Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [54,9,Mod(17,54)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(54, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("54.17");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 54.d (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 |
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 18) |
Sato-Tate group: |
Embedding invariants
Embedding label | 35.4 | ||
Root | of defining polynomial | ||
Character | 54.35 | ||
Dual form | 54.9.d.a.17.4 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
−9.79796 | − | 5.65685i | −0.612372 | − | 0.353553i | |||||
0 | 0 | |||||||||
64.0000 | + | 110.851i | 0.250000 | + | 0.433013i | |||||
944.709 | − | 545.428i | 1.51153 | − | 0.872685i | 0.511625 | − | 0.859209i | ||
0.999909 | − | 0.0134763i | ||||||||
0 | 0 | |||||||||
1250.70 | − | 2166.27i | 0.520906 | − | 0.902236i | −0.478798 | − | 0.877925i | ||
0.999704 | − | 0.0243111i | ||||||||
− | 1448.15i | − | 0.353553i | |||||||
0 | 0 | |||||||||
−12341.6 | −1.23416 | |||||||||
3212.80 | + | 1854.91i | 0.219439 | + | 0.126693i | 0.605690 | − | 0.795700i | ||
−0.386252 | + | 0.922393i | ||||||||
0 | 0 | |||||||||
22409.9 | + | 38815.1i | 0.784633 | + | 1.35902i | 0.929218 | + | 0.369531i | ||
−0.144586 | + | 0.989492i | ||||||||
−24508.5 | + | 14150.0i | −0.637977 | + | 0.368336i | |||||
0 | 0 | |||||||||
−8192.00 | + | 14189.0i | −0.125000 | + | 0.216506i | |||||
− | 54543.2i | − | 0.653048i | −0.945189 | − | 0.326524i | ||||
0.945189 | − | 0.326524i | ||||||||
0 | 0 | |||||||||
125188. | 0.960616 | 0.480308 | − | 0.877100i | ||||||
0.480308 | + | 0.877100i | ||||||||
120923. | + | 69814.8i | 0.755767 | + | 0.436342i | |||||
0 | 0 | |||||||||
−20985.9 | − | 36348.7i | −0.0895855 | − | 0.155167i | |||||
−266411. | + | 153812.i | −0.952007 | + | 0.549642i | −0.893704 | − | 0.448657i | ||
−0.0583033 | + | 0.998299i | ||||||||
0 | 0 | |||||||||
399671. | − | 692251.i | 1.02316 | − | 1.77216i | |||||
− | 507078.i | − | 1.10964i | |||||||
0 | 0 | |||||||||
320178. | 0.520906 | |||||||||
−400230. | − | 231073.i | −0.565872 | − | 0.326706i | 0.189627 | − | 0.981856i | ||
−0.755499 | + | 0.655150i | ||||||||
0 | 0 | |||||||||
−140570. | − | 243475.i | −0.152211 | − | 0.263638i | 0.779829 | − | 0.625993i | ||
−0.932040 | + | 0.362355i | ||||||||
160530. | − | 92681.9i | 0.153093 | − | 0.0883883i | |||||
0 | 0 | |||||||||
−308543. | + | 534412.i | −0.230887 | + | 0.399908i | |||||
− | 2.72866e6i | − | 1.81835i | |||||||
0 | 0 | |||||||||
159985. | 0.0853633 | 0.0426816 | − | 0.999089i | ||||||
0.0426816 | + | 0.999089i | ||||||||
−1.22659e6 | − | 708173.i | −0.588255 | − | 0.339629i | |||||
0 | 0 | |||||||||
−789864. | − | 1.36808e6i | −0.308541 | − | 0.534408i | |||||
4.49810e6 | − | 2.59698e6i | 1.59182 | − | 0.919038i | 0.598825 | − | 0.800880i | ||
0.992995 | − | 0.118158i | ||||||||
0 | 0 | |||||||||
2.49848e6 | − | 4.32750e6i | 0.730807 | − | 1.26580i | −0.225731 | − | 0.974190i | ||
0.956539 | − | 0.291606i | ||||||||
474858.i | 0.126693i | |||||||||
0 | 0 | |||||||||
3.48037e6 | 0.777311 | |||||||||
306798. | + | 177130.i | 0.0628725 | + | 0.0362995i | 0.531107 | − | 0.847305i | ||
−0.468234 | + | 0.883604i | ||||||||
0 | 0 | |||||||||
−246080. | − | 426223.i | −0.0426866 | − | 0.0739354i | |||||
−7.83192e6 | + | 4.52176e6i | −1.25311 | + | 0.723482i | |||||
0 | 0 | |||||||||
−2.86847e6 | + | 4.96833e6i | −0.392316 | + | 0.679512i | |||||
958543.i | 0.121481i | 0.998154 | + | 0.0607405i | ||||||
−0.998154 | + | 0.0607405i | ||||||||
0 | 0 | |||||||||
4.04689e6 | 0.442252 | |||||||||
−3.13709e6 | − | 1.81120e6i | −0.318989 | − | 0.184168i | |||||
0 | 0 | |||||||||
2.61429e6 | + | 4.52809e6i | 0.231016 | + | 0.400132i | |||||
−1.38270e7 | + | 7.98300e6i | −1.14109 | + | 0.658807i | −0.946700 | − | 0.322118i | ||
−0.194387 | + | 0.980925i | ||||||||
0 | 0 | |||||||||
−5.55708e6 | + | 9.62514e6i | −0.401354 | + | 0.695165i | −0.993890 | − | 0.110379i | ||
0.592536 | + | 0.805544i | ||||||||
3.18074e6i | 0.215259i | |||||||||
0 | 0 | |||||||||
−2.09715e6 | −0.125000 | |||||||||
4.23417e7 | + | 2.44460e7i | 2.37200 | + | 1.36947i | |||||
0 | 0 | |||||||||
−1.22942e7 | − | 2.12942e7i | −0.610102 | − | 1.05673i | −0.991223 | − | 0.132202i | ||
0.381121 | − | 0.924525i | ||||||||
6.04618e6 | − | 3.49076e6i | 0.282778 | − | 0.163262i | |||||
0 | 0 | |||||||||
−1.54356e7 | + | 2.67353e7i | −0.642883 | + | 1.11351i | |||||
− | 1.67264e7i | − | 0.658215i | −0.944292 | − | 0.329108i | ||||
0.944292 | − | 0.329108i | ||||||||
0 | 0 | |||||||||
4.77259e6 | 0.168059 | 0.0840297 | − | 0.996463i | ||||||
0.0840297 | + | 0.996463i | ||||||||
−1.56752e6 | − | 905009.i | −0.0522741 | − | 0.0301805i | |||||
0 | 0 | |||||||||
8.01206e6 | + | 1.38773e7i | 0.240154 | + | 0.415959i | |||||
8.03648e6 | − | 4.63986e6i | 0.228614 | − | 0.131990i | |||||
0 | 0 | |||||||||
−1.81889e7 | + | 3.15042e7i | −0.466981 | + | 0.808835i | −0.999288 | − | 0.0377164i | ||
0.532308 | + | 0.846551i | ||||||||
1.78726e7i | 0.436342i | |||||||||
0 | 0 | |||||||||
−5.87630e7 | −1.29972 | |||||||||
−2.53425e7 | − | 1.46315e7i | −0.533994 | − | 0.308302i | 0.208647 | − | 0.977991i | ||
−0.742641 | + | 0.669689i | ||||||||
0 | 0 | |||||||||
−2.97494e7 | − | 5.15274e7i | −0.569905 | − | 0.987104i | |||||
−4.89601e7 | + | 2.82671e7i | −0.895052 | + | 0.516759i | |||||
0 | 0 | |||||||||
2.68620e6 | − | 4.65264e6i | 0.0447927 | − | 0.0775833i | |||||
6.26485e7i | 0.998506i | 0.866456 | + | 0.499253i | ||||||
−0.866456 | + | 0.499253i | ||||||||
0 | 0 | |||||||||
1.12112e8 | 1.63488 | |||||||||
−3.41006e7 | − | 1.96880e7i | −0.476004 | − | 0.274821i | |||||
0 | 0 | |||||||||
−2.00399e6 | − | 3.47102e6i | −0.0256676 | − | 0.0444576i | |||||
1.18267e8 | − | 6.82813e7i | 1.45200 | − | 0.838315i | |||||
0 | 0 | |||||||||
2.42081e7 | − | 4.19297e7i | 0.273447 | − | 0.473625i | −0.696295 | − | 0.717756i | ||
0.969742 | + | 0.244131i | ||||||||
5.56815e6i | 0.0603680i | |||||||||
0 | 0 | |||||||||
1.02316e8 | 1.02316 | |||||||||
−4.53627e7 | − | 2.61902e7i | −0.435927 | − | 0.251682i | 0.265942 | − | 0.963989i | ||
−0.701868 | + | 0.712307i | ||||||||
0 | 0 | |||||||||
−3.13984e7 | − | 5.43835e7i | −0.278970 | − | 0.483191i | 0.692159 | − | 0.721745i | ||
−0.971129 | + | 0.238555i | ||||||||
5.62102e7 | − | 3.24530e7i | 0.480487 | − | 0.277410i | |||||
0 | 0 | |||||||||
5.42234e6 | − | 9.39177e6i | 0.0429500 | − | 0.0743916i | |||||
631989.i | 0.00482142i | 0.999997 | + | 0.00241071i | ||||||
−0.999997 | + | 0.00241071i | ||||||||
0 | 0 | |||||||||
3.60140e7 | 0.255132 | 0.127566 | − | 0.991830i | ||||||
0.127566 | + | 0.991830i | ||||||||
−3.96512e7 | − | 2.28926e7i | −0.270823 | − | 0.156360i | |||||
0 | 0 | |||||||||
2.04914e7 | + | 3.54921e7i | 0.130227 | + | 0.225559i | |||||
−8.33220e7 | + | 4.81060e7i | −0.511030 | + | 0.295043i | −0.733257 | − | 0.679952i | ||
0.222227 | + | 0.974995i | ||||||||
0 | 0 | |||||||||
−1.67787e8 | + | 2.90616e8i | −0.959328 | + | 1.66160i | |||||
− | 5.91547e7i | − | 0.326706i | |||||||
0 | 0 | |||||||||
1.80635e8 | 0.931694 | |||||||||
−1.18155e8 | − | 6.82169e7i | −0.589203 | − | 0.340177i | |||||
0 | 0 | |||||||||
−1.00298e8 | − | 1.73721e8i | −0.467898 | − | 0.810423i | |||||
1.08896e8 | − | 6.28712e7i | 0.491556 | − | 0.283800i | |||||
0 | 0 | |||||||||
1.79930e7 | − | 3.11648e7i | 0.0761057 | − | 0.131819i | |||||
− | 4.45852e8i | − | 1.82621i | |||||||
0 | 0 | |||||||||
3.67312e8 | 1.41195 | 0.705976 | − | 0.708235i | ||||||
0.705976 | + | 0.708235i | ||||||||
2.05478e7 | + | 1.18633e7i | 0.0765466 | + | 0.0441942i | |||||
0 | 0 | |||||||||
−2.76575e8 | − | 4.79041e8i | −0.968364 | − | 1.67726i | |||||
−2.20534e8 | + | 1.27325e8i | −0.748841 | + | 0.432343i | −0.825275 | − | 0.564731i | ||
0.0764341 | + | 0.997075i | ||||||||
0 | 0 | |||||||||
1.56573e8 | − | 2.71192e8i | 0.500391 | − | 0.866702i | |||||
2.78187e8i | 0.862815i | |||||||||
0 | 0 | |||||||||
−7.89870e7 | −0.230887 | |||||||||
3.69065e8 | + | 2.13080e8i | 1.04766 | + | 0.604868i | 0.921994 | − | 0.387205i | ||
0.125668 | + | 0.992072i | ||||||||
0 | 0 | |||||||||
1.03393e8 | + | 1.79082e8i | 0.276969 | + | 0.479725i | 0.970630 | − | 0.240577i | ||
−0.693661 | + | 0.720302i | ||||||||
3.02475e8 | − | 1.74634e8i | 0.787368 | − | 0.454587i | |||||
0 | 0 | |||||||||
−9.46185e7 | + | 1.63884e8i | −0.232714 | + | 0.403073i | |||||
1.66274e8i | 0.397630i | |||||||||
0 | 0 | |||||||||
−5.04135e8 | −1.14045 | |||||||||
−4.67616e7 | − | 2.69978e7i | −0.102915 | − | 0.0594180i | |||||
0 | 0 | |||||||||
1.02390e7 | + | 1.77345e7i | 0.0213408 | + | 0.0369634i | |||||
−5.73316e8 | + | 3.31004e8i | −1.16319 | + | 0.671565i | −0.952065 | − | 0.305895i | ||
−0.211120 | + | 0.977460i | ||||||||
0 | 0 | |||||||||
−2.17181e8 | + | 3.76169e8i | −0.417749 | + | 0.723562i | −0.995713 | − | 0.0925004i | ||
0.577964 | + | 0.816062i | ||||||||
− | 1.81292e8i | − | 0.339629i | |||||||
0 | 0 | |||||||||
−1.04988e8 | −0.186663 | |||||||||
−2.65596e8 | − | 1.53342e8i | −0.460145 | − | 0.265665i | |||||
0 | 0 | |||||||||
5.96980e8 | + | 1.03400e9i | 0.982565 | + | 1.70185i | 0.652293 | + | 0.757967i | ||
0.330272 | + | 0.943886i | ||||||||
3.56429e8 | − | 2.05784e8i | 0.571932 | − | 0.330205i | |||||
0 | 0 | |||||||||
1.01103e8 | − | 1.75115e8i | 0.154270 | − | 0.267204i | |||||
7.69489e8i | 1.14525i | |||||||||
0 | 0 | |||||||||
−1.10437e9 | −1.56446 | −0.782232 | − | 0.622987i | ||||||
−0.782232 | + | 0.622987i | ||||||||
5.75757e8 | + | 3.32414e8i | 0.795910 | + | 0.459519i | |||||
0 | 0 | |||||||||
1.65536e8 | + | 2.86717e8i | 0.218002 | + | 0.377591i | |||||
−2.37674e8 | + | 1.37221e8i | −0.305573 | + | 0.176423i | −0.644944 | − | 0.764230i | ||
0.339371 | + | 0.940653i | ||||||||
0 | 0 | |||||||||
−5.96541e8 | + | 1.03324e9i | −0.731297 | + | 1.26664i | |||||
6.73152e8i | 0.805967i | |||||||||
0 | 0 | |||||||||
6.39612e8 | 0.730807 | |||||||||
7.56506e8 | + | 4.36769e8i | 0.844555 | + | 0.487604i | 0.858810 | − | 0.512294i | ||
−0.0142547 | + | 0.999898i | ||||||||
0 | 0 | |||||||||
−9.99734e8 | − | 1.73159e9i | −1.06594 | − | 1.84626i | |||||
−5.26386e7 | + | 3.03909e7i | −0.0548597 | + | 0.0316733i | |||||
0 | 0 | |||||||||
3.54393e8 | − | 6.13827e8i | 0.353025 | − | 0.611457i | |||||
− | 6.23780e8i | − | 0.607602i | −0.952736 | − | 0.303801i | ||||
0.952736 | − | 0.303801i | ||||||||
0 | 0 | |||||||||
1.47088e9 | 1.37045 | 0.685227 | − | 0.728330i | ||||||
0.685227 | + | 0.728330i | ||||||||
−1.09847e9 | − | 6.34200e8i | −1.00116 | − | 0.578017i | |||||
0 | 0 | |||||||||
2.22744e8 | + | 3.85804e8i | 0.194328 | + | 0.336585i | |||||
1.51139e8 | − | 8.72601e7i | 0.129030 | − | 0.0744952i | |||||
0 | 0 | |||||||||
1.01173e8 | − | 1.75236e8i | 0.0827366 | − | 0.143304i | |||||
4.53452e7i | 0.0362995i | |||||||||
0 | 0 | |||||||||
−1.54503e9 | −1.18556 | |||||||||
8.99674e8 | + | 5.19427e8i | 0.676007 | + | 0.390293i | 0.798349 | − | 0.602195i | ||
−0.122342 | + | 0.992488i | ||||||||
0 | 0 | |||||||||
1.19815e9 | + | 2.07527e9i | 0.863543 | + | 1.49570i | 0.868487 | + | 0.495712i | ||
−0.00494446 | + | 0.999988i | ||||||||
−4.74380e8 | + | 2.73883e8i | −0.334903 | + | 0.193356i | |||||
0 | 0 | |||||||||
3.14982e7 | − | 5.45565e7i | 0.0213433 | − | 0.0369677i | |||||
− | 1.61075e9i | − | 1.06945i | −0.845025 | − | 0.534727i | ||||
0.845025 | − | 0.534727i | ||||||||
0 | 0 | |||||||||
−5.25183e8 | −0.334887 | −0.167444 | − | 0.985882i | ||||||
−0.167444 | + | 0.985882i | ||||||||
−1.00249e9 | − | 5.78786e8i | −0.626554 | − | 0.361741i | |||||
0 | 0 | |||||||||
2.96308e8 | + | 5.13221e8i | 0.177966 | + | 0.308247i | |||||
−1.00113e9 | + | 5.78004e8i | −0.589532 | + | 0.340367i | |||||
0 | 0 | |||||||||
2.83293e9 | − | 4.90678e9i | 1.60406 | − | 2.77831i | |||||
7.10464e8i | 0.394524i | |||||||||
0 | 0 | |||||||||
−7.34327e8 | −0.392316 | |||||||||
4.02206e8 | + | 2.32214e8i | 0.210796 | + | 0.121703i | |||||
0 | 0 | |||||||||
−8.85159e8 | − | 1.53314e9i | −0.446572 | − | 0.773485i | 0.551588 | − | 0.834117i | ||
−0.998160 | + | 0.0606312i | ||||||||
−1.06256e8 | + | 6.13468e7i | −0.0526028 | + | 0.0303702i | |||||
0 | 0 | |||||||||
3.57507e6 | − | 6.19220e6i | 0.00170463 | − | 0.00295250i | |||||
− | 5.45097e9i | − | 2.55106i | |||||||
0 | 0 | |||||||||
−7.03243e8 | −0.317151 | |||||||||
−3.52863e8 | − | 2.03726e8i | −0.156236 | − | 0.0902028i | |||||
0 | 0 | |||||||||
2.59001e8 | + | 4.48602e8i | 0.110563 | + | 0.191501i | |||||
2.11710e9 | − | 1.22231e9i | 0.887507 | − | 0.512402i | |||||
0 | 0 | |||||||||
−2.52764e8 | + | 4.37800e8i | −0.102210 | + | 0.177034i | −0.912595 | − | 0.408865i | ||
0.810385 | + | 0.585898i | ||||||||
− | 4.63667e8i | − | 0.184168i | |||||||
0 | 0 | |||||||||
1.08851e9 | 0.417254 | |||||||||
−6.53594e8 | − | 3.77352e8i | −0.246153 | − | 0.142116i | 0.371849 | − | 0.928293i | ||
−0.618001 | + | 0.786177i | ||||||||
0 | 0 | |||||||||
−2.78927e8 | − | 4.83115e8i | −0.101426 | − | 0.175675i | 0.810847 | − | 0.585259i | ||
−0.912272 | + | 0.409584i | ||||||||
3.28794e9 | − | 1.89829e9i | 1.17493 | − | 0.678347i | |||||
0 | 0 | |||||||||
−3.34630e8 | + | 5.79595e8i | −0.115508 | + | 0.200066i | |||||
3.55157e9i | 1.20503i | 0.798108 | + | 0.602514i | ||||||
−0.798108 | + | 0.602514i | ||||||||
0 | 0 | |||||||||
3.86446e8 | 0.126712 | |||||||||
−1.76985e9 | − | 1.02182e9i | −0.570543 | − | 0.329403i | |||||
0 | 0 | |||||||||
7.71787e8 | + | 1.33677e9i | 0.240541 | + | 0.416629i | |||||
−7.71502e8 | + | 4.45427e8i | −0.236453 | + | 0.136516i | −0.613546 | − | 0.789659i | ||
0.377092 | + | 0.926176i | ||||||||
0 | 0 | |||||||||
1.71946e9 | − | 2.97819e9i | 0.509710 | − | 0.882844i | −0.490227 | − | 0.871595i | ||
0.999937 | − | 0.0112489i | ||||||||
2.26949e9i | 0.661707i | |||||||||
0 | 0 | |||||||||
−1.42261e9 | −0.401354 | |||||||||
−4.64948e8 | − | 2.68438e8i | −0.129045 | − | 0.0745039i | |||||
0 | 0 | |||||||||
2.80546e9 | + | 4.85920e9i | 0.753731 | + | 1.30550i | |||||
−3.52589e8 | + | 2.03568e8i | −0.0932100 | + | 0.0538148i | |||||
0 | 0 | |||||||||
−2.52212e9 | + | 4.36844e9i | −0.645662 | + | 1.11832i | |||||
6.42022e9i | 1.61754i | 0.588124 | + | 0.808770i | ||||||
−0.588124 | + | 0.808770i | ||||||||
0 | 0 | |||||||||
−1.14123e9 | −0.278543 | |||||||||
−3.59891e9 | − | 2.07783e9i | −0.864641 | − | 0.499201i | |||||
0 | 0 | |||||||||
−1.34218e8 | − | 2.32472e8i | −0.0312500 | − | 0.0541266i | |||||
−8.30896e8 | + | 4.79718e8i | −0.190464 | + | 0.109965i | −0.592200 | − | 0.805791i | ||
0.401736 | + | 0.915756i | ||||||||
0 | 0 | |||||||||
2.00092e8 | − | 3.46570e8i | 0.0444663 | − | 0.0770178i | |||||
6.25817e9i | 1.36947i | |||||||||
0 | 0 | |||||||||
2.88104e9 | 0.611426 | |||||||||
2.47754e9 | + | 1.43041e9i | 0.517842 | + | 0.298976i | 0.736051 | − | 0.676926i | ||
−0.218209 | + | 0.975902i | ||||||||
0 | 0 | |||||||||
5.22816e8 | + | 9.05545e8i | 0.106015 | + | 0.183623i | |||||
−3.06819e9 | + | 1.77142e9i | −0.612851 | + | 0.353830i | |||||
0 | 0 | |||||||||
1.57366e9 | − | 2.72566e9i | 0.305051 | − | 0.528364i | |||||
− | 1.20245e9i | − | 0.229646i | −0.993386 | − | 0.114823i | ||||
0.993386 | − | 0.114823i | ||||||||
0 | 0 | |||||||||
−8.98794e9 | −1.66641 | −0.833207 | − | 0.552961i | ||||||
−0.833207 | + | 0.552961i | ||||||||
7.73911e8 | + | 4.46818e8i | 0.141389 | + | 0.0816309i | |||||
0 | 0 | |||||||||
−2.41072e9 | − | 4.17550e9i | −0.427706 | − | 0.740809i | |||||
2.56813e9 | − | 1.48271e9i | 0.449041 | − | 0.259254i | |||||
0 | 0 | |||||||||
−8.05272e8 | + | 1.39477e9i | −0.136780 | + | 0.236911i | −0.926276 | − | 0.376845i | ||
0.789496 | + | 0.613756i | ||||||||
− | 2.33952e9i | − | 0.391694i | |||||||
0 | 0 | |||||||||
−3.95152e9 | −0.642883 | |||||||||
1.00668e10 | + | 5.81207e9i | 1.61461 | + | 0.932193i | 0.988284 | + | 0.152628i | ||
0.626322 | + | 0.779565i | ||||||||
0 | 0 | |||||||||
7.70868e8 | + | 1.33518e9i | 0.120181 | + | 0.208159i | 0.919839 | − | 0.392297i | ||
−0.799658 | + | 0.600455i | ||||||||
1.85414e9 | − | 1.07049e9i | 0.285015 | − | 0.164554i | |||||
0 | 0 | |||||||||
9.40585e8 | − | 1.62914e9i | 0.140583 | − | 0.243498i | |||||
− | 1.29921e10i | − | 1.91493i | |||||||
0 | 0 | |||||||||
4.00080e9 | 0.573529 | |||||||||
4.93949e9 | + | 2.85182e9i | 0.698378 | + | 0.403209i | |||||
0 | 0 | |||||||||
3.05446e8 | + | 5.29048e8i | 0.0420148 | + | 0.0727718i | |||||
−4.98204e9 | + | 2.87638e9i | −0.675984 | + | 0.390280i | −0.798340 | − | 0.602207i | ||
0.122356 | + | 0.992486i | ||||||||
0 | 0 | |||||||||
−8.70831e9 | + | 1.50832e10i | −1.14986 | + | 1.99162i | |||||
− | 2.31682e8i | − | 0.0301805i | |||||||
0 | 0 | |||||||||
7.48977e9 | 0.949737 | |||||||||
−1.19405e10 | − | 6.89383e9i | −1.49395 | − | 0.862533i | |||||
0 | 0 | |||||||||
−6.24969e9 | − | 1.08248e10i | −0.761364 | − | 1.31872i | |||||
4.25587e9 | − | 2.45713e9i | 0.511635 | − | 0.295393i | |||||
0 | 0 | |||||||||
−1.02554e9 | + | 1.77629e9i | −0.120077 | + | 0.207979i | |||||
1.21239e10i | 1.40102i | |||||||||
0 | 0 | |||||||||
−6.49769e9 | −0.731486 | −0.365743 | − | 0.930716i | ||||||
−0.365743 | + | 0.930716i | ||||||||
1.02867e9 | + | 5.93902e8i | 0.114307 | + | 0.0659952i | |||||
0 | 0 | |||||||||
1.73487e9 | + | 3.00488e9i | 0.187854 | + | 0.325372i | |||||
−1.18485e10 | + | 6.84076e9i | −1.26655 | + | 0.731245i | −0.974334 | − | 0.225106i | ||
−0.292219 | + | 0.956351i | ||||||||
0 | 0 | |||||||||
−3.58243e9 | + | 6.20496e9i | −0.373251 | + | 0.646489i | −0.990064 | − | 0.140620i | ||
0.616813 | + | 0.787110i | ||||||||
− | 1.35081e10i | − | 1.38956i | |||||||
0 | 0 | |||||||||
−4.65637e9 | −0.466981 | |||||||||
9.86964e9 | + | 5.69824e9i | 0.977382 | + | 0.564292i | 0.901479 | − | 0.432824i | ||
0.0759031 | + | 0.997115i | ||||||||
0 | 0 | |||||||||
−8.57241e8 | − | 1.48478e9i | −0.0827828 | − | 0.143384i | |||||
−1.98120e9 | + | 1.14385e9i | −0.188942 | + | 0.109086i | |||||
0 | 0 | |||||||||
4.35289e9 | − | 7.53943e9i | 0.404906 | − | 0.701318i | |||||
− | 6.82818e9i | − | 0.627328i | |||||||
0 | 0 | |||||||||
3.58263e10 | 3.21121 | |||||||||
1.08206e10 | + | 6.24728e9i | 0.958035 | + | 0.553122i | |||||
0 | 0 | |||||||||
−3.76083e9 | − | 6.51395e9i | −0.324929 | − | 0.562793i | |||||
7.67421e8 | − | 4.43071e8i | 0.0655014 | − | 0.0378172i | |||||
0 | 0 | |||||||||
8.59454e9 | − | 1.48862e10i | 0.715996 | − | 1.24014i | −0.246578 | − | 0.969123i | ||
0.962574 | − | 0.271018i | ||||||||
− | 3.74566e9i | − | 0.308302i | |||||||
0 | 0 | |||||||||
3.10496e9 | 0.249499 | |||||||||
−2.32290e10 | − | 1.34112e10i | −1.84438 | − | 1.06485i | |||||
0 | 0 | |||||||||
1.61156e9 | + | 2.79131e9i | 0.124947 | + | 0.216415i | 0.921712 | − | 0.387874i | ||
−0.796765 | + | 0.604289i | ||||||||
1.16898e10 | − | 6.74909e9i | 0.895652 | − | 0.517105i | |||||
0 | 0 | |||||||||
3.80792e9 | − | 6.59551e9i | 0.284952 | − | 0.493552i | |||||
− | 1.04298e9i | − | 0.0771364i | |||||||
0 | 0 | |||||||||
1.31889e10 | 0.952870 | |||||||||
−6.26689e9 | − | 3.61819e9i | −0.447526 | − | 0.258379i | |||||
0 | 0 | |||||||||
−4.94148e9 | − | 8.55889e9i | −0.344788 | − | 0.597191i | |||||
2.16831e9 | − | 1.25187e9i | 0.149556 | − | 0.0863461i | −0.423355 | − | 0.905964i | ||
0.572911 | + | 0.819618i | ||||||||
0 | 0 | |||||||||
−8.92317e9 | + | 1.54554e10i | −0.601475 | + | 1.04178i | 0.391123 | + | 0.920338i | ||
−0.992598 | + | 0.121446i | ||||||||
2.26214e10i | 1.50746i | |||||||||
0 | 0 | |||||||||
6.87667e8 | 0.0447927 | |||||||||
−2.33322e9 | − | 1.34709e9i | −0.150265 | − | 0.0867555i | 0.422982 | − | 0.906138i | ||
−0.573247 | + | 0.819382i | ||||||||
0 | 0 | |||||||||
−9.12302e9 | − | 1.58015e10i | −0.574414 | − | 0.994915i | |||||
−6.94466e9 | + | 4.00950e9i | −0.432366 | + | 0.249626i | |||||
0 | 0 | |||||||||
−3.52863e9 | + | 6.11177e9i | −0.214820 | + | 0.372079i | |||||
− | 4.46773e8i | − | 0.0268973i | −0.999910 | − | 0.0134487i | ||||
0.999910 | − | 0.0134487i | ||||||||
0 | 0 | |||||||||
−1.31142e9 | −0.0772168 | |||||||||
−1.44117e10 | − | 8.32058e9i | −0.839228 | − | 0.484529i | |||||
0 | 0 | |||||||||
7.17516e9 | + | 1.24277e10i | 0.408720 | + | 0.707924i | |||||
4.50871e9 | − | 2.60310e9i | 0.254028 | − | 0.146663i | |||||
0 | 0 | |||||||||
−4.50312e9 | + | 7.79963e9i | −0.248227 | + | 0.429942i | −0.963034 | − | 0.269380i | ||
0.714807 | + | 0.699322i | ||||||||
− | 5.04012e9i | − | 0.274821i | |||||||
0 | 0 | |||||||||
−1.97447e9 | −0.105352 | |||||||||
2.07646e9 | + | 1.19885e9i | 0.109605 | + | 0.0632802i | |||||
0 | 0 | |||||||||
3.61769e9 | + | 6.26602e9i | 0.186894 | + | 0.323710i | 0.944213 | − | 0.329335i | ||
−0.757319 | + | 0.653045i | ||||||||
−1.98257e9 | + | 1.14464e9i | −0.101331 | + | 0.0585036i | |||||
0 | 0 | |||||||||
2.56511e8 | − | 4.44291e8i | 0.0128338 | − | 0.0222288i | |||||
− | 2.07133e10i | − | 1.02538i | |||||||
0 | 0 | |||||||||
−2.18940e10 | −1.06113 | −0.530566 | − | 0.847644i | ||||||
−0.530566 | + | 0.847644i | ||||||||
1.51381e10 | + | 8.74001e9i | 0.726002 | + | 0.419158i | |||||
0 | 0 | |||||||||
−5.87664e9 | − | 1.01786e10i | −0.275979 | − | 0.478009i | |||||
1.99158e10 | − | 1.14984e10i | 0.925555 | − | 0.534369i | 0.0401518 | − | 0.999194i | ||
0.885403 | + | 0.464824i | ||||||||
0 | 0 | |||||||||
5.06142e9 | − | 8.76664e9i | 0.230372 | − | 0.399016i | |||||
− | 2.71112e10i | − | 1.22123i | |||||||
0 | 0 | |||||||||
6.19727e9 | 0.273447 | |||||||||
1.71912e10 | + | 9.92532e9i | 0.750770 | + | 0.433457i | 0.825972 | − | 0.563711i | ||
−0.0752021 | + | 0.997168i | ||||||||
0 | 0 | |||||||||
8.38941e9 | + | 1.45309e10i | 0.358942 | + | 0.621706i | |||||
−6.17236e8 | + | 3.56362e8i | −0.0261401 | + | 0.0150920i | |||||
0 | 0 | |||||||||
−9.11175e9 | + | 1.57820e10i | −0.378109 | + | 0.654904i | |||||
3.96830e10i | 1.63011i | |||||||||
0 | 0 | |||||||||
−2.22799e10 | −0.896915 | −0.448458 | − | 0.893804i | ||||||
−0.448458 | + | 0.893804i | ||||||||
5.14572e9 | + | 2.97089e9i | 0.205076 | + | 0.118401i | |||||
0 | 0 | |||||||||
6.54821e9 | + | 1.13418e10i | 0.255789 | + | 0.443040i | |||||
2.03685e10 | − | 1.17598e10i | 0.787738 | − | 0.454801i | −0.0514274 | − | 0.998677i | ||
0.839166 | + | 0.543876i | ||||||||
0 | 0 | |||||||||
6.30033e9 | − | 1.09125e10i | 0.238860 | − | 0.413718i | |||||
− | 6.70469e9i | − | 0.251682i | |||||||
0 | 0 | |||||||||
1.30787e10 | 0.481351 | |||||||||
5.13999e8 | + | 2.96757e8i | 0.0187320 | + | 0.0108149i | |||||
0 | 0 | |||||||||
−2.32825e10 | − | 4.03265e10i | −0.832025 | − | 1.44111i | −0.896430 | − | 0.443186i | ||
0.0644044 | − | 0.997924i | ||||||||
−5.55139e10 | + | 3.20510e10i | −1.96456 | + | 1.13424i | |||||
0 | 0 | |||||||||
4.01899e9 | − | 6.96109e9i | 0.139485 | − | 0.241595i | |||||
3.99372e10i | 1.37271i | |||||||||
0 | 0 | |||||||||
−3.19217e10 | −1.07620 | |||||||||
7.19491e9 | + | 4.15398e9i | 0.240244 | + | 0.138705i | |||||
0 | 0 | |||||||||
−2.62720e9 | − | 4.55044e9i | −0.0860573 | − | 0.149056i | |||||
−3.95877e9 | + | 2.28560e9i | −0.128441 | + | 0.0741556i | −0.562844 | − | 0.826563i | ||
0.434403 | + | 0.900719i | ||||||||
0 | 0 | |||||||||
6.62653e9 | − | 1.14775e10i | 0.210939 | − | 0.365358i | −0.741069 | − | 0.671428i | ||
0.952009 | + | 0.306071i | ||||||||
2.00289e10i | 0.631548i | |||||||||
0 | 0 | |||||||||
1.38812e9 | 0.0429500 | |||||||||
−3.77576e10 | − | 2.17993e10i | −1.15731 | − | 0.668171i | |||||
0 | 0 | |||||||||
1.39004e10 | + | 2.40762e10i | 0.418135 | + | 0.724231i | |||||
−7.00568e7 | + | 4.04473e7i | −0.00208773 | + | 0.00120535i | |||||
0 | 0 | |||||||||
−3.08354e10 | + | 5.34084e10i | −0.901935 | + | 1.56220i | |||||
2.64178e10i | 0.765575i | 0.923836 | + | 0.382787i | ||||||
−0.923836 | + | 0.382787i | ||||||||
0 | 0 | |||||||||
4.70683e10 | 1.33899 | 0.669494 | − | 0.742817i | ||||||
0.669494 | + | 0.742817i | ||||||||
6.89035e9 | + | 3.97814e9i | 0.194215 | + | 0.112130i | |||||
0 | 0 | |||||||||
2.30489e9 | + | 3.99219e9i | 0.0637830 | + | 0.110475i | |||||
−3.33515e10 | + | 1.92555e10i | −0.914513 | + | 0.527995i | |||||
0 | 0 | |||||||||
−1.60624e10 | + | 2.78209e10i | −0.432467 | + | 0.749055i | −0.997085 | − | 0.0762974i | ||
0.564618 | + | 0.825352i | ||||||||
− | 5.86052e9i | − | 0.156360i | |||||||
0 | 0 | |||||||||
−2.76576e10 | −0.724646 | |||||||||
4.36195e10 | + | 2.51837e10i | 1.13257 | + | 0.653891i | 0.944581 | − | 0.328279i | ||
0.187992 | + | 0.982171i | ||||||||
0 | 0 | |||||||||
3.41702e10 | + | 5.91846e10i | 0.871381 | + | 1.50928i | |||||
4.95314e9 | − | 2.85969e9i | 0.125182 | − | 0.0722737i | |||||
0 | 0 | |||||||||
−2.62290e9 | + | 4.54299e9i | −0.0651133 | + | 0.112780i | |||||
− | 2.09633e10i | − | 0.515792i | −0.966173 | − | 0.257896i | ||||
0.966173 | − | 0.257896i | ||||||||
0 | 0 | |||||||||
1.92687e10 | 0.465743 | |||||||||
−1.06652e10 | − | 6.15757e9i | −0.255515 | − | 0.147522i | |||||
0 | 0 | |||||||||
4.26926e9 | + | 7.39457e9i | 0.100491 | + | 0.174056i | |||||
1.05913e11 | − | 6.11489e10i | 2.47118 | − | 1.42674i | |||||
0 | 0 | |||||||||
2.27460e10 | − | 3.93972e10i | 0.521482 | − | 0.903234i | −0.478206 | − | 0.878248i | ||
0.999688 | − | 0.0249858i | ||||||||
6.31139e9i | 0.143438i | |||||||||
0 | 0 | |||||||||
−4.29535e10 | −0.959328 | |||||||||
−3.76919e10 | − | 2.17614e10i | −0.834534 | − | 0.481818i | 0.0208685 | − | 0.999782i | ||
−0.855403 | + | 0.517964i | ||||||||
0 | 0 | |||||||||
−1.88669e10 | − | 3.26784e10i | −0.410560 | − | 0.711111i | 0.584391 | − | 0.811472i | ||
−0.994951 | + | 0.100361i | ||||||||
6.55737e9 | − | 3.78590e9i | 0.141468 | − | 0.0816765i | |||||
0 | 0 | |||||||||
2.00907e10 | − | 3.47982e10i | 0.426042 | − | 0.737926i | |||||
1.94089e10i | 0.408068i | 0.978964 | + | 0.204034i | ||||||
−0.978964 | + | 0.204034i | ||||||||
0 | 0 | |||||||||
−6.15054e10 | −1.27122 | |||||||||
−3.78638e9 | − | 2.18607e9i | −0.0775949 | − | 0.0447994i | |||||
0 | 0 | |||||||||
1.15606e10 | + | 2.00236e10i | 0.232923 | + | 0.403435i | |||||
1.60543e10 | − | 9.26894e9i | 0.320735 | − | 0.185176i | |||||
0 | 0 | |||||||||
5.00342e10 | − | 8.66618e10i | 0.982862 | − | 1.70237i | |||||
− | 1.74635e10i | − | 0.340177i | |||||||
0 | 0 | |||||||||
1.00789e10 | 0.193063 | |||||||||
−1.20390e10 | − | 6.95073e9i | −0.228691 | − | 0.132035i | 0.381277 | − | 0.924461i | ||
−0.609968 | + | 0.792426i | ||||||||
0 | 0 | |||||||||
3.58524e9 | + | 6.20981e9i | 0.0669788 | + | 0.116011i | |||||
−3.36944e10 | + | 1.94534e10i | −0.624265 | + | 0.360420i | |||||
0 | 0 | |||||||||
1.28381e10 | − | 2.22363e10i | 0.233949 | − | 0.405211i | |||||
− | 5.28151e10i | − | 0.954534i | |||||||
0 | 0 | |||||||||
3.69205e10 | 0.656374 | 0.328187 | − | 0.944613i | ||||||
0.328187 | + | 0.944613i | ||||||||
1.39387e10 | + | 8.04751e9i | 0.245778 | + | 0.141900i | |||||
0 | 0 | |||||||||
3.03703e9 | + | 5.26028e9i | 0.0526822 | + | 0.0912483i | |||||
−5.69924e10 | + | 3.29046e10i | −0.980598 | + | 0.566149i | −0.902451 | − | 0.430793i | ||
−0.0781474 | + | 0.996942i | ||||||||
0 | 0 | |||||||||
−1.26035e10 | + | 2.18298e10i | −0.213355 | + | 0.369541i | |||||
− | 6.34803e10i | − | 1.06594i | |||||||
0 | 0 | |||||||||
4.60621e9 | 0.0761057 | |||||||||
−3.62338e10 | − | 2.09196e10i | −0.593865 | − | 0.342868i | |||||
0 | 0 | |||||||||
−4.81781e9 | − | 8.34469e9i | −0.0777047 | − | 0.134589i | 0.824555 | − | 0.565782i | ||
−0.902259 | + | 0.431194i | ||||||||
4.94232e10 | − | 2.85345e10i | 0.790771 | − | 0.456552i | |||||
0 | 0 | |||||||||
3.63183e10 | − | 6.29051e10i | 0.571887 | − | 0.990537i | |||||
− | 2.91551e10i | − | 0.455452i | −0.973725 | − | 0.227726i | ||||
0.973725 | − | 0.227726i | ||||||||
0 | 0 | |||||||||
−5.71394e10 | −0.878558 | |||||||||
1.11818e10 | + | 6.45579e9i | 0.170572 | + | 0.0984798i | |||||
0 | 0 | |||||||||
2.35080e10 | + | 4.07170e10i | 0.352988 | + | 0.611393i | |||||
−6.14696e10 | + | 3.54895e10i | −0.915776 | + | 0.528723i | −0.882285 | − | 0.470716i | ||
−0.0334907 | + | 0.999439i | ||||||||
0 | 0 | |||||||||
5.96906e9 | − | 1.03387e10i | 0.0875432 | − | 0.151629i | |||||
3.03700e9i | 0.0441942i | |||||||||
0 | 0 | |||||||||
1.08548e10 | 0.155514 | |||||||||
−5.93246e10 | − | 3.42511e10i | −0.843347 | − | 0.486906i | |||||
0 | 0 | |||||||||
6.57120e8 | + | 1.13817e9i | 0.00919778 | + | 0.0159310i | |||||
−3.92099e9 | + | 2.26378e9i | −0.0544598 | + | 0.0314424i | |||||
0 | 0 | |||||||||
3.54015e10 | − | 6.13173e10i | 0.484182 | − | 0.838628i | |||||
− | 6.08836e10i | − | 0.826323i | −0.910658 | − | 0.413161i | ||||
0.910658 | − | 0.413161i | ||||||||
0 | 0 | |||||||||
2.81890e10 | 0.376768 | 0.188384 | − | 0.982095i | ||||||
0.188384 | + | 0.982095i | ||||||||
−2.82283e10 | − | 1.62976e10i | −0.374420 | − | 0.216172i | |||||
0 | 0 | |||||||||
−1.61832e10 | − | 2.80301e10i | −0.211408 | − | 0.366170i | |||||
−1.32799e10 | + | 7.66716e9i | −0.172168 | + | 0.0994012i | |||||
0 | 0 | |||||||||
8.16093e9 | − | 1.41351e10i | 0.104212 | − | 0.180500i | |||||
− | 1.18300e10i | − | 0.149927i | |||||||
0 | 0 | |||||||||
4.00826e10 | 0.500391 | |||||||||
2.01604e11 | + | 1.16396e11i | 2.49799 | + | 1.44221i | |||||
0 | 0 | |||||||||
3.44705e8 | + | 5.97046e8i | 0.00420758 | + | 0.00728774i | |||||
−3.08374e10 | + | 1.78040e10i | −0.373610 | + | 0.215704i | |||||
0 | 0 | |||||||||
−6.80210e9 | + | 1.17816e10i | −0.0811921 | + | 0.140629i | |||||
− | 1.82583e9i | − | 0.0216324i | |||||||
0 | 0 | |||||||||
−1.20219e11 | −1.40341 | −0.701703 | − | 0.712470i | ||||||
−0.701703 | + | 0.712470i | ||||||||
8.80634e10 | + | 5.08435e10i | 1.02047 | + | 0.589166i | |||||
0 | 0 | |||||||||
−5.05517e9 | − | 8.75580e9i | −0.0577218 | − | 0.0999771i | |||||
3.40227e10 | − | 1.96430e10i | 0.385641 | − | 0.222650i | |||||
0 | 0 | |||||||||
−6.82534e10 | + | 1.18218e11i | −0.762386 | + | 1.32049i | 0.179231 | + | 0.983807i | ||
−0.941617 | + | 0.336685i | ||||||||
5.45485e10i | 0.604868i | |||||||||
0 | 0 | |||||||||
−3.35499e10 | −0.366640 | |||||||||
−5.01042e10 | − | 2.89277e10i | −0.543585 | − | 0.313839i | |||||
0 | 0 | |||||||||
4.54977e10 | + | 7.88043e10i | 0.486506 | + | 0.842654i | |||||
1.57801e10 | − | 9.11062e9i | 0.167521 | − | 0.0967183i | |||||
0 | 0 | |||||||||
−1.32343e10 | + | 2.29225e10i | −0.138485 | + | 0.239862i | |||||
− | 1.72931e10i | − | 0.179660i | −0.995957 | − | 0.0898300i | ||||
0.995957 | − | 0.0898300i | ||||||||
0 | 0 | |||||||||
2.23963e11 | 2.29366 | |||||||||
3.87168e10 | + | 2.23532e10i | 0.393684 | + | 0.227294i | |||||
0 | 0 | |||||||||
−6.57561e10 | − | 1.13893e11i | −0.659160 | − | 1.14170i | |||||
−4.39485e10 | + | 2.53737e10i | −0.437432 | + | 0.252552i | −0.702508 | − | 0.711676i | ||
0.265076 | + | 0.964228i | ||||||||
0 | 0 | |||||||||
−5.24767e10 | + | 9.08923e10i | −0.514959 | + | 0.891936i | |||||
− | 1.74427e10i | − | 0.169961i | |||||||
0 | 0 | |||||||||
−2.42223e10 | −0.232714 | |||||||||
−7.23149e10 | − | 4.17510e10i | −0.689888 | − | 0.398307i | 0.113682 | − | 0.993517i | ||
−0.803570 | + | 0.595210i | ||||||||
0 | 0 | |||||||||
6.95426e10 | + | 1.20451e11i | 0.654194 | + | 1.13310i | 0.982095 | + | 0.188385i | ||
−0.327901 | + | 0.944712i | ||||||||
−1.84316e10 | + | 1.06415e10i | −0.172179 | + | 0.0994075i | |||||
0 | 0 | |||||||||
−7.34946e10 | + | 1.27296e11i | −0.677030 | + | 1.17265i | |||||
2.45897e11i | 2.24948i | |||||||||
0 | 0 | |||||||||
−1.25735e11 | −1.13437 | −0.567184 | − | 0.823591i | ||||||
−0.567184 | + | 0.823591i | ||||||||
−3.91997e10 | − | 2.26319e10i | −0.351213 | − | 0.202773i | |||||
0 | 0 | |||||||||
−3.22646e10 | − | 5.58840e10i | −0.285112 | − | 0.493828i | |||||
−6.33915e10 | + | 3.65991e10i | −0.556322 | + | 0.321193i | |||||
0 | 0 | |||||||||
−1.77801e9 | + | 3.07961e9i | −0.0153908 | + | 0.0266576i | |||||
− | 6.91145e9i | − | 0.0594180i | |||||||
0 | 0 | |||||||||
6.50851e10 | 0.551939 | |||||||||
6.44083e10 | + | 3.71861e10i | 0.542487 | + | 0.313205i | 0.746086 | − | 0.665849i | ||
−0.203599 | + | 0.979054i | ||||||||
0 | 0 | |||||||||
−1.75978e10 | − | 3.04803e10i | −0.146217 | − | 0.253255i | |||||
1.70647e11 | − | 9.85232e10i | 1.40829 | − | 0.813075i | |||||
0 | 0 | |||||||||
−1.31059e9 | + | 2.27001e9i | −0.0106704 | + | 0.0184817i | |||||
7.64545e10i | 0.618279i | 0.951017 | + | 0.309139i | ||||||
−0.951017 | + | 0.309139i | ||||||||
0 | 0 | |||||||||
−1.48830e11 | −1.18747 | |||||||||
−7.33844e10 | − | 4.23685e10i | −0.581593 | − | 0.335783i | |||||
0 | 0 | |||||||||
7.79948e10 | + | 1.35091e11i | 0.609903 | + | 1.05638i | |||||
−6.63143e10 | + | 3.82866e10i | −0.515110 | + | 0.297399i | −0.734932 | − | 0.678141i | ||
0.219822 | + | 0.975540i | ||||||||
0 | 0 | |||||||||
−2.39823e10 | + | 4.15386e10i | −0.183820 | + | 0.318386i | −0.943178 | − | 0.332287i | ||
0.759358 | + | 0.650673i | ||||||||
1.41414e11i | 1.07673i | |||||||||
0 | 0 | |||||||||
−5.55985e10 | −0.417749 | |||||||||
−1.89505e11 | − | 1.09411e11i | −1.41449 | − | 0.816655i | |||||
0 | 0 | |||||||||
−1.02320e11 | − | 1.77223e11i | −0.753710 | − | 1.30546i | −0.946013 | − | 0.324128i | ||
0.192303 | − | 0.981336i | ||||||||
2.00965e10 | − | 1.16027e10i | 0.147064 | − | 0.0849073i | |||||
0 | 0 | |||||||||
6.85834e10 | − | 1.18790e11i | 0.495336 | − | 0.857946i | |||||
1.58778e10i | 0.113927i | |||||||||
0 | 0 | |||||||||
4.26255e10 | 0.301876 | 0.150938 | − | 0.988543i | ||||||
0.150938 | + | 0.988543i | ||||||||
6.36641e10 | + | 3.67565e10i | 0.447942 | + | 0.258619i | |||||
0 | 0 | |||||||||
−6.71924e9 | − | 1.16381e10i | −0.0466656 | − | 0.0808273i | |||||
2.80277e9 | − | 1.61818e9i | 0.0193396 | − | 0.0111657i | −0.490299 | − | 0.871554i | ||
0.509639 | + | 0.860389i | ||||||||
0 | 0 | |||||||||
7.34200e10 | − | 1.27167e11i | 0.500094 | − | 0.866189i | −0.499906 | − | 0.866080i | ||
1.00000 | 0.000108934i | |||||||||
− | 3.92556e10i | − | 0.265665i | |||||||
0 | 0 | |||||||||
1.54789e11 | 1.03414 | |||||||||
1.35713e11 | + | 7.83542e10i | 0.900888 | + | 0.520128i | |||||
0 | 0 | |||||||||
−8.70585e10 | − | 1.50790e11i | −0.570546 | − | 0.988215i | |||||
7.02011e10 | − | 4.05306e10i | 0.457137 | − | 0.263928i | |||||
0 | 0 | |||||||||
−7.64135e10 | + | 1.32352e11i | −0.491283 | + | 0.850926i | |||||
− | 8.72607e9i | − | 0.0557463i | |||||||
0 | 0 | |||||||||
2.39192e11 | 1.50879 | 0.754397 | − | 0.656419i | ||||||
0.754397 | + | 0.656419i | ||||||||
4.56229e10 | + | 2.63404e10i | 0.285966 | + | 0.165103i | |||||
0 | 0 | |||||||||
−6.44682e10 | − | 1.11662e11i | −0.399014 | − | 0.691113i | |||||
3.47003e11 | − | 2.00342e11i | 2.13422 | − | 1.23219i | |||||
0 | 0 | |||||||||
1.10292e10 | − | 1.91032e10i | 0.0669866 | − | 0.116024i | |||||
1.93971e10i | 0.117073i | |||||||||
0 | 0 | |||||||||
2.58823e10 | 0.154270 | |||||||||
7.33197e8 | + | 4.23311e8i | 0.00434299 | + | 0.00250742i | 0.502170 | − | 0.864769i | ||
−0.497827 | + | 0.867276i | ||||||||
0 | 0 | |||||||||
5.89225e10 | + | 1.02057e11i | 0.344697 | + | 0.597033i | 0.985299 | − | 0.170841i | ||
−0.640602 | + | 0.767873i | ||||||||
−8.52989e10 | + | 4.92473e10i | −0.495906 | + | 0.286312i | |||||
0 | 0 | |||||||||
−3.86260e10 | + | 6.69022e10i | −0.221794 | + | 0.384158i | |||||
− | 2.63434e11i | − | 1.50333i | −0.659546 | − | 0.751665i | ||||
0.659546 | − | 0.751665i | ||||||||
0 | 0 | |||||||||
−5.92311e10 | −0.333865 | |||||||||
−3.51025e11 | − | 2.02664e11i | −1.96646 | − | 1.13534i | |||||
0 | 0 | |||||||||
−7.06799e10 | − | 1.22421e11i | −0.391116 | − | 0.677433i | |||||
−1.08870e11 | + | 6.28559e10i | −0.598761 | + | 0.345695i | −0.768554 | − | 0.639785i | ||
0.169793 | + | 0.985480i | ||||||||
0 | 0 | |||||||||
−1.38893e11 | + | 2.40570e11i | −0.754599 | + | 1.30700i | |||||
8.50979e10i | 0.459519i | |||||||||
0 | 0 | |||||||||
−1.00256e10 | −0.0534816 | |||||||||
3.14417e10 | + | 1.81529e10i | 0.166711 | + | 0.0962506i | 0.581034 | − | 0.813879i | ||
−0.414323 | + | 0.910130i | ||||||||
0 | 0 | |||||||||
−6.52457e10 | − | 1.13009e11i | −0.341779 | − | 0.591979i | 0.642984 | − | 0.765880i | ||
−0.984763 | + | 0.173901i | ||||||||
−1.68418e11 | + | 9.72361e10i | −0.876912 | + | 0.506286i | |||||
0 | 0 | |||||||||
−2.11887e10 | + | 3.66998e10i | −0.109001 | + | 0.188796i | |||||
− | 3.41597e11i | − | 1.74673i | |||||||
0 | 0 | |||||||||
1.42167e11 | 0.718285 | |||||||||
−3.04222e10 | − | 1.75643e10i | −0.152787 | − | 0.0882114i | |||||
0 | 0 | |||||||||
1.51731e11 | + | 2.62806e11i | 0.752965 | + | 1.30417i | |||||
−3.57076e10 | + | 2.06158e10i | −0.176145 | + | 0.101697i | |||||
0 | 0 | |||||||||
−1.99070e10 | + | 3.44799e10i | −0.0970388 | + | 0.168076i | −0.910458 | − | 0.413602i | ||
0.813419 | + | 0.581678i | ||||||||
− | 3.64655e10i | − | 0.176702i | |||||||
0 | 0 | |||||||||
−1.52715e11 | −0.731297 | |||||||||
2.31655e11 | + | 1.33746e11i | 1.10277 | + | 0.636687i | 0.936948 | − | 0.349468i | ||
0.165826 | + | 0.986155i | ||||||||
0 | 0 | |||||||||
−6.05539e10 | − | 1.04882e11i | −0.284881 | − | 0.493428i | |||||
−7.46197e10 | + | 4.30817e10i | −0.348994 | + | 0.201492i | |||||
0 | 0 | |||||||||
−5.90000e9 | + | 1.02191e10i | −0.0272719 | + | 0.0472362i | |||||
− | 3.82963e10i | − | 0.175984i | −0.996121 | − | 0.0879922i | ||||
0.996121 | − | 0.0879922i | ||||||||
0 | 0 | |||||||||
4.64879e11 | 2.11144 | |||||||||
−1.29225e11 | − | 7.46079e10i | −0.583511 | − | 0.336890i | |||||
0 | 0 | |||||||||
4.09352e10 | + | 7.09018e10i | 0.182702 | + | 0.316449i | |||||
−3.72059e10 | + | 2.14809e10i | −0.165096 | + | 0.0953179i | |||||
0 | 0 | |||||||||
2.01386e11 | − | 3.48810e11i | 0.883316 | − | 1.52995i | 0.0356843 | − | 0.999363i | ||
0.847632 | − | 0.530585i | ||||||||
1.11813e11i | 0.487604i | |||||||||
0 | 0 | |||||||||
−2.83267e10 | −0.122112 | |||||||||
1.95353e11 | + | 1.12787e11i | 0.837297 | + | 0.483414i | |||||
0 | 0 | |||||||||
−1.41648e11 | − | 2.45341e11i | −0.600175 | − | 1.03953i | |||||
1.74858e11 | − | 1.00954e11i | 0.736653 | − | 0.425307i | |||||
0 | 0 | |||||||||
1.27966e11 | − | 2.21644e11i | 0.532969 | − | 0.923130i | |||||
− | 4.49866e11i | − | 1.86299i | −0.363750 | − | 0.931497i | ||||
0.363750 | − | 0.931497i | ||||||||
0 | 0 | |||||||||
2.00282e10 | 0.0820013 | |||||||||
−6.73774e9 | − | 3.89003e9i | −0.0274298 | − | 0.0158366i | |||||
0 | 0 | |||||||||
1.52405e10 | + | 2.63974e10i | 0.0613454 | + | 0.106253i | |||||
−1.13470e11 | + | 6.55119e10i | −0.454154 | + | 0.262206i | |||||
0 | 0 | |||||||||
1.26945e11 | − | 2.19875e11i | 0.502378 | − | 0.870145i | −0.497618 | − | 0.867396i | ||
0.999996 | − | 0.00274839i | ||||||||
2.06430e11i | 0.812345i | |||||||||
0 | 0 | |||||||||
9.07247e10 | 0.353025 | |||||||||
7.48989e10 | + | 4.32429e10i | 0.289813 | + | 0.167323i | |||||
0 | 0 | |||||||||
9.06903e10 | + | 1.57080e11i | 0.347006 | + | 0.601031i | |||||
6.91468e10 | − | 3.99219e10i | 0.263099 | − | 0.151901i | |||||
0 | 0 | |||||||||
−2.52733e9 | + | 4.37746e9i | −0.00950964 | + | 0.0164712i | |||||
5.21386e11i | 1.95094i | 0.220134 | + | 0.975470i | ||||||
−0.220134 | + | 0.975470i | ||||||||
0 | 0 | |||||||||
−1.57079e11 | −0.581269 | |||||||||
1.28492e10 | + | 7.41849e9i | 0.0472854 | + | 0.0273003i | |||||
0 | 0 | |||||||||
9.41366e10 | + | 1.63049e11i | 0.342613 | + | 0.593424i | |||||
−3.19921e11 | + | 1.84706e11i | −1.15795 | + | 0.668544i | |||||
0 | 0 | |||||||||
2.86428e9 | − | 4.96107e9i | 0.0102536 | − | 0.0177598i | −0.860853 | − | 0.508854i | ||
0.871107 | + | 0.491094i | ||||||||
− | 1.62355e11i | − | 0.578017i | |||||||
0 | 0 | |||||||||
−5.89015e10 | −0.207413 | |||||||||
−2.36036e11 | − | 1.36275e11i | −0.826625 | − | 0.477252i | |||||
0 | 0 | |||||||||
1.60850e11 | + | 2.78600e11i | 0.557192 | + | 0.965084i | 0.997729 | + | 0.0673502i | ||
−0.440538 | + | 0.897734i | ||||||||
8.82427e10 | − | 5.09469e10i | 0.304015 | − | 0.175523i | |||||
0 | 0 | |||||||||
−2.85112e10 | + | 4.93829e10i | −0.0971638 | + | 0.168293i | |||||
− | 9.12190e10i | − | 0.309183i | |||||||
0 | 0 | |||||||||
−5.10308e11 | −1.71102 | −0.855508 | − | 0.517789i | ||||||
−0.855508 | + | 0.517789i | ||||||||
1.93458e10 | + | 1.11693e10i | 0.0645148 | + | 0.0372476i | |||||
0 | 0 | |||||||||
−1.35634e10 | − | 2.34925e10i | −0.0447459 | − | 0.0775021i | |||||
3.85768e11 | − | 2.22723e11i | 1.26582 | − | 0.730819i | 0.291622 | − | 0.956533i | ||
0.974194 | + | 0.225714i | ||||||||
0 | 0 | |||||||||
−3.61078e11 | + | 6.25405e11i | −1.17213 | + | 2.03019i | |||||
− | 8.18589e10i | − | 0.264308i | |||||||
0 | 0 | |||||||||
2.59002e10 | 0.0827366 | |||||||||
1.36906e9 | + | 7.90426e8i | 0.00435005 | + | 0.00251151i | |||||
0 | 0 | |||||||||
−2.49914e11 | − | 4.32864e11i | −0.785654 | − | 1.36079i | −0.928608 | − | 0.371063i | ||
0.142954 | − | 0.989729i | ||||||||
−5.02657e9 | + | 2.90209e9i | −0.0157181 | + | 0.00907486i | |||||
0 | 0 | |||||||||
−1.17172e11 | + | 2.02948e11i | −0.362526 | + | 0.627913i | |||||
4.73828e11i | 1.45825i | |||||||||
0 | 0 | |||||||||
4.42799e11 | 1.34841 | 0.674207 | − | 0.738542i | ||||||
0.674207 | + | 0.738542i | ||||||||
2.14517e11 | + | 1.23851e11i | 0.649808 | + | 0.375167i | |||||
0 | 0 | |||||||||
−9.88819e10 | − | 1.71268e11i | −0.296389 | − | 0.513361i | |||||
−4.15275e11 | + | 2.39759e11i | −1.23822 | + | 0.714885i | −0.968730 | − | 0.248119i | ||
−0.269488 | + | 0.963004i | ||||||||
0 | 0 | |||||||||
4.50425e10 | − | 7.80159e10i | 0.132900 | − | 0.230189i | |||||
1.32973e11i | 0.390293i | |||||||||
0 | 0 | |||||||||
−2.60179e11 | −0.755712 | |||||||||
−6.19721e11 | − | 3.57796e11i | −1.79067 | − | 1.03384i | |||||
0 | 0 | |||||||||
1.36289e10 | + | 2.36059e10i | 0.0389722 | + | 0.0675018i | 0.884854 | − | 0.465869i | ||
−0.845881 | + | 0.533371i | ||||||||
−9.91832e10 | + | 5.72635e10i | −0.282147 | + | 0.162898i | |||||
0 | 0 | |||||||||
−1.53364e11 | + | 2.65634e11i | −0.431771 | + | 0.747850i | |||||
− | 2.36838e11i | − | 0.663336i | −0.943396 | − | 0.331668i | ||||
0.943396 | − | 0.331668i | ||||||||
0 | 0 | |||||||||
−2.24728e11 | −0.622945 | |||||||||
−6.07206e10 | − | 3.50571e10i | −0.167452 | − | 0.0966782i | |||||
0 | 0 | |||||||||
−1.12292e11 | − | 1.94496e11i | −0.306501 | − | 0.530875i | |||||
5.63110e11 | − | 3.25112e11i | 1.52913 | − | 0.882842i | |||||
0 | 0 | |||||||||
3.10259e10 | − | 5.37385e10i | 0.0833913 | − | 0.144438i | |||||
− | 1.89831e11i | − | 0.507621i | |||||||
0 | 0 | |||||||||
8.06354e9 | 0.0213433 | |||||||||
1.12795e12 | + | 6.51220e11i | 2.97036 | + | 1.71494i | |||||
0 | 0 | |||||||||
1.75898e11 | + | 3.04664e11i | 0.458523 | + | 0.794185i | 0.998883 | − | 0.0472487i | ||
−0.540360 | + | 0.841434i | ||||||||
1.78553e11 | − | 1.03088e11i | 0.463087 | − | 0.267363i | |||||
0 | 0 | |||||||||
2.24481e11 | − | 3.88813e11i | 0.576330 | − | 0.998234i | |||||
2.40664e11i | 0.614759i | |||||||||
0 | 0 | |||||||||
−4.98134e11 | −1.25966 | |||||||||
2.18298e11 | + | 1.26034e11i | 0.549246 | + | 0.317107i | |||||
0 | 0 | |||||||||
−3.36117e10 | − | 5.82172e10i | −0.0837218 | − | 0.145010i | |||||
1.21936e11 | − | 7.03995e10i | 0.302202 | − | 0.174476i | −0.341230 | − | 0.939980i | ||
0.643432 | + | 0.765504i | ||||||||
0 | 0 | |||||||||
9.66122e9 | − | 1.67337e10i | 0.0237053 | − | 0.0410587i | |||||
− | 1.48169e11i | − | 0.361741i | |||||||
0 | 0 | |||||||||
−2.66093e11 | −0.643186 | |||||||||
1.53334e10 | + | 8.85274e9i | 0.0368787 | + | 0.0212919i | |||||
0 | 0 | |||||||||
4.19701e11 | + | 7.26944e11i | 0.999440 | + | 1.73108i | |||||
−1.23461e11 | + | 7.12801e10i | −0.292542 | + | 0.168899i | |||||
0 | 0 | |||||||||
−3.79274e10 | + | 6.56922e10i | −0.0889832 | + | 0.154123i | |||||
− | 5.70685e10i | − | 0.133230i | −0.997779 | − | 0.0666151i | ||||
0.997779 | − | 0.0666151i | ||||||||
0 | 0 | |||||||||
−5.81519e11 | −1.34425 | −0.672126 | − | 0.740437i | ||||||
−0.672126 | + | 0.740437i | ||||||||
−1.28145e11 | − | 7.39845e10i | −0.294766 | − | 0.170183i | |||||
0 | 0 | |||||||||
−3.35743e9 | − | 5.81523e9i | −0.00764731 | − | 0.0132455i | |||||
−1.04331e12 | + | 6.02356e11i | −2.36474 | + | 1.36528i | |||||
0 | 0 | |||||||||
3.12781e11 | − | 5.41753e11i | 0.702025 | − | 1.21594i | |||||
5.26823e11i | 1.17666i | |||||||||
0 | 0 | |||||||||
7.25231e11 | 1.60406 | |||||||||
−2.88515e11 | − | 1.66574e11i | −0.635031 | − | 0.366636i | 0.147667 | − | 0.989037i | ||
−0.782698 | + | 0.622402i | ||||||||
0 | 0 | |||||||||
4.11950e11 | + | 7.13518e11i | 0.897935 | + | 1.55527i | 0.830129 | + | 0.557571i | ||
0.0678057 | + | 0.997699i | ||||||||
−7.87558e10 | + | 4.54697e10i | −0.170834 | + | 0.0986309i | |||||
0 | 0 | |||||||||
2.25919e11 | − | 3.91303e11i | 0.485325 | − | 0.840608i | |||||
− | 8.92051e11i | − | 1.90708i | −0.301274 | − | 0.953538i | ||||
0.301274 | − | 0.953538i | ||||||||
0 | 0 | |||||||||
−1.53632e11 | −0.325284 | −0.162642 | − | 0.986685i | ||||||
−0.162642 | + | 0.986685i | ||||||||
3.12767e11 | + | 1.80576e11i | 0.659036 | + | 0.380495i | |||||
0 | 0 | |||||||||
−4.69970e10 | − | 8.14011e10i | −0.0980791 | − | 0.169878i | |||||
−2.32475e10 | + | 1.34220e10i | −0.0482833 | + | 0.0278764i | |||||
0 | 0 | |||||||||
−1.49688e11 | + | 2.59268e11i | −0.307923 | + | 0.533338i | |||||
5.94467e10i | 0.121703i | |||||||||
0 | 0 | |||||||||
5.17172e10 | 0.104872 | |||||||||
−2.64665e11 | − | 1.52805e11i | −0.534133 | − | 0.308382i | 0.208565 | − | 0.978009i | ||
−0.742698 | + | 0.669627i | ||||||||
0 | 0 | |||||||||
−1.43334e11 | − | 2.48261e11i | −0.286526 | − | 0.496278i | |||||
−1.29853e11 | + | 7.49706e10i | −0.258347 | + | 0.149157i | |||||
0 | 0 | |||||||||
1.13300e11 | − | 1.96242e11i | 0.223286 | − | 0.386743i | |||||
1.30148e12i | 2.55277i | |||||||||
0 | 0 | |||||||||
−5.01769e11 | −0.974923 | |||||||||
−1.36007e10 | − | 7.85239e9i | −0.0263014 | − | 0.0151851i | |||||
0 | 0 | |||||||||
2.46631e11 | + | 4.27178e11i | 0.472468 | + | 0.818339i | |||||
−4.26216e10 | + | 2.46076e10i | −0.0812665 | + | 0.0469192i | |||||
0 | 0 | |||||||||
−2.22811e11 | + | 3.85919e11i | −0.420862 | + | 0.728955i | −0.996024 | − | 0.0890849i | ||
0.575162 | + | 0.818040i | ||||||||
− | 3.14531e11i | − | 0.591332i | |||||||
0 | 0 | |||||||||
9.15218e8 | 0.00170463 | |||||||||
8.02066e10 | + | 4.63073e10i | 0.148692 | + | 0.0858472i | 0.572500 | − | 0.819905i | ||
−0.423808 | + | 0.905752i | ||||||||
0 | 0 | |||||||||
1.29899e11 | + | 2.24992e11i | 0.238580 | + | 0.413233i | 0.960307 | − | 0.278945i | ||
−0.721727 | + | 0.692178i | ||||||||
6.04247e11 | − | 3.48862e11i | 1.10464 | − | 0.637765i | |||||
0 | 0 | |||||||||
1.49442e11 | − | 2.58841e11i | 0.270672 | − | 0.468817i | |||||
− | 8.28592e10i | − | 0.149382i | −0.997207 | − | 0.0746909i | ||||
0.997207 | − | 0.0746909i | ||||||||
0 | 0 | |||||||||
9.52905e11 | 1.70210 | |||||||||
−4.61173e11 | − | 2.66259e11i | −0.819960 | − | 0.473404i | |||||
0 | 0 | |||||||||
−4.50076e10 | − | 7.79554e10i | −0.0792878 | − | 0.137331i | |||||
−1.16875e11 | + | 6.74778e10i | −0.204947 | + | 0.118326i | |||||
0 | 0 | |||||||||
5.51025e11 | − | 9.54404e11i | 0.957412 | − | 1.65829i | |||||
− | 5.21538e10i | − | 0.0902028i | |||||||
0 | 0 | |||||||||
4.35703e11 | 0.746697 | |||||||||
−9.65834e11 | − | 5.57625e11i | −1.64767 | − | 0.951283i | |||||
0 | 0 | |||||||||
−1.71742e11 | − | 2.97466e11i | −0.290321 | − | 0.502851i | 0.683564 | − | 0.729890i | ||
−0.973886 | + | 0.227039i | ||||||||
3.14758e11 | − | 1.81726e11i | 0.529662 | − | 0.305800i | |||||
0 | 0 | |||||||||
−3.31521e10 | + | 5.74211e10i | −0.0552815 | + | 0.0957504i | |||||
− | 7.74337e11i | − | 1.28537i | −0.766132 | − | 0.642683i | ||||
0.766132 | − | 0.642683i | ||||||||
0 | 0 | |||||||||
−3.73068e11 | −0.613685 | −0.306842 | − | 0.951760i | ||||||
−0.306842 | + | 0.951760i | ||||||||
2.70989e11 | + | 1.56455e11i | 0.443754 | + | 0.256201i | |||||
0 | 0 | |||||||||
−2.84922e11 | − | 4.93499e11i | −0.462371 | − | 0.800850i | |||||
5.41302e11 | − | 3.12521e11i | 0.874471 | − | 0.504876i | 0.00563925 | − | 0.999984i | ||
0.868831 | + | 0.495108i | ||||||||
0 | 0 | |||||||||
4.59395e11 | − | 7.95696e11i | 0.735495 | − | 1.27391i | |||||
− | 7.73184e11i | − | 1.23232i | |||||||
0 | 0 | |||||||||
−6.47075e10 | −0.102210 | |||||||||
3.84075e10 | + | 2.21746e10i | 0.0603963 | + | 0.0348698i | |||||
0 | 0 | |||||||||
−3.40227e11 | − | 5.89291e11i | −0.530245 | − | 0.918412i | |||||
5.13981e10 | − | 2.96747e10i | 0.0797472 | − | 0.0460420i | |||||
0 | 0 | |||||||||
−1.18587e11 | + | 2.05398e11i | −0.182360 | + | 0.315857i | |||||
1.29928e11i | 0.198914i | |||||||||
0 | 0 | |||||||||
5.22820e10 | 0.0793329 | |||||||||
−1.88794e11 | − | 1.09000e11i | −0.285208 | − | 0.164665i | |||||
0 | 0 | |||||||||
6.96649e10 | + | 1.20663e11i | 0.104313 | + | 0.180676i | |||||
1.38956e12 | − | 8.02262e11i | 2.07149 | − | 1.19597i | |||||
0 | 0 | |||||||||
−4.55030e11 | + | 7.88136e11i | −0.672375 | + | 1.16459i | 0.304854 | + | 0.952399i | ||
−0.977229 | + | 0.212188i | ||||||||
− | 9.66022e10i | − | 0.142116i | |||||||
0 | 0 | |||||||||
−1.38364e12 | −2.01771 | |||||||||
−9.63591e10 | − | 5.56330e10i | −0.139901 | − | 0.0807716i | 0.428416 | − | 0.903582i | ||
−0.568317 | + | 0.822810i | ||||||||
0 | 0 | |||||||||
−5.42802e10 | − | 9.40162e10i | −0.0781194 | − | 0.135307i | |||||
−4.45728e11 | + | 2.57341e11i | −0.638683 | + | 0.368744i | |||||
0 | 0 | |||||||||
3.57026e10 | − | 6.18388e10i | 0.0507129 | − | 0.0878373i | |||||
6.36980e11i | 0.900842i | |||||||||
0 | 0 | |||||||||
1.32576e12 | 1.85867 | 0.929333 | − | 0.369243i | ||||||
0.929333 | + | 0.369243i | ||||||||
4.20856e11 | + | 2.42982e11i | 0.587466 | + | 0.339174i | |||||
0 | 0 | |||||||||
2.46202e11 | + | 4.26435e11i | 0.340697 | + | 0.590105i | |||||
6.49235e11 | − | 3.74836e11i | 0.894530 | − | 0.516457i | |||||
0 | 0 | |||||||||
6.39412e10 | − | 1.10749e11i | 0.0873401 | − | 0.151278i | |||||
4.26909e11i | 0.580620i | |||||||||
0 | 0 | |||||||||
−8.56652e10 | −0.115508 | |||||||||
−1.11339e12 | − | 6.42815e11i | −1.49480 | − | 0.863024i | −0.494819 | − | 0.868996i | ||
−0.999982 | + | 0.00597212i | ||||||||
0 | 0 | |||||||||
−3.08063e10 | − | 5.33582e10i | −0.0410054 | − | 0.0710235i | |||||
−3.93696e11 | + | 2.27301e11i | −0.521792 | + | 0.301257i | |||||
0 | 0 | |||||||||
1.09793e11 | − | 1.90167e11i | 0.144274 | − | 0.249890i | |||||
− | 2.20730e11i | − | 0.288812i | |||||||
0 | 0 | |||||||||
−3.48380e11 | −0.451955 | −0.225977 | − | 0.974133i | ||||||
−0.225977 | + | 0.974133i | ||||||||
6.02628e11 | + | 3.47927e11i | 0.778462 | + | 0.449446i | |||||
0 | 0 | |||||||||
2.47326e10 | + | 4.28380e10i | 0.0316780 | + | 0.0548679i | |||||
−7.29969e11 | + | 4.21448e11i | −0.930992 | + | 0.537508i | −0.887125 | − | 0.461529i | ||
−0.0438668 | + | 0.999037i | ||||||||
0 | 0 | |||||||||
−7.98895e11 | + | 1.38373e12i | −1.01028 | + | 1.74986i | |||||
− | 2.61587e11i | − | 0.329403i | |||||||
0 | 0 | |||||||||
−2.09732e11 | −0.261879 | |||||||||
−1.07702e12 | − | 6.21820e11i | −1.33914 | − | 0.773152i | −0.352459 | − | 0.935827i | ||
−0.986680 | + | 0.162675i | ||||||||
0 | 0 | |||||||||
1.06953e11 | + | 1.85248e11i | 0.131865 | + | 0.228397i | |||||
−9.80466e11 | + | 5.66072e11i | −1.20376 | + | 0.694988i | |||||
0 | 0 | |||||||||
−9.87887e10 | + | 1.71107e11i | −0.120271 | + | 0.208315i | |||||
2.58906e11i | 0.313885i | 0.987608 | + | 0.156942i | ||||||
−0.987608 | + | 0.156942i | ||||||||
0 | 0 | |||||||||
1.13324e12 | 1.36241 | |||||||||
−9.87523e10 | − | 5.70146e10i | −0.118227 | − | 0.0682582i | |||||
0 | 0 | |||||||||
7.86385e10 | + | 1.36206e11i | 0.0933626 | + | 0.161709i | |||||
9.23177e11 | − | 5.32996e11i | 1.09147 | − | 0.630159i | |||||
0 | 0 | |||||||||
3.86925e11 | − | 6.70175e11i | 0.453663 | − | 0.785768i | |||||
− | 8.11246e10i | − | 0.0947224i | |||||||
0 | 0 | |||||||||
4.40181e11 | 0.509710 | |||||||||
2.26382e12 | + | 1.30701e12i | 2.61055 | + | 1.50720i | |||||
0 | 0 | |||||||||
−5.06389e11 | − | 8.77092e11i | −0.579133 | − | 1.00309i | −0.995579 | − | 0.0939280i | ||
0.416446 | − | 0.909161i | ||||||||
−2.51575e11 | + | 1.45247e11i | −0.286528 | + | 0.165427i | |||||
0 | 0 | |||||||||
−2.98767e11 | + | 5.17480e11i | −0.337479 | + | 0.584530i | |||||
6.44723e11i | 0.725265i | 0.931932 | + | 0.362632i | ||||||
−0.931932 | + | 0.362632i | ||||||||
0 | 0 | |||||||||
5.17253e11 | 0.577100 | |||||||||
−3.61745e11 | − | 2.08854e11i | −0.401945 | − | 0.232063i | |||||
0 | 0 | |||||||||
−9.10472e10 | − | 1.57698e11i | −0.100338 | − | 0.173791i | |||||
−1.30863e12 | + | 7.55535e11i | −1.43627 | + | 0.829233i | −0.997588 | − | 0.0694077i | ||
−0.438685 | + | 0.898641i | ||||||||
0 | 0 | |||||||||
−1.16207e11 | + | 2.01277e11i | −0.126504 | + | 0.219111i | |||||
− | 6.87200e10i | − | 0.0745039i | |||||||
0 | 0 | |||||||||
7.44546e11 | 0.800655 | |||||||||
9.28316e11 | + | 5.35963e11i | 0.994218 | + | 0.574012i | 0.906532 | − | 0.422136i | ||
0.0876854 | + | 0.996148i | ||||||||
0 | 0 | |||||||||
−8.78546e11 | − | 1.52169e12i | −0.933296 | − | 1.61652i | |||||
2.46976e11 | − | 1.42592e11i | 0.261305 | − | 0.150865i | |||||
0 | 0 | |||||||||
−3.59099e11 | + | 6.21977e11i | −0.376865 | + | 0.652750i | |||||
1.53719e12i | 1.60673i | |||||||||
0 | 0 | |||||||||
−8.67927e11 | −0.899888 | −0.449944 | − | 0.893057i | ||||||
−0.449944 | + | 0.893057i | ||||||||
−4.51314e10 | − | 2.60567e10i | −0.0466050 | − | 0.0269074i | |||||
0 | 0 | |||||||||
2.36678e11 | + | 4.09938e11i | 0.242445 | + | 0.419926i | |||||
−4.96146e11 | + | 2.86450e11i | −0.506194 | + | 0.292251i | |||||
0 | 0 | |||||||||
1.19459e11 | − | 2.06909e11i | 0.120903 | − | 0.209411i | −0.799221 | − | 0.601037i | ||
0.920124 | + | 0.391627i | ||||||||
1.09015e11i | 0.109891i | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 54.9.d.a.35.4 | 16 | ||
3.2 | odd | 2 | 18.9.d.a.11.7 | yes | 16 | ||
4.3 | odd | 2 | 432.9.q.c.305.8 | 16 | |||
9.2 | odd | 6 | 162.9.b.c.161.1 | 16 | |||
9.4 | even | 3 | 18.9.d.a.5.7 | ✓ | 16 | ||
9.5 | odd | 6 | inner | 54.9.d.a.17.4 | 16 | ||
9.7 | even | 3 | 162.9.b.c.161.16 | 16 | |||
12.11 | even | 2 | 144.9.q.b.65.3 | 16 | |||
36.23 | even | 6 | 432.9.q.c.17.8 | 16 | |||
36.31 | odd | 6 | 144.9.q.b.113.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.9.d.a.5.7 | ✓ | 16 | 9.4 | even | 3 | ||
18.9.d.a.11.7 | yes | 16 | 3.2 | odd | 2 | ||
54.9.d.a.17.4 | 16 | 9.5 | odd | 6 | inner | ||
54.9.d.a.35.4 | 16 | 1.1 | even | 1 | trivial | ||
144.9.q.b.65.3 | 16 | 12.11 | even | 2 | |||
144.9.q.b.113.3 | 16 | 36.31 | odd | 6 | |||
162.9.b.c.161.1 | 16 | 9.2 | odd | 6 | |||
162.9.b.c.161.16 | 16 | 9.7 | even | 3 | |||
432.9.q.c.17.8 | 16 | 36.23 | even | 6 | |||
432.9.q.c.305.8 | 16 | 4.3 | odd | 2 |