Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(209,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 209.17 | ||
Character | \(\chi\) | \(=\) | 1008.209 |
Dual form | 1008.2.cc.d.545.17 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | −0.962245 | − | 0.272183i | \(-0.912254\pi\) |
0.245405 | − | 0.969421i | \(-0.421079\pi\) | |||||||
\(6\) | 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 | \(-0.589333\pi\) |
−0.970632 | + | 0.240568i | \(0.922666\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.861773 | − | 0.497545i | 0.239013 | − | 0.137994i | −0.375710 | − | 0.926737i | \(-0.622601\pi\) |
0.614723 | + | 0.788743i | \(0.289268\pi\) | |||||||
\(14\) | 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 | \(-0.957026\pi\) |
−0.378884 | + | 0.925444i | \(0.623692\pi\) | |||||||
\(24\) | 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 | 0.201911 | − | 0.979404i | \(-0.435285\pi\) |
−0.747233 | + | 0.664562i | \(0.768618\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.51256 | − | 2.02798i | 0.630874 | − | 0.364235i | −0.150217 | − | 0.988653i | \(-0.547997\pi\) |
0.781090 | + | 0.624418i | \(0.214664\pi\) | |||||||
\(32\) | 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 | 0.998614 | + | 0.0526294i | \(0.0167602\pi\) |
−0.453729 | + | 0.891140i | \(0.649906\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.81364 | + | 6.60542i | −0.581575 | + | 1.00732i | 0.413718 | + | 0.910405i | \(0.364230\pi\) |
−0.995293 | + | 0.0969121i | \(0.969103\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.43528 | + | 7.14716i | −0.959315 | + | 1.06544i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.78098 | − | 6.54884i | 0.551512 | − | 0.955247i | −0.446654 | − | 0.894707i | \(-0.647384\pi\) |
0.998166 | − | 0.0605399i | \(-0.0192822\pi\) | |||||||
\(48\) | 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 | \(-0.820719\pi\) | ||
0.845536 | − | 0.533919i | \(-0.179281\pi\) | |||||||
\(54\) | 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 | \(-0.261568\pi\) |
−0.974692 | + | 0.223551i | \(0.928235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.26324 | − | 3.03873i | −0.673889 | − | 0.389070i | 0.123660 | − | 0.992325i | \(-0.460537\pi\) |
−0.797548 | + | 0.603255i | \(0.793870\pi\) | |||||||
\(62\) | 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 | \(-0.185858\pi\) |
−0.894579 | + | 0.446911i | \(0.852524\pi\) | |||||||
\(68\) | 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 | \(-0.950666\pi\) | ||
0.988014 | − | 0.154367i | \(-0.0493337\pi\) | |||||||
\(74\) | 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 | 0.0634485 | − | 0.997985i | \(-0.479790\pi\) |
0.832556 | − | 0.553941i | \(-0.186877\pi\) | |||||||
\(80\) | 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 | \(-0.997403\pi\) |
0.507048 | + | 0.861918i | \(0.330737\pi\) | |||||||
\(84\) | 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 | 0.650742 | − | 0.759299i | \(-0.274458\pi\) |
−0.332202 | + | 0.943208i | \(0.607791\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.98014 | + | 14.0207i | −0.299516 | + | 1.40914i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.31084 | − | 12.6627i | 0.727456 | − | 1.25999i | −0.230500 | − | 0.973072i | \(-0.574036\pi\) |
0.957955 | − | 0.286918i | \(-0.0926306\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.883186 | + | 0.509908i | −0.0870229 | + | 0.0502427i | −0.542880 | − | 0.839810i | \(-0.682666\pi\) |
0.455857 | + | 0.890053i | \(0.349333\pi\) | |||||||
\(104\) | 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 | −0.228959 | − | 0.973436i | \(-0.573532\pi\) |
0.728541 | + | 0.685003i | \(0.240199\pi\) | |||||||
\(114\) | 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 | \(-0.638072\pi\) | ||||
−0.420291 | + | 0.907389i | \(0.638072\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.37336 | + | 12.0687i | 0.473098 | + | 1.06259i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.59921 | − | 13.1622i | −0.663946 | − | 1.14999i | −0.979570 | − | 0.201104i | \(-0.935547\pi\) |
0.315624 | − | 0.948884i | \(-0.397786\pi\) | |||||||
\(132\) | 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 | 0.392995 | − | 0.919541i | \(-0.371439\pi\) |
−0.599848 | + | 0.800114i | \(0.704772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.55582 | − | 4.93971i | 0.725695 | − | 0.418980i | −0.0911499 | − | 0.995837i | \(-0.529054\pi\) |
0.816845 | + | 0.576857i | \(0.195721\pi\) | |||||||
\(140\) | 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 | 0.725373 | − | 0.688356i | \(-0.241667\pi\) |
0.958820 | − | 0.284013i | \(-0.0916658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.52875 | − | 11.3081i | 0.531302 | − | 0.920242i | −0.468030 | − | 0.883712i | \(-0.655036\pi\) |
0.999333 | − | 0.0365301i | \(-0.0116305\pi\) | |||||||
\(152\) | 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 | −0.510668 | − | 0.859778i | \(-0.670602\pi\) |
0.489256 | + | 0.872140i | \(0.337268\pi\) | |||||||
\(158\) | 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 | \(-0.364389\pi\) | ||||
0.413262 | + | 0.910612i | \(0.364389\pi\) | |||||||
\(164\) | 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 | \(-0.265713\pi\) |
−0.977520 | + | 0.210841i | \(0.932380\pi\) | |||||||
\(168\) | 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 | −0.899274 | − | 0.437387i | \(-0.855904\pi\) |
0.828425 | + | 0.560100i | \(0.189237\pi\) | |||||||
\(174\) | 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 | \(0.135851\pi\) | ||||
−0.910300 | + | 0.413950i | \(0.864149\pi\) | |||||||
\(182\) | 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 | \(-0.284670\pi\) |
−0.362284 | + | 0.932068i | \(0.618003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.43109 | + | 2.47872i | 0.103012 | + | 0.178422i | 0.912924 | − | 0.408129i | \(-0.133819\pi\) |
−0.809912 | + | 0.586551i | \(0.800485\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.04766 | + | 2.24737i | −0.361470 | + | 0.160938i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.46947i | 0.104695i | 0.998629 | + | 0.0523475i | \(0.0166704\pi\) | ||||
−0.998629 | + | 0.0523475i | \(0.983330\pi\) | |||||||
\(198\) | 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 | \(-0.0505310\pi\) |
−0.630616 | + | 0.776095i | \(0.717198\pi\) | |||||||
\(212\) | 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 | \(-0.272966\pi\) |
−0.327777 | + | 0.944755i | \(0.606300\pi\) | |||||||
\(224\) | 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 | \(-0.908549\pi\) |
0.724908 | + | 0.688846i | \(0.241882\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5744 | − | 10.7239i | 1.22743 | − | 0.708657i | 0.260939 | − | 0.965355i | \(-0.415968\pi\) |
0.966492 | + | 0.256698i | \(0.0826346\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.86707 | + | 20.0197i | −0.583410 | + | 1.31720i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6101i | 0.760601i | 0.924863 | + | 0.380300i | \(0.124179\pi\) | ||||
−0.924863 | + | 0.380300i | \(0.875821\pi\) | |||||||
\(234\) | 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 | \(-0.736844\pi\) |
0.298510 | + | 0.954407i | \(0.403510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.60243 | + | 1.50251i | 0.167637 | + | 0.0967854i | 0.581471 | − | 0.813567i | \(-0.302477\pi\) |
−0.413834 | + | 0.910352i | \(0.635811\pi\) | |||||||
\(242\) | 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 | \(-0.155232\pi\) | ||||
0.883424 | + | 0.468575i | \(0.155232\pi\) | |||||||
\(252\) | 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 | 0.900396 | − | 0.435072i | \(-0.143277\pi\) |
−0.826981 | + | 0.562230i | \(0.809944\pi\) | |||||||
\(258\) | 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 | \(-0.469798\pi\) |
−0.814760 | + | 0.579798i | \(0.803132\pi\) | |||||||
\(264\) | 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 | −0.964323 | − | 0.264728i | \(-0.914718\pi\) |
0.711422 | + | 0.702765i | \(0.248051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.04251 | − | 8.14185i | −0.541361 | − | 0.487440i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.1633 | − | 9.33189i | −0.964222 | − | 0.556694i | −0.0667521 | − | 0.997770i | \(-0.521264\pi\) |
−0.897470 | + | 0.441076i | \(0.854597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.7038 | − | 13.6854i | 1.40904 | − | 0.813512i | 0.413748 | − | 0.910392i | \(-0.364220\pi\) |
0.995296 | + | 0.0968797i | \(0.0308862\pi\) | |||||||
\(284\) | 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 | 0.969466 | − | 0.245224i | \(-0.0788615\pi\) |
−0.697103 | + | 0.716971i | \(0.745528\pi\) | |||||||
\(294\) | 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 | \(-0.0229371\pi\) |
−0.561053 | + | 0.827780i | \(0.689604\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.6028 | + | 15.9365i | 1.56020 | + | 0.900784i | 0.997236 | + | 0.0743050i | \(0.0236738\pi\) |
0.562968 | + | 0.826479i | \(0.309659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0491599 | + | 25.4453i | 0.00276985 | + | 1.43368i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3039 | + | 9.99044i | 0.971886 | + | 0.561119i | 0.899811 | − | 0.436280i | \(-0.143704\pi\) |
0.0720756 | + | 0.997399i | \(0.477038\pi\) | |||||||
\(318\) | 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 | \(-0.912570\pi\) |
0.716148 | + | 0.697948i | \(0.245903\pi\) | |||||||
\(332\) | 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 | 0.782375 | − | 0.622808i | \(-0.214008\pi\) |
−0.930555 | + | 0.366153i | \(0.880675\pi\) | |||||||
\(338\) | 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 | \(-0.523543\pi\) |
0.826710 | + | 0.562629i | \(0.190210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1071 | − | 9.87682i | −0.915725 | − | 0.528694i | −0.0334560 | − | 0.999440i | \(-0.510651\pi\) |
−0.882269 | + | 0.470746i | \(0.843985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.05764 | + | 1.07507i | −0.269957 | + | 0.0573828i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3112 | + | 17.8596i | −0.548811 | + | 0.950569i | 0.449545 | + | 0.893258i | \(0.351586\pi\) |
−0.998356 | + | 0.0573115i | \(0.981747\pi\) | |||||||
\(354\) | 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 | \(-0.360968\pi\) |
−0.573209 | + | 0.819409i | \(0.694302\pi\) | |||||||
\(368\) | 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 | −0.992019 | − | 0.126092i | \(-0.959757\pi\) |
0.386811 | − | 0.922159i | \(-0.373577\pi\) | |||||||
\(374\) | 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 | \(-0.616484\pi\) | ||||
−0.357832 | + | 0.933786i | \(0.616484\pi\) | |||||||
\(380\) | 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 | \(-0.102286\pi\) |
−0.747931 | + | 0.663776i | \(0.768953\pi\) | |||||||
\(384\) | 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 | 0.0188226 | − | 0.999823i | \(-0.494008\pi\) |
−0.856461 | + | 0.516212i | \(0.827342\pi\) | |||||||
\(390\) | 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 | \(0.113345\pi\) | ||||
−0.937269 | + | 0.348607i | \(0.886655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.5543 | − | 2.62868i | 1.22925 | − | 0.131599i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.6674 | + | 11.9323i | −1.03208 | + | 0.595872i | −0.917580 | − | 0.397551i | \(-0.869860\pi\) |
−0.114501 | + | 0.993423i | \(0.536527\pi\) | |||||||
\(402\) | 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 | −0.918510 | − | 0.395399i | \(-0.870606\pi\) |
−0.116830 | + | 0.993152i | \(0.537273\pi\) | |||||||
\(410\) | 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 | \(-0.00697551\pi\) |
−0.518857 | + | 0.854861i | \(0.673642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5884 | + | 32.1961i | −0.905944 | + | 1.56914i | −0.0862979 | + | 0.996269i | \(0.527504\pi\) |
−0.819646 | + | 0.572871i | \(0.805830\pi\) | |||||||
\(422\) | 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 | \(-0.678460\pi\) | ||
0.531737 | − | 0.846910i | \(-0.321540\pi\) | |||||||
\(434\) | 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 | \(-0.266951\pi\) |
−0.309865 | + | 0.950781i | \(0.600284\pi\) | |||||||
\(440\) | 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 | \(-0.210672\pi\) |
−0.137807 | + | 0.990459i | \(0.544005\pi\) | |||||||
\(444\) | 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 | \(0.0594996\pi\) | ||||
−0.982581 | + | 0.185837i | \(0.940500\pi\) | |||||||
\(450\) | 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 | −0.707161 | − | 0.707052i | \(-0.750025\pi\) |
0.965906 | + | 0.258894i | \(0.0833580\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −32.1844 | − | 10.4571i | −1.50224 | − | 0.488097i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.73005 | + | 11.6568i | −0.313450 | + | 0.542911i | −0.979107 | − | 0.203347i | \(-0.934818\pi\) |
0.665657 | + | 0.746258i | \(0.268151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.57103 | − | 14.8455i | −0.398329 | − | 0.689927i | 0.595191 | − | 0.803585i | \(-0.297077\pi\) |
−0.993520 | + | 0.113658i | \(0.963743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.5741 | + | 9.16022i | −0.954100 | + | 0.424795i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.67554 | 0.262633 | 0.131316 | − | 0.991341i | \(-0.458080\pi\) | ||||
0.131316 | + | 0.991341i | \(0.458080\pi\) | |||||||
\(468\) | 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 | \(-0.932593\pi\) |
0.670856 | + | 0.741587i | \(0.265927\pi\) | |||||||
\(480\) | 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 | \(-0.416212\pi\) | ||||
0.260197 | + | 0.965556i | \(0.416212\pi\) | |||||||
\(488\) | 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 | \(-0.590924\pi\) |
0.690044 | + | 0.723767i | \(0.257591\pi\) | |||||||
\(492\) | 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 | \(-0.289935\pi\) |
−0.990720 | + | 0.135918i | \(0.956602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6308 | − | 1.43263i | −0.608979 | − | 0.0640051i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.1129 | 0.941379 | 0.470690 | − | 0.882299i | \(-0.344005\pi\) | ||||
0.470690 | + | 0.882299i | \(0.344005\pi\) | |||||||
\(504\) | 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 | 0.999996 | − | 0.00293304i | \(-0.000933617\pi\) |
−0.502538 | + | 0.864555i | \(0.667600\pi\) | |||||||
\(510\) | 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 | 0.00733515 | − | 0.999973i | \(-0.497665\pi\) |
0.862335 | − | 0.506339i | \(-0.169002\pi\) | |||||||
\(548\) | 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 | \(0.0936580\pi\) | ||||
−0.957024 | + | 0.290008i | \(0.906342\pi\) | |||||||
\(558\) | 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 | \(-0.257886\pi\) |
−0.972041 | + | 0.234811i | \(0.924553\pi\) | |||||||
\(564\) | 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 | 0.0283007 | − | 0.999599i | \(-0.490990\pi\) |
−0.851528 | + | 0.524309i | \(0.824324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.77378 | − | 13.4646i | −0.325323 | − | 0.563475i | 0.656255 | − | 0.754539i | \(-0.272140\pi\) |
−0.981578 | + | 0.191064i | \(0.938806\pi\) | |||||||
\(572\) | 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 | \(-0.663932\pi\) | ||
0.492541 | − | 0.870289i | \(-0.336068\pi\) | |||||||
\(578\) | 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 | 0.445372 | + | 0.895346i | \(0.353072\pi\) |
−0.998078 | + | 0.0619696i | \(0.980262\pi\) | |||||||
\(588\) | 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 | \(-0.608236\pi\) |
0.649680 | + | 0.760208i | \(0.274903\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.2085 | − | 11.0901i | −0.783533 | − | 0.452373i | 0.0541481 | − | 0.998533i | \(-0.482756\pi\) |
−0.837681 | + | 0.546160i | \(0.816089\pi\) | |||||||
\(602\) | 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 | \(-0.918935\pi\) |
−0.265695 | + | 0.964057i | \(0.585601\pi\) | |||||||
\(608\) | 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 | 0.482586 | − | 0.875849i | \(-0.339698\pi\) |
0.999800 | + | 0.0199930i | \(0.00636440\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.9906 | + | 15.0057i | 1.04465 | + | 0.603128i | 0.921146 | − | 0.389216i | \(-0.127254\pi\) |
0.123502 | + | 0.992344i | \(0.460587\pi\) | |||||||
\(620\) | 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 | \(-0.635063\pi\) | ||||
−0.411694 | + | 0.911322i | \(0.635063\pi\) | |||||||
\(632\) | 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 | −0.109419 | − | 0.993996i | \(-0.534899\pi\) |
−0.915535 | + | 0.402238i | \(0.868232\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.7961 | + | 16.6254i | −1.13561 | + | 0.655643i | −0.945339 | − | 0.326090i | \(-0.894269\pi\) |
−0.190268 | + | 0.981732i | \(0.560936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.8935 | − | 34.2631i | 0.980179 | − | 1.34911i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.06135 | −0.356238 | −0.178119 | − | 0.984009i | \(-0.557001\pi\) | ||||
−0.178119 | + | 0.984009i | \(0.557001\pi\) | |||||||
\(648\) | 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 | −0.689696 | − | 0.724099i | \(-0.742256\pi\) |
0.282240 | + | 0.959344i | \(0.408923\pi\) | |||||||
\(654\) | 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 | 0.990757 | + | 0.135649i | \(0.0433119\pi\) |
0.612854 | + | 0.790196i | \(0.290021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.5254 | − | 10.6957i | 0.720556 | − | 0.416013i | −0.0944011 | − | 0.995534i | \(-0.530094\pi\) |
0.814957 | + | 0.579521i | \(0.196760\pi\) | |||||||
\(662\) | 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 | −0.645829 | − | 0.763482i | \(-0.723488\pi\) |
0.984109 | + | 0.177563i | \(0.0568213\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.3778 | − | 18.3484i | 0.784341 | − | 0.706232i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.39862 | + | 14.5468i | −0.322785 | + | 0.559081i | −0.981062 | − | 0.193696i | \(-0.937953\pi\) |
0.658276 | + | 0.752776i | \(0.271286\pi\) | |||||||
\(678\) | 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 | \(-0.646204\pi\) |
−0.997934 | + | 0.0642424i | \(0.979537\pi\) | |||||||
\(692\) | 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 | \(0.0702258\pi\) | ||||
−0.975762 | + | 0.218836i | \(0.929774\pi\) | |||||||
\(702\) | 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 | −0.832375 | − | 0.554213i | \(-0.813019\pi\) |
0.896150 | + | 0.443752i | \(0.146353\pi\) | |||||||
\(710\) | 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 | \(-0.487301\pi\) | ||||
0.0398845 | + | 0.999204i | \(0.487301\pi\) | |||||||
\(720\) | 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 | \(-0.106404\pi\) |
0.188191 | + | 0.982132i | \(0.439737\pi\) | |||||||
\(728\) | 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 | −0.300466 | − | 0.953792i | \(-0.597142\pi\) |
0.675775 | + | 0.737108i | \(0.263809\pi\) | |||||||
\(734\) | 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 | \(-0.255276\pi\) | ||||
0.695289 | + | 0.718730i | \(0.255276\pi\) | |||||||
\(740\) | 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 | \(-0.732806\pi\) |
0.310593 | + | 0.950543i | \(0.399472\pi\) | |||||||
\(744\) | 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 | \(-0.325294\pi\) |
−0.999681 | + | 0.0252521i | \(0.991961\pi\) | |||||||
\(752\) | 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 | 0.851647 | + | 0.524116i | \(0.175604\pi\) |
0.0280745 | + | 0.999606i | \(0.491062\pi\) | |||||||
\(762\) | 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 | −0.881592 | − | 0.472011i | \(-0.843528\pi\) |
−0.0320224 | + | 0.999487i | \(0.510195\pi\) | |||||||
\(770\) | 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 | \(-0.721039\pi\) |
0.345512 | + | 0.938414i | \(0.387705\pi\) | |||||||
\(788\) | 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 | 0.959088 | + | 0.283107i | \(0.0913653\pi\) |
−0.234366 | + | 0.972148i | \(0.575301\pi\) | |||||||
\(798\) | 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 | \(0.137149\pi\) | ||||
−0.908605 | + | 0.417657i | \(0.862851\pi\) | |||||||
\(810\) | 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 | 0.939626 | − | 0.342202i | \(-0.111173\pi\) |
0.173457 | + | 0.984841i | \(0.444506\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.98887 | + | 5.17687i | 0.104185 | + | 0.180454i | 0.913405 | − | 0.407052i | \(-0.133443\pi\) |
−0.809220 | + | 0.587506i | \(0.800110\pi\) | |||||||
\(824\) | 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 | \(-0.997496\pi\) | ||
0.999969 | − | 0.00786743i | \(-0.00250431\pi\) | |||||||
\(830\) | 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 | −0.0416932 | + | 0.999130i | \(0.513275\pi\) |
−0.844426 | + | 0.535673i | \(0.820058\pi\) | |||||||
\(840\) | 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 | 0.716869 | − | 0.697208i | \(-0.245575\pi\) |
−0.245365 | + | 0.969431i | \(0.578908\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −38.5147 | − | 34.6785i | −1.31717 | − | 1.18598i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.31574 | − | 12.6712i | 0.249901 | − | 0.432841i | −0.713597 | − | 0.700556i | \(-0.752935\pi\) |
0.963498 | + | 0.267715i | \(0.0862686\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0119 | − | 25.4103i | 1.50167 | − | 0.866988i | 0.501669 | − | 0.865060i | \(-0.332720\pi\) |
0.999998 | − | 0.00192834i | \(-0.000613810\pi\) | |||||||
\(860\) | 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 | 0.963623 | + | 0.267266i | \(0.0861203\pi\) |
−0.250352 | + | 0.968155i | \(0.580546\pi\) | |||||||
\(878\) | 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 | \(-0.348940\pi\) | ||||
0.456955 | + | 0.889490i | \(0.348940\pi\) | |||||||
\(884\) | 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 | \(-0.225995\pi\) |
−0.943680 | + | 0.330860i | \(0.892661\pi\) | |||||||
\(888\) | 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 | \(-0.821010\pi\) |
0.884729 | + | 0.466106i | \(0.154343\pi\) | |||||||
\(908\) | 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 | \(-0.320989\pi\) |
−0.466048 | + | 0.884759i | \(0.654323\pi\) | |||||||
\(912\) | 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 | \(-0.518643\pi\) | ||||
−0.0585339 | + | 0.998285i | \(0.518643\pi\) | |||||||
\(920\) | 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 | −0.297378 | − | 0.954760i | \(-0.596112\pi\) |
0.975535 | − | 0.219843i | \(-0.0705545\pi\) | |||||||
\(930\) | 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 | \(-0.994160\pi\) | ||
0.999832 | − | 0.0183457i | \(-0.00583993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 50.4328 | − | 22.4543i | 1.64581 | − | 0.732767i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3955 | + | 35.3261i | 0.664875 | + | 1.15160i | 0.979319 | + | 0.202322i | \(0.0648486\pi\) |
−0.314444 | + | 0.949276i | \(0.601818\pi\) | |||||||
\(942\) | 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 | \(-0.223741\pi\) |
−0.178344 | + | 0.983968i | \(0.557074\pi\) | |||||||
\(948\) | 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 | \(0.306196\pi\) | ||||
−0.571926 | + | 0.820305i | \(0.693804\pi\) | |||||||
\(954\) | 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 | \(-0.0498735\pi\) |
−0.629011 | + | 0.777396i | \(0.716540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.1776 | + | 35.7295i | 1.57981 | + | 1.14780i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.74260 | −0.248472 | −0.124236 | − | 0.992253i | \(-0.539648\pi\) | ||||
−0.124236 | + | 0.992253i | \(0.539648\pi\) | |||||||
\(972\) | 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 | −0.554955 | − | 0.831881i | \(-0.687264\pi\) |
0.442953 | + | 0.896545i | \(0.353931\pi\) | |||||||
\(978\) | 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 | −0.472402 | − | 0.881383i | \(-0.656613\pi\) |
0.999501 | − | 0.0315798i | \(-0.0100538\pi\) | |||||||
\(984\) | 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 | \(-0.240762\pi\) | ||||
0.727327 | + | 0.686291i | \(0.240762\pi\) | |||||||
\(992\) | 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 | 0.990615 | − | 0.136681i | \(-0.0436434\pi\) |
0.376939 | + | 0.926238i | \(0.376977\pi\) | |||||||
\(998\) | 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 | 1008.2.cc.d.209.17 | 48 | ||
3.2 | odd | 2 | 3024.2.cc.d.2897.21 | 48 | |||
4.3 | odd | 2 | 504.2.bu.a.209.8 | yes | 48 | ||
7.6 | odd | 2 | inner | 1008.2.cc.d.209.8 | 48 | ||
9.4 | even | 3 | 3024.2.cc.d.881.4 | 48 | |||
9.5 | odd | 6 | inner | 1008.2.cc.d.545.8 | 48 | ||
12.11 | even | 2 | 1512.2.bu.a.1385.21 | 48 | |||
21.20 | even | 2 | 3024.2.cc.d.2897.4 | 48 | |||
28.27 | even | 2 | 504.2.bu.a.209.17 | yes | 48 | ||
36.7 | odd | 6 | 4536.2.k.a.3401.42 | 48 | |||
36.11 | even | 6 | 4536.2.k.a.3401.7 | 48 | |||
36.23 | even | 6 | 504.2.bu.a.41.17 | yes | 48 | ||
36.31 | odd | 6 | 1512.2.bu.a.881.4 | 48 | |||
63.13 | odd | 6 | 3024.2.cc.d.881.21 | 48 | |||
63.41 | even | 6 | inner | 1008.2.cc.d.545.17 | 48 | ||
84.83 | odd | 2 | 1512.2.bu.a.1385.4 | 48 | |||
252.83 | odd | 6 | 4536.2.k.a.3401.41 | 48 | |||
252.139 | even | 6 | 1512.2.bu.a.881.21 | 48 | |||
252.167 | odd | 6 | 504.2.bu.a.41.8 | ✓ | 48 | ||
252.223 | even | 6 | 4536.2.k.a.3401.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bu.a.41.8 | ✓ | 48 | 252.167 | odd | 6 | ||
504.2.bu.a.41.17 | yes | 48 | 36.23 | even | 6 | ||
504.2.bu.a.209.8 | yes | 48 | 4.3 | odd | 2 | ||
504.2.bu.a.209.17 | yes | 48 | 28.27 | even | 2 | ||
1008.2.cc.d.209.8 | 48 | 7.6 | odd | 2 | inner | ||
1008.2.cc.d.209.17 | 48 | 1.1 | even | 1 | trivial | ||
1008.2.cc.d.545.8 | 48 | 9.5 | odd | 6 | inner | ||
1008.2.cc.d.545.17 | 48 | 63.41 | even | 6 | inner | ||
1512.2.bu.a.881.4 | 48 | 36.31 | odd | 6 | |||
1512.2.bu.a.881.21 | 48 | 252.139 | even | 6 | |||
1512.2.bu.a.1385.4 | 48 | 84.83 | odd | 2 | |||
1512.2.bu.a.1385.21 | 48 | 12.11 | even | 2 | |||
3024.2.cc.d.881.4 | 48 | 9.4 | even | 3 | |||
3024.2.cc.d.881.21 | 48 | 63.13 | odd | 6 | |||
3024.2.cc.d.2897.4 | 48 | 21.20 | even | 2 | |||
3024.2.cc.d.2897.21 | 48 | 3.2 | odd | 2 | |||
4536.2.k.a.3401.7 | 48 | 36.11 | even | 6 | |||
4536.2.k.a.3401.8 | 48 | 252.223 | even | 6 | |||
4536.2.k.a.3401.41 | 48 | 252.83 | odd | 6 | |||
4536.2.k.a.3401.42 | 48 | 36.7 | odd | 6 |