Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.00000 | −0.384900 | −0.192450 | − | 0.981307i | \(-0.561643\pi\) | ||||
−0.192450 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.0000 | −1.43108 | −0.715542 | − | 0.698570i | \(-0.753820\pi\) | ||||
−0.715542 | + | 0.698570i | \(0.753820\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.00000 | 0.219281 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.0000 | −0.597369 | −0.298685 | − | 0.954352i | \(-0.596548\pi\) | ||||
−0.298685 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 32.0000 | 0.550824 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −54.0000 | −0.770407 | −0.385204 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385204 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −110.000 | −1.32820 | −0.664098 | − | 0.747645i | \(-0.731184\pi\) | ||||
−0.664098 | + | 0.747645i | \(0.731184\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −48.0000 | −0.435161 | −0.217580 | − | 0.976042i | \(-0.569816\pi\) | ||||
−0.217580 | + | 0.976042i | \(0.569816\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 131.000 | 1.04800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 100.000 | 0.712778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −110.000 | −0.704362 | −0.352181 | − | 0.935932i | \(-0.614560\pi\) | ||||
−0.352181 | + | 0.935932i | \(0.614560\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.0000 | 0.0695246 | 0.0347623 | − | 0.999396i | \(-0.488933\pi\) | ||||
0.0347623 | + | 0.999396i | \(0.488933\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −16.0000 | −0.0844013 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −246.000 | −1.09303 | −0.546516 | − | 0.837449i | \(-0.684046\pi\) | ||||
−0.546516 | + | 0.837449i | \(0.684046\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 56.0000 | 0.229928 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −182.000 | −0.693259 | −0.346630 | − | 0.938002i | \(-0.612674\pi\) | ||||
−0.346630 | + | 0.938002i | \(0.612674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −128.000 | −0.453949 | −0.226975 | − | 0.973901i | \(-0.572883\pi\) | ||||
−0.226975 | + | 0.973901i | \(0.572883\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 368.000 | 1.21907 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 324.000 | 1.00554 | 0.502769 | − | 0.864421i | \(-0.332315\pi\) | ||||
0.502769 | + | 0.864421i | \(0.332315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 108.000 | 0.296530 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −162.000 | −0.419857 | −0.209928 | − | 0.977717i | \(-0.567323\pi\) | ||||
−0.209928 | + | 0.977717i | \(0.567323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −128.000 | −0.313809 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 220.000 | 0.511223 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 810.000 | 1.78734 | 0.893670 | − | 0.448725i | \(-0.148122\pi\) | ||||
0.893670 | + | 0.448725i | \(0.148122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 488.000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 448.000 | 0.854886 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −244.000 | −0.444916 | −0.222458 | − | 0.974942i | \(-0.571408\pi\) | ||||
−0.222458 | + | 0.974942i | \(0.571408\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 96.0000 | 0.167493 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 768.000 | 1.28373 | 0.641865 | − | 0.766818i | \(-0.278161\pi\) | ||||
0.641865 | + | 0.766818i | \(0.278161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 702.000 | 1.12552 | 0.562759 | − | 0.826621i | \(-0.309740\pi\) | ||||
0.562759 | + | 0.826621i | \(0.309740\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −262.000 | −0.403375 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −440.000 | −0.626631 | −0.313316 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313316 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1302.00 | −1.72184 | −0.860922 | − | 0.508737i | \(-0.830113\pi\) | ||||
−0.860922 | + | 0.508737i | \(0.830113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 864.000 | 1.10252 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 220.000 | 0.271109 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −730.000 | −0.869436 | −0.434718 | − | 0.900567i | \(-0.643152\pi\) | ||||
−0.434718 | + | 0.900567i | \(0.643152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.0000 | −0.0267600 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1760.00 | 1.90076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −294.000 | −0.307744 | −0.153872 | − | 0.988091i | \(-0.549174\pi\) | ||||
−0.153872 | + | 0.988091i | \(0.549174\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −184.000 | −0.186795 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 688.000 | 0.677808 | 0.338904 | − | 0.940821i | \(-0.389944\pi\) | ||||
0.338904 | + | 0.940821i | \(0.389944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1388.00 | 1.32780 | 0.663901 | − | 0.747820i | \(-0.268899\pi\) | ||||
0.663901 | + | 0.747820i | \(0.268899\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −244.000 | −0.220452 | −0.110226 | − | 0.993907i | \(-0.535157\pi\) | ||||
−0.110226 | + | 0.993907i | \(0.535157\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 90.0000 | 0.0790866 | 0.0395433 | − | 0.999218i | \(-0.487410\pi\) | ||||
0.0395433 | + | 0.999218i | \(0.487410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 492.000 | 0.420708 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1318.00 | 1.09723 | 0.548615 | − | 0.836075i | \(-0.315155\pi\) | ||||
0.548615 | + | 0.836075i | \(0.315155\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 768.000 | 0.622751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 644.000 | 0.508870 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1267.00 | −0.951916 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 364.000 | 0.266836 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −96.0000 | −0.0686920 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1776.00 | 1.24090 | 0.620451 | − | 0.784245i | \(-0.286950\pi\) | ||||
0.620451 | + | 0.784245i | \(0.286950\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 256.000 | 0.174725 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1118.00 | −0.745650 | −0.372825 | − | 0.927902i | \(-0.621611\pi\) | ||||
−0.372825 | + | 0.927902i | \(0.621611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1600.00 | −1.02004 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2274.00 | 1.41811 | 0.709054 | − | 0.705154i | \(-0.249122\pi\) | ||||
0.709054 | + | 0.705154i | \(0.249122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −210.000 | −0.128144 | −0.0640718 | − | 0.997945i | \(-0.520409\pi\) | ||||
−0.0640718 | + | 0.997945i | \(0.520409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −648.000 | −0.387032 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −224.000 | −0.130992 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1760.00 | 1.00800 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2010.00 | −1.10514 | −0.552569 | − | 0.833467i | \(-0.686352\pi\) | ||||
−0.552569 | + | 0.833467i | \(0.686352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1112.00 | −0.599293 | −0.299647 | − | 0.954050i | \(-0.596869\pi\) | ||||
−0.299647 | + | 0.954050i | \(0.596869\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1242.00 | 0.656273 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −192.000 | −0.0994956 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −124.000 | −0.0630336 | −0.0315168 | − | 0.999503i | \(-0.510034\pi\) | ||||
−0.0315168 | + | 0.999503i | \(0.510034\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 324.000 | 0.161603 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2008.00 | −0.964900 | −0.482450 | − | 0.875924i | \(-0.660253\pi\) | ||||
−0.482450 | + | 0.875924i | \(0.660253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 256.000 | 0.120785 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2884.00 | 1.33635 | 0.668176 | − | 0.744004i | \(-0.267076\pi\) | ||||
0.668176 | + | 0.744004i | \(0.267076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2530.00 | 1.13143 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2228.00 | −0.979143 | −0.489571 | − | 0.871963i | \(-0.662847\pi\) | ||||
−0.489571 | + | 0.871963i | \(0.662847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1620.00 | −0.687947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 820.000 | 0.342400 | 0.171200 | − | 0.985236i | \(-0.445236\pi\) | ||||
0.171200 | + | 0.985236i | \(0.445236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3892.00 | −1.59829 | −0.799144 | − | 0.601140i | \(-0.794713\pi\) | ||||
−0.799144 | + | 0.601140i | \(0.794713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −976.000 | −0.394251 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3936.00 | 1.56422 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −432.000 | −0.168936 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5048.00 | 1.91236 | 0.956179 | − | 0.292782i | \(-0.0945810\pi\) | ||||
0.956179 | + | 0.292782i | \(0.0945810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2962.00 | −1.10471 | −0.552356 | − | 0.833608i | \(-0.686271\pi\) | ||||
−0.552356 | + | 0.833608i | \(0.686271\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −896.000 | −0.329046 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3334.00 | 1.20577 | 0.602887 | − | 0.797826i | \(-0.294017\pi\) | ||||
0.602887 | + | 0.797826i | \(0.294017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1860.00 | 0.662572 | 0.331286 | − | 0.943530i | \(-0.392517\pi\) | ||||
0.331286 | + | 0.943530i | \(0.392517\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 488.000 | 0.171248 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2912.00 | 0.992112 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1104.00 | 0.370692 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −880.000 | −0.291248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4268.00 | 1.39252 | 0.696259 | − | 0.717791i | \(-0.254847\pi\) | ||||
0.696259 | + | 0.717791i | \(0.254847\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1536.00 | −0.494108 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2048.00 | 0.649639 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1404.00 | −0.433212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1512.00 | 0.460218 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5432.00 | −1.63118 | −0.815591 | − | 0.578629i | \(-0.803588\pi\) | ||||
−0.815591 | + | 0.578629i | \(0.803588\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3013.00 | −0.892741 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2046.00 | −0.598228 | −0.299114 | − | 0.954217i | \(-0.596691\pi\) | ||||
−0.299114 | + | 0.954217i | \(0.596691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2980.00 | 0.859930 | 0.429965 | − | 0.902846i | \(-0.358526\pi\) | ||||
0.429965 | + | 0.902846i | \(0.358526\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4458.00 | 1.25345 | 0.626724 | − | 0.779241i | \(-0.284395\pi\) | ||||
0.626724 | + | 0.779241i | \(0.284395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5184.00 | −1.43901 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 880.000 | 0.241190 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4440.00 | −1.20167 | −0.600836 | − | 0.799372i | \(-0.705166\pi\) | ||||
−0.600836 | + | 0.799372i | \(0.705166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3302.00 | −0.882575 | −0.441287 | − | 0.897366i | \(-0.645478\pi\) | ||||
−0.441287 | + | 0.897366i | \(0.645478\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3542.00 | −0.935059 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3080.00 | 0.793424 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2604.00 | 0.662738 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1582.00 | 0.397829 | 0.198914 | − | 0.980017i | \(-0.436258\pi\) | ||||
0.198914 | + | 0.980017i | \(0.436258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −384.000 | −0.0954224 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1728.00 | −0.424359 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2354.00 | −0.571356 | −0.285678 | − | 0.958326i | \(-0.592219\pi\) | ||||
−0.285678 | + | 0.958326i | \(0.592219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2530.00 | 0.600012 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3872.00 | 0.907824 | 0.453912 | − | 0.891046i | \(-0.350028\pi\) | ||||
0.453912 | + | 0.891046i | \(0.350028\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2592.00 | 0.600850 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1460.00 | 0.334646 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −180.000 | −0.0407985 | −0.0203992 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0203992 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2032.00 | 0.455480 | 0.227740 | − | 0.973722i | \(-0.426866\pi\) | ||||
0.227740 | + | 0.973722i | \(0.426866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1048.00 | 0.229806 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5426.00 | −1.17696 | −0.588478 | − | 0.808513i | \(-0.700273\pi\) | ||||
−0.588478 | + | 0.808513i | \(0.700273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −276.000 | −0.0592247 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 842.000 | 0.178753 | 0.0893764 | − | 0.995998i | \(-0.471513\pi\) | ||||
0.0893764 | + | 0.995998i | \(0.471513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3782.00 | −0.794405 | −0.397202 | − | 0.917731i | \(-0.630019\pi\) | ||||
−0.397202 | + | 0.917731i | \(0.630019\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3520.00 | −0.731603 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 588.000 | 0.118451 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4312.00 | 0.859760 | 0.429880 | − | 0.902886i | \(-0.358556\pi\) | ||||
0.429880 | + | 0.902886i | \(0.358556\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12960.0 | −2.55783 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 800.000 | 0.156299 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1344.00 | 0.259952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1376.00 | −0.260888 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7808.00 | −1.46585 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2674.00 | 0.497112 | 0.248556 | − | 0.968618i | \(-0.420044\pi\) | ||||
0.248556 | + | 0.968618i | \(0.420044\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2776.00 | −0.511072 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3768.00 | −0.687021 | −0.343511 | − | 0.939149i | \(-0.611616\pi\) | ||||
−0.343511 | + | 0.939149i | \(0.611616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2438.00 | −0.440268 | −0.220134 | − | 0.975470i | \(-0.570649\pi\) | ||||
−0.220134 | + | 0.975470i | \(0.570649\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3186.00 | −0.564491 | −0.282245 | − | 0.959342i | \(-0.591079\pi\) | ||||
−0.282245 | + | 0.959342i | \(0.591079\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −880.000 | −0.154453 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 488.000 | 0.0848520 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5940.00 | 1.02325 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3668.00 | −0.626043 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −180.000 | −0.0304404 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8672.00 | −1.44005 | −0.720025 | − | 0.693949i | \(-0.755869\pi\) | ||||
−0.720025 | + | 0.693949i | \(0.755869\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5658.00 | 0.931101 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3904.00 | 0.636711 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 814.000 | 0.131577 | 0.0657884 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657884 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2636.00 | −0.422324 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 96.0000 | 0.0152454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1536.00 | −0.239697 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9344.00 | −1.44557 | −0.722784 | − | 0.691074i | \(-0.757138\pi\) | ||||
−0.722784 | + | 0.691074i | \(0.757138\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5180.00 | 0.794496 | 0.397248 | − | 0.917711i | \(-0.369965\pi\) | ||||
0.397248 | + | 0.917711i | \(0.369965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2800.00 | −0.425792 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12178.0 | −1.83617 | −0.918087 | − | 0.396379i | \(-0.870267\pi\) | ||||
−0.918087 | + | 0.396379i | \(0.870267\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12288.0 | −1.83712 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −440.000 | −0.0646861 | −0.0323431 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323431 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5241.00 | 0.764106 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2534.00 | 0.366393 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11232.0 | −1.61071 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9816.00 | −1.39616 | −0.698080 | − | 0.716019i | \(-0.745962\pi\) | ||||
−0.698080 | + | 0.716019i | \(0.745962\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4186.00 | 0.590554 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −442.000 | −0.0613563 | −0.0306781 | − | 0.999529i | \(-0.509767\pi\) | ||||
−0.0306781 | + | 0.999529i | \(0.509767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 192.000 | 0.0264396 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3080.00 | 0.420764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3960.00 | 0.536706 | 0.268353 | − | 0.963321i | \(-0.413521\pi\) | ||||
0.268353 | + | 0.963321i | \(0.413521\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3552.00 | −0.477623 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6708.00 | 0.894942 | 0.447471 | − | 0.894298i | \(-0.352325\pi\) | ||||
0.447471 | + | 0.894298i | \(0.352325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2944.00 | 0.386697 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13350.0 | −1.74003 | −0.870015 | − | 0.493025i | \(-0.835891\pi\) | ||||
−0.870015 | + | 0.493025i | \(0.835891\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2592.00 | 0.335251 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2236.00 | 0.287001 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7040.00 | 0.896762 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1356.00 | 0.171425 | 0.0857125 | − | 0.996320i | \(-0.472683\pi\) | ||||
0.0857125 | + | 0.996320i | \(0.472683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6222.00 | 0.774843 | 0.387421 | − | 0.921903i | \(-0.373366\pi\) | ||||
0.387421 | + | 0.921903i | \(0.373366\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −336.000 | −0.0415319 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6736.00 | −0.826456 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1968.00 | −0.239681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5150.00 | −0.622619 | −0.311309 | − | 0.950309i | \(-0.600768\pi\) | ||||
−0.311309 | + | 0.950309i | \(0.600768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4548.00 | −0.545830 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20832.0 | 2.46410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 420.000 | 0.0493225 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2310.00 | 0.269334 | 0.134667 | − | 0.990891i | \(-0.457004\pi\) | ||||
0.134667 | + | 0.990891i | \(0.457004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1262.00 | 0.146095 | 0.0730476 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730476 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7452.00 | −0.856569 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7074.00 | −0.807387 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 448.000 | 0.0504188 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4488.00 | 0.501576 | 0.250788 | − | 0.968042i | \(-0.419310\pi\) | ||||
0.250788 | + | 0.968042i | \(0.419310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17038.0 | −1.89098 | −0.945490 | − | 0.325652i | \(-0.894416\pi\) | ||||
−0.945490 | + | 0.325652i | \(0.894416\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3520.00 | −0.387979 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5280.00 | 0.577979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16200.0 | 1.76124 | 0.880619 | − | 0.473824i | \(-0.157127\pi\) | ||||
0.880619 | + | 0.473824i | \(0.157127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8772.00 | 0.940791 | 0.470395 | − | 0.882456i | \(-0.344111\pi\) | ||||
0.470395 | + | 0.882456i | \(0.344111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11680.0 | 1.24424 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4020.00 | 0.425368 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2130.00 | 0.223877 | 0.111939 | − | 0.993715i | \(-0.464294\pi\) | ||||
0.111939 | + | 0.993715i | \(0.464294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1456.00 | −0.152019 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2224.00 | 0.230668 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10534.0 | 1.07825 | 0.539124 | − | 0.842226i | \(-0.318755\pi\) | ||||
0.539124 | + | 0.842226i | \(0.318755\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5400.00 | −0.549129 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9268.00 | 0.936342 | 0.468171 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468171 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9392.00 | 0.942728 | 0.471364 | − | 0.881939i | \(-0.343762\pi\) | ||||
0.471364 | + | 0.881939i | \(0.343762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 384.000 | 0.0382959 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10806.0 | −1.07075 | −0.535377 | − | 0.844613i | \(-0.679830\pi\) | ||||
−0.535377 | + | 0.844613i | \(0.679830\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 248.000 | 0.0242616 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1024.00 | −0.0995424 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14410.0 | −1.39195 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3726.00 | 0.357656 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4940.00 | 0.471220 | 0.235610 | − | 0.971848i | \(-0.424291\pi\) | ||||
0.235610 | + | 0.971848i | \(0.424291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6888.00 | 0.652943 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4704.00 | 0.440407 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5216.00 | 0.485338 | 0.242669 | − | 0.970109i | \(-0.421977\pi\) | ||||
0.242669 | + | 0.970109i | \(0.421977\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4016.00 | 0.371390 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4412.00 | −0.405521 | −0.202760 | − | 0.979228i | \(-0.564991\pi\) | ||||
−0.202760 | + | 0.979228i | \(0.564991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5940.00 | 0.542645 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2944.00 | 0.267319 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19060.0 | −1.70991 | −0.854953 | − | 0.518706i | \(-0.826414\pi\) | ||||
−0.854953 | + | 0.518706i | \(0.826414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5768.00 | −0.514362 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12768.0 | 1.13180 | 0.565902 | − | 0.824473i | \(-0.308528\pi\) | ||||
0.565902 | + | 0.824473i | \(0.308528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11008.0 | −0.969999 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2826.00 | 0.247548 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5500.00 | 0.478945 | 0.239473 | − | 0.970903i | \(-0.423025\pi\) | ||||
0.239473 | + | 0.970903i | \(0.423025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11000.0 | −0.946709 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22208.0 | −1.90020 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2592.00 | 0.220495 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4456.00 | 0.376872 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7338.00 | 0.617051 | 0.308526 | − | 0.951216i | \(-0.400164\pi\) | ||||
0.308526 | + | 0.951216i | \(0.400164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17582.0 | −1.46999 | −0.734997 | − | 0.678070i | \(-0.762817\pi\) | ||||
−0.734997 | + | 0.678070i | \(0.762817\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −648.000 | −0.0535623 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18630.0 | −1.52255 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5096.00 | 0.414132 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3904.00 | 0.315485 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1640.00 | −0.131790 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1618.00 | −0.128583 | −0.0642914 | − | 0.997931i | \(-0.520479\pi\) | ||||
−0.0642914 | + | 0.997931i | \(0.520479\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7784.00 | 0.615181 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1440.00 | −0.113179 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16144.0 | −1.26192 | −0.630958 | − | 0.775817i | \(-0.717338\pi\) | ||||
−0.630958 | + | 0.775817i | \(0.717338\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11224.0 | −0.872548 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12100.0 | 0.935531 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7872.00 | −0.602068 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4654.00 | 0.354033 | 0.177016 | − | 0.984208i | \(-0.443355\pi\) | ||||
0.177016 | + | 0.984208i | \(0.443355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3584.00 | 0.271175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 864.000 | 0.0650234 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10078.0 | 0.754418 | 0.377209 | − | 0.926128i | \(-0.376884\pi\) | ||||
0.377209 | + | 0.926128i | \(0.376884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21088.0 | −1.57023 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5930.00 | −0.436904 | −0.218452 | − | 0.975848i | \(-0.570101\pi\) | ||||
−0.218452 | + | 0.975848i | \(0.570101\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19048.0 | 1.39603 | 0.698016 | − | 0.716082i | \(-0.254067\pi\) | ||||
0.698016 | + | 0.716082i | \(0.254067\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10096.0 | −0.736067 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6288.00 | −0.456048 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14366.0 | 1.03651 | 0.518253 | − | 0.855227i | \(-0.326582\pi\) | ||||
0.518253 | + | 0.855227i | \(0.326582\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5924.00 | 0.425204 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1296.00 | −0.0920666 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10304.0 | −0.728236 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3626.00 | −0.254959 | −0.127480 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127480 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1320.00 | −0.0923424 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6668.00 | −0.464103 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1062.00 | 0.0735432 | 0.0367716 | − | 0.999324i | \(-0.488293\pi\) | ||||
0.0367716 | + | 0.999324i | \(0.488293\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3720.00 | −0.255024 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10200.0 | 0.695761 | 0.347880 | − | 0.937539i | \(-0.386902\pi\) | ||||
0.347880 | + | 0.937539i | \(0.386902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25158.0 | 1.70751 | 0.853757 | − | 0.520671i | \(-0.174318\pi\) | ||||
0.853757 | + | 0.520671i | \(0.174318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5612.00 | 0.379002 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20272.0 | 1.36227 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25664.0 | 1.71609 | 0.858047 | − | 0.513570i | \(-0.171677\pi\) | ||||
0.858047 | + | 0.513570i | \(0.171677\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9072.00 | −0.600677 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19018.0 | 1.25307 | 0.626533 | − | 0.779395i | \(-0.284473\pi\) | ||||
0.626533 | + | 0.779395i | \(0.284473\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5824.00 | −0.381864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17334.0 | 1.13102 | 0.565511 | − | 0.824741i | \(-0.308679\pi\) | ||||
0.565511 | + | 0.824741i | \(0.308679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18730.0 | 1.21619 | 0.608096 | − | 0.793864i | \(-0.291934\pi\) | ||||
0.608096 | + | 0.793864i | \(0.291934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4800.00 | −0.310173 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14839.0 | −0.949696 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1760.00 | 0.112101 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13284.0 | 0.842079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6928.00 | 0.437083 | 0.218541 | − | 0.975828i | \(-0.429870\pi\) | ||||
0.218541 | + | 0.975828i | \(0.429870\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8536.00 | −0.535980 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28416.0 | −1.77583 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17664.0 | −1.09355 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16302.0 | 1.00451 | 0.502255 | − | 0.864720i | \(-0.332504\pi\) | ||||
0.502255 | + | 0.864720i | \(0.332504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4718.00 | 0.289362 | 0.144681 | − | 0.989478i | \(-0.453784\pi\) | ||||
0.144681 | + | 0.989478i | \(0.453784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4096.00 | −0.250046 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21436.0 | −1.30253 | −0.651264 | − | 0.758851i | \(-0.725761\pi\) | ||||
−0.651264 | + | 0.758851i | \(0.725761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6480.00 | 0.391930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4458.00 | 0.267159 | 0.133580 | − | 0.991038i | \(-0.457353\pi\) | ||||
0.133580 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17888.0 | 1.06709 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16146.0 | −0.958775 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26640.0 | 1.57473 | 0.787365 | − | 0.616487i | \(-0.211445\pi\) | ||||
0.787365 | + | 0.616487i | \(0.211445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7432.00 | −0.437324 | −0.218662 | − | 0.975801i | \(-0.570169\pi\) | ||||
−0.218662 | + | 0.975801i | \(0.570169\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3024.00 | −0.177138 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5280.00 | 0.306510 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10864.0 | 0.627842 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3904.00 | 0.224608 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 58.0000 | 0.00332204 | 0.00166102 | − | 0.999999i | \(-0.499471\pi\) | ||||
0.00166102 | + | 0.999999i | \(0.499471\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13100.0 | 0.746991 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21516.0 | 1.22146 | 0.610729 | − | 0.791840i | \(-0.290876\pi\) | ||||
0.610729 | + | 0.791840i | \(0.290876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4092.00 | 0.230258 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18108.0 | −1.01447 | −0.507235 | − | 0.861808i | \(-0.669332\pi\) | ||||
−0.507235 | + | 0.861808i | \(0.669332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36384.0 | −2.02943 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5960.00 | −0.330987 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4536.00 | 0.250810 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10078.0 | −0.554827 | −0.277413 | − | 0.960751i | \(-0.589477\pi\) | ||||
−0.277413 | + | 0.960751i | \(0.589477\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3360.00 | 0.183384 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9828.00 | 0.534092 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8916.00 | −0.482452 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18762.0 | 1.01089 | 0.505443 | − | 0.862860i | \(-0.331329\pi\) | ||||
0.505443 | + | 0.862860i | \(0.331329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27060.0 | 1.45176 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10368.0 | 0.553874 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6810.00 | 0.360726 | 0.180363 | − | 0.983600i | \(-0.442273\pi\) | ||||
0.180363 | + | 0.983600i | \(0.442273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10120.0 | 0.533797 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −576.000 | −0.0302544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3584.00 | 0.187460 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8880.00 | 0.462524 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4860.00 | 0.252083 | 0.126041 | − | 0.992025i | \(-0.459773\pi\) | ||||
0.126041 | + | 0.992025i | \(0.459773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6604.00 | 0.339703 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14410.0 | −0.738171 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13636.0 | −0.695641 | −0.347821 | − | 0.937561i | \(-0.613078\pi\) | ||||
−0.347821 | + | 0.937561i | \(0.613078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6912.00 | 0.349726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2088.00 | −0.105214 | −0.0526071 | − | 0.998615i | \(-0.516753\pi\) | ||||
−0.0526071 | + | 0.998615i | \(0.516753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1952.00 | −0.0975615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5160.00 | 0.256852 | 0.128426 | − | 0.991719i | \(-0.459008\pi\) | ||||
0.128426 | + | 0.991719i | \(0.459008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6160.00 | −0.305389 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28152.0 | 1.39004 | 0.695018 | − | 0.718992i | \(-0.255396\pi\) | ||||
0.695018 | + | 0.718992i | \(0.255396\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32160.0 | 1.58155 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 29946.0 | 1.46676 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16808.0 | 0.816688 | 0.408344 | − | 0.912828i | \(-0.366106\pi\) | ||||
0.408344 | + | 0.912828i | \(0.366106\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3164.00 | −0.153124 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17792.0 | 0.857639 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21674.0 | 1.04063 | 0.520314 | − | 0.853975i | \(-0.325815\pi\) | ||||
0.520314 | + | 0.853975i | \(0.325815\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 768.000 | 0.0367281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7422.00 | −0.353544 | −0.176772 | − | 0.984252i | \(-0.556566\pi\) | ||||
−0.176772 | + | 0.984252i | \(0.556566\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19872.0 | −0.939181 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22680.0 | −1.06770 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13790.0 | −0.646658 | −0.323329 | − | 0.946287i | \(-0.604802\pi\) | ||||
−0.323329 | + | 0.946287i | \(0.604802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4708.00 | 0.219915 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6232.00 | 0.289973 | 0.144987 | − | 0.989434i | \(-0.453686\pi\) | ||||
0.144987 | + | 0.989434i | \(0.453686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1572.00 | 0.0728618 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20020.0 | 0.920784 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6144.00 | 0.281498 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11000.0 | −0.502054 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1984.00 | 0.0902064 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1766.00 | −0.0799887 | −0.0399943 | − | 0.999200i | \(-0.512734\pi\) | ||||
−0.0399943 | + | 0.999200i | \(0.512734\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7744.00 | −0.349422 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13664.0 | −0.611883 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5184.00 | −0.231267 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1204.00 | −0.0535105 | −0.0267552 | − | 0.999642i | \(-0.508517\pi\) | ||||
−0.0267552 | + | 0.999642i | \(0.508517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17496.0 | −0.774673 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16790.0 | 0.740631 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5616.00 | 0.246805 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 360.000 | 0.0157033 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7050.00 | −0.306384 | −0.153192 | − | 0.988196i | \(-0.548955\pi\) | ||||
−0.153192 | + | 0.988196i | \(0.548955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23282.0 | 1.00807 | 0.504033 | − | 0.863684i | \(-0.331849\pi\) | ||||
0.504033 | + | 0.863684i | \(0.331849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4064.00 | −0.175315 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32128.0 | 1.38085 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14080.0 | 0.602934 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10142.0 | 0.431131 | 0.215565 | − | 0.976489i | \(-0.430841\pi\) | ||||
0.215565 | + | 0.976489i | \(0.430841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9192.00 | 0.389323 | 0.194662 | − | 0.980870i | \(-0.437639\pi\) | ||||
0.194662 | + | 0.980870i | \(0.437639\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2096.00 | −0.0884525 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46716.0 | 1.96430 | 0.982149 | − | 0.188104i | \(-0.0602344\pi\) | ||||
0.982149 | + | 0.188104i | \(0.0602344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11240.0 | −0.470906 | −0.235453 | − | 0.971886i | \(-0.575657\pi\) | ||||
−0.235453 | + | 0.971886i | \(0.575657\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10852.0 | 0.453010 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46144.0 | −1.91243 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1200.00 | 0.0495556 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 700.000 | 0.0288042 | 0.0144021 | − | 0.999896i | \(-0.495416\pi\) | ||||
0.0144021 | + | 0.999896i | \(0.495416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12289.0 | −0.503875 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1684.00 | −0.0688019 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22608.0 | 0.920401 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7564.00 | 0.305767 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11808.0 | 0.475644 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37492.0 | 1.50493 | 0.752463 | − | 0.658635i | \(-0.228866\pi\) | ||||
0.752463 | + | 0.658635i | \(0.228866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −40480.0 | −1.61917 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28894.0 | −1.15169 | −0.575846 | − | 0.817558i | \(-0.695327\pi\) | ||||
−0.575846 | + | 0.817558i | \(0.695327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2770.00 | −0.110025 | −0.0550123 | − | 0.998486i | \(-0.517520\pi\) | ||||
−0.0550123 | + | 0.998486i | \(0.517520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17688.0 | −0.697690 | −0.348845 | − | 0.937180i | \(-0.613426\pi\) | ||||
−0.348845 | + | 0.937180i | \(0.613426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35648.0 | 1.40124 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3994.00 | 0.156451 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3520.00 | −0.137408 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6832.00 | 0.265779 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6762.00 | 0.262152 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33566.0 | −1.29241 | −0.646205 | − | 0.763164i | \(-0.723645\pi\) | ||||
−0.646205 | + | 0.763164i | \(0.723645\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8624.00 | −0.330922 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16758.0 | 0.640853 | 0.320426 | − | 0.947273i | \(-0.396174\pi\) | ||||
0.320426 | + | 0.947273i | \(0.396174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11468.0 | −0.437066 | −0.218533 | − | 0.975830i | \(-0.570127\pi\) | ||||
−0.218533 | + | 0.975830i | \(0.570127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25920.0 | 0.984510 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50356.0 | −1.90619 | −0.953094 | − | 0.302674i | \(-0.902121\pi\) | ||||
−0.953094 | + | 0.302674i | \(0.902121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3368.00 | 0.126636 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35640.0 | −1.33555 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13120.0 | −0.490004 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2688.00 | −0.100055 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1320.00 | −0.0489705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8748.00 | 0.323461 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 62272.0 | 2.28728 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8716.00 | 0.319085 | 0.159542 | − | 0.987191i | \(-0.448998\pi\) | ||||
0.159542 | + | 0.987191i | \(0.448998\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15824.0 | −0.577392 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7632.00 | −0.277563 | −0.138781 | − | 0.990323i | \(-0.544318\pi\) | ||||
−0.138781 | + | 0.990323i | \(0.544318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10416.0 | −0.377568 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15616.0 | 0.564207 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23080.0 | 0.828443 | 0.414221 | − | 0.910176i | \(-0.364054\pi\) | ||||
0.414221 | + | 0.910176i | \(0.364054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5348.00 | −0.191338 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21504.0 | −0.766861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32226.0 | −1.14550 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31924.0 | −1.13109 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45110.0 | −1.59312 | −0.796561 | − | 0.604558i | \(-0.793350\pi\) | ||||
−0.796561 | + | 0.604558i | \(0.793350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7536.00 | 0.264435 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6912.00 | 0.241761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16674.0 | −0.581340 | −0.290670 | − | 0.956823i | \(-0.593878\pi\) | ||||
−0.290670 | + | 0.956823i | \(0.593878\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4876.00 | 0.169459 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43832.0 | −1.51847 | −0.759236 | − | 0.650815i | \(-0.774427\pi\) | ||||
−0.759236 | + | 0.650815i | \(0.774427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8736.00 | 0.301679 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 736.000 | 0.0252553 | 0.0126277 | − | 0.999920i | \(-0.495980\pi\) | ||||
0.0126277 | + | 0.999920i | \(0.495980\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19656.0 | −0.672351 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6372.00 | 0.217273 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38138.0 | 1.29634 | 0.648169 | − | 0.761496i | \(-0.275535\pi\) | ||||
0.648169 | + | 0.761496i | \(0.275535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −80768.0 | −2.73674 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1760.00 | 0.0594490 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29647.0 | −0.995166 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5612.00 | 0.187792 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47392.0 | 1.58094 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26224.0 | −0.872086 | −0.436043 | − | 0.899926i | \(-0.643620\pi\) | ||||
−0.436043 | + | 0.899926i | \(0.643620\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11880.0 | −0.393850 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18762.0 | 0.620084 | 0.310042 | − | 0.950723i | \(-0.399657\pi\) | ||||
0.310042 | + | 0.950723i | \(0.399657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7336.00 | 0.240964 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38394.0 | 1.25725 | 0.628625 | − | 0.777709i | \(-0.283618\pi\) | ||||
0.628625 | + | 0.777709i | \(0.283618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5840.00 | −0.190651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2070.00 | −0.0673700 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5388.00 | 0.174822 | 0.0874112 | − | 0.996172i | \(-0.472141\pi\) | ||||
0.0874112 | + | 0.996172i | \(0.472141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53344.0 | −1.72556 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6144.00 | 0.197541 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25472.0 | −0.816493 | −0.408247 | − | 0.912872i | \(-0.633860\pi\) | ||||
−0.408247 | + | 0.912872i | \(0.633860\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17344.0 | 0.554275 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29760.0 | −0.948196 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17096.0 | 0.543065 | 0.271532 | − | 0.962429i | \(-0.412470\pi\) | ||||
0.271532 | + | 0.962429i | \(0.412470\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24600.0 | −0.779089 |
(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 | 784.4.a.g.1.1 | 1 | ||
4.3 | odd | 2 | 49.4.a.b.1.1 | 1 | |||
7.6 | odd | 2 | 112.4.a.f.1.1 | 1 | |||
12.11 | even | 2 | 441.4.a.i.1.1 | 1 | |||
20.19 | odd | 2 | 1225.4.a.j.1.1 | 1 | |||
21.20 | even | 2 | 1008.4.a.c.1.1 | 1 | |||
28.3 | even | 6 | 49.4.c.c.30.1 | 2 | |||
28.11 | odd | 6 | 49.4.c.b.30.1 | 2 | |||
28.19 | even | 6 | 49.4.c.c.18.1 | 2 | |||
28.23 | odd | 6 | 49.4.c.b.18.1 | 2 | |||
28.27 | even | 2 | 7.4.a.a.1.1 | ✓ | 1 | ||
56.13 | odd | 2 | 448.4.a.e.1.1 | 1 | |||
56.27 | even | 2 | 448.4.a.i.1.1 | 1 | |||
84.11 | even | 6 | 441.4.e.e.226.1 | 2 | |||
84.23 | even | 6 | 441.4.e.e.361.1 | 2 | |||
84.47 | odd | 6 | 441.4.e.h.361.1 | 2 | |||
84.59 | odd | 6 | 441.4.e.h.226.1 | 2 | |||
84.83 | odd | 2 | 63.4.a.b.1.1 | 1 | |||
140.27 | odd | 4 | 175.4.b.b.99.1 | 2 | |||
140.83 | odd | 4 | 175.4.b.b.99.2 | 2 | |||
140.139 | even | 2 | 175.4.a.b.1.1 | 1 | |||
308.307 | odd | 2 | 847.4.a.b.1.1 | 1 | |||
364.363 | even | 2 | 1183.4.a.b.1.1 | 1 | |||
420.419 | odd | 2 | 1575.4.a.e.1.1 | 1 | |||
476.475 | even | 2 | 2023.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.a.a.1.1 | ✓ | 1 | 28.27 | even | 2 | ||
49.4.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
49.4.c.b.18.1 | 2 | 28.23 | odd | 6 | |||
49.4.c.b.30.1 | 2 | 28.11 | odd | 6 | |||
49.4.c.c.18.1 | 2 | 28.19 | even | 6 | |||
49.4.c.c.30.1 | 2 | 28.3 | even | 6 | |||
63.4.a.b.1.1 | 1 | 84.83 | odd | 2 | |||
112.4.a.f.1.1 | 1 | 7.6 | odd | 2 | |||
175.4.a.b.1.1 | 1 | 140.139 | even | 2 | |||
175.4.b.b.99.1 | 2 | 140.27 | odd | 4 | |||
175.4.b.b.99.2 | 2 | 140.83 | odd | 4 | |||
441.4.a.i.1.1 | 1 | 12.11 | even | 2 | |||
441.4.e.e.226.1 | 2 | 84.11 | even | 6 | |||
441.4.e.e.361.1 | 2 | 84.23 | even | 6 | |||
441.4.e.h.226.1 | 2 | 84.59 | odd | 6 | |||
441.4.e.h.361.1 | 2 | 84.47 | odd | 6 | |||
448.4.a.e.1.1 | 1 | 56.13 | odd | 2 | |||
448.4.a.i.1.1 | 1 | 56.27 | even | 2 | |||
784.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
847.4.a.b.1.1 | 1 | 308.307 | odd | 2 | |||
1008.4.a.c.1.1 | 1 | 21.20 | even | 2 | |||
1183.4.a.b.1.1 | 1 | 364.363 | even | 2 | |||
1225.4.a.j.1.1 | 1 | 20.19 | odd | 2 | |||
1575.4.a.e.1.1 | 1 | 420.419 | odd | 2 | |||
2023.4.a.a.1.1 | 1 | 476.475 | even | 2 |