Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.11 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.f.757.12 |
$q$-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 \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.174217 | − | 1.40344i | −0.123190 | − | 0.992383i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.93930 | + | 0.489007i | −0.969648 | + | 0.244503i | ||||
\(5\) | − | 1.26947i | − | 0.567723i | −0.958865 | − | 0.283862i | \(-0.908384\pi\) | ||
0.958865 | − | 0.283862i | \(-0.0916156\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.02415 | + | 2.63650i | 0.362092 | + | 0.932142i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.78162 | + | 0.221163i | −0.563399 | + | 0.0699378i | ||||
\(11\) | 2.02805i | 0.611480i | 0.952115 | + | 0.305740i | \(0.0989039\pi\) | ||||
−0.952115 | + | 0.305740i | \(0.901096\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.05339i | − | 1.12421i | −0.827066 | − | 0.562104i | \(-0.809992\pi\) | ||
0.827066 | − | 0.562104i | \(-0.190008\pi\) | |||||||
\(14\) | −0.174217 | − | 1.40344i | −0.0465614 | − | 0.375086i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.52175 | − | 1.89666i | 0.880436 | − | 0.474164i | ||||
\(17\) | −1.33658 | −0.324167 | −0.162084 | − | 0.986777i | \(-0.551821\pi\) | ||||
−0.162084 | + | 0.986777i | \(0.551821\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.28346i | − | 0.753277i | −0.926360 | − | 0.376638i | \(-0.877080\pi\) | ||
0.926360 | − | 0.376638i | \(-0.122920\pi\) | |||||||
\(20\) | 0.620778 | + | 2.46188i | 0.138810 | + | 0.550492i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.84625 | − | 0.353321i | 0.606823 | − | 0.0753282i | ||||
\(23\) | 2.25680 | 0.470576 | 0.235288 | − | 0.971926i | \(-0.424397\pi\) | ||||
0.235288 | + | 0.971926i | \(0.424397\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.38845 | 0.677690 | ||||||||
\(26\) | −5.68870 | + | 0.706169i | −1.11565 | + | 0.138491i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.93930 | + | 0.489007i | −0.366493 | + | 0.0924136i | ||||
\(29\) | 3.58798i | 0.666272i | 0.942879 | + | 0.333136i | \(0.108107\pi\) | ||||
−0.942879 | + | 0.333136i | \(0.891893\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.464312 | −0.0833930 | −0.0416965 | − | 0.999130i | \(-0.513276\pi\) | ||||
−0.0416965 | + | 0.999130i | \(0.513276\pi\) | |||||||
\(32\) | −3.27540 | − | 4.61213i | −0.579014 | − | 0.815318i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.232854 | + | 1.87581i | 0.0399342 | + | 0.321698i | ||||
\(35\) | − | 1.26947i | − | 0.214579i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11.8743i | − | 1.95212i | −0.217507 | − | 0.976059i | \(-0.569793\pi\) | ||
0.217507 | − | 0.976059i | \(-0.430207\pi\) | |||||||
\(38\) | −4.60814 | + | 0.572034i | −0.747539 | + | 0.0927962i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.34695 | − | 1.30013i | 0.529199 | − | 0.205568i | ||||
\(41\) | −1.73758 | −0.271365 | −0.135683 | − | 0.990752i | \(-0.543323\pi\) | ||||
−0.135683 | + | 0.990752i | \(0.543323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.70380i | − | 0.259827i | −0.991525 | − | 0.129913i | \(-0.958530\pi\) | ||
0.991525 | − | 0.129913i | \(-0.0414699\pi\) | |||||||
\(44\) | −0.991730 | − | 3.93299i | −0.149509 | − | 0.592921i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.393173 | − | 3.16729i | −0.0579702 | − | 0.466991i | ||||
\(47\) | −8.45083 | −1.23268 | −0.616340 | − | 0.787480i | \(-0.711385\pi\) | ||||
−0.616340 | + | 0.787480i | \(0.711385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.590326 | − | 4.75549i | −0.0834846 | − | 0.672528i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.98213 | + | 7.86073i | 0.274873 | + | 1.09009i | ||||
\(53\) | − | 11.7544i | − | 1.61459i | −0.590146 | − | 0.807296i | \(-0.700930\pi\) | ||
0.590146 | − | 0.807296i | \(-0.299070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.57454 | 0.347152 | ||||||||
\(56\) | 1.02415 | + | 2.63650i | 0.136858 | + | 0.352317i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.03553 | − | 0.625087i | 0.661197 | − | 0.0820780i | ||||
\(59\) | − | 5.49489i | − | 0.715374i | −0.933842 | − | 0.357687i | \(-0.883565\pi\) | ||
0.933842 | − | 0.357687i | \(-0.116435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.02150i | − | 0.770975i | −0.922713 | − | 0.385487i | \(-0.874033\pi\) | ||
0.922713 | − | 0.385487i | \(-0.125967\pi\) | |||||||
\(62\) | 0.0808911 | + | 0.651635i | 0.0102732 | + | 0.0827578i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.90223 | + | 5.40034i | −0.737779 | + | 0.675042i | ||||
\(65\) | −5.14565 | −0.638239 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.381481i | − | 0.0466054i | −0.999728 | − | 0.0233027i | \(-0.992582\pi\) | ||
0.999728 | − | 0.0233027i | \(-0.00741815\pi\) | |||||||
\(68\) | 2.59202 | − | 0.653595i | 0.314328 | − | 0.0792600i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.78162 | + | 0.221163i | −0.212945 | + | 0.0264340i | ||||
\(71\) | 9.47622 | 1.12462 | 0.562310 | − | 0.826926i | \(-0.309913\pi\) | ||||
0.562310 | + | 0.826926i | \(0.309913\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0336 | −1.17434 | −0.587171 | − | 0.809463i | \(-0.699759\pi\) | ||||
−0.587171 | + | 0.809463i | \(0.699759\pi\) | |||||||
\(74\) | −16.6648 | + | 2.06870i | −1.93725 | + | 0.240481i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.60563 | + | 6.36760i | 0.184179 | + | 0.730414i | ||||
\(77\) | 2.02805i | 0.231118i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.90442 | 0.551791 | 0.275895 | − | 0.961188i | \(-0.411026\pi\) | ||||
0.275895 | + | 0.961188i | \(0.411026\pi\) | |||||||
\(80\) | −2.40775 | − | 4.47074i | −0.269194 | − | 0.499844i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.302717 | + | 2.43860i | 0.0334295 | + | 0.269298i | ||||
\(83\) | 6.95800i | 0.763740i | 0.924216 | + | 0.381870i | \(0.124720\pi\) | ||||
−0.924216 | + | 0.381870i | \(0.875280\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.69674i | 0.184037i | ||||||||
\(86\) | −2.39118 | + | 0.296830i | −0.257848 | + | 0.0320080i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.34695 | + | 2.07703i | −0.569987 | + | 0.221412i | ||||
\(89\) | −17.4322 | −1.84781 | −0.923903 | − | 0.382628i | \(-0.875019\pi\) | ||||
−0.923903 | + | 0.382628i | \(0.875019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.05339i | − | 0.424911i | ||||||
\(92\) | −4.37661 | + | 1.10359i | −0.456293 | + | 0.115057i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.47228 | + | 11.8602i | 0.151854 | + | 1.22329i | ||||
\(95\) | −4.16824 | −0.427653 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.62794 | 0.774500 | 0.387250 | − | 0.921975i | \(-0.373425\pi\) | ||||
0.387250 | + | 0.921975i | \(0.373425\pi\) | |||||||
\(98\) | −0.174217 | − | 1.40344i | −0.0175986 | − | 0.141769i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.57121 | + | 1.65697i | −0.657121 | + | 0.165697i | ||||
\(101\) | 5.27674i | 0.525055i | 0.964924 | + | 0.262528i | \(0.0845561\pi\) | ||||
−0.964924 | + | 0.262528i | \(0.915444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.07253 | −0.499812 | −0.249906 | − | 0.968270i | \(-0.580400\pi\) | ||||
−0.249906 | + | 0.968270i | \(0.580400\pi\) | |||||||
\(104\) | 10.6868 | − | 4.15128i | 1.04792 | − | 0.407067i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.4966 | + | 2.04782i | −1.60229 | + | 0.198902i | ||||
\(107\) | − | 5.22269i | − | 0.504896i | −0.967610 | − | 0.252448i | \(-0.918764\pi\) | ||
0.967610 | − | 0.252448i | \(-0.0812357\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8354i | 1.03784i | 0.854822 | + | 0.518922i | \(0.173667\pi\) | ||||
−0.854822 | + | 0.518922i | \(0.826333\pi\) | |||||||
\(110\) | −0.448529 | − | 3.61322i | −0.0427656 | − | 0.344507i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.52175 | − | 1.89666i | 0.332774 | − | 0.179217i | ||||
\(113\) | −10.8783 | −1.02334 | −0.511672 | − | 0.859181i | \(-0.670974\pi\) | ||||
−0.511672 | + | 0.859181i | \(0.670974\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.86494i | − | 0.267157i | ||||||
\(116\) | −1.75455 | − | 6.95817i | −0.162906 | − | 0.646049i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.71176 | + | 0.957303i | −0.709925 | + | 0.0881269i | ||||
\(119\) | −1.33658 | −0.122524 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.88701 | 0.626092 | ||||||||
\(122\) | −8.45083 | + | 1.04905i | −0.765102 | + | 0.0949763i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.900440 | − | 0.227052i | 0.0808619 | − | 0.0203899i | ||||
\(125\) | − | 10.6489i | − | 0.952464i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.57175 | 0.139471 | 0.0697353 | − | 0.997566i | \(-0.477785\pi\) | ||||
0.0697353 | + | 0.997566i | \(0.477785\pi\) | |||||||
\(128\) | 8.60733 | + | 7.34261i | 0.760788 | + | 0.649001i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.896459 | + | 7.22162i | 0.0786247 | + | 0.633378i | ||||
\(131\) | − | 11.7947i | − | 1.03051i | −0.857037 | − | 0.515256i | \(-0.827697\pi\) | ||
0.857037 | − | 0.515256i | \(-0.172303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.28346i | − | 0.284712i | ||||||
\(134\) | −0.535387 | + | 0.0664605i | −0.0462504 | + | 0.00574131i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.36886 | − | 3.52388i | −0.117378 | − | 0.302170i | ||||
\(137\) | −18.4006 | −1.57207 | −0.786033 | − | 0.618184i | \(-0.787869\pi\) | ||||
−0.786033 | + | 0.618184i | \(0.787869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.3851i | − | 0.965674i | −0.875710 | − | 0.482837i | \(-0.839606\pi\) | ||
0.875710 | − | 0.482837i | \(-0.160394\pi\) | |||||||
\(140\) | 0.620778 | + | 2.46188i | 0.0524653 | + | 0.208066i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.65092 | − | 13.2993i | −0.138542 | − | 1.11605i | ||||
\(143\) | 8.22048 | 0.687431 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.55483 | 0.378258 | ||||||||
\(146\) | 1.74802 | + | 14.0816i | 0.144667 | + | 1.16540i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.80659 | + | 23.0277i | 0.477299 | + | 1.89287i | ||||
\(149\) | 14.6966i | 1.20400i | 0.798498 | + | 0.601998i | \(0.205628\pi\) | ||||
−0.798498 | + | 0.601998i | \(0.794372\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.220342 | −0.0179312 | −0.00896559 | − | 0.999960i | \(-0.502854\pi\) | ||||
−0.00896559 | + | 0.999960i | \(0.502854\pi\) | |||||||
\(152\) | 8.65683 | − | 3.36276i | 0.702161 | − | 0.272755i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.84625 | − | 0.353321i | 0.229357 | − | 0.0284714i | ||||
\(155\) | 0.589430i | 0.0473441i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.4367i | − | 0.832941i | −0.909149 | − | 0.416471i | \(-0.863267\pi\) | ||
0.909149 | − | 0.416471i | \(-0.136733\pi\) | |||||||
\(158\) | −0.854434 | − | 6.88307i | −0.0679751 | − | 0.547588i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.85496 | + | 4.15801i | −0.462875 | + | 0.328720i | ||||
\(161\) | 2.25680 | 0.177861 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.46955i | − | 0.350082i | −0.984561 | − | 0.175041i | \(-0.943994\pi\) | ||
0.984561 | − | 0.175041i | \(-0.0560058\pi\) | |||||||
\(164\) | 3.36969 | − | 0.849690i | 0.263129 | − | 0.0663497i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.76515 | − | 1.21220i | 0.757923 | − | 0.0940851i | ||||
\(167\) | 14.0617 | 1.08812 | 0.544062 | − | 0.839045i | \(-0.316886\pi\) | ||||
0.544062 | + | 0.839045i | \(0.316886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.42998 | −0.263844 | ||||||||
\(170\) | 2.38128 | − | 0.295601i | 0.182636 | − | 0.0226716i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.833168 | + | 3.30417i | 0.0635284 | + | 0.251940i | ||||
\(173\) | − | 0.334570i | − | 0.0254369i | −0.999919 | − | 0.0127184i | \(-0.995951\pi\) | ||
0.999919 | − | 0.0127184i | \(-0.00404851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.38845 | 0.256143 | ||||||||
\(176\) | 3.84652 | + | 7.14228i | 0.289942 | + | 0.538369i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.03698 | + | 24.4650i | 0.227631 | + | 1.83373i | ||||
\(179\) | 1.85419i | 0.138589i | 0.997596 | + | 0.0692944i | \(0.0220748\pi\) | ||||
−0.997596 | + | 0.0692944i | \(0.977925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.8864i | − | 0.883512i | −0.897135 | − | 0.441756i | \(-0.854356\pi\) | ||
0.897135 | − | 0.441756i | \(-0.145644\pi\) | |||||||
\(182\) | −5.68870 | + | 0.706169i | −0.421674 | + | 0.0523447i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.31130 | + | 5.95005i | 0.170392 | + | 0.438643i | ||||
\(185\) | −15.0740 | −1.10826 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.71064i | − | 0.198222i | ||||||
\(188\) | 16.3887 | − | 4.13251i | 1.19527 | − | 0.301394i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.726179 | + | 5.84989i | 0.0526825 | + | 0.424396i | ||||
\(191\) | 26.4777 | 1.91586 | 0.957928 | − | 0.287008i | \(-0.0926607\pi\) | ||||
0.957928 | + | 0.287008i | \(0.0926607\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.6831 | −1.27285 | −0.636427 | − | 0.771337i | \(-0.719588\pi\) | ||||
−0.636427 | + | 0.771337i | \(0.719588\pi\) | |||||||
\(194\) | −1.32892 | − | 10.7054i | −0.0954106 | − | 0.768600i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.93930 | + | 0.489007i | −0.138521 | + | 0.0349290i | ||||
\(197\) | − | 9.22153i | − | 0.657007i | −0.944503 | − | 0.328504i | \(-0.893456\pi\) | ||
0.944503 | − | 0.328504i | \(-0.106544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.46365 | −0.599973 | −0.299986 | − | 0.953944i | \(-0.596982\pi\) | ||||
−0.299986 | + | 0.953944i | \(0.596982\pi\) | |||||||
\(200\) | 3.47028 | + | 8.93364i | 0.245386 | + | 0.631704i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.40560 | − | 0.919297i | 0.521056 | − | 0.0646815i | ||||
\(203\) | 3.58798i | 0.251827i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.20581i | 0.154060i | ||||||||
\(206\) | 0.883721 | + | 7.11900i | 0.0615718 | + | 0.496005i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.68790 | − | 14.2750i | −0.533060 | − | 0.989794i | ||||
\(209\) | 6.65902 | 0.460614 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.66745i | − | 0.321321i | −0.987010 | − | 0.160660i | \(-0.948638\pi\) | ||
0.987010 | − | 0.160660i | \(-0.0513624\pi\) | |||||||
\(212\) | 5.74798 | + | 22.7953i | 0.394773 | + | 1.56559i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.32974 | + | 0.909880i | −0.501050 | + | 0.0621981i | ||||
\(215\) | −2.16292 | −0.147510 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.464312 | −0.0315196 | ||||||||
\(218\) | 15.2069 | − | 1.88771i | 1.02994 | − | 0.127852i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.99281 | + | 1.25897i | −0.336615 | + | 0.0848797i | ||||
\(221\) | 5.41767i | 0.364432i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.85009 | 0.525681 | 0.262841 | − | 0.964839i | \(-0.415341\pi\) | ||||
0.262841 | + | 0.964839i | \(0.415341\pi\) | |||||||
\(224\) | −3.27540 | − | 4.61213i | −0.218847 | − | 0.308161i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.89518 | + | 15.2670i | 0.126066 | + | 1.01555i | ||||
\(227\) | 19.2857i | 1.28004i | 0.768360 | + | 0.640018i | \(0.221073\pi\) | ||||
−0.768360 | + | 0.640018i | \(0.778927\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.71588i | 0.113389i | 0.998392 | + | 0.0566944i | \(0.0180561\pi\) | ||||
−0.998392 | + | 0.0566944i | \(0.981944\pi\) | |||||||
\(230\) | −4.02077 | + | 0.499120i | −0.265122 | + | 0.0329110i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.45971 | + | 3.67464i | −0.621060 | + | 0.241252i | ||||
\(233\) | 23.8734 | 1.56400 | 0.781999 | − | 0.623280i | \(-0.214200\pi\) | ||||
0.781999 | + | 0.623280i | \(0.214200\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.7281i | 0.699821i | ||||||||
\(236\) | 2.68704 | + | 10.6562i | 0.174911 | + | 0.693661i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.232854 | + | 1.87581i | 0.0150937 | + | 0.121591i | ||||
\(239\) | 21.6697 | 1.40170 | 0.700848 | − | 0.713310i | \(-0.252805\pi\) | ||||
0.700848 | + | 0.713310i | \(0.252805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.8432 | 1.79354 | 0.896770 | − | 0.442497i | \(-0.145907\pi\) | ||||
0.896770 | + | 0.442497i | \(0.145907\pi\) | |||||||
\(242\) | −1.19983 | − | 9.66552i | −0.0771283 | − | 0.621323i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.94455 | + | 11.6775i | 0.188506 | + | 0.747574i | ||||
\(245\) | − | 1.26947i | − | 0.0811033i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3091 | −0.846840 | ||||||||
\(248\) | −0.475526 | − | 1.22416i | −0.0301959 | − | 0.0777341i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.9451 | + | 1.85521i | −0.945209 | + | 0.117334i | ||||
\(251\) | 27.7106i | 1.74908i | 0.484957 | + | 0.874538i | \(0.338835\pi\) | ||||
−0.484957 | + | 0.874538i | \(0.661165\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.57691i | 0.287748i | ||||||||
\(254\) | −0.273826 | − | 2.20586i | −0.0171814 | − | 0.138408i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.80538 | − | 13.3591i | 0.550336 | − | 0.834943i | ||||
\(257\) | −1.90462 | −0.118807 | −0.0594035 | − | 0.998234i | \(-0.518920\pi\) | ||||
−0.0594035 | + | 0.998234i | \(0.518920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11.8743i | − | 0.737831i | ||||||
\(260\) | 9.97894 | − | 2.51626i | 0.618868 | − | 0.156052i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.5532 | + | 2.05484i | −1.02266 | + | 0.126949i | ||||
\(263\) | 19.2186 | 1.18507 | 0.592534 | − | 0.805545i | \(-0.298128\pi\) | ||||
0.592534 | + | 0.805545i | \(0.298128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.9218 | −0.916642 | ||||||||
\(266\) | −4.60814 | + | 0.572034i | −0.282543 | + | 0.0350737i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.186547 | + | 0.739806i | 0.0113952 | + | 0.0451908i | ||||
\(269\) | − | 18.2931i | − | 1.11535i | −0.830059 | − | 0.557676i | \(-0.811693\pi\) | ||
0.830059 | − | 0.557676i | \(-0.188307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1450 | 1.16297 | 0.581487 | − | 0.813555i | \(-0.302471\pi\) | ||||
0.581487 | + | 0.813555i | \(0.302471\pi\) | |||||||
\(272\) | −4.70708 | + | 2.53503i | −0.285409 | + | 0.153709i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.20569 | + | 25.8241i | 0.193663 | + | 1.56009i | ||||
\(275\) | 6.87195i | 0.414394i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6288i | 1.05921i | 0.848244 | + | 0.529606i | \(0.177660\pi\) | ||||
−0.848244 | + | 0.529606i | \(0.822340\pi\) | |||||||
\(278\) | −15.9784 | + | 1.98348i | −0.958318 | + | 0.118961i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.34695 | − | 1.30013i | 0.200018 | − | 0.0776974i | ||||
\(281\) | −12.3772 | −0.738362 | −0.369181 | − | 0.929358i | \(-0.620362\pi\) | ||||
−0.369181 | + | 0.929358i | \(0.620362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.56225i | 0.152310i | 0.997096 | + | 0.0761550i | \(0.0242644\pi\) | ||||
−0.997096 | + | 0.0761550i | \(0.975736\pi\) | |||||||
\(284\) | −18.3772 | + | 4.63394i | −1.09049 | + | 0.274973i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.43215 | − | 11.5370i | −0.0846846 | − | 0.682195i | ||||
\(287\) | −1.73758 | −0.102566 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2136 | −0.894916 | ||||||||
\(290\) | −0.793528 | − | 6.39244i | −0.0465976 | − | 0.375377i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19.4581 | − | 4.90649i | 1.13870 | − | 0.287131i | ||||
\(293\) | − | 1.12608i | − | 0.0657866i | −0.999459 | − | 0.0328933i | \(-0.989528\pi\) | ||
0.999459 | − | 0.0328933i | \(-0.0104721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.97559 | −0.406135 | ||||||||
\(296\) | 31.3065 | − | 12.1610i | 1.81965 | − | 0.706846i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.6259 | − | 2.56040i | 1.19483 | − | 0.148320i | ||||
\(299\) | − | 9.14770i | − | 0.529025i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.70380i | − | 0.0982052i | ||||||
\(302\) | 0.0383873 | + | 0.309237i | 0.00220894 | + | 0.0177946i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.22760 | − | 11.5635i | −0.357177 | − | 0.663212i | ||||
\(305\) | −7.64411 | −0.437700 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.9543i | − | 1.42422i | −0.702070 | − | 0.712108i | \(-0.747741\pi\) | ||
0.702070 | − | 0.712108i | \(-0.252259\pi\) | |||||||
\(308\) | −0.991730 | − | 3.93299i | −0.0565091 | − | 0.224103i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.827230 | − | 0.102689i | 0.0469835 | − | 0.00583232i | ||||
\(311\) | 20.4110 | 1.15740 | 0.578701 | − | 0.815540i | \(-0.303560\pi\) | ||||
0.578701 | + | 0.815540i | \(0.303560\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.5902 | 1.05078 | 0.525389 | − | 0.850862i | \(-0.323920\pi\) | ||||
0.525389 | + | 0.850862i | \(0.323920\pi\) | |||||||
\(314\) | −14.6473 | + | 1.81825i | −0.826597 | + | 0.102610i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.51113 | + | 2.39830i | −0.535043 | + | 0.134915i | ||||
\(317\) | 1.68959i | 0.0948970i | 0.998874 | + | 0.0474485i | \(0.0151090\pi\) | ||||
−0.998874 | + | 0.0474485i | \(0.984891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.27661 | −0.407412 | ||||||||
\(320\) | 6.85556 | + | 7.49269i | 0.383237 | + | 0.418854i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.393173 | − | 3.16729i | −0.0219107 | − | 0.176506i | ||||
\(323\) | 4.38859i | 0.244188i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 13.7347i | − | 0.761865i | ||||||
\(326\) | −6.27275 | + | 0.778671i | −0.347416 | + | 0.0431266i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.77955 | − | 4.58114i | −0.0982591 | − | 0.252951i | ||||
\(329\) | −8.45083 | −0.465909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.4187i | 1.39714i | 0.715542 | + | 0.698570i | \(0.246180\pi\) | ||||
−0.715542 | + | 0.698570i | \(0.753820\pi\) | |||||||
\(332\) | −3.40251 | − | 13.4936i | −0.186737 | − | 0.740559i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.44978 | − | 19.7347i | −0.134046 | − | 1.07984i | ||||
\(335\) | −0.484278 | −0.0264590 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.5368 | −0.573979 | −0.286989 | − | 0.957934i | \(-0.592654\pi\) | ||||
−0.286989 | + | 0.957934i | \(0.592654\pi\) | |||||||
\(338\) | 0.597560 | + | 4.81377i | 0.0325030 | + | 0.261835i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.829717 | − | 3.29048i | −0.0449977 | − | 0.178452i | ||||
\(341\) | − | 0.941649i | − | 0.0509932i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.49206 | − | 1.74494i | 0.242195 | − | 0.0940811i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.469549 | + | 0.0582877i | −0.0252431 | + | 0.00313356i | ||||
\(347\) | − | 12.6098i | − | 0.676930i | −0.940979 | − | 0.338465i | \(-0.890092\pi\) | ||
0.940979 | − | 0.338465i | \(-0.109908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.3681i | − | 0.554990i | −0.960727 | − | 0.277495i | \(-0.910496\pi\) | ||
0.960727 | − | 0.277495i | \(-0.0895043\pi\) | |||||||
\(350\) | −0.590326 | − | 4.75549i | −0.0315542 | − | 0.254192i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.35364 | − | 6.64267i | 0.498551 | − | 0.354055i | ||||
\(353\) | −21.4319 | −1.14071 | −0.570353 | − | 0.821399i | \(-0.693194\pi\) | ||||
−0.570353 | + | 0.821399i | \(0.693194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 12.0298i | − | 0.638473i | ||||||
\(356\) | 33.8061 | − | 8.52444i | 1.79172 | − | 0.451794i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.60225 | − | 0.323031i | 0.137533 | − | 0.0170727i | ||||
\(359\) | 17.5414 | 0.925798 | 0.462899 | − | 0.886411i | \(-0.346809\pi\) | ||||
0.462899 | + | 0.886411i | \(0.346809\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.21890 | 0.432574 | ||||||||
\(362\) | −16.6819 | + | 2.07082i | −0.876783 | + | 0.108840i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.98213 | + | 7.86073i | 0.103892 | + | 0.412014i | ||||
\(365\) | 12.7373i | 0.666702i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.4730 | 1.48628 | 0.743140 | − | 0.669136i | \(-0.233335\pi\) | ||||
0.743140 | + | 0.669136i | \(0.233335\pi\) | |||||||
\(368\) | 7.94788 | − | 4.28038i | 0.414312 | − | 0.223130i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.62615 | + | 21.1555i | 0.136527 | + | 1.09982i | ||||
\(371\) | − | 11.7544i | − | 0.610259i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 11.7775i | − | 0.609818i | −0.952382 | − | 0.304909i | \(-0.901374\pi\) | ||
0.952382 | − | 0.304909i | \(-0.0986260\pi\) | |||||||
\(374\) | −3.80423 | + | 0.472240i | −0.196712 | + | 0.0244190i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.65492 | − | 22.2806i | −0.446343 | − | 1.14903i | ||||
\(377\) | 14.5435 | 0.749028 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4058i | 0.739975i | 0.929037 | + | 0.369988i | \(0.120638\pi\) | ||||
−0.929037 | + | 0.369988i | \(0.879362\pi\) | |||||||
\(380\) | 8.08346 | − | 2.03830i | 0.414673 | − | 0.104563i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.61286 | − | 37.1599i | −0.236014 | − | 1.90126i | ||||
\(383\) | −11.8612 | −0.606078 | −0.303039 | − | 0.952978i | \(-0.598001\pi\) | ||||
−0.303039 | + | 0.952978i | \(0.598001\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.57454 | 0.131211 | ||||||||
\(386\) | 3.08069 | + | 24.8171i | 0.156803 | + | 1.26316i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.7928 | + | 3.73011i | −0.750992 | + | 0.189368i | ||||
\(389\) | 16.3633i | 0.829655i | 0.909900 | + | 0.414827i | \(0.136158\pi\) | ||||
−0.909900 | + | 0.414827i | \(0.863842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.01639 | −0.152545 | ||||||||
\(392\) | 1.02415 | + | 2.63650i | 0.0517274 | + | 0.133163i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.9419 | + | 1.60655i | −0.652003 | + | 0.0809367i | ||||
\(395\) | − | 6.22601i | − | 0.313265i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7133i | 0.537685i | 0.963184 | + | 0.268843i | \(0.0866411\pi\) | ||||
−0.963184 | + | 0.268843i | \(0.913359\pi\) | |||||||
\(398\) | 1.47451 | + | 11.8782i | 0.0739106 | + | 0.595403i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.9333 | − | 6.42673i | 0.596663 | − | 0.321337i | ||||
\(401\) | 21.7286 | 1.08507 | 0.542536 | − | 0.840032i | \(-0.317464\pi\) | ||||
0.542536 | + | 0.840032i | \(0.317464\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.88204i | 0.0937511i | ||||||||
\(404\) | −2.58036 | − | 10.2332i | −0.128378 | − | 0.509119i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.03553 | − | 0.625087i | 0.249909 | − | 0.0310226i | ||||
\(407\) | 24.0816 | 1.19368 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.3607 | −0.710092 | −0.355046 | − | 0.934849i | \(-0.615535\pi\) | ||||
−0.355046 | + | 0.934849i | \(0.615535\pi\) | |||||||
\(410\) | 3.09572 | − | 0.384289i | 0.152887 | − | 0.0189787i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.83715 | − | 2.48050i | 0.484642 | − | 0.122206i | ||||
\(413\) | − | 5.49489i | − | 0.270386i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.83296 | 0.433593 | ||||||||
\(416\) | −18.6948 | + | 13.2765i | −0.916587 | + | 0.650932i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.16011 | − | 9.34554i | −0.0567430 | − | 0.457105i | ||||
\(419\) | − | 33.7826i | − | 1.65039i | −0.564849 | − | 0.825194i | \(-0.691065\pi\) | ||
0.564849 | − | 0.825194i | \(-0.308935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6036i | 0.516788i | 0.966040 | + | 0.258394i | \(0.0831933\pi\) | ||||
−0.966040 | + | 0.258394i | \(0.916807\pi\) | |||||||
\(422\) | −6.55050 | + | 0.813149i | −0.318873 | + | 0.0395835i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.9905 | − | 12.0383i | 1.50503 | − | 0.584631i | ||||
\(425\) | −4.52892 | −0.219685 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.02150i | − | 0.291401i | ||||||
\(428\) | 2.55393 | + | 10.1283i | 0.123449 | + | 0.489572i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.376816 | + | 3.03553i | 0.0181717 | + | 0.146386i | ||||
\(431\) | 19.2155 | 0.925577 | 0.462788 | − | 0.886469i | \(-0.346849\pi\) | ||||
0.462788 | + | 0.886469i | \(0.346849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.8723 | 1.91614 | 0.958070 | − | 0.286534i | \(-0.0925030\pi\) | ||||
0.958070 | + | 0.286534i | \(0.0925030\pi\) | |||||||
\(434\) | 0.0808911 | + | 0.651635i | 0.00388290 | + | 0.0312795i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.29859 | − | 21.0131i | −0.253756 | − | 1.00634i | ||||
\(437\) | − | 7.41011i | − | 0.354474i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.96048 | 0.141296 | 0.0706481 | − | 0.997501i | \(-0.477493\pi\) | ||||
0.0706481 | + | 0.997501i | \(0.477493\pi\) | |||||||
\(440\) | 2.63672 | + | 6.78778i | 0.125701 | + | 0.323595i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.60338 | − | 0.943849i | 0.361656 | − | 0.0448943i | ||||
\(443\) | 12.7091i | 0.603827i | 0.953335 | + | 0.301914i | \(0.0976254\pi\) | ||||
−0.953335 | + | 0.301914i | \(0.902375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.1296i | 1.04904i | ||||||||
\(446\) | −1.36762 | − | 11.0171i | −0.0647586 | − | 0.521677i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.90223 | + | 5.40034i | −0.278854 | + | 0.255142i | ||||
\(449\) | −27.4353 | −1.29475 | −0.647375 | − | 0.762171i | \(-0.724133\pi\) | ||||
−0.647375 | + | 0.762171i | \(0.724133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.52391i | − | 0.165934i | ||||||
\(452\) | 21.0962 | − | 5.31955i | 0.992283 | − | 0.250211i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.0663 | − | 3.35989i | 1.27029 | − | 0.157688i | ||||
\(455\) | −5.14565 | −0.241232 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9049 | 0.884335 | 0.442168 | − | 0.896932i | \(-0.354210\pi\) | ||||
0.442168 | + | 0.896932i | \(0.354210\pi\) | |||||||
\(458\) | 2.40814 | − | 0.298936i | 0.112525 | − | 0.0139684i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.40097 | + | 5.55596i | 0.0653207 | + | 0.259048i | ||||
\(461\) | 30.3182i | 1.41206i | 0.708181 | + | 0.706030i | \(0.249516\pi\) | ||||
−0.708181 | + | 0.706030i | \(0.750484\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2518 | −1.35944 | −0.679722 | − | 0.733470i | \(-0.737900\pi\) | ||||
−0.679722 | + | 0.733470i | \(0.737900\pi\) | |||||||
\(464\) | 6.80518 | + | 12.6360i | 0.315922 | + | 0.586610i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.15915 | − | 33.5049i | −0.192669 | − | 1.55208i | ||||
\(467\) | 32.7692i | 1.51638i | 0.652036 | + | 0.758188i | \(0.273915\pi\) | ||||
−0.652036 | + | 0.758188i | \(0.726085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.381481i | − | 0.0176152i | ||||||
\(470\) | 15.0562 | − | 1.86901i | 0.694491 | − | 0.0862109i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.4873 | − | 5.62760i | 0.666831 | − | 0.259031i | ||||
\(473\) | 3.45539 | 0.158879 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 11.1258i | − | 0.510488i | ||||||
\(476\) | 2.59202 | − | 0.653595i | 0.118805 | − | 0.0299575i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.77523 | − | 30.4122i | −0.172675 | − | 1.39102i | ||||
\(479\) | −25.8900 | −1.18294 | −0.591472 | − | 0.806326i | \(-0.701453\pi\) | ||||
−0.591472 | + | 0.806326i | \(0.701453\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.1310 | −2.19459 | ||||||||
\(482\) | −4.85076 | − | 39.0763i | −0.220946 | − | 1.77988i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.3560 | + | 3.36779i | −0.607089 | + | 0.153082i | ||||
\(485\) | − | 9.68342i | − | 0.439701i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.94127 | −0.269225 | −0.134612 | − | 0.990898i | \(-0.542979\pi\) | ||||
−0.134612 | + | 0.990898i | \(0.542979\pi\) | |||||||
\(488\) | 15.8757 | − | 6.16693i | 0.718658 | − | 0.279164i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.78162 | + | 0.221163i | −0.0804856 | + | 0.00999112i | ||||
\(491\) | 3.77413i | 0.170324i | 0.996367 | + | 0.0851621i | \(0.0271408\pi\) | ||||
−0.996367 | + | 0.0851621i | \(0.972859\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.79561i | − | 0.215984i | ||||||
\(494\) | 2.31868 | + | 18.6786i | 0.104322 | + | 0.840390i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.63519 | + | 0.880642i | −0.0734222 | + | 0.0395420i | ||||
\(497\) | 9.47622 | 0.425067 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.66921i | 0.343321i | 0.985156 | + | 0.171661i | \(0.0549132\pi\) | ||||
−0.985156 | + | 0.171661i | \(0.945087\pi\) | |||||||
\(500\) | 5.20737 | + | 20.6513i | 0.232881 | + | 0.923555i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 38.8902 | − | 4.82765i | 1.73575 | − | 0.215469i | ||||
\(503\) | −7.29637 | −0.325329 | −0.162664 | − | 0.986681i | \(-0.552009\pi\) | ||||
−0.162664 | + | 0.986681i | \(0.552009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.69865 | 0.298086 | ||||||||
\(506\) | 6.42342 | − | 0.797374i | 0.285556 | − | 0.0354476i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.04810 | + | 0.768597i | −0.135237 | + | 0.0341010i | ||||
\(509\) | 7.32231i | 0.324556i | 0.986745 | + | 0.162278i | \(0.0518841\pi\) | ||||
−0.986745 | + | 0.162278i | \(0.948116\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0336 | −0.443860 | ||||||||
\(512\) | −20.2828 | − | 10.0305i | −0.896379 | − | 0.443288i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.331817 | + | 2.67302i | 0.0146358 | + | 0.117902i | ||||
\(515\) | 6.43942i | 0.283755i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 17.1387i | − | 0.753759i | ||||||
\(518\) | −16.6648 | + | 2.06870i | −0.732211 | + | 0.0908934i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.26992 | − | 13.5665i | −0.231101 | − | 0.594930i | ||||
\(521\) | −29.2300 | −1.28059 | −0.640295 | − | 0.768129i | \(-0.721188\pi\) | ||||
−0.640295 | + | 0.768129i | \(0.721188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.4676i | 1.63835i | 0.573547 | + | 0.819173i | \(0.305567\pi\) | ||||
−0.573547 | + | 0.819173i | \(0.694433\pi\) | |||||||
\(524\) | 5.76770 | + | 22.8735i | 0.251963 | + | 0.999234i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.34820 | − | 26.9721i | −0.145988 | − | 1.17604i | ||||
\(527\) | 0.620589 | 0.0270333 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.9068 | −0.778559 | ||||||||
\(530\) | 2.59964 | + | 20.9419i | 0.112921 | + | 0.909660i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.60563 | + | 6.36760i | 0.0696130 | + | 0.276070i | ||||
\(533\) | 7.04311i | 0.305071i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.63003 | −0.286641 | ||||||||
\(536\) | 1.00577 | − | 0.390694i | 0.0434428 | − | 0.0168754i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.6733 | + | 3.18697i | −1.10686 | + | 0.137400i | ||||
\(539\) | 2.02805i | 0.0873543i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.9143i | 0.985164i | 0.870266 | + | 0.492582i | \(0.163947\pi\) | ||||
−0.870266 | + | 0.492582i | \(0.836053\pi\) | |||||||
\(542\) | −3.33538 | − | 26.8689i | −0.143267 | − | 1.15412i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.37782 | + | 6.16447i | 0.187697 | + | 0.264299i | ||||
\(545\) | 13.7552 | 0.589208 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.0319i | − | 0.599959i | −0.953946 | − | 0.299979i | \(-0.903020\pi\) | ||
0.953946 | − | 0.299979i | \(-0.0969798\pi\) | |||||||
\(548\) | 35.6842 | − | 8.99800i | 1.52435 | − | 0.384375i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.64438 | − | 1.19721i | 0.411238 | − | 0.0510492i | ||||
\(551\) | 11.7810 | 0.501887 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.90442 | 0.208557 | ||||||||
\(554\) | 24.7410 | − | 3.07123i | 1.05114 | − | 0.130484i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.56740 | + | 22.0791i | 0.236110 | + | 0.936364i | ||||
\(557\) | − | 29.1958i | − | 1.23706i | −0.785760 | − | 0.618532i | \(-0.787728\pi\) | ||
0.785760 | − | 0.618532i | \(-0.212272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.90615 | −0.292099 | ||||||||
\(560\) | −2.40775 | − | 4.47074i | −0.101746 | − | 0.188923i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.15632 | + | 17.3707i | 0.0909587 | + | 0.732738i | ||||
\(563\) | − | 29.5633i | − | 1.24594i | −0.782245 | − | 0.622971i | \(-0.785925\pi\) | ||
0.782245 | − | 0.622971i | \(-0.214075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.8096i | 0.580976i | ||||||||
\(566\) | 3.59597 | − | 0.446387i | 0.151150 | − | 0.0187631i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.70508 | + | 24.9840i | 0.407216 | + | 1.04831i | ||||
\(569\) | 28.2748 | 1.18534 | 0.592672 | − | 0.805444i | \(-0.298073\pi\) | ||||
0.592672 | + | 0.805444i | \(0.298073\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.3483i | 1.68852i | 0.535932 | + | 0.844261i | \(0.319960\pi\) | ||||
−0.535932 | + | 0.844261i | \(0.680040\pi\) | |||||||
\(572\) | −15.9420 | + | 4.01987i | −0.666567 | + | 0.168079i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.302717 | + | 2.43860i | 0.0126351 | + | 0.101785i | ||||
\(575\) | 7.64706 | 0.318904 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.0318593 | −0.00132632 | −0.000663161 | − | 1.00000i | \(-0.500211\pi\) | ||||
−0.000663161 | 1.00000i | \(0.500211\pi\) | ||||||||
\(578\) | 2.65046 | + | 21.3513i | 0.110245 | + | 0.888099i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.83317 | + | 2.22734i | −0.366777 | + | 0.0924853i | ||||
\(581\) | 6.95800i | 0.288667i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.8385 | 0.987291 | ||||||||
\(584\) | −10.2759 | − | 26.4535i | −0.425220 | − | 1.09465i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.58039 | + | 0.196183i | −0.0652855 | + | 0.00810424i | ||||
\(587\) | − | 22.9245i | − | 0.946195i | −0.881010 | − | 0.473098i | \(-0.843136\pi\) | ||
0.881010 | − | 0.473098i | \(-0.156864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.52455i | 0.0628180i | ||||||||
\(590\) | 1.21527 | + | 9.78983i | 0.0500317 | + | 0.403041i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.5214 | − | 41.8181i | −0.925625 | − | 1.71872i | ||||
\(593\) | 19.8895 | 0.816764 | 0.408382 | − | 0.912811i | \(-0.366093\pi\) | ||||
0.408382 | + | 0.912811i | \(0.366093\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.69674i | 0.0695596i | ||||||||
\(596\) | −7.18675 | − | 28.5012i | −0.294381 | − | 1.16745i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.8383 | + | 1.59368i | −0.524995 | + | 0.0651706i | ||||
\(599\) | −9.01493 | −0.368340 | −0.184170 | − | 0.982894i | \(-0.558960\pi\) | ||||
−0.184170 | + | 0.982894i | \(0.558960\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.3934 | −1.23977 | −0.619886 | − | 0.784692i | \(-0.712821\pi\) | ||||
−0.619886 | + | 0.784692i | \(0.712821\pi\) | |||||||
\(602\) | −2.39118 | + | 0.296830i | −0.0974572 | + | 0.0120979i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.427308 | − | 0.107749i | 0.0173869 | − | 0.00438423i | ||||
\(605\) | − | 8.74284i | − | 0.355447i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.5668 | −1.44361 | −0.721807 | − | 0.692095i | \(-0.756688\pi\) | ||||
−0.721807 | + | 0.692095i | \(0.756688\pi\) | |||||||
\(608\) | −15.1437 | + | 10.7546i | −0.614160 | + | 0.436158i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.33173 | + | 10.7281i | 0.0539203 | + | 0.434366i | ||||
\(611\) | 34.2545i | 1.38579i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.1874i | 1.46159i | 0.682595 | + | 0.730797i | \(0.260851\pi\) | ||||
−0.682595 | + | 0.730797i | \(0.739149\pi\) | |||||||
\(614\) | −35.0219 | + | 4.34746i | −1.41337 | + | 0.175449i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.34695 | + | 2.07703i | −0.215435 | + | 0.0836859i | ||||
\(617\) | −27.7558 | −1.11741 | −0.558704 | − | 0.829367i | \(-0.688701\pi\) | ||||
−0.558704 | + | 0.829367i | \(0.688701\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.0187i | 1.20656i | 0.797531 | + | 0.603278i | \(0.206139\pi\) | ||||
−0.797531 | + | 0.603278i | \(0.793861\pi\) | |||||||
\(620\) | −0.288235 | − | 1.14308i | −0.0115758 | − | 0.0459072i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.55594 | − | 28.6457i | −0.142580 | − | 1.14859i | ||||
\(623\) | −17.4322 | −0.698405 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.42386 | 0.136954 | ||||||||
\(626\) | −3.23872 | − | 26.0902i | −0.129445 | − | 1.04277i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.10363 | + | 20.2399i | 0.203657 | + | 0.807660i | ||||
\(629\) | 15.8709i | 0.632813i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.3724 | 1.84606 | 0.923028 | − | 0.384732i | \(-0.125706\pi\) | ||||
0.923028 | + | 0.384732i | \(0.125706\pi\) | |||||||
\(632\) | 5.02287 | + | 12.9305i | 0.199799 | + | 0.514348i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.37124 | − | 0.294356i | 0.0941741 | − | 0.0116904i | ||||
\(635\) | − | 1.99529i | − | 0.0791807i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.05339i | − | 0.160601i | ||||||
\(638\) | 1.26771 | + | 10.2123i | 0.0501891 | + | 0.404309i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.32120 | − | 10.9267i | 0.368453 | − | 0.431917i | ||||
\(641\) | −16.0590 | −0.634294 | −0.317147 | − | 0.948376i | \(-0.602725\pi\) | ||||
−0.317147 | + | 0.948376i | \(0.602725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11.8356i | − | 0.466752i | −0.972387 | − | 0.233376i | \(-0.925023\pi\) | ||
0.972387 | − | 0.233376i | \(-0.0749774\pi\) | |||||||
\(644\) | −4.37661 | + | 1.10359i | −0.172462 | + | 0.0434876i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.15913 | − | 0.764567i | 0.242328 | − | 0.0300815i | ||||
\(647\) | −5.05582 | −0.198765 | −0.0993824 | − | 0.995049i | \(-0.531687\pi\) | ||||
−0.0993824 | + | 0.995049i | \(0.531687\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1439 | 0.437437 | ||||||||
\(650\) | −19.2759 | + | 2.39282i | −0.756062 | + | 0.0938541i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.18564 | + | 8.66779i | 0.0855963 | + | 0.339457i | ||||
\(653\) | 21.1804i | 0.828851i | 0.910083 | + | 0.414426i | \(0.136018\pi\) | ||||
−0.910083 | + | 0.414426i | \(0.863982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9730 | −0.585045 | ||||||||
\(656\) | −6.11933 | + | 3.29560i | −0.238920 | + | 0.128672i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.47228 | + | 11.8602i | 0.0573953 | + | 0.462360i | ||||
\(659\) | − | 18.6255i | − | 0.725548i | −0.931877 | − | 0.362774i | \(-0.881830\pi\) | ||
0.931877 | − | 0.362774i | \(-0.118170\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.43660i | − | 0.328146i | −0.986448 | − | 0.164073i | \(-0.947537\pi\) | ||
0.986448 | − | 0.164073i | \(-0.0524632\pi\) | |||||||
\(662\) | 35.6737 | − | 4.42837i | 1.38650 | − | 0.172114i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −18.3448 | + | 7.12604i | −0.711915 | + | 0.276544i | ||||
\(665\) | −4.16824 | −0.161638 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.09736i | 0.313531i | ||||||||
\(668\) | −27.2697 | + | 6.87624i | −1.05510 | + | 0.266050i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.0843695 | + | 0.679657i | 0.00325948 | + | 0.0262574i | ||||
\(671\) | 12.2119 | 0.471436 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.6372 | −0.448581 | −0.224291 | − | 0.974522i | \(-0.572006\pi\) | ||||
−0.224291 | + | 0.974522i | \(0.572006\pi\) | |||||||
\(674\) | 1.83570 | + | 14.7878i | 0.0707084 | + | 0.569607i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.65175 | − | 1.67728i | 0.255836 | − | 0.0645108i | ||||
\(677\) | − | 42.4251i | − | 1.63053i | −0.579089 | − | 0.815264i | \(-0.696592\pi\) | ||
0.579089 | − | 0.815264i | \(-0.303408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.62794 | 0.292733 | ||||||||
\(680\) | −4.47345 | + | 1.73772i | −0.171549 | + | 0.0666384i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.32155 | + | 0.164051i | −0.0506047 | + | 0.00628184i | ||||
\(683\) | 26.8253i | 1.02644i | 0.858257 | + | 0.513221i | \(0.171548\pi\) | ||||
−0.858257 | + | 0.513221i | \(0.828452\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.3589i | 0.892499i | ||||||||
\(686\) | −0.174217 | − | 1.40344i | −0.00665163 | − | 0.0535837i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.23152 | − | 6.00034i | −0.123201 | − | 0.228761i | ||||
\(689\) | −47.6452 | −1.81514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.9065i | 1.89853i | 0.314476 | + | 0.949265i | \(0.398171\pi\) | ||||
−0.314476 | + | 0.949265i | \(0.601829\pi\) | |||||||
\(692\) | 0.163607 | + | 0.648830i | 0.00621939 | + | 0.0246648i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.6971 | + | 2.19684i | −0.671774 | + | 0.0833910i | ||||
\(695\) | −14.4530 | −0.548235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.32241 | 0.0879677 | ||||||||
\(698\) | −14.5510 | + | 1.80629i | −0.550763 | + | 0.0683693i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.57121 | + | 1.65697i | −0.248369 | + | 0.0626278i | ||||
\(701\) | − | 47.6375i | − | 1.79924i | −0.436671 | − | 0.899621i | \(-0.643843\pi\) | ||
0.436671 | − | 0.899621i | \(-0.356157\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.9887 | −1.47049 | ||||||||
\(704\) | −10.9522 | − | 11.9700i | −0.412775 | − | 0.451137i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.73381 | + | 30.0785i | 0.140524 | + | 1.13202i | ||||
\(707\) | 5.27674i | 0.198452i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0726i | 0.904064i | 0.892002 | + | 0.452032i | \(0.149301\pi\) | ||||
−0.892002 | + | 0.452032i | \(0.850699\pi\) | |||||||
\(710\) | −16.8831 | + | 2.09579i | −0.633610 | + | 0.0786535i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.8532 | − | 45.9598i | −0.669075 | − | 1.72242i | ||||
\(713\) | −1.04786 | −0.0392427 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 10.4356i | − | 0.390271i | ||||||
\(716\) | −0.906712 | − | 3.59583i | −0.0338854 | − | 0.134382i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.05600 | − | 24.6183i | −0.114049 | − | 0.918746i | ||||
\(719\) | −49.0237 | −1.82827 | −0.914137 | − | 0.405406i | \(-0.867130\pi\) | ||||
−0.914137 | + | 0.405406i | \(0.867130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.07253 | −0.188911 | ||||||||
\(722\) | −1.43187 | − | 11.5347i | −0.0532887 | − | 0.429279i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.81255 | + | 23.0513i | 0.216022 | + | 0.856696i | ||||
\(725\) | 12.1577i | 0.451526i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0843 | 0.670710 | 0.335355 | − | 0.942092i | \(-0.391144\pi\) | ||||
0.335355 | + | 0.942092i | \(0.391144\pi\) | |||||||
\(728\) | 10.6868 | − | 4.15128i | 0.396077 | − | 0.153857i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 17.8761 | − | 2.21906i | 0.661624 | − | 0.0821310i | ||||
\(731\) | 2.27725i | 0.0842273i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.54526i | 0.0940114i | 0.998895 | + | 0.0470057i | \(0.0149679\pi\) | ||||
−0.998895 | + | 0.0470057i | \(0.985032\pi\) | |||||||
\(734\) | −4.96049 | − | 39.9603i | −0.183095 | − | 1.47496i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.39192 | − | 10.4087i | −0.272470 | − | 0.383669i | ||||
\(737\) | 0.773664 | 0.0284983 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.7876i | 1.35326i | 0.736325 | + | 0.676628i | \(0.236559\pi\) | ||||
−0.736325 | + | 0.676628i | \(0.763441\pi\) | |||||||
\(740\) | 29.2330 | − | 7.37129i | 1.07463 | − | 0.270974i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.4966 | + | 2.04782i | −0.605610 | + | 0.0751777i | ||||
\(743\) | 27.1051 | 0.994391 | 0.497196 | − | 0.867638i | \(-0.334363\pi\) | ||||
0.497196 | + | 0.867638i | \(0.334363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6569 | 0.683537 | ||||||||
\(746\) | −16.5291 | + | 2.05185i | −0.605173 | + | 0.0751234i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.32552 | + | 5.25674i | 0.0484659 | + | 0.192206i | ||||
\(749\) | − | 5.22269i | − | 0.190833i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3786 | −1.29098 | −0.645491 | − | 0.763768i | \(-0.723347\pi\) | ||||
−0.645491 | + | 0.763768i | \(0.723347\pi\) | |||||||
\(752\) | −29.7617 | + | 16.0283i | −1.08530 | + | 0.584493i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.53372 | − | 20.4110i | −0.0922728 | − | 0.743323i | ||||
\(755\) | 0.279717i | 0.0101799i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.340328i | 0.0123694i | 0.999981 | + | 0.00618471i | \(0.00196867\pi\) | ||||
−0.999981 | + | 0.00618471i | \(0.998031\pi\) | |||||||
\(758\) | 20.2177 | − | 2.50973i | 0.734339 | − | 0.0911575i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.26891 | − | 10.9896i | −0.154850 | − | 0.398633i | ||||
\(761\) | 30.2601 | 1.09693 | 0.548464 | − | 0.836174i | \(-0.315213\pi\) | ||||
0.548464 | + | 0.836174i | \(0.315213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8354i | 0.392268i | ||||||||
\(764\) | −51.3480 | + | 12.9477i | −1.85771 | + | 0.468433i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.06642 | + | 16.6465i | 0.0746627 | + | 0.601461i | ||||
\(767\) | −22.2729 | −0.804230 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0636 | 0.651389 | 0.325695 | − | 0.945475i | \(-0.394402\pi\) | ||||
0.325695 | + | 0.945475i | \(0.394402\pi\) | |||||||
\(770\) | −0.448529 | − | 3.61322i | −0.0161639 | − | 0.130212i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 34.2927 | − | 8.64713i | 1.23422 | − | 0.311217i | ||||
\(773\) | 3.29847i | 0.118638i | 0.998239 | + | 0.0593188i | \(0.0188929\pi\) | ||||
−0.998239 | + | 0.0593188i | \(0.981107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.57330 | −0.0565146 | ||||||||
\(776\) | 7.81215 | + | 20.1110i | 0.280440 | + | 0.721944i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.9650 | − | 2.85077i | 0.823335 | − | 0.102205i | ||||
\(779\) | 5.70529i | 0.204413i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.2183i | 0.687683i | ||||||||
\(782\) | 0.525506 | + | 4.23332i | 0.0187920 | + | 0.151383i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.52175 | − | 1.89666i | 0.125777 | − | 0.0677378i | ||||
\(785\) | −13.2491 | −0.472880 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 14.6607i | − | 0.522597i | −0.965258 | − | 0.261298i | \(-0.915849\pi\) | ||
0.965258 | − | 0.261298i | \(-0.0841506\pi\) | |||||||
\(788\) | 4.50939 | + | 17.8833i | 0.160640 | + | 0.637066i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.73784 | + | 1.08468i | −0.310878 | + | 0.0385910i | ||||
\(791\) | −10.8783 | −0.386787 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.4075 | −0.866736 | ||||||||
\(794\) | 15.0355 | − | 1.86644i | 0.533590 | − | 0.0662374i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.4135 | − | 4.13878i | 0.581762 | − | 0.146695i | ||||
\(797\) | − | 10.7001i | − | 0.379016i | −0.981879 | − | 0.189508i | \(-0.939311\pi\) | ||
0.981879 | − | 0.189508i | \(-0.0606892\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2952 | 0.399595 | ||||||||
\(800\) | −11.0985 | − | 15.6280i | −0.392392 | − | 0.552533i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.78548 | − | 30.4948i | −0.133670 | − | 1.07681i | ||||
\(803\) | − | 20.3486i | − | 0.718087i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 2.86494i | − | 0.100976i | ||||||
\(806\) | 2.64133 | − | 0.327883i | 0.0930370 | − | 0.0115492i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.9121 | + | 5.40418i | −0.489426 | + | 0.190118i | ||||
\(809\) | −19.7701 | −0.695078 | −0.347539 | − | 0.937666i | \(-0.612983\pi\) | ||||
−0.347539 | + | 0.937666i | \(0.612983\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.8088i | 1.04673i | 0.852109 | + | 0.523364i | \(0.175323\pi\) | ||||
−0.852109 | + | 0.523364i | \(0.824677\pi\) | |||||||
\(812\) | −1.75455 | − | 6.95817i | −0.0615725 | − | 0.244184i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.19542 | − | 33.7971i | −0.147050 | − | 1.18459i | ||||
\(815\) | −5.67395 | −0.198750 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.59435 | −0.195721 | ||||||||
\(818\) | 2.50188 | + | 20.1544i | 0.0874762 | + | 0.704683i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.07865 | − | 4.27772i | −0.0376683 | − | 0.149384i | ||||
\(821\) | − | 38.3014i | − | 1.33673i | −0.743834 | − | 0.668364i | \(-0.766995\pi\) | ||
0.743834 | − | 0.668364i | \(-0.233005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.3640 | 0.918990 | 0.459495 | − | 0.888180i | \(-0.348030\pi\) | ||||
0.459495 | + | 0.888180i | \(0.348030\pi\) | |||||||
\(824\) | −5.19504 | − | 13.3737i | −0.180978 | − | 0.465896i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.71176 | + | 0.957303i | −0.268327 | + | 0.0333088i | ||||
\(827\) | 44.5542i | 1.54930i | 0.632390 | + | 0.774650i | \(0.282074\pi\) | ||||
−0.632390 | + | 0.774650i | \(0.717926\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 48.8761i | − | 1.69754i | −0.528765 | − | 0.848768i | \(-0.677345\pi\) | ||
0.528765 | − | 0.848768i | \(-0.322655\pi\) | |||||||
\(830\) | −1.53885 | − | 12.3965i | −0.0534143 | − | 0.430290i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.8897 | + | 23.9241i | 0.758888 | + | 0.829417i | ||||
\(833\) | −1.33658 | −0.0463096 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 17.8508i | − | 0.617753i | ||||||
\(836\) | −12.9138 | + | 3.25630i | −0.446634 | + | 0.112622i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47.4119 | + | 5.88550i | −1.63782 | + | 0.203311i | ||||
\(839\) | −39.1944 | −1.35314 | −0.676571 | − | 0.736377i | \(-0.736535\pi\) | ||||
−0.676571 | + | 0.736377i | \(0.736535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.1264 | 0.556082 | ||||||||
\(842\) | 14.8816 | − | 1.84733i | 0.512852 | − | 0.0636631i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.28241 | + | 9.05157i | 0.0785639 | + | 0.311568i | ||||
\(845\) | 4.35425i | 0.149791i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.88701 | 0.236641 | ||||||||
\(848\) | −22.2941 | − | 41.3960i | −0.765582 | − | 1.42155i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.789015 | + | 6.35608i | 0.0270630 | + | 0.218012i | ||||
\(851\) | − | 26.7979i | − | 0.918619i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 22.6315i | − | 0.774887i | −0.921893 | − | 0.387444i | \(-0.873358\pi\) | ||
0.921893 | − | 0.387444i | \(-0.126642\pi\) | |||||||
\(854\) | −8.45083 | + | 1.04905i | −0.289181 | + | 0.0358977i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.7696 | − | 5.34882i | 0.470635 | − | 0.182819i | ||||
\(857\) | 25.6866 | 0.877436 | 0.438718 | − | 0.898625i | \(-0.355433\pi\) | ||||
0.438718 | + | 0.898625i | \(0.355433\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.4628i | 1.55117i | 0.631244 | + | 0.775585i | \(0.282545\pi\) | ||||
−0.631244 | + | 0.775585i | \(0.717455\pi\) | |||||||
\(860\) | 4.19454 | − | 1.05768i | 0.143032 | − | 0.0360666i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.34766 | − | 26.9678i | −0.114022 | − | 0.918527i | ||||
\(863\) | −6.81159 | −0.231869 | −0.115935 | − | 0.993257i | \(-0.536986\pi\) | ||||
−0.115935 | + | 0.993257i | \(0.536986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.424725 | −0.0144411 | ||||||||
\(866\) | −6.94643 | − | 55.9584i | −0.236049 | − | 1.90155i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.900440 | − | 0.227052i | 0.0305629 | − | 0.00770664i | ||||
\(869\) | 9.94642i | 0.337409i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.54629 | −0.0523942 | ||||||||
\(872\) | −28.5675 | + | 11.0971i | −0.967418 | + | 0.375795i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.3997 | + | 1.29097i | −0.351774 | + | 0.0436676i | ||||
\(875\) | − | 10.6489i | − | 0.359997i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.9922i | 1.18160i | 0.806817 | + | 0.590802i | \(0.201188\pi\) | ||||
−0.806817 | + | 0.590802i | \(0.798812\pi\) | |||||||
\(878\) | −0.515766 | − | 4.15487i | −0.0174063 | − | 0.140220i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.06689 | − | 4.88303i | 0.305645 | − | 0.164607i | ||||
\(881\) | 16.1155 | 0.542946 | 0.271473 | − | 0.962446i | \(-0.412489\pi\) | ||||
0.271473 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.5075i | − | 1.56510i | −0.622586 | − | 0.782551i | \(-0.713918\pi\) | ||
0.622586 | − | 0.782551i | \(-0.286082\pi\) | |||||||
\(884\) | −2.64927 | − | 10.5065i | −0.0891047 | − | 0.353371i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.8365 | − | 2.21414i | 0.599228 | − | 0.0743855i | ||||
\(887\) | −43.0256 | −1.44466 | −0.722328 | − | 0.691550i | \(-0.756928\pi\) | ||||
−0.722328 | + | 0.691550i | \(0.756928\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.57175 | 0.0527149 | ||||||||
\(890\) | 31.0576 | − | 3.85534i | 1.04105 | − | 0.129231i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.2237 | + | 3.83875i | −0.509726 | + | 0.128531i | ||||
\(893\) | 27.7479i | 0.928550i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.35384 | 0.0786801 | ||||||||
\(896\) | 8.60733 | + | 7.34261i | 0.287551 | + | 0.245299i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.77969 | + | 38.5038i | 0.159500 | + | 1.28489i | ||||
\(899\) | − | 1.66595i | − | 0.0555624i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7107i | 0.523398i | ||||||||
\(902\) | −4.94560 | + | 0.613925i | −0.164671 | + | 0.0204415i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.1410 | − | 28.6806i | −0.370544 | − | 0.953902i | ||||
\(905\) | −15.0895 | −0.501590 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.6912i | 1.64997i | 0.565156 | + | 0.824984i | \(0.308816\pi\) | ||||
−0.565156 | + | 0.824984i | \(0.691184\pi\) | |||||||
\(908\) | −9.43082 | − | 37.4007i | −0.312973 | − | 1.24118i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.896459 | + | 7.22162i | 0.0297173 | + | 0.239394i | ||||
\(911\) | 44.6723 | 1.48006 | 0.740029 | − | 0.672575i | \(-0.234812\pi\) | ||||
0.740029 | + | 0.672575i | \(0.234812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.1112 | −0.467012 | ||||||||
\(914\) | −3.29356 | − | 26.5320i | −0.108941 | − | 0.877599i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.839078 | − | 3.32761i | −0.0277239 | − | 0.109947i | ||||
\(917\) | − | 11.7947i | − | 0.389497i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.7662 | −1.70761 | −0.853804 | − | 0.520594i | \(-0.825710\pi\) | ||||
−0.853804 | + | 0.520594i | \(0.825710\pi\) | |||||||
\(920\) | 7.55340 | − | 2.93413i | 0.249028 | − | 0.0967353i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 42.5499 | − | 5.28195i | 1.40131 | − | 0.173952i | ||||
\(923\) | − | 38.4108i | − | 1.26431i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 40.2354i | − | 1.32293i | ||||||
\(926\) | 5.09615 | + | 41.0531i | 0.167470 | + | 1.34909i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.5483 | − | 11.7521i | 0.543223 | − | 0.385781i | ||||
\(929\) | 16.4271 | 0.538956 | 0.269478 | − | 0.963006i | \(-0.413149\pi\) | ||||
0.269478 | + | 0.963006i | \(0.413149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.28346i | − | 0.107611i | ||||||
\(932\) | −46.2976 | + | 11.6742i | −1.51653 | + | 0.382403i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.9896 | − | 5.70894i | 1.50483 | − | 0.186802i | ||||
\(935\) | −3.44108 | −0.112535 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.9154 | −0.813951 | −0.406976 | − | 0.913439i | \(-0.633417\pi\) | ||||
−0.406976 | + | 0.913439i | \(0.633417\pi\) | |||||||
\(938\) | −0.535387 | + | 0.0664605i | −0.0174810 | + | 0.00217001i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.24609 | − | 20.8049i | −0.171109 | − | 0.678581i | ||||
\(941\) | 35.3088i | 1.15103i | 0.817790 | + | 0.575517i | \(0.195199\pi\) | ||||
−0.817790 | + | 0.575517i | \(0.804801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.92138 | −0.127698 | ||||||||
\(944\) | −10.4219 | − | 19.3516i | −0.339205 | − | 0.629841i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.601987 | − | 4.84943i | −0.0195723 | − | 0.157669i | ||||
\(947\) | − | 41.3026i | − | 1.34215i | −0.741388 | − | 0.671077i | \(-0.765832\pi\) | ||
0.741388 | − | 0.671077i | \(-0.234168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.6701i | 1.32021i | ||||||||
\(950\) | −15.6145 | + | 1.93831i | −0.506600 | + | 0.0628871i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.36886 | − | 3.52388i | −0.0443649 | − | 0.114210i | ||||
\(953\) | 11.2564 | 0.364630 | 0.182315 | − | 0.983240i | \(-0.441641\pi\) | ||||
0.182315 | + | 0.983240i | \(0.441641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 33.6125i | − | 1.08768i | ||||||
\(956\) | −42.0240 | + | 10.5966i | −1.35915 | + | 0.342719i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.51047 | + | 36.3351i | 0.145727 | + | 1.17393i | ||||
\(959\) | −18.4006 | −0.594185 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7844 | −0.993046 | ||||||||
\(962\) | 8.38524 | + | 67.5491i | 0.270351 | + | 2.17787i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −53.9963 | + | 13.6155i | −1.73910 | + | 0.438526i | ||||
\(965\) | 22.4481i | 0.722629i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.51158 | −0.0486093 | −0.0243046 | − | 0.999705i | \(-0.507737\pi\) | ||||
−0.0243046 | + | 0.999705i | \(0.507737\pi\) | |||||||
\(968\) | 7.05334 | + | 18.1576i | 0.226703 | + | 0.583607i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.5901 | + | 1.68702i | −0.436352 | + | 0.0541668i | ||||
\(971\) | − | 9.03959i | − | 0.290094i | −0.989425 | − | 0.145047i | \(-0.953667\pi\) | ||
0.989425 | − | 0.145047i | \(-0.0463334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 11.3851i | − | 0.364990i | ||||||
\(974\) | 1.03507 | + | 8.33823i | 0.0331658 | + | 0.267174i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.4207 | − | 21.2062i | −0.365569 | − | 0.678794i | ||||
\(977\) | 2.32341 | 0.0743325 | 0.0371662 | − | 0.999309i | \(-0.488167\pi\) | ||||
0.0371662 | + | 0.999309i | \(0.488167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 35.3533i | − | 1.12990i | ||||||
\(980\) | 0.620778 | + | 2.46188i | 0.0198300 | + | 0.0786417i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.29678 | − | 0.657518i | 0.169027 | − | 0.0209822i | ||||
\(983\) | 18.8206 | 0.600284 | 0.300142 | − | 0.953894i | \(-0.402966\pi\) | ||||
0.300142 | + | 0.953894i | \(0.402966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.7064 | −0.372998 | ||||||||
\(986\) | −6.73036 | + | 0.835477i | −0.214338 | + | 0.0266070i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.8104 | − | 6.50826i | 0.821137 | − | 0.207055i | ||||
\(989\) | − | 3.84513i | − | 0.122268i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.9699 | −1.20615 | −0.603077 | − | 0.797683i | \(-0.706059\pi\) | ||||
−0.603077 | + | 0.797683i | \(0.706059\pi\) | |||||||
\(992\) | 1.52081 | + | 2.14147i | 0.0482857 | + | 0.0679918i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.65092 | − | 13.2993i | −0.0523640 | − | 0.421829i | ||||
\(995\) | 10.7443i | 0.340618i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.55023i | 0.302459i | 0.988499 | + | 0.151229i | \(0.0483232\pi\) | ||||
−0.988499 | + | 0.151229i | \(0.951677\pi\) | |||||||
\(998\) | 10.7633 | − | 1.33611i | 0.340706 | − | 0.0422937i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.c.f.757.11 | ✓ | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.f.757.14 | yes | 24 | |
4.3 | odd | 2 | 6048.2.c.g.3025.11 | 24 | |||
8.3 | odd | 2 | 6048.2.c.g.3025.14 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.f.757.12 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.g.3025.13 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.f.757.13 | yes | 24 | |
24.11 | even | 2 | 6048.2.c.g.3025.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.11 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1512.2.c.f.757.12 | yes | 24 | 8.5 | even | 2 | inner | |
1512.2.c.f.757.13 | yes | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.f.757.14 | yes | 24 | 3.2 | odd | 2 | inner | |
6048.2.c.g.3025.11 | 24 | 4.3 | odd | 2 | |||
6048.2.c.g.3025.12 | 24 | 24.11 | even | 2 | |||
6048.2.c.g.3025.13 | 24 | 12.11 | even | 2 | |||
6048.2.c.g.3025.14 | 24 | 8.3 | odd | 2 |