Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(1,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("252.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.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: | \(14.8684813214\) |
Analytic rank: | \(1\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.29150 | 0.473286 | 0.236643 | − | 0.971597i | \(-0.423953\pi\) | ||||
0.236643 | + | 0.971597i | \(0.423953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −68.7895 | −1.88553 | −0.942765 | − | 0.333459i | \(-0.891784\pi\) | ||||
−0.942765 | + | 0.333459i | \(0.891784\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.0000 | −0.640039 | −0.320019 | − | 0.947411i | \(-0.603689\pi\) | ||||
−0.320019 | + | 0.947411i | \(0.603689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 121.705 | 1.73633 | 0.868167 | − | 0.496271i | \(-0.165298\pi\) | ||||
0.868167 | + | 0.496271i | \(0.165298\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −100.000 | −1.20745 | −0.603726 | − | 0.797192i | \(-0.706318\pi\) | ||||
−0.603726 | + | 0.797192i | \(0.706318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 89.9555 | 0.815523 | 0.407761 | − | 0.913088i | \(-0.366309\pi\) | ||||
0.407761 | + | 0.913088i | \(0.366309\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −97.0000 | −0.776000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −232.826 | −1.49085 | −0.745426 | − | 0.666588i | \(-0.767754\pi\) | ||||
−0.745426 | + | 0.666588i | \(0.767754\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −180.000 | −1.04287 | −0.521435 | − | 0.853291i | \(-0.674603\pi\) | ||||
−0.521435 | + | 0.853291i | \(0.674603\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −37.0405 | −0.178885 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −118.000 | −0.524299 | −0.262150 | − | 0.965027i | \(-0.584431\pi\) | ||||
−0.262150 | + | 0.965027i | \(0.584431\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15.8745 | −0.0604678 | −0.0302339 | − | 0.999543i | \(-0.509625\pi\) | ||||
−0.0302339 | + | 0.999543i | \(0.509625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −412.000 | −1.46115 | −0.730575 | − | 0.682833i | \(-0.760748\pi\) | ||||
−0.730575 | + | 0.682833i | \(0.760748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 285.741 | 0.886801 | 0.443400 | − | 0.896324i | \(-0.353772\pi\) | ||||
0.443400 | + | 0.896324i | \(0.353772\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 285.741 | 0.740558 | 0.370279 | − | 0.928921i | \(-0.379262\pi\) | ||||
0.370279 | + | 0.928921i | \(0.379262\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −364.000 | −0.892395 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −836.057 | −1.84484 | −0.922419 | − | 0.386191i | \(-0.873790\pi\) | ||||
−0.922419 | + | 0.386191i | \(0.873790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −378.000 | −0.793409 | −0.396704 | − | 0.917946i | \(-0.629846\pi\) | ||||
−0.396704 | + | 0.917946i | \(0.629846\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −158.745 | −0.302922 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 244.000 | 0.444916 | 0.222458 | − | 0.974942i | \(-0.428592\pi\) | ||||
0.222458 | + | 0.974942i | \(0.428592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 439.195 | 0.734124 | 0.367062 | − | 0.930196i | \(-0.380364\pi\) | ||||
0.367062 | + | 0.930196i | \(0.380364\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 670.000 | 1.07421 | 0.537107 | − | 0.843514i | \(-0.319517\pi\) | ||||
0.537107 | + | 0.843514i | \(0.319517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 481.527 | 0.712663 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 216.000 | 0.307619 | 0.153809 | − | 0.988101i | \(-0.450846\pi\) | ||||
0.153809 | + | 0.988101i | \(0.450846\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 804.308 | 1.06367 | 0.531833 | − | 0.846849i | \(-0.321503\pi\) | ||||
0.531833 | + | 0.846849i | \(0.321503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 644.000 | 0.821784 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −968.345 | −1.15331 | −0.576654 | − | 0.816989i | \(-0.695642\pi\) | ||||
−0.576654 | + | 0.816989i | \(0.695642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 210.000 | 0.241912 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −529.150 | −0.571470 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 574.000 | 0.600834 | 0.300417 | − | 0.953808i | \(-0.402874\pi\) | ||||
0.300417 | + | 0.953808i | \(0.402874\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 672.021 | 0.662065 | 0.331033 | − | 0.943619i | \(-0.392603\pi\) | ||||
0.331033 | + | 0.943619i | \(0.392603\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −964.000 | −0.922192 | −0.461096 | − | 0.887350i | \(-0.652544\pi\) | ||||
−0.461096 | + | 0.887350i | \(0.652544\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −428.612 | −0.387247 | −0.193624 | − | 0.981076i | \(-0.562024\pi\) | ||||
−0.193624 | + | 0.981076i | \(0.562024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2122.00 | 1.86469 | 0.932343 | − | 0.361575i | \(-0.117761\pi\) | ||||
0.932343 | + | 0.361575i | \(0.117761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −296.324 | −0.246689 | −0.123344 | − | 0.992364i | \(-0.539362\pi\) | ||||
−0.123344 | + | 0.992364i | \(0.539362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 476.000 | 0.385976 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −851.932 | −0.656273 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3401.00 | 2.55522 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1174.71 | −0.840557 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1464.00 | −1.02291 | −0.511453 | − | 0.859311i | \(-0.670892\pi\) | ||||
−0.511453 | + | 0.859311i | \(0.670892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1926.11 | 1.28462 | 0.642308 | − | 0.766446i | \(-0.277977\pi\) | ||||
0.642308 | + | 0.766446i | \(0.277977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 700.000 | 0.456374 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 52.9150 | 0.0329988 | 0.0164994 | − | 0.999864i | \(-0.494748\pi\) | ||||
0.0164994 | + | 0.999864i | \(0.494748\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 352.000 | 0.214793 | 0.107397 | − | 0.994216i | \(-0.465749\pi\) | ||||
0.107397 | + | 0.994216i | \(0.465749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2063.69 | 1.20681 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1232.00 | −0.705600 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2254.18 | 1.23939 | 0.619697 | − | 0.784841i | \(-0.287256\pi\) | ||||
0.619697 | + | 0.784841i | \(0.287256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 376.000 | 0.202639 | 0.101319 | − | 0.994854i | \(-0.467694\pi\) | ||||
0.101319 | + | 0.994854i | \(0.467694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −952.470 | −0.493576 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2198.00 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −629.689 | −0.308239 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −292.000 | −0.140314 | −0.0701571 | − | 0.997536i | \(-0.522350\pi\) | ||||
−0.0701571 | + | 0.997536i | \(0.522350\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3439.48 | −1.59374 | −0.796870 | − | 0.604150i | \(-0.793513\pi\) | ||||
−0.796870 | + | 0.604150i | \(0.793513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1297.00 | −0.590350 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2058.39 | −0.904606 | −0.452303 | − | 0.891864i | \(-0.649397\pi\) | ||||
−0.452303 | + | 0.891864i | \(0.649397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 679.000 | 0.293300 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1571.58 | 0.656230 | 0.328115 | − | 0.944638i | \(-0.393587\pi\) | ||||
0.328115 | + | 0.944638i | \(0.393587\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3246.00 | −1.33300 | −0.666501 | − | 0.745504i | \(-0.732209\pi\) | ||||
−0.666501 | + | 0.745504i | \(0.732209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −624.397 | −0.248144 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8372.00 | −3.27391 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2206.56 | −0.835921 | −0.417960 | − | 0.908465i | \(-0.637255\pi\) | ||||
−0.417960 | + | 0.908465i | \(0.637255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3998.00 | 1.49110 | 0.745550 | − | 0.666450i | \(-0.232187\pi\) | ||||
0.745550 | + | 0.666450i | \(0.232187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3502.97 | 1.26689 | 0.633443 | − | 0.773789i | \(-0.281641\pi\) | ||||
0.633443 | + | 0.773789i | \(0.281641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 224.000 | 0.0797937 | 0.0398968 | − | 0.999204i | \(-0.487297\pi\) | ||||
0.0398968 | + | 0.999204i | \(0.487297\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1629.78 | 0.563489 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −84.0000 | −0.0286186 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6878.95 | 2.27668 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3460.00 | −1.12889 | −0.564446 | − | 0.825470i | \(-0.690910\pi\) | ||||
−0.564446 | + | 0.825470i | \(0.690910\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2180.10 | −0.691542 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1260.00 | 0.394168 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3651.14 | −1.11132 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4648.00 | −1.39575 | −0.697877 | − | 0.716218i | \(-0.745872\pi\) | ||||
−0.697877 | + | 0.716218i | \(0.745872\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3841.63 | −1.12325 | −0.561626 | − | 0.827392i | \(-0.689824\pi\) | ||||
−0.561626 | + | 0.827392i | \(0.689824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4646.00 | −1.34068 | −0.670341 | − | 0.742053i | \(-0.733852\pi\) | ||||
−0.670341 | + | 0.742053i | \(0.733852\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4878.77 | −1.37175 | −0.685877 | − | 0.727718i | \(-0.740581\pi\) | ||||
−0.685877 | + | 0.727718i | \(0.740581\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1512.00 | 0.419711 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2143.06 | 0.580012 | 0.290006 | − | 0.957025i | \(-0.406343\pi\) | ||||
0.290006 | + | 0.957025i | \(0.406343\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −826.000 | −0.220777 | −0.110389 | − | 0.993888i | \(-0.535210\pi\) | ||||
−0.110389 | + | 0.993888i | \(0.535210\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 259.284 | 0.0676123 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3000.00 | 0.772816 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 857.223 | 0.215568 | 0.107784 | − | 0.994174i | \(-0.465625\pi\) | ||||
0.107784 | + | 0.994174i | \(0.465625\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6188.00 | −1.53769 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3984.50 | 0.967107 | 0.483553 | − | 0.875315i | \(-0.339346\pi\) | ||||
0.483553 | + | 0.875315i | \(0.339346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 826.000 | 0.198167 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6206.93 | 1.45527 | 0.727635 | − | 0.685965i | \(-0.240620\pi\) | ||||
0.727635 | + | 0.685965i | \(0.240620\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1512.00 | 0.350496 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2344.14 | −0.531318 | −0.265659 | − | 0.964067i | \(-0.585589\pi\) | ||||
−0.265659 | + | 0.964067i | \(0.585589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7980.00 | −1.78875 | −0.894374 | − | 0.447321i | \(-0.852378\pi\) | ||||
−0.894374 | + | 0.447321i | \(0.852378\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6672.58 | 1.46317 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1954.00 | −0.423843 | −0.211921 | − | 0.977287i | \(-0.567972\pi\) | ||||
−0.211921 | + | 0.977287i | \(0.567972\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3989.79 | −0.847015 | −0.423507 | − | 0.905893i | \(-0.639201\pi\) | ||||
−0.423507 | + | 0.905893i | \(0.639201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4492.00 | 0.943540 | 0.471770 | − | 0.881722i | \(-0.343615\pi\) | ||||
0.471770 | + | 0.881722i | \(0.343615\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 111.122 | 0.0228547 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9899.00 | 2.01486 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8111.87 | −1.61741 | −0.808704 | − | 0.588215i | \(-0.799831\pi\) | ||||
−0.808704 | + | 0.588215i | \(0.799831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4424.00 | −0.873136 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2698.67 | −0.521966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2884.00 | 0.552262 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2000.19 | −0.375510 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2788.00 | 0.518305 | 0.259152 | − | 0.965836i | \(-0.416557\pi\) | ||||
0.259152 | + | 0.965836i | \(0.416557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3799.30 | 0.692728 | 0.346364 | − | 0.938100i | \(-0.387416\pi\) | ||||
0.346364 | + | 0.938100i | \(0.387416\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7166.00 | −1.29408 | −0.647039 | − | 0.762457i | \(-0.723993\pi\) | ||||
−0.647039 | + | 0.762457i | \(0.723993\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3143.15 | 0.556899 | 0.278450 | − | 0.960451i | \(-0.410179\pi\) | ||||
0.278450 | + | 0.960451i | \(0.410179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16016.0 | 2.81105 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12170.5 | −2.09654 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2910.00 | 0.496670 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2000.19 | −0.335179 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2108.00 | 0.350049 | 0.175024 | − | 0.984564i | \(-0.444000\pi\) | ||||
0.175024 | + | 0.984564i | \(0.444000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1291.13 | 0.210572 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8814.00 | 1.42472 | 0.712358 | − | 0.701816i | \(-0.247627\pi\) | ||||
0.712358 | + | 0.701816i | \(0.247627\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12382.1 | 1.96636 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4905.22 | −0.758865 | −0.379433 | − | 0.925219i | \(-0.623881\pi\) | ||||
−0.379433 | + | 0.925219i | \(0.623881\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8498.00 | −1.30340 | −0.651701 | − | 0.758476i | \(-0.725944\pi\) | ||||
−0.651701 | + | 0.758476i | \(0.725944\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8207.12 | 1.23745 | 0.618727 | − | 0.785606i | \(-0.287649\pi\) | ||||
0.618727 | + | 0.785606i | \(0.287649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2324.00 | 0.347451 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2576.96 | 0.378849 | 0.189425 | − | 0.981895i | \(-0.439338\pi\) | ||||
0.189425 | + | 0.981895i | \(0.439338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3141.00 | 0.457938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3545.31 | 0.508411 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6848.00 | 0.974013 | 0.487006 | − | 0.873398i | \(-0.338089\pi\) | ||||
0.487006 | + | 0.873398i | \(0.338089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2000.19 | −0.279905 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1966.00 | 0.272911 | 0.136455 | − | 0.990646i | \(-0.456429\pi\) | ||||
0.136455 | + | 0.990646i | \(0.456429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6984.78 | 0.954203 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1324.00 | 0.179444 | 0.0897220 | − | 0.995967i | \(-0.471402\pi\) | ||||
0.0897220 | + | 0.995967i | \(0.471402\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7132.95 | −0.951636 | −0.475818 | − | 0.879544i | \(-0.657848\pi\) | ||||
−0.475818 | + | 0.879544i | \(0.657848\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2548.00 | 0.337294 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7154.11 | −0.932462 | −0.466231 | − | 0.884663i | \(-0.654389\pi\) | ||||
−0.466231 | + | 0.884663i | \(0.654389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10948.0 | 1.41602 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1142.96 | 0.145592 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7002.00 | −0.885190 | −0.442595 | − | 0.896722i | \(-0.645942\pi\) | ||||
−0.442595 | + | 0.896722i | \(0.645942\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11397.9 | −1.41941 | −0.709705 | − | 0.704498i | \(-0.751172\pi\) | ||||
−0.709705 | + | 0.704498i | \(0.751172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5400.00 | 0.667477 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8117.17 | 0.988582 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7310.00 | 0.883756 | 0.441878 | − | 0.897075i | \(-0.354312\pi\) | ||||
0.441878 | + | 0.897075i | \(0.354312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5852.40 | 0.697283 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4256.00 | 0.503419 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4032.12 | 0.470125 | 0.235062 | − | 0.971980i | \(-0.424471\pi\) | ||||
0.235062 | + | 0.971980i | \(0.424471\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11586.0 | −1.34125 | −0.670626 | − | 0.741796i | \(-0.733974\pi\) | ||||
−0.670626 | + | 0.741796i | \(0.733974\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11805.3 | −1.34740 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2646.00 | 0.299880 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 460.361 | 0.0514496 | 0.0257248 | − | 0.999669i | \(-0.491811\pi\) | ||||
0.0257248 | + | 0.999669i | \(0.491811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9718.00 | −1.07856 | −0.539281 | − | 0.842126i | \(-0.681304\pi\) | ||||
−0.539281 | + | 0.842126i | \(0.681304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8995.55 | −0.984704 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1680.00 | 0.182647 | 0.0913235 | − | 0.995821i | \(-0.470890\pi\) | ||||
0.0913235 | + | 0.995821i | \(0.470890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3201.36 | 0.343343 | 0.171672 | − | 0.985154i | \(-0.445083\pi\) | ||||
0.171672 | + | 0.985154i | \(0.445083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5124.00 | −0.545845 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1037.13 | 0.109010 | 0.0545049 | − | 0.998514i | \(-0.482642\pi\) | ||||
0.0545049 | + | 0.998514i | \(0.482642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1092.00 | 0.114014 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1111.22 | 0.114494 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2330.00 | −0.238496 | −0.119248 | − | 0.992864i | \(-0.538048\pi\) | ||||
−0.119248 | + | 0.992864i | \(0.538048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9614.66 | −0.971365 | −0.485683 | − | 0.874135i | \(-0.661429\pi\) | ||||
−0.485683 | + | 0.874135i | \(0.661429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4880.00 | −0.489833 | −0.244917 | − | 0.969544i | \(-0.578761\pi\) | ||||
−0.244917 | + | 0.969544i | \(0.578761\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6720.21 | 0.665898 | 0.332949 | − | 0.942945i | \(-0.391956\pi\) | ||||
0.332949 | + | 0.942945i | \(0.391956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1708.00 | −0.168162 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28341.3 | 2.75504 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9700.00 | 0.936982 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16117.9 | −1.53747 | −0.768733 | − | 0.639570i | \(-0.779113\pi\) | ||||
−0.768733 | + | 0.639570i | \(0.779113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3540.00 | 0.335572 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3037.32 | 0.284366 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8728.00 | −0.812122 | −0.406061 | − | 0.913846i | \(-0.633098\pi\) | ||||
−0.406061 | + | 0.913846i | \(0.633098\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14525.2 | 1.33505 | 0.667527 | − | 0.744585i | \(-0.267353\pi\) | ||||
0.667527 | + | 0.744585i | \(0.267353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28336.0 | −2.58862 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3074.36 | −0.277473 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2204.00 | −0.197725 | −0.0988623 | − | 0.995101i | \(-0.531520\pi\) | ||||
−0.0988623 | + | 0.995101i | \(0.531520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7492.77 | −0.664187 | −0.332093 | − | 0.943246i | \(-0.607755\pi\) | ||||
−0.332093 | + | 0.943246i | \(0.607755\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3556.00 | 0.313346 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8461.11 | −0.736802 | −0.368401 | − | 0.929667i | \(-0.620095\pi\) | ||||
−0.368401 | + | 0.929667i | \(0.620095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4690.00 | −0.406014 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5101.01 | −0.436461 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19656.0 | −1.67209 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2460.55 | −0.206907 | −0.103454 | − | 0.994634i | \(-0.532989\pi\) | ||||
−0.103454 | + | 0.994634i | \(0.532989\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9424.00 | −0.787921 | −0.393961 | − | 0.919127i | \(-0.628895\pi\) | ||||
−0.393961 | + | 0.919127i | \(0.628895\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21906.8 | −1.81077 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4075.00 | −0.334922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 476.235 | 0.0387018 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2268.00 | −0.183279 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3370.69 | −0.269361 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8730.00 | −0.693775 | −0.346887 | − | 0.937907i | \(-0.612761\pi\) | ||||
−0.346887 | + | 0.937907i | \(0.612761\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11228.6 | 0.882530 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1668.00 | 0.130381 | 0.0651906 | − | 0.997873i | \(-0.479234\pi\) | ||||
0.0651906 | + | 0.997873i | \(0.479234\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23282.6 | 1.80013 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1512.00 | −0.116269 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −264.575 | −0.0201264 | −0.0100632 | − | 0.999949i | \(-0.503203\pi\) | ||||
−0.0100632 | + | 0.999949i | \(0.503203\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12360.0 | 0.935192 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21536.4 | 1.61217 | 0.806085 | − | 0.591800i | \(-0.201582\pi\) | ||||
0.806085 | + | 0.591800i | \(0.201582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1568.00 | −0.116754 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25304.0 | 1.86432 | 0.932159 | − | 0.362048i | \(-0.117922\pi\) | ||||
0.932159 | + | 0.362048i | \(0.117922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4068.00 | −0.298144 | −0.149072 | − | 0.988826i | \(-0.547629\pi\) | ||||
−0.149072 | + | 0.988826i | \(0.547629\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8725.69 | −0.632846 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7618.00 | 0.549639 | 0.274819 | − | 0.961496i | \(-0.411382\pi\) | ||||
0.274819 | + | 0.961496i | \(0.411382\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5630.16 | −0.402028 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19656.0 | −1.39634 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4497.78 | −0.316257 | −0.158129 | − | 0.987419i | \(-0.550546\pi\) | ||||
−0.158129 | + | 0.987419i | \(0.550546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18000.0 | 1.25921 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21890.9 | −1.51594 | −0.757971 | − | 0.652288i | \(-0.773809\pi\) | ||||
−0.757971 | + | 0.652288i | \(0.773809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4508.00 | −0.310605 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18525.6 | −1.26366 | −0.631831 | − | 0.775106i | \(-0.717696\pi\) | ||||
−0.631831 | + | 0.775106i | \(0.717696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11590.0 | −0.786632 | −0.393316 | − | 0.919403i | \(-0.628672\pi\) | ||||
−0.393316 | + | 0.919403i | \(0.628672\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17996.4 | 1.20935 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9144.00 | 0.611439 | 0.305720 | − | 0.952122i | \(-0.401103\pi\) | ||||
0.305720 | + | 0.952122i | \(0.401103\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8572.23 | −0.567587 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29874.0 | −1.96835 | −0.984176 | − | 0.177195i | \(-0.943298\pi\) | ||||
−0.984176 | + | 0.177195i | \(0.943298\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26722.1 | −1.74358 | −0.871792 | − | 0.489877i | \(-0.837042\pi\) | ||||
−0.871792 | + | 0.489877i | \(0.837042\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4744.00 | 0.308041 | 0.154021 | − | 0.988068i | \(-0.450778\pi\) | ||||
0.154021 | + | 0.988068i | \(0.450778\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6778.41 | 0.435909 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5909.00 | 0.378176 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14361.1 | −0.910359 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13144.0 | −0.829246 | −0.414623 | − | 0.909993i | \(-0.636087\pi\) | ||||
−0.414623 | + | 0.909993i | \(0.636087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7746.76 | −0.484127 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1470.00 | −0.0914341 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23928.2 | −1.47442 | −0.737212 | − | 0.675661i | \(-0.763858\pi\) | ||||
−0.737212 | + | 0.675661i | \(0.763858\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20228.0 | 1.24061 | 0.620307 | − | 0.784359i | \(-0.287008\pi\) | ||||
0.620307 | + | 0.784359i | \(0.287008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20160.6 | 1.22503 | 0.612516 | − | 0.790458i | \(-0.290157\pi\) | ||||
0.612516 | + | 0.790458i | \(0.290157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57512.0 | 3.47850 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16065.0 | 0.962744 | 0.481372 | − | 0.876516i | \(-0.340139\pi\) | ||||
0.481372 | + | 0.876516i | \(0.340139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10192.0 | 0.607991 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16504.2 | 0.975588 | 0.487794 | − | 0.872959i | \(-0.337802\pi\) | ||||
0.487794 | + | 0.872959i | \(0.337802\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27242.0 | −1.60301 | −0.801506 | − | 0.597987i | \(-0.795968\pi\) | ||||
−0.801506 | + | 0.597987i | \(0.795968\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3704.05 | 0.215995 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20944.0 | −1.21582 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 26002.4 | 1.49600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17606.0 | 1.00841 | 0.504206 | − | 0.863583i | \(-0.331785\pi\) | ||||
0.504206 | + | 0.863583i | \(0.331785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15064.9 | 0.855231 | 0.427616 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427616 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4018.00 | −0.227094 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2905.03 | 0.162750 | 0.0813749 | − | 0.996684i | \(-0.474069\pi\) | ||||
0.0813749 | + | 0.996684i | \(0.474069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 280.000 | 0.0156179 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8572.23 | −0.473986 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29720.0 | 1.63618 | 0.818091 | − | 0.575088i | \(-0.195032\pi\) | ||||
0.818091 | + | 0.575088i | \(0.195032\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1862.61 | 0.101659 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1932.00 | −0.104992 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14117.7 | 0.760655 | 0.380328 | − | 0.924852i | \(-0.375811\pi\) | ||||
0.380328 | + | 0.924852i | \(0.375811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11800.0 | 0.633066 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4704.15 | −0.250237 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16658.0 | 0.882376 | 0.441188 | − | 0.897415i | \(-0.354557\pi\) | ||||
0.441188 | + | 0.897415i | \(0.354557\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16192.0 | −0.850484 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10920.0 | 0.571168 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12699.6 | 0.658714 | 0.329357 | − | 0.944205i | \(-0.393168\pi\) | ||||
0.329357 | + | 0.944205i | \(0.393168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6748.00 | 0.348556 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22584.1 | 1.15690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24316.0 | 1.24048 | 0.620241 | − | 0.784411i | \(-0.287035\pi\) | ||||
0.620241 | + | 0.784411i | \(0.287035\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50142.3 | −2.53704 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12570.0 | 0.633402 | 0.316701 | − | 0.948525i | \(-0.397425\pi\) | ||||
0.316701 | + | 0.948525i | \(0.397425\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16784.6 | −0.838901 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7356.00 | 0.366164 | 0.183082 | − | 0.983098i | \(-0.441393\pi\) | ||||
0.183082 | + | 0.983098i | \(0.441393\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36559.0 | −1.80514 | −0.902570 | − | 0.430543i | \(-0.858322\pi\) | ||||
−0.902570 | + | 0.430543i | \(0.858322\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11928.0 | 0.586588 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3000.28 | 0.146366 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27768.0 | −1.34923 | −0.674613 | − | 0.738172i | \(-0.735689\pi\) | ||||
−0.674613 | + | 0.738172i | \(0.735689\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1989.60 | 0.0959061 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23826.0 | 1.14395 | 0.571975 | − | 0.820271i | \(-0.306177\pi\) | ||||
0.571975 | + | 0.820271i | \(0.306177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28727.6 | 1.36843 | 0.684214 | − | 0.729281i | \(-0.260145\pi\) | ||||
0.684214 | + | 0.729281i | \(0.260145\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14854.0 | −0.704785 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25081.7 | 1.18077 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23770.0 | 1.11465 | 0.557326 | − | 0.830293i | \(-0.311827\pi\) | ||||
0.557326 | + | 0.830293i | \(0.311827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29362.5 | −1.36623 | −0.683116 | − | 0.730310i | \(-0.739376\pi\) | ||||
−0.683116 | + | 0.730310i | \(0.739376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17460.0 | 0.809267 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1587.45 | 0.0730120 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30212.0 | −1.38421 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11630.7 | 0.528813 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40656.0 | −1.84146 | −0.920731 | − | 0.390199i | \(-0.872406\pi\) | ||||
−0.920731 | + | 0.390199i | \(0.872406\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2074.27 | 0.0932396 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11340.0 | 0.507812 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30939.4 | 1.37507 | 0.687535 | − | 0.726152i | \(-0.258693\pi\) | ||||
0.687535 | + | 0.726152i | \(0.258693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34776.0 | 1.53978 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −46089.0 | −2.02546 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3332.00 | −0.145885 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20277.0 | 0.881215 | 0.440607 | − | 0.897700i | \(-0.354763\pi\) | ||||
0.440607 | + | 0.897700i | \(0.354763\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3248.00 | −0.140632 | −0.0703161 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703161 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1545.12 | −0.0664088 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41200.0 | 1.76427 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25134.6 | −1.06846 | −0.534230 | − | 0.845339i | \(-0.679398\pi\) | ||||
−0.534230 | + | 0.845339i | \(0.679398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31904.0 | −1.35128 | −0.675640 | − | 0.737232i | \(-0.736133\pi\) | ||||
−0.675640 | + | 0.737232i | \(0.736133\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24589.6 | 1.03394 | 0.516968 | − | 0.856005i | \(-0.327061\pi\) | ||||
0.516968 | + | 0.856005i | \(0.327061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25762.0 | 1.07931 | 0.539657 | − | 0.841885i | \(-0.318554\pi\) | ||||
0.539657 | + | 0.841885i | \(0.318554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5963.52 | 0.248048 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18200.0 | −0.754296 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5450.25 | −0.224271 | −0.112136 | − | 0.993693i | \(-0.535769\pi\) | ||||
−0.112136 | + | 0.993693i | \(0.535769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29819.0 | 1.22264 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6863.08 | −0.279405 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23807.0 | −0.965783 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10614.8 | −0.427578 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17050.0 | −0.684386 | −0.342193 | − | 0.939630i | \(-0.611170\pi\) | ||||
−0.342193 | + | 0.939630i | \(0.611170\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6968.91 | 0.277775 | 0.138888 | − | 0.990308i | \(-0.455647\pi\) | ||||
0.138888 | + | 0.990308i | \(0.455647\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10948.0 | −0.434856 | −0.217428 | − | 0.976076i | \(-0.569767\pi\) | ||||
−0.217428 | + | 0.976076i | \(0.569767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34611.7 | 1.36523 | 0.682617 | − | 0.730777i | \(-0.260842\pi\) | ||||
0.682617 | + | 0.730777i | \(0.260842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10892.0 | −0.428138 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14858.5 | −0.580025 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7320.00 | −0.284763 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8223.00 | 0.317701 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16154.0 | −0.621986 | −0.310993 | − | 0.950412i | \(-0.600662\pi\) | ||||
−0.310993 | + | 0.950412i | \(0.600662\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9318.34 | −0.356348 | −0.178174 | − | 0.983999i | \(-0.557019\pi\) | ||||
−0.178174 | + | 0.983999i | \(0.557019\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45772.0 | −1.74445 | −0.872226 | − | 0.489104i | \(-0.837324\pi\) | ||||
−0.872226 | + | 0.489104i | \(0.837324\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7461.02 | −0.282431 | −0.141216 | − | 0.989979i | \(-0.545101\pi\) | ||||
−0.141216 | + | 0.989979i | \(0.545101\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10248.0 | 0.386622 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28574.1 | −1.07077 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8316.00 | 0.310585 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41908.7 | 1.55476 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34776.0 | 1.28586 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17176.2 | −0.630891 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3900.00 | 0.142775 | 0.0713877 | − | 0.997449i | \(-0.477257\pi\) | ||||
0.0713877 | + | 0.997449i | \(0.477257\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11604.3 | −0.422027 | −0.211013 | − | 0.977483i | \(-0.567676\pi\) | ||||
−0.211013 | + | 0.977483i | \(0.567676\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55328.0 | −2.00557 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13482.7 | −0.485539 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18416.0 | −0.661031 | −0.330516 | − | 0.943801i | \(-0.607223\pi\) | ||||
−0.330516 | + | 0.943801i | \(0.607223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13175.8 | −0.469868 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11446.0 | 0.406856 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42273.8 | 1.49296 | 0.746479 | − | 0.665408i | \(-0.231743\pi\) | ||||
0.746479 | + | 0.665408i | \(0.231743\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4900.00 | −0.172493 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −44300.5 | −1.54950 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30910.0 | −1.07768 | −0.538840 | − | 0.842408i | \(-0.681137\pi\) | ||||
−0.538840 | + | 0.842408i | \(0.681137\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24706.0 | 0.855891 | 0.427945 | − | 0.903805i | \(-0.359238\pi\) | ||||
0.427945 | + | 0.903805i | \(0.359238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1428.00 | −0.0493129 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35405.4 | 1.21491 | 0.607456 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607456 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20100.0 | −0.687538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32362.8 | 1.10004 | 0.550018 | − | 0.835153i | \(-0.314621\pi\) | ||||
0.550018 | + | 0.835153i | \(0.314621\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11676.0 | −0.395630 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −370.405 | −0.0124724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2609.00 | 0.0875768 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21155.4 | 0.705717 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51136.0 | −1.70054 | −0.850270 | − | 0.526346i | \(-0.823562\pi\) | ||||
−0.850270 | + | 0.526346i | \(0.823562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10794.7 | −0.356763 | −0.178382 | − | 0.983961i | \(-0.557086\pi\) | ||||
−0.178382 | + | 0.983961i | \(0.557086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2464.00 | −0.0811842 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45432.8 | −1.48774 | −0.743872 | − | 0.668322i | \(-0.767013\pi\) | ||||
−0.743872 | + | 0.668322i | \(0.767013\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66612.0 | 2.17460 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37146.3 | 1.20527 | 0.602637 | − | 0.798015i | \(-0.294117\pi\) | ||||
0.602637 | + | 0.798015i | \(0.294117\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18536.0 | 0.599600 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37061.7 | −1.19160 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49720.0 | −1.59375 | −0.796876 | − | 0.604143i | \(-0.793516\pi\) | ||||
−0.796876 | + | 0.604143i | \(0.793516\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1185.30 | 0.0377653 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20554.0 | −0.652910 | −0.326455 | − | 0.945213i | \(-0.605854\pi\) | ||||
−0.326455 | + | 0.945213i | \(0.605854\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 252.4.a.e.1.2 | yes | 2 | |
3.2 | odd | 2 | inner | 252.4.a.e.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 1008.4.a.bd.1.2 | 2 | |||
7.2 | even | 3 | 1764.4.k.t.361.1 | 4 | |||
7.3 | odd | 6 | 1764.4.k.w.1549.2 | 4 | |||
7.4 | even | 3 | 1764.4.k.t.1549.1 | 4 | |||
7.5 | odd | 6 | 1764.4.k.w.361.2 | 4 | |||
7.6 | odd | 2 | 1764.4.a.t.1.1 | 2 | |||
12.11 | even | 2 | 1008.4.a.bd.1.1 | 2 | |||
21.2 | odd | 6 | 1764.4.k.t.361.2 | 4 | |||
21.5 | even | 6 | 1764.4.k.w.361.1 | 4 | |||
21.11 | odd | 6 | 1764.4.k.t.1549.2 | 4 | |||
21.17 | even | 6 | 1764.4.k.w.1549.1 | 4 | |||
21.20 | even | 2 | 1764.4.a.t.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.a.e.1.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
252.4.a.e.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
1008.4.a.bd.1.1 | 2 | 12.11 | even | 2 | |||
1008.4.a.bd.1.2 | 2 | 4.3 | odd | 2 | |||
1764.4.a.t.1.1 | 2 | 7.6 | odd | 2 | |||
1764.4.a.t.1.2 | 2 | 21.20 | even | 2 | |||
1764.4.k.t.361.1 | 4 | 7.2 | even | 3 | |||
1764.4.k.t.361.2 | 4 | 21.2 | odd | 6 | |||
1764.4.k.t.1549.1 | 4 | 7.4 | even | 3 | |||
1764.4.k.t.1549.2 | 4 | 21.11 | odd | 6 | |||
1764.4.k.w.361.1 | 4 | 21.5 | even | 6 | |||
1764.4.k.w.361.2 | 4 | 7.5 | odd | 6 | |||
1764.4.k.w.1549.1 | 4 | 21.17 | even | 6 | |||
1764.4.k.w.1549.2 | 4 | 7.3 | odd | 6 |