Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,8,Mod(168,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.168");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | |||
Weight: | |||
Character orbit: | 169.b (of order , degree , not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | |
Analytic rank: | |
Dimension: | |
Coefficient field: | |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
|
Coefficient ring: | |
Coefficient ring index: | |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: |
Embedding invariants
Embedding label | 168.10 | ||
Root | of defining polynomial | ||
Character | 169.168 | ||
Dual form | 169.8.b.d.168.5 |
-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 .
8.41902i | 0.744143i | 0.928204 | + | 0.372071i | ||||||
−0.928204 | + | 0.372071i | ||||||||
−1.14749 | −0.0245371 | −0.0122686 | − | 0.999925i | ||||||
−0.0122686 | + | 0.999925i | ||||||||
57.1202 | 0.446251 | |||||||||
399.024i | 1.42759i | 0.700353 | + | 0.713797i | ||||||
−0.700353 | + | 0.713797i | ||||||||
− 9.66073i | − 0.0182591i | |||||||||
− 944.231i | − 1.04048i | −0.854019 | − | 0.520242i | ||||||
0.854019 | − | 0.520242i | ||||||||
1558.53i | 1.07622i | |||||||||
−2185.68 | −0.999398 | |||||||||
−3359.39 | −1.06233 | |||||||||
5673.16i | 1.28514i | 0.766227 | + | 0.642571i | ||||||
−0.766227 | + | 0.642571i | ||||||||
−65.5447 | −0.0109497 | |||||||||
0 | 0 | |||||||||
7949.50 | 0.774268 | |||||||||
− 457.876i | − 0.0350291i | |||||||||
−5809.90 | −0.354608 | |||||||||
−12214.2 | −0.602968 | −0.301484 | − | 0.953471i | ||||||
−0.301484 | + | 0.953471i | ||||||||
− 18401.3i | − 0.743695i | |||||||||
− 48622.1i | − 1.62628i | −0.582067 | − | 0.813141i | ||||||
0.582067 | − | 0.813141i | ||||||||
22792.3i | 0.637065i | |||||||||
1083.49i | 0.0255305i | |||||||||
−47762.4 | −0.956329 | |||||||||
−3416.52 | −0.0585512 | −0.0292756 | − | 0.999571i | ||||||
−0.0292756 | + | 0.999571i | ||||||||
− 1788.40i | − 0.0264073i | |||||||||
−81095.5 | −1.03802 | |||||||||
0 | 0 | |||||||||
5017.60 | 0.0490595 | |||||||||
− 53934.6i | − 0.464317i | |||||||||
−126824. | −0.965626 | −0.482813 | − | 0.875724i | ||||||
−0.482813 | + | 0.875724i | ||||||||
3854.87 | 0.0260666 | |||||||||
170057.i | 1.02525i | 0.858614 | + | 0.512623i | ||||||
−0.858614 | + | 0.512623i | ||||||||
150578.i | 0.812338i | |||||||||
− 6509.89i | − 0.0315337i | |||||||||
− 102832.i | − 0.448694i | |||||||||
376771. | 1.48539 | |||||||||
−124847. | −0.445983 | |||||||||
149165.i | 0.484129i | 0.970260 | + | 0.242065i | ||||||
−0.970260 | + | 0.242065i | ||||||||
409350. | 1.21019 | |||||||||
0 | 0 | |||||||||
−621892. | −1.53640 | |||||||||
− 645325.i | − 1.46230i | −0.682219 | − | 0.731148i | ||||||
0.682219 | − | 0.731148i | ||||||||
−9121.96 | −0.0189983 | |||||||||
−129943. | −0.249238 | −0.124619 | − | 0.992205i | ||||||
−0.124619 | + | 0.992205i | ||||||||
324052.i | 0.573496i | |||||||||
− 872141.i | − 1.42673i | |||||||||
− 28763.7i | − 0.0435705i | |||||||||
338496.i | 0.475566i | 0.971318 | + | 0.237783i | ||||||
−0.971318 | + | 0.237783i | ||||||||
6666.80 | 0.00870108 | |||||||||
−68029.2 | −0.0826056 | |||||||||
− 682745.i | − 0.772437i | |||||||||
14015.7 | 0.0147951 | |||||||||
0 | 0 | |||||||||
−226916. | −0.209362 | −0.104681 | − | 0.994506i | ||||||
−0.104681 | + | 0.994506i | ||||||||
42243.3i | 0.0365073i | |||||||||
−2.26373e6 | −1.83466 | |||||||||
1.47161e6 | 1.11979 | |||||||||
55793.3i | 0.0399043i | |||||||||
− 1.06773e6i | − 0.718564i | |||||||||
1.60203e6i | 1.01552i | 0.861498 | + | 0.507762i | ||||||
−0.861498 | + | 0.507762i | ||||||||
− 26154.0i | − 0.0156318i | |||||||||
−2.00107e6 | −1.12877 | −0.564387 | − | 0.825510i | ||||||
−0.564387 | + | 0.825510i | ||||||||
−1.43171e6 | −0.762930 | |||||||||
2.06379e6i | 1.03986i | |||||||||
−2.01139e6 | −0.959104 | |||||||||
0 | 0 | |||||||||
54806.9 | 0.0234656 | |||||||||
− 1.38038e6i | − 0.560706i | −0.959897 | − | 0.280353i | ||||||
0.959897 | − | 0.280353i | ||||||||
−697677. | −0.269075 | |||||||||
3920.41 | 0.00143668 | |||||||||
3.17204e6i | 1.10534i | |||||||||
− 5.13680e6i | − 1.70329i | −0.524120 | − | 0.851644i | ||||||
0.524120 | − | 0.851644i | ||||||||
− 3.40645e6i | − 1.07557i | |||||||||
− 5.76900e6i | − 1.73568i | −0.496839 | − | 0.867842i | ||||||
0.496839 | − | 0.867842i | ||||||||
−1.25582e6 | −0.360261 | |||||||||
93056.2 | 0.0254701 | |||||||||
− 2.77730e6i | − 0.725731i | |||||||||
5.35678e6 | 1.33717 | |||||||||
0 | 0 | |||||||||
−4.45623e6 | −1.01689 | −0.508444 | − | 0.861095i | ||||||
−0.508444 | + | 0.861095i | ||||||||
− 2.31829e6i | − 0.506237i | |||||||||
4.77433e6 | 0.998194 | |||||||||
5.43300e6 | 1.08816 | |||||||||
− 811479.i | − 0.155777i | −0.996962 | − | 0.0778886i | ||||||
0.996962 | − | 0.0778886i | ||||||||
61889.4i | 0.0113930i | |||||||||
− 4.87377e6i | − 0.860793i | |||||||||
− 1.09399e6i | − 0.185468i | |||||||||
145529. | 0.0236937 | |||||||||
−8.84179e6 | −1.38309 | |||||||||
− 5.15613e6i | − 0.775281i | −0.921811 | − | 0.387640i | ||||||
0.921811 | − | 0.387640i | ||||||||
7.34257e6 | 1.06169 | |||||||||
0 | 0 | |||||||||
−195152. | −0.0261286 | |||||||||
− 195138.i | − 0.0251566i | |||||||||
−2.84980e6 | −0.353889 | |||||||||
1.94014e7 | 2.32167 | |||||||||
− 172787.i | − 0.0199325i | |||||||||
− 3.83876e6i | − 0.427061i | −0.976936 | − | 0.213530i | ||||||
0.976936 | − | 0.213530i | ||||||||
− 572739.i | − 0.0614703i | |||||||||
− 1.23997e7i | − 1.28437i | |||||||||
−4.63219e6 | −0.463219 | |||||||||
9.61610e6 | 0.928697 | 0.464348 | − | 0.885653i | ||||||
0.464348 | + | 0.885653i | ||||||||
117998.i | 0.0110097i | |||||||||
−2.86658e6 | −0.258484 | −0.129242 | − | 0.991613i | ||||||
−0.129242 | + | 0.991613i | ||||||||
0 | 0 | |||||||||
−432341. | −0.0364472 | |||||||||
− 1.91041e6i | − 0.155796i | |||||||||
−198466. | −0.0156618 | −0.00783091 | − | 0.999969i | ||||||
−0.00783091 | + | 0.999969i | ||||||||
286606. | 0.0218929 | |||||||||
1.82103e7i | 1.34687i | 0.739249 | + | 0.673433i | ||||||
−0.739249 | + | 0.673433i | ||||||||
− 1.90584e7i | − 1.36525i | |||||||||
− 171165.i | − 0.0118791i | |||||||||
5.48589e6i | 0.368964i | |||||||||
−8.14016e6 | −0.530711 | −0.265356 | − | 0.964151i | ||||||
−0.265356 | + | 0.964151i | ||||||||
−469725. | −0.0296945 | |||||||||
− 1.36327e6i | − 0.0835873i | |||||||||
−7.24421e6 | −0.430912 | |||||||||
0 | 0 | |||||||||
−1.34876e7 | −0.755694 | |||||||||
1.15330e7i | 0.627378i | |||||||||
713613. | 0.0376989 | |||||||||
−1.26976e7 | −0.651588 | |||||||||
− 1.68470e7i | − 0.839969i | |||||||||
740504.i | 0.0358806i | |||||||||
9.71368e6i | 0.457517i | |||||||||
− 1.18532e6i | − 0.0542813i | |||||||||
−1.73751e7 | −0.773802 | |||||||||
−3.41396e7 | −1.47892 | −0.739460 | − | 0.673200i | ||||||
−0.739460 | + | 0.673200i | ||||||||
2.34010e6i | 0.0986277i | |||||||||
149108. | 0.00611558 | |||||||||
0 | 0 | |||||||||
6.55064e6 | 0.254586 | 0.127293 | − | 0.991865i | ||||||
0.127293 | + | 0.991865i | ||||||||
− 371846.i | − 0.0140720i | |||||||||
−4.59105e7 | −1.69212 | |||||||||
1.16214e7 | 0.417246 | |||||||||
2.00215e6i | 0.0700370i | |||||||||
− 1.90362e7i | − 0.648924i | |||||||||
− 1.53188e7i | − 0.508984i | −0.967075 | − | 0.254492i | ||||||
0.967075 | − | 0.254492i | ||||||||
33006.0i | 0.00106910i | |||||||||
1.12089e7 | 0.354007 | 0.177004 | − | 0.984210i | ||||||
0.177004 | + | 0.984210i | ||||||||
2.15212e7 | 0.662856 | |||||||||
− 388420.i | − 0.0116690i | |||||||||
4.32468e7 | 1.26749 | |||||||||
0 | 0 | |||||||||
1.26986e7 | 0.354395 | |||||||||
− 5.06059e7i | − 1.37852i | |||||||||
4.85693e7 | 1.29160 | |||||||||
78062.8 | 0.00202690 | |||||||||
8.52034e6i | 0.216043i | |||||||||
3.85311e7i | 0.954243i | 0.878837 | + | 0.477121i | ||||||
−0.878837 | + | 0.477121i | ||||||||
783442.i | 0.0189534i | |||||||||
4.08938e7i | 0.966581i | 0.875460 | + | 0.483290i | ||||||
−0.875460 | + | 0.483290i | ||||||||
7.57790e7 | 1.75023 | |||||||||
2.66964e7 | 0.602605 | |||||||||
4.50988e7i | 0.995044i | |||||||||
−6.78568e7 | −1.46363 | |||||||||
0 | 0 | |||||||||
−2.52905e7 | −0.521565 | −0.260783 | − | 0.965398i | ||||||
−0.260783 | + | 0.965398i | ||||||||
− 3.75171e7i | − 0.756710i | |||||||||
260383. | 0.00513716 | |||||||||
−6.00844e7 | −1.15969 | |||||||||
3.22598e6i | 0.0609216i | |||||||||
4.01952e7i | 0.742799i | |||||||||
6.83917e7i | 1.23693i | 0.785810 | + | 0.618467i | ||||||
−0.785810 | + | 0.618467i | ||||||||
− 3.68611e7i | − 0.652551i | |||||||||
2.59761e6 | 0.0450173 | |||||||||
6.83186e6 | 0.115921 | |||||||||
− 2.92588e7i | − 0.486126i | −0.970010 | − | 0.243063i | ||||||
0.970010 | − | 0.243063i | ||||||||
−1.68866e6 | −0.0274764 | |||||||||
0 | 0 | |||||||||
4.10323e7 | 0.640553 | |||||||||
1.06272e8i | 1.62530i | |||||||||
−7.42237e6 | −0.111223 | |||||||||
−9.01124e7 | −1.32319 | −0.661597 | − | 0.749860i | ||||||
−0.661597 | + | 0.749860i | ||||||||
1.22521e6i | 0.0176315i | |||||||||
7.65729e7i | 1.08005i | |||||||||
− 3.29605e7i | − 0.455722i | |||||||||
− 1.83832e6i | − 0.0249180i | |||||||||
4.34096e7 | 0.576920 | |||||||||
−1.69729e7 | −0.221193 | −0.110596 | − | 0.993865i | ||||||
−0.110596 | + | 0.993865i | ||||||||
− 4.98168e7i | − 0.636682i | |||||||||
−4.68911e7 | −0.587781 | −0.293890 | − | 0.955839i | ||||||
−0.293890 | + | 0.955839i | ||||||||
0 | 0 | |||||||||
2.29620e6 | 0.0276969 | |||||||||
− 5.32474e6i | − 0.0630139i | |||||||||
−5.95206e7 | −0.691140 | |||||||||
1.64287e6 | 0.0187201 | |||||||||
− 6.92932e7i | − 0.774898i | |||||||||
1.93349e7i | 0.212222i | |||||||||
− 4.73778e6i | − 0.0510456i | |||||||||
1.63341e8i | 1.72765i | |||||||||
−1.32211e8 | −1.37294 | −0.686470 | − | 0.727158i | ||||||
−0.686470 | + | 0.727158i | ||||||||
2.30804e6 | 0.0235337 | |||||||||
1.37264e8i | 1.37438i | 0.726480 | + | 0.687188i | ||||||
−0.726480 | + | 0.687188i | ||||||||
3.23186e7 | 0.317794 | |||||||||
0 | 0 | |||||||||
−3.88584e6 | −0.0368628 | |||||||||
1.66568e8i | 1.55225i | 0.630581 | + | 0.776123i | ||||||
−0.630581 | + | 0.776123i | ||||||||
1.04394e8 | 0.955753 | |||||||||
−5.79904e7 | −0.521639 | −0.260819 | − | 0.965388i | ||||||
−0.260819 | + | 0.965388i | ||||||||
− 1.26390e8i | − 1.11714i | |||||||||
1.58396e6i | 0.0137581i | |||||||||
8.09581e7i | 0.691083i | |||||||||
1.19751e8i | 1.00472i | |||||||||
800577. | 0.00660233 | |||||||||
2.57501e8 | 2.08756 | |||||||||
− 2.41338e7i | − 0.192349i | |||||||||
7.46742e6 | 0.0585160 | |||||||||
0 | 0 | |||||||||
2.75841e8 | 2.09000 | |||||||||
− 3.63988e6i | − 0.0271219i | |||||||||
1.21082e8 | 0.887345 | 0.443673 | − | 0.896189i | ||||||
0.443673 | + | 0.896189i | ||||||||
−1.29615e7 | −0.0934283 | |||||||||
5.89442e6i | 0.0417938i | |||||||||
− 1.67089e6i | − 0.0116546i | |||||||||
− 5.18505e7i | − 0.355810i | |||||||||
7.82009e6i | 0.0527987i | |||||||||
1.60573e8 | 1.06675 | |||||||||
−1.53313e8 | −1.00226 | |||||||||
6.61987e6i | 0.0425887i | |||||||||
−1.29305e8 | −0.818719 | |||||||||
0 | 0 | |||||||||
1.44104e6 | 0.00883979 | |||||||||
− 4.62753e7i | − 0.279436i | −0.990191 | − | 0.139718i | ||||||
0.990191 | − | 0.139718i | ||||||||
1.42181e8 | 0.845224 | |||||||||
1.77249e8 | 1.03740 | |||||||||
− 6.85321e7i | − 0.394925i | |||||||||
3.36801e8i | 1.91110i | 0.294834 | + | 0.955548i | ||||||
−0.294834 | + | 0.955548i | ||||||||
3.18692e6i | 0.0178074i | |||||||||
− 2.88661e8i | − 1.58841i | −0.607648 | − | 0.794206i | ||||||
0.607648 | − | 0.794206i | ||||||||
1.14774e7 | 0.0622009 | |||||||||
−6.14684e6 | −0.0328103 | |||||||||
− 1.97659e8i | − 1.03922i | |||||||||
9.81949e7 | 0.508561 | 0.254281 | − | 0.967130i | ||||||
0.254281 | + | 0.967130i | ||||||||
0 | 0 | |||||||||
−1.35068e8 | −0.678914 | |||||||||
9.15085e7i | 0.453179i | |||||||||
5.11348e6 | 0.0249515 | |||||||||
−9.70968e7 | −0.466859 | |||||||||
1.13856e8i | 0.539465i | 0.962935 | + | 0.269733i | ||||||
−0.962935 | + | 0.269733i | ||||||||
2.66022e6i | 0.0124216i | |||||||||
− 7.42915e7i | − 0.341884i | −0.985281 | − | 0.170942i | ||||||
0.985281 | − | 0.170942i | ||||||||
− 1.06901e8i | − 0.484874i | |||||||||
−1.64520e7 | −0.0735523 | |||||||||
−1.14301e8 | −0.503717 | |||||||||
− 2.71453e7i | − 0.117927i | |||||||||
−6.23431e6 | −0.0267003 | |||||||||
0 | 0 | |||||||||
−2.65039e8 | −1.10339 | |||||||||
931163.i | 0.00382233i | |||||||||
9.97923e6 | 0.0403931 | |||||||||
−1.42394e8 | −0.568375 | −0.284188 | − | 0.958769i | ||||||
−0.284188 | + | 0.958769i | ||||||||
1.17884e8i | 0.464038i | |||||||||
− 1.93824e7i | − 0.0752466i | |||||||||
− 2.87421e8i | − 1.10053i | |||||||||
5.59259e6i | 0.0211214i | |||||||||
−2.77159e8 | −1.03250 | |||||||||
2.92823e8 | 1.07607 | 0.538033 | − | 0.842924i | ||||||
0.538033 | + | 0.842924i | ||||||||
1.25534e6i | 0.00455086i | |||||||||
1.40846e8 | 0.503728 | |||||||||
0 | 0 | |||||||||
2.77197e8 | 0.965044 | |||||||||
5.51500e7i | 0.189448i | |||||||||
−3.05065e8 | −1.03406 | −0.517032 | − | 0.855966i | ||||||
−0.517032 | + | 0.855966i | ||||||||
1.01459e7 | 0.0339371 | |||||||||
− 9.05449e7i | − 0.298884i | |||||||||
− 3.86521e8i | − 1.25918i | |||||||||
5.91660e6i | 0.0190232i | |||||||||
− 7.88473e7i | − 0.250216i | |||||||||
2.31855e8 | 0.726246 | 0.363123 | − | 0.931741i | ||||||
0.363123 | + | 0.931741i | ||||||||
−1.68561e7 | −0.0521176 | |||||||||
4.92648e8i | 1.50364i | 0.659368 | + | 0.751821i | ||||||
−0.659368 | + | 0.751821i | ||||||||
7.09634e7 | 0.213817 | |||||||||
0 | 0 | |||||||||
1.28970e8 | 0.378757 | |||||||||
− 4.60068e8i | − 1.33401i | |||||||||
223935. | 0.000641120 0 | |||||||||
4.33329e8 | 1.22501 | 0.612503 | − | 0.790468i | ||||||
0.612503 | + | 0.790468i | ||||||||
9.43681e7i | 0.263432i | |||||||||
− 3.71690e8i | − 1.02463i | |||||||||
5.87209e8i | 1.59860i | |||||||||
2.88578e8i | 0.775874i | 0.921686 | + | 0.387937i | ||||||
−0.921686 | + | 0.387937i | ||||||||
3.27011e6 | 0.00868342 | |||||||||
−5.98945e8 | −1.57085 | −0.785424 | − | 0.618958i | ||||||
−0.785424 | + | 0.618958i | ||||||||
− 2.93415e8i | − 0.760095i | |||||||||
−2.22629e7 | −0.0569671 | |||||||||
0 | 0 | |||||||||
−6.09336e8 | −1.52149 | |||||||||
− 3.29116e8i | − 0.811849i | |||||||||
−2.61152e8 | −0.636430 | |||||||||
4.26052e8 | 1.02582 | |||||||||
4.40493e6i | 0.0104789i | |||||||||
− 3.29527e8i | − 0.774552i | |||||||||
− 3.12931e7i | − 0.0726794i | −0.999339 | − | 0.0363397i | ||||||
0.999339 | − | 0.0363397i | ||||||||
657212.i | 0.00150831i | |||||||||
−6.39251e8 | −1.44975 | |||||||||
−2.32478e8 | −0.521029 | |||||||||
2.84657e7i | 0.0630484i | |||||||||
−3.24394e8 | −0.710093 | |||||||||
0 | 0 | |||||||||
5.31539e6 | 0.0113661 | |||||||||
1.22696e8i | 0.259328i | |||||||||
−3.44286e8 | −0.719274 | |||||||||
−1.10344e7 | −0.0227876 | |||||||||
2.82490e8i | 0.576693i | |||||||||
− 7.98474e8i | − 1.61143i | |||||||||
2.24757e8i | 0.448424i | |||||||||
2.40062e8i | 0.473520i | 0.971568 | + | 0.236760i | ||||||
−0.971568 | + | 0.236760i | ||||||||
3.05980e8 | 0.596713 | |||||||||
3.28937e6 | 0.00634247 | |||||||||
− 5.71288e8i | − 1.08915i | |||||||||
1.13878e8 | 0.214674 | 0.107337 | − | 0.994223i | ||||||
0.107337 | + | 0.994223i | ||||||||
0 | 0 | |||||||||
−2.86637e8 | −0.528356 | −0.264178 | − | 0.964474i | ||||||
−0.264178 | + | 0.964474i | ||||||||
− 2.12921e8i | − 0.388119i | |||||||||
−8.23503e8 | −1.48449 | |||||||||
−2.54541e8 | −0.453788 | |||||||||
9.47644e8i | 1.67085i | 0.549603 | + | 0.835426i | ||||||
−0.549603 | + | 0.835426i | ||||||||
2.19217e6i | 0.00382278i | |||||||||
− 7.19494e8i | − 1.24097i | |||||||||
− 8.02593e8i | − 1.36921i | |||||||||
227737. | 0.000384296 0 | |||||||||
−2.71596e7 | −0.0453344 | |||||||||
5.93880e8i | 0.980596i | |||||||||
2.72711e8 | 0.445445 | |||||||||
0 | 0 | |||||||||
−5.75791e8 | −0.920456 | |||||||||
− 2.08961e7i | − 0.0330482i | |||||||||
1.00576e9 | 1.57375 | |||||||||
3.19618e8 | 0.494818 | |||||||||
2.18693e7i | 0.0334993i | |||||||||
6.84847e8i | 1.03800i | 0.854776 | + | 0.518998i | ||||||
−0.854776 | + | 0.518998i | ||||||||
− 4.63518e7i | − 0.0695158i | |||||||||
− 3.26028e8i | − 0.483838i | |||||||||
2.46330e8 | 0.361747 | |||||||||
5.50804e8 | 0.800460 | |||||||||
− 6.29500e6i | − 0.00905333i | |||||||||
1.12788e9 | 1.60531 | 0.802654 | − | 0.596445i | ||||||
0.802654 | + | 0.596445i | ||||||||
0 | 0 | |||||||||
9.34074e6 | 0.0130221 | |||||||||
− 2.78390e8i | − 0.384130i | |||||||||
−9.64760e8 | −1.31759 | |||||||||
−8.94710e8 | −1.20946 | |||||||||
− 7.13380e8i | − 0.954534i | |||||||||
− 2.02520e8i | − 0.268234i | |||||||||
1.56434e6i | 0.00205099i | |||||||||
− 7.58658e8i | − 0.984645i | |||||||||
−3.84792e8 | −0.494393 | −0.247197 | − | 0.968965i | ||||||
−0.247197 | + | 0.968965i | ||||||||
8.31265e6 | 0.0105733 | |||||||||
− 2.00731e8i | − 0.252770i | −0.991981 | − | 0.126385i | ||||||
0.991981 | − | 0.126385i | ||||||||
−6.44669e8 | −0.803708 | |||||||||
0 | 0 | |||||||||
−8.54254e8 | −1.04397 | |||||||||
− 3.55684e8i | − 0.430381i | −0.976572 | − | 0.215191i | ||||||
0.976572 | − | 0.215191i | ||||||||
1.54768e7 | 0.0185426 | |||||||||
2.04971e9 | 2.43160 | |||||||||
− 2.94519e8i | − 0.345970i | |||||||||
− 1.32340e7i | − 0.0153941i | |||||||||
− 1.42895e8i | − 0.164599i | |||||||||
1.16954e8i | 0.133409i | 0.997773 | + | 0.0667044i | ||||||
−0.997773 | + | 0.0667044i | ||||||||
1.35926e9 | 1.53548 | |||||||||
−1.47023e9 | −1.64479 | |||||||||
− 3.94777e8i | − 0.437393i | |||||||||
1.45703e7 | 0.0159881 | |||||||||
0 | 0 | |||||||||
2.30197e9 | 2.47785 | |||||||||
1.93318e7i | 0.0206104i | |||||||||
1.69538e9 | 1.79034 | 0.895169 | − | 0.445726i | ||||||
0.895169 | + | 0.445726i | ||||||||
1.98496e7 | 0.0207628 | |||||||||
1.41048e9i | 1.46142i | |||||||||
− 5.01104e8i | − 0.514307i | |||||||||
2.14261e8i | 0.217838i | |||||||||
− 1.11463e7i | − 0.0112262i | |||||||||
−1.30728e9 | −1.30433 | −0.652164 | − | 0.758078i | ||||||
−0.652164 | + | 0.758078i | ||||||||
5.83380e8 | 0.576635 | |||||||||
1.36014e6i | 0.00133191i | |||||||||
−5.27555e8 | −0.511812 | |||||||||
0 | 0 | |||||||||
3.98874e7 | 0.0379852 | |||||||||
8.39591e8i | 0.792192i | 0.918209 | + | 0.396096i | ||||||
−0.918209 | + | 0.396096i | ||||||||
1.10821e9 | 1.03605 | |||||||||
3.91748e7 | 0.0362885 | |||||||||
− 1.11309e9i | − 1.02166i | |||||||||
6.31720e8i | 0.574551i | 0.957848 | + | 0.287276i | ||||||
−0.957848 | + | 0.287276i | ||||||||
− 2.68523e6i | − 0.00242004i | |||||||||
2.13748e9i | 1.90893i | |||||||||
−1.15563e9 | −1.02273 | |||||||||
2.84014e8 | 0.249088 | |||||||||
− 2.19271e8i | − 0.190577i | |||||||||
−4.49938e8 | −0.387551 | −0.193776 | − | 0.981046i | ||||||
−0.193776 | + | 0.981046i | ||||||||
0 | 0 | |||||||||
4.17300e7 | 0.0353045 | |||||||||
− 1.06026e8i | − 0.0889016i | |||||||||
−7.51679e6 | −0.00624681 | |||||||||
−1.40234e9 | −1.15509 | |||||||||
− 1.77815e9i | − 1.45170i | |||||||||
− 7.08275e8i | − 0.573151i | |||||||||
− 1.42468e9i | − 1.14275i | −0.820690 | − | 0.571374i | ||||||
0.820690 | − | 0.571374i | ||||||||
− 4.88222e8i | − 0.388174i | |||||||||
5.26817e7 | 0.0415198 | |||||||||
4.71157e8 | 0.368092 | |||||||||
8.70028e8i | 0.673795i | 0.941541 | + | 0.336898i | ||||||
−0.941541 | + | 0.336898i | ||||||||
−1.33354e7 | −0.0102380 | |||||||||
0 | 0 | |||||||||
5.49273e8 | 0.414432 | |||||||||
1.90508e9i | 1.42502i | |||||||||
−1.00819e9 | −0.747653 | |||||||||
−8.46238e8 | −0.622174 | |||||||||
2.18438e7i | 0.0159228i | |||||||||
2.23157e9i | 1.61280i | 0.591373 | + | 0.806398i | ||||||
−0.591373 | + | 0.806398i | ||||||||
2.16790e9i | 1.55345i | |||||||||
1.75782e7i | 0.0124890i | |||||||||
−1.63740e8 | −0.115349 | |||||||||
1.51269e9 | 1.05663 | |||||||||
6.28683e7i | 0.0435442i | |||||||||
3.23800e8 | 0.222387 | |||||||||
0 | 0 | |||||||||
−1.28621e7 | −0.00868632 | |||||||||
2.32231e9i | 1.55526i | |||||||||
−8.31533e8 | −0.552243 | −0.276122 | − | 0.961123i | ||||||
−0.276122 | + | 0.961123i | ||||||||
−2.46954e7 | −0.0162646 | |||||||||
− 9.53842e8i | − 0.623002i | −0.950246 | − | 0.311501i | ||||||
0.950246 | − | 0.311501i | ||||||||
1.01940e9i | 0.660312i | |||||||||
− 7.39844e8i | − 0.475279i | |||||||||
− 3.53655e8i | − 0.225320i | |||||||||
9.90518e8 | 0.625894 | |||||||||
−4.96252e7 | −0.0311006 | |||||||||
1.88947e9i | 1.17447i | |||||||||
−1.13364e7 | −0.00698911 | |||||||||
0 | 0 | |||||||||
4.36530e8 | 0.264773 | |||||||||
− 1.01803e9i | − 0.612479i | −0.951954 | − | 0.306240i | ||||||
0.951954 | − | 0.306240i | ||||||||
−2.91518e7 | −0.0173969 | |||||||||
−1.81766e9 | −1.07598 | −0.537990 | − | 0.842951i | ||||||
−0.537990 | + | 0.842951i | ||||||||
1.35187e9i | 0.793816i | |||||||||
5.80697e7i | 0.0338250i | |||||||||
1.04018e9i | 0.601040i | |||||||||
1.66118e8i | 0.0952208i | |||||||||
−5.57328e7 | −0.0316921 | |||||||||
7.03870e8 | 0.397069 | 0.198535 | − | 0.980094i | ||||||
0.198535 | + | 0.980094i | ||||||||
− 3.52809e9i | − 1.97449i | |||||||||
1.48690e8 | 0.0825558 | |||||||||
0 | 0 | |||||||||
9.00901e7 | 0.0492339 | 0.0246169 | − | 0.999697i | ||||||
0.0246169 | + | 0.999697i | ||||||||
− 9.77699e6i | − 0.00530109i | |||||||||
2.05742e9 | 1.10679 | |||||||||
3.89592e8 | 0.207940 | |||||||||
− 4.42139e7i | − 0.0234144i | |||||||||
1.89921e9i | 0.997932i | |||||||||
− 1.03765e9i | − 0.540992i | −0.962721 | − | 0.270496i | ||||||
0.962721 | − | 0.270496i | ||||||||
1.49226e9i | 0.771972i | |||||||||
3.66104e9 | 1.87926 | |||||||||
−4.64967e8 | −0.236831 | |||||||||
− 4.69252e7i | − 0.0237171i | |||||||||
−2.83553e9 | −1.42213 | |||||||||
0 | 0 | |||||||||
−8.69555e7 | −0.0429457 | |||||||||
− 1.66801e9i | − 0.817507i | −0.912645 | − | 0.408754i | ||||||
0.912645 | − | 0.408754i | ||||||||
2.43024e9 | 1.18201 | |||||||||
−6.12860e7 | −0.0295813 | |||||||||
− 7.78704e7i | − 0.0373010i | |||||||||
2.90964e9i | 1.38320i | 0.722280 | + | 0.691601i | ||||||
−0.722280 | + | 0.691601i | ||||||||
− 5.17503e7i | − 0.0244155i | |||||||||
1.89500e9i | 0.887310i | 0.896198 | + | 0.443655i | ||||||
−0.896198 | + | 0.443655i | ||||||||
7.36836e8 | 0.342419 | |||||||||
7.78650e7 | 0.0359134 | |||||||||
8.26704e8i | 0.378442i | |||||||||
9.95155e8 | 0.452149 | 0.226075 | − | 0.974110i | ||||||
0.226075 | + | 0.974110i | ||||||||
0 | 0 | |||||||||
−1.30339e9 | −0.583405 | |||||||||
− 1.13714e9i | − 0.505209i | |||||||||
2.90206e7 | 0.0127977 | |||||||||
−2.49682e9 | −1.09292 | |||||||||
− 7.37188e8i | − 0.320305i | |||||||||
4.30504e7i | 0.0185675i | |||||||||
3.94303e9i | 1.68812i | |||||||||
6.58769e8i | 0.279968i | |||||||||
4.95966e8 | 0.209236 | |||||||||
−9.58556e8 | −0.401439 | |||||||||
1.39127e9i | 0.578411i | 0.957267 | + | 0.289206i | ||||||
−0.957267 | + | 0.289206i | ||||||||
6.89461e7 | 0.0284555 | |||||||||
0 | 0 | |||||||||
6.25461e8 | 0.254411 | |||||||||
− 3.70178e6i | − 0.00149484i | |||||||||
−7.25289e8 | −0.290772 | |||||||||
1.53176e9 | 0.609669 | |||||||||
− 1.38510e8i | − 0.0547335i | |||||||||
− 2.89212e9i | − 1.13466i | −0.823491 | − | 0.567329i | ||||||
0.823491 | − | 0.567329i | ||||||||
− 3.11872e9i | − 1.21481i | |||||||||
− 7.84787e7i | − 0.0303508i | |||||||||
2.28537e8 | 0.0877547 | |||||||||
3.80132e9 | 1.44927 | 0.724635 | − | 0.689133i | ||||||
0.724635 | + | 0.689133i | ||||||||
4.22977e7i | 0.0160117i | |||||||||
1.54906e9 | 0.582241 | |||||||||
0 | 0 | |||||||||
4.94780e9 | 1.83355 | |||||||||
− 9.88014e8i | − 0.363561i | |||||||||
−4.85032e9 | −1.77224 | |||||||||
−7.83948e6 | −0.00284436 | |||||||||
4.75421e8i | 0.171288i | 0.996326 | + | 0.0856439i | ||||||
−0.996326 | + | 0.0856439i | ||||||||
− 6.77057e7i | − 0.0242231i | |||||||||
3.35742e7i | 0.0119281i | |||||||||
− 1.19882e9i | − 0.422952i | |||||||||
−1.70972e9 | −0.599013 | −0.299506 | − | 0.954094i | ||||||
−0.299506 | + | 0.954094i | ||||||||
−3.21648e9 | −1.11911 | |||||||||
3.83706e9i | 1.32580i | |||||||||
1.63181e8 | 0.0559942 | |||||||||
0 | 0 | |||||||||
−1.95006e9 | −0.659970 | |||||||||
7.59754e8i | 0.255365i | 0.991815 | + | 0.127682i | ||||||
−0.991815 | + | 0.127682i | ||||||||
−4.70841e7 | −0.0157173 | |||||||||
−5.44727e9 | −1.80595 | |||||||||
− 2.03387e9i | − 0.669698i | |||||||||
− 2.43966e8i | − 0.0797846i | |||||||||
2.46528e9i | 0.800747i | |||||||||
− 1.14384e9i | − 0.369011i | |||||||||
8.51709e6 | 0.00272908 | |||||||||
−1.92034e9 | −0.611169 | |||||||||
1.18579e9i | 0.374846i | |||||||||
1.03403e8 | 0.0324674 | |||||||||
0 | 0 | |||||||||
−4.09809e9 | −1.26955 | −0.634774 | − | 0.772698i | ||||||
−0.634774 | + | 0.772698i | ||||||||
2.33373e9i | 0.718131i | |||||||||
−3.85404e9 | −1.17804 | −0.589021 | − | 0.808118i | ||||||
−0.589021 | + | 0.808118i | ||||||||
3.74174e8 | 0.113609 | |||||||||
− 8.78666e7i | − 0.0265012i | |||||||||
− 2.56835e9i | − 0.769491i | |||||||||
− 2.07711e9i | − 0.618190i | |||||||||
3.78218e7i | 0.0111821i | |||||||||
−3.39315e9 | −0.996572 | |||||||||
7.62299e8 | 0.222413 | |||||||||
− 3.50154e9i | − 1.01491i | |||||||||
−2.62241e9 | −0.755111 | |||||||||
0 | 0 | |||||||||
−4.98120e7 | −0.0141560 | |||||||||
− 7.91927e7i | − 0.0223587i | |||||||||
2.15136e9 | 0.603442 | |||||||||
1.94762e7 | 0.00542743 | |||||||||
1.95199e9i | 0.540431i | |||||||||
− 3.85941e8i | − 0.106160i | |||||||||
1.14363e8i | 0.0312541i | |||||||||
1.31488e8i | 0.0357022i | 0.999841 | + | 0.0178511i | ||||||
−0.999841 | + | 0.0178511i | ||||||||
−4.14761e9 | −1.11892 | |||||||||
5.38070e7 | 0.0144225 | |||||||||
− 1.83919e9i | − 0.489814i | |||||||||
−7.26635e9 | −1.92278 | |||||||||
0 | 0 | |||||||||
2.11326e9 | 0.552073 | 0.276037 | − | 0.961147i | ||||||
0.276037 | + | 0.961147i | ||||||||
− 8.75015e8i | − 0.227135i | |||||||||
4.37370e9 | 1.12809 | |||||||||
3.87332e9 | 0.992691 | |||||||||
6.16645e9i | 1.57038i | |||||||||
6.11008e6i | 0.00154618i | |||||||||
4.20771e9i | 1.05805i | |||||||||
3.64820e9i | 0.911579i | |||||||||
6.82992e7 | 0.0169586 | |||||||||
6.40255e8 | 0.157976 | |||||||||
− 2.39033e9i | − 0.586091i | −0.956098 | − | 0.293046i | ||||||
0.956098 | − | 0.293046i | ||||||||
3.12927e9 | 0.762470 | |||||||||
0 | 0 | |||||||||
−2.18901e9 | −0.526731 | |||||||||
7.95131e7i | 0.0190138i | |||||||||
−2.42954e9 | −0.577361 | |||||||||
5.42284e9 | 1.28070 | 0.640350 | − | 0.768083i | ||||||
0.640350 | + | 0.768083i | ||||||||
− 2.21866e7i | − 0.00520732i | |||||||||
− 3.24812e9i | − 0.757640i | |||||||||
− 5.04253e9i | − 1.16894i | |||||||||
− 4.50807e9i | − 1.03860i | |||||||||
8.00585e9 | 1.83311 | |||||||||
−1.61095e9 | −0.366598 | −0.183299 | − | 0.983057i | ||||||
−0.183299 | + | 0.983057i | ||||||||
− 1.87432e8i | − 0.0423917i | |||||||||
5.46762e9 | 1.22906 | 0.614528 | − | 0.788895i | ||||||
0.614528 | + | 0.788895i | ||||||||
0 | 0 | |||||||||
1.51711e8 | 0.0336880 | |||||||||
− 5.13001e9i | − 1.13221i | |||||||||
2.77064e8 | 0.0607775 | |||||||||
4.39626e9 | 0.958527 | |||||||||
− 3.08434e9i | − 0.668417i | −0.942499 | − | 0.334209i | ||||||
0.942499 | − | 0.334209i | ||||||||
− 2.19864e9i | − 0.473595i | |||||||||
− 1.57509e8i | − 0.0337233i | |||||||||
− 2.89062e9i | − 0.615167i | |||||||||
−7.66224e8 | −0.162084 | |||||||||
−3.70852e7 | −0.00779777 | |||||||||
− 1.28733e9i | − 0.269060i | |||||||||
8.99117e9 | 1.86797 | |||||||||
0 | 0 | |||||||||
2.63457e8 | 0.0540839 | |||||||||
1.47215e9i | 0.300413i | 0.988655 | + | 0.150206i | ||||||
−0.988655 | + | 0.150206i | ||||||||
4.45896e6 | 0.000904509 0 | |||||||||
8.26852e9 | 1.66734 | |||||||||
− 5.38186e9i | − 1.07882i | |||||||||
− 1.91135e8i | − 0.0380877i | |||||||||
− 8.66635e8i | − 0.171676i | |||||||||
− 5.98992e9i | − 1.17959i | −0.807554 | − | 0.589793i | ||||||
0.807554 | − | 0.589793i | ||||||||
−2.39653e8 | −0.0469170 | |||||||||
−4.60196e9 | −0.895640 | |||||||||
2.20090e9i | 0.425832i | |||||||||
6.65433e7 | 0.0127995 | |||||||||
0 | 0 | |||||||||
−6.44870e9 | −1.22597 | −0.612983 | − | 0.790096i | ||||||
−0.612983 | + | 0.790096i | ||||||||
1.45031e8i | 0.0274114i | |||||||||
5.19885e9 | 0.976892 | 0.488446 | − | 0.872594i | ||||||
0.488446 | + | 0.872594i | ||||||||
−1.03298e9 | −0.192977 | |||||||||
3.01706e9i | 0.560369i | |||||||||
2.33586e9i | 0.431338i | |||||||||
− 5.06665e9i | − 0.930202i | |||||||||
− 9.28985e7i | − 0.0169572i | |||||||||
−3.63606e9 | −0.659890 | −0.329945 | − | 0.944000i | ||||||
−0.329945 | + | 0.944000i | ||||||||
7.32142e9 | 1.32109 | |||||||||
− 1.37413e8i | − 0.0246529i | |||||||||
6.72237e9 | 1.19913 | |||||||||
0 | 0 | |||||||||
1.52490e9 | 0.268913 | |||||||||
− 1.64970e9i | − 0.289263i | −0.989486 | − | 0.144632i | ||||||
0.989486 | − | 0.144632i | ||||||||
−2.02108e9 | −0.352367 | |||||||||
−2.95479e8 | −0.0512229 | |||||||||
8.34869e9i | 1.43908i | |||||||||
6.85487e8i | 0.117490i | 0.998273 | + | 0.0587450i | ||||||
−0.998273 | + | 0.0587450i | ||||||||
2.76933e7i | 0.00471970i | |||||||||
3.07866e9i | 0.521728i | 0.965376 | + | 0.260864i | ||||||
−0.965376 | + | 0.260864i | ||||||||
−3.87599e9 | −0.653149 | |||||||||
−1.71427e7 | −0.00287249 | |||||||||
9.58744e8i | 0.159748i | |||||||||
−4.86858e9 | −0.806667 | |||||||||
0 | 0 | |||||||||
−5.86262e9 | −0.960531 | |||||||||
− 2.41320e9i | − 0.393172i | |||||||||
−3.16524e8 | −0.0512827 | |||||||||
−1.44460e9 | −0.232749 | |||||||||
− 1.82193e9i | − 0.291914i | |||||||||
− 6.93308e9i | − 1.10467i | |||||||||
− 8.91118e9i | − 1.41199i | −0.708215 | − | 0.705996i | ||||||
0.708215 | − | 0.705996i | ||||||||
− 6.94517e9i | − 1.09439i | |||||||||
−1.38941e8 | −0.0217729 | |||||||||
−7.97823e9 | −1.24335 | |||||||||
− 1.36225e10i | − 2.11130i | |||||||||
1.48731e7 | 0.00229246 | |||||||||
0 | 0 | |||||||||
6.05743e9 | 0.923455 | |||||||||
1.12274e10i | 1.70226i | |||||||||
−9.33756e8 | −0.140800 | |||||||||
−1.19624e9 | −0.179397 | −0.0896984 | − | 0.995969i | ||||||
−0.0896984 | + | 0.995969i | ||||||||
1.91732e6i | 0 0.000285971i | |||||||||
− 7.69066e9i | − 1.14084i | −0.821353 | − | 0.570421i | ||||||
0.821353 | − | 0.570421i | ||||||||
1.84269e8i | 0.0271863i | |||||||||
5.94978e7i | 0.00873056i | |||||||||
−4.99989e9 | −0.729703 | |||||||||
−2.75099e9 | −0.399322 | −0.199661 | − | 0.979865i | ||||||
−0.199661 | + | 0.979865i | ||||||||
7.44094e9i | 1.07427i | |||||||||
−9.08860e9 | −1.30509 | |||||||||
0 | 0 | |||||||||
−1.84256e8 | −0.0261750 | |||||||||
3.90655e9i | 0.551984i | |||||||||
−4.79202e9 | −0.673477 | −0.336738 | − | 0.941598i | ||||||
−0.336738 | + | 0.941598i | ||||||||
1.75925e8 | 0.0245926 | |||||||||
2.61387e9i | 0.363445i | |||||||||
3.74928e9i | 0.518542i | |||||||||
1.26092e10i | 1.73464i | |||||||||
2.69087e9i | 0.368215i | |||||||||
−4.70316e9 | −0.640164 | −0.320082 | − | 0.947390i | ||||||
−0.320082 | + | 0.947390i | ||||||||
1.48376e8 | 0.0200890 | |||||||||
− 4.42747e8i | − 0.0596280i | −0.999555 | − | 0.0298140i | ||||||
0.999555 | − | 0.0298140i | ||||||||
−5.76574e9 | −0.772417 | |||||||||
0 | 0 | |||||||||
1.26471e9 | 0.167650 | |||||||||
− 1.83194e10i | − 2.41566i | |||||||||
2.74483e9 | 0.360044 | |||||||||
4.33297e8 | 0.0565386 | |||||||||
− 1.67127e9i | − 0.216934i | |||||||||
5.31003e7i | 0.00685656i | |||||||||
4.63722e9i | 0.595657i | |||||||||
− 1.13524e10i | − 1.45063i | |||||||||
−1.63151e8 | −0.0207394 | |||||||||
−4.22977e9 | −0.534890 | −0.267445 | − | 0.963573i | ||||||
−0.267445 | + | 0.963573i | ||||||||
9.49564e9i | 1.19458i | |||||||||
−4.06905e8 | −0.0509249 | |||||||||
0 | 0 | |||||||||
2.02881e9 | 0.251294 | 0.125647 | − | 0.992075i | ||||||
0.125647 | + | 0.992075i | ||||||||
7.86398e7i | 0.00969033i | |||||||||
−3.62468e9 | −0.444350 | |||||||||
7.59591e9 | 0.926400 | |||||||||
− 3.86475e8i | − 0.0468929i | |||||||||
− 8.12233e9i | − 0.980472i | |||||||||
1.47606e9i | 0.177268i | 0.996064 | + | 0.0886340i | ||||||
−0.996064 | + | 0.0886340i | ||||||||
6.07030e9i | 0.725294i | |||||||||
6.11259e9 | 0.726622 | |||||||||
6.00595e9 | 0.710309 | |||||||||
3.31235e8i | 0.0389751i | |||||||||
7.54957e8 | 0.0883818 | |||||||||
0 | 0 | |||||||||
−1.31702e7 | −0.00152623 | |||||||||
8.97569e9i | 1.03489i | 0.855716 | + | 0.517445i | ||||||
−0.855716 | + | 0.517445i | ||||||||
−5.14724e9 | −0.590477 | |||||||||
−1.17082e10 | −1.33636 | |||||||||
− 3.23957e9i | − 0.367899i | |||||||||
4.47263e9i | 0.505378i | |||||||||
2.26812e8i | 0.0254996i | |||||||||
7.88214e9i | 0.881717i | |||||||||
1.68996e9 | 0.188097 | |||||||||
−1.12678e8 | −0.0124786 | |||||||||
4.37386e9i | 0.481972i | |||||||||
5.08142e9 | 0.557149 | 0.278575 | − | 0.960415i | ||||||
0.278575 | + | 0.960415i | ||||||||
0 | 0 | |||||||||
7.25272e9 | 0.787331 | |||||||||
− 1.14109e10i | − 1.23258i | |||||||||
1.54989e8 | 0.0166586 | |||||||||
2.99451e9 | 0.320265 | |||||||||
− 9.07982e9i | − 0.966294i | |||||||||
− 1.05005e8i | − 0.0111197i | |||||||||
3.63793e9i | 0.383348i | 0.981459 | + | 0.191674i | ||||||
−0.981459 | + | 0.191674i | ||||||||
1.72565e10i | 1.80946i | |||||||||
9.73991e9 | 1.01628 | |||||||||
8.03598e9 | 0.834371 | |||||||||
− 5.81002e8i | − 0.0600294i | |||||||||
1.11417e8 | 0.0114554 | |||||||||
0 | 0 | |||||||||
−9.69495e8 | −0.0987075 | |||||||||
− 1.30649e8i | − 0.0132369i | |||||||||
−9.84638e8 | −0.0992753 | |||||||||
−8.62579e9 | −0.865462 | −0.432731 | − | 0.901523i | ||||||
−0.432731 | + | 0.901523i | ||||||||
5.06706e9i | 0.505932i | |||||||||
2.70672e9i | 0.268949i | |||||||||
− 1.23779e10i | − 1.22396i | |||||||||
8.52486e7i | 0.00838887i | |||||||||
−2.67843e9 | −0.262298 | |||||||||
1.02849e10 | 1.00234 | |||||||||
1.22668e8i | 0.0118974i | |||||||||
1.23787e10 | 1.19482 | 0.597412 | − | 0.801934i | ||||||
0.597412 | + | 0.801934i | ||||||||
0 | 0 | |||||||||
−1.04226e10 | −0.996389 | |||||||||
1.93804e10i | 1.84388i | |||||||||
1.58715e9 | 0.150282 | |||||||||
1.31159e8 | 0.0123598 | |||||||||
1.32984e10i | 1.24720i | 0.781745 | + | 0.623598i | ||||||
−0.781745 | + | 0.623598i | ||||||||
1.42734e10i | 1.33227i | |||||||||
3.11490e7i | 0.00289360i | |||||||||
− 5.14452e8i | − 0.0475634i | |||||||||
7.83109e9 | 0.720587 | |||||||||
−1.18748e10 | −1.08750 | |||||||||
− 1.28451e10i | − 1.17079i | −0.810747 | − | 0.585397i | ||||||
0.810747 | − | 0.585397i | ||||||||
−3.39982e9 | −0.308422 | |||||||||
0 | 0 | |||||||||
−1.80386e9 | −0.162103 | |||||||||
− 2.01042e10i | − 1.79815i | −0.437793 | − | 0.899076i | ||||||
0.437793 | − | 0.899076i | ||||||||
3.04129e8 | 0.0270740 | |||||||||
−1.53748e10 | −1.36227 | |||||||||
− 1.10060e10i | − 0.970606i | |||||||||
1.77364e9i | 0.155683i | |||||||||
− 3.95804e9i | − 0.345799i | |||||||||
1.87397e8i | 0.0162959i | |||||||||
−1.14511e7 | −0.000991131 0 | |||||||||
−1.99539e8 | −0.0171905 | −0.00859524 | − | 0.999963i | ||||||
−0.00859524 | + | 0.999963i | ||||||||
− 1.96663e9i | − 0.168640i | |||||||||
1.63396e8 | 0.0139463 | |||||||||
0 | 0 | |||||||||
−1.63176e10 | −1.37988 | |||||||||
− 2.70623e8i | − 0.0227792i | |||||||||
2.34770e10 | 1.96701 | 0.983507 | − | 0.180868i | ||||||
0.983507 | + | 0.180868i | ||||||||
−7.06853e9 | −0.589504 | |||||||||
2.22411e7i | 0.00184634i | |||||||||
3.02377e10i | 2.49862i | |||||||||
1.60366e10i | 1.31907i | 0.751676 | + | 0.659533i | ||||||
−0.751676 | + | 0.659533i | ||||||||
3.29813e8i | 0.0270038i | |||||||||
1.71947e10 | 1.40139 | |||||||||
−7.55193e9 | −0.612676 | |||||||||
1.06525e10i | 0.860274i | |||||||||
−5.31846e9 | −0.427548 | |||||||||
0 | 0 | |||||||||
3.18037e8 | 0.0253345 | |||||||||
1.49614e10i | 1.18639i | 0.805057 | + | 0.593197i | ||||||
−0.805057 | + | 0.593197i | ||||||||
−1.79955e10 | −1.42052 | |||||||||
−3.36011e8 | −0.0264036 | |||||||||
7.84053e9i | 0.613317i | |||||||||
− 3.25072e9i | − 0.253135i | −0.991958 | − | 0.126567i | ||||||
0.991958 | − | 0.126567i | ||||||||
2.39112e9i | 0.185357i | |||||||||
− 1.37909e10i | − 1.06423i | |||||||||
5.98282e9 | 0.459611 | |||||||||
−1.61620e8 | −0.0123601 | |||||||||
− 3.78804e9i | − 0.288394i | |||||||||
−3.13771e10 | −2.37811 | |||||||||
0 | 0 | |||||||||
2.91419e10 | 2.18897 | |||||||||
3.51326e8i | 0.0262716i | |||||||||
−6.36353e8 | −0.0473731 | |||||||||
3.95243e8 | 0.0292926 | |||||||||
− 1.00915e10i | − 0.744583i | |||||||||
− 6.32840e7i | − 0.00464852i | |||||||||
1.13640e10i | 0.831033i | 0.909586 | + | 0.415517i | ||||||
−0.909586 | + | 0.415517i | ||||||||
9.51441e9i | 0.692692i | |||||||||
3.50059e8 | 0.0253730 | |||||||||
1.49702e10 | 1.08027 | |||||||||
7.68619e9i | 0.552196i | |||||||||
1.93254e10 | 1.38226 | |||||||||
0 | 0 | |||||||||
1.19944e10 | 0.850367 | |||||||||
1.03899e8i | 0.00733377i | |||||||||
−3.31242e9 | −0.232782 | |||||||||
5.72603e9 | 0.400636 | 0.200318 | − | 0.979731i | ||||||
0.200318 | + | 0.979731i | ||||||||
4.43528e8i | 0.0308967i | |||||||||
− 4.13445e9i | − 0.286751i | |||||||||
− 1.22112e10i | − 0.843226i | |||||||||
1.12697e10i | 0.774814i | |||||||||
−7.32478e9 | −0.501400 | |||||||||
3.27285e10 | 2.23060 | |||||||||
9.04763e7i | 0.00613958i | |||||||||
−1.28725e9 | −0.0869712 | |||||||||
0 | 0 | |||||||||
−2.66051e8 | −0.0178200 | |||||||||
1.49870e10i | 0.999480i | |||||||||
1.88681e10 | 1.25288 | 0.626440 | − | 0.779470i | ||||||
0.626440 | + | 0.779470i | ||||||||
−1.60389e10 | −1.06042 | |||||||||
− 2.28943e10i | − 1.50714i | −0.657367 | − | 0.753570i | ||||||
0.657367 | − | 0.753570i | ||||||||
6.84021e9i | 0.448356i | |||||||||
− 5.65308e8i | − 0.0368951i | |||||||||
− 7.12449e9i | − 0.462987i | |||||||||
−2.72900e10 | −1.76584 | |||||||||
−8.14297e7 | −0.00524647 | |||||||||
6.31810e9i | 0.405331i | |||||||||
−1.87876e10 | −1.20015 | |||||||||
0 | 0 | |||||||||
1.47085e10 | 0.931578 | |||||||||
3.01467e9i | 0.190125i | 0.995471 | + | 0.0950625i | ||||||
−0.995471 | + | 0.0950625i | ||||||||
−1.47991e8 | −0.00929361 | |||||||||
−9.51460e9 | −0.594964 | −0.297482 | − | 0.954727i | ||||||
−0.297482 | + | 0.954727i | ||||||||
− 4.46766e9i | − 0.278185i | |||||||||
5.27923e8i | 0.0327327i | |||||||||
1.27354e10i | 0.786287i | |||||||||
3.09369e10i | 1.90199i | 0.309210 | + | 0.950994i | ||||||
−0.309210 | + | 0.950994i | ||||||||
4.26540e8 | 0.0261128 | |||||||||
−1.75499e10 | −1.06988 | −0.534938 | − | 0.844891i | ||||||
−0.534938 | + | 0.844891i | ||||||||
2.72608e9i | 0.165487i | |||||||||
−4.97240e8 | −0.0300581 | |||||||||
0 | 0 | |||||||||
8.30923e8 | 0.0498085 | |||||||||
− 1.08286e8i | − 0.00646386i | |||||||||
1.16750e10 | 0.693991 | |||||||||
1.57561e10 | 0.932666 | |||||||||
8.53278e8i | 0.0502981i | |||||||||
− 7.00069e9i | − 0.410948i | |||||||||
− 1.26056e10i | − 0.736878i | −0.929652 | − | 0.368439i | ||||||
0.929652 | − | 0.368439i | ||||||||
− 6.73816e8i | − 0.0392251i | |||||||||
−1.16552e9 | −0.0675671 | |||||||||
8.03041e9 | 0.463602 | |||||||||
− 3.31140e8i | − 0.0190377i | |||||||||
6.91625e9 | 0.395979 | |||||||||
0 | 0 | |||||||||
6.22876e9 | 0.353676 | |||||||||
1.19895e10i | 0.677966i | |||||||||
1.31836e9 | 0.0742417 | |||||||||
6.87282e8 | 0.0385441 | |||||||||
8.33918e9i | 0.465755i | |||||||||
− 5.09625e8i | − 0.0283464i | |||||||||
3.36690e8i | 0.0186506i | |||||||||
− 1.77001e10i | − 0.976457i | −0.872716 | − | 0.488229i | ||||||
0.872716 | − | 0.488229i | ||||||||
−1.59075e10 | −0.873974 | |||||||||
−4.24053e10 | −2.32027 | |||||||||
− 3.09315e8i | − 0.0168555i | |||||||||
6.38662e9 | 0.346608 | 0.173304 | − | 0.984868i | ||||||
0.173304 | + | 0.984868i | ||||||||
0 | 0 | |||||||||
9.57498e9 | 0.515421 | 0.257710 | − | 0.966222i | ||||||
0.257710 | + | 0.966222i | ||||||||
− 2.96171e9i | − 0.158781i | |||||||||
6.99206e8 | 0.0373331 | |||||||||
8.57084e9 | 0.455772 | |||||||||
− 3.52438e10i | − 1.86658i | −0.359130 | − | 0.933288i | ||||||
0.359130 | − | 0.933288i | ||||||||
7.55541e8i | 0.0398529i | |||||||||
− 3.59571e10i | − 1.88898i | |||||||||
− 1.53029e10i | − 0.800683i | |||||||||
2.99669e8 | 0.0156162 | |||||||||
9.17195e9 | 0.476039 | |||||||||
− 2.52809e10i | − 1.30684i | |||||||||
−4.88890e8 | −0.0251706 | |||||||||
0 | 0 | |||||||||
−2.83813e10 | −1.44952 | |||||||||
8.39031e9i | 0.426804i | |||||||||
−1.39855e9 | −0.0708579 | |||||||||
−1.11922e9 | −0.0564788 | |||||||||
3.78128e8i | 0.0190053i | |||||||||
− 6.34498e9i | − 0.317638i | −0.987308 | − | 0.158819i | ||||||
0.987308 | − | 0.158819i | ||||||||
5.92589e9i | 0.295476i | |||||||||
3.59084e7i | 0.00178335i | |||||||||
1.31521e10 | 0.650586 | |||||||||
2.92173e8 | 0.0143954 | 0.00719771 | − | 0.999974i | ||||||
0.00719771 | + | 0.999974i | ||||||||
1.25183e9i | 0.0614333i | |||||||||
3.68103e10 | 1.79931 | 0.899656 | − | 0.436600i | ||||||
0.899656 | + | 0.436600i | ||||||||
0 | 0 | |||||||||
7.33533e8 | 0.0355728 | |||||||||
7.58470e8i | 0.0366370i | |||||||||
4.03158e9 | 0.193973 | 0.0969867 | − | 0.995286i | ||||||
0.0969867 | + | 0.995286i | ||||||||
2.66766e8 | 0.0127846 | |||||||||
3.22356e10i | 1.53879i | |||||||||
1.73215e10i | 0.823607i | |||||||||
2.70856e10i | 1.28282i | |||||||||
− 2.64325e9i | − 0.124699i | |||||||||
1.64584e10 | 0.773404 | |||||||||
3.72238e8 | 0.0174237 | |||||||||
− 6.77261e9i | − 0.315773i | |||||||||
2.20959e9 | 0.102620 | |||||||||
0 | 0 | |||||||||
8.73603e9 | 0.402575 | |||||||||
− 2.15673e10i | − 0.990004i | |||||||||
1.01245e10 | 0.462940 | |||||||||
2.77159e9 | 0.126239 | |||||||||
3.08223e10i | 1.39844i | |||||||||
− 1.40793e8i | − 0.00636316i | |||||||||
− 1.26867e10i | − 0.571161i | |||||||||
− 1.87107e10i | − 0.839112i | |||||||||
3.95064e8 | 0.0176489 | |||||||||
2.17702e10 | 0.968807 | 0.484403 | − | 0.874845i | ||||||
0.484403 | + | 0.874845i | ||||||||
1.92381e10i | 0.852830i | |||||||||
−2.10177e10 | −0.928138 | |||||||||
0 | 0 | |||||||||
−3.27391e10 | −1.43467 | −0.717335 | − | 0.696728i | ||||||
−0.717335 | + | 0.696728i | ||||||||
− 3.24154e8i | − 0.0141504i | |||||||||
4.60365e9 | 0.200196 | |||||||||
1.40430e10 | 0.608342 | |||||||||
9.16240e8i | 0.0395399i | |||||||||
− 1.64883e10i | − 0.708831i | |||||||||
− 6.18532e9i | − 0.264892i | |||||||||
− 5.15968e8i | − 0.0220127i | |||||||||
1.03618e10 | 0.440385 | 0.220193 | − | 0.975456i | ||||||
0.220193 | + | 0.975456i | ||||||||
2.12470e9 | 0.0899582 | |||||||||
− 2.75468e8i | − 0.0116188i | |||||||||
−2.44963e10 | −1.02930 | |||||||||
0 | 0 | |||||||||
−3.51108e8 | −0.0146416 | |||||||||
− 1.20966e10i | − 0.502537i | |||||||||
−1.59540e10 | −0.660286 | |||||||||
6.26544e9 | 0.258329 | |||||||||
− 1.90969e10i | − 0.784415i | |||||||||
2.15053e10i | 0.880018i | 0.897993 | + | 0.440009i | ||||||
−0.897993 | + | 0.440009i | ||||||||
6.55546e8i | 0.0267247i | |||||||||
3.30772e9i | 0.134340i | |||||||||
5.60891e9 | 0.226946 | |||||||||
−1.30674e8 | −0.00526750 | |||||||||
8.37823e9i | 0.336464i | |||||||||
2.76497e10 | 1.10624 | |||||||||
0 | 0 | |||||||||
2.31411e8 | 0.00918957 | 0.00459479 | − | 0.999989i | ||||||
0.00459479 | + | 0.999989i | ||||||||
− 1.09733e10i | − 0.434137i | |||||||||
3.28912e8 | 0.0129643 | |||||||||
−7.71511e9 | −0.302966 | |||||||||
2.99031e10i | 1.16991i | 0.811065 | + | 0.584956i | ||||||
−0.811065 | + | 0.584956i | ||||||||
2.44325e8i | 0.00952334i | |||||||||
2.20476e9i | 0.0856192i | |||||||||
− 9.30767e9i | − 0.360113i | |||||||||
1.89049e9 | 0.0728724 | |||||||||
6.20640e9 | 0.238353 | |||||||||
− 3.37889e10i | − 1.29285i | −0.762976 | − | 0.646427i | ||||||
0.762976 | − | 0.646427i | ||||||||
2.92083e8 | 0.0111347 | |||||||||
0 | 0 | |||||||||
−3.31965e10 | −1.25620 | |||||||||
− 1.08741e9i | − 0.0409979i | |||||||||
−1.79746e10 | −0.675195 | |||||||||
4.50079e10 | 1.68447 | 0.842236 | − | 0.539110i | ||||||
0.842236 | + | 0.539110i | ||||||||
4.17554e9i | 0.155702i | |||||||||
− 5.27555e10i | − 1.96000i | |||||||||
6.50348e9i | 0.240737i | |||||||||
8.25611e8i | 0.0304497i | |||||||||
−1.17131e10 | −0.430421 | |||||||||
−1.44645e10 | −0.529589 | |||||||||
9.20966e8i | 0.0335965i | |||||||||
−1.40672e9 | −0.0511298 | |||||||||
0 | 0 | |||||||||
4.33783e8 | 0.0156524 | |||||||||
− 4.24354e9i | − 0.152566i | |||||||||
−5.47716e10 | −1.96205 | |||||||||
3.11653e7 | 0.00111238 | |||||||||
5.77459e9i | 0.205366i | 0.994714 | + | 0.102683i | ||||||
−0.994714 | + | 0.102683i | ||||||||
− 1.97896e10i | − 0.701250i | |||||||||
− 6.81471e8i | − 0.0240610i | |||||||||
1.28959e10i | 0.453681i | |||||||||
−5.40196e10 | −1.89358 | −0.946790 | − | 0.321851i | ||||||
−0.946790 | + | 0.321851i | ||||||||
−9.39741e8 | −0.0328228 | |||||||||
− 1.05838e10i | − 0.368338i | |||||||||
2.43488e10 | 0.844347 | |||||||||
0 | 0 | |||||||||
1.16260e10 | 0.400273 | |||||||||
− 3.21144e10i | − 1.10171i | −0.834600 | − | 0.550857i | ||||||
0.834600 | − | 0.550857i | ||||||||
6.60713e8 | 0.0225854 | |||||||||
2.92516e10 | 0.996345 | |||||||||
− 1.55055e9i | − 0.0526252i | |||||||||
− 3.98019e10i | − 1.34605i | |||||||||
3.20034e10i | 1.07846i | |||||||||
− 1.36597e10i | − 0.458673i | −0.973347 | − | 0.229337i | ||||||
0.973347 | − | 0.229337i | ||||||||
−1.15410e9 | −0.0386153 | |||||||||
−6.64648e10 | −2.21598 | |||||||||
1.30415e10i | 0.433271i | |||||||||
−3.66758e8 | −0.0121414 | |||||||||
0 | 0 | |||||||||
4.43953e8 | 0.0145932 | |||||||||
4.16556e10i | 1.36443i | |||||||||
−3.04984e10 | −0.995450 | −0.497725 | − | 0.867335i | ||||||
−0.497725 | + | 0.867335i | ||||||||
−2.56068e10 | −0.832847 | |||||||||
− 7.85854e8i | − 0.0254694i | |||||||||
− 4.08349e10i | − 1.31880i | |||||||||
− 2.31396e10i | − 0.744688i | |||||||||
5.31882e7i | 0.00170572i | |||||||||
3.41604e10 | 1.09167 | 0.545833 | − | 0.837894i | ||||||
0.545833 | + | 0.837894i | ||||||||
−4.00258e9 | −0.127463 | |||||||||
7.48452e8i | 0.0237511i |
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 169.8.b.d.168.10 | 14 | ||
13.3 | even | 3 | 13.8.e.a.4.3 | ✓ | 14 | ||
13.4 | even | 6 | 13.8.e.a.10.3 | yes | 14 | ||
13.5 | odd | 4 | 169.8.a.g.1.10 | 14 | |||
13.8 | odd | 4 | 169.8.a.g.1.5 | 14 | |||
13.12 | even | 2 | inner | 169.8.b.d.168.5 | 14 | ||
39.17 | odd | 6 | 117.8.q.b.10.5 | 14 | |||
39.29 | odd | 6 | 117.8.q.b.82.5 | 14 | |||
52.3 | odd | 6 | 208.8.w.a.17.4 | 14 | |||
52.43 | odd | 6 | 208.8.w.a.49.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.8.e.a.4.3 | ✓ | 14 | 13.3 | even | 3 | ||
13.8.e.a.10.3 | yes | 14 | 13.4 | even | 6 | ||
117.8.q.b.10.5 | 14 | 39.17 | odd | 6 | |||
117.8.q.b.82.5 | 14 | 39.29 | odd | 6 | |||
169.8.a.g.1.5 | 14 | 13.8 | odd | 4 | |||
169.8.a.g.1.10 | 14 | 13.5 | odd | 4 | |||
169.8.b.d.168.5 | 14 | 13.12 | even | 2 | inner | ||
169.8.b.d.168.10 | 14 | 1.1 | even | 1 | trivial | ||
208.8.w.a.17.4 | 14 | 52.3 | odd | 6 | |||
208.8.w.a.49.4 | 14 | 52.43 | odd | 6 |