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 | 35.8 | ||
Root | of defining polynomial | ||
Character | 54.35 | ||
Dual form | 54.9.d.a.17.8 |
-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 | |||||
719.139 | − | 415.195i | 1.15062 | − | 0.664312i | 0.201584 | − | 0.979471i | ||
0.949039 | + | 0.315159i | ||||||||
0 | 0 | |||||||||
1343.41 | − | 2326.85i | 0.559521 | − | 0.969119i | −0.438015 | − | 0.898967i | ||
0.997536 | − | 0.0701513i | ||||||||
1448.15i | 0.353553i | |||||||||
0 | 0 | |||||||||
9394.80 | 0.939480 | |||||||||
−21366.9 | − | 12336.2i | −1.45939 | − | 0.842577i | −0.460405 | − | 0.887709i | ||
−0.998981 | + | 0.0451321i | ||||||||
0 | 0 | |||||||||
−4848.77 | − | 8398.31i | −0.169769 | − | 0.294048i | 0.768570 | − | 0.639766i | ||
−0.938339 | + | 0.345718i | ||||||||
26325.3 | − | 15198.9i | 0.685270 | − | 0.395641i | |||||
0 | 0 | |||||||||
−8192.00 | + | 14189.0i | −0.125000 | + | 0.216506i | |||||
− | 42669.1i | − | 0.510879i | −0.966825 | − | 0.255440i | ||||
0.966825 | − | 0.255440i | ||||||||
0 | 0 | |||||||||
101194. | 0.776499 | 0.388250 | − | 0.921554i | ||||||
0.388250 | + | 0.921554i | ||||||||
92049.8 | + | 53145.0i | 0.575311 | + | 0.332156i | |||||
0 | 0 | |||||||||
−139568. | − | 241739.i | −0.595792 | − | 1.03194i | |||||
396990. | − | 229203.i | 1.41863 | − | 0.819046i | 0.422450 | − | 0.906386i | ||
0.996179 | + | 0.0873406i | ||||||||
0 | 0 | |||||||||
149462. | − | 258875.i | 0.382622 | − | 0.662721i | |||||
− | 109715.i | − | 0.240089i | |||||||
0 | 0 | |||||||||
343913. | 0.559521 | |||||||||
−577159. | − | 333223.i | −0.816025 | − | 0.471132i | 0.0330188 | − | 0.999455i | ||
−0.849044 | + | 0.528322i | ||||||||
0 | 0 | |||||||||
709545. | + | 1.22897e6i | 0.768305 | + | 1.33074i | 0.938482 | + | 0.345329i | ||
−0.170177 | + | 0.985413i | ||||||||
−160530. | + | 92681.9i | −0.153093 | + | 0.0883883i | |||||
0 | 0 | |||||||||
241373. | − | 418071.i | 0.180623 | − | 0.312848i | |||||
− | 2.23111e6i | − | 1.48679i | |||||||
0 | 0 | |||||||||
1.62583e6 | 0.867500 | 0.433750 | − | 0.901033i | ||||||
0.433750 | + | 0.901033i | ||||||||
991496. | + | 572441.i | 0.475507 | + | 0.274534i | |||||
0 | 0 | |||||||||
601267. | + | 1.04142e6i | 0.234870 | + | 0.406807i | |||||
−1.99920e6 | + | 1.15424e6i | −0.707491 | + | 0.408470i | −0.810131 | − | 0.586249i | ||
0.102641 | + | 0.994719i | ||||||||
0 | 0 | |||||||||
812997. | − | 1.40815e6i | 0.237802 | − | 0.411885i | −0.722281 | − | 0.691599i | ||
0.960083 | + | 0.279714i | ||||||||
− | 3.15806e6i | − | 0.842577i | |||||||
0 | 0 | |||||||||
5.18626e6 | 1.15831 | |||||||||
3.38272e6 | + | 1.95301e6i | 0.693226 | + | 0.400234i | 0.804819 | − | 0.593520i | ||
−0.111594 | + | 0.993754i | ||||||||
0 | 0 | |||||||||
−727099. | − | 1.25937e6i | −0.126127 | − | 0.218459i | |||||
2.92884e6 | − | 1.69097e6i | 0.468614 | − | 0.270555i | |||||
0 | 0 | |||||||||
620642. | − | 1.07498e6i | 0.0848844 | − | 0.147024i | |||||
− | 6.96433e6i | − | 0.882624i | −0.897354 | − | 0.441312i | ||||
0.897354 | − | 0.441312i | ||||||||
0 | 0 | |||||||||
−2.04877e7 | −2.23894 | |||||||||
3.36964e6 | + | 1.94547e6i | 0.342635 | + | 0.197821i | |||||
0 | 0 | |||||||||
−3.76999e6 | − | 6.52981e6i | −0.333141 | − | 0.577017i | |||||
−5.94959e6 | + | 3.43500e6i | −0.490997 | + | 0.283477i | −0.724988 | − | 0.688761i | ||
0.233991 | + | 0.972239i | ||||||||
0 | 0 | |||||||||
1.26576e6 | − | 2.19236e6i | 0.0914182 | − | 0.158341i | −0.816690 | − | 0.577077i | ||
0.908108 | + | 0.418736i | ||||||||
1.60552e7i | 1.08655i | |||||||||
0 | 0 | |||||||||
−2.09715e6 | −0.125000 | |||||||||
−6.97388e6 | − | 4.02637e6i | −0.390680 | − | 0.225559i | |||||
0 | 0 | |||||||||
1.58375e7 | + | 2.74313e7i | 0.785936 | + | 1.36128i | 0.928439 | + | 0.371486i | ||
−0.142503 | + | 0.989794i | ||||||||
4.72993e6 | − | 2.73083e6i | 0.221217 | − | 0.127720i | |||||
0 | 0 | |||||||||
1.26211e7 | − | 2.18603e7i | 0.525659 | − | 0.910467i | |||||
1.75496e7i | 0.690612i | 0.938490 | + | 0.345306i | ||||||
−0.938490 | + | 0.345306i | ||||||||
0 | 0 | |||||||||
−2.86971e7 | −1.01052 | −0.505261 | − | 0.862966i | ||||||
−0.505261 | + | 0.862966i | ||||||||
1.59299e7 | + | 9.19711e6i | 0.531233 | + | 0.306707i | |||||
0 | 0 | |||||||||
6.47643e6 | + | 1.12175e7i | 0.194125 | + | 0.336234i | |||||
−5.74089e7 | + | 3.31451e7i | −1.63311 | + | 0.942879i | |||||
0 | 0 | |||||||||
−3.40323e7 | + | 5.89457e7i | −0.873741 | + | 1.51336i | −0.0156441 | + | 0.999878i | ||
−0.858097 | + | 0.513487i | ||||||||
1.36051e7i | 0.332156i | |||||||||
0 | 0 | |||||||||
−2.61174e7 | −0.577664 | |||||||||
−4.73759e7 | − | 2.73525e7i | −0.998263 | − | 0.576347i | −0.0905288 | − | 0.995894i | ||
−0.907734 | + | 0.419547i | ||||||||
0 | 0 | |||||||||
−1.77160e7 | − | 3.06851e7i | −0.339383 | − | 0.587829i | |||||
1.59314e7 | − | 9.19801e6i | 0.291247 | − | 0.168151i | |||||
0 | 0 | |||||||||
1.78647e7 | − | 3.09425e7i | 0.297896 | − | 0.515971i | |||||
7.04968e6i | 0.112359i | 0.998421 | + | 0.0561797i | ||||||
−0.998421 | + | 0.0561797i | ||||||||
0 | 0 | |||||||||
−2.60555e7 | −0.379957 | |||||||||
5.08148e7 | + | 2.93379e7i | 0.709314 | + | 0.409523i | |||||
0 | 0 | |||||||||
2.20958e7 | + | 3.82711e7i | 0.283008 | + | 0.490185i | |||||
7.27727e7 | − | 4.20153e7i | 0.893458 | − | 0.515838i | |||||
0 | 0 | |||||||||
5.14341e7 | − | 8.90865e7i | 0.580984 | − | 1.00629i | −0.414379 | − | 0.910104i | ||
0.995363 | − | 0.0961894i | ||||||||
− | 1.64524e7i | − | 0.178371i | |||||||
0 | 0 | |||||||||
3.82622e7 | 0.382622 | |||||||||
8.11338e7 | + | 4.68426e7i | 0.779680 | + | 0.450148i | 0.836317 | − | 0.548246i | ||
−0.0566370 | + | 0.998395i | ||||||||
0 | 0 | |||||||||
4.68590e7 | + | 8.11622e7i | 0.416336 | + | 0.721116i | 0.995568 | − | 0.0940475i | ||
−0.579231 | + | 0.815163i | ||||||||
1.21621e7 | − | 7.02177e6i | 0.103962 | − | 0.0600224i | |||||
0 | 0 | |||||||||
3.93962e7 | − | 6.82362e7i | 0.312055 | − | 0.540495i | |||||
− | 1.34556e8i | − | 1.02652i | −0.858232 | − | 0.513262i | ||||
0.858232 | − | 0.513262i | ||||||||
0 | 0 | |||||||||
−5.31868e7 | −0.376788 | −0.188394 | − | 0.982093i | ||||||
−0.188394 | + | 0.982093i | ||||||||
−2.00737e8 | − | 1.15896e8i | −1.37106 | − | 0.791584i | |||||
0 | 0 | |||||||||
2.20104e7 | + | 3.81232e7i | 0.139880 | + | 0.242280i | |||||
1.14368e8 | − | 6.60307e7i | 0.701443 | − | 0.404978i | −0.106442 | − | 0.994319i | ||
0.807885 | + | 0.589341i | ||||||||
0 | 0 | |||||||||
1.90328e8 | − | 3.29657e8i | 1.08820 | − | 1.88483i | |||||
− | 8.53051e7i | − | 0.471132i | |||||||
0 | 0 | |||||||||
−7.77251e7 | −0.400897 | |||||||||
−9.92849e7 | − | 5.73222e7i | −0.495103 | − | 0.285848i | |||||
0 | 0 | |||||||||
1.97183e8 | + | 3.41530e8i | 0.919872 | + | 1.59326i | |||||
2.48038e7 | − | 1.43205e7i | 0.111964 | − | 0.0646424i | |||||
0 | 0 | |||||||||
−9.08218e7 | + | 1.57308e8i | −0.384152 | + | 0.665371i | |||||
7.61481e7i | 0.311903i | |||||||||
0 | 0 | |||||||||
5.72307e7 | 0.219996 | 0.109998 | − | 0.993932i | ||||||
0.109998 | + | 0.993932i | ||||||||
−2.05478e7 | − | 1.18633e7i | −0.0765466 | − | 0.0441942i | |||||
0 | 0 | |||||||||
−4.55532e7 | − | 7.89004e7i | −0.159494 | − | 0.276252i | |||||
9.79607e7 | − | 5.65576e7i | 0.332634 | − | 0.192046i | −0.324376 | − | 0.945928i | ||
0.657010 | + | 0.753882i | ||||||||
0 | 0 | |||||||||
1.35945e8 | − | 2.35464e8i | 0.434468 | − | 0.752520i | |||||
3.58361e8i | 1.11148i | |||||||||
0 | 0 | |||||||||
6.17915e7 | 0.180623 | |||||||||
1.19042e8 | + | 6.87289e7i | 0.337923 | + | 0.195100i | 0.659353 | − | 0.751833i | ||
−0.321430 | + | 0.946933i | ||||||||
0 | 0 | |||||||||
−9.70841e7 | − | 1.68155e8i | −0.260069 | − | 0.450453i | 0.706191 | − | 0.708022i | ||
−0.966260 | + | 0.257568i | ||||||||
2.47321e8 | − | 1.42791e8i | 0.643798 | − | 0.371697i | |||||
0 | 0 | |||||||||
−9.92757e7 | + | 1.71950e8i | −0.244168 | + | 0.422912i | |||||
2.39261e8i | 0.572173i | |||||||||
0 | 0 | |||||||||
−5.53410e8 | −1.25192 | |||||||||
−2.81173e8 | − | 1.62335e8i | −0.618816 | − | 0.357274i | |||||
0 | 0 | |||||||||
1.04053e8 | + | 1.80226e8i | 0.216875 | + | 0.375638i | |||||
−6.70921e8 | + | 3.87357e8i | −1.36121 | + | 0.785897i | −0.989786 | − | 0.142564i | ||
−0.371429 | + | 0.928461i | ||||||||
0 | 0 | |||||||||
−3.48071e8 | + | 6.02877e8i | −0.669515 | + | 1.15963i | 0.308525 | + | 0.951216i | ||
−0.978040 | + | 0.208418i | ||||||||
1.46545e8i | 0.274534i | |||||||||
0 | 0 | |||||||||
−7.49987e8 | −1.33343 | |||||||||
1.02052e9 | + | 5.89200e8i | 1.76806 | + | 1.02079i | |||||
0 | 0 | |||||||||
−4.99364e6 | − | 8.64924e6i | −0.00821900 | − | 0.0142357i | 0.861887 | − | 0.507101i | ||
−0.870106 | + | 0.492865i | ||||||||
−6.66894e8 | + | 3.85032e8i | −1.07011 | + | 0.617829i | |||||
0 | 0 | |||||||||
−7.69622e7 | + | 1.33302e8i | −0.117435 | + | 0.203403i | |||||
− | 1.23165e9i | − | 1.83309i | |||||||
0 | 0 | |||||||||
1.22877e9 | 1.74068 | 0.870340 | − | 0.492451i | ||||||
0.870340 | + | 0.492451i | ||||||||
−2.55898e8 | − | 1.47743e8i | −0.353745 | − | 0.204235i | |||||
0 | 0 | |||||||||
−3.09458e8 | − | 5.35997e8i | −0.407539 | − | 0.705878i | |||||
−7.41092e8 | + | 4.27870e8i | −0.952809 | + | 0.550105i | −0.893953 | − | 0.448162i | ||
−0.0588569 | + | 0.998266i | ||||||||
0 | 0 | |||||||||
3.60844e8 | − | 6.25001e8i | 0.442357 | − | 0.766185i | |||||
− | 4.00868e8i | − | 0.479961i | |||||||
0 | 0 | |||||||||
2.08127e8 | 0.237802 | |||||||||
3.96513e8 | + | 2.28927e8i | 0.442663 | + | 0.255572i | 0.704727 | − | 0.709479i | ||
−0.262064 | + | 0.965051i | ||||||||
0 | 0 | |||||||||
−4.01577e8 | − | 6.95551e8i | −0.428170 | − | 0.741612i | |||||
3.50075e8 | − | 2.02116e8i | 0.364846 | − | 0.210644i | |||||
0 | 0 | |||||||||
−3.98790e7 | + | 6.90725e7i | −0.0397250 | + | 0.0688058i | |||||
1.46762e9i | 1.42956i | 0.699350 | + | 0.714779i | ||||||
−0.699350 | + | 0.714779i | ||||||||
0 | 0 | |||||||||
−1.59274e9 | −1.48399 | −0.741993 | − | 0.670408i | ||||||
−0.741993 | + | 0.670408i | ||||||||
−2.55291e8 | − | 1.47392e8i | −0.232675 | − | 0.134335i | |||||
0 | 0 | |||||||||
3.31921e8 | + | 5.74904e8i | 0.289576 | + | 0.501561i | |||||
1.16920e9 | − | 6.75039e8i | 0.998165 | − | 0.576291i | |||||
0 | 0 | |||||||||
−5.26374e8 | + | 9.11706e8i | −0.430455 | + | 0.745570i | |||||
4.99972e8i | 0.400234i | |||||||||
0 | 0 | |||||||||
9.50699e8 | 0.729505 | |||||||||
1.60894e8 | + | 9.28923e7i | 0.120895 | + | 0.0697985i | 0.559228 | − | 0.829014i | ||
−0.438333 | + | 0.898813i | ||||||||
0 | 0 | |||||||||
−5.85324e8 | − | 1.01381e9i | −0.421859 | − | 0.730681i | 0.574262 | − | 0.818671i | ||
−0.996121 | + | 0.0879903i | ||||||||
1.00790e9 | − | 5.81910e8i | 0.711557 | − | 0.410818i | |||||
0 | 0 | |||||||||
9.30687e7 | − | 1.61200e8i | 0.0630637 | − | 0.109230i | |||||
− | 1.90415e9i | − | 1.26426i | −0.774864 | − | 0.632128i | ||||
0.774864 | − | 0.632128i | ||||||||
0 | 0 | |||||||||
1.59363e9 | 1.01619 | 0.508096 | − | 0.861300i | ||||||
0.508096 | + | 0.861300i | ||||||||
3.74891e8 | + | 2.16444e8i | 0.234307 | + | 0.135277i | |||||
0 | 0 | |||||||||
5.29964e8 | + | 9.17924e8i | 0.318303 | + | 0.551317i | |||||
−1.55072e9 | + | 8.95310e8i | −0.913166 | + | 0.527217i | |||||
0 | 0 | |||||||||
−9.58469e8 | + | 1.66012e9i | −0.542703 | + | 0.939990i | |||||
1.06030e9i | 0.588788i | |||||||||
0 | 0 | |||||||||
1.58884e8 | 0.0848844 | |||||||||
−2.16220e9 | − | 1.24835e9i | −1.13321 | − | 0.654260i | |||||
0 | 0 | |||||||||
4.36444e8 | + | 7.55944e8i | 0.220191 | + | 0.381382i | 0.954866 | − | 0.297038i | ||
−0.734675 | + | 0.678419i | ||||||||
7.72004e8 | − | 4.45717e8i | 0.382187 | − | 0.220656i | |||||
0 | 0 | |||||||||
7.61166e8 | − | 1.31838e9i | 0.362931 | − | 0.628615i | |||||
− | 1.35021e9i | − | 0.631899i | |||||||
0 | 0 | |||||||||
3.81284e9 | 1.71953 | |||||||||
−5.21122e8 | − | 3.00870e8i | −0.230735 | − | 0.133215i | |||||
0 | 0 | |||||||||
−1.31121e9 | − | 2.27108e9i | −0.559734 | − | 0.969488i | |||||
−3.58349e8 | + | 2.06893e8i | −0.150223 | + | 0.0867314i | |||||
0 | 0 | |||||||||
1.69943e8 | − | 2.94349e8i | 0.0687199 | − | 0.119026i | −0.829618 | − | 0.558331i | ||
0.898338 | + | 0.439305i | ||||||||
4.98039e8i | 0.197821i | |||||||||
0 | 0 | |||||||||
1.49410e9 | 0.572726 | |||||||||
7.86249e8 | + | 4.53941e8i | 0.296113 | + | 0.170961i | 0.640695 | − | 0.767795i | ||
−0.344583 | + | 0.938756i | ||||||||
0 | 0 | |||||||||
1.91967e7 | + | 3.32497e7i | 0.00698047 | + | 0.0120905i | 0.869495 | − | 0.493943i | ||
−0.862514 | + | 0.506033i | ||||||||
3.72964e9 | − | 2.15331e9i | 1.33277 | − | 0.769477i | |||||
0 | 0 | |||||||||
4.82558e8 | − | 8.35816e8i | 0.166570 | − | 0.288508i | |||||
− | 3.39626e9i | − | 1.15233i | −0.817334 | − | 0.576165i | ||||
0.817334 | − | 0.576165i | ||||||||
0 | 0 | |||||||||
3.24353e9 | 1.06352 | |||||||||
−7.61547e8 | − | 4.39680e8i | −0.245499 | − | 0.141739i | |||||
0 | 0 | |||||||||
−6.48526e8 | − | 1.12328e9i | −0.202125 | − | 0.350090i | |||||
2.60050e8 | − | 1.50140e8i | 0.0797012 | − | 0.0460155i | −0.459620 | − | 0.888116i | ||
0.539321 | + | 0.842100i | ||||||||
0 | 0 | |||||||||
−2.67282e9 | + | 4.62946e9i | −0.792321 | + | 1.37234i | 0.132205 | + | 0.991222i | ||
−0.924526 | + | 0.381119i | ||||||||
4.46173e9i | 1.30089i | |||||||||
0 | 0 | |||||||||
3.24035e8 | 0.0914182 | |||||||||
−1.04577e9 | − | 6.03776e8i | −0.290250 | − | 0.167576i | |||||
0 | 0 | |||||||||
−4.90667e8 | − | 8.49860e8i | −0.131825 | − | 0.228328i | |||||
−1.77974e9 | + | 1.02753e9i | −0.470489 | + | 0.271637i | |||||
0 | 0 | |||||||||
−4.30759e8 | + | 7.46096e8i | −0.110274 | + | 0.191001i | |||||
2.15800e8i | 0.0543696i | 0.999630 | + | 0.0271848i | ||||||
−0.999630 | + | 0.0271848i | ||||||||
0 | 0 | |||||||||
−1.13099e10 | −2.76044 | |||||||||
5.60744e8 | + | 3.23746e8i | 0.134719 | + | 0.0777802i | |||||
0 | 0 | |||||||||
−1.34218e8 | − | 2.32472e8i | −0.0312500 | − | 0.0541266i | |||||
−1.30255e9 | + | 7.52028e8i | −0.298581 | + | 0.172386i | −0.641805 | − | 0.766868i | ||
0.343224 | + | 0.939254i | ||||||||
0 | 0 | |||||||||
2.18416e9 | − | 3.78308e9i | 0.485384 | − | 0.840710i | |||||
− | 1.03075e9i | − | 0.225559i | |||||||
0 | 0 | |||||||||
1.27975e9 | 0.271595 | |||||||||
4.86114e9 | + | 2.80658e9i | 1.01605 | + | 0.586616i | 0.912957 | − | 0.408055i | ||
0.103092 | + | 0.994672i | ||||||||
0 | 0 | |||||||||
−2.89156e9 | − | 5.00832e9i | −0.586338 | − | 1.01557i | |||||
2.66397e9 | − | 1.53804e9i | 0.532112 | − | 0.307215i | |||||
0 | 0 | |||||||||
−2.02720e9 | + | 3.51121e9i | −0.392968 | + | 0.680640i | |||||
5.36842e9i | 1.02527i | 0.858607 | + | 0.512634i | ||||||
−0.858607 | + | 0.512634i | ||||||||
0 | 0 | |||||||||
−3.34972e9 | −0.621056 | −0.310528 | − | 0.950564i | ||||||
−0.310528 | + | 0.950564i | ||||||||
6.05431e8 | + | 3.49546e8i | 0.110609 | + | 0.0638599i | |||||
0 | 0 | |||||||||
7.77578e8 | + | 1.34681e9i | 0.137956 | + | 0.238948i | |||||
−6.38706e9 | + | 3.68757e9i | −1.11679 | + | 0.644777i | |||||
0 | 0 | |||||||||
4.05893e8 | − | 7.03028e8i | 0.0689434 | − | 0.119413i | −0.829493 | − | 0.558517i | ||
0.898436 | + | 0.439104i | ||||||||
− | 2.19676e9i | − | 0.367793i | |||||||
0 | 0 | |||||||||
3.23099e9 | 0.525659 | |||||||||
9.24159e8 | + | 5.33564e8i | 0.148225 | + | 0.0855778i | 0.572278 | − | 0.820060i | ||
−0.424053 | + | 0.905637i | ||||||||
0 | 0 | |||||||||
4.18292e9 | + | 7.24503e9i | 0.652130 | + | 1.12952i | 0.982605 | + | 0.185707i | ||
−0.330475 | + | 0.943815i | ||||||||
−1.94540e9 | + | 1.12318e9i | −0.299044 | + | 0.172653i | |||||
0 | 0 | |||||||||
−1.35346e9 | + | 2.34427e9i | −0.202294 | + | 0.350383i | |||||
6.20246e9i | 0.914190i | |||||||||
0 | 0 | |||||||||
5.15510e9 | 0.739002 | |||||||||
−5.42229e9 | − | 3.13056e9i | −0.766639 | − | 0.442619i | |||||
0 | 0 | |||||||||
−1.83661e9 | − | 3.18111e9i | −0.252631 | − | 0.437569i | |||||
1.17267e9 | − | 6.77039e8i | 0.159112 | − | 0.0918636i | −0.418330 | − | 0.908295i | ||
0.577442 | + | 0.816432i | ||||||||
0 | 0 | |||||||||
−2.85239e9 | + | 4.94048e9i | −0.376635 | + | 0.652351i | |||||
2.35446e9i | 0.306707i | |||||||||
0 | 0 | |||||||||
−8.76488e9 | −1.11143 | |||||||||
−3.84983e9 | − | 2.22270e9i | −0.481678 | − | 0.278097i | |||||
0 | 0 | |||||||||
−2.18438e9 | − | 3.78345e9i | −0.266110 | − | 0.460916i | |||||
−6.82078e9 | + | 3.93798e9i | −0.819985 | + | 0.473419i | |||||
0 | 0 | |||||||||
−8.28983e8 | + | 1.43584e9i | −0.0970624 | + | 0.168117i | |||||
− | 2.10215e9i | − | 0.242921i | |||||||
0 | 0 | |||||||||
3.34624e9 | 0.376707 | 0.188354 | − | 0.982101i | ||||||
0.188354 | + | 0.982101i | ||||||||
−7.34834e9 | − | 4.24257e9i | −0.816557 | − | 0.471439i | |||||
0 | 0 | |||||||||
6.66603e9 | + | 1.15459e10i | 0.721806 | + | 1.25021i | |||||
7.07501e9 | − | 4.08476e9i | 0.756285 | − | 0.436641i | −0.0716755 | − | 0.997428i | ||
0.827960 | + | 0.560787i | ||||||||
0 | 0 | |||||||||
6.49273e9 | − | 1.12457e10i | 0.676472 | − | 1.17168i | −0.299564 | − | 0.954076i | ||
0.976036 | − | 0.217608i | ||||||||
− | 1.12993e8i | − | 0.0116234i | |||||||
0 | 0 | |||||||||
−8.71227e9 | −0.873741 | |||||||||
2.27583e9 | + | 1.31395e9i | 0.225374 | + | 0.130120i | 0.608436 | − | 0.793603i | ||
−0.383062 | + | 0.923723i | ||||||||
0 | 0 | |||||||||
8.22139e9 | + | 1.42399e10i | 0.793930 | + | 1.37513i | |||||
−1.50814e9 | + | 8.70728e8i | −0.143828 | + | 0.0830391i | |||||
0 | 0 | |||||||||
6.96727e9 | − | 1.20677e10i | 0.648096 | − | 1.12254i | |||||
− | 4.31787e9i | − | 0.396697i | |||||||
0 | 0 | |||||||||
−2.89882e9 | −0.259829 | |||||||||
1.20394e10 | + | 6.95095e9i | 1.06594 | + | 0.615423i | |||||
0 | 0 | |||||||||
−1.67152e9 | − | 2.89515e9i | −0.144416 | − | 0.250136i | |||||
9.08876e9 | − | 5.24740e9i | 0.775749 | − | 0.447879i | |||||
0 | 0 | |||||||||
5.38121e9 | − | 9.32053e9i | 0.448299 | − | 0.776477i | −0.549976 | − | 0.835180i | ||
0.998275 | + | 0.0587032i | ||||||||
− | 7.00223e9i | − | 0.576347i | |||||||
0 | 0 | |||||||||
−9.68158e9 | −0.777966 | |||||||||
2.27787e10 | + | 1.31513e10i | 1.80863 | + | 1.04421i | |||||
0 | 0 | |||||||||
−6.49324e9 | − | 1.12466e10i | −0.503433 | − | 0.871972i | −0.999992 | − | 0.00396864i | ||
0.496559 | − | 0.868003i | ||||||||
7.07107e9 | − | 4.08249e9i | 0.541775 | − | 0.312794i | |||||
0 | 0 | |||||||||
2.26765e9 | − | 3.92769e9i | 0.169692 | − | 0.293915i | |||||
− | 3.50123e10i | − | 2.58942i | |||||||
0 | 0 | |||||||||
1.15818e10 | 0.836758 | |||||||||
2.03922e9 | + | 1.17735e9i | 0.145623 | + | 0.0840757i | |||||
0 | 0 | |||||||||
2.59001e9 | + | 4.48603e9i | 0.180716 | + | 0.313010i | |||||
−2.11272e9 | + | 1.21978e9i | −0.145722 | + | 0.0841324i | −0.571088 | − | 0.820889i | ||
0.425366 | + | 0.905021i | ||||||||
0 | 0 | |||||||||
1.08992e10 | − | 1.88779e10i | 0.734669 | − | 1.27248i | −0.220200 | − | 0.975455i | ||
0.954869 | − | 0.297029i | ||||||||
− | 9.08664e9i | − | 0.605524i | |||||||
0 | 0 | |||||||||
4.57336e9 | 0.297896 | |||||||||
−1.22820e10 | − | 7.09100e9i | −0.790987 | − | 0.456677i | 0.0493227 | − | 0.998783i | ||
−0.840310 | + | 0.542106i | ||||||||
0 | 0 | |||||||||
7.28652e9 | + | 1.26206e10i | 0.458782 | + | 0.794634i | |||||
−7.81466e8 | + | 4.51180e8i | −0.0486530 | + | 0.0280898i | |||||
0 | 0 | |||||||||
−8.30212e9 | + | 1.43797e10i | −0.505425 | + | 0.875422i | |||||
1.62366e10i | 0.977499i | 0.872424 | + | 0.488750i | ||||||
−0.872424 | + | 0.488750i | ||||||||
0 | 0 | |||||||||
−6.74331e9 | −0.397049 | |||||||||
−1.56056e10 | − | 9.00988e9i | −0.908752 | − | 0.524668i | |||||
0 | 0 | |||||||||
−1.66755e9 | − | 2.88829e9i | −0.0949892 | − | 0.164526i | |||||
−2.06372e10 | + | 1.19149e10i | −1.16273 | + | 0.671303i | |||||
0 | 0 | |||||||||
4.72220e9 | − | 8.17909e9i | 0.260303 | − | 0.450859i | −0.706019 | − | 0.708193i | ||
0.966323 | + | 0.257334i | ||||||||
7.51051e9i | 0.409523i | |||||||||
0 | 0 | |||||||||
1.52744e10 | 0.814998 | |||||||||
−1.62050e10 | − | 9.35595e9i | −0.855367 | − | 0.493847i | |||||
0 | 0 | |||||||||
6.87407e9 | + | 1.19062e10i | 0.355123 | + | 0.615091i | 0.987139 | − | 0.159864i | ||
−0.632016 | + | 0.774955i | ||||||||
−1.03148e10 | + | 5.95524e9i | −0.527198 | + | 0.304378i | |||||
0 | 0 | |||||||||
−2.82827e9 | + | 4.89870e9i | −0.141504 | + | 0.245092i | |||||
6.46288e9i | 0.319934i | |||||||||
0 | 0 | |||||||||
−8.10058e9 | −0.392608 | −0.196304 | − | 0.980543i | ||||||
−0.196304 | + | 0.980543i | ||||||||
9.31490e9 | + | 5.37796e9i | 0.446729 | + | 0.257919i | |||||
0 | 0 | |||||||||
1.05096e9 | + | 1.82031e9i | 0.0493550 | + | 0.0854854i | |||||
3.26313e10 | − | 1.88397e10i | 1.51649 | − | 0.875544i | 0.516675 | − | 0.856182i | ||
0.999813 | − | 0.0193625i | ||||||||
0 | 0 | |||||||||
−2.75233e10 | + | 4.76718e10i | −1.25273 | + | 2.16980i | |||||
− | 1.32444e10i | − | 0.596599i | |||||||
0 | 0 | |||||||||
1.31671e10 | 0.580984 | |||||||||
7.44708e9 | + | 4.29957e9i | 0.325228 | + | 0.187770i | 0.653720 | − | 0.756736i | ||
−0.328493 | + | 0.944507i | ||||||||
0 | 0 | |||||||||
−9.77988e9 | − | 1.69392e10i | −0.418433 | − | 0.724748i | |||||
1.82377e9 | − | 1.05295e9i | 0.0772369 | − | 0.0445928i | |||||
0 | 0 | |||||||||
1.07715e10 | − | 1.86567e10i | 0.446982 | − | 0.774196i | |||||
5.65202e10i | 2.32175i | |||||||||
0 | 0 | |||||||||
−7.53858e9 | −0.303478 | −0.151739 | − | 0.988421i | ||||||
−0.151739 | + | 0.988421i | ||||||||
1.56144e10 | + | 9.01495e9i | 0.622289 | + | 0.359278i | |||||
0 | 0 | |||||||||
2.44878e9 | + | 4.24141e9i | 0.0956555 | + | 0.165680i | |||||
2.42910e9 | − | 1.40244e9i | 0.0939436 | − | 0.0542384i | −0.452292 | − | 0.891870i | ||
0.546236 | + | 0.837631i | ||||||||
0 | 0 | |||||||||
6.88084e9 | − | 1.19180e10i | 0.260868 | − | 0.451837i | |||||
1.19917e10i | 0.450148i | |||||||||
0 | 0 | |||||||||
−2.02585e10 | −0.745597 | |||||||||
−3.47390e10 | − | 2.00566e10i | −1.26602 | − | 0.730935i | |||||
0 | 0 | |||||||||
4.31779e9 | + | 7.47864e9i | 0.154301 | + | 0.267257i | 0.932804 | − | 0.360383i | ||
−0.778503 | + | 0.627641i | ||||||||
−1.87821e10 | + | 1.08438e10i | −0.664673 | + | 0.383749i | |||||
0 | 0 | |||||||||
−5.99795e9 | + | 1.03888e10i | −0.208168 | + | 0.360558i | |||||
1.84584e10i | 0.634446i | |||||||||
0 | 0 | |||||||||
−4.54265e10 | −1.53150 | |||||||||
1.55674e9 | + | 8.98786e8i | 0.0519809 | + | 0.0300112i | |||||
0 | 0 | |||||||||
−1.41234e10 | − | 2.44625e10i | −0.462632 | − | 0.801302i | |||||
−2.20697e10 | + | 1.27420e10i | −0.716046 | + | 0.413409i | −0.813296 | − | 0.581851i | ||
0.0972497 | + | 0.995260i | ||||||||
0 | 0 | |||||||||
7.22114e7 | − | 1.25074e8i | 0.00229867 | − | 0.00398142i | −0.864874 | − | 0.501989i | ||
0.867172 | + | 0.498008i | ||||||||
9.87561e9i | 0.311397i | |||||||||
0 | 0 | |||||||||
1.00854e10 | 0.312055 | |||||||||
−1.10460e10 | − | 6.37740e9i | −0.338570 | − | 0.195474i | |||||
0 | 0 | |||||||||
−3.40087e9 | − | 5.89049e9i | −0.102301 | − | 0.177190i | |||||
1.49157e10 | − | 8.61161e9i | 0.444498 | − | 0.256631i | |||||
0 | 0 | |||||||||
7.63794e9 | − | 1.32293e10i | 0.223410 | − | 0.386957i | |||||
− | 6.31640e9i | − | 0.183046i | −0.995803 | − | 0.0915231i | ||||
0.995803 | − | 0.0915231i | ||||||||
0 | 0 | |||||||||
−3.96241e10 | −1.12722 | −0.563609 | − | 0.826042i | ||||||
−0.563609 | + | 0.826042i | ||||||||
3.73581e10 | + | 2.15687e10i | 1.05299 | + | 0.607946i | |||||
0 | 0 | |||||||||
−3.40395e9 | − | 5.89582e9i | −0.0941971 | − | 0.163154i | |||||
4.01731e10 | − | 2.31940e10i | 1.10156 | − | 0.635988i | |||||
0 | 0 | |||||||||
−1.57438e10 | + | 2.72691e10i | −0.423889 | + | 0.734196i | −0.996316 | − | 0.0857589i | ||
0.572427 | + | 0.819955i | ||||||||
− | 2.96693e10i | − | 0.791584i | |||||||
0 | 0 | |||||||||
−4.68145e9 | −0.122657 | |||||||||
−3.86111e10 | − | 2.22921e10i | −1.00253 | − | 0.578810i | −0.0935330 | − | 0.995616i | ||
−0.908995 | + | 0.416806i | ||||||||
0 | 0 | |||||||||
2.92699e9 | + | 5.06970e9i | 0.0746417 | + | 0.129283i | |||||
3.33018e9 | − | 1.92268e9i | 0.0841644 | − | 0.0485923i | |||||
0 | 0 | |||||||||
−2.81733e9 | + | 4.87977e9i | −0.0699401 | + | 0.121140i | |||||
2.35548e10i | 0.579553i | 0.957094 | + | 0.289777i | ||||||
−0.957094 | + | 0.289777i | ||||||||
0 | 0 | |||||||||
5.69555e10 | 1.37667 | |||||||||
1.46392e10 | + | 8.45192e9i | 0.350722 | + | 0.202489i | |||||
0 | 0 | |||||||||
5.13576e9 | + | 8.89540e9i | 0.120887 | + | 0.209383i | |||||
−1.87376e10 | + | 1.08181e10i | −0.437187 | + | 0.252410i | |||||
0 | 0 | |||||||||
−2.05058e10 | + | 3.55170e10i | −0.470122 | + | 0.814276i | −0.999416 | − | 0.0341626i | ||
0.529294 | + | 0.848439i | ||||||||
4.34372e8i | 0.00987188i | |||||||||
0 | 0 | |||||||||
4.87239e10 | 1.08820 | |||||||||
3.37174e9 | + | 1.94668e9i | 0.0746536 | + | 0.0431013i | 0.536862 | − | 0.843670i | ||
−0.462209 | + | 0.886771i | ||||||||
0 | 0 | |||||||||
−2.67932e10 | − | 4.64073e10i | −0.583044 | − | 1.00986i | −0.995116 | − | 0.0987107i | ||
0.412072 | − | 0.911151i | ||||||||
9.45617e9 | − | 5.45952e9i | 0.204006 | − | 0.117783i | |||||
0 | 0 | |||||||||
1.92121e10 | − | 3.32764e10i | 0.407410 | − | 0.705655i | |||||
− | 4.53162e10i | − | 0.952766i | −0.879238 | − | 0.476383i | ||||
0.879238 | − | 0.476383i | ||||||||
0 | 0 | |||||||||
8.51049e10 | 1.75899 | |||||||||
3.17800e10 | + | 1.83482e10i | 0.651272 | + | 0.376012i | |||||
0 | 0 | |||||||||
−4.97441e9 | − | 8.61593e9i | −0.100224 | − | 0.173594i | |||||
−3.47424e10 | + | 2.00585e10i | −0.694089 | + | 0.400733i | |||||
0 | 0 | |||||||||
1.51247e10 | − | 2.61967e10i | 0.297106 | − | 0.514602i | |||||
− | 1.46745e10i | − | 0.285848i | |||||||
0 | 0 | |||||||||
3.39728e9 | 0.0650758 | |||||||||
−4.92416e9 | − | 2.84297e9i | −0.0935385 | − | 0.0540045i | 0.452501 | − | 0.891764i | ||
−0.546040 | + | 0.837759i | ||||||||
0 | 0 | |||||||||
−7.88329e9 | − | 1.36543e10i | −0.147274 | − | 0.255087i | |||||
−5.23763e10 | + | 3.02395e10i | −0.970392 | + | 0.560256i | |||||
0 | 0 | |||||||||
−2.52394e10 | + | 4.37159e10i | −0.459936 | + | 0.796632i | |||||
− | 8.54208e10i | − | 1.54382i | |||||||
0 | 0 | |||||||||
3.64760e10 | 0.648472 | 0.324236 | − | 0.945976i | ||||||
0.324236 | + | 0.945976i | ||||||||
3.17488e9 | + | 1.83302e9i | 0.0559820 | + | 0.0323212i | |||||
0 | 0 | |||||||||
−6.83095e9 | − | 1.18316e10i | −0.118494 | − | 0.205238i | |||||
5.07409e10 | − | 2.92952e10i | 0.873035 | − | 0.504047i | 0.00467962 | − | 0.999989i | ||
0.868356 | + | 0.495942i | ||||||||
0 | 0 | |||||||||
−1.42183e10 | + | 2.46269e10i | −0.240692 | + | 0.416890i | |||||
− | 1.11025e10i | − | 0.186429i | |||||||
0 | 0 | |||||||||
−2.32504e10 | −0.384152 | |||||||||
4.08354e10 | + | 2.35763e10i | 0.669285 | + | 0.386412i | |||||
0 | 0 | |||||||||
3.18425e10 | + | 5.51528e10i | 0.513576 | + | 0.889541i | 0.999876 | + | 0.0157483i | ||
−0.486300 | + | 0.873792i | ||||||||
−8.44112e9 | + | 4.87348e9i | −0.135058 | + | 0.0779757i | |||||
0 | 0 | |||||||||
−1.22075e9 | + | 2.11440e9i | −0.0192225 | + | 0.0332944i | |||||
− | 1.09134e10i | − | 0.170486i | −0.996360 | − | 0.0852430i | ||||
0.996360 | − | 0.0852430i | ||||||||
0 | 0 | |||||||||
7.77953e10 | 1.19616 | |||||||||
−1.10814e11 | − | 6.39786e10i | −1.69041 | − | 0.975961i | |||||
0 | 0 | |||||||||
3.66277e9 | + | 6.34410e9i | 0.0549989 | + | 0.0952609i | |||||
9.71431e9 | − | 5.60856e9i | 0.144724 | − | 0.0835565i | −0.425889 | − | 0.904775i | ||
0.570614 | + | 0.821219i | ||||||||
0 | 0 | |||||||||
−3.85519e10 | + | 6.67739e10i | −0.565409 | + | 0.979316i | |||||
− | 3.03700e9i | − | 0.0441942i | |||||||
0 | 0 | |||||||||
−1.70165e10 | −0.243790 | |||||||||
6.73963e10 | + | 3.89113e10i | 0.958092 | + | 0.553155i | |||||
0 | 0 | |||||||||
−4.81854e10 | − | 8.34596e10i | −0.674456 | − | 1.16819i | |||||
4.28006e10 | − | 2.47110e10i | 0.594472 | − | 0.343218i | |||||
0 | 0 | |||||||||
5.83081e9 | − | 1.00993e10i | 0.0797472 | − | 0.138126i | |||||
1.03375e11i | 1.40302i | 0.712658 | + | 0.701511i | ||||||
−0.712658 | + | 0.701511i | ||||||||
0 | 0 | |||||||||
−6.50405e10 | −0.869314 | −0.434657 | − | 0.900596i | ||||||
−0.434657 | + | 0.900596i | ||||||||
1.25390e10 | + | 7.23938e9i | 0.166317 | + | 0.0960232i | |||||
0 | 0 | |||||||||
3.17528e10 | + | 5.49975e10i | 0.414800 | + | 0.718456i | |||||
5.24390e10 | − | 3.02757e10i | 0.679849 | − | 0.392511i | |||||
0 | 0 | |||||||||
6.59121e10 | − | 1.14163e11i | 0.841671 | − | 1.45782i | |||||
− | 6.54284e10i | − | 0.829207i | |||||||
0 | 0 | |||||||||
3.48020e10 | 0.434468 | |||||||||
1.93873e10 | + | 1.11933e10i | 0.240220 | + | 0.138691i | |||||
0 | 0 | |||||||||
−5.58672e10 | − | 9.67648e10i | −0.681933 | − | 1.18114i | |||||
−3.97248e10 | + | 2.29351e10i | −0.481285 | + | 0.277870i | |||||
0 | 0 | |||||||||
−3.03684e10 | + | 5.25995e10i | −0.362487 | + | 0.627845i | |||||
3.58785e10i | 0.425088i | |||||||||
0 | 0 | |||||||||
9.26356e10 | 1.08141 | 0.540703 | − | 0.841214i | ||||||
0.540703 | + | 0.841214i | ||||||||
−3.28204e10 | − | 1.89489e10i | −0.380318 | − | 0.219577i | |||||
0 | 0 | |||||||||
3.95466e9 | + | 6.84967e9i | 0.0451558 | + | 0.0782121i | |||||
−3.82487e10 | + | 2.20829e10i | −0.433541 | + | 0.250305i | |||||
0 | 0 | |||||||||
−6.17442e9 | + | 1.06944e10i | −0.0689679 | + | 0.119456i | −0.898447 | − | 0.439081i | ||
0.829479 | + | 0.558537i | ||||||||
1.75946e10i | 0.195100i | |||||||||
0 | 0 | |||||||||
−8.34402e10 | −0.911852 | |||||||||
−5.84051e10 | − | 3.37202e10i | −0.633643 | − | 0.365834i | |||||
0 | 0 | |||||||||
9.14387e10 | + | 1.58376e11i | 0.977753 | + | 1.69352i | |||||
7.95385e9 | − | 4.59216e9i | 0.0844381 | − | 0.0487503i | |||||
0 | 0 | |||||||||
1.24268e10 | − | 2.15238e10i | 0.130035 | − | 0.225227i | |||||
1.17871e9i | 0.0122458i | 0.999981 | + | 0.00612290i | ||||||
−0.999981 | + | 0.00612290i | ||||||||
0 | 0 | |||||||||
−1.57681e10 | −0.161485 | |||||||||
3.16571e10 | + | 1.82772e10i | 0.321899 | + | 0.185848i | |||||
0 | 0 | |||||||||
6.03658e9 | + | 1.04557e10i | 0.0605126 | + | 0.104811i | |||||
4.60975e10 | − | 2.66144e10i | 0.458822 | − | 0.264901i | −0.252727 | − | 0.967538i | ||
0.711549 | + | 0.702637i | ||||||||
0 | 0 | |||||||||
5.48312e10 | − | 9.49705e10i | 0.538064 | − | 0.931955i | |||||
9.46487e10i | 0.922251i | |||||||||
0 | 0 | |||||||||
−2.54146e10 | −0.244168 | |||||||||
7.89230e9 | + | 4.55662e9i | 0.0752930 | + | 0.0434704i | 0.537174 | − | 0.843472i | ||
−0.461881 | + | 0.886942i | ||||||||
0 | 0 | |||||||||
−8.93207e10 | − | 1.54708e11i | −0.840248 | − | 1.45535i | −0.889685 | − | 0.456575i | ||
0.0494367 | − | 0.998777i | ||||||||
−2.65224e10 | + | 1.53127e10i | −0.247758 | + | 0.143043i | |||||
0 | 0 | |||||||||
−3.50864e10 | + | 6.07715e10i | −0.323215 | + | 0.559825i | |||||
− | 1.37028e11i | − | 1.25354i | |||||||
0 | 0 | |||||||||
−1.57035e11 | −1.41675 | −0.708374 | − | 0.705837i | ||||||
−0.708374 | + | 0.705837i | ||||||||
5.05095e10 | + | 2.91617e10i | 0.452545 | + | 0.261277i | |||||
0 | 0 | |||||||||
−3.54183e10 | − | 6.13462e10i | −0.312979 | − | 0.542096i | |||||
−1.27290e11 | + | 7.34911e10i | −1.11710 | + | 0.644957i | |||||
0 | 0 | |||||||||
−8.59131e10 | + | 1.48806e11i | −0.743679 | + | 1.28809i | |||||
− | 4.15578e10i | − | 0.357274i | |||||||
0 | 0 | |||||||||
1.53197e10 | 0.129915 | |||||||||
−7.02172e10 | − | 4.05399e10i | −0.591413 | − | 0.341452i | 0.174243 | − | 0.984703i | ||
−0.765656 | + | 0.643250i | ||||||||
0 | 0 | |||||||||
7.18018e10 | + | 1.24364e11i | 0.596588 | + | 1.03332i | |||||
−5.58952e10 | + | 3.22711e10i | −0.461282 | + | 0.266321i | |||||
0 | 0 | |||||||||
−1.33188e10 | + | 2.30689e10i | −0.108437 | + | 0.187819i | |||||
2.32095e11i | 1.87693i | 0.345379 | + | 0.938463i | ||||||
−0.345379 | + | 0.938463i | ||||||||
0 | 0 | |||||||||
−9.51995e10 | −0.759569 | |||||||||
−8.58779e10 | − | 4.95816e10i | −0.680607 | − | 0.392949i | |||||
0 | 0 | |||||||||
−2.51470e10 | − | 4.35558e10i | −0.196644 | − | 0.340598i | |||||
6.67859e9 | − | 3.85589e9i | 0.0518773 | − | 0.0299514i | −0.473837 | − | 0.880613i | ||
0.525714 | + | 0.850661i | ||||||||
0 | 0 | |||||||||
8.64971e10 | − | 1.49817e11i | 0.662985 | − | 1.14832i | −0.316842 | − | 0.948478i | ||
0.979827 | − | 0.199846i | ||||||||
− | 4.94268e10i | − | 0.376337i | |||||||
0 | 0 | |||||||||
−8.91062e10 | −0.669515 | |||||||||
2.83604e11 | + | 1.63739e11i | 2.11685 | + | 1.22216i | |||||
0 | 0 | |||||||||
6.33224e10 | + | 1.09678e11i | 0.466448 | + | 0.807911i | 0.999266 | − | 0.0383189i | ||
−0.532818 | + | 0.846230i | ||||||||
−1.62447e10 | + | 9.37887e9i | −0.118877 | + | 0.0686335i | |||||
0 | 0 | |||||||||
1.18916e10 | − | 2.05968e10i | 0.0858855 | − | 0.148758i | |||||
− | 3.78789e10i | − | 0.271789i | |||||||
0 | 0 | |||||||||
−1.90947e11 | −1.35230 | −0.676148 | − | 0.736765i | ||||||
−0.676148 | + | 0.736765i | ||||||||
3.27863e10 | + | 1.89292e10i | 0.230685 | + | 0.133186i | |||||
0 | 0 | |||||||||
−4.79992e10 | − | 8.31370e10i | −0.333358 | − | 0.577393i | |||||
−3.94255e10 | + | 2.27623e10i | −0.272043 | + | 0.157064i | −0.629816 | − | 0.776745i | ||
0.357773 | + | 0.933809i | ||||||||
0 | 0 | |||||||||
2.52527e10 | − | 4.37390e10i | 0.172007 | − | 0.297925i | −0.767114 | − | 0.641510i | ||
0.939121 | + | 0.343585i | ||||||||
1.50835e11i | 1.02079i | |||||||||
0 | 0 | |||||||||
9.24275e10 | 0.617504 | |||||||||
1.64036e10 | + | 9.47061e9i | 0.108890 | + | 0.0628674i | |||||
0 | 0 | |||||||||
8.99998e10 | + | 1.55884e11i | 0.589823 | + | 1.02160i | |||||
1.27231e11 | − | 7.34569e10i | 0.828506 | − | 0.478338i | |||||
0 | 0 | |||||||||
6.39186e8 | − | 1.10710e9i | 0.00410950 | − | 0.00711786i | |||||
− | 6.93730e10i | − | 0.443188i | |||||||
0 | 0 | |||||||||
7.46120e10 | 0.470642 | 0.235321 | − | 0.971918i | ||||||
0.235321 | + | 0.971918i | ||||||||
−8.53625e10 | − | 4.92840e10i | −0.535055 | − | 0.308914i | |||||
0 | 0 | |||||||||
1.48657e10 | + | 2.57481e10i | 0.0920085 | + | 0.159363i | |||||
4.11568e10 | − | 2.37619e10i | 0.253132 | − | 0.146146i | |||||
0 | 0 | |||||||||
−7.05107e9 | + | 1.22128e10i | −0.0428250 | + | 0.0741751i | |||||
1.86029e11i | 1.12279i | |||||||||
0 | 0 | |||||||||
−1.97023e10 | −0.117435 | |||||||||
−2.44739e11 | − | 1.41300e11i | −1.44968 | − | 0.836972i | −0.451215 | − | 0.892415i | ||
−0.998462 | + | 0.0554435i | ||||||||
0 | 0 | |||||||||
8.57408e10 | + | 1.48507e11i | 0.501584 | + | 0.868769i | 0.999998 | + | 0.00183012i | ||
−0.498414 | + | 0.866939i | ||||||||
1.36530e11 | − | 7.88257e10i | 0.793752 | − | 0.458273i | |||||
0 | 0 | |||||||||
2.44256e10 | − | 4.23063e10i | 0.140254 | − | 0.242927i | |||||
6.51359e10i | 0.371709i | 0.982577 | + | 0.185855i | ||||||
−0.982577 | + | 0.185855i | ||||||||
0 | 0 | |||||||||
1.69499e11 | 0.955406 | |||||||||
−2.84025e10 | − | 1.63982e10i | −0.159112 | − | 0.0918635i | |||||
0 | 0 | |||||||||
7.86411e10 | + | 1.36210e11i | 0.435170 | + | 0.753737i | |||||
−2.27135e10 | + | 1.31137e10i | −0.124920 | + | 0.0721226i | −0.561158 | − | 0.827709i | ||
0.436238 | + | 0.899831i | ||||||||
0 | 0 | |||||||||
4.69649e10 | − | 8.13456e10i | 0.255158 | − | 0.441946i | |||||
− | 3.78221e10i | − | 0.204235i | |||||||
0 | 0 | |||||||||
1.18735e11 | 0.633396 | |||||||||
−2.34946e11 | − | 1.35646e11i | −1.24574 | − | 0.719228i | −0.275483 | − | 0.961306i | ||
−0.970257 | + | 0.242078i | ||||||||
0 | 0 | |||||||||
−1.12700e11 | − | 1.95203e11i | −0.590364 | − | 1.02254i | −0.994183 | − | 0.107702i | ||
0.403819 | − | 0.914839i | ||||||||
1.05450e11 | − | 6.08815e10i | 0.549052 | − | 0.316995i | |||||
0 | 0 | |||||||||
3.96106e10 | − | 6.86076e10i | 0.203769 | − | 0.352939i | |||||
− | 2.25775e11i | − | 1.15449i | |||||||
0 | 0 | |||||||||
−3.05502e11 | −1.54352 | |||||||||
−9.48597e10 | − | 5.47673e10i | −0.476405 | − | 0.275052i | |||||
0 | 0 | |||||||||
1.48790e11 | + | 2.57712e11i | 0.738370 | + | 1.27890i | |||||
−5.40907e10 | + | 3.12293e10i | −0.266829 | + | 0.154054i | |||||
0 | 0 | |||||||||
−7.58538e10 | + | 1.31383e11i | −0.369757 | + | 0.640439i | −0.989527 | − | 0.144345i | ||
0.619770 | + | 0.784784i | ||||||||
− | 1.46925e11i | − | 0.711962i | |||||||
0 | 0 | |||||||||
9.23761e10 | 0.442357 | |||||||||
2.20192e11 | + | 1.27128e11i | 1.04821 | + | 0.605183i | 0.922147 | − | 0.386839i | ||
0.126061 | + | 0.992023i | ||||||||
0 | 0 | |||||||||
−1.38194e11 | − | 2.39359e11i | −0.650145 | − | 1.12608i | |||||
4.44367e10 | − | 2.56555e10i | 0.207829 | − | 0.119990i | |||||
0 | 0 | |||||||||
1.98059e11 | − | 3.43049e11i | 0.915499 | − | 1.58569i | |||||
− | 2.98251e11i | − | 1.37056i | −0.728279 | − | 0.685281i | ||||
0.728279 | − | 0.685281i | ||||||||
0 | 0 | |||||||||
1.14144e11 | 0.518429 | |||||||||
1.13478e11 | + | 6.55166e10i | 0.512408 | + | 0.295839i | |||||
0 | 0 | |||||||||
1.33201e10 | + | 2.30712e10i | 0.0594505 | + | 0.102971i | |||||
−5.84886e10 | + | 3.37684e10i | −0.259534 | + | 0.149842i | |||||
0 | 0 | |||||||||
1.50423e11 | − | 2.60541e11i | 0.659785 | − | 1.14278i | −0.320886 | − | 0.947118i | ||
0.980671 | − | 0.195663i | ||||||||
5.86053e10i | 0.255572i | |||||||||
0 | 0 | |||||||||
−2.76005e10 | −0.118981 | |||||||||
−1.39634e11 | − | 8.06177e10i | −0.598483 | − | 0.345534i | |||||
0 | 0 | |||||||||
4.92504e10 | + | 8.53041e10i | 0.208679 | + | 0.361442i | |||||
2.13579e11 | − | 1.23310e11i | 0.899782 | − | 0.519489i | |||||
0 | 0 | |||||||||
5.14018e10 | − | 8.90305e10i | 0.214085 | − | 0.370806i | |||||
− | 2.33302e11i | − | 0.966156i | −0.875577 | − | 0.483078i | ||||
0.875577 | − | 0.483078i | ||||||||
0 | 0 | |||||||||
1.64525e11 | 0.673613 | |||||||||
4.48096e10 | + | 2.58708e10i | 0.182423 | + | 0.105322i | |||||
0 | 0 | |||||||||
−8.02255e10 | − | 1.38955e11i | −0.322919 | − | 0.559312i | |||||
2.17992e11 | − | 1.25858e11i | 0.872494 | − | 0.503735i | |||||
0 | 0 | |||||||||
−1.36103e11 | + | 2.35737e11i | −0.538620 | + | 0.932918i | 0.460358 | + | 0.887733i | ||
−0.998979 | + | 0.0451845i | ||||||||
1.64875e11i | 0.648816i | |||||||||
0 | 0 | |||||||||
−1.02090e10 | −0.0397250 | |||||||||
5.63365e11 | + | 3.25259e11i | 2.17988 | + | 1.25855i | |||||
0 | 0 | |||||||||
9.93400e10 | + | 1.72062e11i | 0.380102 | + | 0.658356i | |||||
−1.62688e11 | + | 9.39278e10i | −0.619017 | + | 0.357390i | |||||
0 | 0 | |||||||||
−9.18479e10 | + | 1.59085e11i | −0.345598 | + | 0.598594i | |||||
4.94299e11i | 1.84958i | 0.380473 | + | 0.924792i | ||||||
−0.380473 | + | 0.924792i | ||||||||
0 | 0 | |||||||||
2.51803e11 | 0.931796 | |||||||||
−6.60706e10 | − | 3.81459e10i | −0.243142 | − | 0.140378i | |||||
0 | 0 | |||||||||
−1.01935e11 | − | 1.76557e11i | −0.370996 | − | 0.642585i | |||||
−1.72526e11 | + | 9.96081e10i | −0.624458 | + | 0.360531i | |||||
0 | 0 | |||||||||
7.37697e10 | − | 1.27773e11i | 0.264083 | − | 0.457405i | −0.703240 | − | 0.710952i | ||
0.967323 | + | 0.253548i | ||||||||
− | 3.77324e10i | − | 0.134335i | |||||||
0 | 0 | |||||||||
−2.69603e11 | −0.949365 | |||||||||
−6.00847e10 | − | 3.46899e10i | −0.210423 | − | 0.121488i | |||||
0 | 0 | |||||||||
2.03374e10 | + | 3.52254e10i | 0.0704497 | + | 0.122022i | 0.899098 | − | 0.437746i | ||
−0.828649 | + | 0.559769i | ||||||||
9.25358e10 | − | 5.34256e10i | 0.318805 | − | 0.184062i | |||||
0 | 0 | |||||||||
−4.24859e10 | + | 7.35877e10i | −0.144788 | + | 0.250780i | |||||
− | 7.81495e11i | − | 2.64884i | |||||||
0 | 0 | |||||||||
−4.39058e11 | −1.47212 | −0.736062 | − | 0.676915i | ||||||
−0.736062 | + | 0.676915i | ||||||||
1.49658e11 | + | 8.64049e10i | 0.499082 | + | 0.288145i | |||||
0 | 0 | |||||||||
−1.05850e11 | − | 1.83338e11i | −0.349202 | − | 0.604836i | |||||
−2.39798e11 | + | 1.38447e11i | −0.786846 | + | 0.454286i | −0.838851 | − | 0.544361i | ||
0.0520049 | + | 0.998647i | ||||||||
0 | 0 | |||||||||
−3.21657e11 | + | 5.57127e11i | −1.04416 | + | 1.80854i | |||||
1.55543e11i | 0.502220i | |||||||||
0 | 0 | |||||||||
−1.34752e11 | −0.430455 | |||||||||
−3.13093e11 | − | 1.80764e11i | −0.994824 | − | 0.574362i | |||||
0 | 0 | |||||||||
−2.18499e10 | − | 3.78451e10i | −0.0686893 | − | 0.118973i | 0.829635 | − | 0.558306i | ||
−0.898325 | + | 0.439332i | ||||||||
−5.54225e10 | + | 3.19982e10i | −0.173306 | + | 0.100059i | |||||
0 | 0 | |||||||||
−3.65596e10 | + | 6.33231e10i | −0.113114 | + | 0.195919i | |||||
5.78070e11i | 1.77907i | |||||||||
0 | 0 | |||||||||
−2.44223e11 | −0.743708 | −0.371854 | − | 0.928291i | ||||||
−0.371854 | + | 0.928291i | ||||||||
−7.93691e10 | − | 4.58238e10i | −0.240422 | − | 0.138808i | |||||
0 | 0 | |||||||||
6.08447e10 | + | 1.05386e11i | 0.182376 | + | 0.315885i | |||||
−3.60019e11 | + | 2.07857e11i | −1.07346 | + | 0.619764i | −0.929125 | − | 0.369765i | ||
−0.144337 | + | 0.989529i | ||||||||
0 | 0 | |||||||||
−7.14516e10 | + | 1.23758e11i | −0.210821 | + | 0.365153i | |||||
2.37804e10i | 0.0697985i | |||||||||
0 | 0 | |||||||||
4.26293e11 | 1.23821 | |||||||||
5.76964e10 | + | 3.33110e10i | 0.166712 | + | 0.0962512i | |||||
0 | 0 | |||||||||
−5.75903e10 | − | 9.97493e10i | −0.164681 | − | 0.285236i | 0.771861 | − | 0.635792i | ||
−0.936542 | + | 0.350555i | ||||||||
−5.39345e11 | + | 3.11391e11i | −1.53428 | + | 0.885815i | |||||
0 | 0 | |||||||||
7.49215e10 | − | 1.29768e11i | 0.210929 | − | 0.365340i | |||||
1.78665e11i | 0.500406i | 0.968193 | + | 0.250203i | ||||||
−0.968193 | + | 0.250203i | ||||||||
0 | 0 | |||||||||
4.24199e11 | 1.17588 | |||||||||
1.29011e11 | + | 7.44845e10i | 0.355779 | + | 0.205409i | |||||
0 | 0 | |||||||||
4.86441e10 | + | 8.42541e10i | 0.132774 | + | 0.229971i | |||||
−2.02307e11 | + | 1.16802e11i | −0.549366 | + | 0.317177i | |||||
0 | 0 | |||||||||
2.16495e11 | − | 3.74981e11i | 0.581894 | − | 1.00787i | |||||
− | 2.21293e11i | − | 0.591754i | |||||||
0 | 0 | |||||||||
2.38256e10 | 0.0630637 | |||||||||
−7.18225e9 | − | 4.14667e9i | −0.0189139 | − | 0.0109200i | |||||
0 | 0 | |||||||||
2.61255e11 | + | 4.52507e11i | 0.681029 | + | 1.17958i | 0.974667 | + | 0.223660i | ||
−0.293638 | + | 0.955917i | ||||||||
2.11077e11 | − | 1.21865e11i | 0.547439 | − | 0.316064i | |||||
0 | 0 | |||||||||
−3.19727e11 | + | 5.53783e11i | −0.820862 | + | 1.42178i | |||||
− | 3.54825e11i | − | 0.906376i | |||||||
0 | 0 | |||||||||
−2.45495e10 | −0.0620798 | |||||||||
−7.38627e10 | − | 4.26446e10i | −0.185842 | − | 0.107296i | |||||
0 | 0 | |||||||||
1.01993e11 | + | 1.76656e11i | 0.254048 | + | 0.440024i | |||||
−1.67664e11 | + | 9.68008e10i | −0.415534 | + | 0.239908i | −0.693165 | − | 0.720779i | ||
0.277631 | + | 0.960688i | ||||||||
0 | 0 | |||||||||
8.33335e10 | − | 1.44338e11i | 0.204471 | − | 0.354155i | |||||
5.54096e10i | 0.135277i | |||||||||
0 | 0 | |||||||||
3.17336e10 | 0.0767047 | |||||||||
6.13166e11 | + | 3.54012e11i | 1.47474 | + | 0.851443i | |||||
0 | 0 | |||||||||
−5.11376e11 | − | 8.85729e11i | −1.21775 | − | 2.10920i | |||||
1.34836e11 | − | 7.78478e10i | 0.319497 | − | 0.184462i | |||||
0 | 0 | |||||||||
−6.78354e10 | + | 1.17494e11i | −0.159151 | + | 0.275658i | |||||
4.05968e11i | 0.947760i | 0.880590 | + | 0.473880i | ||||||
−0.880590 | + | 0.473880i | ||||||||
0 | 0 | |||||||||
−3.49637e11 | −0.808229 | −0.404115 | − | 0.914708i | ||||||
−0.404115 | + | 0.914708i | ||||||||
−1.98492e11 | − | 1.14600e11i | −0.456583 | − | 0.263608i | |||||
0 | 0 | |||||||||
−2.26914e11 | − | 3.93027e11i | −0.516849 | − | 0.895209i | |||||
8.83654e11 | − | 5.10178e11i | 2.00287 | − | 1.15636i | |||||
0 | 0 | |||||||||
8.22706e10 | − | 1.42497e11i | 0.184653 | − | 0.319828i | |||||
9.77005e10i | 0.218215i | |||||||||
0 | 0 | |||||||||
−2.45368e11 | −0.542703 | |||||||||
1.48992e11 | + | 8.60206e10i | 0.327937 | + | 0.189334i | 0.654925 | − | 0.755694i | ||
−0.326988 | + | 0.945029i | ||||||||
0 | 0 | |||||||||
−1.51520e11 | − | 2.62440e11i | −0.330271 | − | 0.572046i | 0.652294 | − | 0.757966i | ||
−0.982565 | + | 0.185920i | ||||||||
−1.17535e11 | + | 6.78591e10i | −0.254953 | + | 0.147197i | |||||
0 | 0 | |||||||||
−1.04417e11 | + | 1.80855e11i | −0.224311 | + | 0.388517i | |||||
7.71110e11i | 1.64852i | 0.566211 | + | 0.824260i | ||||||
−0.566211 | + | 0.824260i | ||||||||
0 | 0 | |||||||||
1.56682e11 | 0.331742 | 0.165871 | − | 0.986147i | ||||||
0.165871 | + | 0.986147i | ||||||||
−4.45087e11 | − | 2.56971e11i | −0.937847 | − | 0.541466i | |||||
0 | 0 | |||||||||
1.01686e10 | + | 1.76125e10i | 0.0212211 | + | 0.0367560i | |||||
−5.37364e10 | + | 3.10247e10i | −0.111606 | + | 0.0644359i | |||||
0 | 0 | |||||||||
−3.55299e11 | + | 6.15396e11i | −0.730883 | + | 1.26593i | |||||
− | 3.19577e11i | − | 0.654260i | |||||||
0 | 0 | |||||||||
−2.88318e11 | −0.584649 | |||||||||
−4.22447e11 | − | 2.43900e11i | −0.852559 | − | 0.492225i | 0.00895468 | − | 0.999960i | ||
−0.861513 | + | 0.507735i | ||||||||
0 | 0 | |||||||||
−2.80482e10 | − | 4.85809e10i | −0.0560688 | − | 0.0971140i | |||||
1.41505e9 | − | 8.16978e8i | 0.00281529 | − | 0.00162541i | |||||
0 | 0 | |||||||||
−5.58649e10 | + | 9.67608e10i | −0.110095 | + | 0.190691i | |||||
− | 5.99283e11i | − | 1.17545i | |||||||
0 | 0 | |||||||||
1.05959e12 | 2.05875 | |||||||||
9.88166e10 | + | 5.70518e10i | 0.191094 | + | 0.110328i | |||||
0 | 0 | |||||||||
−7.21521e10 | − | 1.24971e11i | −0.138221 | − | 0.239405i | |||||
6.45441e11 | − | 3.72645e11i | 1.23066 | − | 0.710522i | |||||
0 | 0 | |||||||||
−5.07020e10 | + | 8.78185e10i | −0.0957699 | + | 0.165878i | −0.909930 | − | 0.414763i | ||
0.814160 | + | 0.580641i | ||||||||
− | 7.69530e10i | − | 0.144675i | |||||||
0 | 0 | |||||||||
1.94859e11 | 0.362931 | |||||||||
−2.37864e11 | − | 1.37331e11i | −0.440967 | − | 0.254592i | 0.263041 | − | 0.964785i | ||
−0.704008 | + | 0.710192i | ||||||||
0 | 0 | |||||||||
−2.10607e11 | − | 3.64783e11i | −0.386813 | − | 0.669980i | 0.605206 | − | 0.796069i | ||
−0.992019 | + | 0.126089i | ||||||||
1.49673e11 | − | 8.64135e10i | 0.273620 | − | 0.157975i | |||||
0 | 0 | |||||||||
3.57310e10 | − | 6.18879e10i | 0.0647166 | − | 0.112092i | |||||
8.61056e11i | 1.55235i | 0.630520 | + | 0.776173i | ||||||
−0.630520 | + | 0.776173i | ||||||||
0 | 0 | |||||||||
3.80198e11 | 0.679117 | |||||||||
−3.88235e11 | − | 2.24148e11i | −0.690277 | − | 0.398532i | |||||
0 | 0 | |||||||||
2.44022e11 | + | 4.22658e11i | 0.429882 | + | 0.744578i | |||||
1.45433e12 | − | 8.39656e11i | 2.55025 | − | 1.47239i | |||||
0 | 0 | |||||||||
1.53585e11 | − | 2.66016e11i | 0.266855 | − | 0.462206i | |||||
− | 7.70227e10i | − | 0.133215i | |||||||
0 | 0 | |||||||||
5.24819e11 | 0.899423 | |||||||||
1.77186e11 | + | 1.02298e11i | 0.302271 | + | 0.174516i | |||||
0 | 0 | |||||||||
−3.14825e11 | − | 5.45294e11i | −0.532196 | − | 0.921790i | −0.999293 | − | 0.0375845i | ||
0.467098 | − | 0.884206i | ||||||||
−3.08514e11 | + | 1.78121e11i | −0.519155 | + | 0.299734i | |||||
0 | 0 | |||||||||
1.67835e11 | − | 2.90699e11i | 0.279867 | − | 0.484744i | |||||
− | 8.26944e11i | − | 1.37269i | −0.727276 | − | 0.686345i | ||||
0.727276 | − | 0.686345i | ||||||||
0 | 0 | |||||||||
1.00813e12 | 1.65834 | 0.829168 | − | 0.558999i | ||||||
0.829168 | + | 0.558999i | ||||||||
−4.58687e10 | − | 2.64823e10i | −0.0751116 | − | 0.0433657i | |||||
0 | 0 | |||||||||
−2.52206e11 | − | 4.36834e11i | −0.409281 | − | 0.708895i | |||||
−8.45160e11 | + | 4.87954e11i | −1.36535 | + | 0.788286i | −0.990330 | − | 0.138730i | ||
−0.375022 | + | 0.927016i | ||||||||
0 | 0 | |||||||||
7.68843e10 | − | 1.33167e11i | 0.123092 | − | 0.213202i | |||||
6.62303e10i | 0.105559i | |||||||||
0 | 0 | |||||||||
4.35053e10 | 0.0687199 | |||||||||
3.42312e11 | + | 1.97634e11i | 0.538289 | + | 0.310781i | |||||
0 | 0 | |||||||||
6.09349e11 | + | 1.05542e12i | 0.949673 | + | 1.64488i | |||||
−5.52083e10 | + | 3.18745e10i | −0.0856588 | + | 0.0494551i | |||||
0 | 0 | |||||||||
−1.33246e11 | + | 2.30789e11i | −0.204903 | + | 0.354902i | |||||
− | 9.45747e11i | − | 1.44789i | |||||||
0 | 0 | |||||||||
−2.97162e11 | −0.450914 | |||||||||
5.58048e11 | + | 3.22189e11i | 0.843034 | + | 0.486726i | |||||
0 | 0 | |||||||||
9.56226e10 | + | 1.65623e11i | 0.143181 | + | 0.247998i | |||||
−1.14540e12 | + | 6.61297e11i | −1.70751 | + | 0.985830i | |||||
0 | 0 | |||||||||
2.98209e11 | − | 5.16514e11i | 0.440648 | − | 0.763225i | −0.557089 | − | 0.830453i | ||
0.997738 | + | 0.0672273i | ||||||||
1.16209e11i | 0.170961i | |||||||||
0 | 0 | |||||||||
−2.44786e11 | −0.356962 | |||||||||
−1.16083e12 | − | 6.70203e11i | −1.68536 | − | 0.973045i | −0.957989 | − | 0.286804i | ||
−0.727374 | − | 0.686241i | ||||||||
0 | 0 | |||||||||
6.74849e11 | + | 1.16887e12i | 0.971234 | + | 1.68223i | |||||
−4.01829e11 | + | 2.31996e11i | −0.575780 | + | 0.332427i | |||||
0 | 0 | |||||||||
−2.45718e9 | + | 4.25596e9i | −0.00349024 | + | 0.00604527i | |||||
− | 3.03920e11i | − | 0.429816i | |||||||
0 | 0 | |||||||||
−3.60905e11 | −0.505977 | −0.252988 | − | 0.967469i | ||||||
−0.252988 | + | 0.967469i | ||||||||
4.77394e11 | + | 2.75624e11i | 0.666386 | + | 0.384738i | |||||
0 | 0 | |||||||||
2.20241e10 | + | 3.81469e10i | 0.0304772 | + | 0.0527880i | |||||
1.47387e11 | − | 8.50941e10i | 0.203073 | − | 0.117244i | |||||
0 | 0 | |||||||||
2.43000e11 | − | 4.20888e11i | 0.331924 | − | 0.574910i | |||||
− | 6.06262e11i | − | 0.824549i | |||||||
0 | 0 | |||||||||
1.23535e11 | 0.166570 | |||||||||
−8.27772e10 | − | 4.77914e10i | −0.111134 | − | 0.0641634i | 0.443403 | − | 0.896323i | ||
−0.554537 | + | 0.832159i | ||||||||
0 | 0 | |||||||||
−7.35782e10 | − | 1.27441e11i | −0.0979378 | − | 0.169633i | |||||
3.76479e11 | − | 2.17360e11i | 0.498973 | − | 0.288082i | |||||
0 | 0 | |||||||||
2.56347e11 | − | 4.44006e11i | 0.336854 | − | 0.583448i | |||||
8.74192e11i | 1.14383i | |||||||||
0 | 0 | |||||||||
−1.26218e12 | −1.63743 | −0.818714 | − | 0.574201i | ||||||
−0.818714 | + | 0.574201i | ||||||||
8.33855e11 | + | 4.81426e11i | 1.07716 | + | 0.621897i | |||||
0 | 0 | |||||||||
2.07586e11 | + | 3.59549e11i | 0.265880 | + | 0.460519i | |||||
5.84641e11 | − | 3.37543e11i | 0.745643 | − | 0.430497i | −0.0784743 | − | 0.996916i | ||
0.824118 | + | 0.566419i | ||||||||
0 | 0 | |||||||||
−5.29109e11 | + | 9.16443e11i | −0.669111 | + | 1.15893i | |||||
− | 1.12558e11i | − | 0.141739i | |||||||
0 | 0 | |||||||||
−4.53873e11 | −0.566722 | |||||||||
−4.41361e11 | − | 2.54820e11i | −0.548775 | − | 0.316835i | 0.199853 | − | 0.979826i | ||
−0.748628 | + | 0.662991i | ||||||||
0 | 0 | |||||||||
1.39145e11 | + | 2.41007e11i | 0.171555 | + | 0.297142i | |||||
2.96381e11 | − | 1.71116e11i | 0.363879 | − | 0.210085i | |||||
0 | 0 | |||||||||
8.30113e10 | − | 1.43780e11i | 0.101062 | − | 0.175045i | |||||
1.54025e12i | 1.86732i | 0.358160 | + | 0.933660i | ||||||
−0.358160 | + | 0.933660i | ||||||||
0 | 0 | |||||||||
1.54274e11 | 0.185472 | |||||||||
3.32864e10 | + | 1.92179e10i | 0.0398506 | + | 0.0230078i | |||||
0 | 0 | |||||||||
−3.21645e10 | − | 5.57106e10i | −0.0381869 | − | 0.0661417i | |||||
3.19844e11 | − | 1.84662e11i | 0.378150 | − | 0.218325i | |||||
0 | 0 | |||||||||
−5.80464e11 | + | 1.00539e12i | −0.680584 | + | 1.17881i | |||||
− | 1.78379e11i | − | 0.208277i | |||||||
0 | 0 | |||||||||
−6.84242e11 | −0.792321 | |||||||||
−8.41859e11 | − | 4.86048e11i | −0.970801 | − | 0.560492i | |||||
0 | 0 | |||||||||
−4.00962e11 | − | 6.94486e11i | −0.458561 | − | 0.794251i | 0.540324 | − | 0.841457i | ||
−0.998885 | + | 0.0472059i | ||||||||
−4.94589e11 | + | 2.85551e11i | −0.563304 | + | 0.325224i | |||||
0 | 0 | |||||||||
4.83213e11 | − | 8.36949e11i | 0.545823 | − | 0.945393i | |||||
5.82235e11i | 0.654970i | 0.944856 | + | 0.327485i | ||||||
−0.944856 | + | 0.327485i | ||||||||
0 | 0 | |||||||||
−5.21695e11 | −0.582057 | |||||||||
3.57390e11 | + | 2.06339e11i | 0.397106 | + | 0.229269i | |||||
0 | 0 | |||||||||
2.07382e10 | + | 3.59197e10i | 0.0228545 | + | 0.0395852i | |||||
−1.00625e12 | + | 5.80962e11i | −1.10441 | + | 0.637631i | −0.937375 | − | 0.348321i | ||
−0.167033 | + | 0.985951i | ||||||||
0 | 0 | |||||||||
8.69660e10 | − | 1.50630e11i | 0.0946714 | − | 0.163976i | |||||
− | 1.54567e11i | − | 0.167576i | |||||||
0 | 0 | |||||||||
6.62876e11 | 0.712830 | |||||||||
1.19414e12 | + | 6.89439e11i | 1.27892 | + | 0.738383i | 0.976649 | − | 0.214840i | ||
0.302268 | + | 0.953223i | ||||||||
0 | 0 | |||||||||
−7.90592e11 | − | 1.36935e12i | −0.839861 | − | 1.45468i | |||||
−2.78621e11 | + | 1.60862e11i | −0.294786 | + | 0.170195i | |||||
0 | 0 | |||||||||
6.28054e10 | − | 1.08782e11i | 0.0659127 | − | 0.114164i | |||||
− | 7.45364e11i | − | 0.779082i | |||||||
0 | 0 | |||||||||
−8.57390e11 | −0.888963 | −0.444482 | − | 0.895788i | ||||||
−0.444482 | + | 0.895788i | ||||||||
−2.27806e11 | − | 1.31524e11i | −0.235244 | − | 0.135818i | |||||
0 | 0 | |||||||||
2.66736e11 | + | 4.62000e11i | 0.273235 | + | 0.473256i | |||||
1.14604e12 | − | 6.61669e11i | 1.16925 | − | 0.675070i | |||||
0 | 0 | |||||||||
7.94454e11 | − | 1.37603e12i | 0.804060 | − | 1.39267i | −0.112865 | − | 0.993610i | ||
0.916924 | − | 0.399062i | ||||||||
7.20514e11i | 0.726307i | |||||||||
0 | 0 |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 54.9.d.a.35.8 | 16 | ||
3.2 | odd | 2 | 18.9.d.a.11.1 | yes | 16 | ||
4.3 | odd | 2 | 432.9.q.c.305.7 | 16 | |||
9.2 | odd | 6 | 162.9.b.c.161.10 | 16 | |||
9.4 | even | 3 | 18.9.d.a.5.1 | ✓ | 16 | ||
9.5 | odd | 6 | inner | 54.9.d.a.17.8 | 16 | ||
9.7 | even | 3 | 162.9.b.c.161.7 | 16 | |||
12.11 | even | 2 | 144.9.q.b.65.8 | 16 | |||
36.23 | even | 6 | 432.9.q.c.17.7 | 16 | |||
36.31 | odd | 6 | 144.9.q.b.113.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.9.d.a.5.1 | ✓ | 16 | 9.4 | even | 3 | ||
18.9.d.a.11.1 | yes | 16 | 3.2 | odd | 2 | ||
54.9.d.a.17.8 | 16 | 9.5 | odd | 6 | inner | ||
54.9.d.a.35.8 | 16 | 1.1 | even | 1 | trivial | ||
144.9.q.b.65.8 | 16 | 12.11 | even | 2 | |||
144.9.q.b.113.8 | 16 | 36.31 | odd | 6 | |||
162.9.b.c.161.7 | 16 | 9.7 | even | 3 | |||
162.9.b.c.161.10 | 16 | 9.2 | odd | 6 | |||
432.9.q.c.17.7 | 16 | 36.23 | even | 6 | |||
432.9.q.c.305.7 | 16 | 4.3 | odd | 2 |