Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(513,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1024.513");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.b (of order \(2\), degree \(1\), 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: | \(60.4179558459\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 36x^{8} + 405x^{6} + 1380x^{4} + 420x^{2} + 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 513.6 | ||
Root | \(-3.94652i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.513 |
Dual form | 1024.4.b.k.513.5 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.07024i | 0.205968i | 0.994683 | + | 0.102984i | \(0.0328391\pi\) | ||||
−0.994683 | + | 0.102984i | \(0.967161\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 11.6331i | − 1.04050i | −0.854014 | − | 0.520250i | \(-0.825839\pi\) | ||||
0.854014 | − | 0.520250i | \(-0.174161\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.67171 | 0.144259 | 0.0721293 | − | 0.997395i | \(-0.477021\pi\) | ||||
0.0721293 | + | 0.997395i | \(0.477021\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 25.8546 | 0.957577 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 63.9525i | 1.75295i | 0.481451 | + | 0.876473i | \(0.340110\pi\) | ||||
−0.481451 | + | 0.876473i | \(0.659890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.0586i | 1.06798i | 0.845491 | + | 0.533990i | \(0.179308\pi\) | ||||
−0.845491 | + | 0.533990i | \(0.820692\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 12.4503 | 0.214310 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 72.4991 | 1.03433 | 0.517165 | − | 0.855886i | \(-0.326987\pi\) | ||||
0.517165 | + | 0.855886i | \(0.326987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 27.4961i | − 0.332002i | −0.986126 | − | 0.166001i | \(-0.946915\pi\) | ||||
0.986126 | − | 0.166001i | \(-0.0530855\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.85937i | 0.0297127i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −139.462 | −1.26434 | −0.632170 | − | 0.774830i | \(-0.717835\pi\) | ||||
−0.632170 | + | 0.774830i | \(0.717835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.3299 | −0.0826390 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 56.5672i | 0.403199i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 93.3995i | − 0.598064i | −0.954243 | − | 0.299032i | \(-0.903336\pi\) | ||||
0.954243 | − | 0.299032i | \(-0.0966637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −188.682 | −1.09317 | −0.546584 | − | 0.837404i | \(-0.684072\pi\) | ||||
−0.546584 | + | 0.837404i | \(0.684072\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −68.4447 | −0.361051 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 31.0803i | − 0.150101i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 118.886i | 0.528238i | 0.964490 | + | 0.264119i | \(0.0850811\pi\) | ||||
−0.964490 | + | 0.264119i | \(0.914919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −53.5748 | −0.219970 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −104.629 | −0.398545 | −0.199272 | − | 0.979944i | \(-0.563858\pi\) | ||||
−0.199272 | + | 0.979944i | \(0.563858\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 44.5275i | 0.157916i | 0.996878 | + | 0.0789579i | \(0.0251593\pi\) | ||||
−0.996878 | + | 0.0789579i | \(0.974841\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 300.770i | − 0.996358i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −488.151 | −1.51498 | −0.757491 | − | 0.652846i | \(-0.773575\pi\) | ||||
−0.757491 | + | 0.652846i | \(0.773575\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −335.862 | −0.979189 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 77.5916i | 0.213039i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 211.510i | 0.548173i | 0.961705 | + | 0.274087i | \(0.0883755\pi\) | ||||
−0.961705 | + | 0.274087i | \(0.911624\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 743.968 | 1.82394 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 29.4275 | 0.0683819 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 402.624i | 0.888426i | 0.895921 | + | 0.444213i | \(0.146517\pi\) | ||||
−0.895921 | + | 0.444213i | \(0.853483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 322.538i | 0.676997i | 0.940967 | + | 0.338498i | \(0.109919\pi\) | ||||
−0.940967 | + | 0.338498i | \(0.890081\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 69.0758 | 0.138139 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 582.338 | 1.11123 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 196.789i | 0.358829i | 0.983774 | + | 0.179415i | \(0.0574203\pi\) | ||||
−0.983774 | + | 0.179415i | \(0.942580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 149.258i | − 0.260414i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 453.655 | 0.758294 | 0.379147 | − | 0.925336i | \(-0.376217\pi\) | ||||
0.379147 | + | 0.925336i | \(0.376217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 259.747 | 0.416454 | 0.208227 | − | 0.978081i | \(-0.433231\pi\) | ||||
0.208227 | + | 0.978081i | \(0.433231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 11.0555i | − 0.0170210i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 170.862i | 0.252877i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 323.190 | 0.460275 | 0.230138 | − | 0.973158i | \(-0.426082\pi\) | ||||
0.230138 | + | 0.973158i | \(0.426082\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 637.533 | 0.874531 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 797.471i | 1.05462i | 0.849672 | + | 0.527312i | \(0.176800\pi\) | ||||
−0.849672 | + | 0.527312i | \(0.823200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 843.392i | − 1.07622i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 99.9602 | 0.123182 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 866.853 | 1.03243 | 0.516215 | − | 0.856459i | \(-0.327341\pi\) | ||||
0.516215 | + | 0.856459i | \(0.327341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 133.742i | 0.154065i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 201.935i | − 0.225158i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −319.866 | −0.345448 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −936.077 | −0.979837 | −0.489919 | − | 0.871768i | \(-0.662974\pi\) | ||||
−0.489919 | + | 0.871768i | \(0.662974\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1653.47i | 1.67858i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.24639i | 0.00221311i | 0.999999 | + | 0.00110656i | \(0.000352228\pi\) | ||||
−0.999999 | + | 0.00110656i | \(0.999648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1388.28 | 1.32807 | 0.664036 | − | 0.747700i | \(-0.268842\pi\) | ||||
0.664036 | + | 0.747700i | \(0.268842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 33.2635 | 0.0309160 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1161.81i | 1.04969i | 0.851198 | + | 0.524845i | \(0.175877\pi\) | ||||
−0.851198 | + | 0.524845i | \(0.824123\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 753.489i | 0.662121i | 0.943610 | + | 0.331060i | \(0.107406\pi\) | ||||
−0.943610 | + | 0.331060i | \(0.892594\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −127.237 | −0.108800 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 67.2680 | 0.0560003 | 0.0280002 | − | 0.999608i | \(-0.491086\pi\) | ||||
0.0280002 | + | 0.999608i | \(0.491086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1622.38i | 1.31554i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1294.24i | 1.02267i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 193.696 | 0.149211 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2758.92 | −2.07282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 111.979i | − 0.0820876i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1333.97i | − 0.954514i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1903.59 | −1.33005 | −0.665026 | − | 0.746820i | \(-0.731579\pi\) | ||||
−0.665026 | + | 0.746820i | \(0.731579\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −47.6552 | −0.0325257 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1298.86i | 0.866271i | 0.901329 | + | 0.433136i | \(0.142593\pi\) | ||||
−0.901329 | + | 0.433136i | \(0.857407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 73.4615i | − 0.0478941i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 658.054 | 0.419528 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −477.234 | −0.297612 | −0.148806 | − | 0.988866i | \(-0.547543\pi\) | ||||
−0.148806 | + | 0.988866i | \(0.547543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2140.97i | 1.30643i | 0.757171 | + | 0.653217i | \(0.226581\pi\) | ||||
−0.757171 | + | 0.653217i | \(0.773419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 522.440i | − 0.312038i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3201.37 | −1.87211 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1086.53 | −0.622285 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 359.454i | − 0.201682i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 530.829i | 0.291861i | 0.989295 | + | 0.145930i | \(0.0466175\pi\) | ||||
−0.989295 | + | 0.145930i | \(0.953382\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2997.52 | 1.61546 | 0.807730 | − | 0.589553i | \(-0.200696\pi\) | ||||
0.807730 | + | 0.589553i | \(0.200696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1874.43 | 0.990451 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2194.96i | 1.13744i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2134.06i | 1.08482i | 0.840115 | + | 0.542409i | \(0.182488\pi\) | ||||
−0.840115 | + | 0.542409i | \(0.817512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −226.368 | −0.112906 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −372.601 | −0.182392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2015.52i | − 0.968515i | −0.874925 | − | 0.484258i | \(-0.839090\pi\) | ||||
0.874925 | − | 0.484258i | \(-0.160910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 796.227i | 0.375674i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 792.415 | 0.367179 | 0.183590 | − | 0.983003i | \(-0.441228\pi\) | ||||
0.183590 | + | 0.983003i | \(0.441228\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −308.861 | −0.140583 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 710.900i | − 0.317917i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1094.03i | − 0.480794i | −0.970675 | − | 0.240397i | \(-0.922722\pi\) | ||||
0.970675 | − | 0.240397i | \(-0.0772776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.5984 | −0.0119214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −430.905 | −0.182988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 602.526i | − 0.251592i | −0.992056 | − | 0.125796i | \(-0.959852\pi\) | ||||
0.992056 | − | 0.125796i | \(-0.0401484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3702.50i | − 1.52047i | −0.649649 | − | 0.760234i | \(-0.725084\pi\) | ||||
0.649649 | − | 0.760234i | \(-0.274916\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −345.194 | −0.139440 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1383.02 | 0.549631 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4636.50i | 1.81312i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 151.131i | 0.0581649i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3216.39 | −1.21848 | −0.609240 | − | 0.792986i | \(-0.708525\pi\) | ||||
−0.609240 | + | 0.792986i | \(0.708525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2852.57 | 1.06390 | 0.531950 | − | 0.846776i | \(-0.321459\pi\) | ||||
0.531950 | + | 0.846776i | \(0.321459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 623.243i | 0.228879i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2275.50i | − 0.822956i | −0.911420 | − | 0.411478i | \(-0.865013\pi\) | ||||
0.911420 | − | 0.411478i | \(-0.134987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −747.136 | −0.266146 | −0.133073 | − | 0.991106i | \(-0.542484\pi\) | ||||
−0.133073 | + | 0.991106i | \(0.542484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −210.612 | −0.0739074 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 249.536i | − 0.0862758i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1217.17i | 0.414685i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3605.73 | −1.21070 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1758.44 | 0.581981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3149.64i | 1.02763i | 0.857901 | + | 0.513816i | \(0.171769\pi\) | ||||
−0.857901 | + | 0.513816i | \(0.828231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 485.520i | 0.156185i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 517.995 | 0.164311 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −504.102 | −0.157699 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 277.993i | 0.0857763i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3629.20i | 1.10464i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 358.053 | 0.107520 | 0.0537601 | − | 0.998554i | \(-0.482879\pi\) | ||||
0.0537601 | + | 0.998554i | \(0.482879\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −267.075 | −0.0791332 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4886.67i | 1.42881i | 0.699733 | + | 0.714404i | \(0.253302\pi\) | ||||
−0.699733 | + | 0.714404i | \(0.746698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2022.37i | 0.583589i | 0.956481 | + | 0.291794i | \(0.0942523\pi\) | ||||
−0.956481 | + | 0.291794i | \(0.905748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −182.864 | −0.0520847 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 926.479 | 0.260496 | 0.130248 | − | 0.991481i | \(-0.458423\pi\) | ||||
0.130248 | + | 0.991481i | \(0.458423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5678.73i | 1.57634i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 345.892i | 0.0948021i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −792.472 | −0.214480 | −0.107240 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107240 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1449.01 | −0.387299 | −0.193650 | − | 0.981071i | \(-0.562033\pi\) | ||||
−0.193650 | + | 0.981071i | \(0.562033\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2209.63i | 0.583325i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3907.13i | 1.01885i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1376.42 | 0.354572 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −853.487 | −0.217219 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 5062.94i | − 1.27319i | −0.771199 | − | 0.636594i | \(-0.780343\pi\) | ||||
0.771199 | − | 0.636594i | \(-0.219657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 8918.93i | − 2.21632i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 902.634 | 0.221667 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4708.87 | −1.14292 | −0.571461 | − | 0.820629i | \(-0.693623\pi\) | ||||
−0.571461 | + | 0.820629i | \(0.693623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 317.629i | 0.0762028i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2414.81i | − 0.572692i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2967.82 | 0.695830 | 0.347915 | − | 0.937526i | \(-0.386890\pi\) | ||||
0.347915 | + | 0.937526i | \(0.386890\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2460.53 | 0.570374 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 927.743i | 0.212648i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 938.519i | − 0.212723i | −0.994328 | − | 0.106362i | \(-0.966080\pi\) | ||||
0.994328 | − | 0.106362i | \(-0.0339201\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8058.74 | 1.80640 | 0.903199 | − | 0.429223i | \(-0.141212\pi\) | ||||
0.903199 | + | 0.429223i | \(0.141212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −143.136 | −0.0317326 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 660.622i | − 0.144862i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 682.325i | 0.148003i | 0.997258 | + | 0.0740017i | \(0.0235770\pi\) | ||||
−0.997258 | + | 0.0740017i | \(0.976423\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4878.29 | −1.04679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5899.10 | −1.25235 | −0.626175 | − | 0.779682i | \(-0.715381\pi\) | ||||
−0.626175 | + | 0.779682i | \(0.715381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 961.519i | − 0.201966i | −0.994888 | − | 0.100983i | \(-0.967801\pi\) | ||||
0.994888 | − | 0.100983i | \(-0.0321988\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 342.334i | − 0.0711513i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −279.538 | −0.0574935 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 343.118 | 0.0698388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1001.83i | − 0.201815i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5024.51i | 1.00183i | 0.865498 | + | 0.500913i | \(0.167002\pi\) | ||||
−0.865498 | + | 0.500913i | \(0.832998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4683.78 | 0.924407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3617.62 | −0.706786 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 6981.26i | − 1.35029i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 118.964i | 0.0227807i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.40419 | −0.000455831 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3752.13 | 0.704415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3868.67i | − 0.719207i | −0.933105 | − | 0.359603i | \(-0.882912\pi\) | ||||
0.933105 | − | 0.359603i | \(-0.117088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1485.80i | 0.273541i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5796.70 | 1.05692 | 0.528458 | − | 0.848960i | \(-0.322771\pi\) | ||||
0.528458 | + | 0.848960i | \(0.322771\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8362.62 | 1.51017 | 0.755085 | − | 0.655627i | \(-0.227596\pi\) | ||||
0.755085 | + | 0.655627i | \(0.227596\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 803.569i | − 0.143733i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 487.064i | 0.0862973i | 0.999069 | + | 0.0431487i | \(0.0137389\pi\) | ||||
−0.999069 | + | 0.0431487i | \(0.986261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5973.13 | 1.04837 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1243.42 | −0.216203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1993.44i | − 0.343400i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 517.099i | − 0.0882569i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −806.416 | −0.136376 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1304.20 | −0.218549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3801.21i | − 0.631218i | −0.948889 | − | 0.315609i | \(-0.897791\pi\) | ||||
0.948889 | − | 0.315609i | \(-0.102209\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3073.76i | 0.505828i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2289.27 | 0.373361 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1795.31 | 0.290199 | 0.145099 | − | 0.989417i | \(-0.453650\pi\) | ||||
0.145099 | + | 0.989417i | \(0.453650\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 71.9931i | 0.0115343i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 12066.7i | − 1.91627i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1813.72 | −0.285515 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1736.34 | −0.270960 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2782.23i | − 0.430426i | −0.976567 | − | 0.215213i | \(-0.930955\pi\) | ||||
0.976567 | − | 0.215213i | \(-0.0690445\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10413.4i | 1.59718i | 0.601876 | + | 0.798589i | \(0.294420\pi\) | ||||
−0.601876 | + | 0.798589i | \(0.705580\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2831.68 | −0.430609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10644.3 | 1.60493 | 0.802466 | − | 0.596698i | \(-0.203521\pi\) | ||||
0.802466 | + | 0.596698i | \(0.203521\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5277.43i | − 0.789005i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 207.302i | 0.0307327i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7459.42 | −1.09664 | −0.548319 | − | 0.836269i | \(-0.684732\pi\) | ||||
−0.548319 | + | 0.836269i | \(0.684732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6102.96 | 0.889775 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2952.72i | − 0.426935i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 3021.68i | − 0.433320i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6251.35 | −0.889149 | −0.444574 | − | 0.895742i | \(-0.646645\pi\) | ||||
−0.444574 | + | 0.895742i | \(0.646645\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2705.14 | −0.381637 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 565.094i | 0.0790787i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12603.3i | 1.74953i | 0.484552 | + | 0.874763i | \(0.338983\pi\) | ||||
−0.484552 | + | 0.874763i | \(0.661017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1427.68 | 0.196600 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4675.45 | 0.638721 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1674.47i | 0.226943i | 0.993541 | + | 0.113472i | \(0.0361971\pi\) | ||||
−0.993541 | + | 0.113472i | \(0.963803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2037.31i | − 0.273949i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2880.38 | 0.384283 | 0.192142 | − | 0.981367i | \(-0.438457\pi\) | ||||
0.192142 | + | 0.981367i | \(0.438457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1987.66 | 0.263119 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1151.24i | 0.151217i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 13073.3i | − 1.70397i | −0.523567 | − | 0.851984i | \(-0.675399\pi\) | ||||
0.523567 | − | 0.851984i | \(-0.324601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10110.9 | −1.30774 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1390.09 | −0.178424 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3759.72i | − 0.478916i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 6021.44i | − 0.761228i | −0.924734 | − | 0.380614i | \(-0.875713\pi\) | ||||
0.924734 | − | 0.380614i | \(-0.124287\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 78.6216 | 0.00986467 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12722.6 | −1.58437 | −0.792187 | − | 0.610278i | \(-0.791058\pi\) | ||||
−0.792187 | + | 0.610278i | \(0.791058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9445.14i | − 1.16748i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 7416.51i | − 0.909949i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7603.08 | −0.925972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 232.991 | 0.0281678 | 0.0140839 | − | 0.999901i | \(-0.495517\pi\) | ||||
0.0140839 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 510.756i | − 0.0612987i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1075.69i | 0.128163i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9277.08 | 1.09734 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2291.35 | −0.269084 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 8663.03i | − 1.01006i | −0.863101 | − | 0.505032i | \(-0.831481\pi\) | ||||
0.863101 | − | 0.505032i | \(-0.168519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11749.9i | 1.36023i | 0.733107 | + | 0.680113i | \(0.238069\pi\) | ||||
−0.733107 | + | 0.680113i | \(0.761931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12620.9 | −1.45071 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −748.907 | −0.0854760 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 861.727i | 0.0976626i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 3426.24i | − 0.385596i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8737.57 | 0.976506 | 0.488253 | − | 0.872702i | \(-0.337634\pi\) | ||||
0.488253 | + | 0.872702i | \(0.337634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11627.5 | 1.29049 | 0.645247 | − | 0.763974i | \(-0.276755\pi\) | ||||
0.645247 | + | 0.763974i | \(0.276755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1162.85i | − 0.128171i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3834.66i | 0.419763i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17631.8 | −1.91690 | −0.958450 | − | 0.285261i | \(-0.907920\pi\) | ||||
−0.958450 | + | 0.285261i | \(0.907920\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8683.57 | −0.937649 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6434.41i | − 0.690085i | −0.938587 | − | 0.345043i | \(-0.887864\pi\) | ||||
0.938587 | − | 0.345043i | \(-0.112136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 10084.2i | − 1.07424i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −568.116 | −0.0601140 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12926.5 | −1.35867 | −0.679334 | − | 0.733830i | \(-0.737731\pi\) | ||||
−0.679334 | + | 0.733830i | \(0.737731\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 6691.30i | − 0.698627i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3208.07i | 0.332734i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1555.84 | 0.160305 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9320.32 | −0.954018 | −0.477009 | − | 0.878898i | \(-0.658279\pi\) | ||||
−0.477009 | + | 0.878898i | \(0.658279\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4101.07i | 0.417041i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18222.1i | 1.84098i | 0.390771 | + | 0.920488i | \(0.372208\pi\) | ||||
−0.390771 | + | 0.920488i | \(0.627792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7038.37 | 0.706482 | 0.353241 | − | 0.935532i | \(-0.385080\pi\) | ||||
0.353241 | + | 0.935532i | \(0.385080\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2349.14 | −0.234277 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8487.77i | − 0.841043i | −0.907283 | − | 0.420522i | \(-0.861847\pi\) | ||||
0.907283 | − | 0.420522i | \(-0.138153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 525.761i | 0.0517642i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2283.96 | −0.223438 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2847.65 | −0.276818 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 284.031i | 0.0274363i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5468.51i | 0.524918i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 587.317 | 0.0560234 | 0.0280117 | − | 0.999608i | \(-0.491082\pi\) | ||||
0.0280117 | + | 0.999608i | \(0.491082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5951.28 | −0.564148 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 398.773i | − 0.0375669i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10889.5i | 1.01952i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8366.45 | 0.778481 | 0.389240 | − | 0.921136i | \(-0.372738\pi\) | ||||
0.389240 | + | 0.921136i | \(0.372738\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2157.10 | 0.199483 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2162.76i | − 0.198786i | −0.995048 | − | 0.0993929i | \(-0.968310\pi\) | ||||
0.995048 | − | 0.0993929i | \(-0.0316901\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 6771.38i | − 0.618596i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19235.0 | 1.74656 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1212.03 | 0.109390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 16071.8i | − 1.44183i | −0.693026 | − | 0.720913i | \(-0.743723\pi\) | ||||
0.693026 | − | 0.720913i | \(-0.256277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 848.077i | 0.0756273i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12570.2 | −1.11427 | −0.557137 | − | 0.830421i | \(-0.688100\pi\) | ||||
−0.557137 | + | 0.830421i | \(0.688100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.1326 | 0.00230274 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 330.556i | − 0.0289556i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 16801.4i | − 1.46308i | −0.681797 | − | 0.731542i | \(-0.738801\pi\) | ||||
0.681797 | − | 0.731542i | \(-0.261199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 693.968 | 0.0600770 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1555.38 | 0.133863 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 16150.1i | − 1.38186i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 31218.5i | − 2.65568i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1170.87 | 0.0990283 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6612.98 | 0.556085 | 0.278042 | − | 0.960569i | \(-0.410314\pi\) | ||||
0.278042 | + | 0.960569i | \(0.410314\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7253.92i | − 0.606485i | −0.952913 | − | 0.303243i | \(-0.901931\pi\) | ||||
0.952913 | − | 0.303243i | \(-0.0980693\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 29.5370i | − 0.00245543i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13679.3 | −1.13070 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7282.60 | 0.598553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10409.7i | 0.850737i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5237.59i | − 0.425638i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13515.5 | 1.09220 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 644.849 | 0.0518199 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 21479.2i | − 1.71647i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15511.9i | 1.23273i | 0.787461 | + | 0.616365i | \(0.211395\pi\) | ||||
−0.787461 | + | 0.616365i | \(0.788605\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3962.57 | 0.313168 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8765.44 | 0.688936 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18510.4i | 1.44689i | 0.690382 | + | 0.723445i | \(0.257442\pi\) | ||||
−0.690382 | + | 0.723445i | \(0.742558\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8339.09i | 0.648277i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2568.12 | −0.198558 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 863.469 | 0.0663986 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1480.17i | 0.113207i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7141.59i | 0.543266i | 0.962401 | + | 0.271633i | \(0.0875637\pi\) | ||||
−0.962401 | + | 0.271633i | \(0.912436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2228.98 | −0.168651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4962.18 | −0.373446 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4594.86i | 0.343961i | 0.985100 | + | 0.171981i | \(0.0550167\pi\) | ||||
−0.985100 | + | 0.171981i | \(0.944983\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 782.538i | − 0.0582683i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1703.30 | 0.126159 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2806.05 | 0.206741 | 0.103371 | − | 0.994643i | \(-0.467037\pi\) | ||||
0.103371 | + | 0.994643i | \(0.467037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 17025.4i | − 1.24779i | −0.781506 | − | 0.623897i | \(-0.785548\pi\) | ||||
0.781506 | − | 0.623897i | \(-0.214452\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3442.31i | − 0.250968i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1440.62 | 0.104484 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7206.84 | 0.519973 | 0.259987 | − | 0.965612i | \(-0.416282\pi\) | ||||
0.259987 | + | 0.965612i | \(0.416282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3052.95i | 0.219130i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2130.61i | 0.152138i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13526.6 | −0.960918 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15056.1 | 1.06409 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 14675.2i | − 1.03188i | −0.856626 | − | 0.515938i | \(-0.827443\pi\) | ||||
0.856626 | − | 0.515938i | \(-0.172557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5188.01i | 0.362934i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2435.33 | 0.169503 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4758.60 | 0.329531 | 0.164766 | − | 0.986333i | \(-0.447313\pi\) | ||||
0.164766 | + | 0.986333i | \(0.447313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 2253.29i | − 0.155254i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 799.617i | − 0.0548176i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14256.4 | 0.972455 | 0.486227 | − | 0.873832i | \(-0.338373\pi\) | ||||
0.486227 | + | 0.873832i | \(0.338373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10385.2 | 0.704862 | 0.352431 | − | 0.935838i | \(-0.385355\pi\) | ||||
0.352431 | + | 0.935838i | \(0.385355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5087.89i | 0.343606i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32094.9i | 2.15677i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16243.6 | 1.08618 | 0.543088 | − | 0.839676i | \(-0.317255\pi\) | ||||
0.543088 | + | 0.839676i | \(0.317255\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 267.064 | 0.0177701 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 24436.1i | − 1.61797i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 707.817i | 0.0466369i | 0.999728 | + | 0.0233185i | \(0.00742317\pi\) | ||||
−0.999728 | + | 0.0233185i | \(0.992577\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1302.66 | −0.0854121 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11575.9 | −0.755316 | −0.377658 | − | 0.925945i | \(-0.623271\pi\) | ||||
−0.377658 | + | 0.925945i | \(0.623271\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 25959.4i | − 1.68562i | −0.538214 | − | 0.842808i | \(-0.680901\pi\) | ||||
0.538214 | − | 0.842808i | \(-0.319099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 7888.97i | − 0.509780i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2315.98 | 0.148937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16809.5 | −1.07581 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1881.96i | 0.119870i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8619.15i | 0.546372i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10224.8 | −0.645079 | −0.322539 | − | 0.946556i | \(-0.604537\pi\) | ||||
−0.322539 | + | 0.946556i | \(0.604537\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3370.88 | −0.211660 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22144.8i | 1.38392i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 16812.8i | − 1.04576i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11729.0 | 0.726125 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19804.4 | 1.22032 | 0.610162 | − | 0.792277i | \(-0.291104\pi\) | ||||
0.610162 | + | 0.792277i | \(0.291104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22175.9i | 1.36008i | 0.733174 | + | 0.680041i | \(0.238038\pi\) | ||||
−0.733174 | + | 0.680041i | \(0.761962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 554.380i | 0.0338429i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9232.26 | 0.560985 | 0.280493 | − | 0.959856i | \(-0.409502\pi\) | ||||
0.280493 | + | 0.959856i | \(0.409502\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25748.8 | −1.55736 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 539.511i | − 0.0324810i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 27857.1i | − 1.66942i | −0.550690 | − | 0.834710i | \(-0.685635\pi\) | ||||
0.550690 | − | 0.834710i | \(-0.314365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15109.8 | 0.901355 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6715.66 | 0.398786 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 5498.55i | − 0.325028i | −0.986706 | − | 0.162514i | \(-0.948040\pi\) | ||||
0.986706 | − | 0.162514i | \(-0.0519602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 11469.6i | − 0.674908i | −0.941342 | − | 0.337454i | \(-0.890434\pi\) | ||||
0.941342 | − | 0.337454i | \(-0.109566\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3884.13 | −0.227522 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −854.587 | −0.0498338 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13025.7i | 0.756156i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 383.204i | 0.0221458i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20627.1 | −1.18674 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28428.2 | −1.62827 | −0.814135 | − | 0.580676i | \(-0.802788\pi\) | ||||
−0.814135 | + | 0.580676i | \(0.802788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 584.333i | − 0.0333200i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23995.5i | 1.36222i | 0.732181 | + | 0.681110i | \(0.238502\pi\) | ||||
−0.732181 | + | 0.681110i | \(0.761498\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2500.92 | −0.141350 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5229.92 | −0.294289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13506.0i | 0.756650i | 0.925673 | + | 0.378325i | \(0.123500\pi\) | ||||
−0.925673 | + | 0.378325i | \(0.876500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5551.73i | 0.309665i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2164.42 | −0.120201 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10587.9 | −0.585439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29500.1i | 1.62408i | 0.583605 | + | 0.812038i | \(0.301642\pi\) | ||||
−0.583605 | + | 0.812038i | \(0.698358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4417.57i | 0.242150i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24906.1 | 1.35934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7585.52 | −0.412227 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 991.557i | 0.0536540i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 33227.5i | − 1.79028i | −0.445787 | − | 0.895139i | \(-0.647076\pi\) | ||||
0.445787 | − | 0.895139i | \(-0.352924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3268.91 | 0.175376 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6077.62 | −0.324676 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00170i | 0 0.000319261i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 6448.04i | − 0.341553i | −0.985310 | − | 0.170777i | \(-0.945372\pi\) | ||||
0.985310 | − | 0.170777i | \(-0.0546277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8355.95 | 0.440749 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26313.9 | 1.38214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37242.0i | 1.94793i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 848.138i | − 0.0441761i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6494.67 | −0.336871 | −0.168436 | − | 0.985713i | \(-0.553872\pi\) | ||||
−0.168436 | + | 0.985713i | \(0.553872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3709.08 | 0.191586 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1550.80i | − 0.0797714i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 964.806i | 0.0494234i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24866.4 | −1.26856 | −0.634280 | − | 0.773103i | \(-0.718704\pi\) | ||||
−0.634280 | + | 0.773103i | \(0.718704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14848.5 | 0.754384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3228.20i | 0.163337i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21092.1i | 1.06283i | 0.847112 | + | 0.531414i | \(0.178339\pi\) | ||||
−0.847112 | + | 0.531414i | \(0.821661\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4181.58 | −0.209850 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12585.1 | −0.629008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11952.7i | 0.594977i | 0.954725 | + | 0.297489i | \(0.0961491\pi\) | ||||
−0.954725 | + | 0.297489i | \(0.903851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1473.10i | 0.0730305i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5622.43 | 0.277614 | 0.138807 | − | 0.990319i | \(-0.455673\pi\) | ||||
0.138807 | + | 0.990319i | \(0.455673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6175.21 | 0.303681 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20618.3i | 1.00988i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3104.02i | 0.151427i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32314.9 | −1.57016 | −0.785079 | − | 0.619396i | \(-0.787378\pi\) | ||||
−0.785079 | + | 0.619396i | \(0.787378\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5418.58 | 0.262236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 34870.5i | − 1.68089i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17950.4i | 0.861847i | 0.902389 | + | 0.430923i | \(0.141812\pi\) | ||||
−0.902389 | + | 0.430923i | \(0.858188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9545.42 | 0.456491 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13108.2 | −0.624404 | −0.312202 | − | 0.950016i | \(-0.601067\pi\) | ||||
−0.312202 | + | 0.950016i | \(0.601067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2013.10i | 0.0955166i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 21805.5i | − 1.03056i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20154.8 | −0.948822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23661.2 | 1.10955 | 0.554776 | − | 0.832000i | \(-0.312804\pi\) | ||||
0.554776 | + | 0.832000i | \(0.312804\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 5039.63i | − 0.235406i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 30222.4i | − 1.40624i | −0.711071 | − | 0.703120i | \(-0.751790\pi\) | ||||
0.711071 | − | 0.703120i | \(-0.248210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1949.06 | 0.0903384 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −339.940 | −0.0156954 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2876.89i | 0.132318i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29012.3i | 1.32925i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5283.35 | 0.241139 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24825.8 | 1.12875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29544.2i | 1.33817i | 0.743188 | + | 0.669083i | \(0.233313\pi\) | ||||
−0.743188 | + | 0.669083i | \(0.766687\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3176.28i | 0.143319i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 179.720 | 0.00807853 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16145.8 | −0.723020 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2633.36i | 0.117479i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9665.91i | 0.429591i | 0.976659 | + | 0.214795i | \(0.0689085\pi\) | ||||
−0.976659 | + | 0.214795i | \(0.931092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35390.5 | −1.56699 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22412.1 | 0.988631 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16611.5i | 0.730021i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4334.52i | 0.189778i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1004.44 | 0.0438142 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15807.0 | 0.686952 | 0.343476 | − | 0.939162i | \(-0.388396\pi\) | ||||
0.343476 | + | 0.939162i | \(0.388396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16295.5i | 0.705565i | 0.935705 | + | 0.352783i | \(0.114764\pi\) | ||||
−0.935705 | + | 0.352783i | \(0.885236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8624.81i | 0.372061i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23446.9 | −1.00774 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1224.33 | 0.0524284 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3457.84i | 0.147529i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 436.743i | 0.0185657i | 0.999957 | + | 0.00928286i | \(0.00295487\pi\) | ||||
−0.999957 | + | 0.00928286i | \(0.997045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5633.49 | −0.238604 | −0.119302 | − | 0.992858i | \(-0.538066\pi\) | ||||
−0.119302 | + | 0.992858i | \(0.538066\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 707.026 | 0.0298369 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 22394.7i | − 0.941645i | −0.882228 | − | 0.470822i | \(-0.843957\pi\) | ||||
0.882228 | − | 0.470822i | \(-0.156043\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8768.39i | 0.367357i | 0.982986 | + | 0.183678i | \(0.0588005\pi\) | ||||
−0.982986 | + | 0.183678i | \(0.941199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −730.253 | −0.0304840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24349.7 | −1.01281 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 9218.27i | − 0.382050i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 10673.2i | − 0.440764i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30644.3 | 1.26098 | 0.630488 | − | 0.776199i | \(-0.282855\pi\) | ||||
0.630488 | + | 0.776199i | \(0.282855\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15665.5 | 0.642319 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 6313.47i | − 0.257945i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3593.02i | 0.146277i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7371.03 | −0.299022 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1029.06 | 0.0415986 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 16580.1i | − 0.667871i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 43559.2i | − 1.74846i | −0.485508 | − | 0.874232i | \(-0.661365\pi\) | ||||
0.485508 | − | 0.874232i | \(-0.338635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8270.00 | −0.330793 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41788.5 | 1.66566 | 0.832828 | − | 0.553533i | \(-0.186721\pi\) | ||||
0.832828 | + | 0.553533i | \(0.186721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16849.6i | 0.669267i | 0.942348 | + | 0.334633i | \(0.108612\pi\) | ||||
−0.942348 | + | 0.334633i | \(0.891388\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 299.174i | − 0.0118418i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27636.7 | −1.09011 | −0.545054 | − | 0.838401i | \(-0.683491\pi\) | ||||
−0.545054 | + | 0.838401i | \(0.683491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12727.0 | −0.500266 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 367.220i | 0.0143846i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20668.8i | 0.806837i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9850.95 | −0.383223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24201.9 | −0.938270 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3563.98i | − 0.137697i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 16855.0i | − 0.648977i | −0.945890 | − | 0.324488i | \(-0.894808\pi\) | ||||
0.945890 | − | 0.324488i | \(-0.105192\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5377.45 | −0.206344 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13330.0 | 0.509759 | 0.254880 | − | 0.966973i | \(-0.417964\pi\) | ||||
0.254880 | + | 0.966973i | \(0.417964\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35598.7i | 1.35673i | 0.734725 | + | 0.678365i | \(0.237311\pi\) | ||||
−0.734725 | + | 0.678365i | \(0.762689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5012.78i | 0.190399i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48821.3 | 1.84810 | 0.924048 | − | 0.382278i | \(-0.124860\pi\) | ||||
0.924048 | + | 0.382278i | \(0.124860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5085.84 | −0.191871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40771.8i | 1.53301i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13422.2i | 0.502977i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7009.27 | −0.261781 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7471.64 | 0.278117 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17622.8i | 0.653785i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15334.3i | 0.566992i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −127.321 | −0.00469210 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −43071.7 | −1.58205 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7523.90i | − 0.275443i | −0.990471 | − | 0.137722i | \(-0.956022\pi\) | ||||
0.990471 | − | 0.137722i | \(-0.0439779\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 58.0796i | 0.00211923i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26016.0 | −0.946155 | −0.473077 | − | 0.881021i | \(-0.656857\pi\) | ||||
−0.473077 | + | 0.881021i | \(0.656857\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −51000.2 | −1.84870 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4015.69i | 0.145087i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3470.16i | 0.124967i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24082.1 | 0.864413 | 0.432206 | − | 0.901775i | \(-0.357735\pi\) | ||||
0.432206 | + | 0.901775i | \(0.357735\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4140.41 | 0.148134 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22709.3i | 0.809844i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1228.08i | − 0.0436530i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 35893.5 | 1.27173 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9324.93 | 0.329323 | 0.164661 | − | 0.986350i | \(-0.447347\pi\) | ||||
0.164661 | + | 0.986350i | \(0.447347\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9234.89i | 0.325093i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6203.87i | 0.217691i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 53937.0 | 1.88656 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15535.2 | 0.541636 | 0.270818 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270818 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8950.03i | 0.311047i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 48118.3i | − 1.66696i | −0.552547 | − | 0.833482i | \(-0.686344\pi\) | ||||
0.552547 | − | 0.833482i | \(-0.313656\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14591.8 | 0.503896 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1758.13 | 0.0605205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5396.67i | 0.185183i | 0.995704 | + | 0.0925915i | \(0.0295151\pi\) | ||||
−0.995704 | + | 0.0925915i | \(0.970485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13002.6i | 0.444765i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −521.277 | −0.0177745 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21759.7 | −0.739629 | −0.369815 | − | 0.929106i | \(-0.620579\pi\) | ||||
−0.369815 | + | 0.929106i | \(0.620579\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37416.7i | 1.26783i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6392.70i | 0.215932i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1275.03 | −0.0429331 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5809.78 | 0.195018 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30038.2i | 1.00516i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 33184.4i | − 1.10699i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19338.5 | −0.643108 | −0.321554 | − | 0.946891i | \(-0.604205\pi\) | ||||
−0.321554 | + | 0.946891i | \(0.604205\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2133.47 | 0.0707294 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 5918.37i | − 0.195602i | −0.995206 | − | 0.0978009i | \(-0.968819\pi\) | ||||
0.995206 | − | 0.0978009i | \(-0.0311809\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5720.03i | 0.188464i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 553.421 | 0.0181781 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17841.9 | −0.584249 | −0.292125 | − | 0.956380i | \(-0.594362\pi\) | ||||
−0.292125 | + | 0.956380i | \(0.594362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55437.4i | 1.80979i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19481.1i | 0.634032i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 61512.0 | 1.99586 | 0.997929 | − | 0.0643304i | \(-0.0204912\pi\) | ||||
0.997929 | + | 0.0643304i | \(0.0204912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26471.2 | −0.856286 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1395.81i | − 0.0450142i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 6209.89i | − 0.199659i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1827.73 | −0.0585870 | −0.0292935 | − | 0.999571i | \(-0.509326\pi\) | ||||
−0.0292935 | + | 0.999571i | \(0.509326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4068.21 | 0.130011 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8691.53i | 0.276925i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35379.4i | 1.12385i | 0.827188 | + | 0.561925i | \(0.189939\pi\) | ||||
−0.827188 | + | 0.561925i | \(0.810061\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6725.07 | −0.212985 |
(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 | 1024.4.b.k.513.6 | 10 | ||
4.3 | odd | 2 | 1024.4.b.j.513.5 | 10 | |||
8.3 | odd | 2 | 1024.4.b.j.513.6 | 10 | |||
8.5 | even | 2 | inner | 1024.4.b.k.513.5 | 10 | ||
16.3 | odd | 4 | 1024.4.a.n.1.6 | 10 | |||
16.5 | even | 4 | 1024.4.a.m.1.6 | 10 | |||
16.11 | odd | 4 | 1024.4.a.n.1.5 | 10 | |||
16.13 | even | 4 | 1024.4.a.m.1.5 | 10 | |||
32.3 | odd | 8 | 16.4.e.a.5.3 | ✓ | 10 | ||
32.5 | even | 8 | 64.4.e.a.17.3 | 10 | |||
32.11 | odd | 8 | 128.4.e.b.33.3 | 10 | |||
32.13 | even | 8 | 128.4.e.a.97.3 | 10 | |||
32.19 | odd | 8 | 128.4.e.b.97.3 | 10 | |||
32.21 | even | 8 | 128.4.e.a.33.3 | 10 | |||
32.27 | odd | 8 | 16.4.e.a.13.3 | yes | 10 | ||
32.29 | even | 8 | 64.4.e.a.49.3 | 10 | |||
96.5 | odd | 8 | 576.4.k.a.145.2 | 10 | |||
96.29 | odd | 8 | 576.4.k.a.433.2 | 10 | |||
96.35 | even | 8 | 144.4.k.a.37.3 | 10 | |||
96.59 | even | 8 | 144.4.k.a.109.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.3 | ✓ | 10 | 32.3 | odd | 8 | ||
16.4.e.a.13.3 | yes | 10 | 32.27 | odd | 8 | ||
64.4.e.a.17.3 | 10 | 32.5 | even | 8 | |||
64.4.e.a.49.3 | 10 | 32.29 | even | 8 | |||
128.4.e.a.33.3 | 10 | 32.21 | even | 8 | |||
128.4.e.a.97.3 | 10 | 32.13 | even | 8 | |||
128.4.e.b.33.3 | 10 | 32.11 | odd | 8 | |||
128.4.e.b.97.3 | 10 | 32.19 | odd | 8 | |||
144.4.k.a.37.3 | 10 | 96.35 | even | 8 | |||
144.4.k.a.109.3 | 10 | 96.59 | even | 8 | |||
576.4.k.a.145.2 | 10 | 96.5 | odd | 8 | |||
576.4.k.a.433.2 | 10 | 96.29 | odd | 8 | |||
1024.4.a.m.1.5 | 10 | 16.13 | even | 4 | |||
1024.4.a.m.1.6 | 10 | 16.5 | even | 4 | |||
1024.4.a.n.1.5 | 10 | 16.11 | odd | 4 | |||
1024.4.a.n.1.6 | 10 | 16.3 | odd | 4 | |||
1024.4.b.j.513.5 | 10 | 4.3 | odd | 2 | |||
1024.4.b.j.513.6 | 10 | 8.3 | odd | 2 | |||
1024.4.b.k.513.5 | 10 | 8.5 | even | 2 | inner | ||
1024.4.b.k.513.6 | 10 | 1.1 | even | 1 | trivial |