Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,8,Mod(165,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.165");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 196.e (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
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 28) |
Sato-Tate group: |
Embedding invariants
Embedding label | 165.1 | ||
Root | of defining polynomial | ||
Character | 196.165 | ||
Dual form | 196.8.e.b.177.1 |
-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of on generators for .
Coefficient data
For each we display the coefficients of the -expansion , the Satake parameters , and the Satake angles .
0 | 0 | |||||||||
−19.3824 | + | 33.5713i | −0.414460 | + | 0.717866i | −0.995372 | − | 0.0961008i | ||
0.580912 | + | 0.813967i | ||||||||
0 | 0 | |||||||||
248.206 | + | 429.906i | 0.888009 | + | 1.53808i | 0.842225 | + | 0.539126i | ||
0.0457844 | + | 0.998951i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
342.147 | + | 592.615i | 0.156446 | + | 0.270972i | |||||
0 | 0 | |||||||||
−2017.59 | + | 3494.57i | −0.457045 | + | 0.791626i | −0.998803 | − | 0.0489089i | ||
0.541758 | + | 0.840535i | ||||||||
0 | 0 | |||||||||
−14469.7 | −1.82666 | −0.913331 | − | 0.407217i | ||||||
−0.913331 | + | 0.407217i | ||||||||
0 | 0 | |||||||||
−19243.3 | −1.47218 | |||||||||
0 | 0 | |||||||||
13375.1 | − | 23166.3i | 0.660275 | − | 1.14363i | −0.320268 | − | 0.947327i | ||
0.980543 | − | 0.196303i | ||||||||
0 | 0 | |||||||||
−18305.0 | − | 31705.2i | −0.612255 | − | 1.06046i | −0.990859 | − | 0.134898i | ||
0.378605 | − | 0.925558i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
17460.0 | + | 30241.7i | 0.299225 | + | 0.518272i | 0.975959 | − | 0.217955i | ||
−0.676734 | + | 0.736228i | ||||||||
0 | 0 | |||||||||
−84150.1 | + | 145752.i | −1.07712 | + | 1.86563i | |||||
0 | 0 | |||||||||
−111305. | −1.08828 | |||||||||
0 | 0 | |||||||||
35874.3 | 0.273143 | 0.136571 | − | 0.990630i | ||||||
0.136571 | + | 0.990630i | ||||||||
0 | 0 | |||||||||
−99299.2 | + | 171991.i | −0.598660 | + | 1.03691i | 0.394360 | + | 0.918956i | ||
−0.993019 | + | 0.117953i | ||||||||
0 | 0 | |||||||||
−78211.5 | − | 135466.i | −0.378854 | − | 0.656194i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
57206.6 | + | 99084.7i | 0.185669 | + | 0.321589i | 0.943802 | − | 0.330512i | ||
−0.758133 | + | 0.652100i | ||||||||
0 | 0 | |||||||||
280458. | − | 485767.i | 0.757079 | − | 1.31130i | |||||
0 | 0 | |||||||||
245990. | 0.557409 | 0.278704 | − | 0.960377i | ||||||
0.278704 | + | 0.960377i | ||||||||
0 | 0 | |||||||||
30224.0 | 0.0579711 | 0.0289856 | − | 0.999580i | ||||||
0.0289856 | + | 0.999580i | ||||||||
0 | 0 | |||||||||
−169846. | + | 294182.i | −0.277850 | + | 0.481251i | |||||
0 | 0 | |||||||||
152616. | + | 264339.i | 0.214417 | + | 0.371381i | 0.953092 | − | 0.302681i | ||
−0.738675 | + | 0.674061i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
518481. | + | 898036.i | 0.547315 | + | 0.947978i | |||||
0 | 0 | |||||||||
605264. | − | 1.04835e6i | 0.558444 | − | 0.967253i | −0.439183 | − | 0.898398i | ||
0.997627 | − | 0.0688551i | ||||||||
0 | 0 | |||||||||
−2.00312e6 | −1.62344 | |||||||||
0 | 0 | |||||||||
1.41918e6 | 1.01502 | |||||||||
0 | 0 | |||||||||
767785. | − | 1.32984e6i | 0.486696 | − | 0.842981i | −0.513188 | − | 0.858277i | ||
0.999883 | + | 0.0152952i | ||||||||
0 | 0 | |||||||||
22543.2 | + | 39045.9i | 0.0127163 | + | 0.0220253i | 0.872314 | − | 0.488947i | ||
−0.859597 | + | 0.510972i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.59147e6 | − | 6.22061e6i | −1.62209 | − | 2.80955i | |||||
0 | 0 | |||||||||
−1.54250e6 | + | 2.67169e6i | −0.626562 | + | 1.08524i | 0.361674 | + | 0.932305i | ||
−0.988236 | + | 0.152933i | ||||||||
0 | 0 | |||||||||
−1.35367e6 | −0.496067 | |||||||||
0 | 0 | |||||||||
−1.69051e6 | −0.560550 | −0.280275 | − | 0.959920i | ||||||
−0.280275 | + | 0.959920i | ||||||||
0 | 0 | |||||||||
1.93466e6 | − | 3.35093e6i | 0.582069 | − | 1.00817i | −0.413165 | − | 0.910656i | ||
0.995234 | − | 0.0975172i | ||||||||
0 | 0 | |||||||||
−3.26206e6 | − | 5.65005e6i | −0.892848 | − | 1.54646i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.00455e6 | − | 1.73993e6i | −0.229232 | − | 0.397042i | 0.728349 | − | 0.685207i | ||
−0.957581 | + | 0.288165i | ||||||||
0 | 0 | |||||||||
1.40908e6 | − | 2.44060e6i | 0.294604 | − | 0.510269i | |||||
0 | 0 | |||||||||
−8.28720e6 | −1.59087 | −0.795435 | − | 0.606039i | ||||||
−0.795435 | + | 0.606039i | ||||||||
0 | 0 | |||||||||
1.32791e7 | 2.34532 | |||||||||
0 | 0 | |||||||||
−695328. | + | 1.20434e6i | −0.113207 | + | 0.196080i | |||||
0 | 0 | |||||||||
3.25312e6 | + | 5.63457e6i | 0.489142 | + | 0.847219i | 0.999922 | − | 0.0124923i | ||
−0.510780 | + | 0.859712i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.84931e6 | − | 6.66720e6i | −0.496241 | − | 0.859515i | |||||
0 | 0 | |||||||||
9.08683e6 | − | 1.57389e7i | 1.08738 | − | 1.88339i | |||||
0 | 0 | |||||||||
−1.14882e7 | −1.27806 | −0.639028 | − | 0.769183i | ||||||
−0.639028 | + | 0.769183i | ||||||||
0 | 0 | |||||||||
−2.76125e6 | −0.286011 | |||||||||
0 | 0 | |||||||||
3.45226e6 | − | 5.97950e6i | 0.333410 | − | 0.577484i | −0.649768 | − | 0.760133i | ||
0.983178 | + | 0.182649i | ||||||||
0 | 0 | |||||||||
−2.08698e6 | − | 3.61475e6i | −0.188186 | − | 0.325948i | 0.756459 | − | 0.654041i | ||
−0.944646 | + | 0.328093i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
3.32843e6 | + | 5.76501e6i | 0.262661 | + | 0.454942i | 0.966948 | − | 0.254973i | ||
−0.704287 | + | 0.709915i | ||||||||
0 | 0 | |||||||||
5.56972e6 | − | 9.64704e6i | 0.411946 | − | 0.713512i | −0.583156 | − | 0.812360i | ||
0.995103 | + | 0.0988480i | ||||||||
0 | 0 | |||||||||
−4.43520e6 | −0.307810 | |||||||||
0 | 0 | |||||||||
4.18354e6 | 0.272753 | 0.136377 | − | 0.990657i | ||||||
0.136377 | + | 0.990657i | ||||||||
0 | 0 | |||||||||
−8.66737e6 | + | 1.50123e7i | −0.531429 | + | 0.920462i | |||||
0 | 0 | |||||||||
−4.95077e6 | − | 8.57498e6i | −0.285773 | − | 0.494974i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.60222e6 | + | 2.77513e6i | 0.0822193 | + | 0.142408i | |||||
0 | 0 | |||||||||
−4.76787e6 | + | 8.25819e6i | −0.231024 | + | 0.400145i | |||||
0 | 0 | |||||||||
−4.47641e7 | −2.04996 | |||||||||
0 | 0 | |||||||||
3.65300e7 | 1.58247 | 0.791237 | − | 0.611510i | ||||||
0.791237 | + | 0.611510i | ||||||||
0 | 0 | |||||||||
−585812. | + | 1.01466e6i | −0.0240267 | + | 0.0416155i | |||||
0 | 0 | |||||||||
−2.54084e7 | − | 4.40087e7i | −0.987479 | − | 1.71036i | −0.630353 | − | 0.776308i | ||
−0.357126 | − | 0.934056i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.76266e7 | − | 4.78507e7i | −0.966405 | − | 1.67386i | |||||
0 | 0 | |||||||||
−1.51976e7 | + | 2.63230e7i | −0.504955 | + | 0.874608i | 0.495028 | + | 0.868877i | ||
−0.999984 | + | 0.00573133i | ||||||||
0 | 0 | |||||||||
−2.92052e7 | −0.922377 | −0.461189 | − | 0.887302i | ||||||
−0.461189 | + | 0.887302i | ||||||||
0 | 0 | |||||||||
−1.18323e7 | −0.355469 | |||||||||
0 | 0 | |||||||||
2.91940e7 | − | 5.05655e7i | 0.834867 | − | 1.44603i | |||||
0 | 0 | |||||||||
8.90421e6 | + | 1.54225e7i | 0.242553 | + | 0.420115i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.85475e7 | + | 3.21252e7i | 0.459339 | + | 0.795598i | 0.998926 | − | 0.0463317i | ||
−0.539588 | + | 0.841930i | ||||||||
0 | 0 | |||||||||
−9.11971e6 | + | 1.57958e7i | −0.215557 | + | 0.373356i | −0.953445 | − | 0.301568i | ||
0.737888 | + | 0.674923i | ||||||||
0 | 0 | |||||||||
1.83049e7 | 0.413189 | |||||||||
0 | 0 | |||||||||
−9.85867e7 | −2.12646 | |||||||||
0 | 0 | |||||||||
−1.06032e7 | + | 1.83653e7i | −0.218670 | + | 0.378747i | −0.954402 | − | 0.298526i | ||
0.735732 | + | 0.677273i | ||||||||
0 | 0 | |||||||||
2.34629e7 | + | 4.06390e7i | 0.462905 | + | 0.801775i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.25476e7 | − | 3.90537e7i | −0.407797 | − | 0.706326i | 0.586845 | − | 0.809699i | ||
−0.994643 | + | 0.103373i | ||||||||
0 | 0 | |||||||||
3.88252e7 | − | 6.72472e7i | 0.672852 | − | 1.16541i | |||||
0 | 0 | |||||||||
6.32823e7 | 1.05142 | 0.525708 | − | 0.850665i | ||||||
0.525708 | + | 0.850665i | ||||||||
0 | 0 | |||||||||
1.46624e8 | 2.33670 | |||||||||
0 | 0 | |||||||||
1.25260e7 | − | 2.16957e7i | 0.191569 | − | 0.331808i | |||||
0 | 0 | |||||||||
1.67096e7 | + | 2.89420e7i | 0.245361 | + | 0.424978i | 0.962233 | − | 0.272227i | ||
−0.716872 | + | 0.697205i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.97630e7 | + | 5.15510e7i | 0.403432 | + | 0.698764i | |||||
0 | 0 | |||||||||
6.49827e7 | − | 1.12553e8i | 0.846861 | − | 1.46681i | −0.0371339 | − | 0.999310i | ||
0.883995 | − | 0.467496i | ||||||||
0 | 0 | |||||||||
1.91607e7 | 0.240180 | 0.120090 | − | 0.992763i | ||||||
0.120090 | + | 0.992763i | ||||||||
0 | 0 | |||||||||
−1.74776e6 | −0.0210816 | |||||||||
0 | 0 | |||||||||
−2.83981e7 | + | 4.91869e7i | −0.329752 | + | 0.571147i | |||||
0 | 0 | |||||||||
5.39709e7 | + | 9.34803e7i | 0.603551 | + | 1.04538i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.77182e7 | − | 3.06888e7i | −0.183994 | − | 0.318686i | 0.759243 | − | 0.650807i | ||
−0.943237 | + | 0.332121i | ||||||||
0 | 0 | |||||||||
−9.01695e7 | + | 1.56178e8i | −0.902837 | + | 1.56376i | −0.0790419 | + | 0.996871i | ||
−0.823795 | + | 0.566888i | ||||||||
0 | 0 | |||||||||
2.78445e8 | 2.68917 | |||||||||
0 | 0 | |||||||||
−1.39463e8 | −1.29965 | −0.649826 | − | 0.760083i | ||||||
−0.649826 | + | 0.760083i | ||||||||
0 | 0 | |||||||||
−7.31562e7 | + | 1.26710e8i | −0.658060 | + | 1.13979i | 0.323057 | + | 0.946379i | ||
−0.981117 | + | 0.193414i | ||||||||
0 | 0 | |||||||||
−5.97948e7 | − | 1.03568e8i | −0.519370 | − | 0.899576i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.10562e7 | + | 1.05752e8i | 0.494984 | + | 0.857338i | |||||
0 | 0 | |||||||||
−1.19478e7 | + | 2.06942e7i | −0.0936248 | + | 0.162163i | |||||
0 | 0 | |||||||||
1.47728e8 | 1.11931 | |||||||||
0 | 0 | |||||||||
−1.02935e8 | −0.754351 | −0.377176 | − | 0.926142i | ||||||
−0.377176 | + | 0.926142i | ||||||||
0 | 0 | |||||||||
3.27662e7 | − | 5.67527e7i | 0.232326 | − | 0.402400i | |||||
0 | 0 | |||||||||
7.50177e6 | + | 1.29934e7i | 0.0514789 | + | 0.0891641i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.49966e7 | + | 1.29898e8i | 0.482489 | + | 0.835695i | |||||
0 | 0 | |||||||||
−1.93533e8 | + | 3.35210e8i | −1.20610 | + | 2.08903i | |||||
0 | 0 | |||||||||
−3.26446e8 | −1.97126 | −0.985632 | − | 0.168906i | ||||||
−0.985632 | + | 0.168906i | ||||||||
0 | 0 | |||||||||
−1.15167e8 | −0.674044 | |||||||||
0 | 0 | |||||||||
4.49769e7 | − | 7.79023e7i | 0.255211 | − | 0.442038i | −0.709742 | − | 0.704462i | ||
0.964953 | + | 0.262424i | ||||||||
0 | 0 | |||||||||
5.09646e7 | + | 8.82734e7i | 0.280443 | + | 0.485742i | 0.971494 | − | 0.237064i | ||
−0.691051 | + | 0.722806i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.13457e7 | + | 3.69719e7i | 0.110552 | + | 0.191481i | 0.915993 | − | 0.401195i | ||
−0.805441 | + | 0.592676i | ||||||||
0 | 0 | |||||||||
−7.57606e7 | + | 1.31221e8i | −0.380808 | + | 0.659579i | |||||
0 | 0 | |||||||||
7.78821e7 | 0.380030 | |||||||||
0 | 0 | |||||||||
−6.02163e7 | −0.285313 | −0.142656 | − | 0.989772i | ||||||
−0.142656 | + | 0.989772i | ||||||||
0 | 0 | |||||||||
2.35768e7 | − | 4.08362e7i | 0.108499 | − | 0.187926i | −0.806663 | − | 0.591011i | ||
0.915162 | + | 0.403086i | ||||||||
0 | 0 | |||||||||
−6.70893e7 | − | 1.16202e8i | −0.299938 | − | 0.519508i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.64868e8 | + | 4.58765e8i | 1.11838 | + | 1.93710i | |||||
0 | 0 | |||||||||
1.60626e8 | − | 2.78212e8i | 0.659352 | − | 1.14203i | |||||
0 | 0 | |||||||||
1.94014e8 | 0.774416 | 0.387208 | − | 0.921992i | ||||||
0.387208 | + | 0.921992i | ||||||||
0 | 0 | |||||||||
−1.40909e8 | −0.547037 | |||||||||
0 | 0 | |||||||||
−2.57381e8 | + | 4.45796e8i | −0.972042 | + | 1.68363i | |||||
0 | 0 | |||||||||
3.39371e7 | + | 5.87809e7i | 0.124712 | + | 0.216008i | 0.921620 | − | 0.388092i | ||
−0.796908 | + | 0.604101i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.22743e7 | + | 2.12596e7i | 0.0427320 | + | 0.0740140i | |||||
0 | 0 | |||||||||
−8.05998e7 | + | 1.39603e8i | −0.273205 | + | 0.473205i | −0.969681 | − | 0.244375i | ||
0.696476 | + | 0.717580i | ||||||||
0 | 0 | |||||||||
6.00921e8 | 1.98361 | |||||||||
0 | 0 | |||||||||
−2.52213e8 | −0.810920 | |||||||||
0 | 0 | |||||||||
1.32052e8 | − | 2.28721e8i | 0.413631 | − | 0.716429i | −0.581653 | − | 0.813437i | ||
0.995284 | + | 0.0970078i | ||||||||
0 | 0 | |||||||||
2.46217e7 | + | 4.26460e7i | 0.0751493 | + | 0.130162i | 0.901151 | − | 0.433505i | ||
−0.826002 | + | 0.563667i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.39561e8 | − | 5.88138e8i | −0.984587 | − | 1.70535i | |||||
0 | 0 | |||||||||
1.42902e8 | − | 2.47513e8i | 0.403978 | − | 0.699711i | −0.590224 | − | 0.807240i | ||
0.994202 | + | 0.107529i | ||||||||
0 | 0 | |||||||||
−1.35900e8 | −0.374631 | |||||||||
0 | 0 | |||||||||
5.50944e8 | 1.48127 | 0.740637 | − | 0.671905i | ||||||
0.740637 | + | 0.671905i | ||||||||
0 | 0 | |||||||||
−1.42073e8 | + | 2.46077e8i | −0.372613 | + | 0.645385i | −0.989967 | − | 0.141301i | ||
0.617354 | + | 0.786686i | ||||||||
0 | 0 | |||||||||
3.52249e8 | + | 6.10113e8i | 0.901348 | + | 1.56118i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.52616e8 | − | 2.64338e8i | −0.371926 | − | 0.644195i | |||||
0 | 0 | |||||||||
2.22668e8 | − | 3.85673e8i | 0.529704 | − | 0.917474i | |||||
0 | 0 | |||||||||
4.33632e7 | 0.100713 | 0.0503564 | − | 0.998731i | ||||||
0.0503564 | + | 0.998731i | ||||||||
0 | 0 | |||||||||
7.62276e8 | 1.72876 | |||||||||
0 | 0 | |||||||||
2.24568e8 | − | 3.88964e8i | 0.497394 | − | 0.861512i | |||||
0 | 0 | |||||||||
−2.52642e8 | − | 4.37588e8i | −0.546583 | − | 0.946709i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.33826e8 | + | 2.31794e8i | 0.276371 | + | 0.478688i | |||||
0 | 0 | |||||||||
−1.11907e7 | + | 1.93829e7i | −0.0225844 | + | 0.0391173i | |||||
0 | 0 | |||||||||
−4.07582e8 | −0.803954 | −0.401977 | − | 0.915650i | ||||||
−0.401977 | + | 0.915650i | ||||||||
0 | 0 | |||||||||
1.61802e8 | 0.311983 | |||||||||
0 | 0 | |||||||||
−3.84132e8 | + | 6.65336e8i | −0.724134 | + | 1.25424i | 0.235195 | + | 0.971948i | ||
−0.959329 | + | 0.282289i | ||||||||
0 | 0 | |||||||||
−2.15655e8 | − | 3.73525e8i | −0.397515 | − | 0.688517i | 0.595903 | − | 0.803056i | ||
−0.993419 | + | 0.114539i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−7.89918e7 | − | 1.36818e8i | −0.139276 | − | 0.241232i | 0.787947 | − | 0.615743i | ||
−0.927223 | + | 0.374511i | ||||||||
0 | 0 | |||||||||
−7.23797e7 | + | 1.25365e8i | −0.124839 | + | 0.216227i | |||||
0 | 0 | |||||||||
−2.58051e8 | −0.435450 | |||||||||
0 | 0 | |||||||||
−9.79323e8 | −1.61703 | |||||||||
0 | 0 | |||||||||
1.21763e9 | − | 2.10899e9i | 1.96754 | − | 3.40787i | |||||
0 | 0 | |||||||||
2.15909e8 | + | 3.73965e8i | 0.341471 | + | 0.591445i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.87683e8 | − | 8.44692e8i | −0.739162 | − | 1.28027i | −0.952873 | − | 0.303370i | ||
0.213711 | − | 0.976897i | ||||||||
0 | 0 | |||||||||
−3.91461e7 | + | 6.78030e7i | −0.0580943 | + | 0.100622i | |||||
0 | 0 | |||||||||
−1.53144e9 | −2.22557 | |||||||||
0 | 0 | |||||||||
−9.07880e8 | −1.29218 | −0.646091 | − | 0.763260i | ||||||
−0.646091 | + | 0.763260i | ||||||||
0 | 0 | |||||||||
−8.10870e7 | + | 1.40447e8i | −0.113045 | + | 0.195800i | |||||
0 | 0 | |||||||||
−4.00691e8 | − | 6.94017e8i | −0.547229 | − | 0.947828i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.35989e8 | − | 5.81949e8i | −0.440512 | − | 0.762989i | |||||
0 | 0 | |||||||||
2.89860e7 | − | 5.02052e7i | 0.0372422 | − | 0.0645053i | −0.846804 | − | 0.531906i | ||
0.884046 | + | 0.467400i | ||||||||
0 | 0 | |||||||||
−1.33879e9 | −1.68587 | −0.842935 | − | 0.538016i | ||||||
−0.842935 | + | 0.538016i | ||||||||
0 | 0 | |||||||||
1.61055e9 | 1.98792 | |||||||||
0 | 0 | |||||||||
−2.91117e8 | + | 5.04230e8i | −0.352254 | + | 0.610122i | −0.986644 | − | 0.162891i | ||
0.634390 | + | 0.773013i | ||||||||
0 | 0 | |||||||||
−4.19596e8 | − | 7.26762e8i | −0.497774 | − | 0.862170i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.60217e8 | + | 2.77505e8i | 0.182759 | + | 0.316548i | 0.942819 | − | 0.333305i | ||
−0.760060 | + | 0.649853i | ||||||||
0 | 0 | |||||||||
−2.23210e8 | + | 3.86612e8i | −0.249712 | + | 0.432514i | |||||
0 | 0 | |||||||||
−1.24219e8 | −0.136306 | |||||||||
0 | 0 | |||||||||
1.92078e9 | 2.06753 | |||||||||
0 | 0 | |||||||||
−3.27639e8 | + | 5.67487e8i | −0.345990 | + | 0.599273i | −0.985533 | − | 0.169483i | ||
0.639543 | + | 0.768755i | ||||||||
0 | 0 | |||||||||
8.41646e7 | + | 1.45777e8i | 0.0872042 | + | 0.151042i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.71464e8 | + | 4.70189e8i | 0.270851 | + | 0.469128i | 0.969080 | − | 0.246746i | ||
−0.698229 | + | 0.715875i | ||||||||
0 | 0 | |||||||||
8.67635e8 | − | 1.50279e9i | 0.849626 | − | 1.47159i | |||||
0 | 0 | |||||||||
−5.19090e8 | −0.498940 | |||||||||
0 | 0 | |||||||||
−1.57480e9 | −1.48590 | −0.742949 | − | 0.669348i | ||||||
−0.742949 | + | 0.669348i | ||||||||
0 | 0 | |||||||||
−7.08038e8 | + | 1.22636e9i | −0.655872 | + | 1.13600i | |||||
0 | 0 | |||||||||
4.44411e8 | + | 7.69742e8i | 0.404193 | + | 0.700083i | 0.994227 | − | 0.107295i | ||
−0.590034 | + | 0.807378i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.03410e7 | + | 1.79112e7i | 0.00906933 | + | 0.0157085i | |||||
0 | 0 | |||||||||
−6.73363e8 | + | 1.16630e9i | −0.579997 | + | 1.00458i | 0.415482 | + | 0.909601i | ||
−0.995479 | + | 0.0949829i | ||||||||
0 | 0 | |||||||||
9.34116e8 | 0.790282 | |||||||||
0 | 0 | |||||||||
1.96990e9 | 1.63708 | |||||||||
0 | 0 | |||||||||
4.98670e8 | − | 8.63722e8i | 0.407121 | − | 0.705154i | |||||
0 | 0 | |||||||||
−1.07964e9 | − | 1.86998e9i | −0.865985 | − | 1.49993i | −0.866066 | − | 0.499930i | ||
8.13447e−5 | − | 1.00000i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.38083e8 | + | 1.62481e9i | 0.726500 | + | 1.25834i | 0.958354 | + | 0.285585i | ||
−0.231853 | + | 0.972751i | ||||||||
0 | 0 | |||||||||
1.43683e9 | − | 2.48867e9i | 1.09355 | − | 1.89408i | |||||
0 | 0 | |||||||||
1.39897e9 | 1.04644 | |||||||||
0 | 0 | |||||||||
−4.61678e8 | −0.339437 | |||||||||
0 | 0 | |||||||||
−1.13724e6 | + | 1.96976e6i | −0.000821906 | + | 0.00142358i | −0.866436 | − | 0.499288i | ||
0.865614 | + | 0.500712i | ||||||||
0 | 0 | |||||||||
−5.89131e8 | − | 1.02041e9i | −0.418568 | − | 0.724980i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.05694e9 | − | 3.56272e9i | −1.41271 | − | 2.44688i | |||||
0 | 0 | |||||||||
5.66067e8 | − | 9.80456e8i | 0.382289 | − | 0.662143i | |||||
0 | 0 | |||||||||
−2.40944e9 | −1.60017 | −0.800087 | − | 0.599884i | ||||||
−0.800087 | + | 0.599884i | ||||||||
0 | 0 | |||||||||
−1.08307e9 | −0.707404 | −0.353702 | − | 0.935358i | ||||||
−0.353702 | + | 0.935358i | ||||||||
0 | 0 | |||||||||
−1.04434e8 | + | 1.80886e8i | −0.0670891 | + | 0.116202i | |||||
0 | 0 | |||||||||
2.25103e9 | + | 3.89889e9i | 1.42239 | + | 2.46366i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.13170e9 | + | 1.96016e9i | 0.692038 | + | 1.19865i | |||||
0 | 0 | |||||||||
−2.52993e8 | + | 4.38197e8i | −0.152208 | + | 0.263633i | −0.932039 | − | 0.362358i | ||
0.779831 | + | 0.625991i | ||||||||
0 | 0 | |||||||||
3.73323e8 | 0.220992 | 0.110496 | − | 0.993877i | ||||||
0.110496 | + | 0.993877i | ||||||||
0 | 0 | |||||||||
−6.90339e8 | −0.402115 | |||||||||
0 | 0 | |||||||||
6.39212e8 | − | 1.10715e9i | 0.366404 | − | 0.634630i | |||||
0 | 0 | |||||||||
4.44465e6 | + | 7.69836e6i | 0.00250733 | + | 0.00434283i | 0.867276 | − | 0.497827i | ||
−0.864769 | + | 0.502170i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5.12024e8 | − | 8.86851e8i | −0.279819 | − | 0.484661i | 0.691521 | − | 0.722357i | ||
−0.971340 | + | 0.237696i | ||||||||
0 | 0 | |||||||||
−1.61489e9 | + | 2.79707e9i | −0.868726 | + | 1.50468i | |||||
0 | 0 | |||||||||
−1.43798e9 | −0.761510 | |||||||||
0 | 0 | |||||||||
8.32711e8 | 0.434142 | 0.217071 | − | 0.976156i | ||||||
0.217071 | + | 0.976156i | ||||||||
0 | 0 | |||||||||
−4.96308e8 | + | 8.59630e8i | −0.254761 | + | 0.441259i | |||||
0 | 0 | |||||||||
−3.53524e8 | − | 6.12321e8i | −0.178679 | − | 0.309482i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.14391e9 | + | 1.98130e9i | 0.560639 | + | 0.971055i | 0.997441 | + | 0.0714976i | ||
−0.436802 | + | 0.899558i | ||||||||
0 | 0 | |||||||||
−1.48871e9 | + | 2.57852e9i | −0.718565 | + | 1.24459i | |||||
0 | 0 | |||||||||
7.84459e8 | 0.372921 | 0.186461 | − | 0.982462i | ||||||
0.186461 | + | 0.982462i | ||||||||
0 | 0 | |||||||||
−2.31590e9 | −1.08439 | −0.542196 | − | 0.840252i | ||||||
−0.542196 | + | 0.840252i | ||||||||
0 | 0 | |||||||||
1.91085e9 | − | 3.30968e9i | 0.881333 | − | 1.52651i | |||||
0 | 0 | |||||||||
3.06330e8 | + | 5.30578e8i | 0.139181 | + | 0.241068i | 0.927187 | − | 0.374599i | ||
−0.788006 | + | 0.615668i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.11031e8 | − | 7.11927e8i | −0.181260 | − | 0.313951i | |||||
0 | 0 | |||||||||
−6.09796e7 | + | 1.05620e8i | −0.0264954 | + | 0.0458914i | |||||
0 | 0 | |||||||||
6.16147e9 | 2.63789 | |||||||||
0 | 0 | |||||||||
8.28356e8 | 0.349464 | |||||||||
0 | 0 | |||||||||
−3.64475e8 | + | 6.31289e8i | −0.151528 | + | 0.262454i | −0.931789 | − | 0.362999i | ||
0.780261 | + | 0.625454i | ||||||||
0 | 0 | |||||||||
−8.27763e8 | − | 1.43373e9i | −0.339155 | − | 0.587434i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.85144e9 | − | 4.93883e9i | −1.13493 | − | 1.96575i | |||||
0 | 0 | |||||||||
4.34192e8 | − | 7.52043e8i | 0.170346 | − | 0.295047i | −0.768195 | − | 0.640216i | ||
0.938541 | + | 0.345169i | ||||||||
0 | 0 | |||||||||
1.74811e9 | 0.676063 | |||||||||
0 | 0 | |||||||||
−3.47503e9 | −1.32487 | −0.662435 | − | 0.749119i | ||||||
−0.662435 | + | 0.749119i | ||||||||
0 | 0 | |||||||||
4.79821e8 | − | 8.31074e8i | 0.180349 | − | 0.312374i | |||||
0 | 0 | |||||||||
−6.85360e8 | − | 1.18708e9i | −0.253980 | − | 0.439907i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.84086e9 | + | 3.18846e9i | 0.663236 | + | 1.14876i | 0.979760 | + | 0.200174i | ||
−0.316524 | + | 0.948584i | ||||||||
0 | 0 | |||||||||
−1.22656e9 | + | 2.12447e9i | −0.435770 | + | 0.754775i | |||||
0 | 0 | |||||||||
3.79099e9 | 1.32820 | 0.664102 | − | 0.747642i | ||||||
0.664102 | + | 0.747642i | ||||||||
0 | 0 | |||||||||
3.42749e9 | 1.18429 | |||||||||
0 | 0 | |||||||||
−2.84193e9 | + | 4.92236e9i | −0.968467 | + | 1.67743i | |||||
0 | 0 | |||||||||
2.04656e9 | + | 3.54475e9i | 0.687880 | + | 1.19144i | 0.972522 | + | 0.232810i | ||
−0.284642 | + | 0.958634i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.03744e9 | + | 3.52895e9i | 0.666306 | + | 1.15408i | |||||
0 | 0 | |||||||||
1.03600e9 | − | 1.79441e9i | 0.334222 | − | 0.578890i | |||||
0 | 0 | |||||||||
−1.23167e9 | −0.391993 | |||||||||
0 | 0 | |||||||||
−1.29549e9 | −0.406770 | |||||||||
0 | 0 | |||||||||
−8.47729e8 | + | 1.46831e9i | −0.262618 | + | 0.454868i | −0.966937 | − | 0.255016i | ||
0.704319 | + | 0.709884i | ||||||||
0 | 0 | |||||||||
7.68571e8 | + | 1.33120e9i | 0.234924 | + | 0.406901i | 0.959251 | − | 0.282556i | ||
−0.724326 | + | 0.689457i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.65627e9 | + | 4.60079e9i | 0.790560 | + | 1.36929i | |||||
0 | 0 | |||||||||
1.09271e9 | − | 1.89263e9i | 0.320929 | − | 0.555866i | |||||
0 | 0 | |||||||||
1.05078e9 | 0.304566 | |||||||||
0 | 0 | |||||||||
−3.55940e9 | −1.01820 | |||||||||
0 | 0 | |||||||||
−1.65227e9 | + | 2.86182e9i | −0.466491 | + | 0.807986i | |||||
0 | 0 | |||||||||
2.51904e9 | + | 4.36310e9i | 0.701980 | + | 1.21587i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.17255e9 | + | 3.76296e9i | 0.589901 | + | 1.02174i | 0.994245 | + | 0.107131i | ||
−0.404344 | + | 0.914607i | ||||||||
0 | 0 | |||||||||
−3.71380e8 | + | 6.43249e8i | −0.0995449 | + | 0.172417i | |||||
0 | 0 | |||||||||
5.52976e9 | 1.46325 | |||||||||
0 | 0 | |||||||||
2.30195e9 | 0.601367 | 0.300683 | − | 0.953724i | ||||||
0.300683 | + | 0.953724i | ||||||||
0 | 0 | |||||||||
−1.54262e7 | + | 2.67189e7i | −0.00397882 | + | 0.00689152i | |||||
0 | 0 | |||||||||
−6.56678e8 | − | 1.13740e9i | −0.167233 | − | 0.289656i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.10084e9 | − | 1.90672e9i | −0.273338 | − | 0.473435i | |||||
0 | 0 | |||||||||
−8.55534e8 | + | 1.48183e9i | −0.209770 | + | 0.363333i | −0.951642 | − | 0.307209i | ||
0.741872 | + | 0.670542i | ||||||||
0 | 0 | |||||||||
−4.37332e8 | −0.105894 | |||||||||
0 | 0 | |||||||||
−4.18434e9 | −1.00059 | |||||||||
0 | 0 | |||||||||
−1.08317e9 | + | 1.87610e9i | −0.255809 | + | 0.443074i | −0.965115 | − | 0.261827i | ||
0.709306 | + | 0.704901i | ||||||||
0 | 0 | |||||||||
1.03838e9 | + | 1.79853e9i | 0.242207 | + | 0.419515i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.38031e9 | + | 2.39077e9i | 0.314112 | + | 0.544059i | 0.979248 | − | 0.202664i | ||
−0.665136 | + | 0.746722i | ||||||||
0 | 0 | |||||||||
−3.62954e8 | + | 6.28654e8i | −0.0815877 | + | 0.141314i | −0.903932 | − | 0.427676i | ||
0.822344 | + | 0.568990i | ||||||||
0 | 0 | |||||||||
1.37368e9 | 0.305032 | |||||||||
0 | 0 | |||||||||
−5.87705e9 | −1.28921 | |||||||||
0 | 0 | |||||||||
2.68517e9 | − | 4.65086e9i | 0.581911 | − | 1.00790i | −0.413341 | − | 0.910576i | ||
0.995253 | − | 0.0973240i | ||||||||
0 | 0 | |||||||||
−3.49540e9 | − | 6.05421e9i | −0.748380 | − | 1.29623i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
2.44235e9 | + | 4.23028e9i | 0.510468 | + | 0.884157i | |||||
0 | 0 | |||||||||
2.45762e9 | − | 4.25672e9i | 0.507539 | − | 0.879083i | |||||
0 | 0 | |||||||||
−7.86145e9 | −1.60424 | −0.802120 | − | 0.597163i | ||||||
−0.802120 | + | 0.597163i | ||||||||
0 | 0 | |||||||||
7.27069e9 | 1.46613 | |||||||||
0 | 0 | |||||||||
2.70313e9 | − | 4.68195e9i | 0.538654 | − | 0.932976i | |||||
0 | 0 | |||||||||
−2.72206e9 | − | 4.71475e9i | −0.536051 | − | 0.928468i | −0.999112 | − | 0.0421412i | ||
0.463060 | − | 0.886327i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.83588e9 | − | 4.91189e9i | −0.545479 | − | 0.944798i | |||||
0 | 0 | |||||||||
−3.98704e9 | + | 6.90575e9i | −0.757978 | + | 1.31286i | 0.185902 | + | 0.982568i | ||
−0.943880 | + | 0.330288i | ||||||||
0 | 0 | |||||||||
−6.27378e8 | −0.117888 | −0.0589439 | − | 0.998261i | ||||||
−0.0589439 | + | 0.998261i | ||||||||
0 | 0 | |||||||||
−2.11105e9 | −0.392092 | |||||||||
0 | 0 | |||||||||
−7.95362e8 | + | 1.37761e9i | −0.146023 | + | 0.252919i | |||||
0 | 0 | |||||||||
−1.89879e9 | − | 3.28880e9i | −0.344601 | − | 0.596866i | 0.640680 | − | 0.767808i | ||
−0.985281 | + | 0.170941i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.20832e9 | − | 3.82491e9i | −0.391667 | − | 0.678387i | |||||
0 | 0 | |||||||||
−5.30599e9 | + | 9.19025e9i | −0.930369 | + | 1.61145i | −0.147677 | + | 0.989036i | ||
−0.782691 | + | 0.622410i | ||||||||
0 | 0 | |||||||||
−4.73366e9 | −0.820605 | |||||||||
0 | 0 | |||||||||
2.26828e8 | 0.0388776 | 0.0194388 | − | 0.999811i | ||||||
0.0194388 | + | 0.999811i | ||||||||
0 | 0 | |||||||||
−2.45900e9 | + | 4.25912e9i | −0.416718 | + | 0.721776i | −0.995607 | − | 0.0936299i | ||
0.578889 | + | 0.815406i | ||||||||
0 | 0 | |||||||||
−1.94339e9 | − | 3.36605e9i | −0.325641 | − | 0.564027i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.53650e9 | − | 7.85745e9i | −0.743260 | − | 1.28736i | |||||
0 | 0 | |||||||||
−2.86332e9 | + | 4.95942e9i | −0.463910 | + | 0.803516i | |||||
0 | 0 | |||||||||
3.06057e9 | 0.490371 | |||||||||
0 | 0 | |||||||||
6.22228e9 | 0.985931 | 0.492966 | − | 0.870049i | ||||||
0.492966 | + | 0.870049i | ||||||||
0 | 0 | |||||||||
1.99512e9 | − | 3.45565e9i | 0.312648 | − | 0.541523i | |||||
0 | 0 | |||||||||
9.06697e9 | + | 1.57044e10i | 1.40525 | + | 2.43397i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5.78404e8 | − | 1.00182e9i | −0.0876957 | − | 0.151893i | |||||
0 | 0 | |||||||||
1.35677e9 | − | 2.35000e9i | 0.203472 | − | 0.352424i | −0.746173 | − | 0.665752i | ||
0.949645 | + | 0.313328i | ||||||||
0 | 0 | |||||||||
−5.96086e9 | −0.884240 | −0.442120 | − | 0.896956i | ||||||
−0.442120 | + | 0.896956i | ||||||||
0 | 0 | |||||||||
−5.81609e8 | −0.0853438 | |||||||||
0 | 0 | |||||||||
−9.35684e8 | + | 1.62065e9i | −0.135820 | + | 0.235247i | −0.925910 | − | 0.377743i | ||
0.790090 | + | 0.612990i | ||||||||
0 | 0 | |||||||||
3.09815e9 | + | 5.36616e9i | 0.444884 | + | 0.770561i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.34121e9 | − | 7.51920e9i | −0.610120 | − | 1.05676i | −0.991220 | − | 0.132225i | ||
0.381100 | − | 0.924534i | ||||||||
0 | 0 | |||||||||
1.26131e10 | − | 2.18464e10i | 1.75378 | − | 3.03764i | |||||
0 | 0 | |||||||||
2.64775e9 | 0.364249 | |||||||||
0 | 0 | |||||||||
1.17028e10 | 1.59291 | 0.796457 | − | 0.604696i | ||||||
0.796457 | + | 0.604696i | ||||||||
0 | 0 | |||||||||
2.11762e9 | − | 3.66782e9i | 0.285195 | − | 0.493973i | −0.687461 | − | 0.726221i | ||
0.972657 | + | 0.232248i | ||||||||
0 | 0 | |||||||||
−7.50228e9 | − | 1.29943e10i | −0.999760 | − | 1.73164i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.26365e8 | + | 1.08490e9i | 0.0817311 | + | 0.141562i | |||||
0 | 0 | |||||||||
6.32731e9 | − | 1.09592e10i | 0.817010 | − | 1.41510i | |||||
0 | 0 | |||||||||
−1.81932e8 | −0.0232477 | |||||||||
0 | 0 | |||||||||
−1.64366e9 | −0.207854 | −0.103927 | − | 0.994585i | ||||||
−0.103927 | + | 0.994585i | ||||||||
0 | 0 | |||||||||
9.36633e9 | − | 1.62230e10i | 1.17221 | − | 2.03033i | |||||
0 | 0 | |||||||||
−5.44190e9 | − | 9.42565e9i | −0.674048 | − | 1.16748i | −0.976746 | − | 0.214398i | ||
0.302699 | − | 0.953086i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.74352e9 | + | 3.01986e9i | 0.211549 | + | 0.366414i | |||||
0 | 0 | |||||||||
1.92639e9 | − | 3.33660e9i | 0.231351 | − | 0.400711i | −0.726855 | − | 0.686791i | ||
0.958206 | + | 0.286080i | ||||||||
0 | 0 | |||||||||
−1.50885e10 | −1.79362 | |||||||||
0 | 0 | |||||||||
−3.95126e9 | −0.464930 | |||||||||
0 | 0 | |||||||||
−8.75800e9 | + | 1.51693e10i | −1.02009 | + | 1.76684i | |||||
0 | 0 | |||||||||
7.77195e9 | + | 1.34614e10i | 0.896100 | + | 1.55209i | 0.832437 | + | 0.554120i | ||
0.0636633 | + | 0.997971i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−7.24892e9 | − | 1.25555e10i | −0.819080 | − | 1.41869i | |||||
0 | 0 | |||||||||
3.29013e9 | − | 5.69868e9i | 0.368043 | − | 0.637469i | |||||
0 | 0 | |||||||||
−1.65493e9 | −0.183277 | |||||||||
0 | 0 | |||||||||
−7.75099e9 | −0.849854 | −0.424927 | − | 0.905228i | ||||||
−0.424927 | + | 0.905228i | ||||||||
0 | 0 | |||||||||
2.09433e9 | − | 3.62749e9i | 0.227354 | − | 0.393788i | |||||
0 | 0 | |||||||||
−2.93684e9 | − | 5.08676e9i | −0.315660 | − | 0.546738i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.73320e9 | + | 9.93020e9i | 0.604137 | + | 1.04640i | 0.992187 | + | 0.124758i | ||
−0.388050 | + | 0.921638i | ||||||||
0 | 0 | |||||||||
6.87405e8 | − | 1.19062e9i | 0.0717248 | − | 0.124231i | |||||
0 | 0 | |||||||||
−6.93507e9 | −0.716535 | |||||||||
0 | 0 | |||||||||
2.89845e10 | 2.96548 | |||||||||
0 | 0 | |||||||||
1.16713e9 | − | 2.02154e9i | 0.118251 | − | 0.204816i | |||||
0 | 0 | |||||||||
8.19259e9 | + | 1.41900e10i | 0.821997 | + | 1.42374i | 0.904193 | + | 0.427125i | ||
−0.0821957 | + | 0.996616i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.13949e8 | + | 1.58301e9i | 0.0899369 | + | 0.155775i | |||||
0 | 0 | |||||||||
−3.01882e9 | + | 5.22875e9i | −0.294208 | + | 0.509583i | |||||
0 | 0 | |||||||||
1.66277e10 | 1.60495 | 0.802474 | − | 0.596687i | ||||||
0.802474 | + | 0.596687i | ||||||||
0 | 0 | |||||||||
1.13647e10 | 1.08646 | |||||||||
0 | 0 | |||||||||
4.04247e8 | − | 7.00177e8i | 0.0382769 | − | 0.0662975i | |||||
0 | 0 | |||||||||
−7.28863e9 | − | 1.26243e10i | −0.683568 | − | 1.18398i | −0.973884 | − | 0.227044i | ||
0.290316 | − | 0.956931i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−6.22429e9 | − | 1.07808e10i | −0.572735 | − | 0.992006i | |||||
0 | 0 | |||||||||
−2.15001e9 | + | 3.72393e9i | −0.195968 | + | 0.339427i | −0.947218 | − | 0.320592i | ||
0.751249 | + | 0.660019i | ||||||||
0 | 0 | |||||||||
−2.05351e10 | −1.85410 | |||||||||
0 | 0 | |||||||||
−9.14731e9 | −0.818150 | −0.409075 | − | 0.912501i | ||||||
−0.409075 | + | 0.912501i | ||||||||
0 | 0 | |||||||||
−9.20720e9 | + | 1.59473e10i | −0.815794 | + | 1.41300i | |||||
0 | 0 | |||||||||
−2.83544e9 | − | 4.91113e9i | −0.248885 | − | 0.431081i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−8.59368e8 | − | 1.48847e9i | −0.0740354 | − | 0.128233i | 0.826631 | − | 0.562744i | ||
−0.900666 | + | 0.434511i | ||||||||
0 | 0 | |||||||||
−3.76045e9 | + | 6.51328e9i | −0.320964 | + | 0.555927i | |||||
0 | 0 | |||||||||
−9.05428e9 | −0.765666 | |||||||||
0 | 0 | |||||||||
−1.58386e10 | −1.32703 | −0.663517 | − | 0.748161i | ||||||
−0.663517 | + | 0.748161i | ||||||||
0 | 0 | |||||||||
2.73115e9 | − | 4.73049e9i | 0.226725 | − | 0.392699i | |||||
0 | 0 | |||||||||
−1.64664e9 | − | 2.85207e9i | −0.135442 | − | 0.234592i | 0.790324 | − | 0.612689i | ||
−0.925766 | + | 0.378096i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.54340e9 | + | 7.86940e9i | 0.366915 | + | 0.635516i | |||||
0 | 0 | |||||||||
−1.11096e10 | + | 1.92424e10i | −0.889028 | + | 1.53984i | |||||
0 | 0 | |||||||||
−1.80581e10 | −1.43196 | −0.715978 | − | 0.698123i | ||||||
−0.715978 | + | 0.698123i | ||||||||
0 | 0 | |||||||||
−2.63113e9 | −0.206753 | |||||||||
0 | 0 | |||||||||
7.87646e9 | − | 1.36424e10i | 0.613342 | − | 1.06234i | −0.377331 | − | 0.926079i | ||
0.990673 | − | 0.136261i | ||||||||
0 | 0 | |||||||||
−1.67121e10 | − | 2.89462e10i | −1.28966 | − | 2.23375i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−4.50285e9 | − | 7.79916e9i | −0.341276 | − | 0.591108i | |||||
0 | 0 | |||||||||
3.41077e9 | − | 5.90763e9i | 0.256197 | − | 0.443746i | |||||
0 | 0 | |||||||||
−3.99298e9 | −0.297257 | |||||||||
0 | 0 | |||||||||
−1.05271e10 | −0.776724 | |||||||||
0 | 0 | |||||||||
−5.11120e9 | + | 8.85285e9i | −0.373776 | + | 0.647398i | −0.990143 | − | 0.140060i | ||
0.616367 | + | 0.787459i | ||||||||
0 | 0 | |||||||||
−3.12443e9 | − | 5.41167e9i | −0.226465 | − | 0.392249i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−3.26193e8 | − | 5.64984e8i | −0.0232284 | − | 0.0402328i | |||||
0 | 0 | |||||||||
−1.16473e10 | + | 2.01737e10i | −0.822128 | + | 1.42397i | |||||
0 | 0 | |||||||||
1.44391e10 | 1.01027 | 0.505134 | − | 0.863041i | ||||||
0.505134 | + | 0.863041i | ||||||||
0 | 0 | |||||||||
8.16502e9 | 0.566296 | |||||||||
0 | 0 | |||||||||
−2.22609e9 | + | 3.85570e9i | −0.153048 | + | 0.265088i | |||||
0 | 0 | |||||||||
7.80672e9 | + | 1.35216e10i | 0.532064 | + | 0.921562i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.11897e9 | + | 8.86632e9i | 0.342867 | + | 0.593863i | |||||
0 | 0 | |||||||||
5.04427e9 | − | 8.73692e9i | 0.334949 | − | 0.580148i | −0.648526 | − | 0.761192i | ||
0.983475 | + | 0.181044i | ||||||||
0 | 0 | |||||||||
1.35981e9 | 0.0895172 | 0.0447586 | − | 0.998998i | ||||||
0.0447586 | + | 0.998998i | ||||||||
0 | 0 | |||||||||
−1.90890e9 | −0.124585 | |||||||||
0 | 0 | |||||||||
1.11929e10 | − | 1.93867e10i | 0.724256 | − | 1.25445i | |||||
0 | 0 | |||||||||
−5.53250e8 | − | 9.58256e8i | −0.0354931 | − | 0.0614758i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
7.49011e9 | + | 1.29733e10i | 0.472375 | + | 0.818178i | 0.999500 | − | 0.0316097i | ||
−0.527125 | + | 0.849788i | ||||||||
0 | 0 | |||||||||
9.80080e9 | − | 1.69755e10i | 0.612861 | − | 1.06151i | −0.377895 | − | 0.925849i | ||
0.990756 | − | 0.135658i | ||||||||
0 | 0 | |||||||||
2.63260e10 | 1.63229 | |||||||||
0 | 0 | |||||||||
1.68768e9 | 0.103758 | 0.0518789 | − | 0.998653i | ||||||
0.0518789 | + | 0.998653i | ||||||||
0 | 0 | |||||||||
8.22703e8 | − | 1.42496e9i | 0.0501536 | − | 0.0868686i | −0.839859 | − | 0.542805i | ||
0.890012 | + | 0.455936i | ||||||||
0 | 0 | |||||||||
5.53955e9 | + | 9.59478e9i | 0.334866 | + | 0.580005i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
1.57071e10 | + | 2.72054e10i | 0.933667 | + | 1.61716i | |||||
0 | 0 | |||||||||
1.10525e10 | − | 1.91435e10i | 0.651510 | − | 1.12845i | |||||
0 | 0 | |||||||||
−3.49725e9 | −0.204437 | −0.102219 | − | 0.994762i | ||||||
−0.102219 | + | 0.994762i | ||||||||
0 | 0 | |||||||||
−1.59629e10 | −0.925393 | |||||||||
0 | 0 | |||||||||
−1.06786e10 | + | 1.84959e10i | −0.613929 | + | 1.06336i | |||||
0 | 0 | |||||||||
3.63930e10 | + | 6.30346e10i | 2.07501 | + | 3.59402i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5.50741e9 | − | 9.53912e9i | −0.308866 | − | 0.534972i | |||||
0 | 0 | |||||||||
−1.99766e9 | + | 3.46004e9i | −0.111114 | + | 0.192454i | |||||
0 | 0 | |||||||||
2.86798e10 | 1.58218 | 0.791088 | − | 0.611702i | ||||||
0.791088 | + | 0.611702i | ||||||||
0 | 0 | |||||||||
1.24361e10 | 0.680461 | |||||||||
0 | 0 | |||||||||
−1.83667e10 | + | 3.18120e10i | −0.996776 | + | 1.72647i | −0.428901 | + | 0.903351i | ||
−0.567875 | + | 0.823115i | ||||||||
0 | 0 | |||||||||
−2.77367e9 | − | 4.80413e9i | −0.149306 | − | 0.258606i | 0.781665 | − | 0.623699i | ||
−0.930971 | + | 0.365092i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−2.63029e9 | − | 4.55579e9i | −0.139305 | − | 0.241283i | 0.787929 | − | 0.615766i | ||
−0.927234 | + | 0.374484i | ||||||||
0 | 0 | |||||||||
−8.29487e9 | + | 1.43671e10i | −0.435766 | + | 0.754769i | |||||
0 | 0 | |||||||||
1.18322e10 | 0.616594 | |||||||||
0 | 0 | |||||||||
8.10707e9 | 0.419078 | |||||||||
0 | 0 | |||||||||
2.23196e10 | − | 3.86587e10i | 1.14452 | − | 1.98236i | |||||
0 | 0 | |||||||||
−3.93064e9 | − | 6.80807e9i | −0.199946 | − | 0.346317i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.41580e10 | − | 2.45224e10i | −0.708767 | − | 1.22762i | −0.965315 | − | 0.261089i | ||
0.256548 | − | 0.966532i | ||||||||
0 | 0 | |||||||||
−8.40482e8 | + | 1.45576e9i | −0.0417414 | + | 0.0722983i | |||||
0 | 0 | |||||||||
−5.58205e9 | −0.275029 | −0.137514 | − | 0.990500i | ||||||
−0.137514 | + | 0.990500i | ||||||||
0 | 0 | |||||||||
−2.81316e10 | −1.37509 | −0.687547 | − | 0.726140i | ||||||
−0.687547 | + | 0.726140i | ||||||||
0 | 0 | |||||||||
−1.47747e10 | + | 2.55906e10i | −0.716502 | + | 1.24102i | |||||
0 | 0 | |||||||||
4.96052e6 | + | 8.59188e6i | 0.000238668 | + | 0.000413386i | 0.866145 | − | 0.499793i | ||
−0.865906 | + | 0.500207i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.68590e9 | + | 9.84828e9i | 0.269295 | + | 0.466432i | |||||
0 | 0 | |||||||||
5.58729e9 | − | 9.67746e9i | 0.262555 | − | 0.454759i | |||||
0 | 0 | |||||||||
6.45164e10 | 3.00808 | |||||||||
0 | 0 | |||||||||
1.95872e10 | 0.906147 | |||||||||
0 | 0 | |||||||||
−3.56229e9 | + | 6.17006e9i | −0.163520 | + | 0.283224i | |||||
0 | 0 | |||||||||
−1.61909e10 | − | 2.80435e10i | −0.737453 | − | 1.27731i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.75580e9 | + | 8.23730e9i | 0.213282 | + | 0.369415i | |||||
0 | 0 | |||||||||
8.05863e8 | − | 1.39579e9i | 0.0358621 | − | 0.0621149i | −0.847537 | − | 0.530736i | ||
0.883399 | + | 0.468621i | ||||||||
0 | 0 | |||||||||
4.72472e9 | 0.208642 | |||||||||
0 | 0 | |||||||||
−2.31768e10 | −1.01564 | −0.507818 | − | 0.861464i | ||||||
−0.507818 | + | 0.861464i | ||||||||
0 | 0 | |||||||||
1.67202e10 | − | 2.89602e10i | 0.727100 | − | 1.25937i | |||||
0 | 0 | |||||||||
−4.33805e8 | − | 7.51373e8i | −0.0187207 | − | 0.0324251i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
6.83205e9 | + | 1.18335e10i | 0.290367 | + | 0.502930i | 0.973896 | − | 0.226993i | ||
−0.683530 | + | 0.729923i | ||||||||
0 | 0 | |||||||||
7.89992e9 | − | 1.36831e10i | 0.333207 | − | 0.577131i | |||||
0 | 0 | |||||||||
2.44613e10 | 1.02394 | |||||||||
0 | 0 | |||||||||
−1.92558e10 | −0.799953 | |||||||||
0 | 0 | |||||||||
1.42811e9 | − | 2.47355e9i | 0.0588818 | − | 0.101986i | |||||
0 | 0 | |||||||||
1.67141e10 | + | 2.89497e10i | 0.683956 | + | 1.18465i | 0.973764 | + | 0.227562i | ||
−0.289808 | + | 0.957085i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−1.48908e10 | − | 2.57916e10i | −0.600250 | − | 1.03966i | |||||
0 | 0 | |||||||||
−2.67918e10 | + | 4.64048e10i | −1.07192 | + | 1.85662i | |||||
0 | 0 | |||||||||
1.04114e10 | 0.413450 | 0.206725 | − | 0.978399i | ||||||
0.206725 | + | 0.978399i | ||||||||
0 | 0 | |||||||||
1.67196e10 | 0.659017 | |||||||||
0 | 0 | |||||||||
−2.50008e10 | + | 4.33027e10i | −0.978117 | + | 1.69415i | −0.308877 | + | 0.951102i | ||
−0.669240 | + | 0.743047i | ||||||||
0 | 0 | |||||||||
4.29499e9 | + | 7.43914e9i | 0.166790 | + | 0.288890i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
9.13649e9 | + | 1.58249e10i | 0.349586 | + | 0.605501i | 0.986176 | − | 0.165702i | ||
−0.636590 | + | 0.771203i | ||||||||
0 | 0 | |||||||||
−2.79940e10 | + | 4.84870e10i | −1.06324 | + | 1.84159i | |||||
0 | 0 | |||||||||
6.12420e9 | 0.230897 | |||||||||
0 | 0 | |||||||||
−1.24663e10 | −0.466565 | −0.233282 | − | 0.972409i | ||||||
−0.233282 | + | 0.972409i | ||||||||
0 | 0 | |||||||||
8.79553e9 | − | 1.52343e10i | 0.326776 | − | 0.565993i | |||||
0 | 0 | |||||||||
−2.80578e9 | − | 4.85975e9i | −0.103481 | − | 0.179235i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
−5.96436e9 | − | 1.03306e10i | −0.216786 | − | 0.375485i | |||||
0 | 0 | |||||||||
−2.27762e9 | + | 3.94495e9i | −0.0821844 | + | 0.142348i | |||||
0 | 0 | |||||||||
−8.95225e10 | −3.20691 | |||||||||
0 | 0 | |||||||||
4.12045e9 | 0.146539 | 0.0732693 | − | 0.997312i | ||||||
0.0732693 | + | 0.997312i | ||||||||
0 | 0 | |||||||||
1.89816e10 | − | 3.28771e10i | 0.670193 | − | 1.16081i | |||||
0 | 0 | |||||||||
6.21190e9 | + | 1.07593e10i | 0.217749 | + | 0.377153i | 0.954120 | − | 0.299426i | ||
−0.736370 | + | 0.676579i | ||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
4.72011e10 | + | 8.17547e10i | 1.63093 | + | 2.82486i | |||||
0 | 0 | |||||||||
−2.25652e10 | + | 3.90840e10i | −0.774119 | + | 1.34081i | 0.161170 | + | 0.986927i | ||
−0.935289 | + | 0.353886i | ||||||||
0 | 0 | |||||||||
−2.62539e10 | −0.894241 | |||||||||
0 | 0 | |||||||||
7.62265e9 | 0.257789 | |||||||||
0 | 0 | |||||||||
−2.87779e9 | + | 4.98448e9i | −0.0966321 | + | 0.167372i | −0.910289 | − | 0.413974i | ||
0.813656 | + | 0.581346i | ||||||||
0 | 0 | |||||||||
−3.46156e10 | − | 5.99560e10i | −1.15410 | − | 1.99897i | |||||
0 | 0 | |||||||||
0 | 0 | |||||||||
0 | 0 | |||||||||
5.27711e8 | + | 9.14022e8i | 0.0173464 | + | 0.0300448i | |||||
0 | 0 | |||||||||
1.82054e10 | − | 3.15327e10i | 0.594214 | − | 1.02921i | −0.399443 | − | 0.916758i | ||
0.993657 | − | 0.112451i | ||||||||
0 | 0 | |||||||||
3.78098e10 | 1.22541 | |||||||||
0 | 0 | |||||||||
−7.26313e10 | −2.33745 | |||||||||
0 | 0 | |||||||||
−5.65165e9 | + | 9.78895e9i | −0.180610 | + | 0.312826i | −0.942089 | − | 0.335364i | ||
0.761478 | + | 0.648190i | ||||||||
0 | 0 | |||||||||
−6.36738e9 | − | 1.10286e10i | −0.202060 | − | 0.349979i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 196.8.e.b.165.1 | 4 | ||
7.2 | even | 3 | inner | 196.8.e.b.177.1 | 4 | ||
7.3 | odd | 6 | 196.8.a.a.1.1 | 2 | |||
7.4 | even | 3 | 28.8.a.b.1.2 | ✓ | 2 | ||
7.5 | odd | 6 | 196.8.e.c.177.2 | 4 | |||
7.6 | odd | 2 | 196.8.e.c.165.2 | 4 | |||
21.11 | odd | 6 | 252.8.a.f.1.2 | 2 | |||
28.11 | odd | 6 | 112.8.a.h.1.1 | 2 | |||
56.11 | odd | 6 | 448.8.a.q.1.2 | 2 | |||
56.53 | even | 6 | 448.8.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.8.a.b.1.2 | ✓ | 2 | 7.4 | even | 3 | ||
112.8.a.h.1.1 | 2 | 28.11 | odd | 6 | |||
196.8.a.a.1.1 | 2 | 7.3 | odd | 6 | |||
196.8.e.b.165.1 | 4 | 1.1 | even | 1 | trivial | ||
196.8.e.b.177.1 | 4 | 7.2 | even | 3 | inner | ||
196.8.e.c.165.2 | 4 | 7.6 | odd | 2 | |||
196.8.e.c.177.2 | 4 | 7.5 | odd | 6 | |||
252.8.a.f.1.2 | 2 | 21.11 | odd | 6 | |||
448.8.a.o.1.1 | 2 | 56.53 | even | 6 | |||
448.8.a.q.1.2 | 2 | 56.11 | odd | 6 |