Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(1,1024)]
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, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.a (trivial) |
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: | yes |
Analytic conductor: | \(60.4179558459\) |
Analytic rank: | \(1\) |
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) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(3.94652\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.07024 | 0.205968 | 0.102984 | − | 0.994683i | \(-0.467161\pi\) | ||||
0.102984 | + | 0.994683i | \(0.467161\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.6331 | 1.04050 | 0.520250 | − | 0.854014i | \(-0.325839\pi\) | ||||
0.520250 | + | 0.854014i | \(0.325839\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.67171 | −0.144259 | −0.0721293 | − | 0.997395i | \(-0.522979\pi\) | ||||
−0.0721293 | + | 0.997395i | \(0.522979\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.8546 | −0.957577 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −63.9525 | −1.75295 | −0.876473 | − | 0.481451i | \(-0.840110\pi\) | ||||
−0.876473 | + | 0.481451i | \(0.840110\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.0586 | 1.06798 | 0.533990 | − | 0.845491i | \(-0.320692\pi\) | ||||
0.533990 | + | 0.845491i | \(0.320692\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | −27.4961 | −0.332002 | −0.166001 | − | 0.986126i | \(-0.553085\pi\) | ||||
−0.166001 | + | 0.986126i | \(0.553085\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.85937 | −0.0297127 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 139.462 | 1.26434 | 0.632170 | − | 0.774830i | \(-0.282165\pi\) | ||||
0.632170 | + | 0.774830i | \(0.282165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.3299 | 0.0826390 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −56.5672 | −0.403199 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −93.3995 | −0.598064 | −0.299032 | − | 0.954243i | \(-0.596664\pi\) | ||||
−0.299032 | + | 0.954243i | \(0.596664\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −31.0803 | −0.150101 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −118.886 | −0.528238 | −0.264119 | − | 0.964490i | \(-0.585081\pi\) | ||||
−0.264119 | + | 0.964490i | \(0.585081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 53.5748 | 0.219970 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 104.629 | 0.398545 | 0.199272 | − | 0.979944i | \(-0.436142\pi\) | ||||
0.199272 | + | 0.979944i | \(0.436142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −44.5275 | −0.157916 | −0.0789579 | − | 0.996878i | \(-0.525159\pi\) | ||||
−0.0789579 | + | 0.996878i | \(0.525159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −300.770 | −0.996358 | ||||||||
\(46\) | 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 | ||||||||
\(51\) | 77.5916 | 0.213039 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −211.510 | −0.548173 | −0.274087 | − | 0.961705i | \(-0.588376\pi\) | ||||
−0.274087 | + | 0.961705i | \(0.588376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −743.968 | −1.82394 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −29.4275 | −0.0683819 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −402.624 | −0.888426 | −0.444213 | − | 0.895921i | \(-0.646517\pi\) | ||||
−0.444213 | + | 0.895921i | \(0.646517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 322.538 | 0.676997 | 0.338498 | − | 0.940967i | \(-0.390081\pi\) | ||||
0.338498 | + | 0.940967i | \(0.390081\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 69.0758 | 0.138139 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 582.338 | 1.11123 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 196.789 | 0.358829 | 0.179415 | − | 0.983774i | \(-0.442580\pi\) | ||||
0.179415 | + | 0.983774i | \(0.442580\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 149.258 | 0.260414 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −453.655 | −0.758294 | −0.379147 | − | 0.925336i | \(-0.623783\pi\) | ||||
−0.379147 | + | 0.925336i | \(0.623783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −259.747 | −0.416454 | −0.208227 | − | 0.978081i | \(-0.566769\pi\) | ||||
−0.208227 | + | 0.978081i | \(0.566769\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.0555 | 0.0170210 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 170.862 | 0.252877 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 797.471 | 1.05462 | 0.527312 | − | 0.849672i | \(-0.323200\pi\) | ||||
0.527312 | + | 0.849672i | \(0.323200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 843.392 | 1.07622 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −99.9602 | −0.123182 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −866.853 | −1.03243 | −0.516215 | − | 0.856459i | \(-0.672659\pi\) | ||||
−0.516215 | + | 0.856459i | \(0.672659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −133.742 | −0.154065 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −201.935 | −0.225158 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 1653.47 | 1.67858 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.24639 | −0.00221311 | −0.00110656 | − | 0.999999i | \(-0.500352\pi\) | ||||
−0.00110656 | + | 0.999999i | \(0.500352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1388.28 | −1.32807 | −0.664036 | − | 0.747700i | \(-0.731158\pi\) | ||||
−0.664036 | + | 0.747700i | \(0.731158\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −33.2635 | −0.0309160 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1161.81 | −1.04969 | −0.524845 | − | 0.851198i | \(-0.675877\pi\) | ||||
−0.524845 | + | 0.851198i | \(0.675877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 753.489 | 0.662121 | 0.331060 | − | 0.943610i | \(-0.392594\pi\) | ||||
0.331060 | + | 0.943610i | \(0.392594\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 1622.38 | 1.31554 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1294.24 | −1.02267 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −193.696 | −0.149211 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2758.92 | 2.07282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 111.979 | 0.0820876 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1333.97 | −0.954514 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 1298.86 | 0.866271 | 0.433136 | − | 0.901329i | \(-0.357407\pi\) | ||||
0.433136 | + | 0.901329i | \(0.357407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 73.4615 | 0.0478941 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −658.054 | −0.419528 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 477.234 | 0.297612 | 0.148806 | − | 0.988866i | \(-0.452457\pi\) | ||||
0.148806 | + | 0.988866i | \(0.452457\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2140.97 | −1.30643 | −0.653217 | − | 0.757171i | \(-0.726581\pi\) | ||||
−0.653217 | + | 0.757171i | \(0.726581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −522.440 | −0.312038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3201.37 | −1.87211 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1086.53 | −0.622285 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −359.454 | −0.201682 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −530.829 | −0.291861 | −0.145930 | − | 0.989295i | \(-0.546618\pi\) | ||||
−0.145930 | + | 0.989295i | \(0.546618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2997.52 | −1.61546 | −0.807730 | − | 0.589553i | \(-0.799304\pi\) | ||||
−0.807730 | + | 0.589553i | \(0.799304\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1874.43 | −0.990451 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2194.96 | −1.13744 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2134.06 | 1.08482 | 0.542409 | − | 0.840115i | \(-0.317512\pi\) | ||||
0.542409 | + | 0.840115i | \(0.317512\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −226.368 | −0.112906 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −372.601 | −0.182392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2015.52 | −0.968515 | −0.484258 | − | 0.874925i | \(-0.660910\pi\) | ||||
−0.484258 | + | 0.874925i | \(0.660910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −796.227 | −0.375674 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −792.415 | −0.367179 | −0.183590 | − | 0.983003i | \(-0.558772\pi\) | ||||
−0.183590 | + | 0.983003i | \(0.558772\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 308.861 | 0.140583 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 710.900 | 0.317917 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1094.03 | −0.480794 | −0.240397 | − | 0.970675i | \(-0.577278\pi\) | ||||
−0.240397 | + | 0.970675i | \(0.577278\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.5984 | −0.0119214 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −430.905 | −0.182988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −602.526 | −0.251592 | −0.125796 | − | 0.992056i | \(-0.540148\pi\) | ||||
−0.125796 | + | 0.992056i | \(0.540148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3702.50 | 1.52047 | 0.760234 | − | 0.649649i | \(-0.225084\pi\) | ||||
0.760234 | + | 0.649649i | \(0.225084\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 345.194 | 0.139440 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1383.02 | −0.549631 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4636.50 | −1.81312 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 151.131 | 0.0581649 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 623.243 | 0.228879 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2275.50 | 0.822956 | 0.411478 | − | 0.911420i | \(-0.365013\pi\) | ||||
0.411478 | + | 0.911420i | \(0.365013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 747.136 | 0.266146 | 0.133073 | − | 0.991106i | \(-0.457516\pi\) | ||||
0.133073 | + | 0.991106i | \(0.457516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 210.612 | 0.0739074 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 249.536 | 0.0862758 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1217.17 | 0.414685 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3605.73 | −1.21070 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1758.44 | 0.581981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3149.64 | 1.02763 | 0.513816 | − | 0.857901i | \(-0.328231\pi\) | ||||
0.513816 | + | 0.857901i | \(0.328231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −485.520 | −0.156185 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −517.995 | −0.164311 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 504.102 | 0.157699 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −277.993 | −0.0857763 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3629.20 | 1.10464 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 4886.67 | 1.42881 | 0.714404 | − | 0.699733i | \(-0.246698\pi\) | ||||
0.714404 | + | 0.699733i | \(0.246698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2022.37 | −0.583589 | −0.291794 | − | 0.956481i | \(-0.594252\pi\) | ||||
−0.291794 | + | 0.956481i | \(0.594252\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 182.864 | 0.0520847 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −926.479 | −0.260496 | −0.130248 | − | 0.991481i | \(-0.541577\pi\) | ||||
−0.130248 | + | 0.991481i | \(0.541577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5678.73 | −1.57634 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 345.892 | 0.0948021 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 2209.63 | 0.583325 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3907.13 | −1.01885 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1376.42 | −0.354572 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 853.487 | 0.217219 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5062.94 | 1.27319 | 0.636594 | − | 0.771199i | \(-0.280343\pi\) | ||||
0.636594 | + | 0.771199i | \(0.280343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8918.93 | −2.21632 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 317.629 | 0.0762028 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2414.81 | 0.572692 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2967.82 | −0.695830 | −0.347915 | − | 0.937526i | \(-0.613110\pi\) | ||||
−0.347915 | + | 0.937526i | \(0.613110\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2460.53 | −0.570374 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −927.743 | −0.212648 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −938.519 | −0.212723 | −0.106362 | − | 0.994328i | \(-0.533920\pi\) | ||||
−0.106362 | + | 0.994328i | \(0.533920\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −660.622 | −0.144862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −682.325 | −0.148003 | −0.0740017 | − | 0.997258i | \(-0.523577\pi\) | ||||
−0.0740017 | + | 0.997258i | \(0.523577\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4878.29 | 1.04679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5899.10 | 1.25235 | 0.626175 | − | 0.779682i | \(-0.284619\pi\) | ||||
0.626175 | + | 0.779682i | \(0.284619\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 961.519 | 0.201966 | 0.100983 | − | 0.994888i | \(-0.467801\pi\) | ||||
0.100983 | + | 0.994888i | \(0.467801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −342.334 | −0.0711513 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −279.538 | −0.0574935 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 343.118 | 0.0698388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1001.83 | −0.201815 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5024.51 | −1.00183 | −0.500913 | − | 0.865498i | \(-0.667002\pi\) | ||||
−0.500913 | + | 0.865498i | \(0.667002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4683.78 | −0.924407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3617.62 | 0.706786 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6981.26 | 1.35029 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 118.964 | 0.0227807 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.40419 | −0.000455831 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3752.13 | 0.704415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3868.67 | −0.719207 | −0.359603 | − | 0.933105i | \(-0.617088\pi\) | ||||
−0.359603 | + | 0.933105i | \(0.617088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1485.80 | −0.273541 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5796.70 | −1.05692 | −0.528458 | − | 0.848960i | \(-0.677229\pi\) | ||||
−0.528458 | + | 0.848960i | \(0.677229\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8362.62 | −1.51017 | −0.755085 | − | 0.655627i | \(-0.772404\pi\) | ||||
−0.755085 | + | 0.655627i | \(0.772404\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 803.569 | 0.143733 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 487.064 | 0.0862973 | 0.0431487 | − | 0.999069i | \(-0.486261\pi\) | ||||
0.0431487 | + | 0.999069i | \(0.486261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5973.13 | 1.04837 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1243.42 | −0.216203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1993.44 | −0.343400 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 517.099 | 0.0882569 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 806.416 | 0.136376 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1304.20 | 0.218549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3801.21 | 0.631218 | 0.315609 | − | 0.948889i | \(-0.397791\pi\) | ||||
0.315609 | + | 0.948889i | \(0.397791\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3073.76 | 0.505828 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 71.9931 | 0.0115343 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12066.7 | 1.91627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1813.72 | 0.285515 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1736.34 | 0.270960 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2782.23 | 0.430426 | 0.215213 | − | 0.976567i | \(-0.430955\pi\) | ||||
0.215213 | + | 0.976567i | \(0.430955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10413.4 | 1.59718 | 0.798589 | − | 0.601876i | \(-0.205580\pi\) | ||||
0.798589 | + | 0.601876i | \(0.205580\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | −5277.43 | −0.789005 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −207.302 | −0.0307327 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7459.42 | 1.09664 | 0.548319 | − | 0.836269i | \(-0.315268\pi\) | ||||
0.548319 | + | 0.836269i | \(0.315268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6102.96 | −0.889775 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2952.72 | 0.426935 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3021.68 | −0.433320 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | 565.094 | 0.0790787 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12603.3 | −1.74953 | −0.874763 | − | 0.484552i | \(-0.838983\pi\) | ||||
−0.874763 | + | 0.484552i | \(0.838983\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1427.68 | −0.196600 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4675.45 | −0.638721 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1674.47 | −0.226943 | −0.113472 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113472 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2037.31 | −0.273949 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 1151.24 | 0.151217 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13073.3 | 1.70397 | 0.851984 | − | 0.523567i | \(-0.175399\pi\) | ||||
0.851984 | + | 0.523567i | \(0.175399\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10110.9 | 1.30774 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1390.09 | 0.178424 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3759.72 | 0.478916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6021.44 | −0.761228 | −0.380614 | − | 0.924734i | \(-0.624287\pi\) | ||||
−0.380614 | + | 0.924734i | \(0.624287\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −9445.14 | −1.16748 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7416.51 | 0.909949 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7603.08 | 0.925972 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −232.991 | −0.0281678 | −0.0140839 | − | 0.999901i | \(-0.504483\pi\) | ||||
−0.0140839 | + | 0.999901i | \(0.504483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 510.756 | 0.0612987 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1075.69 | 0.128163 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9277.08 | 1.09734 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2291.35 | −0.269084 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8663.03 | −1.01006 | −0.505032 | − | 0.863101i | \(-0.668519\pi\) | ||||
−0.505032 | + | 0.863101i | \(0.668519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11749.9 | −1.36023 | −0.680113 | − | 0.733107i | \(-0.738069\pi\) | ||||
−0.680113 | + | 0.733107i | \(0.738069\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12620.9 | 1.45071 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 748.907 | 0.0854760 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −861.727 | −0.0976626 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3426.24 | −0.385596 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | −1162.85 | −0.128171 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3834.66 | −0.419763 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17631.8 | 1.91690 | 0.958450 | − | 0.285261i | \(-0.0920804\pi\) | ||||
0.958450 | + | 0.285261i | \(0.0920804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8683.57 | 0.937649 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6434.41 | 0.690085 | 0.345043 | − | 0.938587i | \(-0.387864\pi\) | ||||
0.345043 | + | 0.938587i | \(0.387864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10084.2 | −1.07424 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | −6691.30 | −0.698627 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3208.07 | −0.332734 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1555.84 | −0.160305 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9320.32 | 0.954018 | 0.477009 | − | 0.878898i | \(-0.341721\pi\) | ||||
0.477009 | + | 0.878898i | \(0.341721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4101.07 | −0.417041 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18222.1 | 1.84098 | 0.920488 | − | 0.390771i | \(-0.127792\pi\) | ||||
0.920488 | + | 0.390771i | \(0.127792\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | −8487.77 | −0.841043 | −0.420522 | − | 0.907283i | \(-0.638153\pi\) | ||||
−0.420522 | + | 0.907283i | \(0.638153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −525.761 | −0.0517642 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2283.96 | 0.223438 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2847.65 | 0.276818 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −284.031 | −0.0274363 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5468.51 | 0.524918 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | −398.773 | −0.0375669 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10889.5 | −1.01952 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8366.45 | −0.778481 | −0.389240 | − | 0.921136i | \(-0.627262\pi\) | ||||
−0.389240 | + | 0.921136i | \(0.627262\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2157.10 | −0.199483 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2162.76 | 0.198786 | 0.0993929 | − | 0.995048i | \(-0.468310\pi\) | ||||
0.0993929 | + | 0.995048i | \(0.468310\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6771.38 | −0.618596 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19235.0 | 1.74656 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1212.03 | 0.109390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16071.8 | −1.44183 | −0.720913 | − | 0.693026i | \(-0.756277\pi\) | ||||
−0.720913 | + | 0.693026i | \(0.756277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −848.077 | −0.0756273 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12570.2 | 1.11427 | 0.557137 | − | 0.830421i | \(-0.311900\pi\) | ||||
0.557137 | + | 0.830421i | \(0.311900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.1326 | −0.00230274 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 330.556 | 0.0289556 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16801.4 | −1.46308 | −0.731542 | − | 0.681797i | \(-0.761199\pi\) | ||||
−0.731542 | + | 0.681797i | \(0.761199\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 693.968 | 0.0600770 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1555.38 | 0.133863 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16150.1 | −1.38186 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31218.5 | 2.65568 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1170.87 | −0.0990283 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6612.98 | −0.556085 | −0.278042 | − | 0.960569i | \(-0.589686\pi\) | ||||
−0.278042 | + | 0.960569i | \(0.589686\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7253.92 | 0.606485 | 0.303243 | − | 0.952913i | \(-0.401931\pi\) | ||||
0.303243 | + | 0.952913i | \(0.401931\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −29.5370 | −0.00245543 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13679.3 | −1.13070 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7282.60 | 0.598553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10409.7 | 0.850737 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5237.59 | 0.425638 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13515.5 | −1.09220 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −644.849 | −0.0518199 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21479.2 | 1.71647 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15511.9 | 1.23273 | 0.616365 | − | 0.787461i | \(-0.288605\pi\) | ||||
0.616365 | + | 0.787461i | \(0.288605\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3962.57 | 0.313168 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8765.44 | 0.688936 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18510.4 | 1.44689 | 0.723445 | − | 0.690382i | \(-0.242558\pi\) | ||||
0.723445 | + | 0.690382i | \(0.242558\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8339.09 | −0.648277 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2568.12 | 0.198558 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −863.469 | −0.0663986 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1480.17 | −0.113207 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7141.59 | 0.543266 | 0.271633 | − | 0.962401i | \(-0.412436\pi\) | ||||
0.271633 | + | 0.962401i | \(0.412436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2228.98 | −0.168651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4962.18 | −0.373446 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4594.86 | 0.343961 | 0.171981 | − | 0.985100i | \(-0.444983\pi\) | ||||
0.171981 | + | 0.985100i | \(0.444983\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 782.538 | 0.0582683 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1703.30 | −0.126159 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2806.05 | −0.206741 | −0.103371 | − | 0.994643i | \(-0.532963\pi\) | ||||
−0.103371 | + | 0.994643i | \(0.532963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17025.4 | 1.24779 | 0.623897 | − | 0.781506i | \(-0.285548\pi\) | ||||
0.623897 | + | 0.781506i | \(0.285548\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3442.31 | −0.250968 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 3052.95 | 0.219130 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2130.61 | −0.152138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13526.6 | 0.960918 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15056.1 | −1.06409 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14675.2 | 1.03188 | 0.515938 | − | 0.856626i | \(-0.327443\pi\) | ||||
0.515938 | + | 0.856626i | \(0.327443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5188.01 | 0.362934 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | −2253.29 | −0.155254 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 799.617 | 0.0548176 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14256.4 | −0.972455 | −0.486227 | − | 0.873832i | \(-0.661627\pi\) | ||||
−0.486227 | + | 0.873832i | \(0.661627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10385.2 | −0.704862 | −0.352431 | − | 0.935838i | \(-0.614645\pi\) | ||||
−0.352431 | + | 0.935838i | \(0.614645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5087.89 | −0.343606 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32094.9 | 2.15677 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | −24436.1 | −1.61797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −707.817 | −0.0466369 | −0.0233185 | − | 0.999728i | \(-0.507423\pi\) | ||||
−0.0233185 | + | 0.999728i | \(0.507423\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1302.66 | 0.0854121 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11575.9 | 0.755316 | 0.377658 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377658 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25959.4 | 1.68562 | 0.842808 | − | 0.538214i | \(-0.180901\pi\) | ||||
0.842808 | + | 0.538214i | \(0.180901\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7888.97 | −0.509780 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2315.98 | 0.148937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16809.5 | −1.07581 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1881.96 | 0.119870 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8619.15 | −0.546372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10224.8 | 0.645079 | 0.322539 | − | 0.946556i | \(-0.395463\pi\) | ||||
0.322539 | + | 0.946556i | \(0.395463\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3370.88 | 0.211660 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22144.8 | −1.38392 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16812.8 | −1.04576 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 22175.9 | 1.36008 | 0.680041 | − | 0.733174i | \(-0.261962\pi\) | ||||
0.680041 | + | 0.733174i | \(0.261962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −554.380 | −0.0338429 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9232.26 | −0.560985 | −0.280493 | − | 0.959856i | \(-0.590498\pi\) | ||||
−0.280493 | + | 0.959856i | \(0.590498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25748.8 | 1.55736 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 539.511 | 0.0324810 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27857.1 | −1.66942 | −0.834710 | − | 0.550690i | \(-0.814365\pi\) | ||||
−0.834710 | + | 0.550690i | \(0.814365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15109.8 | 0.901355 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6715.66 | 0.398786 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5498.55 | −0.325028 | −0.162514 | − | 0.986706i | \(-0.551960\pi\) | ||||
−0.162514 | + | 0.986706i | \(0.551960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11469.6 | 0.674908 | 0.337454 | − | 0.941342i | \(-0.390434\pi\) | ||||
0.337454 | + | 0.941342i | \(0.390434\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3884.13 | 0.227522 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 854.587 | 0.0498338 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13025.7 | −0.756156 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 383.204 | 0.0221458 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | −584.333 | −0.0333200 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23995.5 | −1.36222 | −0.681110 | − | 0.732181i | \(-0.738502\pi\) | ||||
−0.681110 | + | 0.732181i | \(0.738502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2500.92 | 0.141350 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5229.92 | 0.294289 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13506.0 | −0.756650 | −0.378325 | − | 0.925673i | \(-0.623500\pi\) | ||||
−0.378325 | + | 0.925673i | \(0.623500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5551.73 | 0.309665 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2164.42 | −0.120201 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10587.9 | −0.585439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29500.1 | 1.62408 | 0.812038 | − | 0.583605i | \(-0.198358\pi\) | ||||
0.812038 | + | 0.583605i | \(0.198358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4417.57 | −0.242150 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24906.1 | −1.35934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7585.52 | 0.412227 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −991.557 | −0.0536540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33227.5 | −1.79028 | −0.895139 | − | 0.445787i | \(-0.852924\pi\) | ||||
−0.895139 | + | 0.445787i | \(0.852924\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3268.91 | 0.175376 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6077.62 | −0.324676 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00170 | 0.000319261 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6448.04 | 0.341553 | 0.170777 | − | 0.985310i | \(-0.445372\pi\) | ||||
0.170777 | + | 0.985310i | \(0.445372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8355.95 | −0.440749 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26313.9 | −1.38214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37242.0 | −1.94793 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −848.138 | −0.0441761 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | −1550.80 | −0.0797714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −964.806 | −0.0494234 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24866.4 | 1.26856 | 0.634280 | − | 0.773103i | \(-0.281296\pi\) | ||||
0.634280 | + | 0.773103i | \(0.281296\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14848.5 | −0.754384 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3228.20 | −0.163337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21092.1 | 1.06283 | 0.531414 | − | 0.847112i | \(-0.321661\pi\) | ||||
0.531414 | + | 0.847112i | \(0.321661\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4181.58 | −0.209850 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12585.1 | −0.629008 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11952.7 | 0.594977 | 0.297489 | − | 0.954725i | \(-0.403851\pi\) | ||||
0.297489 | + | 0.954725i | \(0.403851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1473.10 | −0.0730305 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5622.43 | −0.277614 | −0.138807 | − | 0.990319i | \(-0.544327\pi\) | ||||
−0.138807 | + | 0.990319i | \(0.544327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6175.21 | −0.303681 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20618.3 | −1.00988 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3104.02 | 0.151427 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | −34870.5 | −1.68089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17950.4 | −0.861847 | −0.430923 | − | 0.902389i | \(-0.641812\pi\) | ||||
−0.430923 | + | 0.902389i | \(0.641812\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9545.42 | −0.456491 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13108.2 | 0.624404 | 0.312202 | − | 0.950016i | \(-0.398933\pi\) | ||||
0.312202 | + | 0.950016i | \(0.398933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2013.10 | −0.0955166 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21805.5 | −1.03056 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −5039.63 | −0.235406 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30222.4 | 1.40624 | 0.703120 | − | 0.711071i | \(-0.251790\pi\) | ||||
0.703120 | + | 0.711071i | \(0.251790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1949.06 | −0.0903384 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 339.940 | 0.0156954 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2876.89 | −0.132318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29012.3 | 1.32925 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5283.35 | 0.241139 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24825.8 | 1.12875 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29544.2 | 1.33817 | 0.669083 | − | 0.743188i | \(-0.266687\pi\) | ||||
0.669083 | + | 0.743188i | \(0.266687\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3176.28 | −0.143319 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −179.720 | −0.00807853 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16145.8 | 0.723020 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2633.36 | −0.117479 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9665.91 | 0.429591 | 0.214795 | − | 0.976659i | \(-0.431092\pi\) | ||||
0.214795 | + | 0.976659i | \(0.431092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35390.5 | −1.56699 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22412.1 | 0.988631 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16611.5 | 0.730021 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4334.52 | −0.189778 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1004.44 | −0.0438142 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15807.0 | −0.686952 | −0.343476 | − | 0.939162i | \(-0.611604\pi\) | ||||
−0.343476 | + | 0.939162i | \(0.611604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16295.5 | −0.705565 | −0.352783 | − | 0.935705i | \(-0.614764\pi\) | ||||
−0.352783 | + | 0.935705i | \(0.614764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8624.81 | 0.372061 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23446.9 | −1.00774 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1224.33 | 0.0524284 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3457.84 | 0.147529 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −436.743 | −0.0185657 | −0.00928286 | − | 0.999957i | \(-0.502955\pi\) | ||||
−0.00928286 | + | 0.999957i | \(0.502955\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5633.49 | 0.238604 | 0.119302 | − | 0.992858i | \(-0.461934\pi\) | ||||
0.119302 | + | 0.992858i | \(0.461934\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −707.026 | −0.0298369 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22394.7 | 0.941645 | 0.470822 | − | 0.882228i | \(-0.343957\pi\) | ||||
0.470822 | + | 0.882228i | \(0.343957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8768.39 | 0.367357 | 0.183678 | − | 0.982986i | \(-0.441199\pi\) | ||||
0.183678 | + | 0.982986i | \(0.441199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −730.253 | −0.0304840 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24349.7 | −1.01281 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9218.27 | −0.382050 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10673.2 | 0.440764 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30644.3 | −1.26098 | −0.630488 | − | 0.776199i | \(-0.717145\pi\) | ||||
−0.630488 | + | 0.776199i | \(0.717145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15665.5 | −0.642319 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6313.47 | 0.257945 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3593.02 | 0.146277 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7371.03 | −0.299022 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1029.06 | 0.0415986 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16580.1 | −0.667871 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43559.2 | 1.74846 | 0.874232 | − | 0.485508i | \(-0.161365\pi\) | ||||
0.874232 | + | 0.485508i | \(0.161365\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8270.00 | 0.330793 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41788.5 | −1.66566 | −0.832828 | − | 0.553533i | \(-0.813279\pi\) | ||||
−0.832828 | + | 0.553533i | \(0.813279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16849.6 | −0.669267 | −0.334633 | − | 0.942348i | \(-0.608612\pi\) | ||||
−0.334633 | + | 0.942348i | \(0.608612\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −299.174 | −0.0118418 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 367.220 | 0.0143846 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20668.8 | −0.806837 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9850.95 | 0.383223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24201.9 | 0.938270 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3563.98 | 0.137697 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16855.0 | −0.648977 | −0.324488 | − | 0.945890i | \(-0.605192\pi\) | ||||
−0.324488 | + | 0.945890i | \(0.605192\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 35598.7 | 1.35673 | 0.678365 | − | 0.734725i | \(-0.262689\pi\) | ||||
0.678365 | + | 0.734725i | \(0.262689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5012.78 | −0.190399 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48821.3 | −1.84810 | −0.924048 | − | 0.382278i | \(-0.875140\pi\) | ||||
−0.924048 | + | 0.382278i | \(0.875140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5085.84 | 0.191871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40771.8 | −1.53301 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13422.2 | 0.502977 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7009.27 | −0.261781 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7471.64 | 0.278117 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17622.8 | 0.653785 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15334.3 | −0.566992 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 127.321 | 0.00469210 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43071.7 | 1.58205 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7523.90 | 0.275443 | 0.137722 | − | 0.990471i | \(-0.456022\pi\) | ||||
0.137722 | + | 0.990471i | \(0.456022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 58.0796 | 0.00211923 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 4015.69 | 0.145087 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3470.16 | −0.124967 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24082.1 | −0.864413 | −0.432206 | − | 0.901775i | \(-0.642265\pi\) | ||||
−0.432206 | + | 0.901775i | \(0.642265\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4140.41 | −0.148134 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22709.3 | −0.809844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1228.08 | −0.0436530 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 9234.89 | 0.325093 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6203.87 | −0.217691 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −53937.0 | −1.88656 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15535.2 | −0.541636 | −0.270818 | − | 0.962631i | \(-0.587294\pi\) | ||||
−0.270818 | + | 0.962631i | \(0.587294\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8950.03 | −0.311047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48118.3 | −1.66696 | −0.833482 | − | 0.552547i | \(-0.813656\pi\) | ||||
−0.833482 | + | 0.552547i | \(0.813656\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14591.8 | 0.503896 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1758.13 | 0.0605205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5396.67 | 0.185183 | 0.0925915 | − | 0.995704i | \(-0.470485\pi\) | ||||
0.0925915 | + | 0.995704i | \(0.470485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13002.6 | −0.444765 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 521.277 | 0.0177745 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21759.7 | 0.739629 | 0.369815 | − | 0.929106i | \(-0.379421\pi\) | ||||
0.369815 | + | 0.929106i | \(0.379421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37416.7 | −1.26783 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6392.70 | 0.215932 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1275.03 | −0.0429331 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5809.78 | 0.195018 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30038.2 | 1.00516 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33184.4 | 1.10699 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19338.5 | 0.643108 | 0.321554 | − | 0.946891i | \(-0.395795\pi\) | ||||
0.321554 | + | 0.946891i | \(0.395795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2133.47 | −0.0707294 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5918.37 | 0.195602 | 0.0978009 | − | 0.995206i | \(-0.468819\pi\) | ||||
0.0978009 | + | 0.995206i | \(0.468819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5720.03 | 0.188464 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 55437.4 | 1.80979 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19481.1 | −0.634032 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61512.0 | −1.99586 | −0.997929 | − | 0.0643304i | \(-0.979509\pi\) | ||||
−0.997929 | + | 0.0643304i | \(0.979509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26471.2 | 0.856286 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1395.81 | 0.0450142 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6209.89 | −0.199659 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | 8691.53 | 0.276925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35379.4 | −1.12385 | −0.561925 | − | 0.827188i | \(-0.689939\pi\) | ||||
−0.561925 | + | 0.827188i | \(0.689939\pi\) | |||||||
\(998\) | 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.a.m.1.6 | 10 | ||
4.3 | odd | 2 | 1024.4.a.n.1.5 | 10 | |||
8.3 | odd | 2 | 1024.4.a.n.1.6 | 10 | |||
8.5 | even | 2 | inner | 1024.4.a.m.1.5 | 10 | ||
16.3 | odd | 4 | 1024.4.b.j.513.5 | 10 | |||
16.5 | even | 4 | 1024.4.b.k.513.5 | 10 | |||
16.11 | odd | 4 | 1024.4.b.j.513.6 | 10 | |||
16.13 | even | 4 | 1024.4.b.k.513.6 | 10 | |||
32.3 | odd | 8 | 128.4.e.b.33.3 | 10 | |||
32.5 | even | 8 | 64.4.e.a.49.3 | 10 | |||
32.11 | odd | 8 | 128.4.e.b.97.3 | 10 | |||
32.13 | even | 8 | 64.4.e.a.17.3 | 10 | |||
32.19 | odd | 8 | 16.4.e.a.13.3 | yes | 10 | ||
32.21 | even | 8 | 128.4.e.a.97.3 | 10 | |||
32.27 | odd | 8 | 16.4.e.a.5.3 | ✓ | 10 | ||
32.29 | even | 8 | 128.4.e.a.33.3 | 10 | |||
96.5 | odd | 8 | 576.4.k.a.433.2 | 10 | |||
96.59 | even | 8 | 144.4.k.a.37.3 | 10 | |||
96.77 | odd | 8 | 576.4.k.a.145.2 | 10 | |||
96.83 | 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 | 32.27 | odd | 8 | ||
16.4.e.a.13.3 | yes | 10 | 32.19 | odd | 8 | ||
64.4.e.a.17.3 | 10 | 32.13 | even | 8 | |||
64.4.e.a.49.3 | 10 | 32.5 | even | 8 | |||
128.4.e.a.33.3 | 10 | 32.29 | even | 8 | |||
128.4.e.a.97.3 | 10 | 32.21 | even | 8 | |||
128.4.e.b.33.3 | 10 | 32.3 | odd | 8 | |||
128.4.e.b.97.3 | 10 | 32.11 | odd | 8 | |||
144.4.k.a.37.3 | 10 | 96.59 | even | 8 | |||
144.4.k.a.109.3 | 10 | 96.83 | even | 8 | |||
576.4.k.a.145.2 | 10 | 96.77 | odd | 8 | |||
576.4.k.a.433.2 | 10 | 96.5 | odd | 8 | |||
1024.4.a.m.1.5 | 10 | 8.5 | even | 2 | inner | ||
1024.4.a.m.1.6 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.a.n.1.5 | 10 | 4.3 | odd | 2 | |||
1024.4.a.n.1.6 | 10 | 8.3 | odd | 2 | |||
1024.4.b.j.513.5 | 10 | 16.3 | odd | 4 | |||
1024.4.b.j.513.6 | 10 | 16.11 | odd | 4 | |||
1024.4.b.k.513.5 | 10 | 16.5 | even | 4 | |||
1024.4.b.k.513.6 | 10 | 16.13 | even | 4 |