Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.96284 | −1.04752 | −0.523762 | − | 0.851865i | \(-0.675472\pi\) | ||||
−0.523762 | + | 0.851865i | \(0.675472\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.778438 | 0.0973048 | ||||||||
\(5\) | −20.0660 | −1.79476 | −0.897379 | − | 0.441260i | \(-0.854532\pi\) | ||||
−0.897379 | + | 0.441260i | \(0.854532\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.37640 | −0.236304 | −0.118152 | − | 0.992996i | \(-0.537697\pi\) | ||||
−0.118152 | + | 0.992996i | \(0.537697\pi\) | |||||||
\(8\) | 21.3964 | 0.945594 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 59.4524 | 1.88005 | ||||||||
\(11\) | −18.0511 | −0.494783 | −0.247392 | − | 0.968916i | \(-0.579573\pi\) | ||||
−0.247392 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 82.1177 | 1.75195 | 0.875975 | − | 0.482357i | \(-0.160219\pi\) | ||||
0.875975 | + | 0.482357i | \(0.160219\pi\) | |||||||
\(14\) | 12.9666 | 0.247534 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −69.6215 | −1.08784 | ||||||||
\(17\) | 100.079 | 1.42781 | 0.713903 | − | 0.700245i | \(-0.246926\pi\) | ||||
0.713903 | + | 0.700245i | \(0.246926\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 43.8153 | 0.529048 | 0.264524 | − | 0.964379i | \(-0.414785\pi\) | ||||
0.264524 | + | 0.964379i | \(0.414785\pi\) | |||||||
\(20\) | −15.6201 | −0.174639 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 53.4826 | 0.518297 | ||||||||
\(23\) | −19.2488 | −0.174507 | −0.0872533 | − | 0.996186i | \(-0.527809\pi\) | ||||
−0.0872533 | + | 0.996186i | \(0.527809\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 277.645 | 2.22116 | ||||||||
\(26\) | −243.302 | −1.83521 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.40676 | −0.0229935 | ||||||||
\(29\) | 46.3126 | 0.296553 | 0.148276 | − | 0.988946i | \(-0.452627\pi\) | ||||
0.148276 | + | 0.988946i | \(0.452627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 307.269 | 1.78023 | 0.890114 | − | 0.455738i | \(-0.150625\pi\) | ||||
0.890114 | + | 0.455738i | \(0.150625\pi\) | |||||||
\(32\) | 35.1069 | 0.193940 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −296.518 | −1.49566 | ||||||||
\(35\) | 87.8170 | 0.424108 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −176.784 | −0.785489 | −0.392744 | − | 0.919648i | \(-0.628474\pi\) | ||||
−0.392744 | + | 0.919648i | \(0.628474\pi\) | |||||||
\(38\) | −129.818 | −0.554190 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −429.339 | −1.69711 | ||||||||
\(41\) | 15.7068 | 0.0598291 | 0.0299146 | − | 0.999552i | \(-0.490476\pi\) | ||||
0.0299146 | + | 0.999552i | \(0.490476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 483.788 | 1.71574 | 0.857872 | − | 0.513863i | \(-0.171786\pi\) | ||||
0.857872 | + | 0.513863i | \(0.171786\pi\) | |||||||
\(44\) | −14.0517 | −0.0481448 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 57.0312 | 0.182800 | ||||||||
\(47\) | 260.516 | 0.808515 | 0.404258 | − | 0.914645i | \(-0.367530\pi\) | ||||
0.404258 | + | 0.914645i | \(0.367530\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −323.847 | −0.944161 | ||||||||
\(50\) | −822.618 | −2.32671 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 63.9235 | 0.170473 | ||||||||
\(53\) | −217.305 | −0.563190 | −0.281595 | − | 0.959533i | \(-0.590863\pi\) | ||||
−0.281595 | + | 0.959533i | \(0.590863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 362.214 | 0.888016 | ||||||||
\(56\) | −93.6391 | −0.223447 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −137.217 | −0.310646 | ||||||||
\(59\) | −176.201 | −0.388804 | −0.194402 | − | 0.980922i | \(-0.562277\pi\) | ||||
−0.194402 | + | 0.980922i | \(0.562277\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 324.738 | 0.681614 | 0.340807 | − | 0.940133i | \(-0.389300\pi\) | ||||
0.340807 | + | 0.940133i | \(0.389300\pi\) | |||||||
\(62\) | −910.388 | −1.86483 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 452.956 | 0.884680 | ||||||||
\(65\) | −1647.77 | −3.14433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1076.40 | 1.96274 | 0.981368 | − | 0.192138i | \(-0.0615421\pi\) | ||||
0.981368 | + | 0.192138i | \(0.0615421\pi\) | |||||||
\(68\) | 77.9053 | 0.138932 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −260.188 | −0.444263 | ||||||||
\(71\) | −236.616 | −0.395509 | −0.197755 | − | 0.980252i | \(-0.563365\pi\) | ||||
−0.197755 | + | 0.980252i | \(0.563365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −343.940 | −0.551440 | −0.275720 | − | 0.961238i | \(-0.588916\pi\) | ||||
−0.275720 | + | 0.961238i | \(0.588916\pi\) | |||||||
\(74\) | 523.783 | 0.822817 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34.1075 | 0.0514789 | ||||||||
\(77\) | 78.9990 | 0.116919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −326.144 | −0.464482 | −0.232241 | − | 0.972658i | \(-0.574606\pi\) | ||||
−0.232241 | + | 0.972658i | \(0.574606\pi\) | |||||||
\(80\) | 1397.03 | 1.95240 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −46.5369 | −0.0626724 | ||||||||
\(83\) | 245.256 | 0.324342 | 0.162171 | − | 0.986763i | \(-0.448150\pi\) | ||||
0.162171 | + | 0.986763i | \(0.448150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2008.18 | −2.56257 | ||||||||
\(86\) | −1433.39 | −1.79728 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −386.228 | −0.467864 | ||||||||
\(89\) | −1457.23 | −1.73557 | −0.867784 | − | 0.496941i | \(-0.834456\pi\) | ||||
−0.867784 | + | 0.496941i | \(0.834456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −359.380 | −0.413992 | ||||||||
\(92\) | −14.9840 | −0.0169803 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −771.869 | −0.846938 | ||||||||
\(95\) | −879.198 | −0.949514 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 762.159 | 0.797789 | 0.398895 | − | 0.916997i | \(-0.369394\pi\) | ||||
0.398895 | + | 0.916997i | \(0.369394\pi\) | |||||||
\(98\) | 959.508 | 0.989030 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 216.129 | 0.216129 | ||||||||
\(101\) | −778.397 | −0.766865 | −0.383432 | − | 0.923569i | \(-0.625258\pi\) | ||||
−0.383432 | + | 0.923569i | \(0.625258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1026.09 | 0.981588 | 0.490794 | − | 0.871276i | \(-0.336707\pi\) | ||||
0.490794 | + | 0.871276i | \(0.336707\pi\) | |||||||
\(104\) | 1757.02 | 1.65663 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 643.839 | 0.589955 | ||||||||
\(107\) | −1163.26 | −1.05100 | −0.525498 | − | 0.850795i | \(-0.676121\pi\) | ||||
−0.525498 | + | 0.850795i | \(0.676121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1661.88 | −1.46036 | −0.730179 | − | 0.683256i | \(-0.760563\pi\) | ||||
−0.730179 | + | 0.683256i | \(0.760563\pi\) | |||||||
\(110\) | −1073.18 | −0.930218 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 304.692 | 0.257060 | ||||||||
\(113\) | 1348.99 | 1.12303 | 0.561514 | − | 0.827467i | \(-0.310219\pi\) | ||||
0.561514 | + | 0.827467i | \(0.310219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 386.246 | 0.313197 | ||||||||
\(116\) | 36.0515 | 0.0288560 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 522.057 | 0.407282 | ||||||||
\(119\) | −437.986 | −0.337396 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1005.16 | −0.755190 | ||||||||
\(122\) | −962.148 | −0.714006 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 239.190 | 0.173225 | ||||||||
\(125\) | −3062.97 | −2.19168 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −146.701 | −0.102501 | −0.0512504 | − | 0.998686i | \(-0.516321\pi\) | ||||
−0.0512504 | + | 0.998686i | \(0.516321\pi\) | |||||||
\(128\) | −1622.89 | −1.12066 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4882.09 | 3.29375 | ||||||||
\(131\) | 170.987 | 0.114040 | 0.0570199 | − | 0.998373i | \(-0.481840\pi\) | ||||
0.0570199 | + | 0.998373i | \(0.481840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −191.753 | −0.125016 | ||||||||
\(134\) | −3189.21 | −2.05601 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2141.32 | 1.35013 | ||||||||
\(137\) | 2473.93 | 1.54279 | 0.771396 | − | 0.636356i | \(-0.219559\pi\) | ||||
0.771396 | + | 0.636356i | \(0.219559\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1702.66 | 1.03898 | 0.519489 | − | 0.854477i | \(-0.326122\pi\) | ||||
0.519489 | + | 0.854477i | \(0.326122\pi\) | |||||||
\(140\) | 68.3601 | 0.0412677 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 701.056 | 0.414305 | ||||||||
\(143\) | −1482.32 | −0.866835 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −929.309 | −0.532240 | ||||||||
\(146\) | 1019.04 | 0.577647 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −137.615 | −0.0764318 | ||||||||
\(149\) | 2686.59 | 1.47714 | 0.738571 | − | 0.674176i | \(-0.235501\pi\) | ||||
0.738571 | + | 0.674176i | \(0.235501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2213.88 | −1.19313 | −0.596565 | − | 0.802565i | \(-0.703468\pi\) | ||||
−0.596565 | + | 0.802565i | \(0.703468\pi\) | |||||||
\(152\) | 937.488 | 0.500265 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −234.062 | −0.122475 | ||||||||
\(155\) | −6165.65 | −3.19508 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −382.822 | −0.194602 | −0.0973011 | − | 0.995255i | \(-0.531021\pi\) | ||||
−0.0973011 | + | 0.995255i | \(0.531021\pi\) | |||||||
\(158\) | 966.314 | 0.486556 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −704.455 | −0.348075 | ||||||||
\(161\) | 84.2405 | 0.0412365 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2175.67 | 1.04547 | 0.522736 | − | 0.852495i | \(-0.324912\pi\) | ||||
0.522736 | + | 0.852495i | \(0.324912\pi\) | |||||||
\(164\) | 12.2268 | 0.00582166 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −726.656 | −0.339755 | ||||||||
\(167\) | 106.542 | 0.0493680 | 0.0246840 | − | 0.999695i | \(-0.492142\pi\) | ||||
0.0246840 | + | 0.999695i | \(0.492142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4546.31 | 2.06933 | ||||||||
\(170\) | 5949.94 | 2.68435 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 376.599 | 0.166950 | ||||||||
\(173\) | 53.6245 | 0.0235664 | 0.0117832 | − | 0.999931i | \(-0.496249\pi\) | ||||
0.0117832 | + | 0.999931i | \(0.496249\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1215.09 | −0.524868 | ||||||||
\(176\) | 1256.75 | 0.538243 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4317.53 | 1.81805 | ||||||||
\(179\) | 3374.78 | 1.40918 | 0.704588 | − | 0.709616i | \(-0.251132\pi\) | ||||
0.704588 | + | 0.709616i | \(0.251132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −671.276 | −0.275666 | −0.137833 | − | 0.990455i | \(-0.544014\pi\) | ||||
−0.137833 | + | 0.990455i | \(0.544014\pi\) | |||||||
\(182\) | 1064.79 | 0.433666 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −411.854 | −0.165012 | ||||||||
\(185\) | 3547.35 | 1.40976 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1806.54 | −0.706455 | ||||||||
\(188\) | 202.796 | 0.0786724 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2604.93 | 0.994638 | ||||||||
\(191\) | 2129.32 | 0.806660 | 0.403330 | − | 0.915054i | \(-0.367853\pi\) | ||||
0.403330 | + | 0.915054i | \(0.367853\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 70.6759 | 0.0263594 | 0.0131797 | − | 0.999913i | \(-0.495805\pi\) | ||||
0.0131797 | + | 0.999913i | \(0.495805\pi\) | |||||||
\(194\) | −2258.16 | −0.835703 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −252.095 | −0.0918713 | ||||||||
\(197\) | 18.0688 | 0.00653477 | 0.00326739 | − | 0.999995i | \(-0.498960\pi\) | ||||
0.00326739 | + | 0.999995i | \(0.498960\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1416.52 | −0.504596 | −0.252298 | − | 0.967650i | \(-0.581186\pi\) | ||||
−0.252298 | + | 0.967650i | \(0.581186\pi\) | |||||||
\(200\) | 5940.58 | 2.10031 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2306.27 | 0.803309 | ||||||||
\(203\) | −202.683 | −0.0700765 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −315.173 | −0.107379 | ||||||||
\(206\) | −3040.14 | −1.02824 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5717.16 | −1.90583 | ||||||||
\(209\) | −790.915 | −0.261764 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3589.96 | −1.17129 | −0.585646 | − | 0.810567i | \(-0.699159\pi\) | ||||
−0.585646 | + | 0.810567i | \(0.699159\pi\) | |||||||
\(212\) | −169.158 | −0.0548011 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3446.56 | 1.10094 | ||||||||
\(215\) | −9707.70 | −3.07935 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1344.73 | −0.420674 | ||||||||
\(218\) | 4923.88 | 1.52976 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 281.961 | 0.0864082 | ||||||||
\(221\) | 8218.25 | 2.50144 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1859.09 | 0.558269 | 0.279135 | − | 0.960252i | \(-0.409952\pi\) | ||||
0.279135 | + | 0.960252i | \(0.409952\pi\) | |||||||
\(224\) | −153.642 | −0.0458287 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3996.84 | −1.17640 | ||||||||
\(227\) | 722.980 | 0.211392 | 0.105696 | − | 0.994399i | \(-0.466293\pi\) | ||||
0.105696 | + | 0.994399i | \(0.466293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5665.68 | −1.63493 | −0.817465 | − | 0.575979i | \(-0.804621\pi\) | ||||
−0.817465 | + | 0.575979i | \(0.804621\pi\) | |||||||
\(230\) | −1144.39 | −0.328081 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 990.920 | 0.280419 | ||||||||
\(233\) | −860.058 | −0.241821 | −0.120910 | − | 0.992663i | \(-0.538581\pi\) | ||||
−0.120910 | + | 0.992663i | \(0.538581\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5227.52 | −1.45109 | ||||||||
\(236\) | −137.162 | −0.0378325 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1297.68 | 0.353430 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2307.55 | 0.616774 | 0.308387 | − | 0.951261i | \(-0.400211\pi\) | ||||
0.308387 | + | 0.951261i | \(0.400211\pi\) | |||||||
\(242\) | 2978.12 | 0.791079 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 252.789 | 0.0663243 | ||||||||
\(245\) | 6498.32 | 1.69454 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3598.01 | 0.926866 | ||||||||
\(248\) | 6574.43 | 1.68337 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9075.10 | 2.29584 | ||||||||
\(251\) | 182.803 | 0.0459698 | 0.0229849 | − | 0.999736i | \(-0.492683\pi\) | ||||
0.0229849 | + | 0.999736i | \(0.492683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 347.462 | 0.0863429 | ||||||||
\(254\) | 434.652 | 0.107372 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1184.73 | 0.289240 | ||||||||
\(257\) | 2322.56 | 0.563725 | 0.281862 | − | 0.959455i | \(-0.409048\pi\) | ||||
0.281862 | + | 0.959455i | \(0.409048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 773.677 | 0.185614 | ||||||||
\(260\) | −1282.69 | −0.305958 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −506.608 | −0.119459 | ||||||||
\(263\) | 1496.72 | 0.350920 | 0.175460 | − | 0.984487i | \(-0.443859\pi\) | ||||
0.175460 | + | 0.984487i | \(0.443859\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4360.43 | 1.01079 | ||||||||
\(266\) | 568.135 | 0.130957 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 837.912 | 0.190984 | ||||||||
\(269\) | −5169.38 | −1.17168 | −0.585841 | − | 0.810426i | \(-0.699236\pi\) | ||||
−0.585841 | + | 0.810426i | \(0.699236\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3146.26 | −0.705246 | −0.352623 | − | 0.935765i | \(-0.614710\pi\) | ||||
−0.352623 | + | 0.935765i | \(0.614710\pi\) | |||||||
\(272\) | −6967.65 | −1.55322 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7329.88 | −1.61611 | ||||||||
\(275\) | −5011.80 | −1.09899 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2778.10 | −0.602598 | −0.301299 | − | 0.953530i | \(-0.597420\pi\) | ||||
−0.301299 | + | 0.953530i | \(0.597420\pi\) | |||||||
\(278\) | −5044.72 | −1.08835 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1878.96 | 0.401034 | ||||||||
\(281\) | 5089.72 | 1.08052 | 0.540262 | − | 0.841497i | \(-0.318325\pi\) | ||||
0.540262 | + | 0.841497i | \(0.318325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3489.81 | −0.733030 | −0.366515 | − | 0.930412i | \(-0.619449\pi\) | ||||
−0.366515 | + | 0.930412i | \(0.619449\pi\) | |||||||
\(284\) | −184.191 | −0.0384850 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4391.87 | 0.908030 | ||||||||
\(287\) | −68.7394 | −0.0141378 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5102.79 | 1.03863 | ||||||||
\(290\) | 2753.40 | 0.557534 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −267.736 | −0.0536578 | ||||||||
\(293\) | 1983.98 | 0.395581 | 0.197791 | − | 0.980244i | \(-0.436623\pi\) | ||||
0.197791 | + | 0.980244i | \(0.436623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3535.66 | 0.697810 | ||||||||
\(296\) | −3782.53 | −0.742753 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7959.94 | −1.54734 | ||||||||
\(299\) | −1580.67 | −0.305727 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2117.25 | −0.405437 | ||||||||
\(302\) | 6559.37 | 1.24983 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3050.49 | −0.575518 | ||||||||
\(305\) | −6516.20 | −1.22333 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2999.10 | −0.557549 | −0.278775 | − | 0.960357i | \(-0.589928\pi\) | ||||
−0.278775 | + | 0.960357i | \(0.589928\pi\) | |||||||
\(308\) | 61.4958 | 0.0113768 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18267.9 | 3.34692 | ||||||||
\(311\) | 1410.71 | 0.257216 | 0.128608 | − | 0.991696i | \(-0.458949\pi\) | ||||
0.128608 | + | 0.991696i | \(0.458949\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2855.71 | −0.515701 | −0.257851 | − | 0.966185i | \(-0.583014\pi\) | ||||
−0.257851 | + | 0.966185i | \(0.583014\pi\) | |||||||
\(314\) | 1134.24 | 0.203850 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −253.883 | −0.0451963 | ||||||||
\(317\) | 9851.39 | 1.74546 | 0.872728 | − | 0.488207i | \(-0.162349\pi\) | ||||
0.872728 | + | 0.488207i | \(0.162349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −835.993 | −0.146729 | ||||||||
\(320\) | −9089.02 | −1.58779 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −249.591 | −0.0431962 | ||||||||
\(323\) | 4384.99 | 0.755378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22799.5 | 3.89136 | ||||||||
\(326\) | −6446.17 | −1.09516 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 336.069 | 0.0565741 | ||||||||
\(329\) | −1140.13 | −0.191055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4100.89 | 0.680983 | 0.340492 | − | 0.940248i | \(-0.389406\pi\) | ||||
0.340492 | + | 0.940248i | \(0.389406\pi\) | |||||||
\(332\) | 190.917 | 0.0315600 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −315.667 | −0.0517141 | ||||||||
\(335\) | −21599.1 | −3.52264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7998.17 | −1.29284 | −0.646422 | − | 0.762980i | \(-0.723735\pi\) | ||||
−0.646422 | + | 0.762980i | \(0.723735\pi\) | |||||||
\(338\) | −13470.0 | −2.16767 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1563.25 | −0.249350 | ||||||||
\(341\) | −5546.54 | −0.880827 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2918.39 | 0.459412 | ||||||||
\(344\) | 10351.3 | 1.62240 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −158.881 | −0.0246864 | ||||||||
\(347\) | 6813.64 | 1.05411 | 0.527053 | − | 0.849832i | \(-0.323297\pi\) | ||||
0.527053 | + | 0.849832i | \(0.323297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3694.48 | 0.566650 | 0.283325 | − | 0.959024i | \(-0.408563\pi\) | ||||
0.283325 | + | 0.959024i | \(0.408563\pi\) | |||||||
\(350\) | 3600.11 | 0.549811 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −633.718 | −0.0959582 | ||||||||
\(353\) | 5908.53 | 0.890876 | 0.445438 | − | 0.895313i | \(-0.353048\pi\) | ||||
0.445438 | + | 0.895313i | \(0.353048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4747.94 | 0.709844 | ||||||||
\(356\) | −1134.36 | −0.168879 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9998.93 | −1.47614 | ||||||||
\(359\) | −11990.3 | −1.76275 | −0.881374 | − | 0.472420i | \(-0.843381\pi\) | ||||
−0.881374 | + | 0.472420i | \(0.843381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4939.22 | −0.720108 | ||||||||
\(362\) | 1988.89 | 0.288767 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −279.755 | −0.0402834 | ||||||||
\(365\) | 6901.51 | 0.989702 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8916.27 | 1.26819 | 0.634094 | − | 0.773256i | \(-0.281373\pi\) | ||||
0.634094 | + | 0.773256i | \(0.281373\pi\) | |||||||
\(368\) | 1340.13 | 0.189835 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10510.2 | −1.47676 | ||||||||
\(371\) | 951.012 | 0.133084 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12215.6 | −1.69571 | −0.847854 | − | 0.530230i | \(-0.822105\pi\) | ||||
−0.847854 | + | 0.530230i | \(0.822105\pi\) | |||||||
\(374\) | 5352.48 | 0.740027 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5574.10 | 0.764527 | ||||||||
\(377\) | 3803.08 | 0.519545 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6784.64 | −0.919535 | −0.459767 | − | 0.888039i | \(-0.652067\pi\) | ||||
−0.459767 | + | 0.888039i | \(0.652067\pi\) | |||||||
\(380\) | −684.401 | −0.0923922 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6308.84 | −0.844996 | ||||||||
\(383\) | 217.768 | 0.0290534 | 0.0145267 | − | 0.999894i | \(-0.495376\pi\) | ||||
0.0145267 | + | 0.999894i | \(0.495376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1585.19 | −0.209841 | ||||||||
\(386\) | −209.402 | −0.0276121 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 593.294 | 0.0776287 | ||||||||
\(389\) | 5824.23 | 0.759126 | 0.379563 | − | 0.925166i | \(-0.376074\pi\) | ||||
0.379563 | + | 0.925166i | \(0.376074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1926.40 | −0.249162 | ||||||||
\(392\) | −6929.15 | −0.892793 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −53.5351 | −0.00684532 | ||||||||
\(395\) | 6544.41 | 0.833633 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10235.3 | 1.29394 | 0.646970 | − | 0.762515i | \(-0.276036\pi\) | ||||
0.646970 | + | 0.762515i | \(0.276036\pi\) | |||||||
\(398\) | 4196.94 | 0.528576 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19330.1 | −2.41626 | ||||||||
\(401\) | −9747.43 | −1.21387 | −0.606937 | − | 0.794750i | \(-0.707602\pi\) | ||||
−0.606937 | + | 0.794750i | \(0.707602\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25232.2 | 3.11887 | ||||||||
\(404\) | −605.934 | −0.0746196 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 600.517 | 0.0734067 | ||||||||
\(407\) | 3191.14 | 0.388647 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1582.88 | −0.191365 | −0.0956824 | − | 0.995412i | \(-0.530503\pi\) | ||||
−0.0956824 | + | 0.995412i | \(0.530503\pi\) | |||||||
\(410\) | 933.809 | 0.112482 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 798.747 | 0.0955132 | ||||||||
\(413\) | 771.128 | 0.0918759 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4921.31 | −0.582115 | ||||||||
\(416\) | 2882.89 | 0.339773 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2343.36 | 0.274204 | ||||||||
\(419\) | −5163.90 | −0.602083 | −0.301042 | − | 0.953611i | \(-0.597334\pi\) | ||||
−0.301042 | + | 0.953611i | \(0.597334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3768.50 | 0.436259 | 0.218130 | − | 0.975920i | \(-0.430004\pi\) | ||||
0.218130 | + | 0.975920i | \(0.430004\pi\) | |||||||
\(422\) | 10636.5 | 1.22696 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4649.52 | −0.532549 | ||||||||
\(425\) | 27786.4 | 3.17138 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1421.19 | −0.161068 | ||||||||
\(428\) | −905.526 | −0.102267 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 28762.4 | 3.22569 | ||||||||
\(431\) | 10345.6 | 1.15622 | 0.578108 | − | 0.815960i | \(-0.303791\pi\) | ||||
0.578108 | + | 0.815960i | \(0.303791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15595.8 | 1.73092 | 0.865460 | − | 0.500978i | \(-0.167026\pi\) | ||||
0.865460 | + | 0.500978i | \(0.167026\pi\) | |||||||
\(434\) | 3984.23 | 0.440666 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1293.67 | −0.142100 | ||||||||
\(437\) | −843.392 | −0.0923224 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16692.3 | −1.81476 | −0.907379 | − | 0.420314i | \(-0.861920\pi\) | ||||
−0.907379 | + | 0.420314i | \(0.861920\pi\) | |||||||
\(440\) | 7750.05 | 0.839703 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24349.4 | −2.62032 | ||||||||
\(443\) | −13601.6 | −1.45876 | −0.729378 | − | 0.684110i | \(-0.760191\pi\) | ||||
−0.729378 | + | 0.684110i | \(0.760191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29240.7 | 3.11493 | ||||||||
\(446\) | −5508.20 | −0.584800 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1982.32 | −0.209053 | ||||||||
\(449\) | −14742.7 | −1.54955 | −0.774777 | − | 0.632234i | \(-0.782138\pi\) | ||||
−0.774777 | + | 0.632234i | \(0.782138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −283.526 | −0.0296024 | ||||||||
\(452\) | 1050.10 | 0.109276 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2142.08 | −0.221438 | ||||||||
\(455\) | 7211.32 | 0.743016 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16803.5 | 1.71999 | 0.859993 | − | 0.510306i | \(-0.170468\pi\) | ||||
0.859993 | + | 0.510306i | \(0.170468\pi\) | |||||||
\(458\) | 16786.5 | 1.71263 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 300.669 | 0.0304756 | ||||||||
\(461\) | 4075.01 | 0.411697 | 0.205848 | − | 0.978584i | \(-0.434005\pi\) | ||||
0.205848 | + | 0.978584i | \(0.434005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18708.0 | 1.87783 | 0.938915 | − | 0.344150i | \(-0.111833\pi\) | ||||
0.938915 | + | 0.344150i | \(0.111833\pi\) | |||||||
\(464\) | −3224.35 | −0.322601 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2548.22 | 0.253313 | ||||||||
\(467\) | 4242.04 | 0.420339 | 0.210170 | − | 0.977665i | \(-0.432598\pi\) | ||||
0.210170 | + | 0.977665i | \(0.432598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4710.77 | −0.463802 | ||||||||
\(470\) | 15488.3 | 1.52005 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3770.07 | −0.367651 | ||||||||
\(473\) | −8732.91 | −0.848921 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12165.1 | 1.17510 | ||||||||
\(476\) | −340.945 | −0.0328302 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −708.119 | −0.0677586 | ||||||||
\(479\) | −7179.42 | −0.684835 | −0.342418 | − | 0.939548i | \(-0.611246\pi\) | ||||
−0.342418 | + | 0.939548i | \(0.611246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14517.1 | −1.37614 | ||||||||
\(482\) | −6836.91 | −0.646085 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −782.453 | −0.0734836 | ||||||||
\(485\) | −15293.5 | −1.43184 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12366.9 | 1.15071 | 0.575356 | − | 0.817903i | \(-0.304863\pi\) | ||||
0.575356 | + | 0.817903i | \(0.304863\pi\) | |||||||
\(488\) | 6948.21 | 0.644530 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19253.5 | −1.77507 | ||||||||
\(491\) | 7374.98 | 0.677858 | 0.338929 | − | 0.940812i | \(-0.389935\pi\) | ||||
0.338929 | + | 0.940812i | \(0.389935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4634.91 | 0.423420 | ||||||||
\(494\) | −10660.3 | −0.970913 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21392.5 | −1.93660 | ||||||||
\(497\) | 1035.53 | 0.0934603 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20941.4 | −1.87869 | −0.939343 | − | 0.342980i | \(-0.888564\pi\) | ||||
−0.939343 | + | 0.342980i | \(0.888564\pi\) | |||||||
\(500\) | −2384.33 | −0.213261 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −541.617 | −0.0481545 | ||||||||
\(503\) | −677.720 | −0.0600757 | −0.0300378 | − | 0.999549i | \(-0.509563\pi\) | ||||
−0.0300378 | + | 0.999549i | \(0.509563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15619.3 | 1.37634 | ||||||||
\(506\) | −1029.48 | −0.0904462 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −114.198 | −0.00997381 | ||||||||
\(509\) | 10306.5 | 0.897503 | 0.448752 | − | 0.893657i | \(-0.351869\pi\) | ||||
0.448752 | + | 0.893657i | \(0.351869\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1505.22 | 0.130307 | ||||||||
\(512\) | 9472.98 | 0.817677 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6881.38 | −0.590515 | ||||||||
\(515\) | −20589.5 | −1.76171 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4702.61 | −0.400040 | ||||||||
\(518\) | −2292.28 | −0.194435 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −35256.3 | −2.97326 | ||||||||
\(521\) | 9265.72 | 0.779153 | 0.389576 | − | 0.920994i | \(-0.372621\pi\) | ||||
0.389576 | + | 0.920994i | \(0.372621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 596.346 | 0.0498592 | 0.0249296 | − | 0.999689i | \(-0.492064\pi\) | ||||
0.0249296 | + | 0.999689i | \(0.492064\pi\) | |||||||
\(524\) | 133.103 | 0.0110966 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4434.55 | −0.367596 | ||||||||
\(527\) | 30751.1 | 2.54182 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11796.5 | −0.969547 | ||||||||
\(530\) | −12919.3 | −1.05883 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −149.268 | −0.0121647 | ||||||||
\(533\) | 1289.81 | 0.104818 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23342.0 | 1.88628 | ||||||||
\(536\) | 23031.1 | 1.85595 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15316.1 | 1.22736 | ||||||||
\(539\) | 5845.80 | 0.467155 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5386.76 | 0.428087 | 0.214043 | − | 0.976824i | \(-0.431337\pi\) | ||||
0.214043 | + | 0.976824i | \(0.431337\pi\) | |||||||
\(542\) | 9321.87 | 0.738761 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3513.46 | 0.276908 | ||||||||
\(545\) | 33347.3 | 2.62099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8903.74 | 0.695972 | 0.347986 | − | 0.937500i | \(-0.386866\pi\) | ||||
0.347986 | + | 0.937500i | \(0.386866\pi\) | |||||||
\(548\) | 1925.80 | 0.150121 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14849.2 | 1.15122 | ||||||||
\(551\) | 2029.20 | 0.156891 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1427.34 | 0.109759 | ||||||||
\(554\) | 8231.06 | 0.631235 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1325.42 | 0.101098 | ||||||||
\(557\) | 18011.3 | 1.37013 | 0.685064 | − | 0.728483i | \(-0.259774\pi\) | ||||
0.685064 | + | 0.728483i | \(0.259774\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39727.5 | 3.00590 | ||||||||
\(560\) | −6113.95 | −0.461360 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15080.0 | −1.13187 | ||||||||
\(563\) | −22166.2 | −1.65932 | −0.829658 | − | 0.558272i | \(-0.811465\pi\) | ||||
−0.829658 | + | 0.558272i | \(0.811465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27068.8 | −2.01556 | ||||||||
\(566\) | 10339.8 | 0.767866 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5062.72 | −0.373991 | ||||||||
\(569\) | −20278.7 | −1.49407 | −0.747035 | − | 0.664784i | \(-0.768523\pi\) | ||||
−0.747035 | + | 0.664784i | \(0.768523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9135.32 | 0.669529 | 0.334765 | − | 0.942302i | \(-0.391343\pi\) | ||||
0.334765 | + | 0.942302i | \(0.391343\pi\) | |||||||
\(572\) | −1153.89 | −0.0843472 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 203.664 | 0.0148097 | ||||||||
\(575\) | −5344.33 | −0.387607 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15593.3 | 1.12505 | 0.562527 | − | 0.826779i | \(-0.309829\pi\) | ||||
0.562527 | + | 0.826779i | \(0.309829\pi\) | |||||||
\(578\) | −15118.8 | −1.08799 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −723.409 | −0.0517895 | ||||||||
\(581\) | −1073.34 | −0.0766431 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3922.59 | 0.278657 | ||||||||
\(584\) | −7359.07 | −0.521439 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5878.22 | −0.414380 | ||||||||
\(587\) | 20628.7 | 1.45049 | 0.725246 | − | 0.688490i | \(-0.241726\pi\) | ||||
0.725246 | + | 0.688490i | \(0.241726\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13463.1 | 0.941826 | ||||||||
\(590\) | −10475.6 | −0.730972 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12308.0 | 0.854483 | ||||||||
\(593\) | −24665.1 | −1.70805 | −0.854026 | − | 0.520231i | \(-0.825846\pi\) | ||||
−0.854026 | + | 0.520231i | \(0.825846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8788.63 | 0.605544 | ||||||||
\(596\) | 2091.34 | 0.143733 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4683.26 | 0.320256 | ||||||||
\(599\) | −4775.77 | −0.325764 | −0.162882 | − | 0.986646i | \(-0.552079\pi\) | ||||
−0.162882 | + | 0.986646i | \(0.552079\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11733.3 | 0.796359 | 0.398180 | − | 0.917307i | \(-0.369642\pi\) | ||||
0.398180 | + | 0.917307i | \(0.369642\pi\) | |||||||
\(602\) | 6273.09 | 0.424704 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1723.37 | −0.116097 | ||||||||
\(605\) | 20169.5 | 1.35538 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24208.3 | 1.61876 | 0.809378 | − | 0.587288i | \(-0.199804\pi\) | ||||
0.809378 | + | 0.587288i | \(0.199804\pi\) | |||||||
\(608\) | 1538.22 | 0.102604 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19306.5 | 1.28147 | ||||||||
\(611\) | 21393.0 | 1.41648 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3338.26 | −0.219953 | −0.109976 | − | 0.993934i | \(-0.535078\pi\) | ||||
−0.109976 | + | 0.993934i | \(0.535078\pi\) | |||||||
\(614\) | 8885.86 | 0.584046 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1690.29 | 0.110558 | ||||||||
\(617\) | 19730.0 | 1.28736 | 0.643679 | − | 0.765295i | \(-0.277407\pi\) | ||||
0.643679 | + | 0.765295i | \(0.277407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12280.2 | −0.797385 | −0.398692 | − | 0.917085i | \(-0.630536\pi\) | ||||
−0.398692 | + | 0.917085i | \(0.630536\pi\) | |||||||
\(620\) | −4799.58 | −0.310896 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4179.72 | −0.269439 | ||||||||
\(623\) | 6377.41 | 0.410121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 26756.0 | 1.71238 | ||||||||
\(626\) | 8461.03 | 0.540209 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −298.003 | −0.0189357 | ||||||||
\(629\) | −17692.3 | −1.12153 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 797.287 | 0.0503003 | 0.0251502 | − | 0.999684i | \(-0.491994\pi\) | ||||
0.0251502 | + | 0.999684i | \(0.491994\pi\) | |||||||
\(632\) | −6978.29 | −0.439211 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29188.1 | −1.82841 | ||||||||
\(635\) | 2943.70 | 0.183964 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26593.6 | −1.65412 | ||||||||
\(638\) | 2476.92 | 0.153702 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 32565.0 | 2.01132 | ||||||||
\(641\) | −23898.3 | −1.47258 | −0.736292 | − | 0.676664i | \(-0.763425\pi\) | ||||
−0.736292 | + | 0.676664i | \(0.763425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17199.9 | −1.05490 | −0.527449 | − | 0.849587i | \(-0.676851\pi\) | ||||
−0.527449 | + | 0.849587i | \(0.676851\pi\) | |||||||
\(644\) | 65.5760 | 0.00401251 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12992.0 | −0.791276 | ||||||||
\(647\) | 22371.5 | 1.35937 | 0.679686 | − | 0.733503i | \(-0.262116\pi\) | ||||
0.679686 | + | 0.733503i | \(0.262116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3180.63 | 0.192374 | ||||||||
\(650\) | −67551.4 | −4.07628 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1693.63 | 0.101729 | ||||||||
\(653\) | −2778.94 | −0.166536 | −0.0832682 | − | 0.996527i | \(-0.526536\pi\) | ||||
−0.0832682 | + | 0.996527i | \(0.526536\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3431.03 | −0.204674 | ||||||||
\(656\) | −1093.53 | −0.0650843 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3378.01 | 0.200135 | ||||||||
\(659\) | 26408.2 | 1.56103 | 0.780514 | − | 0.625138i | \(-0.214957\pi\) | ||||
0.780514 | + | 0.625138i | \(0.214957\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2574.95 | 0.151519 | 0.0757595 | − | 0.997126i | \(-0.475862\pi\) | ||||
0.0757595 | + | 0.997126i | \(0.475862\pi\) | |||||||
\(662\) | −12150.3 | −0.713346 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5247.59 | 0.306696 | ||||||||
\(665\) | 3847.73 | 0.224374 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −891.461 | −0.0517504 | ||||||||
\(668\) | 82.9362 | 0.00480374 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 63994.7 | 3.69004 | ||||||||
\(671\) | −5861.88 | −0.337251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25686.4 | 1.47123 | 0.735614 | − | 0.677401i | \(-0.236894\pi\) | ||||
0.735614 | + | 0.677401i | \(0.236894\pi\) | |||||||
\(674\) | 23697.3 | 1.35428 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3539.02 | 0.201355 | ||||||||
\(677\) | 9283.47 | 0.527020 | 0.263510 | − | 0.964657i | \(-0.415120\pi\) | ||||
0.263510 | + | 0.964657i | \(0.415120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3335.52 | −0.188521 | ||||||||
\(680\) | −42967.8 | −2.42315 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16433.5 | 0.922686 | ||||||||
\(683\) | −1759.49 | −0.0985722 | −0.0492861 | − | 0.998785i | \(-0.515695\pi\) | ||||
−0.0492861 | + | 0.998785i | \(0.515695\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49642.0 | −2.76894 | ||||||||
\(686\) | −8646.74 | −0.481245 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −33682.1 | −1.86645 | ||||||||
\(689\) | −17844.5 | −0.986680 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5318.04 | 0.292775 | 0.146388 | − | 0.989227i | \(-0.453235\pi\) | ||||
0.146388 | + | 0.989227i | \(0.453235\pi\) | |||||||
\(692\) | 41.7433 | 0.00229313 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20187.7 | −1.10420 | ||||||||
\(695\) | −34165.7 | −1.86472 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1571.92 | 0.0854244 | ||||||||
\(698\) | −10946.2 | −0.593579 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −945.869 | −0.0510721 | ||||||||
\(701\) | −1243.51 | −0.0669994 | −0.0334997 | − | 0.999439i | \(-0.510665\pi\) | ||||
−0.0334997 | + | 0.999439i | \(0.510665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7745.83 | −0.415561 | ||||||||
\(704\) | −8176.36 | −0.437725 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17506.0 | −0.933214 | ||||||||
\(707\) | 3406.58 | 0.181213 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25289.1 | 1.33957 | 0.669783 | − | 0.742557i | \(-0.266387\pi\) | ||||
0.669783 | + | 0.742557i | \(0.266387\pi\) | |||||||
\(710\) | −14067.4 | −0.743578 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31179.3 | −1.64114 | ||||||||
\(713\) | −5914.55 | −0.310661 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29744.1 | 1.55576 | ||||||||
\(716\) | 2627.05 | 0.137120 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35525.5 | 1.84652 | ||||||||
\(719\) | −23122.3 | −1.19932 | −0.599662 | − | 0.800253i | \(-0.704698\pi\) | ||||
−0.599662 | + | 0.800253i | \(0.704698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4490.58 | −0.231953 | ||||||||
\(722\) | 14634.1 | 0.754330 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −522.547 | −0.0268236 | ||||||||
\(725\) | 12858.4 | 0.658690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24532.7 | −1.25154 | −0.625769 | − | 0.780009i | \(-0.715215\pi\) | ||||
−0.625769 | + | 0.780009i | \(0.715215\pi\) | |||||||
\(728\) | −7689.42 | −0.391468 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20448.1 | −1.03674 | ||||||||
\(731\) | 48417.0 | 2.44975 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22966.4 | −1.15728 | −0.578638 | − | 0.815585i | \(-0.696416\pi\) | ||||
−0.578638 | + | 0.815585i | \(0.696416\pi\) | |||||||
\(734\) | −26417.5 | −1.32846 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −675.765 | −0.0338438 | ||||||||
\(737\) | −19430.2 | −0.971129 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27171.0 | −1.35250 | −0.676252 | − | 0.736671i | \(-0.736397\pi\) | ||||
−0.676252 | + | 0.736671i | \(0.736397\pi\) | |||||||
\(740\) | 2761.39 | 0.137177 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2817.70 | −0.139408 | ||||||||
\(743\) | −13694.7 | −0.676192 | −0.338096 | − | 0.941112i | \(-0.609783\pi\) | ||||
−0.338096 | + | 0.941112i | \(0.609783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53909.1 | −2.65111 | ||||||||
\(746\) | 36192.8 | 1.77629 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1406.28 | −0.0687414 | ||||||||
\(749\) | 5090.90 | 0.248354 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1219.25 | 0.0592424 | 0.0296212 | − | 0.999561i | \(-0.490570\pi\) | ||||
0.0296212 | + | 0.999561i | \(0.490570\pi\) | |||||||
\(752\) | −18137.6 | −0.879532 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11267.9 | −0.544236 | ||||||||
\(755\) | 44423.7 | 2.14138 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1138.49 | 0.0546620 | 0.0273310 | − | 0.999626i | \(-0.491299\pi\) | ||||
0.0273310 | + | 0.999626i | \(0.491299\pi\) | |||||||
\(758\) | 20101.8 | 0.963234 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18811.6 | −0.897855 | ||||||||
\(761\) | 16423.4 | 0.782325 | 0.391162 | − | 0.920322i | \(-0.372073\pi\) | ||||
0.391162 | + | 0.920322i | \(0.372073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7273.05 | 0.345088 | ||||||||
\(764\) | 1657.54 | 0.0784919 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −645.214 | −0.0304341 | ||||||||
\(767\) | −14469.2 | −0.681166 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23857.4 | −1.11875 | −0.559376 | − | 0.828914i | \(-0.688959\pi\) | ||||
−0.559376 | + | 0.828914i | \(0.688959\pi\) | |||||||
\(770\) | 4696.68 | 0.219814 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 55.0168 | 0.00256489 | ||||||||
\(773\) | −5404.60 | −0.251475 | −0.125737 | − | 0.992064i | \(-0.540130\pi\) | ||||
−0.125737 | + | 0.992064i | \(0.540130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 85311.5 | 3.95417 | ||||||||
\(776\) | 16307.4 | 0.754385 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17256.3 | −0.795202 | ||||||||
\(779\) | 688.199 | 0.0316525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4271.18 | 0.195691 | ||||||||
\(782\) | 5707.62 | 0.261003 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22546.7 | 1.02709 | ||||||||
\(785\) | 7681.71 | 0.349264 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31446.3 | 1.42432 | 0.712161 | − | 0.702017i | \(-0.247717\pi\) | ||||
0.712161 | + | 0.702017i | \(0.247717\pi\) | |||||||
\(788\) | 14.0655 | 0.000635864 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19390.1 | −0.873250 | ||||||||
\(791\) | −5903.72 | −0.265376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26666.7 | 1.19415 | ||||||||
\(794\) | −30325.5 | −1.35543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1102.68 | −0.0490996 | ||||||||
\(797\) | −36126.4 | −1.60560 | −0.802801 | − | 0.596248i | \(-0.796658\pi\) | ||||
−0.802801 | + | 0.596248i | \(0.796658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26072.2 | 1.15440 | ||||||||
\(800\) | 9747.23 | 0.430771 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28880.1 | 1.27156 | ||||||||
\(803\) | 6208.50 | 0.272843 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1690.37 | −0.0740096 | ||||||||
\(806\) | −74759.0 | −3.26709 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16654.8 | −0.725143 | ||||||||
\(809\) | 39760.7 | 1.72795 | 0.863976 | − | 0.503533i | \(-0.167967\pi\) | ||||
0.863976 | + | 0.503533i | \(0.167967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24265.4 | −1.05065 | −0.525323 | − | 0.850903i | \(-0.676056\pi\) | ||||
−0.525323 | + | 0.850903i | \(0.676056\pi\) | |||||||
\(812\) | −157.776 | −0.00681878 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9454.86 | −0.407116 | ||||||||
\(815\) | −43657.1 | −1.87637 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21197.3 | 0.907711 | ||||||||
\(818\) | 4689.81 | 0.200459 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −245.343 | −0.0104485 | ||||||||
\(821\) | −30503.1 | −1.29667 | −0.648334 | − | 0.761356i | \(-0.724534\pi\) | ||||
−0.648334 | + | 0.761356i | \(0.724534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39552.4 | −1.67523 | −0.837613 | − | 0.546264i | \(-0.816049\pi\) | ||||
−0.837613 | + | 0.546264i | \(0.816049\pi\) | |||||||
\(824\) | 21954.6 | 0.928184 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2284.73 | −0.0962421 | ||||||||
\(827\) | −25903.8 | −1.08920 | −0.544598 | − | 0.838698i | \(-0.683318\pi\) | ||||
−0.544598 | + | 0.838698i | \(0.683318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30363.1 | 1.27208 | 0.636039 | − | 0.771657i | \(-0.280572\pi\) | ||||
0.636039 | + | 0.771657i | \(0.280572\pi\) | |||||||
\(830\) | 14581.1 | 0.609779 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 37195.7 | 1.54991 | ||||||||
\(833\) | −32410.3 | −1.34808 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2137.87 | −0.0886036 | ||||||||
\(836\) | −615.678 | −0.0254709 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15299.8 | 0.630696 | ||||||||
\(839\) | −43564.3 | −1.79262 | −0.896310 | − | 0.443428i | \(-0.853762\pi\) | ||||
−0.896310 | + | 0.443428i | \(0.853762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22244.1 | −0.912056 | ||||||||
\(842\) | −11165.5 | −0.456992 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2794.56 | −0.113972 | ||||||||
\(845\) | −91226.3 | −3.71394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4398.98 | 0.178454 | ||||||||
\(848\) | 15129.1 | 0.612659 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −82326.7 | −3.32210 | ||||||||
\(851\) | 3402.88 | 0.137073 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12912.3 | −0.518299 | −0.259149 | − | 0.965837i | \(-0.583442\pi\) | ||||
−0.259149 | + | 0.965837i | \(0.583442\pi\) | |||||||
\(854\) | 4210.75 | 0.168722 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24889.5 | −0.993816 | ||||||||
\(857\) | −11738.7 | −0.467897 | −0.233948 | − | 0.972249i | \(-0.575165\pi\) | ||||
−0.233948 | + | 0.972249i | \(0.575165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41876.5 | −1.66334 | −0.831670 | − | 0.555271i | \(-0.812615\pi\) | ||||
−0.831670 | + | 0.555271i | \(0.812615\pi\) | |||||||
\(860\) | −7556.84 | −0.299635 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30652.3 | −1.21116 | ||||||||
\(863\) | 17201.8 | 0.678514 | 0.339257 | − | 0.940694i | \(-0.389824\pi\) | ||||
0.339257 | + | 0.940694i | \(0.389824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1076.03 | −0.0422961 | ||||||||
\(866\) | −46208.0 | −1.81318 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1046.79 | −0.0409336 | ||||||||
\(869\) | 5887.26 | 0.229818 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 88391.5 | 3.43861 | ||||||||
\(872\) | −35558.1 | −1.38091 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2498.84 | 0.0967099 | ||||||||
\(875\) | 13404.8 | 0.517903 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33863.8 | −1.30388 | −0.651938 | − | 0.758272i | \(-0.726044\pi\) | ||||
−0.651938 | + | 0.758272i | \(0.726044\pi\) | |||||||
\(878\) | 49456.6 | 1.90100 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −25217.9 | −0.966017 | ||||||||
\(881\) | 28690.0 | 1.09715 | 0.548575 | − | 0.836101i | \(-0.315170\pi\) | ||||
0.548575 | + | 0.836101i | \(0.315170\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40094.8 | −1.52808 | −0.764042 | − | 0.645166i | \(-0.776788\pi\) | ||||
−0.764042 | + | 0.645166i | \(0.776788\pi\) | |||||||
\(884\) | 6397.40 | 0.243402 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40299.3 | 1.52808 | ||||||||
\(887\) | −22456.6 | −0.850079 | −0.425039 | − | 0.905175i | \(-0.639740\pi\) | ||||
−0.425039 | + | 0.905175i | \(0.639740\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 642.022 | 0.0242213 | ||||||||
\(890\) | −86635.6 | −3.26296 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1447.19 | 0.0543223 | ||||||||
\(893\) | 11414.6 | 0.427744 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −67718.3 | −2.52913 | ||||||||
\(896\) | 7102.44 | 0.264817 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 43680.2 | 1.62319 | ||||||||
\(899\) | 14230.4 | 0.527931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21747.6 | −0.804126 | ||||||||
\(902\) | 840.042 | 0.0310092 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28863.4 | 1.06193 | ||||||||
\(905\) | 13469.8 | 0.494754 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7459.02 | 0.273068 | 0.136534 | − | 0.990635i | \(-0.456404\pi\) | ||||
0.136534 | + | 0.990635i | \(0.456404\pi\) | |||||||
\(908\) | 562.795 | 0.0205694 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21366.0 | −0.778326 | ||||||||
\(911\) | 48552.9 | 1.76578 | 0.882892 | − | 0.469576i | \(-0.155593\pi\) | ||||
0.882892 | + | 0.469576i | \(0.155593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4427.15 | −0.160479 | ||||||||
\(914\) | −49786.1 | −1.80172 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4410.38 | −0.159086 | ||||||||
\(917\) | −748.309 | −0.0269480 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22652.3 | 0.813090 | 0.406545 | − | 0.913631i | \(-0.366733\pi\) | ||||
0.406545 | + | 0.913631i | \(0.366733\pi\) | |||||||
\(920\) | 8264.27 | 0.296157 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12073.6 | −0.431262 | ||||||||
\(923\) | −19430.4 | −0.692912 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −49083.1 | −1.74469 | ||||||||
\(926\) | −55428.9 | −1.96707 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1625.89 | 0.0575134 | ||||||||
\(929\) | −11545.0 | −0.407727 | −0.203864 | − | 0.978999i | \(-0.565350\pi\) | ||||
−0.203864 | + | 0.978999i | \(0.565350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14189.5 | −0.499507 | ||||||||
\(932\) | −669.502 | −0.0235303 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12568.5 | −0.440315 | ||||||||
\(935\) | 36250.0 | 1.26792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43731.1 | −1.52469 | −0.762344 | − | 0.647172i | \(-0.775952\pi\) | ||||
−0.762344 | + | 0.647172i | \(0.775952\pi\) | |||||||
\(938\) | 13957.3 | 0.485843 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4069.30 | −0.141198 | ||||||||
\(941\) | 29756.4 | 1.03085 | 0.515426 | − | 0.856934i | \(-0.327634\pi\) | ||||
0.515426 | + | 0.856934i | \(0.327634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −302.338 | −0.0104406 | ||||||||
\(944\) | 12267.4 | 0.422956 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25874.2 | 0.889265 | ||||||||
\(947\) | 14137.3 | 0.485112 | 0.242556 | − | 0.970137i | \(-0.422014\pi\) | ||||
0.242556 | + | 0.970137i | \(0.422014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28243.6 | −0.966096 | ||||||||
\(950\) | −36043.2 | −1.23094 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9371.30 | −0.319039 | ||||||||
\(953\) | 32201.4 | 1.09455 | 0.547274 | − | 0.836953i | \(-0.315665\pi\) | ||||
0.547274 | + | 0.836953i | \(0.315665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42726.9 | −1.44776 | ||||||||
\(956\) | 186.047 | 0.00629412 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21271.5 | 0.717381 | ||||||||
\(959\) | −10826.9 | −0.364567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64622.9 | 2.16921 | ||||||||
\(962\) | 43011.8 | 1.44153 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1796.29 | 0.0600150 | ||||||||
\(965\) | −1418.18 | −0.0473087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4397.57 | 0.146242 | 0.0731211 | − | 0.997323i | \(-0.476704\pi\) | ||||
0.0731211 | + | 0.997323i | \(0.476704\pi\) | |||||||
\(968\) | −21506.7 | −0.714103 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 45312.2 | 1.49988 | ||||||||
\(971\) | 4180.99 | 0.138182 | 0.0690908 | − | 0.997610i | \(-0.477990\pi\) | ||||
0.0690908 | + | 0.997610i | \(0.477990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7451.54 | −0.245514 | ||||||||
\(974\) | −36641.1 | −1.20540 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22608.8 | −0.741485 | ||||||||
\(977\) | 47905.2 | 1.56870 | 0.784351 | − | 0.620317i | \(-0.212996\pi\) | ||||
0.784351 | + | 0.620317i | \(0.212996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26304.5 | 0.858730 | ||||||||
\(980\) | 5058.54 | 0.164887 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21850.9 | −0.710072 | ||||||||
\(983\) | 38331.6 | 1.24373 | 0.621866 | − | 0.783124i | \(-0.286375\pi\) | ||||
0.621866 | + | 0.783124i | \(0.286375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −362.569 | −0.0117283 | ||||||||
\(986\) | −13732.5 | −0.443542 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2800.83 | 0.0901885 | ||||||||
\(989\) | −9312.34 | −0.299409 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44623.8 | −1.43039 | −0.715197 | − | 0.698923i | \(-0.753663\pi\) | ||||
−0.715197 | + | 0.698923i | \(0.753663\pi\) | |||||||
\(992\) | 10787.2 | 0.345257 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3068.11 | −0.0979018 | ||||||||
\(995\) | 28424.0 | 0.905628 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54629.3 | −1.73533 | −0.867667 | − | 0.497146i | \(-0.834381\pi\) | ||||
−0.867667 | + | 0.497146i | \(0.834381\pi\) | |||||||
\(998\) | 62046.0 | 1.96797 | ||||||||
\(999\) | 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 | 2151.4.a.e.1.10 | 32 | ||
3.2 | odd | 2 | 717.4.a.c.1.23 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.4.a.c.1.23 | ✓ | 32 | 3.2 | odd | 2 | ||
2151.4.a.e.1.10 | 32 | 1.1 | even | 1 | trivial |