Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(1,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("624.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 312) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.29150 | −0.652172 | −0.326086 | − | 0.945340i | \(-0.605730\pi\) | ||||
−0.326086 | + | 0.945340i | \(0.605730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.87451 | −0.317194 | −0.158597 | − | 0.987343i | \(-0.550697\pi\) | ||||
−0.158597 | + | 0.987343i | \(0.550697\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 51.1660 | 1.40247 | 0.701233 | − | 0.712932i | \(-0.252633\pi\) | ||||
0.701233 | + | 0.712932i | \(0.252633\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 21.8745 | 0.376532 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −73.7490 | −1.05216 | −0.526081 | − | 0.850434i | \(-0.676339\pi\) | ||||
−0.526081 | + | 0.850434i | \(0.676339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −59.9555 | −0.723934 | −0.361967 | − | 0.932191i | \(-0.617895\pi\) | ||||
−0.361967 | + | 0.932191i | \(0.617895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.6235 | 0.183132 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −69.8301 | −0.633068 | −0.316534 | − | 0.948581i | \(-0.602519\pi\) | ||||
−0.316534 | + | 0.948581i | \(0.602519\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −71.8340 | −0.574672 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −294.826 | −1.88786 | −0.943928 | − | 0.330151i | \(-0.892900\pi\) | ||||
−0.943928 | + | 0.330151i | \(0.892900\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 334.450 | 1.93771 | 0.968854 | − | 0.247634i | \(-0.0796530\pi\) | ||||
0.968854 | + | 0.247634i | \(0.0796530\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −153.498 | −0.809714 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 42.8340 | 0.206865 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 261.409 | 1.16150 | 0.580749 | − | 0.814083i | \(-0.302760\pi\) | ||||
0.580749 | + | 0.814083i | \(0.302760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 222.701 | 0.848293 | 0.424146 | − | 0.905594i | \(-0.360574\pi\) | ||||
0.424146 | + | 0.905594i | \(0.360574\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −79.2470 | −0.281048 | −0.140524 | − | 0.990077i | \(-0.544879\pi\) | ||||
−0.140524 | + | 0.990077i | \(0.544879\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −65.6235 | −0.217391 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 584.405 | 1.81371 | 0.906854 | − | 0.421445i | \(-0.138477\pi\) | ||||
0.906854 | + | 0.421445i | \(0.138477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −308.490 | −0.899388 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 221.247 | 0.607466 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 465.158 | 1.20555 | 0.602777 | − | 0.797910i | \(-0.294061\pi\) | ||||
0.602777 | + | 0.797910i | \(0.294061\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −373.077 | −0.914649 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 179.867 | 0.417963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 530.089 | 1.16969 | 0.584845 | − | 0.811145i | \(-0.301155\pi\) | ||||
0.584845 | + | 0.811145i | \(0.301155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 548.332 | 1.15093 | 0.575465 | − | 0.817826i | \(-0.304821\pi\) | ||||
0.575465 | + | 0.817826i | \(0.304821\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −52.8706 | −0.105731 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 94.7895 | 0.180880 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 384.959 | 0.701945 | 0.350972 | − | 0.936386i | \(-0.385851\pi\) | ||||
0.350972 | + | 0.936386i | \(0.385851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 209.490 | 0.365502 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 307.004 | 0.513164 | 0.256582 | − | 0.966522i | \(-0.417404\pi\) | ||||
0.256582 | + | 0.966522i | \(0.417404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −844.891 | −1.35462 | −0.677309 | − | 0.735699i | \(-0.736854\pi\) | ||||
−0.677309 | + | 0.735699i | \(0.736854\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 215.502 | 0.331787 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −300.575 | −0.444853 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −30.1699 | −0.0429669 | −0.0214834 | − | 0.999769i | \(-0.506839\pi\) | ||||
−0.0214834 | + | 0.999769i | \(0.506839\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −19.5633 | −0.0258717 | −0.0129359 | − | 0.999916i | \(-0.504118\pi\) | ||||
−0.0129359 | + | 0.999916i | \(0.504118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 537.741 | 0.686191 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 884.478 | 1.08995 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −513.017 | −0.611008 | −0.305504 | − | 0.952191i | \(-0.598825\pi\) | ||||
−0.305504 | + | 0.952191i | \(0.598825\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 76.3686 | 0.0879737 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1003.35 | −1.11874 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 437.166 | 0.472129 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 787.903 | 0.824737 | 0.412368 | − | 0.911017i | \(-0.364702\pi\) | ||||
0.412368 | + | 0.911017i | \(0.364702\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 460.494 | 0.467489 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1391.73 | 1.37111 | 0.685554 | − | 0.728022i | \(-0.259560\pi\) | ||||
0.685554 | + | 0.728022i | \(0.259560\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1428.58 | −1.36662 | −0.683309 | − | 0.730129i | \(-0.739460\pi\) | ||||
−0.683309 | + | 0.730129i | \(0.739460\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −128.502 | −0.119433 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1363.30 | 1.23173 | 0.615867 | − | 0.787850i | \(-0.288806\pi\) | ||||
0.615867 | + | 0.787850i | \(0.288806\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 979.182 | 0.860446 | 0.430223 | − | 0.902723i | \(-0.358435\pi\) | ||||
0.430223 | + | 0.902723i | \(0.358435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −784.227 | −0.670591 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1495.83 | 1.24527 | 0.622637 | − | 0.782511i | \(-0.286062\pi\) | ||||
0.622637 | + | 0.782511i | \(0.286062\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 509.166 | 0.412869 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 433.239 | 0.333739 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1286.96 | 0.966913 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −668.102 | −0.489762 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1435.22 | 1.02696 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2221.69 | −1.55231 | −0.776155 | − | 0.630542i | \(-0.782833\pi\) | ||||
−0.776155 | + | 0.630542i | \(0.782833\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 237.741 | 0.162263 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 878.138 | 0.585674 | 0.292837 | − | 0.956162i | \(-0.405401\pi\) | ||||
0.292837 | + | 0.956162i | \(0.405401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 352.209 | 0.229627 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 196.871 | 0.125511 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1176.62 | −0.733762 | −0.366881 | − | 0.930268i | \(-0.619574\pi\) | ||||
−0.366881 | + | 0.930268i | \(0.619574\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −359.514 | −0.219378 | −0.109689 | − | 0.993966i | \(-0.534986\pi\) | ||||
−0.109689 | + | 0.993966i | \(0.534986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1753.22 | −1.04714 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −665.158 | −0.388974 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2149.73 | 1.23121 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 925.470 | 0.519262 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1226.94 | 0.674594 | 0.337297 | − | 0.941398i | \(-0.390487\pi\) | ||||
0.337297 | + | 0.941398i | \(0.390487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 705.665 | 0.380306 | 0.190153 | − | 0.981754i | \(-0.439102\pi\) | ||||
0.190153 | + | 0.981754i | \(0.439102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −663.741 | −0.350721 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2438.64 | −1.26372 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2519.80 | 1.28090 | 0.640452 | − | 0.767998i | \(-0.278747\pi\) | ||||
0.640452 | + | 0.767998i | \(0.278747\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1395.47 | −0.696027 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 410.217 | 0.200805 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1221.40 | −0.586919 | −0.293459 | − | 0.955972i | \(-0.594807\pi\) | ||||
−0.293459 | + | 0.955972i | \(0.594807\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1119.23 | 0.528073 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1099.52 | −0.509480 | −0.254740 | − | 0.967010i | \(-0.581990\pi\) | ||||
−0.254740 | + | 0.967010i | \(0.581990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −539.600 | −0.241311 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1817.39 | −0.798693 | −0.399346 | − | 0.916800i | \(-0.630763\pi\) | ||||
−0.399346 | + | 0.916800i | \(0.630763\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 421.989 | 0.182282 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1590.27 | −0.675321 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4705.22 | 1.96472 | 0.982359 | − | 0.187005i | \(-0.0598781\pi\) | ||||
0.982359 | + | 0.187005i | \(0.0598781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1694.86 | 0.696010 | 0.348005 | − | 0.937493i | \(-0.386859\pi\) | ||||
0.348005 | + | 0.937493i | \(0.386859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1645.00 | −0.664490 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1906.07 | −0.757496 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3773.44 | −1.47562 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 158.612 | 0.0610439 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1839.68 | 0.696933 | 0.348467 | − | 0.937321i | \(-0.386702\pi\) | ||||
0.348467 | + | 0.937321i | \(0.386702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1776.15 | −0.662437 | −0.331219 | − | 0.943554i | \(-0.607460\pi\) | ||||
−0.331219 | + | 0.943554i | \(0.607460\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −284.369 | −0.104431 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 642.894 | 0.232509 | 0.116255 | − | 0.993219i | \(-0.462911\pi\) | ||||
0.116255 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1086.88 | 0.387169 | 0.193584 | − | 0.981084i | \(-0.437989\pi\) | ||||
0.193584 | + | 0.981084i | \(0.437989\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1154.88 | −0.405268 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1731.96 | 0.598816 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1623.82 | −0.553232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −628.470 | −0.211023 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3067.69 | −1.01529 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3275.58 | −1.06872 | −0.534361 | − | 0.845256i | \(-0.679448\pi\) | ||||
−0.534361 | + | 0.845256i | \(0.679448\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −921.012 | −0.296276 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 577.830 | 0.183292 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1964.73 | −0.614628 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2534.67 | 0.782089 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 958.737 | 0.291817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2075.20 | 0.623164 | 0.311582 | − | 0.950219i | \(-0.399141\pi\) | ||||
0.311582 | + | 0.950219i | \(0.399141\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −646.506 | −0.191557 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2673.53 | −0.781712 | −0.390856 | − | 0.920452i | \(-0.627821\pi\) | ||||
−0.390856 | + | 0.920452i | \(0.627821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 558.099 | 0.161049 | 0.0805245 | − | 0.996753i | \(-0.474340\pi\) | ||||
0.0805245 | + | 0.996753i | \(0.474340\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 901.725 | 0.256836 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2436.99 | 0.685204 | 0.342602 | − | 0.939481i | \(-0.388692\pi\) | ||||
0.342602 | + | 0.939481i | \(0.388692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4261.19 | −1.18285 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 90.5098 | 0.0248069 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 968.672 | 0.262168 | 0.131084 | − | 0.991371i | \(-0.458154\pi\) | ||||
0.131084 | + | 0.991371i | \(0.458154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6872.52 | −1.83692 | −0.918460 | − | 0.395513i | \(-0.870567\pi\) | ||||
−0.918460 | + | 0.395513i | \(0.870567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2249.36 | 0.586556 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 779.422 | 0.200783 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 58.6900 | 0.0149370 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3944.62 | 0.991960 | 0.495980 | − | 0.868334i | \(-0.334809\pi\) | ||||
0.495980 | + | 0.868334i | \(0.334809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3572.93 | −0.887857 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1613.22 | −0.396172 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5755.13 | 1.39687 | 0.698434 | − | 0.715674i | \(-0.253881\pi\) | ||||
0.698434 | + | 0.715674i | \(0.253881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1535.65 | −0.368419 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2653.44 | −0.629285 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.67979 | 0.00109722 | 0.000548609 | − | 1.00000i | \(-0.499825\pi\) | ||||
0.000548609 | 1.00000i | \(0.499825\pi\) | ||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3391.70 | −0.786229 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1539.05 | 0.352765 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3269.87 | 0.741143 | 0.370571 | − | 0.928804i | \(-0.379162\pi\) | ||||
0.370571 | + | 0.928804i | \(0.379162\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2656.18 | 0.595393 | 0.297696 | − | 0.954661i | \(-0.403782\pi\) | ||||
0.297696 | + | 0.954661i | \(0.403782\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −229.106 | −0.0507916 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3675.46 | −0.805958 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7909.63 | −1.71568 | −0.857840 | − | 0.513916i | \(-0.828194\pi\) | ||||
−0.857840 | + | 0.513916i | \(0.828194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3010.05 | 0.645902 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7720.91 | −1.63911 | −0.819557 | − | 0.572998i | \(-0.805780\pi\) | ||||
−0.819557 | + | 0.572998i | \(0.805780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1318.54 | −0.276957 | −0.138478 | − | 0.990365i | \(-0.544221\pi\) | ||||
−0.138478 | + | 0.990365i | \(0.544221\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1311.50 | −0.272584 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1308.26 | −0.269073 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 525.917 | 0.107046 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2363.71 | −0.476162 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4038.77 | −0.805281 | −0.402641 | − | 0.915358i | \(-0.631908\pi\) | ||||
−0.402641 | + | 0.915358i | \(0.631908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3865.14 | −0.762839 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1381.48 | −0.269905 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 907.791 | 0.175582 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 465.537 | 0.0891466 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4175.18 | −0.791609 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3998.16 | −0.750604 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9694.98 | 1.80235 | 0.901175 | − | 0.433455i | \(-0.142706\pi\) | ||||
0.901175 | + | 0.433455i | \(0.142706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4285.73 | 0.789017 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7949.12 | 1.44937 | 0.724684 | − | 0.689082i | \(-0.241986\pi\) | ||||
0.724684 | + | 0.689082i | \(0.241986\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5115.77 | 0.923835 | 0.461918 | − | 0.886923i | \(-0.347162\pi\) | ||||
0.461918 | + | 0.886923i | \(0.347162\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 385.506 | 0.0689549 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1218.09 | −0.215820 | −0.107910 | − | 0.994161i | \(-0.534416\pi\) | ||||
−0.107910 | + | 0.994161i | \(0.534416\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15085.1 | −2.64766 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4089.91 | −0.711142 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4421.66 | 0.761696 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 933.842 | 0.159385 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2937.55 | −0.496779 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3433.09 | −0.575296 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9888.33 | 1.64203 | 0.821015 | − | 0.570907i | \(-0.193408\pi\) | ||||
0.821015 | + | 0.570907i | \(0.193408\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2352.68 | 0.387166 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2806.93 | −0.457788 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9544.60 | −1.54281 | −0.771406 | − | 0.636344i | \(-0.780446\pi\) | ||||
−0.771406 | + | 0.636344i | \(0.780446\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4487.49 | −0.718959 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17112.5 | 2.71757 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3827.18 | 0.602474 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1527.50 | −0.238370 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4547.76 | −0.703563 | −0.351782 | − | 0.936082i | \(-0.614424\pi\) | ||||
−0.351782 | + | 0.936082i | \(0.614424\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1513.12 | 0.232079 | 0.116039 | − | 0.993245i | \(-0.462980\pi\) | ||||
0.116039 | + | 0.993245i | \(0.462980\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 61.1114 | 0.00921425 | 0.00460713 | − | 0.999989i | \(-0.498534\pi\) | ||||
0.00460713 | + | 0.999989i | \(0.498534\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2238.52 | −0.334671 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1299.72 | −0.192684 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1065.57 | 0.156653 | 0.0783265 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783265 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3264.33 | −0.475920 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3860.88 | −0.558247 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6160.53 | 0.883443 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8962.02 | 1.27470 | 0.637348 | − | 0.770576i | \(-0.280031\pi\) | ||||
0.637348 | + | 0.770576i | \(0.280031\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2004.31 | 0.282764 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2732.58 | −0.382394 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1250.29 | 0.173560 | 0.0867798 | − | 0.996228i | \(-0.472342\pi\) | ||||
0.0867798 | + | 0.996228i | \(0.472342\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4305.65 | −0.592914 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3832.74 | 0.523597 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8367.05 | −1.13400 | −0.567001 | − | 0.823717i | \(-0.691896\pi\) | ||||
−0.567001 | + | 0.823717i | \(0.691896\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6665.08 | 0.896227 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6241.47 | 0.832700 | 0.416350 | − | 0.909204i | \(-0.363309\pi\) | ||||
0.416350 | + | 0.909204i | \(0.363309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2191.64 | 0.290121 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −713.223 | −0.0936826 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2651.76 | 0.345628 | 0.172814 | − | 0.984954i | \(-0.444714\pi\) | ||||
0.172814 | + | 0.984954i | \(0.444714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5149.90 | 0.666091 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2634.42 | −0.338139 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 219.984 | 0.0280218 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11460.4 | −1.44882 | −0.724408 | − | 0.689372i | \(-0.757887\pi\) | ||||
−0.724408 | + | 0.689372i | \(0.757887\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1056.63 | −0.132575 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6271.25 | −0.780976 | −0.390488 | − | 0.920608i | \(-0.627694\pi\) | ||||
−0.390488 | + | 0.920608i | \(0.627694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4347.85 | −0.537423 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −590.612 | −0.0724635 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13375.3 | 1.62896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4432.82 | −0.535915 | −0.267957 | − | 0.963431i | \(-0.586349\pi\) | ||||
−0.267957 | + | 0.963431i | \(0.586349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3529.86 | 0.423638 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3114.01 | −0.371018 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 142.646 | 0.0168728 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1078.54 | 0.126658 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11383.5 | −1.32726 | −0.663630 | − | 0.748061i | \(-0.730985\pi\) | ||||
−0.663630 | + | 0.748061i | \(0.730985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7422.33 | 0.859245 | 0.429623 | − | 0.903009i | \(-0.358647\pi\) | ||||
0.429623 | + | 0.903009i | \(0.358647\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5259.65 | 0.604569 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5297.69 | 0.604648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3221.18 | −0.365068 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1995.47 | 0.224574 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17065.8 | −1.90727 | −0.953633 | − | 0.300971i | \(-0.902689\pi\) | ||||
−0.953633 | + | 0.300971i | \(0.902689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13703.0 | −1.52084 | −0.760420 | − | 0.649432i | \(-0.775007\pi\) | ||||
−0.760420 | + | 0.649432i | \(0.775007\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6449.18 | −0.710838 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4186.70 | 0.458300 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8990.23 | −0.977404 | −0.488702 | − | 0.872451i | \(-0.662529\pi\) | ||||
−0.488702 | + | 0.872451i | \(0.662529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2776.41 | −0.299796 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11047.9 | −1.18488 | −0.592438 | − | 0.805616i | \(-0.701835\pi\) | ||||
−0.592438 | + | 0.805616i | \(0.701835\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3740.66 | 0.398482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3680.81 | −0.389477 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14780.2 | 1.55350 | 0.776750 | − | 0.629809i | \(-0.216867\pi\) | ||||
0.776750 | + | 0.629809i | \(0.216867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11394.7 | 1.18970 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2117.00 | −0.219570 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −556.842 | −0.0573740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 407.385 | 0.0416995 | 0.0208498 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208498 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1991.22 | 0.202489 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13198.6 | 1.33345 | 0.666725 | − | 0.745303i | \(-0.267695\pi\) | ||||
0.666725 | + | 0.745303i | \(0.267695\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 534.058 | 0.0536064 | 0.0268032 | − | 0.999641i | \(-0.491467\pi\) | ||||
0.0268032 | + | 0.999641i | \(0.491467\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7315.92 | 0.729608 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5150.44 | −0.510351 | −0.255176 | − | 0.966895i | \(-0.582133\pi\) | ||||
−0.255176 | + | 0.966895i | \(0.582133\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2261.45 | −0.222652 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7559.40 | −0.739530 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4054.76 | −0.394160 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4306.85 | 0.416025 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4186.42 | 0.401851 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20668.2 | 1.97151 | 0.985756 | − | 0.168179i | \(-0.0537888\pi\) | ||||
0.985756 | + | 0.168179i | \(0.0537888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3398.32 | −0.322141 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1230.65 | −0.115935 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5745.00 | −0.537870 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3239.32 | −0.301412 | −0.150706 | − | 0.988579i | \(-0.548155\pi\) | ||||
−0.150706 | + | 0.988579i | \(0.548155\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3664.21 | 0.338858 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4704.78 | 0.432432 | 0.216216 | − | 0.976346i | \(-0.430629\pi\) | ||||
0.216216 | + | 0.976346i | \(0.430629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21743.1 | 1.98633 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3357.69 | −0.304883 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1803.50 | −0.162772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12173.8 | 1.09213 | 0.546065 | − | 0.837743i | \(-0.316125\pi\) | ||||
0.546065 | + | 0.837743i | \(0.316125\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3298.55 | 0.294148 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10090.3 | 0.894439 | 0.447219 | − | 0.894424i | \(-0.352414\pi\) | ||||
0.447219 | + | 0.894424i | \(0.352414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10147.8 | −0.894198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12946.5 | 1.12739 | 0.563696 | − | 0.825982i | \(-0.309379\pi\) | ||||
0.563696 | + | 0.825982i | \(0.309379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4963.32 | 0.429676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1618.80 | 0.139321 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10416.5 | 0.891270 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29901.7 | 2.54366 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5452.18 | 0.461126 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2267.25 | −0.190653 | −0.0953265 | − | 0.995446i | \(-0.530390\pi\) | ||||
−0.0953265 | + | 0.995446i | \(0.530390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8850.80 | −0.739997 | −0.369998 | − | 0.929032i | \(-0.620642\pi\) | ||||
−0.369998 | + | 0.929032i | \(0.620642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1265.97 | −0.105241 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24665.3 | −2.03878 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7290.76 | −0.599224 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4770.80 | 0.389897 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2895.11 | −0.235274 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9940.54 | −0.803303 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14115.7 | −1.13433 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15784.2 | −1.26136 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6720.57 | −0.534085 | −0.267042 | − | 0.963685i | \(-0.586046\pi\) | ||||
−0.267042 | + | 0.963685i | \(0.586046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5084.57 | −0.401841 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7139.71 | −0.561159 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3251.85 | 0.254185 | 0.127093 | − | 0.991891i | \(-0.459435\pi\) | ||||
0.127093 | + | 0.991891i | \(0.459435\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4934.99 | 0.383643 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17676.5 | 1.36668 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 177.234 | 0.0136288 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5718.20 | 0.437340 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4215.22 | 0.320655 | 0.160327 | − | 0.987064i | \(-0.448745\pi\) | ||||
0.160327 | + | 0.987064i | \(0.448745\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1030.21 | 0.0779487 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11320.3 | 0.851951 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15802.9 | −1.18297 | −0.591486 | − | 0.806316i | \(-0.701458\pi\) | ||||
−0.591486 | + | 0.806316i | \(0.701458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10906.8 | −0.812132 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −475.835 | −0.0352437 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12964.1 | 0.955155 | 0.477578 | − | 0.878590i | \(-0.341515\pi\) | ||||
0.477578 | + | 0.878590i | \(0.341515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13555.7 | 0.993499 | 0.496750 | − | 0.867894i | \(-0.334527\pi\) | ||||
0.496750 | + | 0.867894i | \(0.334527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5519.03 | −0.402375 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5016.17 | 0.363807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25349.5 | 1.82897 | 0.914483 | − | 0.404624i | \(-0.132598\pi\) | ||||
0.914483 | + | 0.404624i | \(0.132598\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5328.46 | 0.382458 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 114.925 | 0.00820635 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23800.3 | 1.69075 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 853.106 | 0.0602933 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18013.3 | 1.26659 | 0.633296 | − | 0.773910i | \(-0.281702\pi\) | ||||
0.633296 | + | 0.773910i | \(0.281702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20052.1 | −1.40277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1928.68 | −0.134239 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21521.6 | 1.49036 | 0.745181 | − | 0.666862i | \(-0.232363\pi\) | ||||
0.745181 | + | 0.666862i | \(0.232363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3158.96 | −0.217655 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3260.63 | −0.223532 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10081.8 | −0.687700 | −0.343850 | − | 0.939025i | \(-0.611731\pi\) | ||||
−0.343850 | + | 0.939025i | \(0.611731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5180.24 | −0.351591 | −0.175796 | − | 0.984427i | \(-0.556250\pi\) | ||||
−0.175796 | + | 0.984427i | \(0.556250\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3464.64 | 0.233982 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9383.88 | −0.630593 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24166.4 | 1.61595 | 0.807976 | − | 0.589215i | \(-0.200563\pi\) | ||||
0.807976 | + | 0.589215i | \(0.200563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5195.88 | −0.345727 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7597.27 | −0.503032 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23768.7 | 1.56608 | 0.783040 | − | 0.621971i | \(-0.213668\pi\) | ||||
0.783040 | + | 0.621971i | \(0.213668\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4871.47 | 0.319409 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20306.1 | −1.32495 | −0.662475 | − | 0.749084i | \(-0.730494\pi\) | ||||
−0.662475 | + | 0.749084i | \(0.730494\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16062.5 | 1.04299 | 0.521493 | − | 0.853256i | \(-0.325375\pi\) | ||||
0.521493 | + | 0.853256i | \(0.325375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1885.41 | 0.121834 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3013.72 | 0.193808 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1485.63 | −0.0950803 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9203.06 | 0.586180 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19278.7 | −1.22208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6958.72 | −0.439021 | −0.219511 | − | 0.975610i | \(-0.570446\pi\) | ||||
−0.219511 | + | 0.975610i | \(0.570446\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9826.74 | 0.617027 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16199.5 | 1.01237 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4010.37 | 0.249445 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2763.04 | 0.171055 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15200.3 | −0.936625 | −0.468312 | − | 0.883563i | \(-0.655138\pi\) | ||||
−0.468312 | + | 0.883563i | \(0.655138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27963.3 | 1.71503 | 0.857516 | − | 0.514457i | \(-0.172006\pi\) | ||||
0.857516 | + | 0.514457i | \(0.172006\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1733.49 | −0.105823 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3952.07 | −0.240142 | −0.120071 | − | 0.992765i | \(-0.538312\pi\) | ||||
−0.120071 | + | 0.992765i | \(0.538312\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27122.5 | 1.64045 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5894.18 | 0.354856 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3772.15 | −0.226058 | −0.113029 | − | 0.993592i | \(-0.536055\pi\) | ||||
−0.113029 | + | 0.993592i | \(0.536055\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6402.95 | −0.381960 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7604.02 | −0.451539 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7305.22 | −0.431822 | −0.215911 | − | 0.976413i | \(-0.569272\pi\) | ||||
−0.215911 | + | 0.976413i | \(0.569272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10985.6 | −0.646431 | −0.323216 | − | 0.946325i | \(-0.604764\pi\) | ||||
−0.323216 | + | 0.946325i | \(0.604764\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2876.21 | −0.168481 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2568.14 | −0.149756 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20587.7 | 1.19514 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6225.59 | −0.359784 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28056.0 | 1.61414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9236.54 | −0.529038 | −0.264519 | − | 0.964380i | \(-0.585213\pi\) | ||||
−0.264519 | + | 0.964380i | \(0.585213\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1939.52 | 0.110596 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1763.78 | −0.100129 | −0.0500646 | − | 0.998746i | \(-0.515943\pi\) | ||||
−0.0500646 | + | 0.998746i | \(0.515943\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4628.54 | −0.261601 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8020.60 | 0.451322 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9580.46 | 0.536729 | 0.268365 | − | 0.963317i | \(-0.413517\pi\) | ||||
0.268365 | + | 0.963317i | \(0.413517\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8579.32 | 0.478539 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1674.30 | −0.0929817 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6047.06 | −0.334361 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10720.2 | −0.590179 | −0.295090 | − | 0.955470i | \(-0.595349\pi\) | ||||
−0.295090 | + | 0.955470i | \(0.595349\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2705.18 | −0.148284 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2621.40 | 0.143072 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16424.0 | −0.892542 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7310.97 | −0.395603 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9060.31 | −0.488164 | −0.244082 | − | 0.969755i | \(-0.578487\pi\) | ||||
−0.244082 | + | 0.969755i | \(0.578487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15672.9 | −0.840847 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12783.6 | 0.682918 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8175.70 | −0.434907 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26681.4 | 1.41332 | 0.706658 | − | 0.707556i | \(-0.250202\pi\) | ||||
0.706658 | + | 0.707556i | \(0.250202\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −271.530 | −0.0143223 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −23354.6 | −1.22670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4850.00 | 0.253678 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2906.02 | −0.151363 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 491.820 | 0.0255102 | 0.0127551 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127551 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8392.18 | 0.433483 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20617.6 | 1.06055 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21178.5 | 1.08490 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12358.2 | −0.630452 | −0.315226 | − | 0.949017i | \(-0.602080\pi\) | ||||
−0.315226 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5844.39 | 0.295708 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24037.3 | −1.21124 | −0.605620 | − | 0.795754i | \(-0.707075\pi\) | ||||
−0.605620 | + | 0.795754i | \(0.707075\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6748.07 | −0.338648 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19696.8 | 0.984454 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21651.5 | −1.07776 | −0.538879 | − | 0.842383i | \(-0.681152\pi\) | ||||
−0.538879 | + | 0.842383i | \(0.681152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2338.27 | −0.115922 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2580.05 | 0.127393 | 0.0636964 | − | 0.997969i | \(-0.479711\pi\) | ||||
0.0636964 | + | 0.997969i | \(0.479711\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8946.21 | −0.439951 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −176.070 | −0.00862391 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8008.74 | −0.390698 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38542.3 | −1.87274 | −0.936371 | − | 0.351012i | \(-0.885838\pi\) | ||||
−0.936371 | + | 0.351012i | \(0.885838\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11833.9 | −0.572708 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5145.36 | −0.248025 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 997.651 | 0.0478999 | 0.0239500 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239500 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10718.8 | 0.512605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29051.7 | −1.38387 | −0.691933 | − | 0.721962i | \(-0.743241\pi\) | ||||
−0.691933 | + | 0.721962i | \(0.743241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5752.21 | −0.272928 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4839.67 | 0.228730 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6891.16 | −0.324414 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8935.69 | −0.419024 | −0.209512 | − | 0.977806i | \(-0.567188\pi\) | ||||
−0.209512 | + | 0.977806i | \(0.567188\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17265.4 | −0.806482 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22239.3 | −1.03479 | −0.517395 | − | 0.855747i | \(-0.673098\pi\) | ||||
−0.517395 | + | 0.855747i | \(0.673098\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24024.9 | −1.11355 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4606.95 | 0.212707 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13352.1 | −0.614108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15708.2 | 0.719696 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7960.31 | 0.363318 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18373.1 | −0.835369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36698.1 | −1.66219 | −0.831096 | − | 0.556129i | \(-0.812286\pi\) | ||||
−0.831096 | + | 0.556129i | \(0.812286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.0394 | −0.000633479 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8787.27 | −0.394993 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7128.32 | −0.319211 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10175.1 | 0.453929 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35811.1 | −1.59159 | −0.795794 | − | 0.605568i | \(-0.792946\pi\) | ||||
−0.795794 | + | 0.605568i | \(0.792946\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43099.3 | −1.90832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4617.15 | −0.203669 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −43229.7 | −1.89981 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2991.10 | −0.130960 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9809.61 | −0.427899 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28481.2 | 1.23776 | 0.618879 | − | 0.785486i | \(-0.287587\pi\) | ||||
0.618879 | + | 0.785486i | \(0.287587\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18290.5 | 0.791944 | 0.395972 | − | 0.918263i | \(-0.370408\pi\) | ||||
0.395972 | + | 0.918263i | \(0.370408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7968.54 | −0.343750 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8905.87 | 0.382772 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4751.30 | 0.203460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 687.317 | 0.0293246 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21577.5 | −0.917248 | −0.458624 | − | 0.888631i | \(-0.651657\pi\) | ||||
−0.458624 | + | 0.888631i | \(0.651657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25940.2 | 1.09869 | 0.549344 | − | 0.835596i | \(-0.314878\pi\) | ||||
0.549344 | + | 0.835596i | \(0.314878\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11026.4 | 0.465320 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3112.03 | 0.130853 | 0.0654267 | − | 0.997857i | \(-0.479159\pi\) | ||||
0.0654267 | + | 0.997857i | \(0.479159\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3729.80 | −0.156262 | −0.0781312 | − | 0.996943i | \(-0.524895\pi\) | ||||
−0.0781312 | + | 0.996943i | \(0.524895\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23728.9 | 0.990549 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22750.8 | 0.946303 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8017.12 | 0.332268 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9030.14 | −0.372912 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22919.3 | 0.943102 | 0.471551 | − | 0.881839i | \(-0.343694\pi\) | ||||
0.471551 | + | 0.881839i | \(0.343694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62533.4 | 2.56400 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23162.7 | 0.946343 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1232.26 | −0.0501671 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7560.26 | −0.306698 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3955.61 | 0.159901 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18254.2 | −0.735307 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10092.6 | 0.405115 | 0.202557 | − | 0.979270i | \(-0.435075\pi\) | ||||
0.202557 | + | 0.979270i | \(0.435075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3934.49 | 0.157376 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14803.0 | −0.590036 | −0.295018 | − | 0.955492i | \(-0.595326\pi\) | ||||
−0.295018 | + | 0.955492i | \(0.595326\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7164.74 | −0.284584 | −0.142292 | − | 0.989825i | \(-0.545447\pi\) | ||||
−0.142292 | + | 0.989825i | \(0.545447\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3924.77 | 0.155349 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20504.4 | −0.808782 | −0.404391 | − | 0.914586i | \(-0.632517\pi\) | ||||
−0.404391 | + | 0.914586i | \(0.632517\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13251.5 | 0.520885 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1577.75 | −0.0618031 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1543.68 | −0.0602596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5004.47 | −0.194684 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7091.13 | 0.274912 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8431.19 | −0.325744 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23980.1 | −0.923318 | −0.461659 | − | 0.887057i | \(-0.652746\pi\) | ||||
−0.461659 | + | 0.887057i | \(0.652746\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12116.3 | 0.464929 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32577.9 | 1.24583 | 0.622915 | − | 0.782289i | \(-0.285948\pi\) | ||||
0.622915 | + | 0.782289i | \(0.285948\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5201.59 | 0.198242 | 0.0991208 | − | 0.995075i | \(-0.468397\pi\) | ||||
0.0991208 | + | 0.995075i | \(0.468397\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11595.4 | 0.440425 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10719.5 | −0.405779 | −0.202890 | − | 0.979202i | \(-0.565033\pi\) | ||||
−0.202890 | + | 0.979202i | \(0.565033\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13051.4 | 0.492383 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4144.45 | 0.155830 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35038.3 | −1.31300 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34308.1 | −1.28133 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2723.37 | −0.101372 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −98604.5 | −3.65811 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34305.0 | −1.26844 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1396.61 | −0.0514688 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12358.1 | −0.453918 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18995.9 | 0.695424 | 0.347712 | − | 0.937601i | \(-0.386959\pi\) | ||||
0.347712 | + | 0.937601i | \(0.386959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12525.5 | 0.457036 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8475.13 | 0.308226 | 0.154113 | − | 0.988053i | \(-0.450748\pi\) | ||||
0.154113 | + | 0.988053i | \(0.450748\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1000.98 | −0.0362842 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11994.5 | 0.433361 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5158.63 | −0.185772 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41161.3 | 1.47746 | 0.738731 | − | 0.674000i | \(-0.235425\pi\) | ||||
0.738731 | + | 0.674000i | \(0.235425\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29084.9 | −1.04059 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3991.05 | −0.142326 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18778.1 | −0.667480 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12857.2 | −0.455539 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24181.6 | −0.854007 | −0.427004 | − | 0.904250i | \(-0.640431\pi\) | ||||
−0.427004 | + | 0.904250i | \(0.640431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18495.7 | 0.651098 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23847.4 | −0.836792 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27514.1 | 0.962360 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3815.36 | 0.133023 | 0.0665114 | − | 0.997786i | \(-0.478813\pi\) | ||||
0.0665114 | + | 0.997786i | \(0.478813\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15347.3 | −0.533377 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34381.2 | 1.19107 | 0.595534 | − | 0.803330i | \(-0.296940\pi\) | ||||
0.595534 | + | 0.803330i | \(0.296940\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15551.2 | −0.537027 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1156.52 | −0.0398111 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20897.6 | 0.717087 | 0.358543 | − | 0.933513i | \(-0.383274\pi\) | ||||
0.358543 | + | 0.933513i | \(0.383274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10983.6 | 0.375703 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3654.28 | 0.124604 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21656.9 | −0.736136 | −0.368068 | − | 0.929799i | \(-0.619981\pi\) | ||||
−0.368068 | + | 0.929799i | \(0.619981\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13414.0 | −0.454520 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 45255.2 | 1.52862 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6912.06 | 0.232745 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82065.6 | 2.75471 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12269.7 | 0.410578 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12950.8 | 0.432023 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38712.2 | −1.28738 | −0.643691 | − | 0.765285i | \(-0.722598\pi\) | ||||
−0.643691 | + | 0.765285i | \(0.722598\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13265.0 | −0.439766 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11532.4 | −0.381147 | −0.190573 | − | 0.981673i | \(-0.561035\pi\) | ||||
−0.190573 | + | 0.981673i | \(0.561035\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2111.97 | 0.0695853 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2801.53 | −0.0920212 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26477.6 | 0.867036 | 0.433518 | − | 0.901145i | \(-0.357272\pi\) | ||||
0.433518 | + | 0.901145i | \(0.357272\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26249.0 | −0.856918 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8812.64 | 0.286815 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23993.5 | 0.778508 | 0.389254 | − | 0.921131i | \(-0.372733\pi\) | ||||
0.389254 | + | 0.921131i | \(0.372733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4687.66 | −0.151636 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10299.3 | 0.332148 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5533.83 | 0.177923 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9436.25 | 0.302475 | 0.151237 | − | 0.988497i | \(-0.451674\pi\) | ||||
0.151237 | + | 0.988497i | \(0.451674\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29665.0 | −0.948026 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7924.96 | −0.252501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31197.1 | −0.990995 | −0.495498 | − | 0.868609i | \(-0.665014\pi\) | ||||
−0.495498 | + | 0.868609i | \(0.665014\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7058.05 | −0.223530 |
(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 | 624.4.a.k.1.1 | 2 | ||
3.2 | odd | 2 | 1872.4.a.bf.1.2 | 2 | |||
4.3 | odd | 2 | 312.4.a.e.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 2496.4.a.y.1.2 | 2 | |||
8.5 | even | 2 | 2496.4.a.bh.1.2 | 2 | |||
12.11 | even | 2 | 936.4.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.4.a.e.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
624.4.a.k.1.1 | 2 | 1.1 | even | 1 | trivial | ||
936.4.a.f.1.2 | 2 | 12.11 | even | 2 | |||
1872.4.a.bf.1.2 | 2 | 3.2 | odd | 2 | |||
2496.4.a.y.1.2 | 2 | 8.3 | odd | 2 | |||
2496.4.a.bh.1.2 | 2 | 8.5 | even | 2 |