Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,4,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(31.3300142130\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 49x^{6} + 89x^{5} + 648x^{4} - 1023x^{3} - 1476x^{2} + 1940x - 384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.67303\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67303 | 0.591506 | 0.295753 | − | 0.955264i | \(-0.404429\pi\) | ||||
0.295753 | + | 0.955264i | \(0.404429\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.20096 | −0.650120 | ||||||||
\(5\) | 6.76323 | 0.604922 | 0.302461 | − | 0.953162i | \(-0.402192\pi\) | ||||
0.302461 | + | 0.953162i | \(0.402192\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.0526 | −1.02874 | −0.514372 | − | 0.857567i | \(-0.671975\pi\) | ||||
−0.514372 | + | 0.857567i | \(0.671975\pi\) | |||||||
\(8\) | −22.0856 | −0.976057 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.3151 | 0.357815 | ||||||||
\(11\) | 65.4248 | 1.79330 | 0.896651 | − | 0.442737i | \(-0.145993\pi\) | ||||
0.896651 | + | 0.442737i | \(0.145993\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.8971 | −1.00053 | −0.500266 | − | 0.865872i | \(-0.666764\pi\) | ||||
−0.500266 | + | 0.865872i | \(0.666764\pi\) | |||||||
\(14\) | −31.8757 | −0.608509 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.65770 | 0.0727766 | ||||||||
\(17\) | −48.0195 | −0.685085 | −0.342542 | − | 0.939502i | \(-0.611288\pi\) | ||||
−0.342542 | + | 0.939502i | \(0.611288\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 147.256 | 1.77804 | 0.889020 | − | 0.457869i | \(-0.151387\pi\) | ||||
0.889020 | + | 0.457869i | \(0.151387\pi\) | |||||||
\(20\) | −35.1753 | −0.393272 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 109.458 | 1.06075 | ||||||||
\(23\) | −33.1371 | −0.300416 | −0.150208 | − | 0.988654i | \(-0.547994\pi\) | ||||
−0.150208 | + | 0.988654i | \(0.547994\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −79.2587 | −0.634070 | ||||||||
\(26\) | −78.4604 | −0.591821 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 99.0919 | 0.668808 | ||||||||
\(29\) | 73.6497 | 0.471600 | 0.235800 | − | 0.971802i | \(-0.424229\pi\) | ||||
0.235800 | + | 0.971802i | \(0.424229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 142.529 | 0.825771 | 0.412886 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412886 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(32\) | 184.478 | 1.01910 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −80.3382 | −0.405232 | ||||||||
\(35\) | −128.857 | −0.622310 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 397.714 | 1.76713 | 0.883565 | − | 0.468308i | \(-0.155136\pi\) | ||||
0.883565 | + | 0.468308i | \(0.155136\pi\) | |||||||
\(38\) | 246.363 | 1.05172 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −149.370 | −0.590438 | ||||||||
\(41\) | 100.625 | 0.383293 | 0.191646 | − | 0.981464i | \(-0.438617\pi\) | ||||
0.191646 | + | 0.981464i | \(0.438617\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 388.024 | 1.37612 | 0.688060 | − | 0.725654i | \(-0.258463\pi\) | ||||
0.688060 | + | 0.725654i | \(0.258463\pi\) | |||||||
\(44\) | −340.272 | −1.16586 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −55.4395 | −0.177698 | ||||||||
\(47\) | 138.226 | 0.428987 | 0.214493 | − | 0.976725i | \(-0.431190\pi\) | ||||
0.214493 | + | 0.976725i | \(0.431190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.0023 | 0.0583158 | ||||||||
\(50\) | −132.602 | −0.375056 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 243.910 | 0.650466 | ||||||||
\(53\) | 439.471 | 1.13898 | 0.569491 | − | 0.821998i | \(-0.307141\pi\) | ||||
0.569491 | + | 0.821998i | \(0.307141\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 442.483 | 1.08481 | ||||||||
\(56\) | 420.789 | 1.00411 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 123.218 | 0.278954 | ||||||||
\(59\) | 59.0000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −602.884 | −1.26543 | −0.632716 | − | 0.774384i | \(-0.718060\pi\) | ||||
−0.632716 | + | 0.774384i | \(0.718060\pi\) | |||||||
\(62\) | 238.455 | 0.488449 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 271.375 | 0.530030 | ||||||||
\(65\) | −317.176 | −0.605244 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −154.728 | −0.282134 | −0.141067 | − | 0.990000i | \(-0.545053\pi\) | ||||
−0.141067 | + | 0.990000i | \(0.545053\pi\) | |||||||
\(68\) | 249.748 | 0.445388 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −215.582 | −0.368100 | ||||||||
\(71\) | −552.436 | −0.923410 | −0.461705 | − | 0.887033i | \(-0.652762\pi\) | ||||
−0.461705 | + | 0.887033i | \(0.652762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −107.785 | −0.172812 | −0.0864062 | − | 0.996260i | \(-0.527538\pi\) | ||||
−0.0864062 | + | 0.996260i | \(0.527538\pi\) | |||||||
\(74\) | 665.389 | 1.04527 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −765.871 | −1.15594 | ||||||||
\(77\) | −1246.51 | −1.84485 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 989.162 | 1.40873 | 0.704363 | − | 0.709840i | \(-0.251233\pi\) | ||||
0.704363 | + | 0.709840i | \(0.251233\pi\) | |||||||
\(80\) | 31.5011 | 0.0440241 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 168.349 | 0.226720 | ||||||||
\(83\) | 730.585 | 0.966170 | 0.483085 | − | 0.875573i | \(-0.339516\pi\) | ||||
0.483085 | + | 0.875573i | \(0.339516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −324.767 | −0.414423 | ||||||||
\(86\) | 649.177 | 0.813983 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1444.95 | −1.75036 | ||||||||
\(89\) | 1375.89 | 1.63869 | 0.819346 | − | 0.573300i | \(-0.194337\pi\) | ||||
0.819346 | + | 0.573300i | \(0.194337\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 893.513 | 1.02929 | ||||||||
\(92\) | 172.345 | 0.195306 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 231.257 | 0.253748 | ||||||||
\(95\) | 995.923 | 1.07557 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −268.232 | −0.280772 | −0.140386 | − | 0.990097i | \(-0.544834\pi\) | ||||
−0.140386 | + | 0.990097i | \(0.544834\pi\) | |||||||
\(98\) | 33.4645 | 0.0344942 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 412.222 | 0.412222 | ||||||||
\(101\) | −198.697 | −0.195753 | −0.0978766 | − | 0.995199i | \(-0.531205\pi\) | ||||
−0.0978766 | + | 0.995199i | \(0.531205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1107.72 | 1.05968 | 0.529838 | − | 0.848099i | \(-0.322253\pi\) | ||||
0.529838 | + | 0.848099i | \(0.322253\pi\) | |||||||
\(104\) | 1035.75 | 0.976576 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 735.249 | 0.673715 | ||||||||
\(107\) | 562.412 | 0.508134 | 0.254067 | − | 0.967187i | \(-0.418232\pi\) | ||||
0.254067 | + | 0.967187i | \(0.418232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1069.38 | 0.939711 | 0.469855 | − | 0.882743i | \(-0.344306\pi\) | ||||
0.469855 | + | 0.882743i | \(0.344306\pi\) | |||||||
\(110\) | 740.289 | 0.641671 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −88.7414 | −0.0748685 | ||||||||
\(113\) | −1601.88 | −1.33356 | −0.666781 | − | 0.745254i | \(-0.732328\pi\) | ||||
−0.666781 | + | 0.745254i | \(0.732328\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −224.114 | −0.181728 | ||||||||
\(116\) | −383.049 | −0.306597 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 98.7089 | 0.0770076 | ||||||||
\(119\) | 914.898 | 0.704778 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2949.41 | 2.21593 | ||||||||
\(122\) | −1008.64 | −0.748511 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −741.286 | −0.536850 | ||||||||
\(125\) | −1381.45 | −0.988484 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −251.661 | −0.175837 | −0.0879184 | − | 0.996128i | \(-0.528021\pi\) | ||||
−0.0879184 | + | 0.996128i | \(0.528021\pi\) | |||||||
\(128\) | −1021.80 | −0.705588 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −530.646 | −0.358005 | ||||||||
\(131\) | −2491.36 | −1.66161 | −0.830806 | − | 0.556562i | \(-0.812120\pi\) | ||||
−0.830806 | + | 0.556562i | \(0.812120\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2805.60 | −1.82915 | ||||||||
\(134\) | −258.864 | −0.166884 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1060.54 | 0.668682 | ||||||||
\(137\) | −2395.27 | −1.49374 | −0.746869 | − | 0.664971i | \(-0.768444\pi\) | ||||
−0.746869 | + | 0.664971i | \(0.768444\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1720.23 | −1.04970 | −0.524850 | − | 0.851195i | \(-0.675879\pi\) | ||||
−0.524850 | + | 0.851195i | \(0.675879\pi\) | |||||||
\(140\) | 670.182 | 0.404576 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −924.244 | −0.546203 | ||||||||
\(143\) | −3068.24 | −1.79426 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 498.110 | 0.285281 | ||||||||
\(146\) | −180.328 | −0.102220 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2068.50 | −1.14885 | ||||||||
\(149\) | 3053.69 | 1.67898 | 0.839490 | − | 0.543375i | \(-0.182854\pi\) | ||||
0.839490 | + | 0.543375i | \(0.182854\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1862.79 | 1.00392 | 0.501960 | − | 0.864891i | \(-0.332612\pi\) | ||||
0.501960 | + | 0.864891i | \(0.332612\pi\) | |||||||
\(152\) | −3252.23 | −1.73547 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2085.46 | −1.09124 | ||||||||
\(155\) | 963.954 | 0.499527 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2654.55 | 1.34940 | 0.674701 | − | 0.738091i | \(-0.264272\pi\) | ||||
0.674701 | + | 0.738091i | \(0.264272\pi\) | |||||||
\(158\) | 1654.90 | 0.833271 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1247.66 | 0.616478 | ||||||||
\(161\) | 631.349 | 0.309051 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1355.54 | −0.651375 | −0.325688 | − | 0.945477i | \(-0.605596\pi\) | ||||
−0.325688 | + | 0.945477i | \(0.605596\pi\) | |||||||
\(164\) | −523.348 | −0.249186 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1222.29 | 0.571496 | ||||||||
\(167\) | −1406.91 | −0.651915 | −0.325958 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325958 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.33930 | 0.00106477 | ||||||||
\(170\) | −543.346 | −0.245134 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2018.10 | −0.894643 | ||||||||
\(173\) | −3037.13 | −1.33473 | −0.667366 | − | 0.744730i | \(-0.732578\pi\) | ||||
−0.667366 | + | 0.744730i | \(0.732578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1510.09 | 0.652296 | ||||||||
\(176\) | 304.729 | 0.130510 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2301.90 | 0.969296 | ||||||||
\(179\) | 1561.28 | 0.651932 | 0.325966 | − | 0.945382i | \(-0.394311\pi\) | ||||
0.325966 | + | 0.945382i | \(0.394311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1573.85 | −0.646316 | −0.323158 | − | 0.946345i | \(-0.604745\pi\) | ||||
−0.323158 | + | 0.946345i | \(0.604745\pi\) | |||||||
\(182\) | 1494.88 | 0.608833 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 731.854 | 0.293223 | ||||||||
\(185\) | 2689.83 | 1.06898 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3141.67 | −1.22856 | ||||||||
\(188\) | −718.910 | −0.278893 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1666.21 | 0.636209 | ||||||||
\(191\) | −820.690 | −0.310906 | −0.155453 | − | 0.987843i | \(-0.549684\pi\) | ||||
−0.155453 | + | 0.987843i | \(0.549684\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4227.89 | 1.57684 | 0.788419 | − | 0.615138i | \(-0.210900\pi\) | ||||
0.788419 | + | 0.615138i | \(0.210900\pi\) | |||||||
\(194\) | −448.761 | −0.166078 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −104.031 | −0.0379123 | ||||||||
\(197\) | 319.247 | 0.115459 | 0.0577295 | − | 0.998332i | \(-0.481614\pi\) | ||||
0.0577295 | + | 0.998332i | \(0.481614\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −265.391 | −0.0945381 | −0.0472691 | − | 0.998882i | \(-0.515052\pi\) | ||||
−0.0472691 | + | 0.998882i | \(0.515052\pi\) | |||||||
\(200\) | 1750.48 | 0.618888 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −332.426 | −0.115789 | ||||||||
\(203\) | −1403.22 | −0.485156 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 680.551 | 0.231862 | ||||||||
\(206\) | 1853.25 | 0.626805 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −218.433 | −0.0728153 | ||||||||
\(209\) | 9634.17 | 3.18856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3536.65 | −1.15390 | −0.576950 | − | 0.816779i | \(-0.695757\pi\) | ||||
−0.576950 | + | 0.816779i | \(0.695757\pi\) | |||||||
\(212\) | −2285.67 | −0.740475 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 940.933 | 0.300565 | ||||||||
\(215\) | 2624.30 | 0.832445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2715.54 | −0.849508 | ||||||||
\(218\) | 1789.12 | 0.555845 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2301.34 | −0.705255 | ||||||||
\(221\) | 2251.98 | 0.685450 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4045.80 | 1.21492 | 0.607460 | − | 0.794350i | \(-0.292189\pi\) | ||||
0.607460 | + | 0.794350i | \(0.292189\pi\) | |||||||
\(224\) | −3514.78 | −1.04840 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2680.00 | −0.788811 | ||||||||
\(227\) | −4609.18 | −1.34767 | −0.673837 | − | 0.738880i | \(-0.735355\pi\) | ||||
−0.673837 | + | 0.738880i | \(0.735355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1842.43 | −0.531663 | −0.265832 | − | 0.964019i | \(-0.585647\pi\) | ||||
−0.265832 | + | 0.964019i | \(0.585647\pi\) | |||||||
\(230\) | −374.950 | −0.107493 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1626.60 | −0.460308 | ||||||||
\(233\) | 1938.03 | 0.544913 | 0.272456 | − | 0.962168i | \(-0.412164\pi\) | ||||
0.272456 | + | 0.962168i | \(0.412164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 934.857 | 0.259503 | ||||||||
\(236\) | −306.857 | −0.0846384 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1530.65 | 0.416880 | ||||||||
\(239\) | −4453.09 | −1.20522 | −0.602608 | − | 0.798038i | \(-0.705872\pi\) | ||||
−0.602608 | + | 0.798038i | \(0.705872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1268.11 | −0.338948 | −0.169474 | − | 0.985535i | \(-0.554207\pi\) | ||||
−0.169474 | + | 0.985535i | \(0.554207\pi\) | |||||||
\(242\) | 4934.46 | 1.31074 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3135.57 | 0.822683 | ||||||||
\(245\) | 135.280 | 0.0352765 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6905.86 | −1.77899 | ||||||||
\(248\) | −3147.84 | −0.805999 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2311.21 | −0.584695 | ||||||||
\(251\) | −3848.45 | −0.967776 | −0.483888 | − | 0.875130i | \(-0.660776\pi\) | ||||
−0.483888 | + | 0.875130i | \(0.660776\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2167.99 | −0.538737 | ||||||||
\(254\) | −421.037 | −0.104009 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3880.51 | −0.947390 | ||||||||
\(257\) | −3723.47 | −0.903749 | −0.451874 | − | 0.892082i | \(-0.649244\pi\) | ||||
−0.451874 | + | 0.892082i | \(0.649244\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7577.50 | −1.81793 | ||||||||
\(260\) | 1649.62 | 0.393481 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4168.13 | −0.982854 | ||||||||
\(263\) | 1776.07 | 0.416414 | 0.208207 | − | 0.978085i | \(-0.433237\pi\) | ||||
0.208207 | + | 0.978085i | \(0.433237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2972.24 | 0.688994 | ||||||||
\(266\) | −4693.87 | −1.08195 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 804.733 | 0.183421 | ||||||||
\(269\) | 6356.42 | 1.44073 | 0.720367 | − | 0.693593i | \(-0.243973\pi\) | ||||
0.720367 | + | 0.693593i | \(0.243973\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3734.20 | 0.837036 | 0.418518 | − | 0.908209i | \(-0.362550\pi\) | ||||
0.418518 | + | 0.908209i | \(0.362550\pi\) | |||||||
\(272\) | −223.661 | −0.0498581 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4007.37 | −0.883556 | ||||||||
\(275\) | −5185.49 | −1.13708 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2987.88 | 0.648102 | 0.324051 | − | 0.946040i | \(-0.394955\pi\) | ||||
0.324051 | + | 0.946040i | \(0.394955\pi\) | |||||||
\(278\) | −2878.01 | −0.620904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2845.89 | 0.607410 | ||||||||
\(281\) | 8120.56 | 1.72396 | 0.861978 | − | 0.506945i | \(-0.169225\pi\) | ||||
0.861978 | + | 0.506945i | \(0.169225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5876.00 | 1.23425 | 0.617123 | − | 0.786866i | \(-0.288298\pi\) | ||||
0.617123 | + | 0.786866i | \(0.288298\pi\) | |||||||
\(284\) | 2873.20 | 0.600328 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5133.26 | −1.06131 | ||||||||
\(287\) | −1917.17 | −0.394311 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2607.13 | −0.530659 | ||||||||
\(290\) | 833.354 | 0.168746 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 560.587 | 0.112349 | ||||||||
\(293\) | 1680.29 | 0.335029 | 0.167515 | − | 0.985870i | \(-0.446426\pi\) | ||||
0.167515 | + | 0.985870i | \(0.446426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 399.031 | 0.0787541 | ||||||||
\(296\) | −8783.77 | −1.72482 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5108.92 | 0.993127 | ||||||||
\(299\) | 1554.03 | 0.300576 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7392.88 | −1.41568 | ||||||||
\(302\) | 3116.51 | 0.593825 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 685.872 | 0.129400 | ||||||||
\(305\) | −4077.44 | −0.765487 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10436.9 | −1.94028 | −0.970138 | − | 0.242552i | \(-0.922015\pi\) | ||||
−0.970138 | + | 0.242552i | \(0.922015\pi\) | |||||||
\(308\) | 6483.07 | 1.19937 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1612.73 | 0.295473 | ||||||||
\(311\) | 46.2544 | 0.00843359 | 0.00421680 | − | 0.999991i | \(-0.498658\pi\) | ||||
0.00421680 | + | 0.999991i | \(0.498658\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1814.13 | −0.327607 | −0.163803 | − | 0.986493i | \(-0.552376\pi\) | ||||
−0.163803 | + | 0.986493i | \(0.552376\pi\) | |||||||
\(314\) | 4441.15 | 0.798180 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5144.59 | −0.915842 | ||||||||
\(317\) | 2234.67 | 0.395935 | 0.197968 | − | 0.980209i | \(-0.436566\pi\) | ||||
0.197968 | + | 0.980209i | \(0.436566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4818.52 | 0.845722 | ||||||||
\(320\) | 1835.37 | 0.320627 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1056.27 | 0.182806 | ||||||||
\(323\) | −7071.14 | −1.21811 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3717.01 | 0.634407 | ||||||||
\(326\) | −2267.87 | −0.385293 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2222.37 | −0.374116 | ||||||||
\(329\) | −2633.57 | −0.441318 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8239.89 | 1.36829 | 0.684147 | − | 0.729344i | \(-0.260175\pi\) | ||||
0.684147 | + | 0.729344i | \(0.260175\pi\) | |||||||
\(332\) | −3799.74 | −0.628127 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2353.80 | −0.385612 | ||||||||
\(335\) | −1046.46 | −0.170669 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12009.1 | −1.94118 | −0.970590 | − | 0.240738i | \(-0.922610\pi\) | ||||
−0.970590 | + | 0.240738i | \(0.922610\pi\) | |||||||
\(338\) | 3.91372 | 0.000629818 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1689.10 | 0.269425 | ||||||||
\(341\) | 9324.91 | 1.48086 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6153.95 | 0.968753 | ||||||||
\(344\) | −8569.76 | −1.34317 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5081.21 | −0.789502 | ||||||||
\(347\) | −2372.02 | −0.366965 | −0.183483 | − | 0.983023i | \(-0.558737\pi\) | ||||
−0.183483 | + | 0.983023i | \(0.558737\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9595.08 | 1.47167 | 0.735835 | − | 0.677161i | \(-0.236790\pi\) | ||||
0.735835 | + | 0.677161i | \(0.236790\pi\) | |||||||
\(350\) | 2526.42 | 0.385837 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12069.4 | 1.82756 | ||||||||
\(353\) | 1102.51 | 0.166234 | 0.0831168 | − | 0.996540i | \(-0.473513\pi\) | ||||
0.0831168 | + | 0.996540i | \(0.473513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3736.25 | −0.558591 | ||||||||
\(356\) | −7155.93 | −1.06535 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2612.08 | 0.385622 | ||||||||
\(359\) | 1670.88 | 0.245643 | 0.122821 | − | 0.992429i | \(-0.460806\pi\) | ||||
0.122821 | + | 0.992429i | \(0.460806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14825.2 | 2.16142 | ||||||||
\(362\) | −2633.10 | −0.382300 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4647.13 | −0.669164 | ||||||||
\(365\) | −728.976 | −0.104538 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6862.08 | 0.976015 | 0.488008 | − | 0.872839i | \(-0.337724\pi\) | ||||
0.488008 | + | 0.872839i | \(0.337724\pi\) | |||||||
\(368\) | −154.343 | −0.0218632 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4500.18 | 0.632306 | ||||||||
\(371\) | −8373.08 | −1.17172 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6460.37 | −0.896796 | −0.448398 | − | 0.893834i | \(-0.648005\pi\) | ||||
−0.448398 | + | 0.893834i | \(0.648005\pi\) | |||||||
\(374\) | −5256.11 | −0.726704 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3052.82 | −0.418716 | ||||||||
\(377\) | −3453.96 | −0.471851 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1758.86 | −0.238382 | −0.119191 | − | 0.992871i | \(-0.538030\pi\) | ||||
−0.119191 | + | 0.992871i | \(0.538030\pi\) | |||||||
\(380\) | −5179.76 | −0.699253 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1373.04 | −0.183903 | ||||||||
\(383\) | −5111.74 | −0.681978 | −0.340989 | − | 0.940067i | \(-0.610762\pi\) | ||||
−0.340989 | + | 0.940067i | \(0.610762\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8430.46 | −1.11599 | ||||||||
\(386\) | 7073.39 | 0.932710 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1395.07 | 0.182535 | ||||||||
\(389\) | 7458.10 | 0.972084 | 0.486042 | − | 0.873936i | \(-0.338440\pi\) | ||||
0.486042 | + | 0.873936i | \(0.338440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1591.23 | 0.205810 | ||||||||
\(392\) | −441.764 | −0.0569195 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 534.111 | 0.0682947 | ||||||||
\(395\) | 6689.93 | 0.852169 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12359.2 | 1.56245 | 0.781223 | − | 0.624252i | \(-0.214596\pi\) | ||||
0.781223 | + | 0.624252i | \(0.214596\pi\) | |||||||
\(398\) | −444.008 | −0.0559199 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −369.163 | −0.0461454 | ||||||||
\(401\) | 4262.28 | 0.530793 | 0.265396 | − | 0.964139i | \(-0.414497\pi\) | ||||
0.265396 | + | 0.964139i | \(0.414497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6684.18 | −0.826211 | ||||||||
\(404\) | 1033.41 | 0.127263 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2347.63 | −0.286973 | ||||||||
\(407\) | 26020.4 | 3.16900 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3546.96 | −0.428816 | −0.214408 | − | 0.976744i | \(-0.568782\pi\) | ||||
−0.214408 | + | 0.976744i | \(0.568782\pi\) | |||||||
\(410\) | 1138.58 | 0.137148 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5761.20 | −0.688917 | ||||||||
\(413\) | −1124.10 | −0.133931 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4941.11 | 0.584457 | ||||||||
\(416\) | −8651.47 | −1.01965 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16118.3 | 1.88605 | ||||||||
\(419\) | 7458.96 | 0.869676 | 0.434838 | − | 0.900509i | \(-0.356806\pi\) | ||||
0.434838 | + | 0.900509i | \(0.356806\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8742.87 | 1.01212 | 0.506059 | − | 0.862499i | \(-0.331102\pi\) | ||||
0.506059 | + | 0.862499i | \(0.331102\pi\) | |||||||
\(422\) | −5916.93 | −0.682540 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9706.00 | −1.11171 | ||||||||
\(425\) | 3805.97 | 0.434392 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11486.5 | 1.30181 | ||||||||
\(428\) | −2925.08 | −0.330348 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4390.53 | 0.492396 | ||||||||
\(431\) | 784.232 | 0.0876452 | 0.0438226 | − | 0.999039i | \(-0.486046\pi\) | ||||
0.0438226 | + | 0.999039i | \(0.486046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13723.6 | 1.52313 | 0.761564 | − | 0.648090i | \(-0.224432\pi\) | ||||
0.761564 | + | 0.648090i | \(0.224432\pi\) | |||||||
\(434\) | −4543.19 | −0.502489 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5561.83 | −0.610925 | ||||||||
\(437\) | −4879.62 | −0.534151 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17585.6 | 1.91188 | 0.955939 | − | 0.293564i | \(-0.0948415\pi\) | ||||
0.955939 | + | 0.293564i | \(0.0948415\pi\) | |||||||
\(440\) | −9772.52 | −1.05883 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3767.63 | 0.405448 | ||||||||
\(443\) | −12123.5 | −1.30023 | −0.650117 | − | 0.759834i | \(-0.725280\pi\) | ||||
−0.650117 | + | 0.759834i | \(0.725280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9305.43 | 0.991280 | ||||||||
\(446\) | 6768.76 | 0.718633 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5170.41 | −0.545266 | ||||||||
\(449\) | −12374.8 | −1.30068 | −0.650338 | − | 0.759645i | \(-0.725373\pi\) | ||||
−0.650338 | + | 0.759645i | \(0.725373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6583.38 | 0.687360 | ||||||||
\(452\) | 8331.34 | 0.866976 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7711.31 | −0.797158 | ||||||||
\(455\) | 6043.03 | 0.622641 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4878.50 | 0.499358 | 0.249679 | − | 0.968329i | \(-0.419675\pi\) | ||||
0.249679 | + | 0.968329i | \(0.419675\pi\) | |||||||
\(458\) | −3082.44 | −0.314482 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1165.61 | 0.118145 | ||||||||
\(461\) | −3931.03 | −0.397150 | −0.198575 | − | 0.980086i | \(-0.563631\pi\) | ||||
−0.198575 | + | 0.980086i | \(0.563631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −342.424 | −0.0343710 | −0.0171855 | − | 0.999852i | \(-0.505471\pi\) | ||||
−0.0171855 | + | 0.999852i | \(0.505471\pi\) | |||||||
\(464\) | 343.038 | 0.0343214 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3242.39 | 0.322319 | ||||||||
\(467\) | −7929.38 | −0.785713 | −0.392857 | − | 0.919600i | \(-0.628513\pi\) | ||||
−0.392857 | + | 0.919600i | \(0.628513\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2947.97 | 0.290244 | ||||||||
\(470\) | 1564.05 | 0.153498 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1303.05 | −0.127072 | ||||||||
\(473\) | 25386.4 | 2.46780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11671.3 | −1.12740 | ||||||||
\(476\) | −4758.35 | −0.458190 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7450.16 | −0.712892 | ||||||||
\(479\) | 15158.1 | 1.44591 | 0.722957 | − | 0.690893i | \(-0.242783\pi\) | ||||
0.722957 | + | 0.690893i | \(0.242783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18651.7 | −1.76807 | ||||||||
\(482\) | −2121.60 | −0.200490 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15339.8 | −1.44062 | ||||||||
\(485\) | −1814.12 | −0.169845 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3551.47 | −0.330457 | −0.165228 | − | 0.986255i | \(-0.552836\pi\) | ||||
−0.165228 | + | 0.986255i | \(0.552836\pi\) | |||||||
\(488\) | 13315.1 | 1.23513 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 226.328 | 0.0208663 | ||||||||
\(491\) | −1681.06 | −0.154511 | −0.0772556 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772556 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3536.62 | −0.323086 | ||||||||
\(494\) | −11553.7 | −1.05228 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 663.856 | 0.0600968 | ||||||||
\(497\) | 10525.4 | 0.949953 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5475.45 | −0.491212 | −0.245606 | − | 0.969370i | \(-0.578987\pi\) | ||||
−0.245606 | + | 0.969370i | \(0.578987\pi\) | |||||||
\(500\) | 7184.86 | 0.642634 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6438.58 | −0.572446 | ||||||||
\(503\) | −11336.5 | −1.00491 | −0.502453 | − | 0.864604i | \(-0.667569\pi\) | ||||
−0.502453 | + | 0.864604i | \(0.667569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1343.83 | −0.118415 | ||||||||
\(506\) | −3627.12 | −0.318666 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1308.88 | 0.114315 | ||||||||
\(509\) | 15867.2 | 1.38173 | 0.690866 | − | 0.722983i | \(-0.257229\pi\) | ||||
0.690866 | + | 0.722983i | \(0.257229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2053.59 | 0.177780 | ||||||||
\(512\) | 1682.19 | 0.145201 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6229.48 | −0.534573 | ||||||||
\(515\) | 7491.75 | 0.641021 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9043.44 | 0.769303 | ||||||||
\(518\) | −12677.4 | −1.07531 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7005.03 | 0.590752 | ||||||||
\(521\) | −831.612 | −0.0699301 | −0.0349650 | − | 0.999389i | \(-0.511132\pi\) | ||||
−0.0349650 | + | 0.999389i | \(0.511132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2839.22 | −0.237381 | −0.118690 | − | 0.992931i | \(-0.537870\pi\) | ||||
−0.118690 | + | 0.992931i | \(0.537870\pi\) | |||||||
\(524\) | 12957.5 | 1.08025 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2971.42 | 0.246312 | ||||||||
\(527\) | −6844.16 | −0.565723 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11068.9 | −0.909750 | ||||||||
\(530\) | 4972.66 | 0.407545 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14591.8 | 1.18917 | ||||||||
\(533\) | −4719.03 | −0.383497 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3803.72 | 0.307381 | ||||||||
\(536\) | 3417.26 | 0.275379 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10634.5 | 0.852204 | ||||||||
\(539\) | 1308.65 | 0.104578 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2903.19 | −0.230717 | −0.115359 | − | 0.993324i | \(-0.536802\pi\) | ||||
−0.115359 | + | 0.993324i | \(0.536802\pi\) | |||||||
\(542\) | 6247.44 | 0.495112 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8858.53 | −0.698173 | ||||||||
\(545\) | 7232.49 | 0.568451 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5807.96 | −0.453986 | −0.226993 | − | 0.973896i | \(-0.572889\pi\) | ||||
−0.226993 | + | 0.973896i | \(0.572889\pi\) | |||||||
\(548\) | 12457.7 | 0.971109 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8675.49 | −0.672589 | ||||||||
\(551\) | 10845.3 | 0.838524 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18846.1 | −1.44922 | ||||||||
\(554\) | 4998.82 | 0.383356 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8946.87 | 0.682431 | ||||||||
\(557\) | −20165.3 | −1.53399 | −0.766993 | − | 0.641656i | \(-0.778248\pi\) | ||||
−0.766993 | + | 0.641656i | \(0.778248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18197.2 | −1.37685 | ||||||||
\(560\) | −600.178 | −0.0452896 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13586.0 | 1.01973 | ||||||||
\(563\) | 5801.26 | 0.434270 | 0.217135 | − | 0.976142i | \(-0.430329\pi\) | ||||
0.217135 | + | 0.976142i | \(0.430329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10833.9 | −0.806701 | ||||||||
\(566\) | 9830.74 | 0.730065 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12200.9 | 0.901301 | ||||||||
\(569\) | 24062.5 | 1.77285 | 0.886425 | − | 0.462873i | \(-0.153181\pi\) | ||||
0.886425 | + | 0.462873i | \(0.153181\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9913.83 | 0.726586 | 0.363293 | − | 0.931675i | \(-0.381652\pi\) | ||||
0.363293 | + | 0.931675i | \(0.381652\pi\) | |||||||
\(572\) | 15957.8 | 1.16648 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3207.49 | −0.233237 | ||||||||
\(575\) | 2626.41 | 0.190485 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18980.4 | 1.36944 | 0.684718 | − | 0.728808i | \(-0.259925\pi\) | ||||
0.684718 | + | 0.728808i | \(0.259925\pi\) | |||||||
\(578\) | −4361.81 | −0.313888 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2590.65 | −0.185467 | ||||||||
\(581\) | −13919.6 | −0.993942 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28752.3 | 2.04254 | ||||||||
\(584\) | 2380.51 | 0.168675 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2811.18 | 0.198172 | ||||||||
\(587\) | −2678.77 | −0.188356 | −0.0941778 | − | 0.995555i | \(-0.530022\pi\) | ||||
−0.0941778 | + | 0.995555i | \(0.530022\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20988.1 | 1.46825 | ||||||||
\(590\) | 667.591 | 0.0465835 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1852.43 | 0.128606 | ||||||||
\(593\) | −15769.4 | −1.09202 | −0.546012 | − | 0.837777i | \(-0.683855\pi\) | ||||
−0.546012 | + | 0.837777i | \(0.683855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6187.66 | 0.426335 | ||||||||
\(596\) | −15882.1 | −1.09154 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2599.95 | 0.177792 | ||||||||
\(599\) | 20847.2 | 1.42202 | 0.711012 | − | 0.703180i | \(-0.248237\pi\) | ||||
0.711012 | + | 0.703180i | \(0.248237\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7083.71 | −0.480783 | −0.240392 | − | 0.970676i | \(-0.577276\pi\) | ||||
−0.240392 | + | 0.970676i | \(0.577276\pi\) | |||||||
\(602\) | −12368.5 | −0.837381 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9688.31 | −0.652669 | ||||||||
\(605\) | 19947.5 | 1.34047 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9394.28 | 0.628175 | 0.314087 | − | 0.949394i | \(-0.398301\pi\) | ||||
0.314087 | + | 0.949394i | \(0.398301\pi\) | |||||||
\(608\) | 27165.4 | 1.81201 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6821.69 | −0.452790 | ||||||||
\(611\) | −6482.42 | −0.429215 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8222.66 | −0.541778 | −0.270889 | − | 0.962611i | \(-0.587318\pi\) | ||||
−0.270889 | + | 0.962611i | \(0.587318\pi\) | |||||||
\(614\) | −17461.3 | −1.14769 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27530.1 | 1.80068 | ||||||||
\(617\) | −23878.4 | −1.55803 | −0.779017 | − | 0.627003i | \(-0.784281\pi\) | ||||
−0.779017 | + | 0.627003i | \(0.784281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5763.65 | −0.374250 | −0.187125 | − | 0.982336i | \(-0.559917\pi\) | ||||
−0.187125 | + | 0.982336i | \(0.559917\pi\) | |||||||
\(620\) | −5013.49 | −0.324752 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 77.3851 | 0.00498852 | ||||||||
\(623\) | −26214.2 | −1.68580 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 564.287 | 0.0361143 | ||||||||
\(626\) | −3035.11 | −0.193782 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13806.2 | −0.877274 | ||||||||
\(629\) | −19098.0 | −1.21063 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1351.42 | −0.0852601 | −0.0426301 | − | 0.999091i | \(-0.513574\pi\) | ||||
−0.0426301 | + | 0.999091i | \(0.513574\pi\) | |||||||
\(632\) | −21846.3 | −1.37500 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3738.67 | 0.234198 | ||||||||
\(635\) | −1702.04 | −0.106368 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −938.051 | −0.0583468 | ||||||||
\(638\) | 8061.54 | 0.500250 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6910.67 | −0.426826 | ||||||||
\(641\) | 3444.20 | 0.212227 | 0.106114 | − | 0.994354i | \(-0.466159\pi\) | ||||
0.106114 | + | 0.994354i | \(0.466159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4572.20 | −0.280420 | −0.140210 | − | 0.990122i | \(-0.544778\pi\) | ||||
−0.140210 | + | 0.990122i | \(0.544778\pi\) | |||||||
\(644\) | −3283.62 | −0.200920 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11830.3 | −0.720519 | ||||||||
\(647\) | 2938.89 | 0.178578 | 0.0892889 | − | 0.996006i | \(-0.471541\pi\) | ||||
0.0892889 | + | 0.996006i | \(0.471541\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3860.06 | 0.233468 | ||||||||
\(650\) | 6218.67 | 0.375256 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7050.12 | 0.423472 | ||||||||
\(653\) | −15550.7 | −0.931924 | −0.465962 | − | 0.884805i | \(-0.654292\pi\) | ||||
−0.465962 | + | 0.884805i | \(0.654292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16849.6 | −1.00515 | ||||||||
\(656\) | 468.682 | 0.0278947 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4406.06 | −0.261042 | ||||||||
\(659\) | 10697.7 | 0.632356 | 0.316178 | − | 0.948700i | \(-0.397600\pi\) | ||||
0.316178 | + | 0.948700i | \(0.397600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4979.38 | −0.293004 | −0.146502 | − | 0.989210i | \(-0.546801\pi\) | ||||
−0.146502 | + | 0.989210i | \(0.546801\pi\) | |||||||
\(662\) | 13785.6 | 0.809355 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16135.4 | −0.943037 | ||||||||
\(665\) | −18974.9 | −1.10649 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2440.54 | −0.141676 | ||||||||
\(668\) | 7317.27 | 0.423823 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1750.76 | −0.100952 | ||||||||
\(671\) | −39443.6 | −2.26930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26662.2 | 1.52712 | 0.763559 | − | 0.645738i | \(-0.223450\pi\) | ||||
0.763559 | + | 0.645738i | \(0.223450\pi\) | |||||||
\(674\) | −20091.6 | −1.14822 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1666 | −0.000692228 0 | ||||||||
\(677\) | 27190.8 | 1.54362 | 0.771808 | − | 0.635856i | \(-0.219353\pi\) | ||||
0.771808 | + | 0.635856i | \(0.219353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5110.53 | 0.288842 | ||||||||
\(680\) | 7172.69 | 0.404500 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15600.9 | 0.875937 | ||||||||
\(683\) | −4166.70 | −0.233433 | −0.116716 | − | 0.993165i | \(-0.537237\pi\) | ||||
−0.116716 | + | 0.993165i | \(0.537237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16199.8 | −0.903594 | ||||||||
\(686\) | 10295.8 | 0.573023 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1807.30 | 0.100149 | ||||||||
\(689\) | −20609.9 | −1.13959 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25963.4 | 1.42937 | 0.714684 | − | 0.699447i | \(-0.246570\pi\) | ||||
0.714684 | + | 0.699447i | \(0.246570\pi\) | |||||||
\(692\) | 15796.0 | 0.867736 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3968.48 | −0.217062 | ||||||||
\(695\) | −11634.3 | −0.634986 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4831.97 | −0.262588 | ||||||||
\(698\) | 16052.9 | 0.870502 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7853.90 | −0.424071 | ||||||||
\(701\) | 31569.0 | 1.70092 | 0.850459 | − | 0.526041i | \(-0.176324\pi\) | ||||
0.850459 | + | 0.526041i | \(0.176324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58565.6 | 3.14203 | ||||||||
\(704\) | 17754.7 | 0.950504 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1844.53 | 0.0983283 | ||||||||
\(707\) | 3785.70 | 0.201380 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10296.1 | 0.545383 | 0.272691 | − | 0.962102i | \(-0.412086\pi\) | ||||
0.272691 | + | 0.962102i | \(0.412086\pi\) | |||||||
\(710\) | −6250.87 | −0.330410 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −30387.3 | −1.59946 | ||||||||
\(713\) | −4722.99 | −0.248075 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20751.2 | −1.08538 | ||||||||
\(716\) | −8120.18 | −0.423834 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2795.44 | 0.145299 | ||||||||
\(719\) | −14401.2 | −0.746976 | −0.373488 | − | 0.927635i | \(-0.621838\pi\) | ||||
−0.373488 | + | 0.927635i | \(0.621838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21104.9 | −1.09014 | ||||||||
\(722\) | 24803.0 | 1.27850 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8185.53 | 0.420183 | ||||||||
\(725\) | −5837.38 | −0.299027 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1687.62 | −0.0860940 | −0.0430470 | − | 0.999073i | \(-0.513707\pi\) | ||||
−0.0430470 | + | 0.999073i | \(0.513707\pi\) | |||||||
\(728\) | −19733.8 | −1.00465 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1219.60 | −0.0618349 | ||||||||
\(731\) | −18632.7 | −0.942759 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28217.6 | −1.42189 | −0.710943 | − | 0.703250i | \(-0.751732\pi\) | ||||
−0.710943 | + | 0.703250i | \(0.751732\pi\) | |||||||
\(734\) | 11480.5 | 0.577319 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6113.05 | −0.306155 | ||||||||
\(737\) | −10123.0 | −0.505952 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21535.4 | −1.07198 | −0.535989 | − | 0.844225i | \(-0.680061\pi\) | ||||
−0.535989 | + | 0.844225i | \(0.680061\pi\) | |||||||
\(740\) | −13989.7 | −0.694963 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14008.4 | −0.693080 | ||||||||
\(743\) | −7391.04 | −0.364941 | −0.182470 | − | 0.983211i | \(-0.558409\pi\) | ||||
−0.182470 | + | 0.983211i | \(0.558409\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20652.8 | 1.01565 | ||||||||
\(746\) | −10808.4 | −0.530461 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16339.7 | 0.798715 | ||||||||
\(749\) | −10715.4 | −0.522741 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4661.31 | 0.226489 | 0.113245 | − | 0.993567i | \(-0.463876\pi\) | ||||
0.113245 | + | 0.993567i | \(0.463876\pi\) | |||||||
\(752\) | 643.817 | 0.0312202 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5778.58 | −0.279103 | ||||||||
\(755\) | 12598.5 | 0.607293 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20667.4 | −0.992297 | −0.496149 | − | 0.868238i | \(-0.665253\pi\) | ||||
−0.496149 | + | 0.868238i | \(0.665253\pi\) | |||||||
\(758\) | −2942.63 | −0.141004 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21995.6 | −1.04982 | ||||||||
\(761\) | −35282.4 | −1.68066 | −0.840332 | − | 0.542071i | \(-0.817640\pi\) | ||||
−0.840332 | + | 0.542071i | \(0.817640\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20374.6 | −0.966722 | ||||||||
\(764\) | 4268.38 | 0.202126 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8552.11 | −0.403395 | ||||||||
\(767\) | −2766.93 | −0.130258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3764.58 | −0.176533 | −0.0882667 | − | 0.996097i | \(-0.528133\pi\) | ||||
−0.0882667 | + | 0.996097i | \(0.528133\pi\) | |||||||
\(770\) | −14104.4 | −0.660115 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21989.1 | −1.02513 | ||||||||
\(773\) | −13143.1 | −0.611547 | −0.305773 | − | 0.952104i | \(-0.598915\pi\) | ||||
−0.305773 | + | 0.952104i | \(0.598915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11296.6 | −0.523596 | ||||||||
\(776\) | 5924.08 | 0.274049 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12477.6 | 0.574994 | ||||||||
\(779\) | 14817.6 | 0.681510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36143.0 | −1.65595 | ||||||||
\(782\) | 2662.18 | 0.121738 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 93.1648 | 0.00424402 | ||||||||
\(785\) | 17953.3 | 0.816283 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34738.5 | −1.57344 | −0.786718 | − | 0.617312i | \(-0.788222\pi\) | ||||
−0.786718 | + | 0.617312i | \(0.788222\pi\) | |||||||
\(788\) | −1660.39 | −0.0750622 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11192.5 | 0.504064 | ||||||||
\(791\) | 30520.1 | 1.37190 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28273.5 | 1.26611 | ||||||||
\(794\) | 20677.4 | 0.924196 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1380.29 | 0.0614612 | ||||||||
\(797\) | 4155.16 | 0.184672 | 0.0923359 | − | 0.995728i | \(-0.470567\pi\) | ||||
0.0923359 | + | 0.995728i | \(0.470567\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6637.56 | −0.293892 | ||||||||
\(800\) | −14621.5 | −0.646183 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7130.93 | 0.313967 | ||||||||
\(803\) | −7051.83 | −0.309905 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4269.96 | 0.186952 | ||||||||
\(806\) | −11182.9 | −0.488709 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4388.35 | 0.191066 | ||||||||
\(809\) | −25096.7 | −1.09067 | −0.545335 | − | 0.838218i | \(-0.683598\pi\) | ||||
−0.545335 | + | 0.838218i | \(0.683598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15819.9 | −0.684969 | −0.342485 | − | 0.939523i | \(-0.611268\pi\) | ||||
−0.342485 | + | 0.939523i | \(0.611268\pi\) | |||||||
\(812\) | 7298.09 | 0.315410 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 43533.0 | 1.87448 | ||||||||
\(815\) | −9167.84 | −0.394031 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 57138.7 | 2.44679 | ||||||||
\(818\) | −5934.18 | −0.253647 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3539.52 | −0.150738 | ||||||||
\(821\) | −4697.39 | −0.199684 | −0.0998418 | − | 0.995003i | \(-0.531834\pi\) | ||||
−0.0998418 | + | 0.995003i | \(0.531834\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26318.7 | −1.11472 | −0.557359 | − | 0.830272i | \(-0.688185\pi\) | ||||
−0.557359 | + | 0.830272i | \(0.688185\pi\) | |||||||
\(824\) | −24464.7 | −1.03430 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1880.66 | −0.0792211 | ||||||||
\(827\) | −24232.9 | −1.01894 | −0.509469 | − | 0.860489i | \(-0.670158\pi\) | ||||
−0.509469 | + | 0.860489i | \(0.670158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6139.03 | −0.257198 | −0.128599 | − | 0.991697i | \(-0.541048\pi\) | ||||
−0.128599 | + | 0.991697i | \(0.541048\pi\) | |||||||
\(830\) | 8266.64 | 0.345710 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12726.7 | −0.530312 | ||||||||
\(833\) | −960.502 | −0.0399513 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9515.24 | −0.394357 | ||||||||
\(836\) | −50107.0 | −2.07295 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12479.1 | 0.514419 | ||||||||
\(839\) | −19605.1 | −0.806727 | −0.403364 | − | 0.915040i | \(-0.632159\pi\) | ||||
−0.403364 | + | 0.915040i | \(0.632159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18964.7 | −0.777593 | ||||||||
\(842\) | 14627.1 | 0.598674 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18394.0 | 0.750174 | ||||||||
\(845\) | 15.8212 | 0.000644102 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −56194.0 | −2.27963 | ||||||||
\(848\) | 2046.92 | 0.0828911 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6367.51 | 0.256945 | ||||||||
\(851\) | −13179.1 | −0.530874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33730.2 | −1.35393 | −0.676963 | − | 0.736017i | \(-0.736704\pi\) | ||||
−0.676963 | + | 0.736017i | \(0.736704\pi\) | |||||||
\(854\) | 19217.3 | 0.770027 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12421.2 | −0.495968 | ||||||||
\(857\) | 28613.3 | 1.14050 | 0.570251 | − | 0.821470i | \(-0.306846\pi\) | ||||
0.570251 | + | 0.821470i | \(0.306846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3049.90 | −0.121142 | −0.0605712 | − | 0.998164i | \(-0.519292\pi\) | ||||
−0.0605712 | + | 0.998164i | \(0.519292\pi\) | |||||||
\(860\) | −13648.9 | −0.541189 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1312.04 | 0.0518427 | ||||||||
\(863\) | 26717.9 | 1.05387 | 0.526934 | − | 0.849906i | \(-0.323341\pi\) | ||||
0.526934 | + | 0.849906i | \(0.323341\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20540.8 | −0.807408 | ||||||||
\(866\) | 22960.0 | 0.900940 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14123.4 | 0.552282 | ||||||||
\(869\) | 64715.8 | 2.52627 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7256.28 | 0.282284 | ||||||||
\(872\) | −23618.0 | −0.917211 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8163.77 | −0.315954 | ||||||||
\(875\) | 26320.2 | 1.01690 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10007.0 | −0.385303 | −0.192652 | − | 0.981267i | \(-0.561709\pi\) | ||||
−0.192652 | + | 0.981267i | \(0.561709\pi\) | |||||||
\(878\) | 29421.3 | 1.13089 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2060.95 | 0.0789486 | ||||||||
\(881\) | −19155.2 | −0.732527 | −0.366263 | − | 0.930511i | \(-0.619363\pi\) | ||||
−0.366263 | + | 0.930511i | \(0.619363\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37716.3 | −1.43743 | −0.718716 | − | 0.695303i | \(-0.755270\pi\) | ||||
−0.718716 | + | 0.695303i | \(0.755270\pi\) | |||||||
\(884\) | −11712.4 | −0.445625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20283.0 | −0.769096 | ||||||||
\(887\) | −44807.5 | −1.69616 | −0.848078 | − | 0.529872i | \(-0.822240\pi\) | ||||
−0.848078 | + | 0.529872i | \(0.822240\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4794.80 | 0.180891 | ||||||||
\(890\) | 15568.3 | 0.586348 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21042.1 | −0.789844 | ||||||||
\(893\) | 20354.6 | 0.762756 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10559.3 | 0.394368 | ||||||||
\(896\) | 19468.0 | 0.725870 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20703.5 | −0.769358 | ||||||||
\(899\) | 10497.2 | 0.389434 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21103.2 | −0.780299 | ||||||||
\(902\) | 11014.2 | 0.406578 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35378.6 | 1.30163 | ||||||||
\(905\) | −10644.3 | −0.390971 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 548.725 | 0.0200883 | 0.0100442 | − | 0.999950i | \(-0.496803\pi\) | ||||
0.0100442 | + | 0.999950i | \(0.496803\pi\) | |||||||
\(908\) | 23972.2 | 0.876151 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 10110.2 | 0.368296 | ||||||||
\(911\) | −23571.3 | −0.857246 | −0.428623 | − | 0.903483i | \(-0.641001\pi\) | ||||
−0.428623 | + | 0.903483i | \(0.641001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47798.4 | 1.73264 | ||||||||
\(914\) | 8161.89 | 0.295373 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9582.38 | 0.345645 | ||||||||
\(917\) | 47467.0 | 1.70938 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24363.5 | 0.874513 | 0.437256 | − | 0.899337i | \(-0.355950\pi\) | ||||
0.437256 | + | 0.899337i | \(0.355950\pi\) | |||||||
\(920\) | 4949.70 | 0.177377 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6576.73 | −0.234917 | ||||||||
\(923\) | 25907.7 | 0.923902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31522.3 | −1.12048 | ||||||||
\(926\) | −572.886 | −0.0203307 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13586.7 | 0.480610 | ||||||||
\(929\) | −7503.02 | −0.264980 | −0.132490 | − | 0.991184i | \(-0.542297\pi\) | ||||
−0.132490 | + | 0.991184i | \(0.542297\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2945.45 | 0.103688 | ||||||||
\(932\) | −10079.6 | −0.354259 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13266.1 | −0.464754 | ||||||||
\(935\) | −21247.8 | −0.743185 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33994.7 | 1.18523 | 0.592613 | − | 0.805487i | \(-0.298096\pi\) | ||||
0.592613 | + | 0.805487i | \(0.298096\pi\) | |||||||
\(938\) | 4932.05 | 0.171681 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4862.15 | −0.168708 | ||||||||
\(941\) | −35769.7 | −1.23917 | −0.619585 | − | 0.784929i | \(-0.712699\pi\) | ||||
−0.619585 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3334.43 | −0.115147 | ||||||||
\(944\) | 274.804 | 0.00947470 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42472.3 | 1.45972 | ||||||||
\(947\) | −15352.1 | −0.526798 | −0.263399 | − | 0.964687i | \(-0.584844\pi\) | ||||
−0.263399 | + | 0.964687i | \(0.584844\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5054.81 | 0.172904 | ||||||||
\(950\) | −19526.4 | −0.666865 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20206.1 | −0.687903 | ||||||||
\(953\) | 38129.6 | 1.29605 | 0.648027 | − | 0.761617i | \(-0.275594\pi\) | ||||
0.648027 | + | 0.761617i | \(0.275594\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5550.52 | −0.188074 | ||||||||
\(956\) | 23160.3 | 0.783535 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25360.0 | 0.855267 | ||||||||
\(959\) | 45636.3 | 1.53668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9476.58 | −0.318102 | ||||||||
\(962\) | −31204.8 | −1.04583 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6595.41 | 0.220357 | ||||||||
\(965\) | 28594.2 | 0.953864 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32504.3 | −1.08094 | −0.540469 | − | 0.841364i | \(-0.681753\pi\) | ||||
−0.540469 | + | 0.841364i | \(0.681753\pi\) | |||||||
\(968\) | −65139.6 | −2.16288 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3035.08 | −0.100464 | ||||||||
\(971\) | 20184.6 | 0.667100 | 0.333550 | − | 0.942732i | \(-0.391753\pi\) | ||||
0.333550 | + | 0.942732i | \(0.391753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32775.0 | 1.07987 | ||||||||
\(974\) | −5941.72 | −0.195467 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2808.05 | −0.0920938 | ||||||||
\(977\) | −34251.1 | −1.12159 | −0.560794 | − | 0.827956i | \(-0.689504\pi\) | ||||
−0.560794 | + | 0.827956i | \(0.689504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 90017.0 | 2.93867 | ||||||||
\(980\) | −703.587 | −0.0229340 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2812.46 | −0.0913944 | ||||||||
\(983\) | −26633.5 | −0.864169 | −0.432084 | − | 0.901833i | \(-0.642222\pi\) | ||||
−0.432084 | + | 0.901833i | \(0.642222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2159.14 | 0.0698436 | ||||||||
\(986\) | −5916.89 | −0.191108 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 35917.1 | 1.15655 | ||||||||
\(989\) | −12858.0 | −0.413408 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28729.1 | −0.920900 | −0.460450 | − | 0.887686i | \(-0.652312\pi\) | ||||
−0.460450 | + | 0.887686i | \(0.652312\pi\) | |||||||
\(992\) | 26293.3 | 0.841547 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17609.3 | 0.561903 | ||||||||
\(995\) | −1794.90 | −0.0571882 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8221.82 | −0.261171 | −0.130586 | − | 0.991437i | \(-0.541686\pi\) | ||||
−0.130586 | + | 0.991437i | \(0.541686\pi\) | |||||||
\(998\) | −9160.61 | −0.290555 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.4.a.f.1.6 | 8 | ||
3.2 | odd | 2 | 177.4.a.c.1.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.c.1.3 | ✓ | 8 | 3.2 | odd | 2 | ||
531.4.a.f.1.6 | 8 | 1.1 | even | 1 | trivial |