Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(52.0396846251\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 294) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 8.00000 | 0.715542 | 0.357771 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357771 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 16.0000 | 0.505964 | ||||||||
\(11\) | −40.0000 | −1.09640 | −0.548202 | − | 0.836346i | \(-0.684688\pi\) | ||||
−0.548202 | + | 0.836346i | \(0.684688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −0.0853385 | −0.0426692 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426692 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −84.0000 | −1.19841 | −0.599206 | − | 0.800595i | \(-0.704517\pi\) | ||||
−0.599206 | + | 0.800595i | \(0.704517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −148.000 | −1.78703 | −0.893514 | − | 0.449036i | \(-0.851768\pi\) | ||||
−0.893514 | + | 0.449036i | \(0.851768\pi\) | |||||||
\(20\) | 32.0000 | 0.357771 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −80.0000 | −0.775275 | ||||||||
\(23\) | −84.0000 | −0.761531 | −0.380765 | − | 0.924672i | \(-0.624339\pi\) | ||||
−0.380765 | + | 0.924672i | \(0.624339\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −61.0000 | −0.488000 | ||||||||
\(26\) | −8.00000 | −0.0603434 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136.000 | 0.787946 | 0.393973 | − | 0.919122i | \(-0.371100\pi\) | ||||
0.393973 | + | 0.919122i | \(0.371100\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −168.000 | −0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −222.000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | −296.000 | −1.26362 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 64.0000 | 0.252982 | ||||||||
\(41\) | 420.000 | 1.59983 | 0.799914 | − | 0.600114i | \(-0.204878\pi\) | ||||
0.799914 | + | 0.600114i | \(0.204878\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | −160.000 | −0.548202 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −168.000 | −0.538484 | ||||||||
\(47\) | 488.000 | 1.51451 | 0.757257 | − | 0.653118i | \(-0.226539\pi\) | ||||
0.757257 | + | 0.653118i | \(0.226539\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −122.000 | −0.345068 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −16.0000 | −0.0426692 | ||||||||
\(53\) | −478.000 | −1.23884 | −0.619418 | − | 0.785061i | \(-0.712632\pi\) | ||||
−0.619418 | + | 0.785061i | \(0.712632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −320.000 | −0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −116.000 | −0.262613 | ||||||||
\(59\) | 548.000 | 1.20921 | 0.604606 | − | 0.796525i | \(-0.293331\pi\) | ||||
0.604606 | + | 0.796525i | \(0.293331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −692.000 | −1.45248 | −0.726242 | − | 0.687439i | \(-0.758735\pi\) | ||||
−0.726242 | + | 0.687439i | \(0.758735\pi\) | |||||||
\(62\) | 272.000 | 0.557162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −32.0000 | −0.0610633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −908.000 | −1.65567 | −0.827835 | − | 0.560972i | \(-0.810428\pi\) | ||||
−0.827835 | + | 0.560972i | \(0.810428\pi\) | |||||||
\(68\) | −336.000 | −0.599206 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 524.000 | 0.875878 | 0.437939 | − | 0.899005i | \(-0.355709\pi\) | ||||
0.437939 | + | 0.899005i | \(0.355709\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −440.000 | −0.705453 | −0.352727 | − | 0.935726i | \(-0.614745\pi\) | ||||
−0.352727 | + | 0.935726i | \(0.614745\pi\) | |||||||
\(74\) | −444.000 | −0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −592.000 | −0.893514 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1216.00 | 1.73178 | 0.865890 | − | 0.500234i | \(-0.166753\pi\) | ||||
0.865890 | + | 0.500234i | \(0.166753\pi\) | |||||||
\(80\) | 128.000 | 0.178885 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 840.000 | 1.13125 | ||||||||
\(83\) | −684.000 | −0.904563 | −0.452282 | − | 0.891875i | \(-0.649390\pi\) | ||||
−0.452282 | + | 0.891875i | \(0.649390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −672.000 | −0.857513 | ||||||||
\(86\) | −328.000 | −0.411269 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −320.000 | −0.387638 | ||||||||
\(89\) | 604.000 | 0.719369 | 0.359685 | − | 0.933074i | \(-0.382884\pi\) | ||||
0.359685 | + | 0.933074i | \(0.382884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −336.000 | −0.380765 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 976.000 | 1.07092 | ||||||||
\(95\) | −1184.00 | −1.27869 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 832.000 | 0.870895 | 0.435447 | − | 0.900214i | \(-0.356590\pi\) | ||||
0.435447 | + | 0.900214i | \(0.356590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −244.000 | −0.244000 | ||||||||
\(101\) | 464.000 | 0.457126 | 0.228563 | − | 0.973529i | \(-0.426597\pi\) | ||||
0.228563 | + | 0.973529i | \(0.426597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 632.000 | 0.604590 | 0.302295 | − | 0.953214i | \(-0.402247\pi\) | ||||
0.302295 | + | 0.953214i | \(0.402247\pi\) | |||||||
\(104\) | −32.0000 | −0.0301717 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −956.000 | −0.875990 | ||||||||
\(107\) | 160.000 | 0.144559 | 0.0722794 | − | 0.997384i | \(-0.476973\pi\) | ||||
0.0722794 | + | 0.997384i | \(0.476973\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2198.00 | −1.93147 | −0.965735 | − | 0.259530i | \(-0.916432\pi\) | ||||
−0.965735 | + | 0.259530i | \(0.916432\pi\) | |||||||
\(110\) | −640.000 | −0.554742 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −770.000 | −0.641022 | −0.320511 | − | 0.947245i | \(-0.603855\pi\) | ||||
−0.320511 | + | 0.947245i | \(0.603855\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −672.000 | −0.544907 | ||||||||
\(116\) | −232.000 | −0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1096.00 | 0.855042 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 269.000 | 0.202104 | ||||||||
\(122\) | −1384.00 | −1.02706 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 544.000 | 0.393973 | ||||||||
\(125\) | −1488.00 | −1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −184.000 | −0.128562 | −0.0642809 | − | 0.997932i | \(-0.520475\pi\) | ||||
−0.0642809 | + | 0.997932i | \(0.520475\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −64.0000 | −0.0431782 | ||||||||
\(131\) | −1452.00 | −0.968411 | −0.484205 | − | 0.874954i | \(-0.660891\pi\) | ||||
−0.484205 | + | 0.874954i | \(0.660891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1816.00 | −1.17074 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −672.000 | −0.423702 | ||||||||
\(137\) | −646.000 | −0.402858 | −0.201429 | − | 0.979503i | \(-0.564558\pi\) | ||||
−0.201429 | + | 0.979503i | \(0.564558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3012.00 | 1.83795 | 0.918973 | − | 0.394320i | \(-0.129020\pi\) | ||||
0.918973 | + | 0.394320i | \(0.129020\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1048.00 | 0.619339 | ||||||||
\(143\) | 160.000 | 0.0935655 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −464.000 | −0.265746 | ||||||||
\(146\) | −880.000 | −0.498831 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −888.000 | −0.493197 | ||||||||
\(149\) | 3170.00 | 1.74293 | 0.871465 | − | 0.490458i | \(-0.163170\pi\) | ||||
0.871465 | + | 0.490458i | \(0.163170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1880.00 | −1.01319 | −0.506597 | − | 0.862183i | \(-0.669097\pi\) | ||||
−0.506597 | + | 0.862183i | \(0.669097\pi\) | |||||||
\(152\) | −1184.00 | −0.631810 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1088.00 | 0.563808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −604.000 | −0.307035 | −0.153517 | − | 0.988146i | \(-0.549060\pi\) | ||||
−0.153517 | + | 0.988146i | \(0.549060\pi\) | |||||||
\(158\) | 2432.00 | 1.22455 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 256.000 | 0.126491 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1116.00 | 0.536269 | 0.268135 | − | 0.963381i | \(-0.413593\pi\) | ||||
0.268135 | + | 0.963381i | \(0.413593\pi\) | |||||||
\(164\) | 1680.00 | 0.799914 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1368.00 | −0.639623 | ||||||||
\(167\) | −1784.00 | −0.826647 | −0.413324 | − | 0.910584i | \(-0.635632\pi\) | ||||
−0.413324 | + | 0.910584i | \(0.635632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2181.00 | −0.992717 | ||||||||
\(170\) | −1344.00 | −0.606353 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −656.000 | −0.290811 | ||||||||
\(173\) | −344.000 | −0.151178 | −0.0755891 | − | 0.997139i | \(-0.524084\pi\) | ||||
−0.0755891 | + | 0.997139i | \(0.524084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −640.000 | −0.274101 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1208.00 | 0.508671 | ||||||||
\(179\) | −1392.00 | −0.581246 | −0.290623 | − | 0.956838i | \(-0.593862\pi\) | ||||
−0.290623 | + | 0.956838i | \(0.593862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4052.00 | −1.66399 | −0.831997 | − | 0.554781i | \(-0.812802\pi\) | ||||
−0.831997 | + | 0.554781i | \(0.812802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −672.000 | −0.269242 | ||||||||
\(185\) | −1776.00 | −0.705806 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3360.00 | 1.31394 | ||||||||
\(188\) | 1952.00 | 0.757257 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2368.00 | −0.904173 | ||||||||
\(191\) | 3108.00 | 1.17742 | 0.588709 | − | 0.808345i | \(-0.299636\pi\) | ||||
0.588709 | + | 0.808345i | \(0.299636\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 50.0000 | 0.0186481 | 0.00932404 | − | 0.999957i | \(-0.497032\pi\) | ||||
0.00932404 | + | 0.999957i | \(0.497032\pi\) | |||||||
\(194\) | 1664.00 | 0.615816 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 162.000 | 0.0585889 | 0.0292945 | − | 0.999571i | \(-0.490674\pi\) | ||||
0.0292945 | + | 0.999571i | \(0.490674\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1544.00 | −0.550006 | −0.275003 | − | 0.961443i | \(-0.588679\pi\) | ||||
−0.275003 | + | 0.961443i | \(0.588679\pi\) | |||||||
\(200\) | −488.000 | −0.172534 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 928.000 | 0.323237 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3360.00 | 1.14474 | ||||||||
\(206\) | 1264.00 | 0.427510 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −64.0000 | −0.0213346 | ||||||||
\(209\) | 5920.00 | 1.95931 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1204.00 | −0.392828 | −0.196414 | − | 0.980521i | \(-0.562930\pi\) | ||||
−0.196414 | + | 0.980521i | \(0.562930\pi\) | |||||||
\(212\) | −1912.00 | −0.619418 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 320.000 | 0.102218 | ||||||||
\(215\) | −1312.00 | −0.416175 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4396.00 | −1.36576 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1280.00 | −0.392262 | ||||||||
\(221\) | 336.000 | 0.102271 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2000.00 | −0.600583 | −0.300291 | − | 0.953848i | \(-0.597084\pi\) | ||||
−0.300291 | + | 0.953848i | \(0.597084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1540.00 | −0.453271 | ||||||||
\(227\) | 388.000 | 0.113447 | 0.0567235 | − | 0.998390i | \(-0.481935\pi\) | ||||
0.0567235 | + | 0.998390i | \(0.481935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4180.00 | −1.20621 | −0.603105 | − | 0.797662i | \(-0.706070\pi\) | ||||
−0.603105 | + | 0.797662i | \(0.706070\pi\) | |||||||
\(230\) | −1344.00 | −0.385308 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −464.000 | −0.131306 | ||||||||
\(233\) | 1322.00 | 0.371704 | 0.185852 | − | 0.982578i | \(-0.440495\pi\) | ||||
0.185852 | + | 0.982578i | \(0.440495\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3904.00 | 1.08370 | ||||||||
\(236\) | 2192.00 | 0.604606 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2412.00 | −0.652800 | −0.326400 | − | 0.945232i | \(-0.605836\pi\) | ||||
−0.326400 | + | 0.945232i | \(0.605836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4336.00 | 1.15895 | 0.579474 | − | 0.814991i | \(-0.303258\pi\) | ||||
0.579474 | + | 0.814991i | \(0.303258\pi\) | |||||||
\(242\) | 538.000 | 0.142909 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2768.00 | −0.726242 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 592.000 | 0.152502 | ||||||||
\(248\) | 1088.00 | 0.278581 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2976.00 | −0.752875 | ||||||||
\(251\) | 764.000 | 0.192125 | 0.0960623 | − | 0.995375i | \(-0.469375\pi\) | ||||
0.0960623 | + | 0.995375i | \(0.469375\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3360.00 | 0.834946 | ||||||||
\(254\) | −368.000 | −0.0909070 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4300.00 | 1.04368 | 0.521842 | − | 0.853042i | \(-0.325245\pi\) | ||||
0.521842 | + | 0.853042i | \(0.325245\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −128.000 | −0.0305316 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2904.00 | −0.684770 | ||||||||
\(263\) | 3860.00 | 0.905011 | 0.452505 | − | 0.891762i | \(-0.350530\pi\) | ||||
0.452505 | + | 0.891762i | \(0.350530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3824.00 | −0.886439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3632.00 | −0.827835 | ||||||||
\(269\) | −2800.00 | −0.634643 | −0.317322 | − | 0.948318i | \(-0.602783\pi\) | ||||
−0.317322 | + | 0.948318i | \(0.602783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4880.00 | 1.09387 | 0.546935 | − | 0.837175i | \(-0.315794\pi\) | ||||
0.546935 | + | 0.837175i | \(0.315794\pi\) | |||||||
\(272\) | −1344.00 | −0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1292.00 | −0.284863 | ||||||||
\(275\) | 2440.00 | 0.535046 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6674.00 | −1.44766 | −0.723830 | − | 0.689978i | \(-0.757620\pi\) | ||||
−0.723830 | + | 0.689978i | \(0.757620\pi\) | |||||||
\(278\) | 6024.00 | 1.29962 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9402.00 | 1.99600 | 0.998001 | − | 0.0632056i | \(-0.0201324\pi\) | ||||
0.998001 | + | 0.0632056i | \(0.0201324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9100.00 | 1.91144 | 0.955722 | − | 0.294270i | \(-0.0950765\pi\) | ||||
0.955722 | + | 0.294270i | \(0.0950765\pi\) | |||||||
\(284\) | 2096.00 | 0.437939 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 320.000 | 0.0661608 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | −928.000 | −0.187910 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1760.00 | −0.352727 | ||||||||
\(293\) | 5952.00 | 1.18676 | 0.593378 | − | 0.804924i | \(-0.297794\pi\) | ||||
0.593378 | + | 0.804924i | \(0.297794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4384.00 | 0.865242 | ||||||||
\(296\) | −1776.00 | −0.348743 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6340.00 | 1.23244 | ||||||||
\(299\) | 336.000 | 0.0649879 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3760.00 | −0.716436 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2368.00 | −0.446757 | ||||||||
\(305\) | −5536.00 | −1.03931 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3004.00 | 0.558460 | 0.279230 | − | 0.960224i | \(-0.409921\pi\) | ||||
0.279230 | + | 0.960224i | \(0.409921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2176.00 | 0.398673 | ||||||||
\(311\) | 688.000 | 0.125443 | 0.0627217 | − | 0.998031i | \(-0.480022\pi\) | ||||
0.0627217 | + | 0.998031i | \(0.480022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5592.00 | −1.00984 | −0.504918 | − | 0.863167i | \(-0.668477\pi\) | ||||
−0.504918 | + | 0.863167i | \(0.668477\pi\) | |||||||
\(314\) | −1208.00 | −0.217106 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4864.00 | 0.865890 | ||||||||
\(317\) | 2922.00 | 0.517716 | 0.258858 | − | 0.965915i | \(-0.416654\pi\) | ||||
0.258858 | + | 0.965915i | \(0.416654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2320.00 | 0.407195 | ||||||||
\(320\) | 512.000 | 0.0894427 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12432.0 | 2.14159 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 244.000 | 0.0416452 | ||||||||
\(326\) | 2232.00 | 0.379200 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3360.00 | 0.565625 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7492.00 | −1.24410 | −0.622051 | − | 0.782977i | \(-0.713700\pi\) | ||||
−0.622051 | + | 0.782977i | \(0.713700\pi\) | |||||||
\(332\) | −2736.00 | −0.452282 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3568.00 | −0.584528 | ||||||||
\(335\) | −7264.00 | −1.18470 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10766.0 | 1.74024 | 0.870121 | − | 0.492839i | \(-0.164041\pi\) | ||||
0.870121 | + | 0.492839i | \(0.164041\pi\) | |||||||
\(338\) | −4362.00 | −0.701957 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2688.00 | −0.428757 | ||||||||
\(341\) | −5440.00 | −0.863908 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1312.00 | −0.205635 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −688.000 | −0.106899 | ||||||||
\(347\) | 3984.00 | 0.616347 | 0.308173 | − | 0.951330i | \(-0.400282\pi\) | ||||
0.308173 | + | 0.951330i | \(0.400282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 180.000 | 0.0276080 | 0.0138040 | − | 0.999905i | \(-0.495606\pi\) | ||||
0.0138040 | + | 0.999905i | \(0.495606\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1280.00 | −0.193819 | ||||||||
\(353\) | −10428.0 | −1.57231 | −0.786156 | − | 0.618028i | \(-0.787932\pi\) | ||||
−0.786156 | + | 0.618028i | \(0.787932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4192.00 | 0.626727 | ||||||||
\(356\) | 2416.00 | 0.359685 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2784.00 | −0.411003 | ||||||||
\(359\) | −8684.00 | −1.27667 | −0.638334 | − | 0.769759i | \(-0.720376\pi\) | ||||
−0.638334 | + | 0.769759i | \(0.720376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15045.0 | 2.19347 | ||||||||
\(362\) | −8104.00 | −1.17662 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3520.00 | −0.504781 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5648.00 | −0.803333 | −0.401666 | − | 0.915786i | \(-0.631569\pi\) | ||||
−0.401666 | + | 0.915786i | \(0.631569\pi\) | |||||||
\(368\) | −1344.00 | −0.190383 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3552.00 | −0.499080 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2546.00 | −0.353423 | −0.176712 | − | 0.984263i | \(-0.556546\pi\) | ||||
−0.176712 | + | 0.984263i | \(0.556546\pi\) | |||||||
\(374\) | 6720.00 | 0.929099 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3904.00 | 0.535461 | ||||||||
\(377\) | 232.000 | 0.0316939 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8268.00 | 1.12058 | 0.560288 | − | 0.828298i | \(-0.310690\pi\) | ||||
0.560288 | + | 0.828298i | \(0.310690\pi\) | |||||||
\(380\) | −4736.00 | −0.639347 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6216.00 | 0.832561 | ||||||||
\(383\) | −10872.0 | −1.45048 | −0.725239 | − | 0.688497i | \(-0.758271\pi\) | ||||
−0.725239 | + | 0.688497i | \(0.758271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 100.000 | 0.0131862 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3328.00 | 0.435447 | ||||||||
\(389\) | −10434.0 | −1.35996 | −0.679980 | − | 0.733230i | \(-0.738012\pi\) | ||||
−0.679980 | + | 0.733230i | \(0.738012\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7056.00 | 0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 324.000 | 0.0414286 | ||||||||
\(395\) | 9728.00 | 1.23916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3044.00 | 0.384821 | 0.192411 | − | 0.981315i | \(-0.438369\pi\) | ||||
0.192411 | + | 0.981315i | \(0.438369\pi\) | |||||||
\(398\) | −3088.00 | −0.388913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −976.000 | −0.122000 | ||||||||
\(401\) | −8910.00 | −1.10959 | −0.554793 | − | 0.831988i | \(-0.687203\pi\) | ||||
−0.554793 | + | 0.831988i | \(0.687203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −544.000 | −0.0672421 | ||||||||
\(404\) | 1856.00 | 0.228563 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8880.00 | 1.08149 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5616.00 | −0.678957 | −0.339478 | − | 0.940614i | \(-0.610251\pi\) | ||||
−0.339478 | + | 0.940614i | \(0.610251\pi\) | |||||||
\(410\) | 6720.00 | 0.809456 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2528.00 | 0.302295 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5472.00 | −0.647253 | ||||||||
\(416\) | −128.000 | −0.0150859 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11840.0 | 1.38544 | ||||||||
\(419\) | −8932.00 | −1.04142 | −0.520712 | − | 0.853732i | \(-0.674334\pi\) | ||||
−0.520712 | + | 0.853732i | \(0.674334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5538.00 | −0.641106 | −0.320553 | − | 0.947231i | \(-0.603869\pi\) | ||||
−0.320553 | + | 0.947231i | \(0.603869\pi\) | |||||||
\(422\) | −2408.00 | −0.277772 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3824.00 | −0.437995 | ||||||||
\(425\) | 5124.00 | 0.584825 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 640.000 | 0.0722794 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2624.00 | −0.294280 | ||||||||
\(431\) | 6700.00 | 0.748788 | 0.374394 | − | 0.927270i | \(-0.377851\pi\) | ||||
0.374394 | + | 0.927270i | \(0.377851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5048.00 | 0.560257 | 0.280129 | − | 0.959962i | \(-0.409623\pi\) | ||||
0.280129 | + | 0.959962i | \(0.409623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8792.00 | −0.965735 | ||||||||
\(437\) | 12432.0 | 1.36088 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1344.00 | 0.146118 | 0.0730588 | − | 0.997328i | \(-0.476724\pi\) | ||||
0.0730588 | + | 0.997328i | \(0.476724\pi\) | |||||||
\(440\) | −2560.00 | −0.277371 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 672.000 | 0.0723162 | ||||||||
\(443\) | 4392.00 | 0.471039 | 0.235519 | − | 0.971870i | \(-0.424321\pi\) | ||||
0.235519 | + | 0.971870i | \(0.424321\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4832.00 | 0.514739 | ||||||||
\(446\) | −4000.00 | −0.424676 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3666.00 | −0.385321 | −0.192661 | − | 0.981265i | \(-0.561712\pi\) | ||||
−0.192661 | + | 0.981265i | \(0.561712\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16800.0 | −1.75406 | ||||||||
\(452\) | −3080.00 | −0.320511 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 776.000 | 0.0802191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.0000 | 0.00266133 | 0.00133067 | − | 0.999999i | \(-0.499576\pi\) | ||||
0.00133067 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(458\) | −8360.00 | −0.852920 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2688.00 | −0.272454 | ||||||||
\(461\) | 7656.00 | 0.773483 | 0.386741 | − | 0.922188i | \(-0.373601\pi\) | ||||
0.386741 | + | 0.922188i | \(0.373601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12608.0 | 1.26554 | 0.632768 | − | 0.774341i | \(-0.281919\pi\) | ||||
0.632768 | + | 0.774341i | \(0.281919\pi\) | |||||||
\(464\) | −928.000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2644.00 | 0.262835 | ||||||||
\(467\) | −3068.00 | −0.304005 | −0.152002 | − | 0.988380i | \(-0.548572\pi\) | ||||
−0.152002 | + | 0.988380i | \(0.548572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7808.00 | 0.766290 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4384.00 | 0.427521 | ||||||||
\(473\) | 6560.00 | 0.637694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9028.00 | 0.872070 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4824.00 | −0.461600 | ||||||||
\(479\) | 6456.00 | 0.615829 | 0.307915 | − | 0.951414i | \(-0.400369\pi\) | ||||
0.307915 | + | 0.951414i | \(0.400369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 888.000 | 0.0841774 | ||||||||
\(482\) | 8672.00 | 0.819500 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1076.00 | 0.101052 | ||||||||
\(485\) | 6656.00 | 0.623162 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11896.0 | 1.10690 | 0.553449 | − | 0.832883i | \(-0.313311\pi\) | ||||
0.553449 | + | 0.832883i | \(0.313311\pi\) | |||||||
\(488\) | −5536.00 | −0.513531 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 264.000 | 0.0242651 | 0.0121325 | − | 0.999926i | \(-0.496138\pi\) | ||||
0.0121325 | + | 0.999926i | \(0.496138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4872.00 | 0.445079 | ||||||||
\(494\) | 1184.00 | 0.107835 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2176.00 | 0.196986 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2628.00 | −0.235762 | −0.117881 | − | 0.993028i | \(-0.537610\pi\) | ||||
−0.117881 | + | 0.993028i | \(0.537610\pi\) | |||||||
\(500\) | −5952.00 | −0.532363 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1528.00 | 0.135853 | ||||||||
\(503\) | −13568.0 | −1.20272 | −0.601359 | − | 0.798979i | \(-0.705374\pi\) | ||||
−0.601359 | + | 0.798979i | \(0.705374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3712.00 | 0.327093 | ||||||||
\(506\) | 6720.00 | 0.590396 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −736.000 | −0.0642809 | ||||||||
\(509\) | 20656.0 | 1.79874 | 0.899372 | − | 0.437183i | \(-0.144024\pi\) | ||||
0.899372 | + | 0.437183i | \(0.144024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8600.00 | 0.737996 | ||||||||
\(515\) | 5056.00 | 0.432610 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19520.0 | −1.66052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −256.000 | −0.0215891 | ||||||||
\(521\) | 3628.00 | 0.305078 | 0.152539 | − | 0.988297i | \(-0.451255\pi\) | ||||
0.152539 | + | 0.988297i | \(0.451255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4852.00 | −0.405666 | −0.202833 | − | 0.979213i | \(-0.565015\pi\) | ||||
−0.202833 | + | 0.979213i | \(0.565015\pi\) | |||||||
\(524\) | −5808.00 | −0.484205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7720.00 | 0.639939 | ||||||||
\(527\) | −11424.0 | −0.944283 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5111.00 | −0.420071 | ||||||||
\(530\) | −7648.00 | −0.626807 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1680.00 | −0.136527 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1280.00 | 0.103438 | ||||||||
\(536\) | −7264.00 | −0.585368 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5600.00 | −0.448760 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7130.00 | −0.566622 | −0.283311 | − | 0.959028i | \(-0.591433\pi\) | ||||
−0.283311 | + | 0.959028i | \(0.591433\pi\) | |||||||
\(542\) | 9760.00 | 0.773483 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2688.00 | −0.211851 | ||||||||
\(545\) | −17584.0 | −1.38205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12788.0 | −0.999589 | −0.499795 | − | 0.866144i | \(-0.666591\pi\) | ||||
−0.499795 | + | 0.866144i | \(0.666591\pi\) | |||||||
\(548\) | −2584.00 | −0.201429 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4880.00 | 0.378334 | ||||||||
\(551\) | 8584.00 | 0.663685 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13348.0 | −1.02365 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12048.0 | 0.918973 | ||||||||
\(557\) | −2406.00 | −0.183026 | −0.0915130 | − | 0.995804i | \(-0.529170\pi\) | ||||
−0.0915130 | + | 0.995804i | \(0.529170\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 656.000 | 0.0496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18804.0 | 1.41139 | ||||||||
\(563\) | −25412.0 | −1.90229 | −0.951144 | − | 0.308748i | \(-0.900090\pi\) | ||||
−0.951144 | + | 0.308748i | \(0.900090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6160.00 | −0.458678 | ||||||||
\(566\) | 18200.0 | 1.35160 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4192.00 | 0.309670 | ||||||||
\(569\) | 9690.00 | 0.713930 | 0.356965 | − | 0.934118i | \(-0.383812\pi\) | ||||
0.356965 | + | 0.934118i | \(0.383812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5604.00 | 0.410718 | 0.205359 | − | 0.978687i | \(-0.434164\pi\) | ||||
0.205359 | + | 0.978687i | \(0.434164\pi\) | |||||||
\(572\) | 640.000 | 0.0467828 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5124.00 | 0.371627 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21568.0 | 1.55613 | 0.778066 | − | 0.628183i | \(-0.216201\pi\) | ||||
0.778066 | + | 0.628183i | \(0.216201\pi\) | |||||||
\(578\) | 4286.00 | 0.308433 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1856.00 | −0.132873 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19120.0 | 1.35827 | ||||||||
\(584\) | −3520.00 | −0.249415 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11904.0 | 0.839163 | ||||||||
\(587\) | 20300.0 | 1.42738 | 0.713689 | − | 0.700463i | \(-0.247023\pi\) | ||||
0.713689 | + | 0.700463i | \(0.247023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20128.0 | −1.40808 | ||||||||
\(590\) | 8768.00 | 0.611818 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3552.00 | −0.246598 | ||||||||
\(593\) | 13812.0 | 0.956477 | 0.478238 | − | 0.878230i | \(-0.341275\pi\) | ||||
0.478238 | + | 0.878230i | \(0.341275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12680.0 | 0.871465 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 672.000 | 0.0459534 | ||||||||
\(599\) | 21996.0 | 1.50039 | 0.750194 | − | 0.661218i | \(-0.229960\pi\) | ||||
0.750194 | + | 0.661218i | \(0.229960\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8368.00 | −0.567950 | −0.283975 | − | 0.958832i | \(-0.591653\pi\) | ||||
−0.283975 | + | 0.958832i | \(0.591653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7520.00 | −0.506597 | ||||||||
\(605\) | 2152.00 | 0.144614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21504.0 | −1.43792 | −0.718962 | − | 0.695049i | \(-0.755383\pi\) | ||||
−0.718962 | + | 0.695049i | \(0.755383\pi\) | |||||||
\(608\) | −4736.00 | −0.315905 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11072.0 | −0.734905 | ||||||||
\(611\) | −1952.00 | −0.129246 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10270.0 | −0.676674 | −0.338337 | − | 0.941025i | \(-0.609864\pi\) | ||||
−0.338337 | + | 0.941025i | \(0.609864\pi\) | |||||||
\(614\) | 6008.00 | 0.394891 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28358.0 | −1.85032 | −0.925162 | − | 0.379572i | \(-0.876071\pi\) | ||||
−0.925162 | + | 0.379572i | \(0.876071\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16292.0 | −1.05788 | −0.528942 | − | 0.848658i | \(-0.677411\pi\) | ||||
−0.528942 | + | 0.848658i | \(0.677411\pi\) | |||||||
\(620\) | 4352.00 | 0.281904 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1376.00 | 0.0887019 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4279.00 | −0.273856 | ||||||||
\(626\) | −11184.0 | −0.714062 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2416.00 | −0.153517 | ||||||||
\(629\) | 18648.0 | 1.18211 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11256.0 | 0.710134 | 0.355067 | − | 0.934841i | \(-0.384458\pi\) | ||||
0.355067 | + | 0.934841i | \(0.384458\pi\) | |||||||
\(632\) | 9728.00 | 0.612277 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5844.00 | 0.366080 | ||||||||
\(635\) | −1472.00 | −0.0919914 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4640.00 | 0.287930 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1024.00 | 0.0632456 | ||||||||
\(641\) | −15518.0 | −0.956200 | −0.478100 | − | 0.878305i | \(-0.658674\pi\) | ||||
−0.478100 | + | 0.878305i | \(0.658674\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10452.0 | 0.641037 | 0.320518 | − | 0.947242i | \(-0.396143\pi\) | ||||
0.320518 | + | 0.947242i | \(0.396143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24864.0 | 1.51434 | ||||||||
\(647\) | 72.0000 | 0.00437498 | 0.00218749 | − | 0.999998i | \(-0.499304\pi\) | ||||
0.00218749 | + | 0.999998i | \(0.499304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21920.0 | −1.32579 | ||||||||
\(650\) | 488.000 | 0.0294476 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4464.00 | 0.268135 | ||||||||
\(653\) | −11962.0 | −0.716859 | −0.358430 | − | 0.933557i | \(-0.616688\pi\) | ||||
−0.358430 | + | 0.933557i | \(0.616688\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11616.0 | −0.692938 | ||||||||
\(656\) | 6720.00 | 0.399957 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6016.00 | 0.355615 | 0.177807 | − | 0.984065i | \(-0.443100\pi\) | ||||
0.177807 | + | 0.984065i | \(0.443100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26068.0 | −1.53393 | −0.766965 | − | 0.641689i | \(-0.778234\pi\) | ||||
−0.766965 | + | 0.641689i | \(0.778234\pi\) | |||||||
\(662\) | −14984.0 | −0.879713 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5472.00 | −0.319811 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4872.00 | 0.282825 | ||||||||
\(668\) | −7136.00 | −0.413324 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14528.0 | −0.837710 | ||||||||
\(671\) | 27680.0 | 1.59251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20530.0 | −1.17589 | −0.587945 | − | 0.808901i | \(-0.700063\pi\) | ||||
−0.587945 | + | 0.808901i | \(0.700063\pi\) | |||||||
\(674\) | 21532.0 | 1.23054 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8724.00 | −0.496359 | ||||||||
\(677\) | −10056.0 | −0.570877 | −0.285438 | − | 0.958397i | \(-0.592139\pi\) | ||||
−0.285438 | + | 0.958397i | \(0.592139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5376.00 | −0.303177 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10880.0 | −0.610875 | ||||||||
\(683\) | −6152.00 | −0.344656 | −0.172328 | − | 0.985040i | \(-0.555129\pi\) | ||||
−0.172328 | + | 0.985040i | \(0.555129\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5168.00 | −0.288262 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2624.00 | −0.145406 | ||||||||
\(689\) | 1912.00 | 0.105720 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14716.0 | 0.810164 | 0.405082 | − | 0.914280i | \(-0.367243\pi\) | ||||
0.405082 | + | 0.914280i | \(0.367243\pi\) | |||||||
\(692\) | −1376.00 | −0.0755891 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7968.00 | 0.435823 | ||||||||
\(695\) | 24096.0 | 1.31513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35280.0 | −1.91725 | ||||||||
\(698\) | 360.000 | 0.0195218 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28202.0 | −1.51951 | −0.759754 | − | 0.650211i | \(-0.774681\pi\) | ||||
−0.759754 | + | 0.650211i | \(0.774681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32856.0 | 1.76271 | ||||||||
\(704\) | −2560.00 | −0.137051 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20856.0 | −1.11179 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22114.0 | 1.17138 | 0.585690 | − | 0.810535i | \(-0.300824\pi\) | ||||
0.585690 | + | 0.810535i | \(0.300824\pi\) | |||||||
\(710\) | 8384.00 | 0.443163 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4832.00 | 0.254335 | ||||||||
\(713\) | −11424.0 | −0.600045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1280.00 | 0.0669501 | ||||||||
\(716\) | −5568.00 | −0.290623 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17368.0 | −0.902741 | ||||||||
\(719\) | −9288.00 | −0.481758 | −0.240879 | − | 0.970555i | \(-0.577436\pi\) | ||||
−0.240879 | + | 0.970555i | \(0.577436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30090.0 | 1.55102 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16208.0 | −0.831997 | ||||||||
\(725\) | 3538.00 | 0.181239 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23848.0 | −1.21661 | −0.608304 | − | 0.793704i | \(-0.708150\pi\) | ||||
−0.608304 | + | 0.793704i | \(0.708150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7040.00 | −0.356934 | ||||||||
\(731\) | 13776.0 | 0.697023 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34756.0 | 1.75135 | 0.875677 | − | 0.482898i | \(-0.160416\pi\) | ||||
0.875677 | + | 0.482898i | \(0.160416\pi\) | |||||||
\(734\) | −11296.0 | −0.568042 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2688.00 | −0.134621 | ||||||||
\(737\) | 36320.0 | 1.81528 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26044.0 | 1.29641 | 0.648203 | − | 0.761468i | \(-0.275521\pi\) | ||||
0.648203 | + | 0.761468i | \(0.275521\pi\) | |||||||
\(740\) | −7104.00 | −0.352903 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36204.0 | −1.78761 | −0.893806 | − | 0.448454i | \(-0.851975\pi\) | ||||
−0.893806 | + | 0.448454i | \(0.851975\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25360.0 | 1.24714 | ||||||||
\(746\) | −5092.00 | −0.249908 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13440.0 | 0.656972 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11424.0 | −0.555083 | −0.277542 | − | 0.960714i | \(-0.589520\pi\) | ||||
−0.277542 | + | 0.960714i | \(0.589520\pi\) | |||||||
\(752\) | 7808.00 | 0.378628 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 464.000 | 0.0224110 | ||||||||
\(755\) | −15040.0 | −0.724982 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16622.0 | −0.798067 | −0.399034 | − | 0.916936i | \(-0.630654\pi\) | ||||
−0.399034 | + | 0.916936i | \(0.630654\pi\) | |||||||
\(758\) | 16536.0 | 0.792368 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9472.00 | −0.452086 | ||||||||
\(761\) | −38524.0 | −1.83508 | −0.917539 | − | 0.397646i | \(-0.869827\pi\) | ||||
−0.917539 | + | 0.397646i | \(0.869827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12432.0 | 0.588709 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21744.0 | −1.02564 | ||||||||
\(767\) | −2192.00 | −0.103192 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18440.0 | 0.864712 | 0.432356 | − | 0.901703i | \(-0.357682\pi\) | ||||
0.432356 | + | 0.901703i | \(0.357682\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 200.000 | 0.00932404 | ||||||||
\(773\) | −13968.0 | −0.649928 | −0.324964 | − | 0.945726i | \(-0.605352\pi\) | ||||
−0.324964 | + | 0.945726i | \(0.605352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8296.00 | −0.384518 | ||||||||
\(776\) | 6656.00 | 0.307908 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20868.0 | −0.961638 | ||||||||
\(779\) | −62160.0 | −2.85894 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20960.0 | −0.960317 | ||||||||
\(782\) | 14112.0 | 0.645325 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4832.00 | −0.219696 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10916.0 | −0.494426 | −0.247213 | − | 0.968961i | \(-0.579515\pi\) | ||||
−0.247213 | + | 0.968961i | \(0.579515\pi\) | |||||||
\(788\) | 648.000 | 0.0292945 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 19456.0 | 0.876220 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2768.00 | 0.123953 | ||||||||
\(794\) | 6088.00 | 0.272110 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6176.00 | −0.275003 | ||||||||
\(797\) | 12360.0 | 0.549327 | 0.274664 | − | 0.961540i | \(-0.411434\pi\) | ||||
0.274664 | + | 0.961540i | \(0.411434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40992.0 | −1.81501 | ||||||||
\(800\) | −1952.00 | −0.0862670 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17820.0 | −0.784596 | ||||||||
\(803\) | 17600.0 | 0.773463 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1088.00 | −0.0475474 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3712.00 | 0.161618 | ||||||||
\(809\) | −3402.00 | −0.147847 | −0.0739233 | − | 0.997264i | \(-0.523552\pi\) | ||||
−0.0739233 | + | 0.997264i | \(0.523552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −292.000 | −0.0126430 | −0.00632152 | − | 0.999980i | \(-0.502012\pi\) | ||||
−0.00632152 | + | 0.999980i | \(0.502012\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17760.0 | 0.764727 | ||||||||
\(815\) | 8928.00 | 0.383723 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24272.0 | 1.03938 | ||||||||
\(818\) | −11232.0 | −0.480095 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13440.0 | 0.572372 | ||||||||
\(821\) | −6910.00 | −0.293740 | −0.146870 | − | 0.989156i | \(-0.546920\pi\) | ||||
−0.146870 | + | 0.989156i | \(0.546920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 568.000 | 0.0240574 | 0.0120287 | − | 0.999928i | \(-0.496171\pi\) | ||||
0.0120287 | + | 0.999928i | \(0.496171\pi\) | |||||||
\(824\) | 5056.00 | 0.213755 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12144.0 | 0.510627 | 0.255313 | − | 0.966858i | \(-0.417821\pi\) | ||||
0.255313 | + | 0.966858i | \(0.417821\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14828.0 | −0.621228 | −0.310614 | − | 0.950536i | \(-0.600535\pi\) | ||||
−0.310614 | + | 0.950536i | \(0.600535\pi\) | |||||||
\(830\) | −10944.0 | −0.457677 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −256.000 | −0.0106673 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14272.0 | −0.591501 | ||||||||
\(836\) | 23680.0 | 0.979653 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17864.0 | −0.736398 | ||||||||
\(839\) | −22824.0 | −0.939180 | −0.469590 | − | 0.882885i | \(-0.655598\pi\) | ||||
−0.469590 | + | 0.882885i | \(0.655598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | −11076.0 | −0.453330 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4816.00 | −0.196414 | ||||||||
\(845\) | −17448.0 | −0.710331 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7648.00 | −0.309709 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10248.0 | 0.413534 | ||||||||
\(851\) | 18648.0 | 0.751169 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41780.0 | 1.67705 | 0.838523 | − | 0.544866i | \(-0.183420\pi\) | ||||
0.838523 | + | 0.544866i | \(0.183420\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1280.00 | 0.0511092 | ||||||||
\(857\) | −21420.0 | −0.853784 | −0.426892 | − | 0.904303i | \(-0.640392\pi\) | ||||
−0.426892 | + | 0.904303i | \(0.640392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18132.0 | 0.720205 | 0.360102 | − | 0.932913i | \(-0.382742\pi\) | ||||
0.360102 | + | 0.932913i | \(0.382742\pi\) | |||||||
\(860\) | −5248.00 | −0.208088 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13400.0 | 0.529473 | ||||||||
\(863\) | −24036.0 | −0.948082 | −0.474041 | − | 0.880503i | \(-0.657205\pi\) | ||||
−0.474041 | + | 0.880503i | \(0.657205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2752.00 | −0.108174 | ||||||||
\(866\) | 10096.0 | 0.396162 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48640.0 | −1.89873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3632.00 | 0.141292 | ||||||||
\(872\) | −17584.0 | −0.682878 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24864.0 | 0.962285 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4374.00 | −0.168414 | −0.0842072 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842072 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(878\) | 2688.00 | 0.103321 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5120.00 | −0.196131 | ||||||||
\(881\) | −46348.0 | −1.77242 | −0.886211 | − | 0.463282i | \(-0.846672\pi\) | ||||
−0.886211 | + | 0.463282i | \(0.846672\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20660.0 | −0.787389 | −0.393694 | − | 0.919241i | \(-0.628803\pi\) | ||||
−0.393694 | + | 0.919241i | \(0.628803\pi\) | |||||||
\(884\) | 1344.00 | 0.0511353 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8784.00 | 0.333075 | ||||||||
\(887\) | −1800.00 | −0.0681376 | −0.0340688 | − | 0.999419i | \(-0.510847\pi\) | ||||
−0.0340688 | + | 0.999419i | \(0.510847\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9664.00 | 0.363975 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8000.00 | −0.300291 | ||||||||
\(893\) | −72224.0 | −2.70648 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11136.0 | −0.415906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7332.00 | −0.272463 | ||||||||
\(899\) | −7888.00 | −0.292636 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40152.0 | 1.48464 | ||||||||
\(902\) | −33600.0 | −1.24031 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6160.00 | −0.226636 | ||||||||
\(905\) | −32416.0 | −1.19066 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41996.0 | −1.53744 | −0.768718 | − | 0.639588i | \(-0.779105\pi\) | ||||
−0.768718 | + | 0.639588i | \(0.779105\pi\) | |||||||
\(908\) | 1552.00 | 0.0567235 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41308.0 | 1.50230 | 0.751150 | − | 0.660132i | \(-0.229500\pi\) | ||||
0.751150 | + | 0.660132i | \(0.229500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27360.0 | 0.991768 | ||||||||
\(914\) | 52.0000 | 0.00188185 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16720.0 | −0.603105 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3936.00 | 0.141280 | 0.0706402 | − | 0.997502i | \(-0.477496\pi\) | ||||
0.0706402 | + | 0.997502i | \(0.477496\pi\) | |||||||
\(920\) | −5376.00 | −0.192654 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15312.0 | 0.546935 | ||||||||
\(923\) | −2096.00 | −0.0747461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13542.0 | 0.481360 | ||||||||
\(926\) | 25216.0 | 0.894870 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1856.00 | −0.0656532 | ||||||||
\(929\) | −7212.00 | −0.254702 | −0.127351 | − | 0.991858i | \(-0.540647\pi\) | ||||
−0.127351 | + | 0.991858i | \(0.540647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5288.00 | 0.185852 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6136.00 | −0.214964 | ||||||||
\(935\) | 26880.0 | 0.940182 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38976.0 | 1.35890 | 0.679451 | − | 0.733721i | \(-0.262218\pi\) | ||||
0.679451 | + | 0.733721i | \(0.262218\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15616.0 | 0.541849 | ||||||||
\(941\) | 53544.0 | 1.85493 | 0.927463 | − | 0.373916i | \(-0.121985\pi\) | ||||
0.927463 | + | 0.373916i | \(0.121985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35280.0 | −1.21832 | ||||||||
\(944\) | 8768.00 | 0.302303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13120.0 | 0.450918 | ||||||||
\(947\) | 21392.0 | 0.734051 | 0.367026 | − | 0.930211i | \(-0.380376\pi\) | ||||
0.367026 | + | 0.930211i | \(0.380376\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1760.00 | 0.0602023 | ||||||||
\(950\) | 18056.0 | 0.616646 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21162.0 | −0.719312 | −0.359656 | − | 0.933085i | \(-0.617106\pi\) | ||||
−0.359656 | + | 0.933085i | \(0.617106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24864.0 | 0.842492 | ||||||||
\(956\) | −9648.00 | −0.326400 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12912.0 | 0.435457 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11295.0 | −0.379141 | ||||||||
\(962\) | 1776.00 | 0.0595224 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17344.0 | 0.579474 | ||||||||
\(965\) | 400.000 | 0.0133435 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8224.00 | 0.273491 | 0.136746 | − | 0.990606i | \(-0.456336\pi\) | ||||
0.136746 | + | 0.990606i | \(0.456336\pi\) | |||||||
\(968\) | 2152.00 | 0.0714544 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13312.0 | 0.440642 | ||||||||
\(971\) | −8140.00 | −0.269027 | −0.134513 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134513 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23792.0 | 0.782695 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11072.0 | −0.363121 | ||||||||
\(977\) | −32158.0 | −1.05305 | −0.526523 | − | 0.850161i | \(-0.676505\pi\) | ||||
−0.526523 | + | 0.850161i | \(0.676505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24160.0 | −0.788720 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 528.000 | 0.0171580 | ||||||||
\(983\) | −41416.0 | −1.34381 | −0.671905 | − | 0.740637i | \(-0.734524\pi\) | ||||
−0.671905 | + | 0.740637i | \(0.734524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1296.00 | 0.0419228 | ||||||||
\(986\) | 9744.00 | 0.314718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2368.00 | 0.0762511 | ||||||||
\(989\) | 13776.0 | 0.442923 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12296.0 | 0.394143 | 0.197071 | − | 0.980389i | \(-0.436857\pi\) | ||||
0.197071 | + | 0.980389i | \(0.436857\pi\) | |||||||
\(992\) | 4352.00 | 0.139290 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12352.0 | −0.393552 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57652.0 | −1.83135 | −0.915676 | − | 0.401918i | \(-0.868344\pi\) | ||||
−0.915676 | + | 0.401918i | \(0.868344\pi\) | |||||||
\(998\) | −5256.00 | −0.166709 | ||||||||
\(999\) | 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 | 882.4.a.q.1.1 | 1 | ||
3.2 | odd | 2 | 294.4.a.b.1.1 | ✓ | 1 | ||
7.2 | even | 3 | 882.4.g.c.361.1 | 2 | |||
7.3 | odd | 6 | 882.4.g.j.667.1 | 2 | |||
7.4 | even | 3 | 882.4.g.c.667.1 | 2 | |||
7.5 | odd | 6 | 882.4.g.j.361.1 | 2 | |||
7.6 | odd | 2 | 882.4.a.j.1.1 | 1 | |||
12.11 | even | 2 | 2352.4.a.z.1.1 | 1 | |||
21.2 | odd | 6 | 294.4.e.j.67.1 | 2 | |||
21.5 | even | 6 | 294.4.e.f.67.1 | 2 | |||
21.11 | odd | 6 | 294.4.e.j.79.1 | 2 | |||
21.17 | even | 6 | 294.4.e.f.79.1 | 2 | |||
21.20 | even | 2 | 294.4.a.f.1.1 | yes | 1 | ||
84.83 | odd | 2 | 2352.4.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
294.4.a.f.1.1 | yes | 1 | 21.20 | even | 2 | ||
294.4.e.f.67.1 | 2 | 21.5 | even | 6 | |||
294.4.e.f.79.1 | 2 | 21.17 | even | 6 | |||
294.4.e.j.67.1 | 2 | 21.2 | odd | 6 | |||
294.4.e.j.79.1 | 2 | 21.11 | odd | 6 | |||
882.4.a.j.1.1 | 1 | 7.6 | odd | 2 | |||
882.4.a.q.1.1 | 1 | 1.1 | even | 1 | trivial | ||
882.4.g.c.361.1 | 2 | 7.2 | even | 3 | |||
882.4.g.c.667.1 | 2 | 7.4 | even | 3 | |||
882.4.g.j.361.1 | 2 | 7.5 | odd | 6 | |||
882.4.g.j.667.1 | 2 | 7.3 | odd | 6 | |||
2352.4.a.m.1.1 | 1 | 84.83 | odd | 2 | |||
2352.4.a.z.1.1 | 1 | 12.11 | even | 2 |