Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(49,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.49 |
Dual form | 60.4.d.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.0000 | + | 5.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0000i | 1.18789i | 0.804506 | + | 0.593944i | \(0.202430\pi\) | ||||
−0.804506 | + | 0.593944i | \(0.797570\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.0000 | −0.383742 | −0.191871 | − | 0.981420i | \(-0.561455\pi\) | ||||
−0.191871 | + | 0.981420i | \(0.561455\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 30.0000i | 0.640039i | 0.947411 | + | 0.320019i | \(0.103689\pi\) | ||||
−0.947411 | + | 0.320019i | \(0.896311\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | − | 30.0000i | −0.258199 | − | 0.516398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 62.0000i | 0.884542i | 0.896882 | + | 0.442271i | \(0.145827\pi\) | ||||
−0.896882 | + | 0.442271i | \(0.854173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 120.000 | 1.44894 | 0.724471 | − | 0.689306i | \(-0.242084\pi\) | ||||
0.724471 | + | 0.689306i | \(0.242084\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −66.0000 | −0.685828 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 188.000i | − | 1.70438i | −0.523234 | − | 0.852189i | \(-0.675274\pi\) | ||
0.523234 | − | 0.852189i | \(-0.324726\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 75.0000 | − | 100.000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −96.0000 | −0.614716 | −0.307358 | − | 0.951594i | \(-0.599445\pi\) | ||||
−0.307358 | + | 0.951594i | \(0.599445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 184.000 | 1.06604 | 0.533022 | − | 0.846101i | \(-0.321056\pi\) | ||||
0.533022 | + | 0.846101i | \(0.321056\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 42.0000i | − | 0.221553i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −110.000 | − | 220.000i | −0.531240 | − | 1.06248i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 406.000i | 1.80395i | 0.431793 | + | 0.901973i | \(0.357881\pi\) | ||||
−0.431793 | + | 0.901973i | \(0.642119\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −90.0000 | −0.369527 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 130.000 | 0.495185 | 0.247593 | − | 0.968864i | \(-0.420361\pi\) | ||||
0.247593 | + | 0.968864i | \(0.420361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 148.000i | − | 0.524879i | −0.964948 | − | 0.262439i | \(-0.915473\pi\) | ||
0.964948 | − | 0.262439i | \(-0.0845270\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 90.0000 | − | 45.0000i | 0.298142 | − | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 448.000i | 1.39037i | 0.718830 | + | 0.695186i | \(0.244678\pi\) | ||||
−0.718830 | + | 0.695186i | \(0.755322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −141.000 | −0.411079 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −186.000 | −0.510690 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 414.000i | 1.07297i | 0.843911 | + | 0.536484i | \(0.180248\pi\) | ||||
−0.843911 | + | 0.536484i | \(0.819752\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 140.000 | − | 70.0000i | 0.343229 | − | 0.171615i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 360.000i | 0.836547i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −266.000 | −0.586953 | −0.293477 | − | 0.955966i | \(-0.594812\pi\) | ||||
−0.293477 | + | 0.955966i | \(0.594812\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −838.000 | −1.75893 | −0.879466 | − | 0.475961i | \(-0.842100\pi\) | ||||
−0.879466 | + | 0.475961i | \(0.842100\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 198.000i | − | 0.395963i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −150.000 | − | 300.000i | −0.286234 | − | 0.572468i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 248.000i | 0.452209i | 0.974103 | + | 0.226105i | \(0.0725991\pi\) | ||||
−0.974103 | + | 0.226105i | \(0.927401\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 564.000 | 0.984023 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1020.00 | 1.70495 | 0.852477 | − | 0.522765i | \(-0.175099\pi\) | ||||
0.852477 | + | 0.522765i | \(0.175099\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 484.000i | − | 0.775999i | −0.921660 | − | 0.387999i | \(-0.873166\pi\) | ||
0.921660 | − | 0.387999i | \(-0.126834\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 300.000 | + | 225.000i | 0.461880 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 308.000i | − | 0.455842i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 48.0000 | 0.0683598 | 0.0341799 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341799 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 548.000i | − | 0.724709i | −0.932040 | − | 0.362354i | \(-0.881973\pi\) | ||
0.932040 | − | 0.362354i | \(-0.118027\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −310.000 | − | 620.000i | −0.395579 | − | 0.791158i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 288.000i | − | 0.354906i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 650.000 | 0.774156 | 0.387078 | − | 0.922047i | \(-0.373484\pi\) | ||||
0.387078 | + | 0.922047i | \(0.373484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −660.000 | −0.760294 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 552.000i | 0.615481i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1200.00 | + | 600.000i | −1.29597 | + | 0.647986i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1816.00i | − | 1.90090i | −0.310884 | − | 0.950448i | \(-0.600625\pi\) | ||
0.310884 | − | 0.950448i | \(-0.399375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 126.000 | 0.127914 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1688.00 | 1.66299 | 0.831496 | − | 0.555530i | \(-0.187485\pi\) | ||||
0.831496 | + | 0.555530i | \(0.187485\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 298.000i | 0.285076i | 0.989789 | + | 0.142538i | \(0.0455263\pi\) | ||||
−0.989789 | + | 0.142538i | \(0.954474\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 660.000 | − | 330.000i | 0.613423 | − | 0.306711i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 276.000i | 0.249364i | 0.992197 | + | 0.124682i | \(0.0397910\pi\) | ||||
−0.992197 | + | 0.124682i | \(0.960209\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −322.000 | −0.282954 | −0.141477 | − | 0.989942i | \(-0.545185\pi\) | ||||
−0.141477 | + | 0.989942i | \(0.545185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1218.00 | −1.04151 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 486.000i | 0.404593i | 0.979324 | + | 0.202297i | \(0.0648405\pi\) | ||||
−0.979324 | + | 0.202297i | \(0.935159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 940.000 | + | 1880.00i | 0.762221 | + | 1.52444i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 270.000i | − | 0.213346i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1364.00 | −1.05074 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1135.00 | −0.852742 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 390.000i | 0.285895i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −250.000 | + | 1375.00i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 502.000i | 0.350750i | 0.984502 | + | 0.175375i | \(0.0561138\pi\) | ||||
−0.984502 | + | 0.175375i | \(0.943886\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 444.000 | 0.303039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −0.0120051 | −0.00600255 | − | 0.999982i | \(-0.501911\pi\) | ||||
−0.00600255 | + | 0.999982i | \(0.501911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2640.00i | 1.72118i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | + | 270.000i | 0.0860663 | + | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2334.00i | − | 1.45553i | −0.685829 | − | 0.727763i | \(-0.740560\pi\) | ||
0.685829 | − | 0.727763i | \(-0.259440\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1676.00 | 1.02271 | 0.511354 | − | 0.859370i | \(-0.329144\pi\) | ||||
0.511354 | + | 0.859370i | \(0.329144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1344.00 | −0.802732 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 420.000i | − | 0.245610i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 960.000 | − | 480.000i | 0.549818 | − | 0.274909i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 423.000i | − | 0.237336i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3452.00 | −1.89798 | −0.948989 | − | 0.315308i | \(-0.897892\pi\) | ||||
−0.948989 | + | 0.315308i | \(0.897892\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1720.00 | 0.926964 | 0.463482 | − | 0.886106i | \(-0.346600\pi\) | ||||
0.463482 | + | 0.886106i | \(0.346600\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 558.000i | − | 0.294847i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1840.00 | + | 920.000i | −0.953499 | + | 0.476750i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1246.00i | − | 0.633386i | −0.948528 | − | 0.316693i | \(-0.897427\pi\) | ||
0.948528 | − | 0.316693i | \(-0.102573\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1242.00 | −0.619478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4136.00 | 2.02461 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1760.00i | − | 0.845729i | −0.906193 | − | 0.422865i | \(-0.861025\pi\) | ||
0.906193 | − | 0.422865i | \(-0.138975\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 210.000 | + | 420.000i | 0.0990817 | + | 0.198163i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2724.00i | − | 1.26221i | −0.775696 | − | 0.631106i | \(-0.782601\pi\) | ||
0.775696 | − | 0.631106i | \(-0.217399\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1297.00 | 0.590350 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1080.00 | −0.482980 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2378.00i | 1.04506i | 0.852620 | + | 0.522532i | \(0.175012\pi\) | ||||
−0.852620 | + | 0.522532i | \(0.824988\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2200.00 | + | 1650.00i | 0.950311 | + | 0.712733i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 798.000i | − | 0.338878i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3094.00 | 1.29194 | 0.645968 | − | 0.763365i | \(-0.276454\pi\) | ||||
0.645968 | + | 0.763365i | \(0.276454\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −310.000 | −0.127305 | −0.0636523 | − | 0.997972i | \(-0.520275\pi\) | ||||
−0.0636523 | + | 0.997972i | \(0.520275\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2514.00i | − | 1.01552i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2030.00 | − | 4060.00i | −0.806749 | − | 1.61350i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 868.000i | − | 0.339436i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 594.000 | 0.228609 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −516.000 | −0.195479 | −0.0977394 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977394 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 188.000i | 0.0701168i | 0.999385 | + | 0.0350584i | \(0.0111617\pi\) | ||||
−0.999385 | + | 0.0350584i | \(0.988838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 900.000 | − | 450.000i | 0.330515 | − | 0.165257i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2578.00i | 0.932360i | 0.884690 | + | 0.466180i | \(0.154370\pi\) | ||||
−0.884690 | + | 0.466180i | \(0.845630\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 528.000 | 0.188085 | 0.0940425 | − | 0.995568i | \(-0.470021\pi\) | ||||
0.0940425 | + | 0.995568i | \(0.470021\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −744.000 | −0.261083 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 2112.00i | − | 0.730213i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1300.00 | + | 650.000i | −0.442907 | + | 0.221454i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1692.00i | 0.568126i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1680.00 | −0.556019 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3660.00 | −1.19415 | −0.597073 | − | 0.802187i | \(-0.703670\pi\) | ||||
−0.597073 | + | 0.802187i | \(0.703670\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3060.00i | 0.984356i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 740.000 | + | 1480.00i | 0.234733 | + | 0.469466i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4048.00i | 1.26634i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1452.00 | 0.448023 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1860.00 | −0.566141 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2350.00i | − | 0.705684i | −0.935683 | − | 0.352842i | \(-0.885215\pi\) | ||
0.935683 | − | 0.352842i | \(-0.114785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −675.000 | + | 900.000i | −0.200000 | + | 0.266667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3260.00i | 0.953189i | 0.879123 | + | 0.476594i | \(0.158129\pi\) | ||||
−0.879123 | + | 0.476594i | \(0.841871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 466.000 | 0.134472 | 0.0672361 | − | 0.997737i | \(-0.478582\pi\) | ||||
0.0672361 | + | 0.997737i | \(0.478582\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 924.000 | 0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3170.00i | 0.891303i | 0.895207 | + | 0.445652i | \(0.147028\pi\) | ||||
−0.895207 | + | 0.445652i | \(0.852972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2240.00 | − | 4480.00i | −0.621794 | − | 1.24359i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 144.000i | 0.0394675i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −292.000 | −0.0790289 | −0.0395145 | − | 0.999219i | \(-0.512581\pi\) | ||||
−0.0395145 | + | 0.999219i | \(0.512581\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −842.000 | −0.225054 | −0.112527 | − | 0.993649i | \(-0.535894\pi\) | ||||
−0.112527 | + | 0.993649i | \(0.535894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1410.00 | − | 705.000i | 0.367680 | − | 0.183840i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3600.00i | 0.927379i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1644.00 | 0.418411 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5838.00 | 1.46809 | 0.734046 | − | 0.679099i | \(-0.237629\pi\) | ||||
0.734046 | + | 0.679099i | \(0.237629\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2632.00i | 0.654041i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1860.00 | − | 930.000i | 0.456775 | − | 0.228388i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4626.00i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8932.00 | −2.14289 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 864.000 | 0.204905 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5468.00i | − | 1.28202i | −0.767532 | − | 0.641010i | \(-0.778516\pi\) | ||
0.767532 | − | 0.641010i | \(-0.221484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2070.00 | − | 4140.00i | −0.479846 | − | 0.959691i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1950.00i | 0.446959i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2976.00 | 0.674535 | 0.337268 | − | 0.941409i | \(-0.390497\pi\) | ||||
0.337268 | + | 0.941409i | \(0.390497\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −56.0000 | −0.0125526 | −0.00627631 | − | 0.999980i | \(-0.501998\pi\) | ||||
−0.00627631 | + | 0.999980i | \(0.501998\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1980.00i | − | 0.438956i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1050.00 | + | 1400.00i | −0.230245 | + | 0.306993i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4106.00i | − | 0.890634i | −0.895373 | − | 0.445317i | \(-0.853091\pi\) | ||
0.895373 | − | 0.445317i | \(-0.146909\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1656.00 | −0.355348 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2274.00 | −0.482760 | −0.241380 | − | 0.970431i | \(-0.577600\pi\) | ||||
−0.241380 | + | 0.970431i | \(0.577600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5504.00i | − | 1.15611i | −0.815998 | − | 0.578054i | \(-0.803812\pi\) | ||
0.815998 | − | 0.578054i | \(-0.196188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1800.00 | − | 3600.00i | −0.374115 | − | 0.748230i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2860.00i | 0.588225i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1069.00 | 0.217586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5448.00 | 1.09748 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8034.00i | − | 1.60188i | −0.598744 | − | 0.800941i | \(-0.704333\pi\) | ||
0.598744 | − | 0.800941i | \(-0.295667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2660.00 | − | 1330.00i | 0.524987 | − | 0.262494i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 378.000i | 0.0738511i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5640.00 | 1.09087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3256.00 | 0.623497 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5064.00i | 0.960129i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8380.00 | − | 4190.00i | 1.57324 | − | 0.786619i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 996.000i | 0.185162i | 0.995705 | + | 0.0925810i | \(0.0295117\pi\) | ||||
−0.995705 | + | 0.0925810i | \(0.970488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −894.000 | −0.164589 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8676.00 | −1.58190 | −0.790950 | − | 0.611881i | \(-0.790413\pi\) | ||||
−0.790950 | + | 0.611881i | \(0.790413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1732.00i | − | 0.312775i | −0.987696 | − | 0.156387i | \(-0.950015\pi\) | ||
0.987696 | − | 0.156387i | \(-0.0499848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 990.000 | + | 1980.00i | 0.177080 | + | 0.354160i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2938.00i | − | 0.520551i | −0.965534 | − | 0.260275i | \(-0.916187\pi\) | ||
0.965534 | − | 0.260275i | \(-0.0838133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1344.00 | 0.235892 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −828.000 | −0.143970 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7440.00i | 1.28165i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3000.00 | + | 2250.00i | 0.512031 | + | 0.384023i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 966.000i | − | 0.163364i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9856.00 | −1.65161 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −128.000 | −0.0212553 | −0.0106277 | − | 0.999944i | \(-0.503383\pi\) | ||||
−0.0106277 | + | 0.999944i | \(0.503383\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3654.00i | − | 0.601315i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1240.00 | − | 2480.00i | −0.202234 | − | 0.404468i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5596.00i | 0.904551i | 0.891878 | + | 0.452275i | \(0.149388\pi\) | ||||
−0.891878 | + | 0.452275i | \(0.850612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1458.00 | −0.233592 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2576.00 | −0.409086 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4444.00i | 0.699573i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5640.00 | + | 2820.00i | −0.880137 | + | 0.440069i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 924.000i | − | 0.142948i | −0.997442 | − | 0.0714739i | \(-0.977230\pi\) | ||
0.997442 | − | 0.0714739i | \(-0.0227703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6206.00 | 0.951861 | 0.475931 | − | 0.879483i | \(-0.342111\pi\) | ||||
0.475931 | + | 0.879483i | \(0.342111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 810.000 | 0.123176 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3506.00i | 0.528628i | 0.964437 | + | 0.264314i | \(0.0851455\pi\) | ||||
−0.964437 | + | 0.264314i | \(0.914855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10200.0 | + | 5100.00i | −1.52496 | + | 0.762479i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 4092.00i | − | 0.606643i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7104.00 | 1.04439 | 0.522193 | − | 0.852827i | \(-0.325114\pi\) | ||||
0.522193 | + | 0.852827i | \(0.325114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7541.00 | 1.09943 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3405.00i | − | 0.492331i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2420.00 | + | 4840.00i | 0.347037 | + | 0.694074i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2902.00i | 0.412761i | 0.978472 | + | 0.206380i | \(0.0661684\pi\) | ||||
−0.978472 | + | 0.206380i | \(0.933832\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1170.00 | −0.165062 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9108.00 | −1.27457 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4542.00i | 0.630498i | 0.949009 | + | 0.315249i | \(0.102088\pi\) | ||||
−0.949009 | + | 0.315249i | \(0.897912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4125.00 | − | 750.000i | −0.568038 | − | 0.103280i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2880.00i | − | 0.393442i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5852.00 | −0.793132 | −0.396566 | − | 0.918006i | \(-0.629798\pi\) | ||||
−0.396566 | + | 0.918006i | \(0.629798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1506.00 | −0.202506 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8936.00i | 1.19219i | 0.802914 | + | 0.596094i | \(0.203282\pi\) | ||||
−0.802914 | + | 0.596094i | \(0.796718\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1540.00 | + | 3080.00i | 0.203859 | + | 0.407718i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1332.00i | 0.174960i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1924.00 | −0.250773 | −0.125386 | − | 0.992108i | \(-0.540017\pi\) | ||||
−0.125386 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11656.0 | 1.50759 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 54.0000i | − | 0.00693114i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −480.000 | + | 240.000i | −0.0611428 | + | 0.0305714i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 9194.00i | − | 1.16230i | −0.813796 | − | 0.581151i | \(-0.802603\pi\) | ||
0.813796 | − | 0.581151i | \(-0.197397\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7920.00 | −0.993724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10714.0 | −1.33424 | −0.667122 | − | 0.744949i | \(-0.732474\pi\) | ||||
−0.667122 | + | 0.744949i | \(0.732474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5520.00i | 0.682310i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −810.000 | + | 405.000i | −0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5684.00i | − | 0.692249i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12346.0 | 1.49259 | 0.746296 | − | 0.665614i | \(-0.231830\pi\) | ||||
0.746296 | + | 0.665614i | \(0.231830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7002.00 | 0.840348 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5852.00i | − | 0.697235i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2740.00 | + | 5480.00i | 0.324100 | + | 0.648199i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5028.00i | 0.590461i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13562.0 | 1.58126 | 0.790629 | − | 0.612296i | \(-0.209754\pi\) | ||||
0.790629 | + | 0.612296i | \(0.209754\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5230.00 | 0.605450 | 0.302725 | − | 0.953078i | \(-0.402104\pi\) | ||||
0.302725 | + | 0.953078i | \(0.402104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4032.00i | − | 0.463458i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6200.00 | + | 4650.00i | 0.707633 | + | 0.530725i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 18436.0i | − | 2.08942i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1260.00 | 0.141803 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11552.0 | −1.29104 | −0.645522 | − | 0.763741i | \(-0.723360\pi\) | ||||
−0.645522 | + | 0.763741i | \(0.723360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7972.00i | − | 0.884780i | −0.896823 | − | 0.442390i | \(-0.854131\pi\) | ||
0.896823 | − | 0.442390i | \(-0.145869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1440.00 | + | 2880.00i | 0.158719 | + | 0.317438i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 22560.0i | − | 2.46954i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7152.00 | −0.777554 | −0.388777 | − | 0.921332i | \(-0.627102\pi\) | ||||
−0.388777 | + | 0.921332i | \(0.627102\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1269.00 | 0.137026 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2652.00i | − | 0.284425i | −0.989836 | − | 0.142213i | \(-0.954578\pi\) | ||
0.989836 | − | 0.142213i | \(-0.0454217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6500.00 | + | 3250.00i | −0.692426 | + | 0.346213i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 10356.0i | − | 1.09580i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4542.00 | −0.477395 | −0.238697 | − | 0.971094i | \(-0.576720\pi\) | ||||
−0.238697 | + | 0.971094i | \(0.576720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1820.00 | −0.190023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5160.00i | 0.535183i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6600.00 | − | 3300.00i | 0.680028 | − | 0.340014i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16000.0i | 1.63774i | 0.573977 | + | 0.818871i | \(0.305400\pi\) | ||||
−0.573977 | + | 0.818871i | \(0.694600\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1674.00 | 0.170230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2076.00 | 0.209737 | 0.104869 | − | 0.994486i | \(-0.466558\pi\) | ||||
0.104869 | + | 0.994486i | \(0.466558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5406.00i | 0.542631i | 0.962490 | + | 0.271315i | \(0.0874587\pi\) | ||||
−0.962490 | + | 0.271315i | \(0.912541\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2760.00 | − | 5520.00i | −0.275251 | − | 0.550503i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 444.000i | − | 0.0439954i | −0.999758 | − | 0.0219977i | \(-0.992997\pi\) | ||
0.999758 | − | 0.0219977i | \(-0.00700266\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5456.00 | −0.537174 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3738.00 | 0.365686 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2072.00i | 0.201418i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9000.00 | − | 12000.0i | 0.869365 | − | 1.15915i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3726.00i | − | 0.357656i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1724.00 | 0.164450 | 0.0822250 | − | 0.996614i | \(-0.473797\pi\) | ||||
0.0822250 | + | 0.996614i | \(0.473797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12180.0 | −1.15460 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12408.0i | 1.16891i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9080.00 | + | 18160.0i | 0.850106 | + | 1.70021i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17046.0i | − | 1.58609i | −0.609160 | − | 0.793047i | \(-0.708493\pi\) | ||
0.609160 | − | 0.793047i | \(-0.291507\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5280.00 | 0.488282 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8814.00 | 0.810123 | 0.405061 | − | 0.914290i | \(-0.367250\pi\) | ||||
0.405061 | + | 0.914290i | \(0.367250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5952.00i | − | 0.543742i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1260.00 | + | 630.000i | −0.114410 | + | 0.0572048i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22440.0i | 2.02529i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5256.00 | −0.471525 | −0.235762 | − | 0.971811i | \(-0.575759\pi\) | ||||
−0.235762 | + | 0.971811i | \(0.575759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8172.00 | 0.728739 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5232.00i | − | 0.463784i | −0.972742 | − | 0.231892i | \(-0.925508\pi\) | ||
0.972742 | − | 0.231892i | \(-0.0744916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16880.0 | + | 8440.00i | −1.48743 | + | 0.743713i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3891.00i | 0.340839i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4128.00 | −0.359470 | −0.179735 | − | 0.983715i | \(-0.557524\pi\) | ||||
−0.179735 | + | 0.983715i | \(0.557524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10648.0 | 0.921800 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3240.00i | − | 0.278849i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1490.00 | − | 2980.00i | −0.127490 | − | 0.254980i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6272.00i | − | 0.533544i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7134.00 | −0.603368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −538.000 | −0.0452403 | −0.0226202 | − | 0.999744i | \(-0.507201\pi\) | ||||
−0.0226202 | + | 0.999744i | \(0.507201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10336.0i | 0.864172i | 0.901833 | + | 0.432086i | \(0.142222\pi\) | ||||
−0.901833 | + | 0.432086i | \(0.857778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4950.00 | + | 6600.00i | −0.411497 | + | 0.548662i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11408.0i | 0.942961i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23177.0 | −1.90491 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2394.00 | 0.195651 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3900.00i | 0.316938i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1380.00 | − | 2760.00i | −0.111519 | − | 0.223038i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9282.00i | 0.745899i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1974.00 | 0.157748 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8942.00 | −0.710622 | −0.355311 | − | 0.934748i | \(-0.615625\pi\) | ||||
−0.355311 | + | 0.934748i | \(0.615625\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 930.000i | − | 0.0734993i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3220.00 | − | 1610.00i | 0.253082 | − | 0.126541i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11404.0i | 0.891407i | 0.895181 | + | 0.445704i | \(0.147046\pi\) | ||||
−0.895181 | + | 0.445704i | \(0.852954\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7542.00 | 0.586311 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11520.0 | −0.890687 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1056.00i | 0.0812038i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12180.0 | − | 6090.00i | 0.931554 | − | 0.465777i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3114.00i | 0.236884i | 0.992961 | + | 0.118442i | \(0.0377900\pi\) | ||||
−0.992961 | + | 0.118442i | \(0.962210\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4440.00 | 0.335943 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2604.00 | 0.195973 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3620.00i | 0.270985i | 0.990778 | + | 0.135493i | \(0.0432617\pi\) | ||||
−0.990778 | + | 0.135493i | \(0.956738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2430.00 | − | 4860.00i | −0.180940 | − | 0.361879i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1782.00i | 0.131988i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6506.00 | 0.479342 | 0.239671 | − | 0.970854i | \(-0.422960\pi\) | ||||
0.239671 | + | 0.970854i | \(0.422960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17600.0 | −1.28991 | −0.644954 | − | 0.764222i | \(-0.723123\pi\) | ||||
−0.644954 | + | 0.764222i | \(0.723123\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1548.00i | − | 0.112860i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18800.0 | − | 14100.0i | −1.36350 | − | 1.02263i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4864.00i | 0.350938i | 0.984485 | + | 0.175469i | \(0.0561441\pi\) | ||||
−0.984485 | + | 0.175469i | \(0.943856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −564.000 | −0.0404819 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12056.0 | 0.860873 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5796.00i | − | 0.411742i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1350.00 | + | 2700.00i | 0.0954113 | + | 0.190823i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18348.0i | − | 1.29012i | −0.764130 | − | 0.645062i | \(-0.776831\pi\) | ||
0.764130 | − | 0.645062i | \(-0.223169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22080.0 | 1.54464 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7734.00 | −0.538298 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16218.0i | − | 1.12309i | −0.827446 | − | 0.561546i | \(-0.810207\pi\) | ||
0.827446 | − | 0.561546i | \(-0.189793\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13640.0 | − | 6820.00i | 0.939808 | − | 0.469904i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1584.00i | 0.108591i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24576.0 | 1.67637 | 0.838187 | − | 0.545383i | \(-0.183616\pi\) | ||||
0.838187 | + | 0.545383i | \(0.183616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6578.00 | 0.446460 | 0.223230 | − | 0.974766i | \(-0.428340\pi\) | ||||
0.223230 | + | 0.974766i | \(0.428340\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 2232.00i | − | 0.150736i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11350.0 | − | 5675.00i | 0.762716 | − | 0.381358i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25346.0i | 1.69483i | 0.530930 | + | 0.847415i | \(0.321843\pi\) | ||||
−0.530930 | + | 0.847415i | \(0.678157\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6336.00 | 0.421589 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13440.0 | −0.889892 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 27214.0i | − | 1.79309i | −0.442954 | − | 0.896544i | \(-0.646070\pi\) | ||
0.442954 | − | 0.896544i | \(-0.353930\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1950.00 | − | 3900.00i | −0.127856 | − | 0.255712i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22478.0i | 1.46666i | 0.679872 | + | 0.733331i | \(0.262035\pi\) | ||||
−0.679872 | + | 0.733331i | \(0.737965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3356.00 | −0.217914 | −0.108957 | − | 0.994046i | \(-0.534751\pi\) | ||||
−0.108957 | + | 0.994046i | \(0.534751\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5076.00 | −0.328008 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14300.0i | 0.919611i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4375.00 | − | 15000.0i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 5040.00i | − | 0.321018i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25172.0 | −1.59567 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19952.0 | 1.25876 | 0.629379 | − | 0.777098i | \(-0.283309\pi\) | ||||
0.629379 | + | 0.777098i | \(0.283309\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10980.0i | − | 0.689440i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2510.00 | − | 5020.00i | −0.156860 | − | 0.313721i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4230.00i | − | 0.263106i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9180.00 | −0.568318 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26434.0 | 1.62883 | 0.814415 | − | 0.580283i | \(-0.197058\pi\) | ||||
0.814415 | + | 0.580283i | \(0.197058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10632.0i | − | 0.652076i | −0.945357 | − | 0.326038i | \(-0.894286\pi\) | ||
0.945357 | − | 0.326038i | \(-0.105714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4440.00 | + | 2220.00i | −0.271046 | + | 0.135523i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9384.00i | − | 0.570206i | −0.958497 | − | 0.285103i | \(-0.907972\pi\) | ||
0.958497 | − | 0.285103i | \(-0.0920278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3724.00 | 0.225239 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12144.0 | −0.731123 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3922.00i | 0.235038i | 0.993071 | + | 0.117519i | \(0.0374941\pi\) | ||||
−0.993071 | + | 0.117519i | \(0.962506\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 180.000 | − | 90.0000i | 0.0107377 | − | 0.00536884i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4356.00i | 0.258666i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12542.0 | −0.741376 | −0.370688 | − | 0.928757i | \(-0.620878\pi\) | ||||
−0.370688 | + | 0.928757i | \(0.620878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8662.00 | −0.509702 | −0.254851 | − | 0.966980i | \(-0.582026\pi\) | ||||
−0.254851 | + | 0.966980i | \(0.582026\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 5580.00i | − | 0.326862i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13200.0 | − | 26400.0i | −0.769735 | − | 1.53947i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18048.0i | 1.04771i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7050.00 | 0.407427 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11732.0 | 0.674976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5820.00i | − | 0.333350i | −0.986012 | − | 0.166675i | \(-0.946697\pi\) | ||
0.986012 | − | 0.166675i | \(-0.0533031\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2700.00 | − | 2025.00i | −0.153960 | − | 0.115470i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 778.000i | − | 0.0441669i | −0.999756 | − | 0.0220834i | \(-0.992970\pi\) | ||
0.999756 | − | 0.0220834i | \(-0.00702995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39952.0 | 2.25805 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9780.00 | −0.550324 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5548.00i | 0.310817i | 0.987850 | + | 0.155409i | \(0.0496695\pi\) | ||||
−0.987850 | + | 0.155409i | \(0.950331\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11670.0 | + | 23340.0i | 0.650931 | + | 1.30186i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1398.00i | 0.0776376i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12420.0 | −0.686741 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5488.00 | 0.302132 | 0.151066 | − | 0.988524i | \(-0.451729\pi\) | ||||
0.151066 | + | 0.988524i | \(0.451729\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2772.00i | 0.151947i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16760.0 | + | 8380.00i | −0.914738 | + | 0.457369i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8060.00i | 0.438012i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9510.00 | −0.514594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1216.00 | 0.0655174 | 0.0327587 | − | 0.999463i | \(-0.489571\pi\) | ||||
0.0327587 | + | 0.999463i | \(0.489571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48720.0i | 2.61381i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13440.0 | − | 6720.00i | 0.717985 | − | 0.358993i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37136.0i | 1.97545i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20406.0 | −1.08091 | −0.540454 | − | 0.841374i | \(-0.681747\pi\) | ||||
−0.540454 | + | 0.841374i | \(0.681747\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −432.000 | −0.0227866 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 34592.0i | − | 1.81694i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2100.00 | + | 4200.00i | 0.109840 | + | 0.219680i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 876.000i | − | 0.0456274i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19672.0 | −1.02036 | −0.510182 | − | 0.860066i | \(-0.670422\pi\) | ||||
−0.510182 | + | 0.860066i | \(0.670422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6556.00 | −0.338638 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2526.00i | − | 0.129935i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7200.00 | + | 9600.00i | −0.368829 | + | 0.491772i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1194.00i | 0.0609120i | 0.999536 | + | 0.0304560i | \(0.00969594\pi\) | ||||
−0.999536 | + | 0.0304560i | \(0.990304\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9176.00 | 0.464277 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21802.0i | 1.09860i | 0.835625 | + | 0.549301i | \(0.185106\pi\) | ||||
−0.835625 | + | 0.549301i | \(0.814894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2115.00 | + | 4230.00i | 0.106140 | + | 0.212280i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3472.00i | − | 0.173532i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15280.0 | −0.760601 | −0.380300 | − | 0.924863i | \(-0.624179\pi\) | ||||
−0.380300 | + | 0.924863i | \(0.624179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10800.0 | −0.535422 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6672.00i | − | 0.329437i | −0.986341 | − | 0.164719i | \(-0.947328\pi\) | ||
0.986341 | − | 0.164719i | \(-0.0526716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34520.0 | − | 17260.0i | 1.69760 | − | 0.848802i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4932.00i | 0.241570i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6072.00 | −0.296216 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11008.0 | −0.534870 | −0.267435 | − | 0.963576i | \(-0.586176\pi\) | ||||
−0.267435 | + | 0.963576i | \(0.586176\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17514.0i | 0.847604i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17200.0 | + | 8600.00i | −0.829102 | + | 0.414551i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 3242.00i | − | 0.155657i | −0.996967 | − | 0.0778286i | \(-0.975201\pi\) | ||
0.996967 | − | 0.0778286i | \(-0.0247987\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7896.00 | −0.377611 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17982.0 | 0.856566 | 0.428283 | − | 0.903645i | \(-0.359119\pi\) | ||||
0.428283 | + | 0.903645i | \(0.359119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 7084.00i | − | 0.336118i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2790.00 | + | 5580.00i | 0.131860 | + | 0.263719i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 7980.00i | − | 0.375673i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30462.0 | 1.42846 | 0.714231 | − | 0.699910i | \(-0.246776\pi\) | ||||
0.714231 | + | 0.699910i | \(0.246776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13878.0 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17394.0i | 0.809339i | 0.914463 | + | 0.404669i | \(0.132613\pi\) | ||||
−0.914463 | + | 0.404669i | \(0.867387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13800.0 | − | 18400.0i | 0.639627 | − | 0.852835i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 26796.0i | − | 1.23720i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15600.0 | 0.717494 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14280.0 | −0.654262 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2592.00i | 0.118302i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6230.00 | + | 12460.0i | 0.283259 | + | 0.566518i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20336.0i | − | 0.921093i | −0.887636 | − | 0.460546i | \(-0.847653\pi\) | ||
0.887636 | − | 0.460546i | \(-0.152347\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16404.0 | 0.740175 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10692.0 | −0.480612 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25140.0i | − | 1.12579i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12420.0 | − | 6210.00i | 0.554078 | − | 0.277039i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 19546.0i | − | 0.868701i | −0.900744 | − | 0.434351i | \(-0.856978\pi\) | ||
0.900744 | − | 0.434351i | \(-0.143022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27776.0 | −1.22984 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5850.00 | −0.258052 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6776.00i | 0.297783i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41360.0 | + | 20680.0i | −1.81087 | + | 0.905434i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8928.00i | 0.389443i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3954.00 | −0.171836 | −0.0859179 | − | 0.996302i | \(-0.527382\pi\) | ||||
−0.0859179 | + | 0.996302i | \(0.527382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3860.00 | −0.167131 | −0.0835653 | − | 0.996502i | \(-0.526631\pi\) | ||||
−0.0835653 | + | 0.996502i | \(0.526631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 168.000i | − | 0.00724725i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8800.00 | + | 17600.0i | 0.378222 | + | 0.756443i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 17760.0i | − | 0.760519i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5940.00 | 0.253431 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37016.0 | 1.57353 | 0.786764 | − | 0.617253i | \(-0.211755\pi\) | ||||
0.786764 | + | 0.617253i | \(0.211755\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25794.0i | − | 1.09249i | −0.837624 | − | 0.546247i | \(-0.816056\pi\) | ||
0.837624 | − | 0.546247i | \(-0.183944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4200.00 | − | 3150.00i | −0.177243 | − | 0.132932i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 44116.0i | − | 1.85497i | −0.373855 | − | 0.927487i | \(-0.621964\pi\) | ||
0.373855 | − | 0.927487i | \(-0.378036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11622.0 | 0.486910 | 0.243455 | − | 0.969912i | \(-0.421719\pi\) | ||||
0.243455 | + | 0.969912i | \(0.421719\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12318.0 | 0.514208 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 8742.00i | − | 0.363616i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13620.0 | + | 27240.0i | 0.564478 | + | 1.12896i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4968.00i | − | 0.205160i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2584.00 | 0.106328 | 0.0531642 | − | 0.998586i | \(-0.483069\pi\) | ||||
0.0531642 | + | 0.998586i | \(0.483069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15173.0 | −0.622125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 6822.00i | − | 0.278721i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12970.0 | + | 6485.00i | −0.528026 | + | 0.264013i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 24970.0i | − | 1.01296i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16512.0 | 0.667480 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 76328.0 | 3.07461 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39754.0i | 1.59572i | 0.602841 | + | 0.797861i | \(0.294035\pi\) | ||||
−0.602841 | + | 0.797861i | \(0.705965\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10800.0 | − | 5400.00i | 0.431991 | − | 0.215995i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18534.0i | 0.738751i | 0.929280 | + | 0.369375i | \(0.120428\pi\) | ||||
−0.929280 | + | 0.369375i | \(0.879572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11140.0 | 0.442482 | 0.221241 | − | 0.975219i | \(-0.428989\pi\) | ||||
0.221241 | + | 0.975219i | \(0.428989\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8580.00 | −0.339612 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 28356.0i | − | 1.11848i | −0.829005 | − | 0.559241i | \(-0.811093\pi\) | ||
0.829005 | − | 0.559241i | \(-0.188907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11890.0 | − | 23780.0i | −0.467367 | − | 0.934733i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3207.00i | 0.125623i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −672.000 | −0.0262325 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7440.00 | −0.289431 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16344.0i | 0.633632i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30250.0 | − | 5500.00i | −1.16873 | − | 0.212496i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 34942.0i | − | 1.34539i | −0.739920 | − | 0.672695i | \(-0.765137\pi\) | ||
0.739920 | − | 0.672695i | \(-0.234863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24102.0 | 0.924847 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13890.0 | −0.531176 | −0.265588 | − | 0.964087i | \(-0.585566\pi\) | ||||
−0.265588 | + | 0.964087i | \(0.585566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 11496.0i | − | 0.438133i | −0.975710 | − | 0.219066i | \(-0.929699\pi\) | ||
0.975710 | − | 0.219066i | \(-0.0703011\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3990.00 | + | 7980.00i | 0.151551 | + | 0.303101i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 29988.0i | − | 1.13517i | −0.823314 | − | 0.567587i | \(-0.807877\pi\) | ||
0.823314 | − | 0.567587i | \(-0.192123\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11044.0 | −0.416652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1134.00 | −0.0426380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53760.0i | 2.01457i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30940.0 | + | 15470.0i | −1.15554 | + | 0.577771i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16920.0i | 0.629813i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17664.0 | −0.655314 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25668.0 | −0.949084 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9768.00i | 0.359976i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3100.00 | − | 1550.00i | 0.113865 | − | 0.0569323i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16764.0i | − | 0.613715i | −0.951755 | − | 0.306857i | \(-0.900723\pi\) | ||
0.951755 | − | 0.306857i | \(-0.0992775\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15192.0 | −0.554331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19152.0 | −0.696525 | −0.348262 | − | 0.937397i | \(-0.613228\pi\) | ||||
−0.348262 | + | 0.937397i | \(0.613228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7672.00i | 0.278101i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12570.0 | + | 25140.0i | 0.454155 | + | 0.908309i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 396.000i | − | 0.0142607i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35712.0 | −1.28186 | −0.640930 | − | 0.767599i | \(-0.721451\pi\) | ||||
−0.640930 | + | 0.767599i | \(0.721451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2988.00 | −0.106903 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30600.0i | 1.09124i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40600.0 | + | 30450.0i | 1.44316 | + | 1.08237i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2682.00i | − | 0.0950253i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16098.0 | 0.568523 | 0.284262 | − | 0.958747i | \(-0.408252\pi\) | ||||
0.284262 | + | 0.958747i | \(0.408252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16920.0 | −0.595629 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 26028.0i | − | 0.913310i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4340.00 | + | 8680.00i | 0.151800 | + | 0.303600i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24776.0i | 0.863817i | 0.901917 | + | 0.431909i | \(0.142160\pi\) | ||||
−0.901917 | + | 0.431909i | \(0.857840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5196.00 | 0.180580 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39500.0 | −1.36840 | −0.684199 | − | 0.729295i | \(-0.739848\pi\) | ||||
−0.684199 | + | 0.729295i | \(0.739848\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 24440.0i | − | 0.843983i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5940.00 | + | 2970.00i | −0.204474 | + | 0.102237i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22836.0i | 0.783601i | 0.920050 | + | 0.391801i | \(0.128148\pi\) | ||||
−0.920050 | + | 0.391801i | \(0.871852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14520.0 | 0.496669 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8814.00 | 0.300540 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28478.0i | 0.967988i | 0.875071 | + | 0.483994i | \(0.160814\pi\) | ||||
−0.875071 | + | 0.483994i | \(0.839186\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5160.00 | − | 2580.00i | 0.174842 | − | 0.0874208i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4032.00i | 0.136192i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 51348.0 | 1.72900 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4065.00 | 0.136451 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2484.00i | − | 0.0831213i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −940.000 | − | 1880.00i | −0.0313572 | − | 0.0627143i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24830.0i | 0.825728i | 0.910793 | + | 0.412864i | \(0.135472\pi\) | ||||
−0.910793 | + | 0.412864i | \(0.864528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22320.0 | −0.739960 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37038.0 | 1.22411 | 0.612053 | − | 0.790817i | \(-0.290344\pi\) | ||||
0.612053 | + | 0.790817i | \(0.290344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36872.0i | 1.21486i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6750.00 | + | 9000.00i | −0.221716 | + | 0.295621i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26346.0i | − | 0.862726i | −0.902178 | − | 0.431363i | \(-0.858033\pi\) | ||
0.902178 | − | 0.431363i | \(-0.141967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9100.00 | −0.297076 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2898.00 | 0.0943181 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 11464.0i | − | 0.371968i | −0.982553 | − | 0.185984i | \(-0.940453\pi\) | ||
0.982553 | − | 0.185984i | \(-0.0595473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12890.0 | − | 25780.0i | −0.416964 | − | 0.833928i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 29568.0i | − | 0.953556i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27824.0 | −0.894592 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28952.0 | −0.928043 | −0.464021 | − | 0.885824i | \(-0.653594\pi\) | ||||
−0.464021 | + | 0.885824i | \(0.653594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 384.000i | − | 0.0122718i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5280.00 | + | 2640.00i | −0.168228 | + | 0.0841142i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 8022.00i | − | 0.254824i | −0.991850 | − | 0.127412i | \(-0.959333\pi\) | ||
0.991850 | − | 0.127412i | \(-0.0406670\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10962.0 | 0.347170 |
(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 | 60.4.d.a.49.2 | yes | 2 | |
3.2 | odd | 2 | 180.4.d.b.109.1 | 2 | |||
4.3 | odd | 2 | 240.4.f.a.49.1 | 2 | |||
5.2 | odd | 4 | 300.4.a.f.1.1 | 1 | |||
5.3 | odd | 4 | 300.4.a.d.1.1 | 1 | |||
5.4 | even | 2 | inner | 60.4.d.a.49.1 | ✓ | 2 | |
8.3 | odd | 2 | 960.4.f.i.769.2 | 2 | |||
8.5 | even | 2 | 960.4.f.j.769.1 | 2 | |||
12.11 | even | 2 | 720.4.f.h.289.1 | 2 | |||
15.2 | even | 4 | 900.4.a.d.1.1 | 1 | |||
15.8 | even | 4 | 900.4.a.o.1.1 | 1 | |||
15.14 | odd | 2 | 180.4.d.b.109.2 | 2 | |||
20.3 | even | 4 | 1200.4.a.w.1.1 | 1 | |||
20.7 | even | 4 | 1200.4.a.q.1.1 | 1 | |||
20.19 | odd | 2 | 240.4.f.a.49.2 | 2 | |||
40.19 | odd | 2 | 960.4.f.i.769.1 | 2 | |||
40.29 | even | 2 | 960.4.f.j.769.2 | 2 | |||
60.59 | even | 2 | 720.4.f.h.289.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.d.a.49.1 | ✓ | 2 | 5.4 | even | 2 | inner | |
60.4.d.a.49.2 | yes | 2 | 1.1 | even | 1 | trivial | |
180.4.d.b.109.1 | 2 | 3.2 | odd | 2 | |||
180.4.d.b.109.2 | 2 | 15.14 | odd | 2 | |||
240.4.f.a.49.1 | 2 | 4.3 | odd | 2 | |||
240.4.f.a.49.2 | 2 | 20.19 | odd | 2 | |||
300.4.a.d.1.1 | 1 | 5.3 | odd | 4 | |||
300.4.a.f.1.1 | 1 | 5.2 | odd | 4 | |||
720.4.f.h.289.1 | 2 | 12.11 | even | 2 | |||
720.4.f.h.289.2 | 2 | 60.59 | even | 2 | |||
900.4.a.d.1.1 | 1 | 15.2 | even | 4 | |||
900.4.a.o.1.1 | 1 | 15.8 | even | 4 | |||
960.4.f.i.769.1 | 2 | 40.19 | odd | 2 | |||
960.4.f.i.769.2 | 2 | 8.3 | odd | 2 | |||
960.4.f.j.769.1 | 2 | 8.5 | even | 2 | |||
960.4.f.j.769.2 | 2 | 40.29 | even | 2 | |||
1200.4.a.q.1.1 | 1 | 20.7 | even | 4 | |||
1200.4.a.w.1.1 | 1 | 20.3 | even | 4 |