Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(41,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bu (of order \(6\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.8 | ||
Character | \(\chi\) | \(=\) | 504.41 |
Dual form | 504.2.bu.a.209.8 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0 | ||||||||
\(3\) | −1.01807 | − | 1.40126i | −0.587784 | − | 0.809018i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.60290 | + | 2.77631i | −0.716840 | + | 1.24160i | 0.245405 | + | 0.969421i | \(0.421079\pi\) |
−0.962245 | + | 0.272183i | \(0.912254\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.96276 | − | 1.77414i | −0.741853 | − | 0.670562i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.927062 | + | 2.85317i | −0.309021 | + | 0.951055i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.13786 | − | 2.38899i | 1.24761 | − | 0.720308i | 0.276978 | − | 0.960876i | \(-0.410667\pi\) |
0.970632 | + | 0.240568i | \(0.0773337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.861773 | + | 0.497545i | 0.239013 | + | 0.137994i | 0.614723 | − | 0.788743i | \(-0.289268\pi\) |
−0.375710 | + | 0.926737i | \(0.622601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.52220 | − | 0.580396i | 1.42583 | − | 0.149858i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.51262 | 1.57954 | 0.789771 | − | 0.613401i | \(-0.210199\pi\) | ||||
0.789771 | + | 0.613401i | \(0.210199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.38881i | 1.23628i | 0.786069 | + | 0.618138i | \(0.212113\pi\) | ||||
−0.786069 | + | 0.618138i | \(0.787887\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.487805 | + | 4.55654i | −0.106448 | + | 0.994318i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.56926 | + | 3.79276i | 1.36978 | + | 0.790846i | 0.990900 | − | 0.134598i | \(-0.0429745\pi\) |
0.378884 | + | 0.925444i | \(0.376308\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.63860 | − | 4.57019i | −0.527720 | − | 0.914038i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.94184 | − | 1.60567i | 0.951058 | − | 0.309011i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.93665 | + | 1.69548i | −0.545322 | + | 0.314842i | −0.747233 | − | 0.664562i | \(-0.768618\pi\) |
0.201911 | + | 0.979404i | \(0.435285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.51256 | − | 2.02798i | −0.630874 | − | 0.364235i | 0.150217 | − | 0.988653i | \(-0.452003\pi\) |
−0.781090 | + | 0.624418i | \(0.785336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.56023 | − | 3.36605i | −1.31607 | − | 0.585954i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.07168 | − | 2.60545i | 1.36436 | − | 0.440402i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.29763 | 1.03532 | 0.517662 | − | 0.855585i | \(-0.326802\pi\) | ||||
0.517662 | + | 0.855585i | \(0.326802\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.180156 | − | 1.71410i | −0.0288481 | − | 0.274476i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.48897 | − | 6.04307i | 0.544885 | − | 0.943769i | −0.453729 | − | 0.891140i | \(-0.649906\pi\) |
0.998614 | − | 0.0526294i | \(-0.0167602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.81364 | + | 6.60542i | 0.581575 | + | 1.00732i | 0.995293 | + | 0.0969121i | \(0.0308966\pi\) |
−0.413718 | + | 0.910405i | \(0.635770\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.43528 | − | 7.14716i | −0.959315 | − | 1.06544i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.78098 | − | 6.54884i | −0.551512 | − | 0.955247i | −0.998166 | − | 0.0605399i | \(-0.980718\pi\) |
0.446654 | − | 0.894707i | \(-0.352616\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.704849 | + | 6.96442i | 0.100693 | + | 0.994918i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.63031 | − | 9.12588i | −0.928430 | − | 1.27788i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.77397i | 1.06784i | 0.845536 | + | 0.533919i | \(0.179281\pi\) | ||||
−0.845536 | + | 0.533919i | \(0.820719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.3173i | 2.06538i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.55112 | − | 5.48619i | 1.00017 | − | 0.726663i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.25630 | − | 3.90802i | 0.293745 | − | 0.508781i | −0.680947 | − | 0.732333i | \(-0.738432\pi\) |
0.974692 | + | 0.223551i | \(0.0717650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.26324 | + | 3.03873i | −0.673889 | + | 0.389070i | −0.797548 | − | 0.603255i | \(-0.793870\pi\) |
0.123660 | + | 0.992325i | \(0.460537\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.88152 | − | 3.95534i | 0.866990 | − | 0.498326i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.76268 | + | 1.59503i | −0.342668 | + | 0.197839i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.493196 | − | 0.854240i | 0.0602534 | − | 0.104362i | −0.834325 | − | 0.551273i | \(-0.814142\pi\) |
0.894579 | + | 0.446911i | \(0.147476\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.37332 | − | 13.0665i | −0.165329 | − | 1.57303i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.20090i | 0.379877i | 0.981796 | + | 0.189939i | \(0.0608289\pi\) | ||||
−0.981796 | + | 0.189939i | \(0.939171\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.63782i | 0.308733i | 0.988014 | + | 0.154367i | \(0.0493337\pi\) | ||||
−0.988014 | + | 0.154367i | \(0.950666\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.71774 | + | 8.35014i | −0.429288 | + | 0.964192i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.3600 | − | 2.65212i | −1.40856 | − | 0.302237i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.96386 | − | 13.7938i | −0.896005 | − | 1.55193i | −0.832556 | − | 0.553941i | \(-0.813123\pi\) |
−0.0634485 | − | 0.997985i | \(-0.520210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28111 | − | 5.29012i | −0.809012 | − | 0.587792i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.49071 | + | 7.77813i | 0.492919 | + | 0.853761i | 0.999967 | − | 0.00815719i | \(-0.00259654\pi\) |
−0.507048 | + | 0.861918i | \(0.669263\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4391 | + | 18.0811i | −1.13228 | + | 1.96117i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.36552 | + | 2.38890i | 0.575244 | + | 0.256117i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.42081 | 0.468605 | 0.234303 | − | 0.972164i | \(-0.424719\pi\) | ||||
0.234303 | + | 0.972164i | \(0.424719\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.808738 | − | 2.50547i | −0.0847788 | − | 0.262644i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.734311 | + | 6.98663i | 0.0761445 | + | 0.724480i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.9610 | − | 8.63774i | −1.53497 | − | 0.886213i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.13726 | − | 1.81130i | 0.318540 | − | 0.183909i | −0.332202 | − | 0.943208i | \(-0.607791\pi\) |
0.650742 | + | 0.759299i | \(0.274458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.98014 | + | 14.0207i | 0.299516 | + | 1.40914i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.31084 | + | 12.6627i | 0.727456 | + | 1.25999i | 0.957955 | + | 0.286918i | \(0.0926306\pi\) |
−0.230500 | + | 0.973072i | \(0.574036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.883186 | + | 0.509908i | 0.0870229 | + | 0.0502427i | 0.542880 | − | 0.839810i | \(-0.317334\pi\) |
−0.455857 | + | 0.890053i | \(0.650667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.8685 | − | 8.65799i | −1.15824 | − | 0.844933i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0089i | 1.06428i | 0.846658 | + | 0.532138i | \(0.178611\pi\) | ||||
−0.846658 | + | 0.532138i | \(0.821389\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.38735 | −0.707579 | −0.353790 | − | 0.935325i | \(-0.615107\pi\) | ||||
−0.353790 | + | 0.935325i | \(0.615107\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.41144 | − | 8.82462i | −0.608547 | − | 0.837596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.31062 | + | 3.06609i | 0.499581 | + | 0.288433i | 0.728541 | − | 0.685003i | \(-0.240199\pi\) |
−0.228959 | + | 0.973436i | \(0.573532\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.0598 | + | 12.1589i | −1.96383 | + | 1.13382i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.21850 | + | 1.99753i | −0.205100 | + | 0.184671i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.7827 | − | 11.5543i | −1.17179 | − | 1.05918i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.91457 | − | 10.2443i | 0.537688 | − | 0.931303i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.0199 | + | 1.26332i | −1.08380 | + | 0.113910i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.888649 | 0.0794832 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.47289 | 0.840583 | 0.420291 | − | 0.907389i | \(-0.361928\pi\) | ||||
0.420291 | + | 0.907389i | \(0.361928\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.37336 | − | 12.0687i | 0.473098 | − | 1.06259i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.59921 | − | 13.1622i | 0.663946 | − | 1.14999i | −0.315624 | − | 0.948884i | \(-0.602214\pi\) |
0.979570 | − | 0.201104i | \(-0.0644528\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.56050 | − | 10.5769i | 0.829000 | − | 0.917136i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.46346 | + | 16.2938i | −0.298087 | + | 1.40235i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.42115 | + | 1.39785i | −0.206853 | + | 0.119427i | −0.599848 | − | 0.800114i | \(-0.704772\pi\) |
0.392995 | + | 0.919541i | \(0.371439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.55582 | − | 4.93971i | −0.725695 | − | 0.418980i | 0.0911499 | − | 0.995837i | \(-0.470946\pi\) |
−0.816845 | + | 0.576857i | \(0.804279\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.32733 | + | 11.9653i | −0.448642 | + | 1.00766i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.75452 | 0.397593 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.8707i | − | 0.902766i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.04138 | − | 8.07796i | 0.745721 | − | 0.666259i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.5582 | + | 11.8693i | 1.68419 | + | 0.972369i | 0.958820 | + | 0.284013i | \(0.0916658\pi\) |
0.725373 | + | 0.688356i | \(0.241667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.52875 | − | 11.3081i | −0.531302 | − | 0.920242i | −0.999333 | − | 0.0365301i | \(-0.988370\pi\) |
0.468030 | − | 0.883712i | \(-0.344964\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.03761 | + | 18.5816i | −0.488111 | + | 1.50223i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.2606 | − | 6.50130i | 0.904471 | − | 0.522197i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.268291 | − | 0.154898i | −0.0214120 | − | 0.0123622i | 0.489256 | − | 0.872140i | \(-0.337268\pi\) |
−0.510668 | + | 0.859778i | \(0.670602\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.8934 | − | 7.91446i | 0.863900 | − | 0.627657i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.16498 | − | 19.0991i | −0.485868 | − | 1.50522i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.5524 | −0.826525 | −0.413262 | − | 0.910612i | \(-0.635611\pi\) | ||||
−0.413262 | + | 0.910612i | \(0.635611\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.4635 | − | 15.5941i | 1.67093 | − | 1.21400i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.95655 | − | 6.85294i | 0.306167 | − | 0.530296i | −0.671354 | − | 0.741137i | \(-0.734287\pi\) |
0.977520 | + | 0.210841i | \(0.0676201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00490 | − | 10.4008i | −0.461915 | − | 0.800061i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.3752 | − | 4.99576i | −1.17577 | − | 0.382035i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.931870 | − | 1.61405i | −0.0708487 | − | 0.122714i | 0.828425 | − | 0.560100i | \(-0.189237\pi\) |
−0.899274 | + | 0.437387i | \(0.855904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.92922 | + | 13.6514i | −0.221428 | + | 1.03195i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.77323 | + | 0.816984i | −0.584272 | + | 0.0614083i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.50222i | − | 0.411255i | −0.978630 | − | 0.205628i | \(-0.934076\pi\) | ||
0.978630 | − | 0.205628i | \(-0.0659236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 11.1382i | − | 0.827900i | −0.910300 | − | 0.413950i | \(-0.864149\pi\) | ||
0.910300 | − | 0.413950i | \(-0.135851\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.61641 | + | 4.28152i | 0.710865 | + | 0.316499i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.0945 | + | 17.4842i | −0.742162 | + | 1.28546i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.9483 | − | 15.5586i | 1.97065 | − | 1.13776i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.5483 | − | 5.61598i | −0.912757 | − | 0.408503i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.64535 | + | 2.10464i | −0.263768 | + | 0.152287i | −0.626052 | − | 0.779781i | \(-0.715330\pi\) |
0.362284 | + | 0.932068i | \(0.381997\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.43109 | − | 2.47872i | 0.103012 | − | 0.178422i | −0.809912 | − | 0.586551i | \(-0.800485\pi\) |
0.912924 | + | 0.408129i | \(0.133819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.04766 | + | 2.24737i | 0.361470 | + | 0.160938i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.46947i | − | 0.104695i | −0.998629 | − | 0.0523475i | \(-0.983330\pi\) | ||
0.998629 | − | 0.0523475i | \(-0.0166704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3790i | 1.16108i | 0.814232 | + | 0.580539i | \(0.197158\pi\) | ||||
−0.814232 | + | 0.580539i | \(0.802842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.69912 | + | 0.178581i | −0.119847 | + | 0.0125962i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.77195 | + | 1.88222i | 0.615670 | + | 0.132106i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1850 | + | 19.3729i | 0.781192 | + | 1.35306i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.9115 | + | 15.2271i | −1.17543 | + | 1.05835i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.8738 | + | 22.2981i | 0.890500 | + | 1.54239i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.18297 | + | 8.97716i | −0.356810 | + | 0.618013i | −0.987426 | − | 0.158082i | \(-0.949469\pi\) |
0.630616 | + | 0.776095i | \(0.282802\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.48530 | − | 3.25875i | 0.307328 | − | 0.223286i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.4516 | −1.66759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.29639 | + | 10.2122i | 0.223773 | + | 0.693249i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.69627 | − | 2.68549i | 0.249771 | − | 0.181468i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.61240 | + | 3.24032i | 0.377531 | + | 0.217968i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.87592 | + | 2.81511i | −0.326516 | + | 0.188514i | −0.654293 | − | 0.756241i | \(-0.727034\pi\) |
0.327777 | + | 0.944755i | \(0.393700\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.4857 | − | 3.29151i | 1.03238 | − | 0.219434i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.52714 | + | 6.10919i | 0.234105 | + | 0.405481i | 0.959012 | − | 0.283365i | \(-0.0914509\pi\) |
−0.724908 | + | 0.688846i | \(0.758118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5744 | + | 10.7239i | 1.22743 | + | 0.708657i | 0.966492 | − | 0.256698i | \(-0.0826346\pi\) |
0.260939 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.86707 | + | 20.0197i | 0.583410 | + | 1.31720i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.6101i | − | 0.760601i | −0.924863 | − | 0.380300i | \(-0.875821\pi\) | ||
0.924863 | − | 0.380300i | \(-0.124179\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.2422 | 1.58138 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.2210 | + | 25.2025i | −0.728879 | + | 1.63708i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.85573 | + | 3.38081i | 0.378776 | + | 0.218686i | 0.677285 | − | 0.735720i | \(-0.263156\pi\) |
−0.298510 | + | 0.954407i | \(0.596490\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.60243 | − | 1.50251i | 0.167637 | − | 0.0967854i | −0.413834 | − | 0.910352i | \(-0.635811\pi\) |
0.581471 | + | 0.813567i | \(0.302477\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.000152282 | 15.5885i | −9.76892e−6 | 1.00000i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −20.4652 | − | 9.20642i | −1.30747 | − | 0.588177i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.68117 | + | 4.64393i | −0.170599 | + | 0.295486i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.32733 | − | 14.2113i | 0.400978 | − | 0.900607i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.9921 | −1.76685 | −0.883424 | − | 0.468575i | \(-0.844768\pi\) | ||||
−0.883424 | + | 0.468575i | \(0.844768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.2435 | 2.27861 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 35.9640 | − | 3.77990i | 2.25216 | − | 0.236707i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.17693 | − | 2.03850i | 0.0734147 | − | 0.127158i | −0.826981 | − | 0.562230i | \(-0.809944\pi\) |
0.900396 | + | 0.435072i | \(0.143277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.3607 | − | 11.1729i | −0.768059 | − | 0.694249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.11502 | − | 9.95056i | −0.130916 | − | 0.615924i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.6768 | − | 6.74159i | 0.720021 | − | 0.415704i | −0.0947394 | − | 0.995502i | \(-0.530202\pi\) |
0.814760 | + | 0.579798i | \(0.196868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.5830 | − | 12.4609i | −1.32583 | − | 0.765469i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.50070 | − | 6.19471i | −0.275438 | − | 0.379110i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.0797 | 0.675543 | 0.337772 | − | 0.941228i | \(-0.390327\pi\) | ||||
0.337772 | + | 0.941228i | \(0.390327\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.31052i | 0.261845i | 0.991393 | + | 0.130923i | \(0.0417940\pi\) | ||||
−0.991393 | + | 0.130923i | \(0.958206\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.68746 | + | 3.68400i | −0.162652 | + | 0.222966i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.8363 | − | 12.6072i | −1.31678 | − | 0.760242i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.20911 | − | 7.29039i | −0.252901 | − | 0.438037i | 0.711422 | − | 0.702765i | \(-0.248051\pi\) |
−0.964323 | + | 0.264728i | \(0.914718\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.04251 | − | 8.14185i | 0.541361 | − | 0.487440i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1633 | + | 9.33189i | −0.964222 | + | 0.556694i | −0.897470 | − | 0.441076i | \(-0.854597\pi\) |
−0.0667521 | + | 0.997770i | \(0.521264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.7038 | − | 13.6854i | −1.40904 | − | 0.813512i | −0.413748 | − | 0.910392i | \(-0.635780\pi\) |
−0.995296 | + | 0.0968797i | \(0.969114\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.12764 | + | 29.7581i | 0.185266 | + | 1.76272i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.5693 | + | 5.67117i | −1.03708 | + | 0.334759i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.4143 | 1.49496 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.73205 | − | 2.55209i | −0.336019 | − | 0.149606i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.66210 | − | 8.07500i | 0.272363 | − | 0.471747i | −0.697103 | − | 0.716971i | \(-0.745528\pi\) |
0.969466 | + | 0.245224i | \(0.0788615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.23326 | + | 12.5284i | 0.421136 | + | 0.729430i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.6127 | − | 18.4501i | 0.963967 | − | 1.07058i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.77414 | + | 6.53700i | 0.218264 | + | 0.378044i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.23369 | − | 19.7308i | 0.244026 | − | 1.13726i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.3008 | − | 23.1360i | 0.591768 | − | 1.32913i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 19.4832i | − | 1.11560i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 33.6506i | − | 1.92054i | −0.279069 | − | 0.960271i | \(-0.590026\pi\) | ||
0.279069 | − | 0.960271i | \(-0.409974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.184633 | − | 1.75670i | −0.0105034 | − | 0.0999350i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.69514 | + | 13.3284i | −0.436351 | + | 0.755783i | −0.997405 | − | 0.0719967i | \(-0.977063\pi\) |
0.561053 | + | 0.827780i | \(0.310396\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.6028 | − | 15.9365i | 1.56020 | − | 0.900784i | 0.562968 | − | 0.826479i | \(-0.309659\pi\) |
0.997236 | − | 0.0743050i | \(-0.0236738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0491599 | + | 25.4453i | −0.00276985 | + | 1.43368i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3039 | − | 9.99044i | 0.971886 | − | 0.561119i | 0.0720756 | − | 0.997399i | \(-0.477038\pi\) |
0.899811 | + | 0.436280i | \(0.143704\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.10096 | + | 14.0313i | −0.453567 | + | 0.785600i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.4264 | − | 11.2079i | 0.861018 | − | 0.625564i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.0953i | 1.95275i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.25129i | − | 0.291289i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.52084 | + | 10.3516i | 0.415904 | + | 0.572445i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.19742 | + | 19.5618i | −0.231411 | + | 1.07848i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.48225 | + | 7.76348i | 0.246367 | + | 0.426719i | 0.962515 | − | 0.271229i | \(-0.0874300\pi\) |
−0.716148 | + | 0.697948i | \(0.754097\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.83830 | + | 17.9682i | −0.319937 | + | 0.984651i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.58109 | + | 2.73853i | 0.0863842 | + | 0.149622i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.72022 | + | 4.71155i | −0.148180 | + | 0.256655i | −0.930555 | − | 0.366153i | \(-0.880675\pi\) |
0.782375 | + | 0.622808i | \(0.214008\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.11020 | − | 10.5631i | −0.0602978 | − | 0.573706i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.3793 | −1.04945 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9724 | − | 14.9200i | 0.592455 | − | 0.805604i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 38.4781 | + | 17.1316i | 2.07159 | + | 0.922336i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0234 | − | 8.09639i | −0.752813 | − | 0.434637i | 0.0738962 | − | 0.997266i | \(-0.476457\pi\) |
−0.826710 | + | 0.562629i | \(0.809790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1071 | + | 9.87682i | −0.915725 | + | 0.528694i | −0.882269 | − | 0.470746i | \(-0.843985\pi\) |
−0.0334560 | + | 0.999440i | \(0.510651\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.05764 | + | 1.07507i | 0.269957 | + | 0.0573828i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3112 | − | 17.8596i | −0.548811 | − | 0.950569i | −0.998356 | − | 0.0573115i | \(-0.981747\pi\) |
0.449545 | − | 0.893258i | \(-0.351586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.88670 | − | 5.13074i | −0.471657 | − | 0.272311i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.17689 | + | 29.6750i | −0.168139 | + | 1.57057i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 15.2442i | − | 0.804557i | −0.915517 | − | 0.402278i | \(-0.868218\pi\) | ||
0.915517 | − | 0.402278i | \(-0.131782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0392 | −0.528380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.3764 | + | 2.14161i | −1.06949 | + | 0.112405i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.32340 | − | 4.22817i | −0.383324 | − | 0.221312i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.87711 | − | 1.66110i | 0.150184 | − | 0.0867087i | −0.423025 | − | 0.906118i | \(-0.639032\pi\) |
0.573209 | + | 0.819409i | \(0.305698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.0074 | + | 15.5569i | 0.729196 | + | 0.809860i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.7921 | − | 15.2584i | 0.716051 | − | 0.792178i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.6885 | + | 20.2451i | −0.605208 | + | 1.04825i | 0.386811 | + | 0.922159i | \(0.373577\pi\) |
−0.992019 | + | 0.126092i | \(0.959757\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.904708 | − | 1.24523i | −0.0467189 | − | 0.0643033i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.37430 | −0.173785 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.9325 | 0.715663 | 0.357832 | − | 0.933786i | \(-0.383516\pi\) | ||||
0.357832 | + | 0.933786i | \(0.383516\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.64407 | − | 13.2740i | −0.494081 | − | 0.680047i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.93132 | + | 6.80925i | −0.200881 | + | 0.347936i | −0.948813 | − | 0.315840i | \(-0.897714\pi\) |
0.747931 | + | 0.663776i | \(0.231047\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.1750 | − | 30.0642i | 1.38497 | − | 1.53221i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.3818 | + | 4.75732i | −1.13773 | + | 0.241828i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5208 | + | 9.53829i | −0.837638 | + | 0.483611i | −0.856461 | − | 0.516212i | \(-0.827342\pi\) |
0.0188226 | + | 0.999823i | \(0.494008\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 42.7831 | + | 24.7008i | 2.16363 | + | 1.24917i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.1802 | + | 2.75160i | −1.32062 | + | 0.138800i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 51.0612 | 2.56917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13.8919i | − | 0.697214i | −0.937269 | − | 0.348607i | \(-0.886655\pi\) | ||
0.937269 | − | 0.348607i | \(-0.113345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −24.5543 | − | 2.62868i | −1.22925 | − | 0.131599i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.6674 | − | 11.9323i | −1.03208 | − | 0.595872i | −0.114501 | − | 0.993423i | \(-0.536527\pi\) |
−0.917580 | + | 0.397551i | \(0.869860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.01802 | − | 3.49531i | −0.100525 | − | 0.174114i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 26.3579 | − | 11.7351i | 1.30974 | − | 0.583120i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.0587 | − | 15.0450i | 1.29168 | − | 0.745753i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.9384 | − | 12.0888i | −1.03534 | − | 0.597753i | −0.116830 | − | 0.993152i | \(-0.537273\pi\) |
−0.918510 | + | 0.395399i | \(0.870606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.42366 | + | 1.96955i | 0.218203 | + | 0.0971507i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.3620 | + | 3.66752i | −0.559085 | + | 0.180467i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.7927 | −1.41338 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.78862 | + | 17.0179i | 0.0875891 | + | 0.833371i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.84384 | + | 17.0500i | −0.480903 | + | 0.832949i | −0.999760 | − | 0.0219125i | \(-0.993024\pi\) |
0.518857 | + | 0.854861i | \(0.326358\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5884 | − | 32.1961i | −0.905944 | − | 1.56914i | −0.819646 | − | 0.572871i | \(-0.805830\pi\) |
−0.0862979 | − | 0.996269i | \(-0.527504\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.1901 | − | 4.71657i | 1.07892 | − | 0.229327i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.1842 | − | 29.7639i | −0.833556 | − | 1.44376i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.7216 | + | 3.37343i | 0.760822 | + | 0.163252i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.84044 | − | 6.66233i | −0.233699 | − | 0.321660i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.86241i | 0.426887i | 0.976955 | + | 0.213444i | \(0.0684680\pi\) | ||||
−0.976955 | + | 0.213444i | \(0.931532\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.2461i | 1.69382i | 0.531737 | + | 0.846910i | \(0.321540\pi\) | ||||
−0.531737 | + | 0.846910i | \(0.678460\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.2327 | + | 11.0672i | −0.730354 | + | 0.530631i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.4385 | + | 35.4004i | −0.977704 | + | 1.69343i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.51356 | + | 4.33796i | −0.358603 | + | 0.207039i | −0.668468 | − | 0.743741i | \(-0.733049\pi\) |
0.309865 | + | 0.950781i | \(0.399716\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.5241 | − | 4.44540i | −0.977338 | − | 0.211686i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.7031 | + | 7.91148i | −0.651053 | + | 0.375886i | −0.788860 | − | 0.614574i | \(-0.789328\pi\) |
0.137807 | + | 0.990459i | \(0.455995\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.08613 | + | 12.2735i | −0.335915 | + | 0.581822i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.29775 | − | 40.8912i | −0.203277 | − | 1.93409i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 7.87563i | − | 0.371674i | −0.982581 | − | 0.185837i | \(-0.940500\pi\) | ||
0.982581 | − | 0.185837i | \(-0.0594996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 33.3405i | − | 1.56994i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.19890 | + | 20.6610i | −0.432202 | + | 0.970737i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.25229 | + | 1.77071i | 0.386873 | + | 0.0830124i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.53132 | + | 9.58053i | 0.258744 | + | 0.448158i | 0.965906 | − | 0.258894i | \(-0.0833580\pi\) |
−0.707161 | + | 0.707052i | \(0.750025\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.1844 | − | 10.4571i | 1.50224 | − | 0.488097i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.73005 | − | 11.6568i | −0.313450 | − | 0.542911i | 0.665657 | − | 0.746258i | \(-0.268151\pi\) |
−0.979107 | + | 0.203347i | \(0.934818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.57103 | − | 14.8455i | 0.398329 | − | 0.689927i | −0.595191 | − | 0.803585i | \(-0.702923\pi\) |
0.993520 | + | 0.113658i | \(0.0362568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.5741 | − | 9.16022i | −0.954100 | − | 0.424795i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.67554 | −0.262633 | −0.131316 | − | 0.991341i | \(-0.541920\pi\) | ||||
−0.131316 | + | 0.991341i | \(0.541920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.48357 | + | 0.801669i | −0.114680 | + | 0.0370176i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0560871 | + | 0.533643i | 0.00258436 | + | 0.0245890i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.5606 | + | 18.2215i | 1.45116 | + | 0.837826i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.6279 | − | 14.2189i | 1.13000 | − | 0.652408i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.1804 | − | 7.20695i | −1.01557 | − | 0.329984i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.71476 | + | 11.6303i | 0.306805 | + | 0.531402i | 0.977662 | − | 0.210185i | \(-0.0674066\pi\) |
−0.670856 | + | 0.741587i | \(0.734073\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.42713 | + | 3.13335i | 0.247456 | + | 0.142869i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.4864 | + | 28.0829i | −0.932163 | + | 1.27782i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.6133i | 0.527334i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.4841 | −0.520394 | −0.260197 | − | 0.965556i | \(-0.583788\pi\) | ||||
−0.260197 | + | 0.965556i | \(0.583788\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.7431 | + | 14.7866i | 0.485818 | + | 0.668673i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.04656 | − | 5.22303i | −0.408265 | − | 0.235712i | 0.281779 | − | 0.959479i | \(-0.409076\pi\) |
−0.690044 | + | 0.723767i | \(0.742409\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.1253 | + | 11.0420i | −0.861360 | + | 0.497306i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −43.7028 | − | 14.2001i | −1.96429 | − | 0.638246i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.67885 | − | 6.28260i | 0.254731 | − | 0.281813i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.43609 | − | 14.6117i | 0.377651 | − | 0.654111i | −0.613069 | − | 0.790030i | \(-0.710065\pi\) |
0.990720 | + | 0.135918i | \(0.0433985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6308 | + | 1.43263i | −0.608979 | + | 0.0640051i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.1129 | −0.941379 | −0.470690 | − | 0.882299i | \(-0.655995\pi\) | ||||
−0.470690 | + | 0.882299i | \(0.655995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −46.8743 | −2.08588 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.46080 | + | 19.0032i | −0.375757 | + | 0.843960i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.2232 | − | 19.4391i | 0.497458 | − | 0.861622i | −0.502538 | − | 0.864555i | \(-0.667600\pi\) |
0.999996 | + | 0.00293304i | \(0.000933617\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.67986 | − | 5.17740i | 0.207025 | − | 0.229035i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.65265 | + | 26.6306i | 0.382024 | + | 1.17577i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.83132 | + | 1.63467i | −0.124763 | + | 0.0720320i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.2903 | − | 18.0654i | −1.37614 | − | 0.794517i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.31299 | + | 2.94901i | −0.0576338 | + | 0.129447i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8533 | 1.22027 | 0.610137 | − | 0.792296i | \(-0.291114\pi\) | ||||
0.610137 | + | 0.792296i | \(0.291114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.02647i | 0.132338i | 0.997808 | + | 0.0661691i | \(0.0210777\pi\) | ||||
−0.997808 | + | 0.0661691i | \(0.978922\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.1114 | − | 9.79352i | 0.965019 | − | 0.427424i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.8760 | − | 13.2074i | −0.996492 | − | 0.575325i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.2701 | + | 29.9127i | 0.750873 | + | 1.30055i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.05851 | + | 10.0606i | 0.393106 | + | 0.436592i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.01340 | − | 3.47184i | 0.260469 | − | 0.150382i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.5643 | − | 17.6463i | −1.32141 | − | 0.762915i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.71004 | + | 5.60165i | −0.332713 | + | 0.241729i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.5545 | + | 27.1339i | 0.842273 | + | 1.16874i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.4800 | −1.86935 | −0.934677 | − | 0.355499i | \(-0.884311\pi\) | ||||
−0.934677 | + | 0.355499i | \(0.884311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.6076 | + | 11.3395i | −0.669786 | + | 0.486626i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.8412 | − | 20.5096i | 0.507221 | − | 0.878533i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3399 | − | 35.2297i | −0.869670 | − | 1.50631i | −0.862335 | − | 0.506339i | \(-0.830998\pi\) |
−0.00733515 | − | 0.999973i | \(-0.502335\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.79066 | − | 17.8340i | −0.161781 | − | 0.761136i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.13659 | − | 15.8250i | −0.389232 | − | 0.674169i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.84103 | + | 41.2030i | −0.375959 | + | 1.75213i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.7768 | − | 3.65512i | 1.47619 | − | 0.155151i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 13.6889i | − | 0.580016i | −0.957024 | − | 0.290008i | \(-0.906342\pi\) | ||
0.957024 | − | 0.290008i | \(-0.0936580\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.58983i | 0.321016i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −49.2369 | − | 21.9218i | −2.07879 | − | 0.925540i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.70705 | − | 11.6169i | 0.282668 | − | 0.489596i | −0.689373 | − | 0.724407i | \(-0.742114\pi\) |
0.972041 | + | 0.234811i | \(0.0754471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.0248 | + | 9.82929i | −0.716240 | + | 0.413521i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.90564 | + | 23.3010i | 0.206018 | + | 0.978548i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.6370 | + | 11.3374i | −0.823227 | + | 0.475291i | −0.851528 | − | 0.524309i | \(-0.824324\pi\) |
0.0283007 | + | 0.999599i | \(0.490990\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.77378 | − | 13.4646i | 0.325323 | − | 0.563475i | −0.656255 | − | 0.754539i | \(-0.727860\pi\) |
0.981578 | + | 0.191064i | \(0.0611938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.66038 | + | 2.96541i | 0.278241 | + | 0.123882i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 40.0303i | − | 1.66938i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.8101i | 1.74058i | 0.492541 | + | 0.870289i | \(0.336068\pi\) | ||||
−0.492541 | + | 0.870289i | \(0.663932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.93028 | + | 0.518183i | −0.204895 | + | 0.0215350i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.98532 | − | 23.2337i | 0.206826 | − | 0.963898i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.5720 | + | 32.1676i | 0.769172 | + | 1.33224i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.98972 | − | 9.36107i | −0.0822648 | − | 0.387033i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.3910 | + | 23.1939i | 0.552706 | + | 0.957315i | 0.998078 | + | 0.0619696i | \(0.0197382\pi\) |
−0.445372 | + | 0.895346i | \(0.646928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.9284 | − | 18.9285i | 0.450295 | − | 0.779935i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.05910 | + | 1.49602i | −0.0847002 | + | 0.0615381i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.3434 | −1.16392 | −0.581962 | − | 0.813216i | \(-0.697715\pi\) | ||||
−0.581962 | + | 0.813216i | \(0.697715\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 52.5678 | − | 16.9683i | 2.15507 | − | 0.695634i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.9513 | − | 16.6750i | 0.939333 | − | 0.682463i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.73785 | − | 4.46745i | −0.316160 | − | 0.182535i | 0.333520 | − | 0.942743i | \(-0.391764\pi\) |
−0.649680 | + | 0.760208i | \(0.725097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2085 | + | 11.0901i | −0.783533 | + | 0.452373i | −0.837681 | − | 0.546160i | \(-0.816089\pi\) |
0.0541481 | + | 0.998533i | \(0.482756\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.98007 | + | 2.19910i | 0.0806345 | + | 0.0895544i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.9610 | + | 32.8414i | 0.770873 | + | 1.33519i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.3887 | + | 17.5449i | 1.23344 | + | 0.712127i | 0.967746 | − | 0.251930i | \(-0.0810652\pi\) |
0.265695 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.29299 | − | 14.2080i | −0.255005 | − | 0.575738i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 7.52482i | − | 0.304422i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4883 | 0.625566 | 0.312783 | − | 0.949825i | \(-0.398739\pi\) | ||||
0.312783 | + | 0.949825i | \(0.398739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.7594 | − | 35.3961i | 0.635481 | − | 1.42731i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.8217 | + | 21.2590i | 1.48239 | + | 0.855856i | 0.999800 | − | 0.0199930i | \(-0.00636440\pi\) |
0.482586 | + | 0.875849i | \(0.339698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.9906 | + | 15.0057i | −1.04465 | + | 0.603128i | −0.921146 | − | 0.389216i | \(-0.872746\pi\) |
−0.123502 | + | 0.992344i | \(0.539413\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.5542 | + | 8.19518i | 1.54713 | + | 0.328861i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.67699 | − | 7.84314i | −0.347636 | − | 0.314229i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.7686 | − | 20.3838i | 0.470743 | − | 0.815351i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.1390 | − | 40.7406i | 0.724401 | − | 1.62702i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 41.0141 | 1.63534 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.6833 | 0.823388 | 0.411694 | − | 0.911322i | \(-0.364937\pi\) | ||||
0.411694 | + | 0.911322i | \(0.364937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.8560 | − | 1.87670i | 0.709711 | − | 0.0745922i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.1841 | + | 26.2997i | −0.602564 | + | 1.04367i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.85769 | + | 6.35245i | −0.113226 | + | 0.251693i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.13271 | − | 2.96744i | −0.361284 | − | 0.117390i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.9498 | + | 14.9821i | −1.02495 | + | 0.591758i | −0.915535 | − | 0.402238i | \(-0.868232\pi\) |
−0.109419 | + | 0.993996i | \(0.534899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7961 | + | 16.6254i | 1.13561 | + | 0.655643i | 0.945339 | − | 0.326090i | \(-0.105731\pi\) |
0.190268 | + | 0.981732i | \(0.439064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.8935 | + | 34.2631i | 0.980179 | + | 1.34911i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.06135 | 0.356238 | 0.178119 | − | 0.984009i | \(-0.442999\pi\) | ||||
0.178119 | + | 0.984009i | \(0.442999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 21.5611i | − | 0.846348i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.9540 | − | 15.0158i | 0.429321 | − | 0.588517i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.4121 | − | 6.01142i | −0.407456 | − | 0.235245i | 0.282240 | − | 0.959344i | \(-0.408923\pi\) |
−0.689696 | + | 0.724099i | \(0.742256\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.3616 | + | 42.1955i | 0.951886 | + | 1.64872i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.52613 | − | 2.44542i | −0.293622 | − | 0.0954049i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.1663 | + | 23.7674i | −1.60361 | + | 0.925845i | −0.612854 | + | 0.790196i | \(0.709979\pi\) |
−0.990757 | + | 0.135649i | \(0.956688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.5254 | + | 10.6957i | 0.720556 | + | 0.416013i | 0.814957 | − | 0.579521i | \(-0.196760\pi\) |
−0.0944011 | + | 0.995534i | \(0.530094\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.17329 | − | 11.1633i | −0.0455668 | − | 0.433547i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.0403 | + | 43.4967i | 0.544459 | + | 1.68673i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.7221 | −0.995966 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.90874 | + | 3.96645i | 0.344432 | + | 0.153352i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.5190 | + | 25.1477i | −0.560500 | + | 0.970815i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.77577 | + | 15.2001i | 0.338281 | + | 0.585920i | 0.984109 | − | 0.177563i | \(-0.0568213\pi\) |
−0.645829 | + | 0.763482i | \(0.723488\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.3778 | − | 18.3484i | −0.784341 | − | 0.706232i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.39862 | − | 14.5468i | −0.322785 | − | 0.559081i | 0.658276 | − | 0.752776i | \(-0.271286\pi\) |
−0.981062 | + | 0.193696i | \(0.937953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.37117 | − | 2.01080i | −0.359633 | − | 0.0771673i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.96968 | − | 11.1620i | 0.190439 | − | 0.427730i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4518i | 0.667773i | 0.942613 | + | 0.333887i | \(0.108360\pi\) | ||||
−0.942613 | + | 0.333887i | \(0.891640\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.96248i | − | 0.342439i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.88303 | − | 36.9453i | −0.148147 | − | 1.40955i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.86790 | + | 6.69940i | −0.147355 | + | 0.255227i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.8864 | − | 21.8737i | 1.44127 | − | 0.832115i | 0.443332 | − | 0.896358i | \(-0.353796\pi\) |
0.997934 | + | 0.0642424i | \(0.0204631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.0255 | − | 32.8065i | 0.722717 | − | 1.24622i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.4283 | − | 15.8357i | 1.04042 | − | 0.600684i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.7223 | − | 39.3562i | 0.860670 | − | 1.49072i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.2687 | + | 11.8199i | −0.615340 | + | 0.447069i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 11.5880i | − | 0.437671i | −0.975762 | − | 0.218836i | \(-0.929774\pi\) | ||
0.975762 | − | 0.218836i | \(-0.0702258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.9367i | 1.27995i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.6802 | − | 33.9696i | −0.929512 | − | 1.27937i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.11607 | − | 37.8244i | 0.305236 | − | 1.42253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.69813 | + | 2.94125i | 0.0637747 | + | 0.110461i | 0.896150 | − | 0.443752i | \(-0.146353\pi\) |
−0.832375 | + | 0.554213i | \(0.813019\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.7390 | − | 9.93450i | 1.75285 | − | 0.372573i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3833 | − | 26.6446i | −0.576107 | − | 0.997847i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.62104 | + | 13.2000i | −0.285011 | + | 0.493653i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.22416 | − | 11.6473i | −0.0457170 | − | 0.434976i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.13894 | −0.0797690 | −0.0398845 | − | 0.999204i | \(-0.512699\pi\) | ||||
−0.0398845 | + | 0.999204i | \(0.512699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.828834 | − | 2.56772i | −0.0308674 | − | 0.0956270i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.75487 | − | 2.11702i | −0.176836 | − | 0.0787327i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.4973 | + | 8.94737i | 0.575555 | + | 0.332297i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.5447 | + | 17.6350i | −1.13284 | + | 0.654045i | −0.944647 | − | 0.328088i | \(-0.893596\pi\) |
−0.188191 | + | 0.982132i | \(0.560263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.8436 | − | 15.8699i | 0.809024 | − | 0.587776i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.8368 | + | 43.0186i | 0.918622 | + | 1.59110i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.1611 | + | 5.86652i | 0.375309 | + | 0.216685i | 0.675775 | − | 0.737108i | \(-0.263809\pi\) |
−0.300466 | + | 0.953792i | \(0.597142\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.93444 | + | 38.0499i | 0.292666 | + | 1.40349i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.71296i | − | 0.173604i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.8023 | −1.39058 | −0.695289 | − | 0.718730i | \(-0.744724\pi\) | ||||
−0.695289 | + | 0.718730i | \(0.744724\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.23698 | − | 0.970827i | 0.339329 | − | 0.0356642i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.73943 | + | 5.62306i | 0.357305 | + | 0.206290i | 0.667898 | − | 0.744253i | \(-0.267194\pi\) |
−0.310593 | + | 0.950543i | \(0.600528\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −65.9056 | + | 38.0506i | −2.41459 | + | 1.39407i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.3555 | + | 5.60192i | −0.964296 | + | 0.204963i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.5314 | − | 21.6079i | 0.713663 | − | 0.789536i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0985 | − | 22.6873i | 0.477972 | − | 0.827871i | −0.521709 | − | 0.853123i | \(-0.674706\pi\) |
0.999681 | + | 0.0252521i | \(0.00803883\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.4980 | + | 39.2243i | 1.03852 | + | 1.42941i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.8598 | 1.52344 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.529802 | −0.0192560 | −0.00962799 | − | 0.999954i | \(-0.503065\pi\) | ||||
−0.00962799 | + | 0.999954i | \(0.503065\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −36.8985 | − | 50.7866i | −1.33933 | − | 1.84344i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2682 | − | 42.0337i | 0.879721 | − | 1.52372i | 0.0280745 | − | 0.999606i | \(-0.491062\pi\) |
0.851647 | − | 0.524116i | \(-0.175604\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.4996 | + | 13.1062i | 0.524920 | + | 0.474476i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.9106 | − | 46.5468i | −1.51528 | − | 1.68290i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.88883 | − | 2.24522i | 0.140418 | − | 0.0810702i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.3353 | − | 14.6274i | −0.913615 | − | 0.527476i | −0.0320224 | − | 0.999487i | \(-0.510195\pi\) |
−0.881592 | + | 0.472011i | \(0.843528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.05466 | + | 0.426154i | −0.146025 | + | 0.0153476i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.5569 | −1.56663 | −0.783317 | − | 0.621623i | \(-0.786474\pi\) | ||||
−0.783317 | + | 0.621623i | \(0.786474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.4041i | 0.768857i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.07201 | + | 28.6954i | −0.110208 | + | 1.02944i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.5649 | + | 18.8014i | 1.16676 | + | 0.673629i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.64693 | + | 13.2449i | 0.273629 | + | 0.473939i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.7901 | + | 13.0941i | −0.421344 | + | 0.467944i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.860090 | − | 0.496573i | 0.0306979 | − | 0.0177235i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.25959 | + | 4.76868i | 0.294423 | + | 0.169985i | 0.639935 | − | 0.768429i | \(-0.278961\pi\) |
−0.345512 | + | 0.938414i | \(0.612295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.3345 | − | 9.49879i | −0.759529 | − | 0.338166i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.98380 | − | 15.4398i | −0.177203 | − | 0.548975i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.04762 | −0.214757 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.51198 | + | 42.9295i | 0.160024 | + | 1.52255i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.4598 | − | 35.4374i | 0.724722 | − | 1.25526i | −0.234366 | − | 0.972148i | \(-0.575301\pi\) |
0.959088 | − | 0.283107i | \(-0.0913653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.6241 | − | 42.6501i | −0.871137 | − | 1.50885i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.09837 | + | 12.6133i | −0.144809 | + | 0.445669i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.30172 | + | 10.9149i | 0.222383 | + | 0.385179i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 62.9068 | + | 13.4981i | 2.21717 | + | 0.475745i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.2800 | − | 15.5256i | −0.397073 | − | 0.546527i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 23.7588i | − | 0.835314i | −0.908605 | − | 0.417657i | \(-0.862851\pi\) | ||
0.908605 | − | 0.417657i | \(-0.137149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9638i | 0.946828i | 0.880840 | + | 0.473414i | \(0.156979\pi\) | ||||
−0.880840 | + | 0.473414i | \(0.843021\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.04016 | − | 4.38842i | 0.211838 | − | 0.153908i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.9144 | − | 29.2966i | 0.592486 | − | 1.02622i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.5953 | + | 20.5510i | −1.24532 | + | 0.718987i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.89827 | + | 0.0152593i | 0.275988 | + | 0.000533205i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.8933 | − | 18.4136i | 1.11308 | − | 0.642639i | 0.173457 | − | 0.984841i | \(-0.444506\pi\) |
0.939626 | + | 0.342202i | \(0.111173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.98887 | + | 5.17687i | −0.104185 | + | 0.180454i | −0.913405 | − | 0.407052i | \(-0.866557\pi\) |
0.809220 | + | 0.587506i | \(0.199890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.56494 | + | 43.4333i | 0.158931 | + | 1.51216i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.21366i | 0.181297i | 0.995883 | + | 0.0906484i | \(0.0288939\pi\) | ||||
−0.995883 | + | 0.0906484i | \(0.971106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.453044i | 0.0157349i | 0.999969 | + | 0.00786743i | \(0.00250431\pi\) | ||||
−0.999969 | + | 0.00786743i | \(0.997496\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.93056 | + | 13.3202i | −0.205729 | + | 0.462072i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.59041 | + | 45.3567i | 0.159048 | + | 1.57152i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6839 | + | 21.9692i | 0.438945 | + | 0.760276i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.6148 | − | 4.38193i | −0.712550 | − | 0.151462i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.6669 | + | 44.4563i | 0.886119 | + | 1.53480i | 0.844426 | + | 0.535673i | \(0.179942\pi\) |
0.0416932 | + | 0.999130i | \(0.486725\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.75072 | + | 15.1567i | −0.301749 | + | 0.522645i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.5318 | + | 13.1485i | 1.01713 | + | 0.452857i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38.5011 | 1.32448 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.7838 | + | 9.61388i | −1.02338 | + | 0.330337i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.95535 | + | 47.1479i | 0.170067 | + | 1.61811i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.3708 | + | 23.8854i | 1.41817 | + | 0.818782i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.7708 | − | 7.95059i | 0.471504 | − | 0.272223i | −0.245365 | − | 0.969431i | \(-0.578908\pi\) |
0.716869 | + | 0.697208i | \(0.245575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 38.5147 | − | 34.6785i | 1.31717 | − | 1.18598i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.31574 | + | 12.6712i | 0.249901 | + | 0.432841i | 0.963498 | − | 0.267715i | \(-0.0862686\pi\) |
−0.713597 | + | 0.700556i | \(0.752935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0119 | − | 25.4103i | −1.50167 | − | 0.866988i | −0.999998 | − | 0.00192834i | \(-0.999386\pi\) |
−0.501669 | − | 0.865060i | \(-0.667280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.8336 | + | 18.8455i | 0.880405 | + | 0.642252i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.00667i | 0.102348i | 0.998690 | + | 0.0511742i | \(0.0162964\pi\) | ||||
−0.998690 | + | 0.0511742i | \(0.983704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.97479 | 0.203149 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.8735 | − | 35.6120i | −0.878711 | − | 1.20945i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.9066 | − | 38.0512i | −2.23573 | − | 1.29080i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.850046 | − | 0.490774i | 0.0288027 | − | 0.0166292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.25950 | + | 10.6303i | 0.0764724 | + | 0.359781i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.74420 | − | 1.57659i | −0.0589648 | − | 0.0532984i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.1229 | − | 36.5860i | 0.713271 | − | 1.23542i | −0.250352 | − | 0.968155i | \(-0.580546\pi\) |
0.963623 | − | 0.267266i | \(-0.0861203\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.0615 | + | 1.68810i | −0.541742 | + | 0.0569383i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.4719 | 0.992933 | 0.496467 | − | 0.868056i | \(-0.334630\pi\) | ||||
0.496467 | + | 0.868056i | \(0.334630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.1571 | −0.913910 | −0.456955 | − | 0.889490i | \(-0.651060\pi\) | ||||
−0.456955 | + | 0.889490i | \(0.651060\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1915 | − | 22.8904i | 0.342585 | − | 0.769454i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.51892 | − | 9.55905i | 0.185307 | − | 0.320962i | −0.758373 | − | 0.651821i | \(-0.774005\pi\) |
0.943680 | + | 0.330860i | \(0.107339\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.5930 | − | 16.8062i | −0.623589 | − | 0.563663i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −42.7663 | − | 4.49525i | −1.43272 | − | 0.150597i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.2904 | − | 20.3749i | 1.18095 | − | 0.681821i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.2759 | + | 8.81953i | 0.510616 | + | 0.294804i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.31770 | − | 11.9437i | 0.177553 | − | 0.398788i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.7535 | 0.458706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.6289i | 1.68669i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.9582 | + | 14.1548i | −1.06350 | + | 0.471044i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.9232 | + | 17.8535i | 1.02792 | + | 0.593472i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.16565 | − | 2.01896i | −0.0387047 | − | 0.0670386i | 0.846024 | − | 0.533145i | \(-0.178990\pi\) |
−0.884729 | + | 0.466106i | \(0.845657\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42.9065 | + | 9.11989i | −1.42312 | + | 0.302488i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.02681 | + | 1.17018i | −0.0671512 | + | 0.0387698i | −0.533200 | − | 0.845989i | \(-0.679011\pi\) |
0.466048 | + | 0.884759i | \(0.345677\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.1638 | + | 21.4565i | 1.22994 | + | 0.710107i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.3010 | + | 19.8353i | −0.902544 | + | 0.655734i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.2670 | + | 12.3522i | −1.26369 | + | 0.407905i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.54891 | 0.117068 | 0.0585339 | − | 0.998285i | \(-0.481357\pi\) | ||||
0.0585339 | + | 0.998285i | \(0.481357\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −47.1533 | + | 34.2587i | −1.55375 | + | 1.12886i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.59259 | + | 2.75845i | −0.0524208 | + | 0.0907955i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.6169 | − | 28.7814i | −0.546361 | − | 0.946326i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.27362 | + | 2.04716i | −0.0746755 | + | 0.0672376i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.6699 | + | 35.8013i | 0.678157 | + | 1.17460i | 0.975535 | + | 0.219843i | \(0.0705545\pi\) |
−0.297378 | + | 0.954760i | \(0.596112\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.5299 | + | 3.79829i | −1.22999 | + | 0.124484i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.5107 | − | 2.78634i | 0.867922 | − | 0.0912206i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 99.7558i | 3.26236i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.12314i | 0.0366913i | 0.999832 | + | 0.0183457i | \(0.00583993\pi\) | ||||
−0.999832 | + | 0.0183457i | \(0.994160\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −50.4328 | − | 22.4543i | −1.64581 | − | 0.732767i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3955 | − | 35.3261i | 0.664875 | − | 1.15160i | −0.314444 | − | 0.949276i | \(-0.601818\pi\) |
0.979319 | − | 0.202322i | \(-0.0648486\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.8399 | − | 26.4657i | 1.49275 | − | 0.861840i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 35.7055 | − | 25.8362i | 1.16150 | − | 0.840452i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.9909 | + | 10.3871i | −0.584626 | + | 0.337534i | −0.762970 | − | 0.646434i | \(-0.776259\pi\) |
0.178344 | + | 0.983968i | \(0.442926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.31243 | + | 2.27320i | −0.0426034 | + | 0.0737912i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.6159 | − | 14.0764i | −1.02521 | − | 0.456457i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50.6468i | − | 1.64061i | −0.571926 | − | 0.820305i | \(-0.693804\pi\) | ||
0.571926 | − | 0.820305i | \(-0.306196\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 13.4942i | − | 0.436661i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.9088 | − | 2.93328i | 0.902164 | − | 0.0948195i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.23212 | + | 1.55181i | 0.233537 | + | 0.0501107i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.27463 | − | 12.6000i | −0.234666 | − | 0.406453i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −31.4104 | − | 10.2060i | −1.01218 | − | 0.328883i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.58779 | + | 7.94629i | 0.147686 | + | 0.255800i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.1556 | + | 19.3220i | −0.358739 | + | 0.621354i | −0.987750 | − | 0.156042i | \(-0.950127\pi\) |
0.629011 | + | 0.777396i | \(0.283460\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.1776 | − | 35.7295i | 1.57981 | − | 1.14780i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.74260 | 0.248472 | 0.124236 | − | 0.992253i | \(-0.460352\pi\) | ||||
0.124236 | + | 0.992253i | \(0.460352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.02929 | + | 24.8747i | 0.257407 | + | 0.797446i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.35842 | + | 5.34618i | −0.235658 | + | 0.171215i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.50084 | − | 2.02121i | −0.112002 | − | 0.0646644i | 0.442953 | − | 0.896545i | \(-0.353931\pi\) |
−0.554955 | + | 0.831881i | \(0.687264\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.2927 | − | 10.5613i | 0.584637 | − | 0.337540i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.84853 | − | 21.0773i | 0.218657 | − | 0.672947i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.5261 | − | 28.6240i | −0.527100 | − | 0.912963i | −0.999501 | − | 0.0315798i | \(-0.989946\pi\) |
0.472402 | − | 0.881383i | \(-0.343387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.07969 | + | 2.35541i | 0.129990 | + | 0.0750496i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.6844 | − | 14.0336i | 1.00853 | − | 0.446695i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.8569i | 1.83974i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.7928 | −1.45465 | −0.727327 | − | 0.686291i | \(-0.759238\pi\) | ||||
−0.727327 | + | 0.686291i | \(0.759238\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.31541 | − | 14.1846i | 0.200413 | − | 0.450134i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.4733 | − | 26.2540i | −1.44160 | − | 0.832308i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.1809 | − | 24.9305i | 1.36755 | − | 0.789558i | 0.376939 | − | 0.926238i | \(-0.376977\pi\) |
0.990615 | + | 0.136681i | \(0.0436434\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.1219 | − | 10.1119i | 0.984654 | − | 0.319927i |
(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 | 504.2.bu.a.41.8 | ✓ | 48 | |
3.2 | odd | 2 | 1512.2.bu.a.881.21 | 48 | |||
4.3 | odd | 2 | 1008.2.cc.d.545.17 | 48 | |||
7.6 | odd | 2 | inner | 504.2.bu.a.41.17 | yes | 48 | |
9.2 | odd | 6 | inner | 504.2.bu.a.209.17 | yes | 48 | |
9.4 | even | 3 | 4536.2.k.a.3401.41 | 48 | |||
9.5 | odd | 6 | 4536.2.k.a.3401.8 | 48 | |||
9.7 | even | 3 | 1512.2.bu.a.1385.4 | 48 | |||
12.11 | even | 2 | 3024.2.cc.d.881.21 | 48 | |||
21.20 | even | 2 | 1512.2.bu.a.881.4 | 48 | |||
28.27 | even | 2 | 1008.2.cc.d.545.8 | 48 | |||
36.7 | odd | 6 | 3024.2.cc.d.2897.4 | 48 | |||
36.11 | even | 6 | 1008.2.cc.d.209.8 | 48 | |||
63.13 | odd | 6 | 4536.2.k.a.3401.7 | 48 | |||
63.20 | even | 6 | inner | 504.2.bu.a.209.8 | yes | 48 | |
63.34 | odd | 6 | 1512.2.bu.a.1385.21 | 48 | |||
63.41 | even | 6 | 4536.2.k.a.3401.42 | 48 | |||
84.83 | odd | 2 | 3024.2.cc.d.881.4 | 48 | |||
252.83 | odd | 6 | 1008.2.cc.d.209.17 | 48 | |||
252.223 | even | 6 | 3024.2.cc.d.2897.21 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bu.a.41.8 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.2.bu.a.41.17 | yes | 48 | 7.6 | odd | 2 | inner | |
504.2.bu.a.209.8 | yes | 48 | 63.20 | even | 6 | inner | |
504.2.bu.a.209.17 | yes | 48 | 9.2 | odd | 6 | inner | |
1008.2.cc.d.209.8 | 48 | 36.11 | even | 6 | |||
1008.2.cc.d.209.17 | 48 | 252.83 | odd | 6 | |||
1008.2.cc.d.545.8 | 48 | 28.27 | even | 2 | |||
1008.2.cc.d.545.17 | 48 | 4.3 | odd | 2 | |||
1512.2.bu.a.881.4 | 48 | 21.20 | even | 2 | |||
1512.2.bu.a.881.21 | 48 | 3.2 | odd | 2 | |||
1512.2.bu.a.1385.4 | 48 | 9.7 | even | 3 | |||
1512.2.bu.a.1385.21 | 48 | 63.34 | odd | 6 | |||
3024.2.cc.d.881.4 | 48 | 84.83 | odd | 2 | |||
3024.2.cc.d.881.21 | 48 | 12.11 | even | 2 | |||
3024.2.cc.d.2897.4 | 48 | 36.7 | odd | 6 | |||
3024.2.cc.d.2897.21 | 48 | 252.223 | even | 6 | |||
4536.2.k.a.3401.7 | 48 | 63.13 | odd | 6 | |||
4536.2.k.a.3401.8 | 48 | 9.5 | odd | 6 | |||
4536.2.k.a.3401.41 | 48 | 9.4 | even | 3 | |||
4536.2.k.a.3401.42 | 48 | 63.41 | even | 6 |