Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,4,Mod(1,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, 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("294.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(17.3465615417\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 294.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 8.00000 | 0.715542 | 0.357771 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357771 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −16.0000 | −0.505964 | ||||||||
\(11\) | 40.0000 | 1.09640 | 0.548202 | − | 0.836346i | \(-0.315312\pi\) | ||||
0.548202 | + | 0.836346i | \(0.315312\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 4.00000 | 0.0853385 | 0.0426692 | − | 0.999089i | \(-0.486414\pi\) | ||||
0.0426692 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.0000 | 0.413118 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −84.0000 | −1.19841 | −0.599206 | − | 0.800595i | \(-0.704517\pi\) | ||||
−0.599206 | + | 0.800595i | \(0.704517\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 148.000 | 1.78703 | 0.893514 | − | 0.449036i | \(-0.148232\pi\) | ||||
0.893514 | + | 0.449036i | \(0.148232\pi\) | |||||||
\(20\) | 32.0000 | 0.357771 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −80.0000 | −0.775275 | ||||||||
\(23\) | 84.0000 | 0.761531 | 0.380765 | − | 0.924672i | \(-0.375661\pi\) | ||||
0.380765 | + | 0.924672i | \(0.375661\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −61.0000 | −0.488000 | ||||||||
\(26\) | −8.00000 | −0.0603434 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 58.0000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −48.0000 | −0.292119 | ||||||||
\(31\) | −136.000 | −0.787946 | −0.393973 | − | 0.919122i | \(-0.628900\pi\) | ||||
−0.393973 | + | 0.919122i | \(0.628900\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 120.000 | 0.633010 | ||||||||
\(34\) | 168.000 | 0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −222.000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | −296.000 | −1.26362 | ||||||||
\(39\) | 12.0000 | 0.0492702 | ||||||||
\(40\) | −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 | ||||||||
\(45\) | 72.0000 | 0.238514 | ||||||||
\(46\) | −168.000 | −0.538484 | ||||||||
\(47\) | 488.000 | 1.51451 | 0.757257 | − | 0.653118i | \(-0.226539\pi\) | ||||
0.757257 | + | 0.653118i | \(0.226539\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 122.000 | 0.345068 | ||||||||
\(51\) | −252.000 | −0.691903 | ||||||||
\(52\) | 16.0000 | 0.0426692 | ||||||||
\(53\) | 478.000 | 1.23884 | 0.619418 | − | 0.785061i | \(-0.287368\pi\) | ||||
0.619418 | + | 0.785061i | \(0.287368\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 320.000 | 0.784523 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 444.000 | 1.03174 | ||||||||
\(58\) | −116.000 | −0.262613 | ||||||||
\(59\) | 548.000 | 1.20921 | 0.604606 | − | 0.796525i | \(-0.293331\pi\) | ||||
0.604606 | + | 0.796525i | \(0.293331\pi\) | |||||||
\(60\) | 96.0000 | 0.206559 | ||||||||
\(61\) | 692.000 | 1.45248 | 0.726242 | − | 0.687439i | \(-0.241265\pi\) | ||||
0.726242 | + | 0.687439i | \(0.241265\pi\) | |||||||
\(62\) | 272.000 | 0.557162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 32.0000 | 0.0610633 | ||||||||
\(66\) | −240.000 | −0.447605 | ||||||||
\(67\) | −908.000 | −1.65567 | −0.827835 | − | 0.560972i | \(-0.810428\pi\) | ||||
−0.827835 | + | 0.560972i | \(0.810428\pi\) | |||||||
\(68\) | −336.000 | −0.599206 | ||||||||
\(69\) | 252.000 | 0.439670 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −524.000 | −0.875878 | −0.437939 | − | 0.899005i | \(-0.644291\pi\) | ||||
−0.437939 | + | 0.899005i | \(0.644291\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | 440.000 | 0.705453 | 0.352727 | − | 0.935726i | \(-0.385255\pi\) | ||||
0.352727 | + | 0.935726i | \(0.385255\pi\) | |||||||
\(74\) | 444.000 | 0.697486 | ||||||||
\(75\) | −183.000 | −0.281747 | ||||||||
\(76\) | 592.000 | 0.893514 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −24.0000 | −0.0348393 | ||||||||
\(79\) | 1216.00 | 1.73178 | 0.865890 | − | 0.500234i | \(-0.166753\pi\) | ||||
0.865890 | + | 0.500234i | \(0.166753\pi\) | |||||||
\(80\) | 128.000 | 0.178885 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −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 | ||||||||
\(87\) | 174.000 | 0.214423 | ||||||||
\(88\) | −320.000 | −0.387638 | ||||||||
\(89\) | 604.000 | 0.719369 | 0.359685 | − | 0.933074i | \(-0.382884\pi\) | ||||
0.359685 | + | 0.933074i | \(0.382884\pi\) | |||||||
\(90\) | −144.000 | −0.168655 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 336.000 | 0.380765 | ||||||||
\(93\) | −408.000 | −0.454921 | ||||||||
\(94\) | −976.000 | −1.07092 | ||||||||
\(95\) | 1184.00 | 1.27869 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −832.000 | −0.870895 | −0.435447 | − | 0.900214i | \(-0.643410\pi\) | ||||
−0.435447 | + | 0.900214i | \(0.643410\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 360.000 | 0.365468 | ||||||||
\(100\) | −244.000 | −0.244000 | ||||||||
\(101\) | 464.000 | 0.457126 | 0.228563 | − | 0.973529i | \(-0.426597\pi\) | ||||
0.228563 | + | 0.973529i | \(0.426597\pi\) | |||||||
\(102\) | 504.000 | 0.489249 | ||||||||
\(103\) | −632.000 | −0.604590 | −0.302295 | − | 0.953214i | \(-0.597753\pi\) | ||||
−0.302295 | + | 0.953214i | \(0.597753\pi\) | |||||||
\(104\) | −32.0000 | −0.0301717 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −956.000 | −0.875990 | ||||||||
\(107\) | −160.000 | −0.144559 | −0.0722794 | − | 0.997384i | \(-0.523027\pi\) | ||||
−0.0722794 | + | 0.997384i | \(0.523027\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −2198.00 | −1.93147 | −0.965735 | − | 0.259530i | \(-0.916432\pi\) | ||||
−0.965735 | + | 0.259530i | \(0.916432\pi\) | |||||||
\(110\) | −640.000 | −0.554742 | ||||||||
\(111\) | −666.000 | −0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 770.000 | 0.641022 | 0.320511 | − | 0.947245i | \(-0.396145\pi\) | ||||
0.320511 | + | 0.947245i | \(0.396145\pi\) | |||||||
\(114\) | −888.000 | −0.729551 | ||||||||
\(115\) | 672.000 | 0.544907 | ||||||||
\(116\) | 232.000 | 0.185695 | ||||||||
\(117\) | 36.0000 | 0.0284462 | ||||||||
\(118\) | −1096.00 | −0.855042 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −192.000 | −0.146059 | ||||||||
\(121\) | 269.000 | 0.202104 | ||||||||
\(122\) | −1384.00 | −1.02706 | ||||||||
\(123\) | 1260.00 | 0.923662 | ||||||||
\(124\) | −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 | ||||||||
\(129\) | −492.000 | −0.335800 | ||||||||
\(130\) | −64.0000 | −0.0431782 | ||||||||
\(131\) | −1452.00 | −0.968411 | −0.484205 | − | 0.874954i | \(-0.660891\pi\) | ||||
−0.484205 | + | 0.874954i | \(0.660891\pi\) | |||||||
\(132\) | 480.000 | 0.316505 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1816.00 | 1.17074 | ||||||||
\(135\) | 216.000 | 0.137706 | ||||||||
\(136\) | 672.000 | 0.423702 | ||||||||
\(137\) | 646.000 | 0.402858 | 0.201429 | − | 0.979503i | \(-0.435442\pi\) | ||||
0.201429 | + | 0.979503i | \(0.435442\pi\) | |||||||
\(138\) | −504.000 | −0.310894 | ||||||||
\(139\) | −3012.00 | −1.83795 | −0.918973 | − | 0.394320i | \(-0.870980\pi\) | ||||
−0.918973 | + | 0.394320i | \(0.870980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1464.00 | 0.874405 | ||||||||
\(142\) | 1048.00 | 0.619339 | ||||||||
\(143\) | 160.000 | 0.0935655 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 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 | \(-0.836830\pi\) | ||||
−0.871465 | + | 0.490458i | \(0.836830\pi\) | |||||||
\(150\) | 366.000 | 0.199225 | ||||||||
\(151\) | −1880.00 | −1.01319 | −0.506597 | − | 0.862183i | \(-0.669097\pi\) | ||||
−0.506597 | + | 0.862183i | \(0.669097\pi\) | |||||||
\(152\) | −1184.00 | −0.631810 | ||||||||
\(153\) | −756.000 | −0.399470 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1088.00 | −0.563808 | ||||||||
\(156\) | 48.0000 | 0.0246351 | ||||||||
\(157\) | 604.000 | 0.307035 | 0.153517 | − | 0.988146i | \(-0.450940\pi\) | ||||
0.153517 | + | 0.988146i | \(0.450940\pi\) | |||||||
\(158\) | −2432.00 | −1.22455 | ||||||||
\(159\) | 1434.00 | 0.715243 | ||||||||
\(160\) | −256.000 | −0.126491 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | 1116.00 | 0.536269 | 0.268135 | − | 0.963381i | \(-0.413593\pi\) | ||||
0.268135 | + | 0.963381i | \(0.413593\pi\) | |||||||
\(164\) | 1680.00 | 0.799914 | ||||||||
\(165\) | 960.000 | 0.452945 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 1332.00 | 0.595676 | ||||||||
\(172\) | −656.000 | −0.290811 | ||||||||
\(173\) | −344.000 | −0.151178 | −0.0755891 | − | 0.997139i | \(-0.524084\pi\) | ||||
−0.0755891 | + | 0.997139i | \(0.524084\pi\) | |||||||
\(174\) | −348.000 | −0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 640.000 | 0.274101 | ||||||||
\(177\) | 1644.00 | 0.698139 | ||||||||
\(178\) | −1208.00 | −0.508671 | ||||||||
\(179\) | 1392.00 | 0.581246 | 0.290623 | − | 0.956838i | \(-0.406138\pi\) | ||||
0.290623 | + | 0.956838i | \(0.406138\pi\) | |||||||
\(180\) | 288.000 | 0.119257 | ||||||||
\(181\) | 4052.00 | 1.66399 | 0.831997 | − | 0.554781i | \(-0.187198\pi\) | ||||
0.831997 | + | 0.554781i | \(0.187198\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2076.00 | 0.838592 | ||||||||
\(184\) | −672.000 | −0.269242 | ||||||||
\(185\) | −1776.00 | −0.705806 | ||||||||
\(186\) | 816.000 | 0.321678 | ||||||||
\(187\) | −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 | \(-0.700364\pi\) | ||||
−0.588709 | + | 0.808345i | \(0.700364\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 50.0000 | 0.0186481 | 0.00932404 | − | 0.999957i | \(-0.497032\pi\) | ||||
0.00932404 | + | 0.999957i | \(0.497032\pi\) | |||||||
\(194\) | 1664.00 | 0.615816 | ||||||||
\(195\) | 96.0000 | 0.0352549 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −162.000 | −0.0585889 | −0.0292945 | − | 0.999571i | \(-0.509326\pi\) | ||||
−0.0292945 | + | 0.999571i | \(0.509326\pi\) | |||||||
\(198\) | −720.000 | −0.258425 | ||||||||
\(199\) | 1544.00 | 0.550006 | 0.275003 | − | 0.961443i | \(-0.411321\pi\) | ||||
0.275003 | + | 0.961443i | \(0.411321\pi\) | |||||||
\(200\) | 488.000 | 0.172534 | ||||||||
\(201\) | −2724.00 | −0.955901 | ||||||||
\(202\) | −928.000 | −0.323237 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1008.00 | −0.345952 | ||||||||
\(205\) | 3360.00 | 1.14474 | ||||||||
\(206\) | 1264.00 | 0.427510 | ||||||||
\(207\) | 756.000 | 0.253844 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | −1572.00 | −0.505689 | ||||||||
\(214\) | 320.000 | 0.102218 | ||||||||
\(215\) | −1312.00 | −0.416175 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4396.00 | 1.36576 | ||||||||
\(219\) | 1320.00 | 0.407294 | ||||||||
\(220\) | 1280.00 | 0.392262 | ||||||||
\(221\) | −336.000 | −0.102271 | ||||||||
\(222\) | 1332.00 | 0.402694 | ||||||||
\(223\) | 2000.00 | 0.600583 | 0.300291 | − | 0.953848i | \(-0.402916\pi\) | ||||
0.300291 | + | 0.953848i | \(0.402916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −549.000 | −0.162667 | ||||||||
\(226\) | −1540.00 | −0.453271 | ||||||||
\(227\) | 388.000 | 0.113447 | 0.0567235 | − | 0.998390i | \(-0.481935\pi\) | ||||
0.0567235 | + | 0.998390i | \(0.481935\pi\) | |||||||
\(228\) | 1776.00 | 0.515870 | ||||||||
\(229\) | 4180.00 | 1.20621 | 0.603105 | − | 0.797662i | \(-0.293930\pi\) | ||||
0.603105 | + | 0.797662i | \(0.293930\pi\) | |||||||
\(230\) | −1344.00 | −0.385308 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −464.000 | −0.131306 | ||||||||
\(233\) | −1322.00 | −0.371704 | −0.185852 | − | 0.982578i | \(-0.559505\pi\) | ||||
−0.185852 | + | 0.982578i | \(0.559505\pi\) | |||||||
\(234\) | −72.0000 | −0.0201145 | ||||||||
\(235\) | 3904.00 | 1.08370 | ||||||||
\(236\) | 2192.00 | 0.604606 | ||||||||
\(237\) | 3648.00 | 0.999844 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2412.00 | 0.652800 | 0.326400 | − | 0.945232i | \(-0.394164\pi\) | ||||
0.326400 | + | 0.945232i | \(0.394164\pi\) | |||||||
\(240\) | 384.000 | 0.103280 | ||||||||
\(241\) | −4336.00 | −1.15895 | −0.579474 | − | 0.814991i | \(-0.696742\pi\) | ||||
−0.579474 | + | 0.814991i | \(0.696742\pi\) | |||||||
\(242\) | −538.000 | −0.142909 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2768.00 | 0.726242 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2520.00 | −0.653127 | ||||||||
\(247\) | 592.000 | 0.152502 | ||||||||
\(248\) | 1088.00 | 0.278581 | ||||||||
\(249\) | −2052.00 | −0.522250 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | −2016.00 | −0.495086 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4300.00 | 1.04368 | 0.521842 | − | 0.853042i | \(-0.325245\pi\) | ||||
0.521842 | + | 0.853042i | \(0.325245\pi\) | |||||||
\(258\) | 984.000 | 0.237446 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 128.000 | 0.0305316 | ||||||||
\(261\) | 522.000 | 0.123797 | ||||||||
\(262\) | 2904.00 | 0.684770 | ||||||||
\(263\) | −3860.00 | −0.905011 | −0.452505 | − | 0.891762i | \(-0.649470\pi\) | ||||
−0.452505 | + | 0.891762i | \(0.649470\pi\) | |||||||
\(264\) | −960.000 | −0.223803 | ||||||||
\(265\) | 3824.00 | 0.886439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1812.00 | 0.415328 | ||||||||
\(268\) | −3632.00 | −0.827835 | ||||||||
\(269\) | −2800.00 | −0.634643 | −0.317322 | − | 0.948318i | \(-0.602783\pi\) | ||||
−0.317322 | + | 0.948318i | \(0.602783\pi\) | |||||||
\(270\) | −432.000 | −0.0973729 | ||||||||
\(271\) | −4880.00 | −1.09387 | −0.546935 | − | 0.837175i | \(-0.684206\pi\) | ||||
−0.546935 | + | 0.837175i | \(0.684206\pi\) | |||||||
\(272\) | −1344.00 | −0.299603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1292.00 | −0.284863 | ||||||||
\(275\) | −2440.00 | −0.535046 | ||||||||
\(276\) | 1008.00 | 0.219835 | ||||||||
\(277\) | −6674.00 | −1.44766 | −0.723830 | − | 0.689978i | \(-0.757620\pi\) | ||||
−0.723830 | + | 0.689978i | \(0.757620\pi\) | |||||||
\(278\) | 6024.00 | 1.29962 | ||||||||
\(279\) | −1224.00 | −0.262649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9402.00 | −1.99600 | −0.998001 | − | 0.0632056i | \(-0.979868\pi\) | ||||
−0.998001 | + | 0.0632056i | \(0.979868\pi\) | |||||||
\(282\) | −2928.00 | −0.618297 | ||||||||
\(283\) | −9100.00 | −1.91144 | −0.955722 | − | 0.294270i | \(-0.904924\pi\) | ||||
−0.955722 | + | 0.294270i | \(0.904924\pi\) | |||||||
\(284\) | −2096.00 | −0.437939 | ||||||||
\(285\) | 3552.00 | 0.738254 | ||||||||
\(286\) | −320.000 | −0.0661608 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | −928.000 | −0.187910 | ||||||||
\(291\) | −2496.00 | −0.502811 | ||||||||
\(292\) | 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 | ||||||||
\(297\) | 1080.00 | 0.211003 | ||||||||
\(298\) | 6340.00 | 1.23244 | ||||||||
\(299\) | 336.000 | 0.0649879 | ||||||||
\(300\) | −732.000 | −0.140873 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3760.00 | 0.716436 | ||||||||
\(303\) | 1392.00 | 0.263922 | ||||||||
\(304\) | 2368.00 | 0.446757 | ||||||||
\(305\) | 5536.00 | 1.03931 | ||||||||
\(306\) | 1512.00 | 0.282468 | ||||||||
\(307\) | −3004.00 | −0.558460 | −0.279230 | − | 0.960224i | \(-0.590079\pi\) | ||||
−0.279230 | + | 0.960224i | \(0.590079\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1896.00 | −0.349060 | ||||||||
\(310\) | 2176.00 | 0.398673 | ||||||||
\(311\) | 688.000 | 0.125443 | 0.0627217 | − | 0.998031i | \(-0.480022\pi\) | ||||
0.0627217 | + | 0.998031i | \(0.480022\pi\) | |||||||
\(312\) | −96.0000 | −0.0174196 | ||||||||
\(313\) | 5592.00 | 1.00984 | 0.504918 | − | 0.863167i | \(-0.331523\pi\) | ||||
0.504918 | + | 0.863167i | \(0.331523\pi\) | |||||||
\(314\) | −1208.00 | −0.217106 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4864.00 | 0.865890 | ||||||||
\(317\) | −2922.00 | −0.517716 | −0.258858 | − | 0.965915i | \(-0.583346\pi\) | ||||
−0.258858 | + | 0.965915i | \(0.583346\pi\) | |||||||
\(318\) | −2868.00 | −0.505753 | ||||||||
\(319\) | 2320.00 | 0.407195 | ||||||||
\(320\) | 512.000 | 0.0894427 | ||||||||
\(321\) | −480.000 | −0.0834610 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12432.0 | −2.14159 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −244.000 | −0.0416452 | ||||||||
\(326\) | −2232.00 | −0.379200 | ||||||||
\(327\) | −6594.00 | −1.11513 | ||||||||
\(328\) | −3360.00 | −0.565625 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1920.00 | −0.320280 | ||||||||
\(331\) | −7492.00 | −1.24410 | −0.622051 | − | 0.782977i | \(-0.713700\pi\) | ||||
−0.622051 | + | 0.782977i | \(0.713700\pi\) | |||||||
\(332\) | −2736.00 | −0.452282 | ||||||||
\(333\) | −1998.00 | −0.328798 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 2310.00 | 0.370094 | ||||||||
\(340\) | −2688.00 | −0.428757 | ||||||||
\(341\) | −5440.00 | −0.863908 | ||||||||
\(342\) | −2664.00 | −0.421206 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1312.00 | 0.205635 | ||||||||
\(345\) | 2016.00 | 0.314602 | ||||||||
\(346\) | 688.000 | 0.106899 | ||||||||
\(347\) | −3984.00 | −0.616347 | −0.308173 | − | 0.951330i | \(-0.599718\pi\) | ||||
−0.308173 | + | 0.951330i | \(0.599718\pi\) | |||||||
\(348\) | 696.000 | 0.107211 | ||||||||
\(349\) | −180.000 | −0.0276080 | −0.0138040 | − | 0.999905i | \(-0.504394\pi\) | ||||
−0.0138040 | + | 0.999905i | \(0.504394\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 108.000 | 0.0164234 | ||||||||
\(352\) | −1280.00 | −0.193819 | ||||||||
\(353\) | −10428.0 | −1.57231 | −0.786156 | − | 0.618028i | \(-0.787932\pi\) | ||||
−0.786156 | + | 0.618028i | \(0.787932\pi\) | |||||||
\(354\) | −3288.00 | −0.493659 | ||||||||
\(355\) | −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 | \(-0.279624\pi\) | ||||
0.638334 | + | 0.769759i | \(0.279624\pi\) | |||||||
\(360\) | −576.000 | −0.0843274 | ||||||||
\(361\) | 15045.0 | 2.19347 | ||||||||
\(362\) | −8104.00 | −1.17662 | ||||||||
\(363\) | 807.000 | 0.116685 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3520.00 | 0.504781 | ||||||||
\(366\) | −4152.00 | −0.592974 | ||||||||
\(367\) | 5648.00 | 0.803333 | 0.401666 | − | 0.915786i | \(-0.368431\pi\) | ||||
0.401666 | + | 0.915786i | \(0.368431\pi\) | |||||||
\(368\) | 1344.00 | 0.190383 | ||||||||
\(369\) | 3780.00 | 0.533276 | ||||||||
\(370\) | 3552.00 | 0.499080 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1632.00 | −0.227460 | ||||||||
\(373\) | −2546.00 | −0.353423 | −0.176712 | − | 0.984263i | \(-0.556546\pi\) | ||||
−0.176712 | + | 0.984263i | \(0.556546\pi\) | |||||||
\(374\) | 6720.00 | 0.929099 | ||||||||
\(375\) | −4464.00 | −0.614720 | ||||||||
\(376\) | −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 | ||||||||
\(381\) | −552.000 | −0.0742252 | ||||||||
\(382\) | 6216.00 | 0.832561 | ||||||||
\(383\) | −10872.0 | −1.45048 | −0.725239 | − | 0.688497i | \(-0.758271\pi\) | ||||
−0.725239 | + | 0.688497i | \(0.758271\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −100.000 | −0.0131862 | ||||||||
\(387\) | −1476.00 | −0.193874 | ||||||||
\(388\) | −3328.00 | −0.435447 | ||||||||
\(389\) | 10434.0 | 1.35996 | 0.679980 | − | 0.733230i | \(-0.261988\pi\) | ||||
0.679980 | + | 0.733230i | \(0.261988\pi\) | |||||||
\(390\) | −192.000 | −0.0249290 | ||||||||
\(391\) | −7056.00 | −0.912627 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4356.00 | −0.559112 | ||||||||
\(394\) | 324.000 | 0.0414286 | ||||||||
\(395\) | 9728.00 | 1.23916 | ||||||||
\(396\) | 1440.00 | 0.182734 | ||||||||
\(397\) | −3044.00 | −0.384821 | −0.192411 | − | 0.981315i | \(-0.561631\pi\) | ||||
−0.192411 | + | 0.981315i | \(0.561631\pi\) | |||||||
\(398\) | −3088.00 | −0.388913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −976.000 | −0.122000 | ||||||||
\(401\) | 8910.00 | 1.10959 | 0.554793 | − | 0.831988i | \(-0.312797\pi\) | ||||
0.554793 | + | 0.831988i | \(0.312797\pi\) | |||||||
\(402\) | 5448.00 | 0.675924 | ||||||||
\(403\) | −544.000 | −0.0672421 | ||||||||
\(404\) | 1856.00 | 0.228563 | ||||||||
\(405\) | 648.000 | 0.0795046 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8880.00 | −1.08149 | ||||||||
\(408\) | 2016.00 | 0.244625 | ||||||||
\(409\) | 5616.00 | 0.678957 | 0.339478 | − | 0.940614i | \(-0.389749\pi\) | ||||
0.339478 | + | 0.940614i | \(0.389749\pi\) | |||||||
\(410\) | −6720.00 | −0.809456 | ||||||||
\(411\) | 1938.00 | 0.232590 | ||||||||
\(412\) | −2528.00 | −0.302295 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1512.00 | −0.179495 | ||||||||
\(415\) | −5472.00 | −0.647253 | ||||||||
\(416\) | −128.000 | −0.0150859 | ||||||||
\(417\) | −9036.00 | −1.06114 | ||||||||
\(418\) | −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 | ||||||||
\(423\) | 4392.00 | 0.504838 | ||||||||
\(424\) | −3824.00 | −0.437995 | ||||||||
\(425\) | 5124.00 | 0.584825 | ||||||||
\(426\) | 3144.00 | 0.357576 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −640.000 | −0.0722794 | ||||||||
\(429\) | 480.000 | 0.0540201 | ||||||||
\(430\) | 2624.00 | 0.294280 | ||||||||
\(431\) | −6700.00 | −0.748788 | −0.374394 | − | 0.927270i | \(-0.622149\pi\) | ||||
−0.374394 | + | 0.927270i | \(0.622149\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | −5048.00 | −0.560257 | −0.280129 | − | 0.959962i | \(-0.590377\pi\) | ||||
−0.280129 | + | 0.959962i | \(0.590377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1392.00 | 0.153428 | ||||||||
\(436\) | −8792.00 | −0.965735 | ||||||||
\(437\) | 12432.0 | 1.36088 | ||||||||
\(438\) | −2640.00 | −0.288000 | ||||||||
\(439\) | −1344.00 | −0.146118 | −0.0730588 | − | 0.997328i | \(-0.523276\pi\) | ||||
−0.0730588 | + | 0.997328i | \(0.523276\pi\) | |||||||
\(440\) | −2560.00 | −0.277371 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 672.000 | 0.0723162 | ||||||||
\(443\) | −4392.00 | −0.471039 | −0.235519 | − | 0.971870i | \(-0.575679\pi\) | ||||
−0.235519 | + | 0.971870i | \(0.575679\pi\) | |||||||
\(444\) | −2664.00 | −0.284747 | ||||||||
\(445\) | 4832.00 | 0.514739 | ||||||||
\(446\) | −4000.00 | −0.424676 | ||||||||
\(447\) | −9510.00 | −1.00628 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3666.00 | 0.385321 | 0.192661 | − | 0.981265i | \(-0.438288\pi\) | ||||
0.192661 | + | 0.981265i | \(0.438288\pi\) | |||||||
\(450\) | 1098.00 | 0.115023 | ||||||||
\(451\) | 16800.0 | 1.75406 | ||||||||
\(452\) | 3080.00 | 0.320511 | ||||||||
\(453\) | −5640.00 | −0.584968 | ||||||||
\(454\) | −776.000 | −0.0802191 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3552.00 | −0.364776 | ||||||||
\(457\) | 26.0000 | 0.00266133 | 0.00133067 | − | 0.999999i | \(-0.499576\pi\) | ||||
0.00133067 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(458\) | −8360.00 | −0.852920 | ||||||||
\(459\) | −2268.00 | −0.230634 | ||||||||
\(460\) | 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 | ||||||||
\(465\) | −3264.00 | −0.325515 | ||||||||
\(466\) | 2644.00 | 0.262835 | ||||||||
\(467\) | −3068.00 | −0.304005 | −0.152002 | − | 0.988380i | \(-0.548572\pi\) | ||||
−0.152002 | + | 0.988380i | \(0.548572\pi\) | |||||||
\(468\) | 144.000 | 0.0142231 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7808.00 | −0.766290 | ||||||||
\(471\) | 1812.00 | 0.177267 | ||||||||
\(472\) | −4384.00 | −0.427521 | ||||||||
\(473\) | −6560.00 | −0.637694 | ||||||||
\(474\) | −7296.00 | −0.706997 | ||||||||
\(475\) | −9028.00 | −0.872070 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4302.00 | 0.412946 | ||||||||
\(478\) | −4824.00 | −0.461600 | ||||||||
\(479\) | 6456.00 | 0.615829 | 0.307915 | − | 0.951414i | \(-0.400369\pi\) | ||||
0.307915 | + | 0.951414i | \(0.400369\pi\) | |||||||
\(480\) | −768.000 | −0.0730297 | ||||||||
\(481\) | −888.000 | −0.0841774 | ||||||||
\(482\) | 8672.00 | 0.819500 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1076.00 | 0.101052 | ||||||||
\(485\) | −6656.00 | −0.623162 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 11896.0 | 1.10690 | 0.553449 | − | 0.832883i | \(-0.313311\pi\) | ||||
0.553449 | + | 0.832883i | \(0.313311\pi\) | |||||||
\(488\) | −5536.00 | −0.513531 | ||||||||
\(489\) | 3348.00 | 0.309615 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −264.000 | −0.0242651 | −0.0121325 | − | 0.999926i | \(-0.503862\pi\) | ||||
−0.0121325 | + | 0.999926i | \(0.503862\pi\) | |||||||
\(492\) | 5040.00 | 0.461831 | ||||||||
\(493\) | −4872.00 | −0.445079 | ||||||||
\(494\) | −1184.00 | −0.107835 | ||||||||
\(495\) | 2880.00 | 0.261508 | ||||||||
\(496\) | −2176.00 | −0.196986 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4104.00 | 0.369286 | ||||||||
\(499\) | −2628.00 | −0.235762 | −0.117881 | − | 0.993028i | \(-0.537610\pi\) | ||||
−0.117881 | + | 0.993028i | \(0.537610\pi\) | |||||||
\(500\) | −5952.00 | −0.532363 | ||||||||
\(501\) | −5352.00 | −0.477265 | ||||||||
\(502\) | −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 | ||||||||
\(507\) | −6543.00 | −0.573146 | ||||||||
\(508\) | −736.000 | −0.0642809 | ||||||||
\(509\) | 20656.0 | 1.79874 | 0.899372 | − | 0.437183i | \(-0.144024\pi\) | ||||
0.899372 | + | 0.437183i | \(0.144024\pi\) | |||||||
\(510\) | 4032.00 | 0.350078 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 3996.00 | 0.343914 | ||||||||
\(514\) | −8600.00 | −0.737996 | ||||||||
\(515\) | −5056.00 | −0.432610 | ||||||||
\(516\) | −1968.00 | −0.167900 | ||||||||
\(517\) | 19520.0 | 1.66052 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1032.00 | −0.0872828 | ||||||||
\(520\) | −256.000 | −0.0215891 | ||||||||
\(521\) | 3628.00 | 0.305078 | 0.152539 | − | 0.988297i | \(-0.451255\pi\) | ||||
0.152539 | + | 0.988297i | \(0.451255\pi\) | |||||||
\(522\) | −1044.00 | −0.0875376 | ||||||||
\(523\) | 4852.00 | 0.405666 | 0.202833 | − | 0.979213i | \(-0.434985\pi\) | ||||
0.202833 | + | 0.979213i | \(0.434985\pi\) | |||||||
\(524\) | −5808.00 | −0.484205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7720.00 | 0.639939 | ||||||||
\(527\) | 11424.0 | 0.944283 | ||||||||
\(528\) | 1920.00 | 0.158252 | ||||||||
\(529\) | −5111.00 | −0.420071 | ||||||||
\(530\) | −7648.00 | −0.626807 | ||||||||
\(531\) | 4932.00 | 0.403071 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1680.00 | 0.136527 | ||||||||
\(534\) | −3624.00 | −0.293681 | ||||||||
\(535\) | −1280.00 | −0.103438 | ||||||||
\(536\) | 7264.00 | 0.585368 | ||||||||
\(537\) | 4176.00 | 0.335582 | ||||||||
\(538\) | 5600.00 | 0.448760 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 864.000 | 0.0688530 | ||||||||
\(541\) | −7130.00 | −0.566622 | −0.283311 | − | 0.959028i | \(-0.591433\pi\) | ||||
−0.283311 | + | 0.959028i | \(0.591433\pi\) | |||||||
\(542\) | 9760.00 | 0.773483 | ||||||||
\(543\) | 12156.0 | 0.960707 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 6228.00 | 0.484161 | ||||||||
\(550\) | 4880.00 | 0.378334 | ||||||||
\(551\) | 8584.00 | 0.663685 | ||||||||
\(552\) | −2016.00 | −0.155447 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13348.0 | 1.02365 | ||||||||
\(555\) | −5328.00 | −0.407497 | ||||||||
\(556\) | −12048.0 | −0.918973 | ||||||||
\(557\) | 2406.00 | 0.183026 | 0.0915130 | − | 0.995804i | \(-0.470830\pi\) | ||||
0.0915130 | + | 0.995804i | \(0.470830\pi\) | |||||||
\(558\) | 2448.00 | 0.185721 | ||||||||
\(559\) | −656.000 | −0.0496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10080.0 | −0.758606 | ||||||||
\(562\) | 18804.0 | 1.41139 | ||||||||
\(563\) | −25412.0 | −1.90229 | −0.951144 | − | 0.308748i | \(-0.900090\pi\) | ||||
−0.951144 | + | 0.308748i | \(0.900090\pi\) | |||||||
\(564\) | 5856.00 | 0.437202 | ||||||||
\(565\) | 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 | \(-0.616188\pi\) | ||||
−0.356965 | + | 0.934118i | \(0.616188\pi\) | |||||||
\(570\) | −7104.00 | −0.522024 | ||||||||
\(571\) | 5604.00 | 0.410718 | 0.205359 | − | 0.978687i | \(-0.434164\pi\) | ||||
0.205359 | + | 0.978687i | \(0.434164\pi\) | |||||||
\(572\) | 640.000 | 0.0467828 | ||||||||
\(573\) | −9324.00 | −0.679783 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5124.00 | −0.371627 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −21568.0 | −1.55613 | −0.778066 | − | 0.628183i | \(-0.783799\pi\) | ||||
−0.778066 | + | 0.628183i | \(0.783799\pi\) | |||||||
\(578\) | −4286.00 | −0.308433 | ||||||||
\(579\) | 150.000 | 0.0107665 | ||||||||
\(580\) | 1856.00 | 0.132873 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4992.00 | 0.355541 | ||||||||
\(583\) | 19120.0 | 1.35827 | ||||||||
\(584\) | −3520.00 | −0.249415 | ||||||||
\(585\) | 288.000 | 0.0203544 | ||||||||
\(586\) | −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 | ||||||||
\(591\) | −486.000 | −0.0338263 | ||||||||
\(592\) | −3552.00 | −0.246598 | ||||||||
\(593\) | 13812.0 | 0.956477 | 0.478238 | − | 0.878230i | \(-0.341275\pi\) | ||||
0.478238 | + | 0.878230i | \(0.341275\pi\) | |||||||
\(594\) | −2160.00 | −0.149202 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12680.0 | −0.871465 | ||||||||
\(597\) | 4632.00 | 0.317546 | ||||||||
\(598\) | −672.000 | −0.0459534 | ||||||||
\(599\) | −21996.0 | −1.50039 | −0.750194 | − | 0.661218i | \(-0.770040\pi\) | ||||
−0.750194 | + | 0.661218i | \(0.770040\pi\) | |||||||
\(600\) | 1464.00 | 0.0996126 | ||||||||
\(601\) | 8368.00 | 0.567950 | 0.283975 | − | 0.958832i | \(-0.408347\pi\) | ||||
0.283975 | + | 0.958832i | \(0.408347\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8172.00 | −0.551890 | ||||||||
\(604\) | −7520.00 | −0.506597 | ||||||||
\(605\) | 2152.00 | 0.144614 | ||||||||
\(606\) | −2784.00 | −0.186621 | ||||||||
\(607\) | 21504.0 | 1.43792 | 0.718962 | − | 0.695049i | \(-0.244617\pi\) | ||||
0.718962 | + | 0.695049i | \(0.244617\pi\) | |||||||
\(608\) | −4736.00 | −0.315905 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11072.0 | −0.734905 | ||||||||
\(611\) | 1952.00 | 0.129246 | ||||||||
\(612\) | −3024.00 | −0.199735 | ||||||||
\(613\) | −10270.0 | −0.676674 | −0.338337 | − | 0.941025i | \(-0.609864\pi\) | ||||
−0.338337 | + | 0.941025i | \(0.609864\pi\) | |||||||
\(614\) | 6008.00 | 0.394891 | ||||||||
\(615\) | 10080.0 | 0.660918 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28358.0 | 1.85032 | 0.925162 | − | 0.379572i | \(-0.123929\pi\) | ||||
0.925162 | + | 0.379572i | \(0.123929\pi\) | |||||||
\(618\) | 3792.00 | 0.246823 | ||||||||
\(619\) | 16292.0 | 1.05788 | 0.528942 | − | 0.848658i | \(-0.322589\pi\) | ||||
0.528942 | + | 0.848658i | \(0.322589\pi\) | |||||||
\(620\) | −4352.00 | −0.281904 | ||||||||
\(621\) | 2268.00 | 0.146557 | ||||||||
\(622\) | −1376.00 | −0.0887019 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 192.000 | 0.0123176 | ||||||||
\(625\) | −4279.00 | −0.273856 | ||||||||
\(626\) | −11184.0 | −0.714062 | ||||||||
\(627\) | 17760.0 | 1.13121 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | −3612.00 | −0.226800 | ||||||||
\(634\) | 5844.00 | 0.366080 | ||||||||
\(635\) | −1472.00 | −0.0919914 | ||||||||
\(636\) | 5736.00 | 0.357621 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4640.00 | −0.287930 | ||||||||
\(639\) | −4716.00 | −0.291959 | ||||||||
\(640\) | −1024.00 | −0.0632456 | ||||||||
\(641\) | 15518.0 | 0.956200 | 0.478100 | − | 0.878305i | \(-0.341326\pi\) | ||||
0.478100 | + | 0.878305i | \(0.341326\pi\) | |||||||
\(642\) | 960.000 | 0.0590159 | ||||||||
\(643\) | −10452.0 | −0.641037 | −0.320518 | − | 0.947242i | \(-0.603857\pi\) | ||||
−0.320518 | + | 0.947242i | \(0.603857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3936.00 | −0.240279 | ||||||||
\(646\) | 24864.0 | 1.51434 | ||||||||
\(647\) | 72.0000 | 0.00437498 | 0.00218749 | − | 0.999998i | \(-0.499304\pi\) | ||||
0.00218749 | + | 0.999998i | \(0.499304\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 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 | \(-0.383312\pi\) | ||||
0.358430 | + | 0.933557i | \(0.383312\pi\) | |||||||
\(654\) | 13188.0 | 0.788519 | ||||||||
\(655\) | −11616.0 | −0.692938 | ||||||||
\(656\) | 6720.00 | 0.399957 | ||||||||
\(657\) | 3960.00 | 0.235151 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6016.00 | −0.355615 | −0.177807 | − | 0.984065i | \(-0.556900\pi\) | ||||
−0.177807 | + | 0.984065i | \(0.556900\pi\) | |||||||
\(660\) | 3840.00 | 0.226472 | ||||||||
\(661\) | 26068.0 | 1.53393 | 0.766965 | − | 0.641689i | \(-0.221766\pi\) | ||||
0.766965 | + | 0.641689i | \(0.221766\pi\) | |||||||
\(662\) | 14984.0 | 0.879713 | ||||||||
\(663\) | −1008.00 | −0.0590460 | ||||||||
\(664\) | 5472.00 | 0.319811 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3996.00 | 0.232495 | ||||||||
\(667\) | 4872.00 | 0.282825 | ||||||||
\(668\) | −7136.00 | −0.413324 | ||||||||
\(669\) | 6000.00 | 0.346746 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | −1647.00 | −0.0939156 | ||||||||
\(676\) | −8724.00 | −0.496359 | ||||||||
\(677\) | −10056.0 | −0.570877 | −0.285438 | − | 0.958397i | \(-0.592139\pi\) | ||||
−0.285438 | + | 0.958397i | \(0.592139\pi\) | |||||||
\(678\) | −4620.00 | −0.261696 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5376.00 | 0.303177 | ||||||||
\(681\) | 1164.00 | 0.0654986 | ||||||||
\(682\) | 10880.0 | 0.610875 | ||||||||
\(683\) | 6152.00 | 0.344656 | 0.172328 | − | 0.985040i | \(-0.444871\pi\) | ||||
0.172328 | + | 0.985040i | \(0.444871\pi\) | |||||||
\(684\) | 5328.00 | 0.297838 | ||||||||
\(685\) | 5168.00 | 0.288262 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12540.0 | 0.696406 | ||||||||
\(688\) | −2624.00 | −0.145406 | ||||||||
\(689\) | 1912.00 | 0.105720 | ||||||||
\(690\) | −4032.00 | −0.222457 | ||||||||
\(691\) | −14716.0 | −0.810164 | −0.405082 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405082 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(692\) | −1376.00 | −0.0755891 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7968.00 | 0.435823 | ||||||||
\(695\) | −24096.0 | −1.31513 | ||||||||
\(696\) | −1392.00 | −0.0758098 | ||||||||
\(697\) | −35280.0 | −1.91725 | ||||||||
\(698\) | 360.000 | 0.0195218 | ||||||||
\(699\) | −3966.00 | −0.214604 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28202.0 | 1.51951 | 0.759754 | − | 0.650211i | \(-0.225319\pi\) | ||||
0.759754 | + | 0.650211i | \(0.225319\pi\) | |||||||
\(702\) | −216.000 | −0.0116131 | ||||||||
\(703\) | −32856.0 | −1.76271 | ||||||||
\(704\) | 2560.00 | 0.137051 | ||||||||
\(705\) | 11712.0 | 0.625673 | ||||||||
\(706\) | 20856.0 | 1.11179 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6576.00 | 0.349070 | ||||||||
\(709\) | 22114.0 | 1.17138 | 0.585690 | − | 0.810535i | \(-0.300824\pi\) | ||||
0.585690 | + | 0.810535i | \(0.300824\pi\) | |||||||
\(710\) | 8384.00 | 0.443163 | ||||||||
\(711\) | 10944.0 | 0.577260 | ||||||||
\(712\) | −4832.00 | −0.254335 | ||||||||
\(713\) | −11424.0 | −0.600045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1280.00 | 0.0669501 | ||||||||
\(716\) | 5568.00 | 0.290623 | ||||||||
\(717\) | 7236.00 | 0.376895 | ||||||||
\(718\) | −17368.0 | −0.902741 | ||||||||
\(719\) | −9288.00 | −0.481758 | −0.240879 | − | 0.970555i | \(-0.577436\pi\) | ||||
−0.240879 | + | 0.970555i | \(0.577436\pi\) | |||||||
\(720\) | 1152.00 | 0.0596285 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −30090.0 | −1.55102 | ||||||||
\(723\) | −13008.0 | −0.669119 | ||||||||
\(724\) | 16208.0 | 0.831997 | ||||||||
\(725\) | −3538.00 | −0.181239 | ||||||||
\(726\) | −1614.00 | −0.0825085 | ||||||||
\(727\) | 23848.0 | 1.21661 | 0.608304 | − | 0.793704i | \(-0.291850\pi\) | ||||
0.608304 | + | 0.793704i | \(0.291850\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −7040.00 | −0.356934 | ||||||||
\(731\) | 13776.0 | 0.697023 | ||||||||
\(732\) | 8304.00 | 0.419296 | ||||||||
\(733\) | −34756.0 | −1.75135 | −0.875677 | − | 0.482898i | \(-0.839584\pi\) | ||||
−0.875677 | + | 0.482898i | \(0.839584\pi\) | |||||||
\(734\) | −11296.0 | −0.568042 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2688.00 | −0.134621 | ||||||||
\(737\) | −36320.0 | −1.81528 | ||||||||
\(738\) | −7560.00 | −0.377083 | ||||||||
\(739\) | 26044.0 | 1.29641 | 0.648203 | − | 0.761468i | \(-0.275521\pi\) | ||||
0.648203 | + | 0.761468i | \(0.275521\pi\) | |||||||
\(740\) | −7104.00 | −0.352903 | ||||||||
\(741\) | 1776.00 | 0.0880472 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36204.0 | 1.78761 | 0.893806 | − | 0.448454i | \(-0.148025\pi\) | ||||
0.893806 | + | 0.448454i | \(0.148025\pi\) | |||||||
\(744\) | 3264.00 | 0.160839 | ||||||||
\(745\) | −25360.0 | −1.24714 | ||||||||
\(746\) | 5092.00 | 0.249908 | ||||||||
\(747\) | −6156.00 | −0.301521 | ||||||||
\(748\) | −13440.0 | −0.656972 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8928.00 | 0.434673 | ||||||||
\(751\) | −11424.0 | −0.555083 | −0.277542 | − | 0.960714i | \(-0.589520\pi\) | ||||
−0.277542 | + | 0.960714i | \(0.589520\pi\) | |||||||
\(752\) | 7808.00 | 0.378628 | ||||||||
\(753\) | 2292.00 | 0.110923 | ||||||||
\(754\) | −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 | ||||||||
\(759\) | 10080.0 | 0.482056 | ||||||||
\(760\) | −9472.00 | −0.452086 | ||||||||
\(761\) | −38524.0 | −1.83508 | −0.917539 | − | 0.397646i | \(-0.869827\pi\) | ||||
−0.917539 | + | 0.397646i | \(0.869827\pi\) | |||||||
\(762\) | 1104.00 | 0.0524852 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12432.0 | −0.588709 | ||||||||
\(765\) | −6048.00 | −0.285838 | ||||||||
\(766\) | 21744.0 | 1.02564 | ||||||||
\(767\) | 2192.00 | 0.103192 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −18440.0 | −0.864712 | −0.432356 | − | 0.901703i | \(-0.642318\pi\) | ||||
−0.432356 | + | 0.901703i | \(0.642318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12900.0 | 0.602571 | ||||||||
\(772\) | 200.000 | 0.00932404 | ||||||||
\(773\) | −13968.0 | −0.649928 | −0.324964 | − | 0.945726i | \(-0.605352\pi\) | ||||
−0.324964 | + | 0.945726i | \(0.605352\pi\) | |||||||
\(774\) | 2952.00 | 0.137090 | ||||||||
\(775\) | 8296.00 | 0.384518 | ||||||||
\(776\) | 6656.00 | 0.307908 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20868.0 | −0.961638 | ||||||||
\(779\) | 62160.0 | 2.85894 | ||||||||
\(780\) | 384.000 | 0.0176274 | ||||||||
\(781\) | −20960.0 | −0.960317 | ||||||||
\(782\) | 14112.0 | 0.645325 | ||||||||
\(783\) | 1566.00 | 0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4832.00 | 0.219696 | ||||||||
\(786\) | 8712.00 | 0.395352 | ||||||||
\(787\) | 10916.0 | 0.494426 | 0.247213 | − | 0.968961i | \(-0.420485\pi\) | ||||
0.247213 | + | 0.968961i | \(0.420485\pi\) | |||||||
\(788\) | −648.000 | −0.0292945 | ||||||||
\(789\) | −11580.0 | −0.522508 | ||||||||
\(790\) | −19456.0 | −0.876220 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2880.00 | −0.129213 | ||||||||
\(793\) | 2768.00 | 0.123953 | ||||||||
\(794\) | 6088.00 | 0.272110 | ||||||||
\(795\) | 11472.0 | 0.511786 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 5436.00 | 0.239790 | ||||||||
\(802\) | −17820.0 | −0.784596 | ||||||||
\(803\) | 17600.0 | 0.773463 | ||||||||
\(804\) | −10896.0 | −0.477951 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1088.00 | 0.0475474 | ||||||||
\(807\) | −8400.00 | −0.366411 | ||||||||
\(808\) | −3712.00 | −0.161618 | ||||||||
\(809\) | 3402.00 | 0.147847 | 0.0739233 | − | 0.997264i | \(-0.476448\pi\) | ||||
0.0739233 | + | 0.997264i | \(0.476448\pi\) | |||||||
\(810\) | −1296.00 | −0.0562183 | ||||||||
\(811\) | 292.000 | 0.0126430 | 0.00632152 | − | 0.999980i | \(-0.497988\pi\) | ||||
0.00632152 | + | 0.999980i | \(0.497988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14640.0 | −0.631546 | ||||||||
\(814\) | 17760.0 | 0.764727 | ||||||||
\(815\) | 8928.00 | 0.383723 | ||||||||
\(816\) | −4032.00 | −0.172976 | ||||||||
\(817\) | −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 | \(-0.453080\pi\) | ||||
0.146870 | + | 0.989156i | \(0.453080\pi\) | |||||||
\(822\) | −3876.00 | −0.164466 | ||||||||
\(823\) | 568.000 | 0.0240574 | 0.0120287 | − | 0.999928i | \(-0.496171\pi\) | ||||
0.0120287 | + | 0.999928i | \(0.496171\pi\) | |||||||
\(824\) | 5056.00 | 0.213755 | ||||||||
\(825\) | −7320.00 | −0.308909 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12144.0 | −0.510627 | −0.255313 | − | 0.966858i | \(-0.582179\pi\) | ||||
−0.255313 | + | 0.966858i | \(0.582179\pi\) | |||||||
\(828\) | 3024.00 | 0.126922 | ||||||||
\(829\) | 14828.0 | 0.621228 | 0.310614 | − | 0.950536i | \(-0.399465\pi\) | ||||
0.310614 | + | 0.950536i | \(0.399465\pi\) | |||||||
\(830\) | 10944.0 | 0.457677 | ||||||||
\(831\) | −20022.0 | −0.835807 | ||||||||
\(832\) | 256.000 | 0.0106673 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18072.0 | 0.750338 | ||||||||
\(835\) | −14272.0 | −0.591501 | ||||||||
\(836\) | 23680.0 | 0.979653 | ||||||||
\(837\) | −3672.00 | −0.151640 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | −28206.0 | −1.15239 | ||||||||
\(844\) | −4816.00 | −0.196414 | ||||||||
\(845\) | −17448.0 | −0.710331 | ||||||||
\(846\) | −8784.00 | −0.356974 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7648.00 | 0.309709 | ||||||||
\(849\) | −27300.0 | −1.10357 | ||||||||
\(850\) | −10248.0 | −0.413534 | ||||||||
\(851\) | −18648.0 | −0.751169 | ||||||||
\(852\) | −6288.00 | −0.252844 | ||||||||
\(853\) | −41780.0 | −1.67705 | −0.838523 | − | 0.544866i | \(-0.816580\pi\) | ||||
−0.838523 | + | 0.544866i | \(0.816580\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10656.0 | 0.426231 | ||||||||
\(856\) | 1280.00 | 0.0511092 | ||||||||
\(857\) | −21420.0 | −0.853784 | −0.426892 | − | 0.904303i | \(-0.640392\pi\) | ||||
−0.426892 | + | 0.904303i | \(0.640392\pi\) | |||||||
\(858\) | −960.000 | −0.0381980 | ||||||||
\(859\) | −18132.0 | −0.720205 | −0.360102 | − | 0.932913i | \(-0.617258\pi\) | ||||
−0.360102 | + | 0.932913i | \(0.617258\pi\) | |||||||
\(860\) | −5248.00 | −0.208088 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13400.0 | 0.529473 | ||||||||
\(863\) | 24036.0 | 0.948082 | 0.474041 | − | 0.880503i | \(-0.342795\pi\) | ||||
0.474041 | + | 0.880503i | \(0.342795\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −2752.00 | −0.108174 | ||||||||
\(866\) | 10096.0 | 0.396162 | ||||||||
\(867\) | 6429.00 | 0.251834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48640.0 | 1.89873 | ||||||||
\(870\) | −2784.00 | −0.108490 | ||||||||
\(871\) | −3632.00 | −0.141292 | ||||||||
\(872\) | 17584.0 | 0.682878 | ||||||||
\(873\) | −7488.00 | −0.290298 | ||||||||
\(874\) | −24864.0 | −0.962285 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5280.00 | 0.203647 | ||||||||
\(877\) | −4374.00 | −0.168414 | −0.0842072 | − | 0.996448i | \(-0.526836\pi\) | ||||
−0.0842072 | + | 0.996448i | \(0.526836\pi\) | |||||||
\(878\) | 2688.00 | 0.103321 | ||||||||
\(879\) | 17856.0 | 0.685174 | ||||||||
\(880\) | 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 | ||||||||
\(885\) | 13152.0 | 0.499548 | ||||||||
\(886\) | 8784.00 | 0.333075 | ||||||||
\(887\) | −1800.00 | −0.0681376 | −0.0340688 | − | 0.999419i | \(-0.510847\pi\) | ||||
−0.0340688 | + | 0.999419i | \(0.510847\pi\) | |||||||
\(888\) | 5328.00 | 0.201347 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9664.00 | −0.363975 | ||||||||
\(891\) | 3240.00 | 0.121823 | ||||||||
\(892\) | 8000.00 | 0.300291 | ||||||||
\(893\) | 72224.0 | 2.70648 | ||||||||
\(894\) | 19020.0 | 0.711548 | ||||||||
\(895\) | 11136.0 | 0.415906 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1008.00 | 0.0375208 | ||||||||
\(898\) | −7332.00 | −0.272463 | ||||||||
\(899\) | −7888.00 | −0.292636 | ||||||||
\(900\) | −2196.00 | −0.0813333 | ||||||||
\(901\) | −40152.0 | −1.48464 | ||||||||
\(902\) | −33600.0 | −1.24031 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6160.00 | −0.226636 | ||||||||
\(905\) | 32416.0 | 1.19066 | ||||||||
\(906\) | 11280.0 | 0.413635 | ||||||||
\(907\) | −41996.0 | −1.53744 | −0.768718 | − | 0.639588i | \(-0.779105\pi\) | ||||
−0.768718 | + | 0.639588i | \(0.779105\pi\) | |||||||
\(908\) | 1552.00 | 0.0567235 | ||||||||
\(909\) | 4176.00 | 0.152375 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41308.0 | −1.50230 | −0.751150 | − | 0.660132i | \(-0.770500\pi\) | ||||
−0.751150 | + | 0.660132i | \(0.770500\pi\) | |||||||
\(912\) | 7104.00 | 0.257935 | ||||||||
\(913\) | −27360.0 | −0.991768 | ||||||||
\(914\) | −52.0000 | −0.00188185 | ||||||||
\(915\) | 16608.0 | 0.600048 | ||||||||
\(916\) | 16720.0 | 0.603105 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4536.00 | 0.163083 | ||||||||
\(919\) | 3936.00 | 0.141280 | 0.0706402 | − | 0.997502i | \(-0.477496\pi\) | ||||
0.0706402 | + | 0.997502i | \(0.477496\pi\) | |||||||
\(920\) | −5376.00 | −0.192654 | ||||||||
\(921\) | −9012.00 | −0.322427 | ||||||||
\(922\) | −15312.0 | −0.546935 | ||||||||
\(923\) | −2096.00 | −0.0747461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13542.0 | 0.481360 | ||||||||
\(926\) | −25216.0 | −0.894870 | ||||||||
\(927\) | −5688.00 | −0.201530 | ||||||||
\(928\) | −1856.00 | −0.0656532 | ||||||||
\(929\) | −7212.00 | −0.254702 | −0.127351 | − | 0.991858i | \(-0.540647\pi\) | ||||
−0.127351 | + | 0.991858i | \(0.540647\pi\) | |||||||
\(930\) | 6528.00 | 0.230174 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5288.00 | −0.185852 | ||||||||
\(933\) | 2064.00 | 0.0724248 | ||||||||
\(934\) | 6136.00 | 0.214964 | ||||||||
\(935\) | −26880.0 | −0.940182 | ||||||||
\(936\) | −288.000 | −0.0100572 | ||||||||
\(937\) | −38976.0 | −1.35890 | −0.679451 | − | 0.733721i | \(-0.737782\pi\) | ||||
−0.679451 | + | 0.733721i | \(0.737782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16776.0 | 0.583029 | ||||||||
\(940\) | 15616.0 | 0.541849 | ||||||||
\(941\) | 53544.0 | 1.85493 | 0.927463 | − | 0.373916i | \(-0.121985\pi\) | ||||
0.927463 | + | 0.373916i | \(0.121985\pi\) | |||||||
\(942\) | −3624.00 | −0.125346 | ||||||||
\(943\) | 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 | \(-0.619624\pi\) | ||||
−0.367026 | + | 0.930211i | \(0.619624\pi\) | |||||||
\(948\) | 14592.0 | 0.499922 | ||||||||
\(949\) | 1760.00 | 0.0602023 | ||||||||
\(950\) | 18056.0 | 0.616646 | ||||||||
\(951\) | −8766.00 | −0.298903 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21162.0 | 0.719312 | 0.359656 | − | 0.933085i | \(-0.382894\pi\) | ||||
0.359656 | + | 0.933085i | \(0.382894\pi\) | |||||||
\(954\) | −8604.00 | −0.291997 | ||||||||
\(955\) | −24864.0 | −0.842492 | ||||||||
\(956\) | 9648.00 | 0.326400 | ||||||||
\(957\) | 6960.00 | 0.235094 | ||||||||
\(958\) | −12912.0 | −0.435457 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1536.00 | 0.0516398 | ||||||||
\(961\) | −11295.0 | −0.379141 | ||||||||
\(962\) | 1776.00 | 0.0595224 | ||||||||
\(963\) | −1440.00 | −0.0481862 | ||||||||
\(964\) | −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 | ||||||||
\(969\) | −37296.0 | −1.23645 | ||||||||
\(970\) | 13312.0 | 0.440642 | ||||||||
\(971\) | −8140.00 | −0.269027 | −0.134513 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134513 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23792.0 | −0.782695 | ||||||||
\(975\) | −732.000 | −0.0240439 | ||||||||
\(976\) | 11072.0 | 0.363121 | ||||||||
\(977\) | 32158.0 | 1.05305 | 0.526523 | − | 0.850161i | \(-0.323495\pi\) | ||||
0.526523 | + | 0.850161i | \(0.323495\pi\) | |||||||
\(978\) | −6696.00 | −0.218931 | ||||||||
\(979\) | 24160.0 | 0.788720 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19782.0 | −0.643823 | ||||||||
\(982\) | 528.000 | 0.0171580 | ||||||||
\(983\) | −41416.0 | −1.34381 | −0.671905 | − | 0.740637i | \(-0.734524\pi\) | ||||
−0.671905 | + | 0.740637i | \(0.734524\pi\) | |||||||
\(984\) | −10080.0 | −0.326564 | ||||||||
\(985\) | −1296.00 | −0.0419228 | ||||||||
\(986\) | 9744.00 | 0.314718 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2368.00 | 0.0762511 | ||||||||
\(989\) | −13776.0 | −0.442923 | ||||||||
\(990\) | −5760.00 | −0.184914 | ||||||||
\(991\) | 12296.0 | 0.394143 | 0.197071 | − | 0.980389i | \(-0.436857\pi\) | ||||
0.197071 | + | 0.980389i | \(0.436857\pi\) | |||||||
\(992\) | 4352.00 | 0.139290 | ||||||||
\(993\) | −22476.0 | −0.718282 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12352.0 | 0.393552 | ||||||||
\(996\) | −8208.00 | −0.261125 | ||||||||
\(997\) | 57652.0 | 1.83135 | 0.915676 | − | 0.401918i | \(-0.131656\pi\) | ||||
0.915676 | + | 0.401918i | \(0.131656\pi\) | |||||||
\(998\) | 5256.00 | 0.166709 | ||||||||
\(999\) | −5994.00 | −0.189832 |
(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 | 294.4.a.f.1.1 | yes | 1 | |
3.2 | odd | 2 | 882.4.a.j.1.1 | 1 | |||
4.3 | odd | 2 | 2352.4.a.m.1.1 | 1 | |||
7.2 | even | 3 | 294.4.e.f.67.1 | 2 | |||
7.3 | odd | 6 | 294.4.e.j.79.1 | 2 | |||
7.4 | even | 3 | 294.4.e.f.79.1 | 2 | |||
7.5 | odd | 6 | 294.4.e.j.67.1 | 2 | |||
7.6 | odd | 2 | 294.4.a.b.1.1 | ✓ | 1 | ||
21.2 | odd | 6 | 882.4.g.j.361.1 | 2 | |||
21.5 | even | 6 | 882.4.g.c.361.1 | 2 | |||
21.11 | odd | 6 | 882.4.g.j.667.1 | 2 | |||
21.17 | even | 6 | 882.4.g.c.667.1 | 2 | |||
21.20 | even | 2 | 882.4.a.q.1.1 | 1 | |||
28.27 | even | 2 | 2352.4.a.z.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.b.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
294.4.a.f.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
294.4.e.f.67.1 | 2 | 7.2 | even | 3 | |||
294.4.e.f.79.1 | 2 | 7.4 | even | 3 | |||
294.4.e.j.67.1 | 2 | 7.5 | odd | 6 | |||
294.4.e.j.79.1 | 2 | 7.3 | odd | 6 | |||
882.4.a.j.1.1 | 1 | 3.2 | odd | 2 | |||
882.4.a.q.1.1 | 1 | 21.20 | even | 2 | |||
882.4.g.c.361.1 | 2 | 21.5 | even | 6 | |||
882.4.g.c.667.1 | 2 | 21.17 | even | 6 | |||
882.4.g.j.361.1 | 2 | 21.2 | odd | 6 | |||
882.4.g.j.667.1 | 2 | 21.11 | odd | 6 | |||
2352.4.a.m.1.1 | 1 | 4.3 | odd | 2 | |||
2352.4.a.z.1.1 | 1 | 28.27 | even | 2 |