e8i | −0.255985 | + | 0.147793i | |||||
0 | 0 | |||||||||
−5.80149e8 | + | 1.00485e9i | −0.662866 | + | 1.14812i | |||||
8.39464e8 | + | 1.00043e9i | 0.937169 | + | 1.11687i | 0.992962 | + | 0.118432i | ||
−0.0557937 | + | 0.998442i | ||||||||
0 | 0 | |||||||||
−9.56415e7 | + | 5.42410e8i | −0.101975 | + | 0.578330i | |||||
−6.28574e8 | − | 1.10835e8i | −0.655098 | − | 0.115511i | |||||
0 | 0 | |||||||||
1.16849e9 | − | 9.80476e8i | 1.16397 | − | 0.976691i | |||||
1.21670e9 | + | 7.02464e8i | 1.18515 | + | 0.684245i | 0.957200 | − | 0.289428i | ||
0.227948 | + | 0.973673i | ||||||||
0 | 0 | |||||||||
5.89616e8 | + | 1.02124e9i | 0.549357 | + | 0.951514i | 0.998319 | + | 0.0579632i | ||
−0.448962 | + | 0.893551i | ||||||||
−1.69657e8 | + | 4.66129e8i | −0.154627 | + | 0.424835i | |||||
0 | 0 | |||||||||
−8.92033e7 | − | 7.48505e7i | −0.0778233 | − | 0.0653015i | |||||
−1.28785e8 | − | 3.53835e8i | −0.109946 | − | 0.302074i | |||||
0 | 0 | |||||||||
8.51361e7 | + | 4.82831e8i | 0.0696222 | + | 0.394847i | |||||
− | 1.19997e9i | − | 0.960591i | |||||||
0 | 0 | |||||||||
−2.13457e8 | −0.163793 | |||||||||
1.37346e9 | − | 2.42179e8i | 1.03201 | − | 0.181971i | 0.368102 | − | 0.929785i | ||
0.663908 | + | 0.747814i | ||||||||
0 | 0 | |||||||||
−2.42195e9 | + | 8.81518e8i | −1.74557 | + | 0.635334i | −0.999532 | − | 0.0305752i | ||
−0.746033 | + | 0.665909i | ||||||||
−5.25847e8 | + | 6.26680e8i | −0.371238 | + | 0.442424i | |||||
0 | 0 | |||||||||
−6.92709e8 | − | 2.52126e8i | −0.469382 | − | 0.170841i | |||||
1.45799e9 | − | 8.41768e8i | 0.968029 | − | 0.558892i | 0.0693939 | − | 0.997589i | ||
0.898635 | + | 0.438698i | ||||||||
0 | 0 | |||||||||
3.37619e8 | − | 5.84773e8i | 0.215285 | − | 0.372885i | −0.738076 | − | 0.674718i | ||
0.953361 | + | 0.301833i | ||||||||
−1.56287e8 | − | 1.86255e8i | −0.0976791 | − | 0.116409i | |||||
0 | 0 | |||||||||
5.50700e8 | − | 3.12318e9i | 0.330758 | − | 1.87582i | |||||
8.31131e7 | + | 1.46551e7i | 0.0489424 | + | 0.00862987i | |||||
0 | 0 | |||||||||
−6.91848e8 | + | 5.80529e8i | −0.391738 | + | 0.328707i | |||||
−2.23701e9 | − | 1.29154e9i | −1.24222 | − | 0.717198i | |||||
0 | 0 | |||||||||
−5.22275e8 | − | 9.04608e8i | −0.279027 | − | 0.483289i | |||||
−1.44986e8 | + | 3.98345e8i | −0.0759872 | + | 0.208773i | |||||
0 | 0 | |||||||||
1.43470e9 | + | 1.20386e9i | 0.723823 | + | 0.607359i | 0.928440 | − | 0.371483i | ||
−0.204617 | + | 0.978842i | ||||||||
−7.90787e8 | − | 2.17267e9i | −0.391486 | − | 1.07560i | |||||
0 | 0 | |||||||||
−7.31603e8 | − | 4.14913e9i | −0.348835 | − | 1.97834i | |||||
− | 1.04429e9i | − | 0.488730i | |||||||
0 | 0 | |||||||||
1.62670e9 | 0.733618 | |||||||||
−1.91458e9 | + | 3.37592e8i | −0.847710 | + | 0.149474i | |||||
0 | 0 | |||||||||
−3.73802e8 | + | 1.36053e8i | −0.159570 | + | 0.0580787i | |||||
−5.15746e8 | + | 6.14642e8i | −0.216205 | + | 0.257664i | |||||
0 | 0 | |||||||||
−2.38952e8 | − | 8.69713e7i | −0.0966252 | − | 0.0351687i | 0.293255 | − | 0.956034i | ||
−0.389880 | + | 0.920865i | ||||||||
−1.92802e9 | + | 1.11314e9i | −0.765806 | + | 0.442139i | |||||
0 | 0 | |||||||||
3.37937e8 | − | 5.85325e8i | 0.129540 | − | 0.224369i | |||||
−2.65807e9 | − | 3.16776e9i | −1.00106 | − | 1.19302i | −0.981155 | − | 0.193221i | ||
−0.0199095 | − | 0.999802i | ||||||||
0 | 0 | |||||||||
8.13979e8 | − | 4.61631e9i | 0.295986 | − | 1.67862i | −0.367181 | − | 0.930150i | ||
0.663167 | − | 0.748472i | ||||||||
−7.30052e8 | − | 1.28728e8i | −0.260881 | − | 0.0460003i | |||||
0 | 0 | |||||||||
−2.85397e7 | + | 2.39477e7i | −0.00985140 | + | 0.00826631i | |||||
1.81802e9 | + | 1.04964e9i | 0.616844 | + | 0.356135i | 0.775639 | − | 0.631176i | ||
−0.158795 | + | 0.987312i | ||||||||
0 | 0 | |||||||||
5.39999e8 | + | 9.35306e8i | 0.177061 | + | 0.306678i | |||||
6.63326e7 | − | 1.82247e8i | 0.0213835 | − | 0.0587507i | |||||
0 | 0 | |||||||||
1.47480e9 | + | 1.23750e9i | 0.459647 | + | 0.385690i | |||||
2.15785e9 | + | 5.92864e9i | 0.661347 | + | 1.81704i | 0.570708 | + | 0.821153i | ||
0.0906399 | + | 0.995884i | ||||||||
0 | 0 | |||||||||
1.06267e9 | + | 6.02671e9i | 0.315015 | + | 1.78654i | 0.572137 | + | 0.820158i | ||
−0.257122 | + | 0.966379i | ||||||||
− | 3.00613e9i | − | 0.876488i | |||||||
0 | 0 | |||||||||
−3.66897e9 | −1.03511 | |||||||||
6.53386e8 | − | 1.15210e8i | 0.181345 | − | 0.0319760i | |||||
0 | 0 | |||||||||
−6.51905e8 | + | 2.37274e8i | −0.175144 | + | 0.0637473i | |||||
−4.61588e8 | + | 5.50099e8i | −0.122025 | + | 0.145423i | |||||
0 | 0 | |||||||||
−3.07841e9 | − | 1.12045e9i | −0.788074 | − | 0.286836i | |||||
1.88232e9 | − | 1.08676e9i | 0.474241 | − | 0.273803i | −0.243773 | − | 0.969832i | ||
0.718013 | + | 0.696029i | ||||||||
0 | 0 | |||||||||
−7.36100e8 | + | 1.27496e9i | −0.179661 | + | 0.311182i | |||||
−8.47272e8 | − | 1.00974e9i | −0.203558 | − | 0.242591i | |||||
0 | 0 | |||||||||
8.95004e8 | − | 5.07582e9i | 0.208384 | − | 1.18181i | |||||
3.64585e9 | + | 6.42861e8i | 0.835730 | + | 0.147362i | 0.575106 | − | 0.818079i | ||
0.260624 | + | 0.965440i | ||||||||
0 | 0 | |||||||||
−2.24941e9 | + | 1.88748e9i | −0.499884 | + | 0.419452i | |||||
−5.63782e8 | − | 3.25500e8i | −0.123372 | − | 0.0712290i | |||||
0 | 0 | |||||||||
1.13848e9 | + | 1.97190e9i | 0.241612 | + | 0.418485i | |||||
−1.37284e9 | + | 3.77183e9i | −0.286943 | + | 0.788369i | 0.709547 | + | 0.704658i | ||
−0.996490 | + | 0.0837112i | ||||||||
0 | 0 | |||||||||
1.59410e9 | + | 1.33761e9i | 0.323245 | + | 0.271235i | |||||
5.69325e8 | + | 1.56421e9i | 0.113719 | + | 0.312441i | |||||
0 | 0 | |||||||||
−3.10232e8 | − | 1.75941e9i | −0.0601377 | − | 0.341058i | |||||
− | 8.40864e8i | − | 0.160589i | −0.996771 | − | 0.0802946i | ||||
0.996771 | − | 0.0802946i | ||||||||
0 | 0 | |||||||||
7.85425e9 | 1.45622 | 0.728111 | − | 0.685459i | ||||||
0.728111 | + | 0.685459i | ||||||||
−3.99244e9 | + | 7.03976e8i | −0.729396 | + | 0.128612i | |||||
0 | 0 | |||||||||
3.60510e9 | − | 1.31215e9i | 0.639609 | − | 0.232799i | |||||
−1.97588e9 | + | 2.35476e9i | −0.345486 | + | 0.411734i | |||||
0 | 0 | |||||||||
1.01728e9 | + | 3.70260e8i | 0.172792 | + | 0.0628910i | 0.426967 | − | 0.904267i | ||
−0.254176 | + | 0.967158i | ||||||||
−7.72986e9 | + | 4.46283e9i | −1.29417 | + | 0.747191i | |||||
0 | 0 | |||||||||
1.10418e8 | − | 1.91249e8i | 0.0179642 | − | 0.0311148i | |||||
−6.63691e9 | − | 7.90956e9i | −1.06449 | − | 1.26861i | −0.961759 | − | 0.273897i | ||
−0.102728 | − | 0.994709i | ||||||||
0 | 0 | |||||||||
1.22974e9 | − | 6.97420e9i | 0.191720 | − | 1.08730i | −0.725293 | − | 0.688440i | ||
0.917013 | − | 0.398858i | ||||||||
4.18186e9 | + | 7.37374e8i | 0.642830 | + | 0.113348i | |||||
0 | 0 | |||||||||
−2.12076e9 | + | 1.77953e9i | −0.316977 | + | 0.265975i | |||||
6.09939e9 | + | 3.52148e9i | 0.898998 | + | 0.519037i | |||||
0 | 0 | |||||||||
−1.93085e9 | − | 3.34433e9i | −0.276795 | − | 0.479422i | |||||
−8.11190e7 | + | 2.22873e8i | −0.0114691 | + | 0.0315112i | |||||
0 | 0 | |||||||||
8.56641e9 | + | 7.18807e9i | 1.17833 | + | 0.988738i | |||||
−1.02284e9 | − | 2.81023e9i | −0.138783 | − | 0.381304i | 0.850757 | − | 0.525559i | ||
−0.989541 | + | 0.144255i | ||||||||
0 | 0 | |||||||||
3.03109e7 | + | 1.71902e8i | 0.00400231 | + | 0.0226982i | |||||
− | 1.29626e9i | − | 0.168859i | |||||||
0 | 0 | |||||||||
−6.30950e9 | −0.800073 | |||||||||
−2.37270e9 | + | 4.18371e8i | −0.296864 | + | 0.0523451i | |||||
0 | 0 | |||||||||
−7.65258e9 | + | 2.78531e9i | −0.932271 | + | 0.339319i | |||||
9.43299e9 | − | 1.12418e10i | 1.13402 | − | 1.35148i | |||||
0 | 0 | |||||||||
−3.29385e9 | − | 1.19886e9i | −0.385664 | − | 0.140370i | |||||
2.85975e9 | − | 1.65108e9i | 0.330467 | − | 0.190795i | |||||
0 | 0 | |||||||||
3.33707e9 | − | 5.77997e9i | 0.375675 | − | 0.650687i | −0.614753 | − | 0.788720i | ||
0.990428 | + | 0.138032i | ||||||||
1.99399e9 | + | 2.37634e9i | 0.221574 | + | 0.264062i | |||||
0 | 0 | |||||||||
−7.93838e8 | + | 4.50208e9i | −0.0859578 | + | 0.487491i | |||||
−3.83851e9 | − | 6.76833e8i | −0.410319 | − | 0.0723502i | −0.0353210 | − | 0.999376i | ||
−0.374998 | + | 0.927026i | ||||||||
0 | 0 | |||||||||
−9.12437e9 | + | 7.65626e9i | −0.950661 | + | 0.797699i | −0.979409 | − | 0.201887i | ||
0.0287476 | + | 0.999587i | ||||||||
1.61062e10 | + | 9.29891e9i | 1.65681 | + | 0.956563i | |||||
0 | 0 | |||||||||
−1.69879e9 | − | 2.94238e9i | −0.170369 | − | 0.295088i | |||||
2.42078e9 | − | 6.65105e9i | 0.239728 | − | 0.658647i | −0.760232 | − | 0.649652i | ||
0.999960 | − | 0.00899508i | ||||||||
0 | 0 | |||||||||
3.60819e8 | + | 3.02763e8i | 0.0348439 | + | 0.0292375i | |||||
−8.55813e8 | − | 2.35133e9i | −0.0816167 | − | 0.224240i | |||||
0 | 0 | |||||||||
1.00386e9 | + | 5.69315e9i | 0.0933787 | + | 0.529577i | |||||
2.69250e9i | 0.247369i | |||||||||
0 | 0 | |||||||||
−5.03058e9 | −0.450904 | |||||||||
9.90752e9 | − | 1.74696e9i | 0.877192 | − | 0.154673i | |||||
0 | 0 | |||||||||
−2.92159e9 | + | 1.06337e9i | −0.252420 | + | 0.0918734i | |||||
5.41364e9 | − | 6.45173e9i | 0.462068 | − | 0.550671i | |||||
0 | 0 | |||||||||
1.33703e9 | + | 4.86637e8i | 0.111385 | + | 0.0405409i | 0.397112 | − | 0.917770i | ||
−0.285726 | + | 0.958311i | ||||||||
−1.71160e10 | + | 9.88195e9i | −1.40881 | + | 0.813374i | |||||
0 | 0 | |||||||||
−2.46478e9 | + | 4.26912e9i | −0.198058 | + | 0.343046i | |||||
1.03356e9 | + | 1.23175e9i | 0.0820649 | + | 0.0978012i | |||||
0 | 0 | |||||||||
−9.90440e8 | + | 5.61706e9i | −0.0767907 | + | 0.435502i | 0.922037 | + | 0.387101i | ||
−0.998828 | + | 0.0484006i | ||||||||
1.31437e10 | + | 2.31760e9i | 1.00705 | + | 0.177571i | |||||
0 | 0 | |||||||||
−1.93550e9 | + | 1.62407e9i | −0.144836 | + | 0.121532i | |||||
7.86243e9 | + | 4.53938e9i | 0.581486 | + | 0.335721i | |||||
0 | 0 | |||||||||
−7.12446e9 | − | 1.23399e10i | −0.514725 | − | 0.891530i | |||||
1.22957e9 | − | 3.37820e9i | 0.0878047 | − | 0.241242i | |||||
0 | 0 | |||||||||
2.19250e10 | + | 1.83973e10i | 1.52981 | + | 1.28366i | |||||
−1.18946e9 | − | 3.26801e9i | −0.0820412 | − | 0.225406i | 0.891889 | − | 0.452254i | ||
−0.973930 | + | 0.226848i | ||||||||
0 | 0 | |||||||||
1.12421e9 | + | 6.37569e9i | 0.0757782 | + | 0.429759i | 0.998968 | + | 0.0454155i | ||
−0.923190 | + | 0.384344i | ||||||||
1.20706e10i | 0.804370i | |||||||||
0 | 0 | |||||||||
−1.24250e10 | −0.809333 | |||||||||
−1.33418e10 | + | 2.35251e9i | −0.859240 | + | 0.151507i | −0.585873 | − | 0.810403i | ||
−0.273366 | + | 0.961910i | ||||||||
0 | 0 | |||||||||
−3.59134e9 | + | 1.30714e9i | −0.226122 | + | 0.0823018i | |||||
1.00345e10 | − | 1.19587e10i | 0.624735 | − | 0.744530i | |||||
0 | 0 | |||||||||
2.89329e10 | + | 1.05307e10i | 1.76141 | + | 0.641099i | |||||
−1.20904e10 | + | 6.98039e9i | −0.727885 | + | 0.420244i | −0.817648 | − | 0.575719i | ||
0.0897632 | + | 0.995963i | ||||||||
0 | 0 | |||||||||
7.32777e9 | − | 1.26921e10i | 0.431463 | − | 0.747315i | |||||
1.66119e10 | + | 1.97973e10i | 0.967351 | + | 1.15284i | |||||
0 | 0 | |||||||||
−8.81555e8 | + | 4.99955e9i | −0.0502162 | + | 0.284790i | |||||
−9.91174e9 | − | 1.74771e9i | −0.558442 | − | 0.0984685i | |||||
0 | 0 | |||||||||
3.14341e9 | − | 2.63763e9i | 0.173275 | − | 0.145395i | −0.552026 | − | 0.833827i | ||
0.725301 | + | 0.688432i | ||||||||
−1.05424e10 | − | 6.08668e9i | −0.574843 | − | 0.331886i | |||||
0 | 0 | |||||||||
−4.12607e9 | − | 7.14657e9i | −0.220156 | − | 0.381321i | |||||
5.55024e9 | − | 1.52492e10i | 0.292965 | − | 0.804916i | |||||
0 | 0 | |||||||||
−7.37158e9 | − | 6.18549e9i | −0.380825 | − | 0.319550i | 0.432201 | − | 0.901777i | ||
−0.813026 | + | 0.582227i | ||||||||
3.67492e9 | + | 1.00967e10i | 0.187828 | + | 0.516054i | |||||
0 | 0 | |||||||||
6.45610e8 | + | 3.66144e9i | 0.0323012 | + | 0.183189i | |||||
7.70832e8i | 0.0381588i | |||||||||
0 | 0 | |||||||||
−1.08158e9 | −0.0524205 | −0.0262102 | − | 0.999656i | ||||||
−0.0262102 | + | 0.999656i | ||||||||
−2.15139e9 | + | 3.79349e8i | −0.103178 | + | 0.0181930i | |||||
0 | 0 | |||||||||
2.87213e10 | − | 1.04537e10i | 1.34881 | − | 0.490926i | |||||
−9.63162e9 | + | 1.14785e10i | −0.447615 | + | 0.533446i | −0.941918 | − | 0.335843i | ||
0.494303 | + | 0.869290i | ||||||||
0 | 0 | |||||||||
−2.62358e9 | − | 9.54905e8i | −0.119413 | − | 0.0434627i | |||||
−4.89173e10 | + | 2.82424e10i | −2.20350 | + | 1.27219i | |||||
0 | 0 | |||||||||
−4.18621e9 | + | 7.25072e9i | −0.184711 | + | 0.319930i | |||||
−5.18750e9 | − | 6.18222e9i | −0.226548 | − | 0.269989i | 0.640782 | − | 0.767723i | ||
−0.867330 | + | 0.497734i | ||||||||
0 | 0 | |||||||||
−1.62375e9 | + | 9.20874e9i | −0.0694723 | + | 0.393997i | |||||
2.24930e9 | + | 3.96612e8i | 0.0952583 | + | 0.0167966i | |||||
0 | 0 | |||||||||
2.82637e10 | − | 2.37160e10i | 1.17285 | − | 0.984140i | |||||
2.64821e9 | + | 1.52895e9i | 0.108784 | + | 0.0628064i | |||||
0 | 0 | |||||||||
−1.52733e10 | − | 2.64542e10i | −0.614854 | − | 1.06496i | −0.990410 | − | 0.138158i | ||
0.375556 | − | 0.926800i | ||||||||
5.06128e9 | − | 1.39057e10i | 0.201710 | − | 0.554194i | |||||
0 | 0 | |||||||||
−1.94711e10 | − | 1.63382e10i | −0.760591 | − | 0.638212i | |||||
−6.89815e9 | − | 1.89525e10i | −0.266781 | − | 0.732975i | −0.998670 | − | 0.0515517i | ||
0.731889 | − | 0.681424i | ||||||||
0 | 0 | |||||||||
2.58001e9 | + | 1.46319e10i | 0.0978139 | + | 0.554730i | |||||
− | 3.24567e10i | − | 1.21837i | |||||||
0 | 0 | |||||||||
1.84957e9 | 0.0680716 | |||||||||
−1.61392e10 | + | 2.84578e9i | −0.588173 | + | 0.103711i | |||||
0 | 0 | |||||||||
2.42731e10 | − | 8.83468e9i | 0.867424 | − | 0.315717i | 0.130301 | − | 0.991475i | ||
0.737124 | + | 0.675758i | ||||||||
−1.27226e10 | + | 1.51622e10i | −0.450237 | + | 0.536571i | |||||
0 | 0 | |||||||||
−2.48418e10 | − | 9.04166e9i | −0.862171 | − | 0.313805i | |||||
1.17885e9 | − | 6.80609e8i | 0.0405189 | − | 0.0233936i | |||||
0 | 0 | |||||||||
8.89398e9 | − | 1.54048e10i | 0.299850 | − | 0.519355i | |||||
−1.30704e10 | − | 1.55767e10i | −0.436432 | − | 0.520119i | |||||
0 | 0 | |||||||||
−1.61323e9 | + | 9.14908e9i | −0.0528434 | + | 0.299690i | |||||
1.14285e10 | + | 2.01516e9i | 0.370796 | + | 0.0653813i | 0.355941 | − | 0.934508i | ||
0.0148546 | + | 0.999890i | ||||||||
0 | 0 | |||||||||
−6.33667e9 | + | 5.31710e9i | −0.201713 | + | 0.169257i | −0.738049 | − | 0.674748i | ||
0.536336 | + | 0.844005i | ||||||||
3.55460e10 | + | 2.05225e10i | 1.12083 | + | 0.647113i | |||||
0 | 0 | |||||||||
3.58186e9 | + | 6.20396e9i | 0.110827 | + | 0.191958i | |||||
−6.67771e9 | + | 1.83469e10i | −0.204678 | + | 0.562349i | |||||
0 | 0 | |||||||||
−1.97265e10 | − | 1.65525e10i | −0.593388 | − | 0.497912i | |||||
−1.47474e10 | − | 4.05182e10i | −0.439482 | − | 1.20747i | |||||
0 | 0 | |||||||||
−3.97416e9 | − | 2.25386e10i | −0.116244 | − | 0.659254i | |||||
− | 4.80677e10i | − | 1.39298i | −0.717567 | − | 0.696490i | ||||
0.717567 | − | 0.696490i | ||||||||
0 | 0 | |||||||||
9.18386e9 | 0.261260 | 0.130630 | − | 0.991431i | ||||||
0.130630 | + | 0.991431i | ||||||||
3.51085e10 | − | 6.19057e9i | 0.989585 | − | 0.174491i | |||||
0 | 0 | |||||||||
−1.86968e10 | + | 6.80507e9i | −0.517393 | + | 0.188316i | |||||
−5.19692e9 | + | 6.19345e9i | −0.142502 | + | 0.169827i | |||||
0 | 0 | |||||||||
−5.28907e10 | − | 1.92506e10i | −1.42404 | − | 0.518307i | −0.488821 | − | 0.872384i | ||
−0.935216 | + | 0.354077i | ||||||||
1.06737e9 | − | 6.16249e8i | 0.0284778 | − | 0.0164417i | |||||
0 | 0 | |||||||||
−8.79205e9 | + | 1.52283e10i | −0.230357 | + | 0.398990i | |||||
−2.37382e9 | − | 2.82901e9i | −0.0616357 | − | 0.0734546i | 0.734346 | − | 0.678776i | ||
−0.795981 | + | 0.605321i | ||||||||
0 | 0 | |||||||||
−2.43979e9 | + | 1.38367e10i | −0.0622174 | + | 0.352853i | |||||
−5.48817e9 | − | 9.67713e8i | −0.138704 | − | 0.0244572i | |||||
0 | 0 | |||||||||
−1.49479e10 | + | 1.25428e10i | −0.371081 | + | 0.311374i | |||||
3.11307e10 | + | 1.79733e10i | 0.765956 | + | 0.442225i | 0.831430 | − | 0.555629i | ||
−0.0654738 | + | 0.997854i | ||||||||
0 | 0 | |||||||||
1.96536e10 | + | 3.40411e10i | 0.475047 | + | 0.822806i | |||||
2.36579e9 | − | 6.49997e9i | 0.0566791 | − | 0.155725i | |||||
0 | 0 | |||||||||
−6.94231e10 | − | 5.82529e10i | −1.63411 | − | 1.37118i | |||||
−1.56273e9 | − | 4.29357e9i | −0.0364619 | − | 0.100178i | |||||
0 | 0 | |||||||||
−8.23273e9 | − | 4.66901e10i | −0.188747 | − | 1.07044i | −0.921046 | − | 0.389453i | ||
0.732300 | − | 0.680982i | ||||||||
− | 1.02729e11i | − | 2.33471i | |||||||
0 | 0 | |||||||||
−7.58684e9 | −0.169445 | |||||||||
−5.56762e10 | + | 9.81722e9i | −1.23272 | + | 0.217363i | −0.751795 | − | 0.659397i | ||
−0.480930 | + | 0.876759i | ||||||||
0 | 0 | |||||||||
3.32703e10 | − | 1.21094e10i | 0.723990 | − | 0.263511i | 0.0463714 | − | 0.998924i | ||
0.677619 | + | 0.735413i | ||||||||
−2.50349e9 | + | 2.98355e9i | −0.0540101 | + | 0.0643667i | |||||
0 | 0 | |||||||||
4.32321e10 | + | 1.57352e10i | 0.916775 | + | 0.333679i | |||||
3.69556e10 | − | 2.13363e10i | 0.776984 | − | 0.448592i | −0.0583762 | − | 0.998295i | ||
0.835360 | + | 0.549703i | ||||||||
0 | 0 | |||||||||
6.26958e9 | − | 1.08592e10i | 0.129583 | − | 0.224444i | |||||
1.52140e10 | + | 1.81313e10i | 0.311782 | + | 0.371568i | |||||
0 | 0 | |||||||||
−1.04346e8 | + | 5.91776e8i | −0.00210236 | + | 0.0119231i | |||||
−4.47601e10 | − | 7.89241e9i | −0.894224 | − | 0.157676i | |||||
0 | 0 | |||||||||
−1.29318e10 | + | 1.08511e10i | −0.254030 | + | 0.213157i | |||||
1.70635e10 | + | 9.85161e9i | 0.332384 | + | 0.191902i | |||||
0 | 0 | |||||||||
6.91340e10 | + | 1.19744e11i | 1.32428 | + | 2.29372i | |||||
−1.59069e10 | + | 4.37038e10i | −0.302164 | + | 0.830189i | 0.691959 | + | 0.721936i | ||
−0.994123 | + | 0.108252i | ||||||||
0 | 0 | |||||||||
−2.05452e10 | − | 1.72394e10i | −0.383822 | − | 0.322065i | |||||
4.58704e10 | + | 1.26028e11i | 0.849854 | + | 2.33495i | |||||
0 | 0 | |||||||||
−5.34240e9 | − | 3.02983e10i | −0.0973543 | − | 0.552124i | |||||
− | 7.53536e9i | − | 0.136187i | |||||||
0 | 0 | |||||||||
8.34928e10 | 1.48434 | 0.742170 | − | 0.670212i | ||||||
0.742170 | + | 0.670212i | ||||||||
1.11950e10 | − | 1.97399e9i | 0.197400 | − | 0.0348069i | |||||
0 | 0 | |||||||||
1.36633e10 | − | 4.97304e9i | 0.237013 | − | 0.0862657i | |||||
−1.56381e10 | + | 1.86368e10i | −0.269066 | + | 0.320660i | −0.883611 | − | 0.468221i | ||
0.614545 | + | 0.788882i | ||||||||
0 | 0 | |||||||||
2.81128e9 | + | 1.02322e9i | 0.0475900 | + | 0.0173213i | |||||
−1.31668e10 | + | 7.60187e9i | −0.221092 | + | 0.127648i | |||||
0 | 0 | |||||||||
−3.75353e10 | + | 6.50130e10i | −0.620173 | + | 1.07417i | |||||
1.91575e10 | + | 2.28310e10i | 0.313987 | + | 0.374196i | |||||
0 | 0 | |||||||||
−9.77907e9 | + | 5.54599e10i | −0.157723 | + | 0.894493i | 0.798531 | + | 0.601954i | ||
−0.956254 | + | 0.292538i | ||||||||
−3.30181e10 | − | 5.82198e9i | −0.528289 | − | 0.0931516i | |||||
0 | 0 | |||||||||
3.64896e10 | − | 3.06184e10i | 0.574585 | − | 0.482134i | |||||
6.61060e10 | + | 3.81663e10i | 1.03269 | + | 0.596223i | 0.917754 | − | 0.397150i | ||
0.114935 | + | 0.993373i | ||||||||
0 | 0 | |||||||||
1.46059e10 | + | 2.52981e10i | 0.224575 | + | 0.388976i | |||||
−1.10349e10 | + | 3.03183e10i | −0.168333 | + | 0.462490i | |||||
0 | 0 | |||||||||
−1.03340e10 | − | 8.67125e9i | −0.155172 | − | 0.130205i | |||||
2.18554e10 | + | 6.00473e10i | 0.325603 | + | 0.894586i | 0.989210 | + | 0.146505i | ||
−0.663607 | + | 0.748081i | ||||||||
0 | 0 | |||||||||
1.36291e10 | + | 7.72946e10i | 0.199887 | + | 1.13361i | |||||
− | 8.98162e10i | − | 1.30700i | |||||||
0 | 0 | |||||||||
8.11333e10 | 1.16238 | |||||||||
2.34316e10 | − | 4.13162e9i | 0.333098 | − | 0.0587342i | |||||
0 | 0 | |||||||||
4.41698e10 | − | 1.60765e10i | 0.618249 | − | 0.225024i | |||||
−4.13650e10 | + | 4.92969e10i | −0.574532 | + | 0.684701i | |||||
0 | 0 | |||||||||
1.89538e9 | + | 6.89862e8i | 0.0259229 | + | 0.00943516i | |||||
−6.91938e10 | + | 3.99491e10i | −0.939110 | + | 0.542195i | −0.889681 | − | 0.456582i | ||
−0.0494285 | + | 0.998778i | ||||||||
0 | 0 | |||||||||
−2.22994e10 | + | 3.86237e10i | −0.298048 | + | 0.516235i | −0.975689 | − | 0.219158i | ||
0.677641 | + | 0.735393i | ||||||||
1.49789e10 | + | 1.78512e10i | 0.198681 | + | 0.236779i | |||||
0 | 0 | |||||||||
−1.52753e10 | + | 8.66304e10i | −0.199547 | + | 1.13169i | |||||
5.67884e10 | + | 1.00133e10i | 0.736236 | + | 0.129818i | |||||
0 | 0 | |||||||||
3.84804e10 | − | 3.22889e10i | 0.491380 | − | 0.412317i | |||||
3.94952e10 | + | 2.28026e10i | 0.500542 | + | 0.288988i | |||||
0 | 0 | |||||||||
8.51799e9 | + | 1.47536e10i | 0.106339 | + | 0.184184i | |||||
−2.20013e10 | + | 6.04482e10i | −0.272609 | + | 0.748987i | |||||
0 | 0 | |||||||||
2.97284e10 | + | 2.49451e10i | 0.362874 | + | 0.304488i | |||||
1.89321e9 | + | 5.20154e9i | 0.0229371 | + | 0.0630192i | |||||
0 | 0 | |||||||||
−3.19998e9 | − | 1.81480e10i | −0.0381961 | − | 0.216621i | |||||
− | 2.88759e10i | − | 0.342121i | |||||||
0 | 0 | |||||||||
−1.16720e11 | −1.36256 | −0.681282 | − | 0.732021i | ||||||
−0.681282 | + | 0.732021i | ||||||||
1.69515e11 | − | 2.98901e10i | 1.96432 | − | 0.346362i | |||||
0 | 0 | |||||||||
−7.41593e10 | + | 2.69918e10i | −0.846779 | + | 0.308202i | |||||
1.15107e10 | − | 1.37179e10i | 0.130471 | − | 0.155490i | |||||
0 | 0 | |||||||||
−3.09611e10 | − | 1.12689e10i | −0.345834 | − | 0.125873i | 0.163263 | − | 0.986583i | ||
−0.509097 | + | 0.860709i | ||||||||
3.40033e10 | − | 1.96318e10i | 0.377050 | − | 0.217690i | |||||
0 | 0 | |||||||||
−3.36834e10 | + | 5.83413e10i | −0.368099 | + | 0.637566i | |||||
1.66271e9 | + | 1.98154e9i | 0.0180389 | + | 0.0214979i | |||||
0 | 0 | |||||||||
4.14087e9 | − | 2.34840e10i | 0.0442783 | − | 0.251115i | |||||
2.33646e10 | + | 4.11982e9i | 0.248039 | + | 0.0437360i | |||||
0 | 0 | |||||||||
−6.99767e10 | + | 5.87175e10i | −0.732242 | + | 0.614424i | |||||
−1.80115e10 | − | 1.03990e10i | −0.187124 | − | 0.108036i | 0.403511 | − | 0.914975i | ||
−0.590636 | + | 0.806938i | ||||||||
0 | 0 | |||||||||
−3.71907e10 | − | 6.44161e10i | −0.380879 | − | 0.659701i | |||||
7.89594e9 | − | 2.16939e10i | 0.0802882 | − | 0.220590i | |||||
0 | 0 | |||||||||
−1.73342e11 | − | 1.45451e11i | −1.73764 | − | 1.45805i | |||||
−5.32759e10 | − | 1.46374e11i | −0.530270 | − | 1.45690i | −0.858750 | − | 0.512394i | ||
0.328480 | − | 0.944511i | ||||||||
0 | 0 | |||||||||
1.08106e9 | + | 6.13098e9i | 0.0106085 | + | 0.0601639i | |||||
− | 1.55201e11i | − | 1.51227i | |||||||
0 | 0 | |||||||||
−1.31567e10 | −0.126402 | |||||||||
3.54658e10 | − | 6.25358e9i | 0.338346 | − | 0.0596595i | −0.00189393 | − | 0.999998i | ||
0.340240 | + | 0.940339i | ||||||||
0 | 0 | |||||||||
8.81956e10 | − | 3.21006e10i | 0.829664 | − | 0.301973i | 0.107943 | − | 0.994157i | ||
0.721721 | + | 0.692184i | ||||||||
−1.82123e10 | + | 2.17045e10i | −0.170130 | + | 0.202753i | |||||
0 | 0 | |||||||||
1.45042e11 | + | 5.27909e10i | 1.33612 | + | 0.486309i | |||||
−5.07726e10 | + | 2.93136e10i | −0.464470 | + | 0.268162i | |||||
0 | 0 | |||||||||
6.26865e10 | − | 1.08576e11i | 0.565549 | − | 0.979560i | −0.431449 | − | 0.902137i | ||
0.996998 | − | 0.0774229i | ||||||||
−5.44000e10 | − | 6.48313e10i | −0.487402 | − | 0.580863i | |||||
0 | 0 | |||||||||
−4.21503e8 | + | 2.39046e9i | −0.00372467 | + | 0.0211237i | |||||
−1.36608e11 | − | 2.40877e10i | −1.19887 | − | 0.211393i | |||||
0 | 0 | |||||||||
6.93796e10 | − | 5.82164e10i | 0.600562 | − | 0.503931i | |||||
−3.00059e10 | − | 1.73239e10i | −0.257961 | − | 0.148934i | |||||
0 | 0 | |||||||||
−3.27702e10 | − | 5.67596e10i | −0.277900 | − | 0.481336i | |||||
5.98853e9 | − | 1.64533e10i | 0.0504392 | − | 0.138580i | −0.911915 | − | 0.410379i | ||
0.962354 | + | 0.271799i | ||||||||
0 | 0 | |||||||||
3.81938e10 | + | 3.20484e10i | 0.317345 | + | 0.266284i | |||||
1.30838e9 | + | 3.59473e9i | 0.0107975 | + | 0.0296660i | |||||
0 | 0 | |||||||||
−2.35313e10 | − | 1.33452e11i | −0.191584 | − | 1.08653i | |||||
8.13815e10i | 0.658123i | 0.944309 | + | 0.329061i | ||||||
−0.944309 | + | 0.329061i | ||||||||
0 | 0 | |||||||||
−1.77333e10 | −0.141489 | |||||||||
−6.35924e10 | + | 1.12131e10i | −0.503988 | + | 0.0888666i | |||||
0 | 0 | |||||||||
−4.96168e10 | + | 1.80590e10i | −0.387993 | + | 0.141218i | |||||
1.44379e11 | − | 1.72064e11i | 1.12149 | − | 1.33654i | 0.186260 | − | 0.982500i | ||
0.935230 | − | 0.354040i | ||||||||
0 | 0 | |||||||||
−1.43492e11 | − | 5.22268e10i | −1.09984 | − | 0.400309i | −0.272583 | − | 0.962132i | ||
−0.827257 | + | 0.561823i | ||||||||
−1.54563e11 | + | 8.92368e10i | −1.17684 | + | 0.679451i | |||||
0 | 0 | |||||||||
7.50950e10 | − | 1.30068e11i | 0.564239 | − | 0.977291i | |||||
1.77987e10 | + | 2.12116e10i | 0.132851 | + | 0.158326i | |||||
0 | 0 | |||||||||
−2.34613e10 | + | 1.33056e11i | −0.172821 | + | 0.980119i | 0.767807 | + | 0.640681i | ||
−0.940628 | + | 0.339438i | ||||||||
−6.71988e10 | − | 1.18490e10i | −0.491753 | − | 0.0867094i | |||||
0 | 0 | |||||||||
5.54374e10 | − | 4.65175e10i | 0.400391 | − | 0.335968i | |||||
6.66185e10 | + | 3.84622e10i | 0.478002 | + | 0.275975i | |||||
0 | 0 | |||||||||
−8.05944e10 | − | 1.39594e11i | −0.570772 | − | 0.988606i | −0.996487 | − | 0.0837489i | ||
0.425715 | − | 0.904857i | ||||||||
5.00264e10 | − | 1.37446e11i | 0.351986 | − | 0.967074i | |||||
0 | 0 | |||||||||
−7.36274e9 | − | 6.17807e9i | −0.0511348 | − | 0.0429072i | |||||
−6.78498e10 | − | 1.86416e11i | −0.468175 | − | 1.28630i | −0.919201 | − | 0.393789i | ||
0.451026 | − | 0.892511i | ||||||||
0 | 0 | |||||||||
−5.42660e9 | − | 3.07758e10i | −0.0369628 | − | 0.209626i | 0.960733 | − | 0.277475i | ||
−0.997696 | + | 0.0678486i | ||||||||
4.67865e10i | 0.316631i | |||||||||
0 | 0 | |||||||||
−8.54207e10 | −0.570692 | |||||||||
1.07903e11 | − | 1.90262e10i | 0.716276 | − | 0.126299i | |||||
0 | 0 | |||||||||
−1.00072e11 | + | 3.64232e10i | −0.655832 | + | 0.238703i | |||||
−1.67791e11 | + | 1.99966e11i | −1.09263 | + | 1.30214i | |||||
0 | 0 | |||||||||
1.78857e11 | + | 6.50987e10i | 1.14992 | + | 0.418537i | |||||
−9.01456e10 | + | 5.20456e10i | −0.575893 | + | 0.332492i | |||||
0 | 0 | |||||||||
−6.49274e10 | + | 1.12458e11i | −0.409553 | + | 0.709367i | −0.994840 | − | 0.101460i | ||
0.585286 | + | 0.810827i | ||||||||
6.76654e9 | + | 8.06405e9i | 0.0424129 | + | 0.0505458i | |||||
0 | 0 | |||||||||
2.69356e10 | − | 1.52759e11i | 0.166713 | − | 0.945476i | |||||
1.19569e10 | + | 2.10833e9i | 0.0735401 | + | 0.0129671i | |||||
0 | 0 | |||||||||
3.62004e10 | − | 3.03757e10i | 0.219865 | − | 0.184488i | |||||
8.93960e9 | + | 5.16128e9i | 0.0539555 | + | 0.0311512i | |||||
0 | 0 | |||||||||
9.12307e9 | + | 1.58016e10i | 0.0543777 | + | 0.0941850i | |||||
−4.87804e10 | + | 1.34023e11i | −0.288944 | + | 0.793867i | 0.707271 | + | 0.706943i | ||
−0.996215 | + | 0.0869244i | ||||||||
0 | 0 | |||||||||
1.87640e11 | + | 1.57449e11i | 1.09770 | + | 0.921076i | 0.997268 | − | 0.0738681i | ||
0.100428 | + | 0.994944i | ||||||||
2.02354e10 | + | 5.55963e10i | 0.117644 | + | 0.323223i | |||||
0 | 0 | |||||||||
1.02466e10 | + | 5.81112e10i | 0.0588367 | + | 0.333679i | |||||
3.75157e9i | 0.0214090i | 0.999943 | + | 0.0107045i | ||||||
−0.999943 | + | 0.0107045i | ||||||||
0 | 0 | |||||||||
7.59705e9 | 0.0428219 | |||||||||
−1.08573e11 | + | 1.91443e10i | −0.608230 | + | 0.107247i | |||||
0 | 0 | |||||||||
9.67516e10 | − | 3.52147e10i | 0.535387 | − | 0.194865i | |||||
1.12531e11 | − | 1.34110e11i | 0.618900 | − | 0.737577i | −0.361981 | − | 0.932186i | ||
0.980881 | + | 0.194609i | ||||||||
0 | 0 | |||||||||
−1.97085e10 | − | 7.17329e9i | −0.107075 | − | 0.0389721i | |||||
−2.81480e11 | + | 1.62513e11i | −1.51996 | + | 0.877549i | |||||
0 | 0 | |||||||||
9.22878e10 | − | 1.59847e11i | 0.492312 | − | 0.852710i | |||||
1.07843e11 | + | 1.28523e11i | 0.571810 | + | 0.681457i | 0.972001 | − | 0.234975i | ||
−0.400191 | + | 0.916432i | ||||||||
0 | 0 | |||||||||
−3.24693e10 | + | 1.84143e11i | −0.170086 | + | 0.964603i | 0.773579 | + | 0.633700i | ||
−0.943665 | + | 0.330903i | ||||||||
3.07084e10 | + | 5.41472e9i | 0.159891 | + | 0.0281932i | |||||
0 | 0 | |||||||||
4.69091e10 | − | 3.93614e10i | 0.241315 | − | 0.202487i | |||||
−1.32786e10 | − | 7.66639e9i | −0.0678992 | − | 0.0392016i | |||||
0 | 0 | |||||||||
4.49170e9 | + | 7.77985e9i | 0.0226938 | + | 0.0393068i | |||||
−1.72551e10 | + | 4.74080e10i | −0.0866587 | + | 0.238093i | |||||
0 | 0 | |||||||||
2.69945e10 | + | 2.26511e10i | 0.133960 | + | 0.112406i | |||||
−4.91547e10 | − | 1.35052e11i | −0.242480 | − | 0.666207i | |||||
0 | 0 | |||||||||
−8.32962e8 | − | 4.72396e9i | −0.00406037 | − | 0.0230275i | 0.982710 | − | 0.185150i | ||
−0.986771 | + | 0.162123i | ||||||||
1.25000e11i | 0.605718i | |||||||||
0 | 0 | |||||||||
1.36592e11 | 0.654093 | |||||||||
−1.91119e11 | + | 3.36994e10i | −0.909807 | + | 0.160423i | −0.608916 | − | 0.793235i | ||
−0.300891 | + | 0.953659i | ||||||||
0 | 0 | |||||||||
−5.52190e10 | + | 2.00981e10i | −0.259782 | + | 0.0945531i | |||||
5.03195e9 | − | 5.99684e9i | 0.0235343 | − | 0.0280470i | |||||
0 | 0 | |||||||||
1.86967e11 | + | 6.80503e10i | 0.864224 | + | 0.314552i | |||||
2.62322e11 | − | 1.51452e11i | 1.20546 | − | 0.695972i | 0.243695 | − | 0.969852i | ||
0.961764 | + | 0.273880i | ||||||||
0 | 0 | |||||||||
−1.76691e10 | + | 3.06037e10i | −0.0802512 | + | 0.138999i | |||||
−2.00725e11 | − | 2.39215e11i | −0.906369 | − | 1.08017i | |||||
0 | 0 | |||||||||
6.52610e10 | − | 3.70113e11i | 0.291273 | − | 1.65189i | |||||
1.45967e11 | + | 2.57379e10i | 0.647704 | + | 0.114208i | |||||
0 | 0 | |||||||||
−2.26657e11 | + | 1.90187e11i | −0.994160 | + | 0.834199i | −0.986165 | − | 0.165769i | ||
−0.00799511 | + | 0.999968i | ||||||||
2.53674e11 | + | 1.46459e11i | 1.10625 | + | 0.638691i | |||||
0 | 0 | |||||||||
−3.81083e10 | − | 6.60056e10i | −0.164279 | − | 0.284540i | |||||
2.81193e10 | − | 7.72572e10i | 0.120522 | − | 0.331131i | |||||
0 | 0 | |||||||||
1.91253e11 | + | 1.60481e11i | 0.810360 | + | 0.679973i | |||||
4.85265e10 | + | 1.33326e11i | 0.204436 | + | 0.561684i | |||||
0 | 0 | |||||||||
2.14515e10 | + | 1.21657e11i | 0.0893439 | + | 0.506695i | |||||
2.45235e10i | 0.101557i | 0.998710 | + | 0.0507785i | ||||||
−0.998710 | + | 0.0507785i | ||||||||
0 | 0 | |||||||||
−9.00003e10 | −0.368487 | |||||||||
−1.07249e11 | + | 1.89110e10i | −0.436621 | + | 0.0769880i | |||||
0 | 0 | |||||||||
−2.78997e11 | + | 1.01547e11i | −1.12300 | + | 0.408739i | |||||
1.46428e11 | − | 1.74506e11i | 0.586066 | − | 0.698446i | |||||
0 | 0 | |||||||||
−3.53052e11 | − | 1.28500e11i | −1.39718 | − | 0.508533i | −0.469843 | − | 0.882750i | ||
−0.927341 | + | 0.374217i | ||||||||
−7.25360e10 | + | 4.18787e10i | −0.285444 | + | 0.164801i | |||||
0 | 0 | |||||||||
−2.41840e10 | + | 4.18880e10i | −0.0941042 | + | 0.162993i | |||||
1.11301e11 | + | 1.32643e11i | 0.430666 | + | 0.513248i | |||||
0 | 0 | |||||||||
4.42813e9 | − | 2.51132e10i | 0.0169432 | − | 0.0960899i | |||||
3.10325e11 | + | 5.47186e10i | 1.18077 | + | 0.208201i | |||||
0 | 0 | |||||||||
−2.34377e11 | + | 1.96666e11i | −0.881897 | + | 0.739999i | |||||
1.30207e11 | + | 7.51752e10i | 0.487214 | + | 0.281293i | 0.723418 | − | 0.690410i | ||
−0.236204 | + | 0.971703i | ||||||||
0 | 0 | |||||||||
−9.27725e10 | − | 1.60687e11i | −0.343303 | − | 0.594619i | |||||
1.09851e11 | − | 3.01814e11i | 0.404256 | − | 1.11069i | |||||
0 | 0 | |||||||||
2.02611e11 | + | 1.70011e11i | 0.737411 | + | 0.618761i | |||||
6.41533e9 | + | 1.76260e10i | 0.0232203 | + | 0.0637972i | |||||
0 | 0 | |||||||||
7.72535e10 | + | 4.38126e11i | 0.276554 | + | 1.56842i | 0.733981 | + | 0.679170i | ||
−0.457427 | + | 0.889247i | ||||||||
− | 1.57293e10i | − | 0.0559995i | |||||||
0 | 0 | |||||||||
−2.20572e11 | −0.776710 | |||||||||
−2.84298e11 | + | 5.01293e10i | −0.995643 | + | 0.175559i | |||||
0 | 0 | |||||||||
2.01572e11 | − | 7.33664e10i | 0.698257 | − | 0.254145i | 0.0315904 | − | 0.999501i | ||
0.666666 | + | 0.745356i | ||||||||
5.78051e10 | − | 6.88894e10i | 0.199151 | − | 0.237338i | |||||
0 | 0 | |||||||||
−2.22684e11 | − | 8.10503e10i | −0.758888 | − | 0.276212i | |||||
6.06061e10 | − | 3.49909e10i | 0.205422 | − | 0.118600i | |||||
0 | 0 | |||||||||
5.48728e10 | − | 9.50425e10i | 0.183984 | − | 0.318669i | −0.759250 | − | 0.650799i | ||
0.943234 | + | 0.332130i | ||||||||
−5.42867e10 | − | 6.46964e10i | −0.181037 | − | 0.215751i | |||||
0 | 0 | |||||||||
6.17565e10 | − | 3.50239e11i | 0.203736 | − | 1.15544i | |||||
3.62815e11 | + | 6.39740e10i | 1.19050 | + | 0.209917i | 0.733588 | − | 0.679594i | ||
0.456912 | + | 0.889512i | ||||||||
0 | 0 | |||||||||
4.45206e10 | − | 3.73572e10i | 0.144523 | − | 0.121269i | |||||
−1.82637e11 | − | 1.05446e11i | −0.589704 | − | 0.340466i | |||||
0 | 0 | |||||||||
5.49825e10 | + | 9.52325e10i | 0.175638 | + | 0.304214i | |||||
1.03507e11 | − | 2.84382e11i | 0.328883 | − | 0.903597i | |||||
0 | 0 | |||||||||
4.65384e11 | + | 3.90504e11i | 1.46303 | + | 1.22762i | 0.922329 | + | 0.386406i | ||
0.540696 | + | 0.841218i | ||||||||
1.32934e11 | + | 3.65232e11i | 0.415684 | + | 1.14208i | |||||
0 | 0 | |||||||||
2.93347e9 | + | 1.66366e10i | 0.00907605 | + | 0.0514728i | |||||
1.35174e11i | 0.416013i | |||||||||
0 | 0 | |||||||||
−7.74160e10 | −0.235747 | −0.117874 | − | 0.993029i | ||||||
−0.117874 | + | 0.993029i | ||||||||
−2.33432e10 | + | 4.11604e9i | −0.0707106 | + | 0.0124682i | |||||
0 | 0 | |||||||||
6.36040e9 | − | 2.31500e9i | 0.0190647 | − | 0.00693899i | |||||
−2.33613e11 | + | 2.78409e11i | −0.696560 | + | 0.830128i | −0.992132 | − | 0.125193i | ||
0.295573 | + | 0.955320i | ||||||||
0 | 0 | |||||||||
−1.31226e11 | − | 4.77622e10i | −0.387187 | − | 0.140925i | |||||
2.70899e11 | − | 1.56404e11i | 0.795122 | − | 0.459064i | |||||
0 | 0 | |||||||||
−1.64193e11 | + | 2.84390e11i | −0.476913 | + | 0.826037i | |||||
7.99166e9 | + | 9.52409e9i | 0.0230917 | + | 0.0275196i | |||||
0 | 0 | |||||||||
1.08599e11 | − | 6.15897e11i | 0.310543 | − | 1.76117i | −0.285651 | − | 0.958334i | ||
0.596193 | − | 0.802841i | ||||||||
−6.02576e10 | − | 1.06250e10i | −0.171415 | − | 0.0302251i | |||||
0 | 0 | |||||||||
−4.42838e11 | + | 3.71585e11i | −1.24674 | + | 1.04614i | |||||
−1.31183e11 | − | 7.57386e10i | −0.367418 | − | 0.212129i | 0.304912 | − | 0.952381i | ||
−0.672330 | + | 0.740252i | ||||||||
0 | 0 | |||||||||
1.80771e11 | + | 3.13104e11i | 0.501096 | + | 0.867925i | |||||
8.87223e9 | − | 2.43762e10i | 0.0244673 | − | 0.0672233i | |||||
0 | 0 | |||||||||
−1.35487e11 | − | 1.13687e11i | −0.369810 | − | 0.310307i | |||||
7.38307e10 | + | 2.02848e11i | 0.200488 | + | 0.550835i | |||||
0 | 0 | |||||||||
2.88840e10 | + | 1.63810e11i | 0.0776343 | + | 0.440286i | |||||
2.04928e11i | 0.547991i | |||||||||
0 | 0 | |||||||||
2.38769e11 | 0.631996 | |||||||||
−1.68704e11 | + | 2.97471e10i | −0.444270 | + | 0.0783368i | |||||
0 | 0 | |||||||||
2.31521e11 | − | 8.42667e10i | 0.603520 | − | 0.219663i | −0.0221457 | − | 0.999755i | ||
0.625665 | + | 0.780092i | ||||||||
2.42717e11 | − | 2.89259e11i | 0.629500 | − | 0.750209i | |||||
0 | 0 | |||||||||
6.29738e10 | + | 2.29206e10i | 0.161678 | + | 0.0588461i | |||||
4.20444e10 | − | 2.42744e10i | 0.107400 | − | 0.0620071i | |||||
0 | 0 | |||||||||
1.17600e11 | − | 2.03690e11i | 0.297382 | − | 0.515081i | |||||
−4.30312e11 | − | 5.12826e11i | −1.08268 | − | 1.29029i | |||||
0 | 0 | |||||||||
2.62989e10 | − | 1.49148e11i | 0.0655066 | − | 0.371507i | |||||
−5.26169e10 | − | 9.27778e9i | −0.130404 | − | 0.0229938i | 0.108065 | − | 0.994144i | ||
−0.238469 | + | 0.971150i | ||||||||
0 | 0 | |||||||||
2.28705e11 | − | 1.91906e11i | 0.561163 | − | 0.470871i | |||||
−4.28510e11 | − | 2.47400e11i | −1.04617 | − | 0.604004i | |||||
0 | 0 | |||||||||
−2.21006e11 | − | 3.82793e11i | −0.534202 | − | 0.925265i | |||||
−1.49819e11 | + | 4.11624e11i | −0.360333 | + | 0.990008i | |||||
0 | 0 | |||||||||
−4.07913e10 | − | 3.42280e10i | −0.0971368 | − | 0.0815075i | |||||
1.11366e11 | + | 3.05977e11i | 0.263885 | + | 0.725017i | |||||
0 | 0 | |||||||||
1.74624e10 | + | 9.90344e10i | 0.0409694 | + | 0.232349i | |||||
1.30189e11i | 0.303935i | 0.988385 | + | 0.151968i | ||||||
−0.988385 | + | 0.151968i | ||||||||
0 | 0 | |||||||||
1.10741e11 | 0.255990 | 0.127995 | − | 0.991775i | ||||||
0.127995 | + | 0.991775i | ||||||||
1.86415e10 | − | 3.28700e9i | 0.0428802 | − | 0.00756093i | |||||
0 | 0 | |||||||||
−3.37496e11 | + | 1.22839e11i | −0.768726 | + | 0.279793i | |||||
−5.95653e10 | + | 7.09871e10i | −0.135009 | + | 0.160897i | |||||
0 | 0 | |||||||||
−2.34551e11 | − | 8.53697e10i | −0.526441 | − | 0.191609i | |||||
4.90255e11 | − | 2.83049e11i | 1.09499 | − | 0.632190i | |||||
0 | 0 | |||||||||
−1.01283e11 | + | 1.75428e11i | −0.224018 | + | 0.388010i | |||||
−1.21666e11 | − | 1.44996e11i | −0.267792 | − | 0.319142i | 0.615344 | − | 0.788258i | ||
−0.883136 | + | 0.469116i | ||||||||
0 | 0 | |||||||||
4.72310e10 | − | 2.67860e11i | 0.102950 | − | 0.583860i | −0.889069 | − | 0.457773i | ||
0.992019 | − | 0.126087i | ||||||||
8.06638e10 | + | 1.42232e10i | 0.174972 | + | 0.0308524i | |||||
0 | 0 | |||||||||
2.28525e10 | − | 1.91755e10i | 0.0490923 | − | 0.0411933i | |||||
4.83513e11 | + | 2.79156e11i | 1.03368 | + | 0.596795i | 0.918037 | − | 0.396496i | ||
0.115643 | + | 0.993291i | ||||||||
0 | 0 | |||||||||
3.05847e11 | + | 5.29743e11i | 0.647569 | + | 1.12162i | 0.983702 | + | 0.179808i | ||
−0.336132 | + | 0.941815i | ||||||||
1.33331e11 | − | 3.66323e11i | 0.280942 | − | 0.771883i | |||||
0 | 0 | |||||||||
−1.36528e11 | − | 1.14561e11i | −0.284924 | − | 0.239079i | |||||
−6.27291e10 | − | 1.72347e11i | −0.130283 | − | 0.357951i | |||||
0 | 0 | |||||||||
−7.88478e9 | − | 4.47168e10i | −0.0162197 | − | 0.0919867i | |||||
9.50790e10i | 0.194652i | |||||||||
0 | 0 | |||||||||
2.54326e11 | 0.515722 | |||||||||
9.49572e10 | − | 1.67435e10i | 0.191637 | − | 0.0337908i | −0.0770056 | − | 0.997031i | ||
0.268643 | + | 0.963240i | ||||||||
0 | 0 | |||||||||
−4.67377e11 | + | 1.70111e11i | −0.934294 | + | 0.340055i | |||||
−1.16527e11 | + | 1.38872e11i | −0.231835 | + | 0.276290i | |||||
0 | 0 | |||||||||
3.94734e11 | + | 1.43671e11i | 0.777920 | + | 0.283140i | |||||
−1.06466e11 | + | 6.14681e10i | −0.208826 | + | 0.120565i | |||||
0 | 0 | |||||||||
1.07966e11 | − | 1.87003e11i | 0.209776 | − | 0.363342i | |||||
4.81381e11 | + | 5.73688e11i | 0.930906 | + | 1.10941i | |||||
0 | 0 | |||||||||
−7.43016e10 | + | 4.21385e11i | −0.142338 | + | 0.807242i | |||||
−3.07814e11 | − | 5.42759e10i | −0.586908 | − | 0.103488i | |||||
0 | 0 | |||||||||
−3.15446e10 | + | 2.64690e10i | −0.0595839 | + | 0.0499968i | −0.672093 | − | 0.740467i | ||
0.612509 | + | 0.790463i | ||||||||
−4.88741e11 | − | 2.82175e11i | −0.918856 | − | 0.530502i | |||||
0 | 0 | |||||||||
6.67981e10 | + | 1.15698e11i | 0.124414 | + | 0.215491i | |||||
−3.20388e11 | + | 8.80260e11i | −0.593955 | + | 1.63188i | 0.169140 | + | 0.985592i | ||
−0.763095 | + | 0.646286i | ||||||||
0 | 0 | |||||||||
4.21815e11 | + | 3.53945e11i | 0.774728 | + | 0.650074i | 0.941915 | − | 0.335851i | ||
−0.167187 | + | 0.985925i | ||||||||
−8.01098e10 | − | 2.20100e11i | −0.146451 | − | 0.402370i | |||||
0 | 0 | |||||||||
−1.82926e11 | − | 1.03743e12i | −0.331319 | − | 1.87901i | |||||
1.57375e11i | 0.283722i | 0.989887 | + | 0.141861i | ||||||
−0.989887 | + | 0.141861i | ||||||||
0 | 0 | |||||||||
−2.63632e11 | −0.470906 | |||||||||
1.98211e11 | − | 3.49500e10i | 0.352417 | − | 0.0621407i | |||||
0 | 0 | |||||||||
3.42851e11 | − | 1.24788e11i | 0.603985 | − | 0.219833i | |||||
8.55473e10 | − | 1.01951e11i | 0.150012 | − | 0.178778i | |||||
0 | 0 | |||||||||
1.07621e11 | + | 3.91707e10i | 0.186992 | + | 0.0680596i | |||||
5.33877e10 | − | 3.08234e10i | 0.0923370 | − | 0.0533108i | |||||
0 | 0 | |||||||||
−8.85933e10 | + | 1.53448e11i | −0.151829 | + | 0.262976i | |||||
−1.51259e11 | − | 1.80263e11i | −0.258041 | − | 0.307521i | |||||
0 | 0 | |||||||||
−6.44658e10 | + | 3.65604e11i | −0.108976 | + | 0.618034i | 0.880581 | + | 0.473895i | ||
−0.989557 | + | 0.144139i | ||||||||
−1.21478e12 | − | 2.14198e11i | −2.04418 | − | 0.360444i | |||||
0 | 0 | |||||||||
9.87015e10 | − | 8.28204e10i | 0.164586 | − | 0.138104i | |||||
−3.48108e11 | − | 2.00980e11i | −0.577844 | − | 0.333618i | 0.182432 | − | 0.983218i | ||
−0.760276 | + | 0.649600i | ||||||||
0 | 0 | |||||||||
−3.70632e11 | − | 6.41954e11i | −0.609677 | − | 1.05599i | −0.991293 | − | 0.131671i | ||
0.381616 | − | 0.924321i | ||||||||
−6.15504e10 | + | 1.69108e11i | −0.100791 | + | 0.276921i | |||||
0 | 0 | |||||||||
−6.19992e10 | − | 5.20235e10i | −0.100612 | − | 0.0844237i | |||||
−8.13054e10 | − | 2.23385e11i | −0.131348 | − | 0.360877i | 0.856532 | − | 0.516094i | ||
−0.987880 | + | 0.155217i | ||||||||
0 | 0 | |||||||||
−1.64413e10 | − | 9.32434e10i | −0.0263227 | − | 0.149283i | |||||
3.07917e11i | 0.490765i | |||||||||
0 | 0 | |||||||||
−5.70342e10 | −0.0900898 | |||||||||
2.54216e11 | − | 4.48252e10i | 0.399758 | − | 0.0704882i | |||||
0 | 0 | |||||||||
−2.66504e11 | + | 9.69996e10i | −0.415348 | + | 0.151174i | |||||
9.14613e10 | − | 1.08999e11i | 0.141908 | − | 0.169119i | |||||
0 | 0 | |||||||||
7.40281e11 | + | 2.69440e11i | 1.13839 | + | 0.414340i | |||||
4.79767e10 | − | 2.76994e10i | 0.0734500 | − | 0.0424064i | |||||
0 | 0 | |||||||||
2.87627e11 | − | 4.98185e11i | 0.436446 | − | 0.755947i | |||||
5.53723e11 | + | 6.59902e11i | 0.836501 | + | 0.996903i | |||||
0 | 0 | |||||||||
−3.72157e9 | + | 2.11061e10i | −0.00557253 | + | 0.0316034i | |||||
−2.34431e11 | − | 4.13365e10i | −0.349478 | − | 0.0616225i | |||||
0 | 0 | |||||||||
7.52329e11 | − | 6.31279e11i | 1.11168 | − | 0.932807i | 0.113522 | − | 0.993535i | ||
0.998154 | + | 0.0607281i | ||||||||
−8.03229e11 | − | 4.63745e11i | −1.18167 | − | 0.682238i | |||||
0 | 0 | |||||||||
−5.00674e10 | − | 8.67192e10i | −0.0730112 | − | 0.126459i | |||||
−1.30412e10 | + | 3.58304e10i | −0.0189341 | + | 0.0520210i | −0.948800 | − | 0.315879i | ||
0.929866 | + | 0.367900i | ||||||||
0 | 0 | |||||||||
−5.93057e11 | − | 4.97634e11i | −0.853519 | − | 0.716188i | |||||
−3.55367e11 | − | 9.76364e11i | −0.509205 | − | 1.39903i | |||||
0 | 0 | |||||||||
−1.82568e11 | − | 1.03539e12i | −0.259324 | − | 1.47070i | |||||
1.63556e11i | 0.231307i | |||||||||
0 | 0 | |||||||||
8.74067e11 | 1.22541 | 0.612707 | − | 0.790310i | ||||||
0.612707 | + | 0.790310i | ||||||||
2.31496e10 | − | 4.08189e9i | 0.0323141 | − | 0.00569784i | |||||
0 | 0 | |||||||||
−1.16428e12 | + | 4.23762e11i | −1.61114 | + | 0.586406i | |||||
−1.74976e11 | + | 2.08529e11i | −0.241086 | + | 0.287316i | |||||
0 | 0 | |||||||||
−6.13267e11 | − | 2.23211e11i | −0.837688 | − | 0.304894i | |||||
6.71976e11 | − | 3.87965e11i | 0.913923 | − | 0.527654i | |||||
0 | 0 | |||||||||
−3.79090e10 | + | 6.56602e10i | −0.0511152 | + | 0.0885341i | |||||
−8.86492e11 | − | 1.05648e12i | −1.19018 | − | 1.41840i | −0.884675 | − | 0.466208i | ||
−0.305503 | − | 0.952191i | ||||||||
0 | 0 | |||||||||
2.75371e10 | − | 1.56170e11i | 0.0366538 | − | 0.207874i | |||||
4.63693e11 | + | 8.17616e10i | 0.614564 | + | 0.108364i | |||||
0 | 0 | |||||||||
7.16399e11 | − | 6.01130e11i | 0.941386 | − | 0.789916i | |||||
−8.57114e10 | − | 4.94855e10i | −0.112148 | − | 0.0647488i | |||||
0 | 0 | |||||||||
−4.16564e11 | − | 7.21510e11i | −0.540410 | − | 0.936018i | −0.998880 | − | 0.0473080i | ||
0.458470 | − | 0.888710i | ||||||||
9.39879e10 | − | 2.58230e11i | 0.121412 | − | 0.333576i | |||||
0 | 0 | |||||||||
1.85562e11 | + | 1.55705e11i | 0.237671 | + | 0.199430i | |||||
−2.80549e11 | − | 7.70802e11i | −0.357808 | − | 0.983070i | −0.979788 | − | 0.200037i | ||
0.621980 | − | 0.783033i | ||||||||
0 | 0 | |||||||||
1.30181e11 | + | 7.38295e11i | 0.164627 | + | 0.933647i | |||||
6.28187e10i | 0.0791045i | |||||||||
0 | 0 | |||||||||
−9.96074e11 | −1.24373 | |||||||||
9.44642e11 | − | 1.66566e11i | 1.17454 | − | 0.207103i | 0.447875 | − | 0.894096i | ||
0.726664 | + | 0.686993i | ||||||||
0 | 0 | |||||||||
−6.73636e11 | + | 2.45183e11i | −0.830539 | + | 0.302292i | |||||
−2.37807e11 | + | 2.83408e11i | −0.291965 | + | 0.347950i | |||||
0 | 0 | |||||||||
−5.73658e10 | − | 2.08795e10i | −0.0698402 | − | 0.0254198i | |||||
2.03870e11 | − | 1.17705e11i | 0.247162 | − | 0.142699i | −0.371302 | − | 0.928512i | ||
0.618464 | + | 0.785813i | ||||||||
0 | 0 | |||||||||
−1.40767e11 | + | 2.43815e11i | −0.169234 | + | 0.293121i | |||||
9.09595e11 | + | 1.08401e12i | 1.08897 | + | 1.29779i | |||||
0 | 0 | |||||||||
−1.76993e11 | + | 1.00378e12i | −0.210133 | + | 1.19172i | |||||
2.71390e11 | + | 4.78534e10i | 0.320863 | + | 0.0565768i | |||||
0 | 0 | |||||||||
1.64631e11 | − | 1.38142e11i | 0.193027 | − | 0.161969i | |||||
−5.09024e11 | − | 2.93885e11i | −0.594344 | − | 0.343145i | |||||
0 | 0 | |||||||||
6.86293e11 | + | 1.18869e12i | 0.794697 | + | 1.37646i | |||||
1.77949e11 | − | 4.88911e11i | 0.205204 | − | 0.563794i | |||||
0 | 0 | |||||||||
−1.27323e12 | − | 1.06837e12i | −1.45613 | − | 1.22184i | −0.927948 | − | 0.372709i | ||
−0.528183 | − | 0.849130i | ||||||||
3.26023e10 | + | 8.95741e10i | 0.0371319 | + | 0.102019i | |||||
0 | 0 | |||||||||
−2.86765e10 | − | 1.62633e11i | −0.0323921 | − | 0.183705i | |||||
− | 7.56001e11i | − | 0.850443i | −0.905089 | − | 0.425222i | ||||
0.905089 | − | 0.425222i | ||||||||
0 | 0 | |||||||||
−6.41139e11 | −0.715321 | |||||||||
1.80199e12 | − | 3.17740e11i | 2.00224 | − | 0.353049i | |||||
0 | 0 | |||||||||
1.11672e12 | − | 4.06452e11i | 1.23068 | − | 0.447930i | |||||
−6.91971e11 | + | 8.24659e11i | −0.759468 | + | 0.905099i | −0.997814 | − | 0.0660815i | ||
0.238346 | + | 0.971180i | ||||||||
0 | 0 | |||||||||
5.74624e11 | + | 2.09146e11i | 0.625537 | + | 0.227677i | |||||
1.28872e11 | − | 7.44046e10i | 0.139719 | − | 0.0806669i | |||||
0 | 0 | |||||||||
−2.66587e11 | + | 4.61743e11i | −0.286677 | + | 0.496540i | |||||
5.84236e11 | + | 6.96265e11i | 0.625711 | + | 0.745694i | 0.982041 | − | 0.188667i | ||
−0.356330 | + | 0.934360i | ||||||||
0 | 0 | |||||||||
−5.90143e10 | + | 3.34687e11i | −0.0626920 | + | 0.355544i | |||||
6.45686e10 | + | 1.13852e10i | 0.0683146 | + | 0.0120457i | |||||
0 | 0 | |||||||||
−1.19196e11 | + | 1.00018e11i | −0.125094 | + | 0.104966i | |||||
−7.50715e11 | − | 4.33426e11i | −0.784675 | − | 0.453033i | |||||
0 | 0 | |||||||||
8.93401e10 | + | 1.54742e11i | 0.0926300 | + | 0.160440i | 0.908617 | − | 0.417630i | ||
−0.815987 | + | 0.578070i | ||||||||
−4.99821e11 | + | 1.37325e12i | −0.516140 | + | 1.41808i | |||||
0 | 0 | |||||||||
5.00353e11 | + | 4.19846e11i | 0.512543 | + | 0.430075i | |||||
4.66200e10 | + | 1.28087e11i | 0.0475642 | + | 0.130682i | |||||
0 | 0 | |||||||||
1.88373e11 | + | 1.06831e12i | 0.190650 | + | 1.08123i | 0.918478 | + | 0.395471i | ||
−0.727828 | + | 0.685759i | ||||||||
1.23418e12i | 1.24411i | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 81.9.f.a.71.19 | 138 | ||
3.2 | odd | 2 | 27.9.f.a.14.5 | yes | 138 | ||
27.2 | odd | 18 | inner | 81.9.f.a.8.19 | 138 | ||
27.25 | even | 9 | 27.9.f.a.2.5 | ✓ | 138 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.9.f.a.2.5 | ✓ | 138 | 27.25 | even | 9 | ||
27.9.f.a.14.5 | yes | 138 | 3.2 | odd | 2 | ||
81.9.f.a.8.19 | 138 | 27.2 | odd | 18 | inner | ||
81.9.f.a.71.19 | 138 | 1.1 | even | 1 | trivial |