Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(287,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.287");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.s (of order \(6\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 287.10 | ||
Character | \(\chi\) | \(=\) | 864.287 |
Dual form | 864.2.s.a.575.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.68236 | + | 0.971313i | 0.752376 | + | 0.434384i | 0.826552 | − | 0.562861i | \(-0.190299\pi\) |
−0.0741759 | + | 0.997245i | \(0.523633\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61432 | − | 1.50938i | 0.988118 | − | 0.570490i | 0.0834070 | − | 0.996516i | \(-0.473420\pi\) |
0.904711 | + | 0.426025i | \(0.140087\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20445 | + | 3.81822i | 0.664667 | + | 1.15124i | 0.979376 | + | 0.202048i | \(0.0647597\pi\) |
−0.314709 | + | 0.949188i | \(0.601907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.65994 | + | 4.60716i | −0.737736 | + | 1.27780i | 0.215777 | + | 0.976443i | \(0.430772\pi\) |
−0.953513 | + | 0.301353i | \(0.902562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.16396i | 1.00991i | 0.863146 | + | 0.504954i | \(0.168491\pi\) | ||||
−0.863146 | + | 0.504954i | \(0.831509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.66253i | − | 1.06966i | −0.844961 | − | 0.534828i | \(-0.820376\pi\) | ||
0.844961 | − | 0.534828i | \(-0.179624\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.30500 | − | 2.26033i | 0.272112 | − | 0.471312i | −0.697290 | − | 0.716789i | \(-0.745611\pi\) |
0.969402 | + | 0.245477i | \(0.0789445\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.613102 | − | 1.06192i | −0.122620 | − | 0.212385i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.13594 | + | 0.655836i | −0.210939 | + | 0.121786i | −0.601748 | − | 0.798686i | \(-0.705529\pi\) |
0.390809 | + | 0.920472i | \(0.372195\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0648938 | + | 0.0374664i | 0.0116553 | + | 0.00672917i | 0.505816 | − | 0.862641i | \(-0.331191\pi\) |
−0.494161 | + | 0.869370i | \(0.664525\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.86431 | 0.991249 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.43839 | 1.38726 | 0.693632 | − | 0.720330i | \(-0.256010\pi\) | ||||
0.693632 | + | 0.720330i | \(0.256010\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.16220 | − | 4.71245i | −1.27472 | − | 0.735960i | −0.298848 | − | 0.954301i | \(-0.596602\pi\) |
−0.975873 | + | 0.218340i | \(0.929936\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.06694 | − | 2.92540i | 0.772702 | − | 0.446119i | −0.0611359 | − | 0.998129i | \(-0.519472\pi\) |
0.833838 | + | 0.552010i | \(0.186139\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.40374 | + | 4.16340i | 0.350622 | + | 0.607294i | 0.986358 | − | 0.164611i | \(-0.0526370\pi\) |
−0.635737 | + | 0.771906i | \(0.719304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.05643 | − | 1.82979i | 0.150919 | − | 0.261399i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.96419i | 1.23133i | 0.788009 | + | 0.615663i | \(0.211112\pi\) | ||||
−0.788009 | + | 0.615663i | \(0.788888\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.56484i | 1.15488i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.74923 | + | 3.02976i | −0.227731 | + | 0.394441i | −0.957135 | − | 0.289642i | \(-0.906464\pi\) |
0.729405 | + | 0.684083i | \(0.239797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.32247 | + | 10.9508i | 0.809509 | + | 1.40211i | 0.913204 | + | 0.407502i | \(0.133600\pi\) |
−0.103695 | + | 0.994609i | \(0.533067\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.94999 | + | 5.16728i | −1.11011 | + | 0.640922i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.38773 | − | 1.37856i | −0.291708 | − | 0.168418i | 0.347004 | − | 0.937864i | \(-0.387199\pi\) |
−0.638712 | + | 0.769446i | \(0.720532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.910434 | 0.108049 | 0.0540243 | − | 0.998540i | \(-0.482795\pi\) | ||||
0.0540243 | + | 0.998540i | \(0.482795\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.86281 | 0.803232 | 0.401616 | − | 0.915808i | \(-0.368449\pi\) | ||||
0.401616 | + | 0.915808i | \(0.368449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.5263 | + | 6.65469i | 1.31354 | + | 0.758372i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8815 | − | 6.28242i | 1.22426 | − | 0.706828i | 0.258438 | − | 0.966028i | \(-0.416792\pi\) |
0.965824 | + | 0.259200i | \(0.0834590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.61553 | − | 14.9225i | −0.945677 | − | 1.63796i | −0.754390 | − | 0.656426i | \(-0.772067\pi\) |
−0.191286 | − | 0.981534i | \(-0.561266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.04451 | + | 7.00530i | −0.438689 | + | 0.759831i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.96419i | − | 0.950202i | −0.879931 | − | 0.475101i | \(-0.842411\pi\) | ||
0.879931 | − | 0.475101i | \(-0.157589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0594i | 1.68348i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.52877 | − | 7.84406i | 0.464642 | − | 0.804784i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.03909 | − | 15.6562i | −0.917780 | − | 1.58964i | −0.802779 | − | 0.596276i | \(-0.796646\pi\) |
−0.115001 | − | 0.993365i | \(-0.536687\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.58134 | − | 3.79974i | 0.654868 | − | 0.378088i | −0.135451 | − | 0.990784i | \(-0.543248\pi\) |
0.790319 | + | 0.612696i | \(0.209915\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.5607 | − | 7.82926i | −1.33617 | − | 0.771440i | −0.349936 | − | 0.936774i | \(-0.613797\pi\) |
−0.986238 | + | 0.165333i | \(0.947130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.51103 | 0.822792 | 0.411396 | − | 0.911457i | \(-0.365041\pi\) | ||||
0.411396 | + | 0.911457i | \(0.365041\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.886656 | −0.0849263 | −0.0424631 | − | 0.999098i | \(-0.513521\pi\) | ||||
−0.0424631 | + | 0.999098i | \(0.513521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.44033 | − | 0.831573i | −0.135494 | − | 0.0782278i | 0.430721 | − | 0.902485i | \(-0.358259\pi\) |
−0.566215 | + | 0.824258i | \(0.691593\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.39098 | − | 2.53513i | 0.409461 | − | 0.236402i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.28498 | + | 10.8859i | 0.576143 | + | 0.997909i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21920 | + | 7.30786i | −0.383563 | + | 0.664351i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.0952i | − | 1.08183i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.92732i | − | 0.703436i | −0.936106 | − | 0.351718i | \(-0.885598\pi\) | ||
0.936106 | − | 0.351718i | \(-0.114402\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.51564 | + | 9.55337i | −0.481904 | + | 0.834682i | −0.999784 | − | 0.0207712i | \(-0.993388\pi\) |
0.517880 | + | 0.855453i | \(0.326721\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.03750 | − | 12.1893i | −0.610229 | − | 1.05695i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.101511 | + | 0.0586073i | −0.00867266 | + | 0.00500716i | −0.504330 | − | 0.863511i | \(-0.668261\pi\) |
0.495657 | + | 0.868518i | \(0.334927\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.03232 | − | 1.75071i | −0.257198 | − | 0.148494i | 0.365858 | − | 0.930671i | \(-0.380776\pi\) |
−0.623056 | + | 0.782177i | \(0.714109\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.4549 | −1.96139 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.54809 | −0.211607 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.91915 | − | 1.68537i | −0.239146 | − | 0.138071i | 0.375638 | − | 0.926766i | \(-0.377424\pi\) |
−0.614784 | + | 0.788695i | \(0.710757\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.57011 | + | 5.52530i | −0.778804 | + | 0.449643i | −0.836006 | − | 0.548720i | \(-0.815115\pi\) |
0.0572021 | + | 0.998363i | \(0.481782\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0727833 | + | 0.126064i | 0.00584610 | + | 0.0101257i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.84164 | + | 3.18981i | −0.146979 | + | 0.254575i | −0.930109 | − | 0.367282i | \(-0.880288\pi\) |
0.783131 | + | 0.621857i | \(0.213622\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.87896i | − | 0.620949i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.39773i | 0.109478i | 0.998501 | + | 0.0547392i | \(0.0174327\pi\) | ||||
−0.998501 | + | 0.0547392i | \(0.982567\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.89041 | + | 10.2025i | −0.455814 | + | 0.789493i | −0.998735 | − | 0.0502913i | \(-0.983985\pi\) |
0.542921 | + | 0.839784i | \(0.317318\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.65060 | − | 13.2512i | −0.588508 | − | 1.01933i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.11135 | − | 4.10574i | 0.540666 | − | 0.312154i | −0.204683 | − | 0.978828i | \(-0.565616\pi\) |
0.745349 | + | 0.666675i | \(0.232283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.20568 | − | 1.85080i | −0.242327 | − | 0.139907i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1876 | −0.985689 | −0.492844 | − | 0.870118i | \(-0.664043\pi\) | ||||
−0.492844 | + | 0.870118i | \(0.664043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.98599 | −0.444935 | −0.222467 | − | 0.974940i | \(-0.571411\pi\) | ||||
−0.222467 | + | 0.974940i | \(0.571411\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.1964 | + | 8.19632i | 1.04374 | + | 0.602606i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.8989 | + | 9.17924i | −1.16264 | + | 0.671253i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.07853 | − | 8.79626i | −0.367469 | − | 0.636475i | 0.621700 | − | 0.783256i | \(-0.286442\pi\) |
−0.989169 | + | 0.146780i | \(0.953109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.81288 | − | 11.8003i | 0.490402 | − | 0.849401i | −0.509537 | − | 0.860449i | \(-0.670183\pi\) |
0.999939 | + | 0.0110476i | \(0.00351664\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.65685i | 0.403034i | 0.979485 | + | 0.201517i | \(0.0645872\pi\) | ||||
−0.979485 | + | 0.201517i | \(0.935413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9330i | 0.987682i | 0.869552 | + | 0.493841i | \(0.164408\pi\) | ||||
−0.869552 | + | 0.493841i | \(0.835592\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.97981 | + | 3.42913i | −0.138955 | + | 0.240677i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.15452 | − | 15.8561i | −0.639379 | − | 1.10744i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.8025 | − | 10.2783i | 1.23143 | − | 0.710965i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.72603 | − | 2.72857i | −0.325353 | − | 0.187843i | 0.328423 | − | 0.944531i | \(-0.393483\pi\) |
−0.653776 | + | 0.756688i | \(0.726816\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.3659 | 0.775149 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.226204 | 0.0153557 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.1840 | − | 11.0759i | −1.29046 | − | 0.745046i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.87757 | + | 5.70282i | −0.661451 | + | 0.381889i | −0.792830 | − | 0.609443i | \(-0.791393\pi\) |
0.131379 | + | 0.991332i | \(0.458060\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4469 | − | 23.2907i | −0.892502 | − | 1.54586i | −0.836866 | − | 0.547408i | \(-0.815615\pi\) |
−0.0556363 | − | 0.998451i | \(-0.517719\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.55925 | + | 2.70071i | −0.103038 | + | 0.178468i | −0.912935 | − | 0.408105i | \(-0.866190\pi\) |
0.809897 | + | 0.586573i | \(0.199523\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3.82047i | − | 0.250288i | −0.992139 | − | 0.125144i | \(-0.960061\pi\) | ||
0.992139 | − | 0.125144i | \(-0.0399392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.33914i | 0.609218i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2692 | − | 17.7868i | 0.664259 | − | 1.15053i | −0.315227 | − | 0.949016i | \(-0.602081\pi\) |
0.979486 | − | 0.201514i | \(-0.0645861\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4262 | + | 18.0588i | 0.671613 | + | 1.16327i | 0.977447 | + | 0.211182i | \(0.0677314\pi\) |
−0.305834 | + | 0.952085i | \(0.598935\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.55460 | − | 2.05225i | 0.227095 | − | 0.131113i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.4810 | + | 12.4021i | 1.36680 | + | 0.789124i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.02844 | 0.443631 | 0.221815 | − | 0.975089i | \(-0.428802\pi\) | ||||
0.221815 | + | 0.975089i | \(0.428802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5073 | 0.723455 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2464 | − | 7.64784i | −0.826290 | − | 0.477059i | 0.0262904 | − | 0.999654i | \(-0.491631\pi\) |
−0.852581 | + | 0.522595i | \(0.824964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.0606 | − | 12.7367i | 1.37078 | − | 0.791421i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.35108 | + | 7.53629i | 0.268299 | + | 0.464707i | 0.968423 | − | 0.249314i | \(-0.0802052\pi\) |
−0.700124 | + | 0.714022i | \(0.746872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.70703 | + | 15.0810i | −0.534869 | + | 0.926420i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 9.15090i | − | 0.557940i | −0.960300 | − | 0.278970i | \(-0.910007\pi\) | ||
0.960300 | − | 0.278970i | \(-0.0899930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.85013i | − | 0.233879i | −0.993139 | − | 0.116939i | \(-0.962692\pi\) | ||
0.993139 | − | 0.116939i | \(-0.0373084\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.70310 | − | 4.68191i | 0.163003 | − | 0.282330i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.32948 | − | 5.76682i | −0.200049 | − | 0.346495i | 0.748495 | − | 0.663140i | \(-0.230777\pi\) |
−0.948544 | + | 0.316646i | \(0.897443\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0097 | + | 7.51114i | −0.776092 | + | 0.448077i | −0.835044 | − | 0.550184i | \(-0.814558\pi\) |
0.0589513 | + | 0.998261i | \(0.481224\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7216 | − | 8.49955i | −0.875111 | − | 0.505246i | −0.00606768 | − | 0.999982i | \(-0.501931\pi\) |
−0.869043 | + | 0.494736i | \(0.835265\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.4514 | −1.67943 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.338567 | −0.0199157 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.09302 | − | 2.94046i | −0.297538 | − | 0.171783i | 0.343799 | − | 0.939043i | \(-0.388286\pi\) |
−0.641336 | + | 0.767260i | \(0.721620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.88569 | + | 3.39811i | −0.342678 | + | 0.197845i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.94247 | + | 12.0247i | 0.401493 | + | 0.695407i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.83106 | − | 15.2958i | 0.509014 | − | 0.881638i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.5644i | 1.40655i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.11493i | − | 0.406071i | −0.979171 | − | 0.203035i | \(-0.934919\pi\) | ||
0.979171 | − | 0.203035i | \(-0.0650806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.7568 | − | 20.3633i | 0.666665 | − | 1.15470i | −0.312166 | − | 0.950028i | \(-0.601054\pi\) |
0.978831 | − | 0.204671i | \(-0.0656123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.04609 | + | 10.4721i | 0.341745 | + | 0.591920i | 0.984757 | − | 0.173936i | \(-0.0556486\pi\) |
−0.643012 | + | 0.765856i | \(0.722315\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1235 | + | 8.73157i | −0.849421 | + | 0.490414i | −0.860456 | − | 0.509525i | \(-0.829821\pi\) |
0.0110342 | + | 0.999939i | \(0.496488\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.00825 | − | 2.89152i | −0.280408 | − | 0.161894i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4146 | 1.08026 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.52327 | 0.361846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.5683 | + | 7.25629i | 0.692911 | + | 0.400052i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.40914 | + | 4.85502i | −0.462208 | + | 0.266856i | −0.712972 | − | 0.701192i | \(-0.752652\pi\) |
0.250764 | + | 0.968048i | \(0.419318\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.67802 | − | 4.63847i | −0.146316 | − | 0.253427i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.87607 | + | 4.98150i | −0.156669 | + | 0.271360i | −0.933666 | − | 0.358146i | \(-0.883409\pi\) |
0.776996 | + | 0.629505i | \(0.216742\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.330372i | 0.0178906i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.7531i | 0.796590i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.6350 | + | 21.8845i | −0.678283 | + | 1.17482i | 0.297214 | + | 0.954811i | \(0.403942\pi\) |
−0.975498 | + | 0.220010i | \(0.929391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.61543 | + | 2.79802i | 0.0864722 | + | 0.149774i | 0.906018 | − | 0.423240i | \(-0.139107\pi\) |
−0.819545 | + | 0.573014i | \(0.805774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.5683 | − | 11.8751i | 1.09474 | − | 0.632047i | 0.159904 | − | 0.987133i | \(-0.448882\pi\) |
0.934834 | + | 0.355086i | \(0.115548\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.53168 | + | 0.884317i | 0.0812932 | + | 0.0469347i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.9748 | −1.21256 | −0.606281 | − | 0.795250i | \(-0.707339\pi\) | ||||
−0.606281 | + | 0.795250i | \(0.707339\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.73914 | −0.144166 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.5457 | + | 6.66594i | 0.604332 | + | 0.348911i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.9990 | − | 12.7012i | 1.14834 | − | 0.662995i | 0.199859 | − | 0.979825i | \(-0.435952\pi\) |
0.948482 | + | 0.316830i | \(0.102618\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5303 | + | 23.4352i | 0.702460 | + | 1.21670i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9237 | − | 22.3844i | 0.669161 | − | 1.15902i | −0.308978 | − | 0.951069i | \(-0.599987\pi\) |
0.978139 | − | 0.207952i | \(-0.0666798\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.97795i | − | 0.359383i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.19144i | − | 0.163933i | −0.996635 | − | 0.0819666i | \(-0.973880\pi\) | ||
0.996635 | − | 0.0819666i | \(-0.0261201\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.07378 | − | 5.32394i | 0.157063 | − | 0.272041i | −0.776745 | − | 0.629815i | \(-0.783131\pi\) |
0.933808 | + | 0.357774i | \(0.116464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9276 | + | 22.3912i | 0.658850 | + | 1.14116i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.1730 | + | 14.5336i | −1.27632 | + | 0.736885i | −0.976170 | − | 0.217006i | \(-0.930371\pi\) |
−0.300152 | + | 0.953891i | \(0.597037\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.41193 | + | 5.43398i | 0.475982 | + | 0.274808i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.4088 | 1.22814 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.7930 | −1.69602 | −0.848010 | − | 0.529980i | \(-0.822199\pi\) | ||||
−0.848010 | + | 0.529980i | \(0.822199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.93722 | + | 4.00521i | 0.346428 | + | 0.200011i | 0.663111 | − | 0.748521i | \(-0.269236\pi\) |
−0.316683 | + | 0.948532i | \(0.602569\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.345228 | + | 0.199317i | −0.0171970 | + | 0.00992870i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.6020 | + | 32.2196i | 0.922068 | + | 1.59707i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.61851 | − | 7.99949i | 0.228370 | − | 0.395549i | −0.728955 | − | 0.684562i | \(-0.759994\pi\) |
0.957325 | + | 0.289013i | \(0.0933269\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.5610i | 0.519673i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 33.4735i | − | 1.64315i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.96784 | + | 8.60455i | −0.242695 | + | 0.420360i | −0.961481 | − | 0.274871i | \(-0.911365\pi\) |
0.718786 | + | 0.695231i | \(0.244698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7911 | + | 25.6190i | 0.720876 | + | 1.24859i | 0.960649 | + | 0.277764i | \(0.0895934\pi\) |
−0.239774 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.42181 | − | 2.55293i | 0.214489 | − | 0.123835i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.0579 | + | 19.0860i | 1.59978 | + | 0.923635i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.6306 | 1.90894 | 0.954470 | − | 0.298307i | \(-0.0964219\pi\) | ||||
0.954470 | + | 0.298307i | \(0.0964219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.31522 | −0.447661 | −0.223831 | − | 0.974628i | \(-0.571856\pi\) | ||||
−0.223831 | + | 0.974628i | \(0.571856\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.5389 | − | 6.08461i | −0.504142 | − | 0.291066i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.98348 | + | 1.14516i | −0.0946664 | + | 0.0546557i | −0.546586 | − | 0.837403i | \(-0.684073\pi\) |
0.451919 | + | 0.892059i | \(0.350739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.3819 | − | 21.4461i | −0.588283 | − | 1.01894i | −0.994457 | − | 0.105141i | \(-0.966471\pi\) |
0.406174 | − | 0.913796i | \(-0.366863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.70703 | − | 15.0810i | 0.412753 | − | 0.714909i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.6070i | 1.44443i | 0.691667 | + | 0.722216i | \(0.256876\pi\) | ||||
−0.691667 | + | 0.722216i | \(0.743124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 41.5534i | − | 1.95667i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.5987 | + | 27.0178i | −0.731279 | + | 1.26661i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.09417 | + | 15.7516i | 0.425408 | + | 0.736827i | 0.996458 | − | 0.0840872i | \(-0.0267974\pi\) |
−0.571051 | + | 0.820915i | \(0.693464\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.3019 | + | 17.4948i | −1.41130 | + | 0.814813i | −0.995511 | − | 0.0946485i | \(-0.969827\pi\) |
−0.415787 | + | 0.909462i | \(0.636494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.9627 | − | 8.06138i | −0.648903 | − | 0.374644i | 0.139133 | − | 0.990274i | \(-0.455568\pi\) |
−0.788036 | + | 0.615630i | \(0.788902\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.34589 | −0.293653 | −0.146826 | − | 0.989162i | \(-0.546906\pi\) | ||||
−0.146826 | + | 0.989162i | \(0.546906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.32305 | −0.384323 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.3396 | + | 12.8978i | 1.02718 | + | 0.593041i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.95125 | + | 2.85860i | −0.227179 | + | 0.131162i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.745307 | + | 1.29091i | 0.0340539 | + | 0.0589832i | 0.882550 | − | 0.470218i | \(-0.155825\pi\) |
−0.848496 | + | 0.529202i | \(0.822492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.4457 | + | 38.8770i | −1.02343 | + | 1.77264i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 35.1191i | − | 1.59468i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 40.5671i | − | 1.83827i | −0.393942 | − | 0.919135i | \(-0.628889\pi\) | ||
0.393942 | − | 0.919135i | \(-0.371111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.02050 | − | 10.4278i | 0.271701 | − | 0.470601i | −0.697596 | − | 0.716491i | \(-0.745747\pi\) |
0.969298 | + | 0.245891i | \(0.0790804\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.73088 | − | 4.73002i | −0.122992 | − | 0.213029i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.38016 | − | 1.37419i | 0.106765 | − | 0.0616407i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.94438 | + | 3.43199i | 0.266107 | + | 0.153637i | 0.627117 | − | 0.778925i | \(-0.284235\pi\) |
−0.361010 | + | 0.932562i | \(0.617568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.0653 | 1.56348 | 0.781741 | − | 0.623603i | \(-0.214332\pi\) | ||||
0.781741 | + | 0.623603i | \(0.214332\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.7629 | 0.656943 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1369 | + | 6.42991i | 0.493635 | + | 0.285001i | 0.726081 | − | 0.687609i | \(-0.241340\pi\) |
−0.232446 | + | 0.972609i | \(0.574673\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.9416 | − | 10.3586i | 0.793688 | − | 0.458236i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.2093 | − | 26.3433i | −0.670203 | − | 1.16083i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.5978 | + | 18.3560i | −0.466093 | + | 0.807296i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.6447i | 1.03589i | 0.855413 | + | 0.517947i | \(0.173303\pi\) | ||||
−0.855413 | + | 0.517947i | \(0.826697\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.3335i | − | 0.801670i | −0.916150 | − | 0.400835i | \(-0.868720\pi\) | ||
0.916150 | − | 0.400835i | \(-0.131280\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.156009 | + | 0.270215i | −0.00679585 | + | 0.0117708i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.09393 | + | 14.0191i | 0.351910 | + | 0.609526i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.4220 | − | 25.0697i | 1.88081 | − | 1.08589i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.3186 | + | 8.26687i | 0.619049 | + | 0.357408i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.31539 | 0.401242 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.5508 | 0.496606 | 0.248303 | − | 0.968682i | \(-0.420127\pi\) | ||||
0.248303 | + | 0.968682i | \(0.420127\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.49168 | − | 0.861221i | −0.0638965 | − | 0.0368906i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.89458 | + | 2.24854i | −0.166520 | + | 0.0961405i | −0.580944 | − | 0.813944i | \(-0.697316\pi\) |
0.414424 | + | 0.910084i | \(0.363983\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.05785 | + | 5.29636i | 0.130269 | + | 0.225632i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.9651 | − | 32.8485i | 0.806477 | − | 1.39686i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.0115i | 1.14451i | 0.820074 | + | 0.572257i | \(0.193932\pi\) | ||||
−0.820074 | + | 0.572257i | \(0.806068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.1256i | 1.31647i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.37475 | − | 14.5055i | 0.352954 | − | 0.611334i | −0.633812 | − | 0.773487i | \(-0.718511\pi\) |
0.986766 | + | 0.162153i | \(0.0518439\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.61543 | − | 2.79802i | −0.0679619 | − | 0.117713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.7647 | + | 20.0714i | −1.45741 | + | 0.841437i | −0.998883 | − | 0.0472425i | \(-0.984957\pi\) |
−0.458529 | + | 0.888680i | \(0.651623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.5848 | + | 21.6996i | 1.57288 | + | 0.908101i | 0.995814 | + | 0.0914001i | \(0.0291342\pi\) |
0.577062 | + | 0.816700i | \(0.304199\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.20040 | −0.133466 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.4136 | 0.849829 | 0.424914 | − | 0.905234i | \(-0.360304\pi\) | ||||
0.424914 | + | 0.905234i | \(0.360304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.0474 | − | 26.0081i | −1.86888 | − | 1.07900i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.2272 | + | 19.7611i | −1.41755 | + | 0.818421i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.1493 | + | 26.2394i | 0.625279 | + | 1.08301i | 0.988487 | + | 0.151306i | \(0.0483480\pi\) |
−0.363208 | + | 0.931708i | \(0.618319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.174688 | − | 0.302569i | 0.00719791 | − | 0.0124671i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.5261i | − | 1.45888i | −0.684043 | − | 0.729442i | \(-0.739780\pi\) | ||
0.684043 | − | 0.729442i | \(-0.260220\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.4187i | 1.00107i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.29720 | − | 12.6391i | 0.298156 | − | 0.516421i | −0.677558 | − | 0.735469i | \(-0.736962\pi\) |
0.975714 | + | 0.219048i | \(0.0702952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.343128 | + | 0.594315i | 0.0139965 | + | 0.0242426i | 0.872939 | − | 0.487830i | \(-0.162211\pi\) |
−0.858942 | + | 0.512072i | \(0.828878\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.1964 | + | 8.19632i | −0.577168 | + | 0.333228i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.6114 | + | 11.3227i | 0.796004 | + | 0.459573i | 0.842072 | − | 0.539365i | \(-0.181336\pi\) |
−0.0460679 | + | 0.998938i | \(0.514669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.5753 | −1.03466 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.738126 | 0.0298126 | 0.0149063 | − | 0.999889i | \(-0.495255\pi\) | ||||
0.0149063 | + | 0.999889i | \(0.495255\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.96274 | + | 4.59729i | 0.320568 | + | 0.185080i | 0.651646 | − | 0.758524i | \(-0.274079\pi\) |
−0.331078 | + | 0.943603i | \(0.607412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5675 | + | 9.56526i | −0.665905 | + | 0.384460i | −0.794523 | − | 0.607234i | \(-0.792279\pi\) |
0.128618 | + | 0.991694i | \(0.458946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.5303 | − | 23.4352i | −0.542081 | − | 0.938912i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.68270 | − | 15.0389i | 0.347308 | − | 0.601555i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.1371i | 1.40101i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.5536i | 0.658989i | 0.944157 | + | 0.329495i | \(0.106878\pi\) | ||||
−0.944157 | + | 0.329495i | \(0.893122\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.69991 | − | 13.3366i | 0.305562 | − | 0.529248i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.62009 | + | 9.73428i | 0.222676 | + | 0.385686i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.62226 | − | 1.51396i | 0.103573 | − | 0.0597978i | −0.447319 | − | 0.894375i | \(-0.647621\pi\) |
0.550892 | + | 0.834577i | \(0.314288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.77000 | + | 2.75396i | 0.188110 | + | 0.108606i | 0.591098 | − | 0.806600i | \(-0.298695\pi\) |
−0.402987 | + | 0.915206i | \(0.632028\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.6014 | −0.888551 | −0.444276 | − | 0.895890i | \(-0.646539\pi\) | ||||
−0.444276 | + | 0.895890i | \(0.646539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.4244 | −0.605460 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.0192 | + | 19.6410i | 1.33127 | + | 0.768611i | 0.985495 | − | 0.169705i | \(-0.0542814\pi\) |
0.345779 | + | 0.938316i | \(0.387615\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.5586 | + | 10.7148i | −0.725146 | + | 0.418663i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.48091 | − | 7.76116i | −0.174551 | − | 0.302332i | 0.765454 | − | 0.643490i | \(-0.222514\pi\) |
−0.940006 | + | 0.341158i | \(0.889181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.44282 | − | 5.96314i | 0.133910 | − | 0.231939i | −0.791270 | − | 0.611466i | \(-0.790580\pi\) |
0.925181 | + | 0.379527i | \(0.123913\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 27.3425i | − | 1.06030i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.42347i | 0.132557i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.8751 | + | 48.2811i | −1.07611 | + | 1.86387i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.5054 | − | 18.1959i | −0.404954 | − | 0.701401i | 0.589362 | − | 0.807869i | \(-0.299379\pi\) |
−0.994316 | + | 0.106468i | \(0.966046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.85645 | − | 3.95858i | 0.263515 | − | 0.152140i | −0.362422 | − | 0.932014i | \(-0.618050\pi\) |
0.625937 | + | 0.779874i | \(0.284717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −47.2620 | − | 27.2868i | −1.81375 | − | 1.04717i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.1669 | −0.962983 | −0.481492 | − | 0.876451i | \(-0.659905\pi\) | ||||
−0.481492 | + | 0.876451i | \(0.659905\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.227704 | −0.00870013 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.2994 | − | 23.8442i | −1.57338 | − | 0.908393i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0586 | + | 9.27142i | −0.610897 | + | 0.352701i | −0.773316 | − | 0.634020i | \(-0.781404\pi\) |
0.162420 | + | 0.986722i | \(0.448070\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.40098 | − | 5.89067i | −0.129007 | − | 0.223446i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.6224 | − | 33.9871i | 0.743253 | − | 1.28735i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.2203i | − | 1.67018i | −0.550116 | − | 0.835088i | \(-0.685417\pi\) | ||
0.550116 | − | 0.835088i | \(-0.314583\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 39.3442i | − | 1.48390i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4705 | − | 19.8674i | 0.431391 | − | 0.747192i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.89832 | + | 10.2162i | 0.221516 | + | 0.383677i | 0.955268 | − | 0.295740i | \(-0.0955662\pi\) |
−0.733753 | + | 0.679417i | \(0.762233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.169373 | − | 0.0977877i | 0.00634308 | − | 0.00366218i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.4596 | − | 22.7820i | −1.47570 | − | 0.851999i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.11638 | −0.0416339 | −0.0208169 | − | 0.999783i | \(-0.506627\pi\) | ||||
−0.0208169 | + | 0.999783i | \(0.506627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.2692 | −1.76040 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.39290 | + | 0.804189i | 0.0517309 | + | 0.0298668i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.6152 | − | 6.70606i | 0.430785 | − | 0.248714i | −0.268896 | − | 0.963169i | \(-0.586659\pi\) |
0.699681 | + | 0.714455i | \(0.253325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1813 | + | 21.0986i | 0.450540 | + | 0.780358i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.97824 | − | 6.89052i | 0.146940 | − | 0.254507i | −0.783155 | − | 0.621826i | \(-0.786391\pi\) |
0.930095 | + | 0.367319i | \(0.119724\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.1559i | − | 0.447767i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.13143i | 0.0784058i | 0.999231 | + | 0.0392029i | \(0.0124819\pi\) | ||||
−0.999231 | + | 0.0392029i | \(0.987518\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.7656 | − | 46.3594i | 0.981934 | − | 1.70076i | 0.327095 | − | 0.944992i | \(-0.393930\pi\) |
0.654839 | − | 0.755768i | \(-0.272736\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.27404 | − | 5.67081i | −0.119952 | − | 0.207762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.2505 | − | 12.8463i | 0.813016 | − | 0.469395i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.0885 | + | 17.9489i | 1.13443 | + | 0.654966i | 0.945046 | − | 0.326936i | \(-0.106016\pi\) |
0.189388 | + | 0.981902i | \(0.439350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.4672 | −0.781271 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.9513 | −0.579762 | −0.289881 | − | 0.957063i | \(-0.593616\pi\) | ||||
−0.289881 | + | 0.957063i | \(0.593616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.5944 | − | 7.27140i | −0.456548 | − | 0.263588i | 0.254044 | − | 0.967193i | \(-0.418239\pi\) |
−0.710592 | + | 0.703605i | \(0.751573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.31800 | + | 1.33830i | −0.0839172 | + | 0.0484496i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.30572 | − | 16.1180i | −0.336010 | − | 0.581987i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.545353 | − | 0.944579i | 0.0196659 | − | 0.0340624i | −0.856025 | − | 0.516934i | \(-0.827073\pi\) |
0.875691 | + | 0.482872i | \(0.160406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.0697i | 1.11750i | 0.829336 | + | 0.558750i | \(0.188719\pi\) | ||||
−0.829336 | + | 0.558750i | \(0.811281\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.0918830i | − | 0.00330054i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.9719 | + | 38.0564i | −0.787225 | + | 1.36351i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00701 | + | 3.47624i | 0.0718163 | + | 0.124390i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.19661 | + | 3.57762i | −0.221167 | + | 0.127691i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0751371 | + | 0.0433804i | 0.00267835 | + | 0.00154635i | 0.501339 | − | 0.865251i | \(-0.332841\pi\) |
−0.498660 | + | 0.866798i | \(0.666174\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.02062 | −0.178513 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −67.2697 | −2.38882 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.88596 | − | 2.24356i | −0.137648 | − | 0.0794710i | 0.429595 | − | 0.903022i | \(-0.358656\pi\) |
−0.567242 | + | 0.823551i | \(0.691990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.3362 | + | 10.0091i | −0.613312 | + | 0.354096i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1287 | + | 26.2037i | 0.533881 | + | 0.924710i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.65294 | − | 13.2553i | 0.269731 | − | 0.467187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 30.9732i | − | 1.08896i | −0.838774 | − | 0.544480i | \(-0.816727\pi\) | ||
0.838774 | − | 0.544480i | \(-0.183273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.5248i | 0.896298i | 0.893959 | + | 0.448149i | \(0.147917\pi\) | ||||
−0.893959 | + | 0.448149i | \(0.852083\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.35763 | + | 2.35148i | −0.0475557 | + | 0.0823689i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6398 | − | 23.6248i | −0.477195 | − | 0.826525i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.1380 | − | 22.0190i | 1.33102 | − | 0.768467i | 0.345567 | − | 0.938394i | \(-0.387686\pi\) |
0.985457 | + | 0.169927i | \(0.0543531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.3847 | + | 21.5841i | 1.30315 | + | 0.752373i | 0.980943 | − | 0.194297i | \(-0.0622425\pi\) |
0.322205 | + | 0.946670i | \(0.395576\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.24861 | 0.252059 | 0.126029 | − | 0.992027i | \(-0.459777\pi\) | ||||
0.126029 | + | 0.992027i | \(0.459777\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.5377 | 0.470185 | 0.235092 | − | 0.971973i | \(-0.424461\pi\) | ||||
0.235092 | + | 0.971973i | \(0.424461\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.61918 | + | 4.39893i | 0.263989 | + | 0.152414i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.8196 | + | 11.4429i | −0.685887 | + | 0.395997i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.6704 | − | 35.8022i | −0.713622 | − | 1.23603i | −0.963489 | − | 0.267749i | \(-0.913720\pi\) |
0.249867 | − | 0.968280i | \(-0.419613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.6398 | + | 23.6248i | −0.470336 | + | 0.814647i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 29.7245i | − | 1.02255i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.4734i | 0.875277i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.0121 | − | 19.0736i | 0.377491 | − | 0.653834i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.39474 | + | 7.61191i | 0.150473 | + | 0.260627i | 0.931401 | − | 0.363994i | \(-0.118587\pi\) |
−0.780928 | + | 0.624620i | \(0.785254\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.5978 | − | 16.5109i | 0.976881 | − | 0.564003i | 0.0755543 | − | 0.997142i | \(-0.475927\pi\) |
0.901327 | + | 0.433139i | \(0.142594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0192 | − | 9.82606i | −0.580689 | − | 0.335261i | 0.180718 | − | 0.983535i | \(-0.442158\pi\) |
−0.761407 | + | 0.648274i | \(0.775491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.3994 | −0.388040 | −0.194020 | − | 0.980998i | \(-0.562153\pi\) | ||||
−0.194020 | + | 0.980998i | \(0.562153\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.9518 | 0.542379 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.9753 | + | 27.6986i | 1.62745 | + | 0.939609i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.7025 | − | 7.33378i | 0.430407 | − | 0.248496i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.2562 | − | 31.6206i | −0.617172 | − | 1.06897i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5243 | + | 30.3531i | −0.591755 | + | 1.02495i | 0.402241 | + | 0.915534i | \(0.368231\pi\) |
−0.993996 | + | 0.109416i | \(0.965102\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.1147i | 0.745064i | 0.928019 | + | 0.372532i | \(0.121510\pi\) | ||||
−0.928019 | + | 0.372532i | \(0.878490\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 48.4270i | − | 1.62970i | −0.579673 | − | 0.814849i | \(-0.696820\pi\) | ||
0.579673 | − | 0.814849i | \(-0.303180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6506 | + | 23.6436i | −0.458343 | + | 0.793873i | −0.998874 | − | 0.0474512i | \(-0.984890\pi\) |
0.540531 | + | 0.841324i | \(0.318223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.9653 | − | 20.7245i | −0.401304 | − | 0.695078i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.4120 | − | 11.2075i | 0.649596 | − | 0.375045i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.1864 | − | 12.8093i | −0.741608 | − | 0.428168i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.0982874 | −0.00327807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.3265 | −1.24353 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.0706 | − | 5.81427i | −0.334758 | − | 0.193273i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0823 | − | 9.86248i | 0.567209 | − | 0.327478i | −0.188825 | − | 0.982011i | \(-0.560468\pi\) |
0.756034 | + | 0.654532i | \(0.227135\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.0924 | + | 29.6049i | 0.566296 | + | 0.980854i | 0.996928 | + | 0.0783259i | \(0.0249575\pi\) |
−0.430632 | + | 0.902528i | \(0.641709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.9850 | − | 65.7919i | 1.25712 | − | 2.17739i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.3007i | 1.09969i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.2819i | 1.09787i | 0.835866 | + | 0.548934i | \(0.184966\pi\) | ||||
−0.835866 | + | 0.548934i | \(0.815034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.42170 | + | 4.19451i | −0.0797114 | + | 0.138064i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.17360 | − | 8.96093i | −0.170107 | − | 0.294634i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.4859 | − | 15.8690i | 0.901784 | − | 0.520645i | 0.0240056 | − | 0.999712i | \(-0.492358\pi\) |
0.877779 | + | 0.479066i | \(0.159025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.53144 | − | 4.92563i | −0.279607 | − | 0.161431i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.6637 | −1.16633 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.7310 | 1.00394 | 0.501969 | − | 0.864886i | \(-0.332609\pi\) | ||||
0.501969 | + | 0.864886i | \(0.332609\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.0527 | + | 13.8868i | 0.784095 | + | 0.452697i | 0.837880 | − | 0.545855i | \(-0.183795\pi\) |
−0.0537847 | + | 0.998553i | \(0.517128\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.3034 | + | 12.2995i | −0.693734 | + | 0.400527i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.4561 | + | 19.8426i | 0.372273 | + | 0.644796i | 0.989915 | − | 0.141663i | \(-0.0452450\pi\) |
−0.617641 | + | 0.786460i | \(0.711912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.2547 | + | 31.6181i | −0.592573 | + | 1.02637i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.34110i | 0.270195i | 0.990832 | + | 0.135097i | \(0.0431347\pi\) | ||||
−0.990832 | + | 0.135097i | \(0.956865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 19.7314i | − | 0.638492i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.176921 | + | 0.306436i | −0.00571308 | + | 0.00989534i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4972 | − | 26.8419i | −0.499909 | − | 0.865869i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.9235 | − | 13.2349i | 0.737933 | − | 0.426046i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.6181 | − | 28.6470i | −1.59561 | − | 0.921227i | −0.992319 | − | 0.123708i | \(-0.960522\pi\) |
−0.603293 | − | 0.797519i | \(-0.706145\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.2853 | −0.747259 | −0.373630 | − | 0.927578i | \(-0.621887\pi\) | ||||
−0.373630 | + | 0.927578i | \(0.621887\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.5699 | −0.338857 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.8129 | − | 20.6766i | −1.14576 | − | 0.661504i | −0.197908 | − | 0.980221i | \(-0.563415\pi\) |
−0.947850 | + | 0.318717i | \(0.896748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.2272 | − | 19.7611i | 1.09391 | − | 0.631568i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.9396 | − | 39.7326i | −0.731661 | − | 1.26727i | −0.956173 | − | 0.292802i | \(-0.905412\pi\) |
0.224512 | − | 0.974471i | \(-0.427921\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.49458 | + | 9.51689i | −0.175072 | + | 0.303233i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 15.2706i | − | 0.485578i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.4407i | 1.31641i | 0.752840 | + | 0.658204i | \(0.228683\pi\) | ||||
−0.752840 | + | 0.658204i | \(0.771317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.5333 | + | 23.4403i | −0.429034 | + | 0.743108i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.03515 | + | 15.6493i | 0.286146 | + | 0.495620i | 0.972886 | − | 0.231283i | \(-0.0742924\pi\) |
−0.686740 | + | 0.726903i | \(0.740959\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 864.2.s.a.287.10 | 24 | ||
3.2 | odd | 2 | 288.2.s.a.95.6 | ✓ | 24 | ||
4.3 | odd | 2 | inner | 864.2.s.a.287.9 | 24 | ||
8.3 | odd | 2 | 1728.2.s.g.1151.3 | 24 | |||
8.5 | even | 2 | 1728.2.s.g.1151.4 | 24 | |||
9.2 | odd | 6 | inner | 864.2.s.a.575.9 | 24 | ||
9.4 | even | 3 | 2592.2.c.c.2591.8 | 24 | |||
9.5 | odd | 6 | 2592.2.c.c.2591.18 | 24 | |||
9.7 | even | 3 | 288.2.s.a.191.7 | yes | 24 | ||
12.11 | even | 2 | 288.2.s.a.95.7 | yes | 24 | ||
24.5 | odd | 2 | 576.2.s.g.383.7 | 24 | |||
24.11 | even | 2 | 576.2.s.g.383.6 | 24 | |||
36.7 | odd | 6 | 288.2.s.a.191.6 | yes | 24 | ||
36.11 | even | 6 | inner | 864.2.s.a.575.10 | 24 | ||
36.23 | even | 6 | 2592.2.c.c.2591.17 | 24 | |||
36.31 | odd | 6 | 2592.2.c.c.2591.7 | 24 | |||
72.5 | odd | 6 | 5184.2.c.m.5183.8 | 24 | |||
72.11 | even | 6 | 1728.2.s.g.575.4 | 24 | |||
72.13 | even | 6 | 5184.2.c.m.5183.18 | 24 | |||
72.29 | odd | 6 | 1728.2.s.g.575.3 | 24 | |||
72.43 | odd | 6 | 576.2.s.g.191.7 | 24 | |||
72.59 | even | 6 | 5184.2.c.m.5183.7 | 24 | |||
72.61 | even | 6 | 576.2.s.g.191.6 | 24 | |||
72.67 | odd | 6 | 5184.2.c.m.5183.17 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.s.a.95.6 | ✓ | 24 | 3.2 | odd | 2 | ||
288.2.s.a.95.7 | yes | 24 | 12.11 | even | 2 | ||
288.2.s.a.191.6 | yes | 24 | 36.7 | odd | 6 | ||
288.2.s.a.191.7 | yes | 24 | 9.7 | even | 3 | ||
576.2.s.g.191.6 | 24 | 72.61 | even | 6 | |||
576.2.s.g.191.7 | 24 | 72.43 | odd | 6 | |||
576.2.s.g.383.6 | 24 | 24.11 | even | 2 | |||
576.2.s.g.383.7 | 24 | 24.5 | odd | 2 | |||
864.2.s.a.287.9 | 24 | 4.3 | odd | 2 | inner | ||
864.2.s.a.287.10 | 24 | 1.1 | even | 1 | trivial | ||
864.2.s.a.575.9 | 24 | 9.2 | odd | 6 | inner | ||
864.2.s.a.575.10 | 24 | 36.11 | even | 6 | inner | ||
1728.2.s.g.575.3 | 24 | 72.29 | odd | 6 | |||
1728.2.s.g.575.4 | 24 | 72.11 | even | 6 | |||
1728.2.s.g.1151.3 | 24 | 8.3 | odd | 2 | |||
1728.2.s.g.1151.4 | 24 | 8.5 | even | 2 | |||
2592.2.c.c.2591.7 | 24 | 36.31 | odd | 6 | |||
2592.2.c.c.2591.8 | 24 | 9.4 | even | 3 | |||
2592.2.c.c.2591.17 | 24 | 36.23 | even | 6 | |||
2592.2.c.c.2591.18 | 24 | 9.5 | odd | 6 | |||
5184.2.c.m.5183.7 | 24 | 72.59 | even | 6 | |||
5184.2.c.m.5183.8 | 24 | 72.5 | odd | 6 | |||
5184.2.c.m.5183.17 | 24 | 72.67 | odd | 6 | |||
5184.2.c.m.5183.18 | 24 | 72.13 | even | 6 |