Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(95,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, 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("288.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.s (of order \(6\), degree \(2\), 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: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.7 | ||
Character | \(\chi\) | \(=\) | 288.191 |
Dual form | 288.2.s.a.95.7 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.324214 | − | 1.70144i | 0.187185 | − | 0.982325i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.68236 | + | 0.971313i | −0.752376 | + | 0.434384i | −0.826552 | − | 0.562861i | \(-0.809701\pi\) |
0.0741759 | + | 0.997245i | \(0.476367\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61432 | − | 1.50938i | −0.988118 | − | 0.570490i | −0.0834070 | − | 0.996516i | \(-0.526580\pi\) |
−0.904711 | + | 0.426025i | \(0.859913\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.78977 | − | 1.10326i | −0.929924 | − | 0.367753i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20445 | − | 3.81822i | 0.664667 | − | 1.15124i | −0.314709 | − | 0.949188i | \(-0.601907\pi\) |
0.979376 | − | 0.202048i | \(-0.0647597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.65994 | − | 4.60716i | −0.737736 | − | 1.27780i | −0.953513 | − | 0.301353i | \(-0.902562\pi\) |
0.215777 | − | 0.976443i | \(-0.430772\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.10718 | + | 3.17735i | 0.285873 | + | 0.820388i | ||||
\(16\) | 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 | ||||||||
\(21\) | −3.41570 | + | 3.95873i | −0.745368 | + | 0.863866i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.30500 | + | 2.26033i | 0.272112 | + | 0.471312i | 0.969402 | − | 0.245477i | \(-0.0789445\pi\) |
−0.697290 | + | 0.716789i | \(0.745611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.613102 | + | 1.06192i | −0.122620 | + | 0.212385i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.78161 | + | 4.38892i | −0.535321 | + | 0.844649i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.13594 | + | 0.655836i | 0.210939 | + | 0.121786i | 0.601748 | − | 0.798686i | \(-0.294471\pi\) |
−0.390809 | + | 0.920472i | \(0.627805\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0648938 | + | 0.0374664i | −0.0116553 | + | 0.00672917i | −0.505816 | − | 0.862641i | \(-0.668809\pi\) |
0.494161 | + | 0.869370i | \(0.335475\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.78174 | − | 4.98865i | −1.00647 | − | 0.868413i | ||||
\(34\) | 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 | ||||||||
\(39\) | −8.70118 | + | 3.03202i | −1.39330 | + | 0.485512i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.16220 | − | 4.71245i | 1.27472 | − | 0.735960i | 0.298848 | − | 0.954301i | \(-0.403398\pi\) |
0.975873 | + | 0.218340i | \(0.0700643\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.06694 | − | 2.92540i | −0.772702 | − | 0.446119i | 0.0611359 | − | 0.998129i | \(-0.480528\pi\) |
−0.833838 | + | 0.552010i | \(0.813861\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.76502 | − | 0.853658i | 0.859398 | − | 0.127256i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.40374 | − | 4.16340i | 0.350622 | − | 0.607294i | −0.635737 | − | 0.771906i | \(-0.719304\pi\) |
0.986358 | + | 0.164611i | \(0.0526370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.05643 | + | 1.82979i | 0.150919 | + | 0.261399i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.08471 | + | 1.35001i | 0.992058 | + | 0.189040i | ||||
\(52\) | 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 | ||||||||
\(57\) | −7.93299 | − | 1.51166i | −1.05075 | − | 0.200224i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.74923 | − | 3.02976i | −0.227731 | − | 0.394441i | 0.729405 | − | 0.684083i | \(-0.239797\pi\) |
−0.957135 | + | 0.289642i | \(0.906464\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.32247 | − | 10.9508i | 0.809509 | − | 1.40211i | −0.103695 | − | 0.994609i | \(-0.533067\pi\) |
0.913204 | − | 0.407502i | \(-0.133600\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.62811 | + | 7.09508i | 0.709075 | + | 0.893896i | ||||
\(64\) | 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 | \(-0.612801\pi\) |
0.638712 | + | 0.769446i | \(0.279468\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.26891 | − | 1.48755i | 0.513917 | − | 0.179080i | ||||
\(70\) | 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 | ||||||||
\(75\) | 1.60802 | + | 1.38744i | 0.185678 | + | 0.160208i | ||||
\(76\) | 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 | \(-0.583208\pi\) |
−0.965824 | + | 0.259200i | \(0.916541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.56564 | + | 6.15568i | 0.729516 | + | 0.683964i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.61553 | + | 14.9225i | −0.945677 | + | 1.63796i | −0.191286 | + | 0.981534i | \(0.561266\pi\) |
−0.754390 | + | 0.656426i | \(0.772067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.04451 | − | 7.00530i | −0.438689 | − | 0.759831i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.48415 | − | 1.72010i | 0.159118 | − | 0.184414i | ||||
\(88\) | 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 | ||||||||
\(93\) | 0.0427073 | + | 0.122560i | 0.00442854 | + | 0.0127089i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.52877 | + | 7.84406i | 0.464642 | + | 0.804784i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.03909 | + | 15.6562i | −0.917780 | + | 1.58964i | −0.115001 | + | 0.993365i | \(0.536687\pi\) |
−0.802779 | + | 0.596276i | \(0.796646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.3624 | + | 8.21988i | −1.04146 | + | 0.826129i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.58134 | − | 3.79974i | −0.654868 | − | 0.378088i | 0.135451 | − | 0.990784i | \(-0.456752\pi\) |
−0.790319 | + | 0.612696i | \(0.790085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5607 | − | 7.82926i | 1.33617 | − | 0.771440i | 0.349936 | − | 0.936774i | \(-0.386203\pi\) |
0.986238 | + | 0.165333i | \(0.0528700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.90129 | − | 9.97774i | 0.185547 | − | 0.973728i | ||||
\(106\) | 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 | ||||||||
\(111\) | 2.73585 | − | 14.3574i | 0.259675 | − | 1.36274i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.44033 | − | 0.831573i | 0.135494 | − | 0.0782278i | −0.430721 | − | 0.902485i | \(-0.641741\pi\) |
0.566215 | + | 0.824258i | \(0.308407\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.39098 | − | 2.53513i | −0.409461 | − | 0.236402i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.33775 | + | 15.7875i | 0.216125 | + | 1.45956i | ||||
\(118\) | 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 | ||||||||
\(123\) | −5.37163 | − | 15.4153i | −0.484343 | − | 1.38995i | ||||
\(124\) | 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 | ||||||||
\(129\) | −6.62016 | + | 7.67263i | −0.582872 | + | 0.675537i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.51564 | − | 9.55337i | −0.481904 | − | 0.834682i | 0.517880 | − | 0.855453i | \(-0.326721\pi\) |
−0.999784 | + | 0.0207712i | \(0.993388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.03750 | + | 12.1893i | −0.610229 | + | 1.05695i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.416655 | − | 10.0856i | 0.0358599 | − | 0.868028i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.101511 | + | 0.0586073i | 0.00867266 | + | 0.00500716i | 0.504330 | − | 0.863511i | \(-0.331739\pi\) |
−0.495657 | + | 0.868518i | \(0.665073\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.03232 | − | 1.75071i | 0.257198 | − | 0.148494i | −0.365858 | − | 0.930671i | \(-0.619224\pi\) |
0.623056 | + | 0.782177i | \(0.285891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.30443 | − | 5.43964i | −0.530929 | − | 0.458101i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.4549 | −1.96139 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.54809 | −0.211607 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.45578 | − | 1.20420i | 0.285028 | − | 0.0993211i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.91915 | − | 1.68537i | 0.239146 | − | 0.138071i | −0.375638 | − | 0.926766i | \(-0.622576\pi\) |
0.614784 | + | 0.788695i | \(0.289243\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.57011 | + | 5.52530i | 0.778804 | + | 0.449643i | 0.836006 | − | 0.548720i | \(-0.184885\pi\) |
−0.0572021 | + | 0.998363i | \(0.518218\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.59393 | − | 11.6165i | 0.371397 | − | 0.939138i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0727833 | − | 0.126064i | 0.00584610 | − | 0.0101257i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.84164 | − | 3.18981i | −0.146979 | − | 0.254575i | 0.783131 | − | 0.621857i | \(-0.213622\pi\) |
−0.930109 | + | 0.367282i | \(0.880288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.2520 | + | 2.90632i | 1.20956 | + | 0.230486i | ||||
\(160\) | 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 | ||||||||
\(165\) | 14.5725 | + | 2.77684i | 1.13447 | + | 0.216177i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.89041 | − | 10.2025i | −0.455814 | − | 0.789493i | 0.542921 | − | 0.839784i | \(-0.317318\pi\) |
−0.998735 | + | 0.0502913i | \(0.983985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.65060 | + | 13.2512i | −0.588508 | + | 1.01933i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.14397 | + | 13.0074i | −0.393369 | + | 0.994699i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.11135 | − | 4.10574i | −0.540666 | − | 0.312154i | 0.204683 | − | 0.978828i | \(-0.434384\pi\) |
−0.745349 | + | 0.666675i | \(0.767717\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.20568 | − | 1.85080i | 0.242327 | − | 0.139907i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.72207 | + | 1.99392i | −0.430097 | + | 0.149872i | ||||
\(178\) | 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 | ||||||||
\(183\) | −16.5823 | − | 14.3077i | −1.22580 | − | 1.05766i | ||||
\(184\) | 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 | ||||||||
\(189\) | 13.8965 | − | 7.27554i | 1.01082 | − | 0.529218i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.07853 | + | 8.79626i | −0.367469 | + | 0.636475i | −0.989169 | − | 0.146780i | \(-0.953109\pi\) |
0.621700 | + | 0.783256i | \(0.286442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.81288 | + | 11.8003i | 0.490402 | + | 0.849401i | 0.999939 | − | 0.0110476i | \(-0.00351664\pi\) |
−0.509537 | + | 0.860449i | \(0.670183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.6935 | − | 13.5525i | 0.837389 | − | 0.970517i | ||||
\(196\) | 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 | ||||||||
\(201\) | −1.57139 | − | 4.50953i | −0.110838 | − | 0.318077i | ||||
\(202\) | 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 | ||||||||
\(207\) | −1.14693 | − | 7.74556i | −0.0797170 | − | 0.538354i | ||||
\(208\) | 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 | \(-0.606517\pi\) |
0.653776 | + | 0.756688i | \(0.273184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.295175 | − | 1.54905i | 0.0202251 | − | 0.106139i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.3659 | 0.775149 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.226204 | 0.0153557 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.22502 | − | 11.6766i | 0.150353 | − | 0.789034i | ||||
\(220\) | 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 | \(-0.208607\pi\) |
−0.131379 | + | 0.991332i | \(0.541940\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.88199 | − | 2.28611i | 0.192133 | − | 0.152408i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4469 | + | 23.2907i | −0.892502 | + | 1.54586i | −0.0556363 | + | 0.998451i | \(0.517719\pi\) |
−0.836866 | + | 0.547408i | \(0.815615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.55925 | − | 2.70071i | −0.103038 | − | 0.178468i | 0.809897 | − | 0.586573i | \(-0.199523\pi\) |
−0.912935 | + | 0.408105i | \(0.866190\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.58555 | + | 21.7687i | 0.499093 | + | 1.43228i | ||||
\(232\) | 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 | ||||||||
\(237\) | −14.2171 | + | 16.4773i | −0.923498 | + | 1.07031i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2692 | + | 17.7868i | 0.664259 | + | 1.15053i | 0.979486 | + | 0.201514i | \(0.0645861\pi\) |
−0.315227 | + | 0.949016i | \(0.602081\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4262 | − | 18.0588i | 0.671613 | − | 1.16327i | −0.305834 | − | 0.952085i | \(-0.598935\pi\) |
0.977447 | − | 0.211182i | \(-0.0677314\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.6022 | − | 9.17526i | 0.808429 | − | 0.588593i | ||||
\(244\) | 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 | ||||||||
\(249\) | 22.5965 | + | 19.4969i | 1.43199 | + | 1.23556i | ||||
\(250\) | 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 | ||||||||
\(255\) | −13.2303 | + | 4.61026i | −0.828517 | + | 0.288706i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.2464 | − | 7.64784i | 0.826290 | − | 0.477059i | −0.0262904 | − | 0.999654i | \(-0.508369\pi\) |
0.852581 | + | 0.522595i | \(0.175036\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.0606 | − | 12.7367i | −1.37078 | − | 0.791421i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.44546 | − | 3.08287i | −0.151370 | − | 0.190825i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.35108 | − | 7.53629i | 0.268299 | − | 0.464707i | −0.700124 | − | 0.714022i | \(-0.746872\pi\) |
0.968423 | + | 0.249314i | \(0.0802052\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.70703 | − | 15.0810i | −0.534869 | − | 0.926420i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.2520 | − | 2.90632i | −0.933407 | − | 0.177864i | ||||
\(268\) | 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 | ||||||||
\(273\) | 27.3241 | + | 5.20669i | 1.65373 | + | 0.315123i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.70310 | + | 4.68191i | 0.163003 | + | 0.282330i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.32948 | + | 5.76682i | −0.200049 | + | 0.346495i | −0.948544 | − | 0.316646i | \(-0.897443\pi\) |
0.748495 | + | 0.663140i | \(0.230777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.222374 | − | 0.0329281i | 0.0133132 | − | 0.00197136i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0097 | + | 7.51114i | 0.776092 | + | 0.448077i | 0.835044 | − | 0.550184i | \(-0.185442\pi\) |
−0.0589513 | + | 0.998261i | \(0.518776\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.7216 | − | 8.49955i | 0.875111 | − | 0.505246i | 0.00606768 | − | 0.999982i | \(-0.498069\pi\) |
0.869043 | + | 0.494736i | \(0.164735\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.8145 | − | 5.16226i | 0.877533 | − | 0.305786i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.4514 | −1.67943 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.338567 | −0.0199157 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.7074 | + | 20.4554i | 1.38975 | + | 1.19912i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.09302 | − | 2.94046i | 0.297538 | − | 0.171783i | −0.343799 | − | 0.939043i | \(-0.611714\pi\) |
0.641336 | + | 0.767260i | \(0.278380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.88569 | + | 3.39811i | 0.342678 | + | 0.197845i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.6260 | + | 20.2959i | 0.616581 | + | 1.17769i | ||||
\(298\) | 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 | ||||||||
\(303\) | −8.59878 | + | 9.96581i | −0.493987 | + | 0.572521i | ||||
\(304\) | 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 | ||||||||
\(309\) | −8.92443 | − | 25.6110i | −0.507693 | − | 1.45696i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.7568 | + | 20.3633i | 0.666665 | + | 1.15470i | 0.978831 | + | 0.204671i | \(0.0656123\pi\) |
−0.312166 | + | 0.950028i | \(0.601054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.04609 | − | 10.4721i | 0.341745 | − | 0.591920i | −0.643012 | − | 0.765856i | \(-0.722315\pi\) |
0.984757 | + | 0.173936i | \(0.0556486\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.3601 | − | 6.46985i | −0.921785 | − | 0.364535i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1235 | + | 8.73157i | 0.849421 | + | 0.490414i | 0.860456 | − | 0.509525i | \(-0.170179\pi\) |
−0.0110342 | + | 0.999939i | \(0.503512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.00825 | − | 2.89152i | 0.280408 | − | 0.161894i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.75939 | − | 14.4810i | 0.154014 | − | 0.808249i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4146 | 1.08026 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.52327 | 0.361846 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.287466 | + | 1.50859i | −0.0158969 | + | 0.0834252i | ||||
\(328\) | 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 | \(-0.247348\pi\) |
−0.250764 | + | 0.968048i | \(0.580682\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.5412 | − | 9.30973i | −1.29005 | − | 0.510170i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.67802 | + | 4.63847i | −0.146316 | + | 0.253427i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.87607 | − | 4.98150i | −0.156669 | − | 0.271360i | 0.776996 | − | 0.629505i | \(-0.216742\pi\) |
−0.933666 | + | 0.358146i | \(0.883409\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.947894 | − | 2.72023i | −0.0514825 | − | 0.147743i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.330372i | 0.0178906i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.7531i | 0.796590i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.73699 | + | 6.64905i | −0.308869 | + | 0.357973i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.6350 | − | 21.8845i | −0.678283 | − | 1.17482i | −0.975498 | − | 0.220010i | \(-0.929391\pi\) |
0.297214 | − | 0.954811i | \(-0.403942\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.61543 | − | 2.79802i | 0.0864722 | − | 0.149774i | −0.819545 | − | 0.573014i | \(-0.805774\pi\) |
0.906018 | + | 0.423240i | \(0.139107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.6194 | + | 1.14101i | 1.47421 | + | 0.0609026i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.5683 | − | 11.8751i | −1.09474 | − | 0.632047i | −0.159904 | − | 0.987133i | \(-0.551118\pi\) |
−0.934834 | + | 0.355086i | \(0.884452\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.53168 | + | 0.884317i | −0.0812932 | + | 0.0469347i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.4840 | − | 14.2229i | −0.872426 | − | 0.752753i | ||||
\(358\) | 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 | ||||||||
\(363\) | −13.8018 | + | 4.80938i | −0.724406 | + | 0.252427i | ||||
\(364\) | 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 | \(-0.564048\pi\) |
−0.948482 | + | 0.316830i | \(0.897382\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.9697 | + | 4.14163i | −1.45604 | + | 0.215605i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.5303 | − | 23.4352i | 0.702460 | − | 1.21670i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.9237 | + | 22.3844i | 0.669161 | + | 1.15902i | 0.978139 | + | 0.207952i | \(0.0666798\pi\) |
−0.308978 | + | 0.951069i | \(0.599987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.5792 | − | 3.92143i | −1.06270 | − | 0.202502i | ||||
\(376\) | 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 | ||||||||
\(381\) | −13.4878 | − | 2.57015i | −0.691003 | − | 0.131673i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.07378 | + | 5.32394i | 0.157063 | + | 0.272041i | 0.933808 | − | 0.357774i | \(-0.116464\pi\) |
−0.776745 | + | 0.629815i | \(0.783131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9276 | − | 22.3912i | 0.658850 | − | 1.14116i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.9081 | + | 13.7513i | 0.554492 | + | 0.699020i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.1730 | + | 14.5336i | 1.27632 | + | 0.736885i | 0.976170 | − | 0.217006i | \(-0.0696292\pi\) |
0.300152 | + | 0.953891i | \(0.402963\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.41193 | + | 5.43398i | −0.475982 | + | 0.274808i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.0427 | + | 6.28717i | −0.910134 | + | 0.317146i | ||||
\(394\) | 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 | ||||||||
\(399\) | 18.4577 | + | 15.9258i | 0.924040 | + | 0.797288i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.93722 | + | 4.00521i | −0.346428 | + | 0.200011i | −0.663111 | − | 0.748521i | \(-0.730764\pi\) |
0.316683 | + | 0.948532i | \(0.397431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.345228 | + | 0.199317i | 0.0171970 | + | 0.00992870i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.0249 | − | 3.97880i | −0.845973 | − | 0.197708i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.6020 | − | 32.2196i | 0.922068 | − | 1.59707i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.61851 | + | 7.99949i | 0.228370 | + | 0.395549i | 0.957325 | − | 0.289013i | \(-0.0933269\pi\) |
−0.728955 | + | 0.684562i | \(0.759994\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.132628 | − | 0.153713i | 0.00654205 | − | 0.00758210i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.5610i | 0.519673i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 33.4735i | − | 1.64315i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.99560 | − | 5.72691i | −0.0977252 | − | 0.280448i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.96784 | − | 8.60455i | −0.242695 | − | 0.420360i | 0.718786 | − | 0.695231i | \(-0.244698\pi\) |
−0.961481 | + | 0.274871i | \(0.911365\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7911 | − | 25.6190i | 0.720876 | − | 1.24859i | −0.239774 | − | 0.970829i | \(-0.577073\pi\) |
0.960649 | − | 0.277764i | \(-0.0895934\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.2992 | + | 8.96298i | −0.549385 | + | 0.435795i | ||||
\(424\) | 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 | ||||||||
\(429\) | −7.60439 | + | 39.9069i | −0.367143 | + | 1.92672i | ||||
\(430\) | 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 | ||||||||
\(435\) | −0.826126 | + | 4.33541i | −0.0396097 | + | 0.207867i | ||||
\(436\) | 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 | \(-0.315927\pi\) |
−0.451919 | + | 0.892059i | \(0.649261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.928465 | − | 6.27021i | −0.0442126 | − | 0.298581i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.3819 | + | 21.4461i | −0.588283 | + | 1.01894i | 0.406174 | + | 0.913796i | \(0.366863\pi\) |
−0.994457 | + | 0.105141i | \(0.966471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.70703 | + | 15.0810i | 0.412753 | + | 0.714909i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.92112 | − | 5.51316i | −0.0908660 | − | 0.260764i | ||||
\(448\) | 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 | ||||||||
\(453\) | 12.5037 | − | 14.4915i | 0.587476 | − | 0.680872i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.5987 | − | 27.0178i | −0.731279 | − | 1.26661i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.09417 | − | 15.7516i | 0.425408 | − | 0.736827i | −0.571051 | − | 0.820915i | \(-0.693464\pi\) |
0.996458 | + | 0.0840872i | \(0.0267974\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.2753 | − | 11.5825i | −0.853018 | − | 0.540625i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.3019 | + | 17.4948i | 1.41130 | + | 0.814813i | 0.995511 | − | 0.0946485i | \(-0.0301727\pi\) |
0.415787 | + | 0.909462i | \(0.363506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9627 | − | 8.06138i | 0.648903 | − | 0.374644i | −0.139133 | − | 0.990274i | \(-0.544432\pi\) |
0.788036 | + | 0.615630i | \(0.211098\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.190893 | − | 0.164708i | −0.00885246 | − | 0.00763815i | ||||
\(466\) | 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 | ||||||||
\(471\) | −6.02435 | + | 2.09925i | −0.277587 | + | 0.0967283i | ||||
\(472\) | 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 | ||||||||
\(477\) | 9.88982 | − | 25.0080i | 0.452824 | − | 1.14504i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.745307 | − | 1.29091i | 0.0340539 | − | 0.0589832i | −0.848496 | − | 0.529202i | \(-0.822492\pi\) |
0.882550 | + | 0.470218i | \(0.155825\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.4457 | − | 38.8770i | −1.02343 | − | 1.77264i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.4055 | − | 2.55447i | −0.609974 | − | 0.116232i | ||||
\(484\) | 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 | ||||||||
\(489\) | 2.37814 | + | 0.453163i | 0.107543 | + | 0.0204927i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.02050 | + | 10.4278i | 0.271701 | + | 0.470601i | 0.969298 | − | 0.245891i | \(-0.0790804\pi\) |
−0.697596 | + | 0.716491i | \(0.745747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.73088 | + | 4.73002i | −0.122992 | + | 0.213029i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.44924 | − | 23.8939i | 0.424712 | − | 1.07395i | ||||
\(496\) | 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 | \(-0.715765\pi\) |
0.361010 | + | 0.932562i | \(0.382432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.2686 | + | 6.71437i | −0.860860 | + | 0.299976i | ||||
\(502\) | 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 | ||||||||
\(507\) | 20.0657 | + | 17.3133i | 0.891149 | + | 0.768909i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.1369 | + | 6.42991i | −0.493635 | + | 0.285001i | −0.726081 | − | 0.687609i | \(-0.758660\pi\) |
0.232446 | + | 0.972609i | \(0.425327\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.9416 | − | 10.3586i | −0.793688 | − | 0.458236i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.4635 | + | 12.9693i | 0.903484 | + | 0.572609i | ||||
\(514\) | 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 | ||||||||
\(519\) | −9.29125 | + | 10.7684i | −0.407841 | + | 0.472679i | ||||
\(520\) | 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 | ||||||||
\(525\) | −2.10969 | − | 6.05432i | −0.0920746 | − | 0.264232i | ||||
\(526\) | 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 | ||||||||
\(531\) | 1.53735 | + | 10.3822i | 0.0667152 | + | 0.450549i | ||||
\(532\) | 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 | ||||||||
\(537\) | −4.27561 | + | 22.4379i | −0.184506 | + | 0.968266i | ||||
\(538\) | 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 | ||||||||
\(543\) | −1.94074 | + | 10.1848i | −0.0832852 | + | 0.437071i | ||||
\(544\) | 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 | \(-0.302684\pi\) |
−0.414424 | + | 0.910084i | \(0.636017\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −29.7198 | + | 23.5750i | −1.26841 | + | 1.00616i | ||||
\(550\) | 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 | ||||||||
\(555\) | 9.34283 | + | 26.8117i | 0.396581 | + | 1.13809i | ||||
\(556\) | 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 | ||||||||
\(561\) | 20.7725 | − | 24.0749i | 0.877018 | − | 1.01645i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.37475 | + | 14.5055i | 0.352954 | + | 0.611334i | 0.986766 | − | 0.162153i | \(-0.0518439\pi\) |
−0.633812 | + | 0.773487i | \(0.718511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.61543 | + | 2.79802i | −0.0679619 | + | 0.117713i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.87342 | − | 26.0029i | −0.330653 | − | 1.09202i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.7647 | + | 20.0714i | 1.45741 | + | 0.841437i | 0.998883 | − | 0.0472425i | \(-0.0150433\pi\) |
0.458529 | + | 0.888680i | \(0.348377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.5848 | + | 21.6996i | −1.57288 | + | 0.908101i | −0.577062 | + | 0.816700i | \(0.695801\pi\) |
−0.995814 | + | 0.0914001i | \(0.970866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.3198 | + | 11.4927i | 0.556441 | + | 0.480113i | ||||
\(574\) | 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 | ||||||||
\(579\) | 22.2862 | − | 7.76588i | 0.926184 | − | 0.322739i | ||||
\(580\) | 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 | ||||||||
\(585\) | −19.2676 | − | 24.2897i | −0.796616 | − | 1.00425i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.1493 | − | 26.2394i | 0.625279 | − | 1.08301i | −0.363208 | − | 0.931708i | \(-0.618319\pi\) |
0.988487 | − | 0.151306i | \(-0.0483480\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.174688 | + | 0.302569i | 0.00719791 | + | 0.0124671i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.62478 | + | 1.83403i | 0.395910 | + | 0.0754420i | ||||
\(592\) | 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 | ||||||||
\(597\) | 23.7061 | + | 4.51726i | 0.970225 | + | 0.184879i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.29720 | + | 12.6391i | 0.298156 | + | 0.516421i | 0.975714 | − | 0.219048i | \(-0.0702952\pi\) |
−0.677558 | + | 0.735469i | \(0.736962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.343128 | − | 0.594315i | 0.0139965 | − | 0.0242426i | −0.858942 | − | 0.512072i | \(-0.828878\pi\) |
0.872939 | + | 0.487830i | \(0.162211\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.18214 | + | 1.21157i | −0.333202 | + | 0.0493391i | ||||
\(604\) | 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 | \(-0.818664\pi\) |
0.0460679 | + | 0.998938i | \(0.485331\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.47632 | + | 2.25674i | −0.262434 | + | 0.0914479i | ||||
\(610\) | 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 | ||||||||
\(615\) | 24.0101 | + | 20.7166i | 0.968181 | + | 0.835374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.96274 | + | 4.59729i | −0.320568 | + | 0.185080i | −0.651646 | − | 0.758524i | \(-0.725921\pi\) |
0.331078 | + | 0.943603i | \(0.392588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5675 | + | 9.56526i | 0.665905 | + | 0.384460i | 0.794523 | − | 0.607234i | \(-0.207721\pi\) |
−0.128618 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.5504 | − | 0.559794i | −0.543760 | − | 0.0224638i | ||||
\(622\) | 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 | ||||||||
\(627\) | −23.2597 | + | 26.9575i | −0.928903 | + | 1.07658i | ||||
\(628\) | 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 | ||||||||
\(633\) | −3.11025 | − | 8.92568i | −0.123621 | − | 0.354764i | ||||
\(634\) | 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 | ||||||||
\(639\) | −2.53990 | − | 1.00444i | −0.100477 | − | 0.0397352i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.62226 | − | 1.51396i | −0.103573 | − | 0.0597978i | 0.447319 | − | 0.894375i | \(-0.352379\pi\) |
−0.550892 | + | 0.834577i | \(0.685712\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.77000 | + | 2.75396i | −0.188110 | + | 0.108606i | −0.591098 | − | 0.806600i | \(-0.701305\pi\) |
0.402987 | + | 0.915206i | \(0.367972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.68499 | − | 19.3384i | 0.145096 | − | 0.761448i | ||||
\(646\) | 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 | ||||||||
\(651\) | 0.0733384 | − | 0.384871i | 0.00287436 | − | 0.0150843i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.0192 | + | 19.6410i | −1.33127 | + | 0.768611i | −0.985495 | − | 0.169705i | \(-0.945719\pi\) |
−0.345779 | + | 0.938316i | \(0.612385\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.5586 | + | 10.7148i | 0.725146 | + | 0.418663i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.1457 | − | 7.57146i | −0.746944 | − | 0.295391i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.48091 | + | 7.76116i | −0.174551 | + | 0.302332i | −0.940006 | − | 0.341158i | \(-0.889181\pi\) |
0.765454 | + | 0.643490i | \(0.222514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.44282 | + | 5.96314i | 0.133910 | + | 0.231939i | 0.925181 | − | 0.379527i | \(-0.123913\pi\) |
−0.791270 | + | 0.611466i | \(0.790580\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.6252 | − | 36.2314i | −0.490323 | − | 1.40711i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 27.3425i | − | 1.06030i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.42347i | 0.132557i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.9054 | − | 14.9571i | 0.498952 | − | 0.578276i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.8751 | − | 48.2811i | −1.07611 | − | 1.86387i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.5054 | + | 18.1959i | −0.404954 | + | 0.701401i | −0.994316 | − | 0.106468i | \(-0.966046\pi\) |
0.589362 | + | 0.807869i | \(0.299379\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.95529 | − | 5.64471i | −0.113749 | − | 0.217265i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.85645 | − | 3.95858i | −0.263515 | − | 0.152140i | 0.362422 | − | 0.932014i | \(-0.381950\pi\) |
−0.625937 | + | 0.779874i | \(0.715283\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 47.2620 | − | 27.2868i | 1.81375 | − | 1.04717i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35.2680 | + | 30.4302i | 1.35147 | + | 1.16609i | ||||
\(682\) | 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 | ||||||||
\(687\) | −5.10061 | + | 1.77736i | −0.194600 | + | 0.0678106i | ||||
\(688\) | 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 | \(-0.218596\pi\) |
−0.162420 | + | 0.986722i | \(0.551930\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 39.4974 | − | 5.84861i | 1.50038 | − | 0.222170i | ||||
\(694\) | 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 | ||||||||
\(699\) | −6.50029 | − | 1.23865i | −0.245864 | − | 0.0468501i | ||||
\(700\) | 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 | ||||||||
\(705\) | 15.8899 | + | 3.02788i | 0.598450 | + | 0.114037i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.4705 | + | 19.8674i | 0.431391 | + | 0.747192i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.89832 | − | 10.2162i | 0.221516 | − | 0.383677i | −0.733753 | − | 0.679417i | \(-0.762233\pi\) |
0.955268 | + | 0.295740i | \(0.0955662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.4257 | + | 29.5316i | 0.878532 | + | 1.10752i | ||||
\(712\) | 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 | ||||||||
\(717\) | 33.5925 | − | 11.7057i | 1.25453 | − | 0.437156i | ||||
\(718\) | 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 | ||||||||
\(723\) | −27.3455 | − | 23.5945i | −1.01699 | − | 0.877488i | ||||
\(724\) | 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 | \(-0.413341\pi\) |
−0.699681 | + | 0.714455i | \(0.746675\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.5253 | − | 24.4165i | −0.426864 | − | 0.904316i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.1813 | − | 21.0986i | 0.450540 | − | 0.780358i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.97824 | + | 6.89052i | 0.146940 | + | 0.254507i | 0.930095 | − | 0.367319i | \(-0.119724\pi\) |
−0.783155 | + | 0.621826i | \(0.786391\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.64422 | + | 5.38256i | −0.171305 | + | 0.198539i | ||||
\(736\) | 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 | ||||||||
\(741\) | 14.1369 | + | 40.5695i | 0.519331 | + | 1.49036i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.7656 | + | 46.3594i | 0.981934 | + | 1.70076i | 0.654839 | + | 0.755768i | \(0.272736\pi\) |
0.327095 | + | 0.944992i | \(0.393930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.27404 | + | 5.67081i | −0.119952 | + | 0.207762i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.4987 | − | 32.1253i | 1.48177 | − | 1.17540i | ||||
\(748\) | 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 | \(-0.893984\pi\) |
−0.189388 | + | 0.981902i | \(0.560650\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.27872 | − | 11.9584i | 0.0830411 | − | 0.435790i | ||||
\(754\) | 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 | ||||||||
\(759\) | 3.73081 | − | 19.5789i | 0.135420 | − | 0.710668i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.5944 | − | 7.27140i | 0.456548 | − | 0.263588i | −0.254044 | − | 0.967193i | \(-0.581761\pi\) |
0.710592 | + | 0.703605i | \(0.248427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.31800 | + | 1.33830i | 0.0839172 | + | 0.0484496i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.55460 | + | 24.0053i | 0.128517 | + | 0.867914i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.30572 | + | 16.1180i | −0.336010 | + | 0.581987i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.545353 | + | 0.944579i | 0.0196659 | + | 0.0340624i | 0.875691 | − | 0.482872i | \(-0.160406\pi\) |
−0.856025 | + | 0.516934i | \(0.827073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.71763 | − | 25.0175i | −0.313958 | − | 0.900984i | ||||
\(772\) | 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 | ||||||||
\(777\) | −28.8231 | + | 33.4053i | −1.03402 | + | 1.19841i | ||||
\(778\) | 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 | ||||||||
\(783\) | −6.03816 | + | 3.16128i | −0.215786 | + | 0.112975i | ||||
\(784\) | 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 | \(-0.667159\pi\) |
0.498660 | + | 0.866798i | \(0.333826\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.4118 | − | 9.84645i | −0.406272 | − | 0.350543i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.02062 | −0.178513 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −67.2697 | −2.38882 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.4823 | + | 9.92498i | −1.01016 | + | 0.352003i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.88596 | − | 2.24356i | 0.137648 | − | 0.0794710i | −0.429595 | − | 0.903022i | \(-0.641344\pi\) |
0.567242 | + | 0.823551i | \(0.308010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.3362 | + | 10.0091i | 0.613312 | + | 0.354096i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.88982 | + | 25.0080i | −0.349440 | + | 0.883615i | ||||
\(802\) | 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 | ||||||||
\(807\) | −15.5697 | − | 2.96685i | −0.548078 | − | 0.104438i | ||||
\(808\) | 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 | ||||||||
\(813\) | −6.55076 | − | 1.24827i | −0.229745 | − | 0.0437786i | ||||
\(814\) | 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 | ||||||||
\(819\) | 17.7177 | − | 44.8021i | 0.619106 | − | 1.56551i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.1380 | − | 22.0190i | −1.33102 | − | 0.768467i | −0.345567 | − | 0.938394i | \(-0.612314\pi\) |
−0.985457 | + | 0.169927i | \(0.945647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.3847 | + | 21.5841i | −1.30315 | + | 0.752373i | −0.980943 | − | 0.194297i | \(-0.937757\pi\) |
−0.322205 | + | 0.946670i | \(0.604424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.84236 | − | 3.08122i | 0.307852 | − | 0.107274i | ||||
\(826\) | 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 | ||||||||
\(831\) | 8.73242 | + | 7.53458i | 0.302924 | + | 0.261372i | ||||
\(832\) | 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 | ||||||||
\(837\) | 0.0160716 | − | 0.389031i | 0.000555516 | − | 0.0134469i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.6704 | + | 35.8022i | −0.713622 | + | 1.23603i | 0.249867 | + | 0.968280i | \(0.419613\pi\) |
−0.963489 | + | 0.267749i | \(0.913720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.6398 | − | 23.6248i | −0.470336 | − | 0.814647i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.9976 | − | 19.6999i | 0.585430 | − | 0.678501i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 29.7245i | − | 1.02255i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.4734i | 0.875277i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.68847 | − | 27.8036i | −0.332508 | − | 0.954218i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.0121 | + | 19.0736i | 0.377491 | + | 0.653834i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.39474 | − | 7.61191i | 0.150473 | − | 0.260627i | −0.780928 | − | 0.624620i | \(-0.785254\pi\) |
0.931401 | + | 0.363994i | \(0.118587\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.98020 | − | 26.8795i | −0.136120 | − | 0.919261i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.5978 | − | 16.5109i | −0.976881 | − | 0.564003i | −0.0755543 | − | 0.997142i | \(-0.524073\pi\) |
−0.901327 | + | 0.433139i | \(0.857406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.0192 | − | 9.82606i | 0.580689 | − | 0.335261i | −0.180718 | − | 0.983535i | \(-0.557842\pi\) |
0.761407 | + | 0.648274i | \(0.224509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.22434 | + | 48.4083i | −0.314365 | + | 1.64975i | ||||
\(862\) | 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 | ||||||||
\(867\) | −0.109768 | + | 0.576050i | −0.00372792 | + | 0.0195637i | ||||
\(868\) | 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 | ||||||||
\(873\) | 42.4898 | − | 33.7046i | 1.43806 | − | 1.14073i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.2562 | + | 31.6206i | −0.617172 | + | 1.06897i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5243 | − | 30.3531i | −0.591755 | − | 1.02495i | −0.993996 | − | 0.109416i | \(-0.965102\pi\) |
0.402241 | − | 0.915534i | \(-0.368231\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.35177 | − | 9.61879i | −0.113052 | − | 0.324434i | ||||
\(880\) | 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 | ||||||||
\(885\) | 7.68988 | − | 8.91241i | 0.258493 | − | 0.299588i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6506 | − | 23.6436i | −0.458343 | − | 0.793873i | 0.540531 | − | 0.841324i | \(-0.318223\pi\) |
−0.998874 | + | 0.0474512i | \(0.984890\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.9653 | + | 20.7245i | −0.401304 | + | 0.695078i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 37.9774 | − | 11.4992i | 1.27229 | − | 0.385237i | ||||
\(892\) | 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 | ||||||||
\(897\) | −18.2084 | − | 15.7108i | −0.607962 | − | 0.524567i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.0982874 | −0.00327807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.3265 | −1.24353 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.8881 | − | 10.0664i | 0.961334 | − | 0.334987i | ||||
\(904\) | 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 | \(-0.439532\pi\) |
−0.756034 | + | 0.654532i | \(0.772865\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.1683 | + | 17.8613i | 0.469934 | + | 0.592423i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.0924 | − | 29.6049i | 0.566296 | − | 0.980854i | −0.430632 | − | 0.902528i | \(-0.641709\pi\) |
0.996928 | − | 0.0783259i | \(-0.0249575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.9850 | + | 65.7919i | 1.25712 | + | 2.17739i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.7947 | + | 7.96412i | 1.38169 | + | 0.263286i | ||||
\(916\) | 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 | ||||||||
\(921\) | −12.1056 | − | 2.30676i | −0.398893 | − | 0.0760104i | ||||
\(922\) | 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 | ||||||||
\(927\) | −46.4689 | + | 6.88091i | −1.52624 | + | 0.225999i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.4859 | − | 15.8690i | −0.901784 | − | 0.520645i | −0.0240056 | − | 0.999712i | \(-0.507642\pi\) |
−0.877779 | + | 0.479066i | \(0.840975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.53144 | − | 4.92563i | 0.279607 | − | 0.161431i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.4586 | − | 13.4013i | 1.25908 | − | 0.438740i | ||||
\(934\) | 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 | ||||||||
\(939\) | −15.8574 | − | 13.6823i | −0.517488 | − | 0.446503i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.0527 | + | 13.8868i | −0.784095 | + | 0.452697i | −0.837880 | − | 0.545855i | \(-0.816205\pi\) |
0.0537847 | + | 0.998553i | \(0.482872\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.3034 | + | 12.2995i | 0.693734 | + | 0.400527i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.3122 | + | 25.7380i | −0.530636 | + | 0.837257i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.4561 | − | 19.8426i | 0.372273 | − | 0.644796i | −0.617641 | − | 0.786460i | \(-0.711912\pi\) |
0.989915 | + | 0.141663i | \(0.0452450\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.2547 | − | 31.6181i | −0.592573 | − | 1.02637i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.7595 | − | 22.9008i | 0.640744 | − | 0.742610i | ||||
\(952\) | 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 | ||||||||
\(957\) | −3.29599 | − | 9.45869i | −0.106544 | − | 0.305756i | ||||
\(958\) | 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 | ||||||||
\(963\) | −23.7438 | − | 9.38987i | −0.765134 | − | 0.302584i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.9235 | − | 13.2349i | −0.737933 | − | 0.426046i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.6181 | − | 28.6470i | 1.59561 | − | 0.921227i | 0.603293 | − | 0.797519i | \(-0.293855\pi\) |
0.992319 | − | 0.123708i | \(-0.0394785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.29448 | − | 33.0327i | 0.202208 | − | 1.06116i | ||||
\(970\) | 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 | ||||||||
\(975\) | 2.11493 | − | 11.0989i | 0.0677321 | − | 0.355450i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.8129 | − | 20.6766i | 1.14576 | − | 0.661504i | 0.197908 | − | 0.980221i | \(-0.436585\pi\) |
0.947850 | + | 0.318717i | \(0.103252\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.2272 | − | 19.7611i | −1.09391 | − | 0.631568i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.47357 | + | 0.978211i | 0.0789749 | + | 0.0312319i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.9396 | + | 39.7326i | −0.731661 | + | 1.26727i | 0.224512 | + | 0.974471i | \(0.427921\pi\) |
−0.956173 | + | 0.292802i | \(0.905412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.49458 | − | 9.51689i | −0.175072 | − | 0.303233i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.27131 | + | 23.7367i | 0.263279 | + | 0.755548i | ||||
\(988\) | 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 | ||||||||
\(993\) | 10.9869 | − | 12.7336i | 0.348658 | − | 0.404087i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.5333 | − | 23.4403i | −0.429034 | − | 0.743108i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.03515 | − | 15.6493i | 0.286146 | − | 0.495620i | −0.686740 | − | 0.726903i | \(-0.740959\pi\) |
0.972886 | + | 0.231283i | \(0.0742924\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.4723 | + | 37.0355i | −0.742631 | + | 1.17175i |
(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 | 288.2.s.a.191.7 | yes | 24 | |
3.2 | odd | 2 | 864.2.s.a.575.9 | 24 | |||
4.3 | odd | 2 | inner | 288.2.s.a.191.6 | yes | 24 | |
8.3 | odd | 2 | 576.2.s.g.191.7 | 24 | |||
8.5 | even | 2 | 576.2.s.g.191.6 | 24 | |||
9.2 | odd | 6 | 2592.2.c.c.2591.18 | 24 | |||
9.4 | even | 3 | 864.2.s.a.287.10 | 24 | |||
9.5 | odd | 6 | inner | 288.2.s.a.95.6 | ✓ | 24 | |
9.7 | even | 3 | 2592.2.c.c.2591.8 | 24 | |||
12.11 | even | 2 | 864.2.s.a.575.10 | 24 | |||
24.5 | odd | 2 | 1728.2.s.g.575.3 | 24 | |||
24.11 | even | 2 | 1728.2.s.g.575.4 | 24 | |||
36.7 | odd | 6 | 2592.2.c.c.2591.7 | 24 | |||
36.11 | even | 6 | 2592.2.c.c.2591.17 | 24 | |||
36.23 | even | 6 | inner | 288.2.s.a.95.7 | yes | 24 | |
36.31 | odd | 6 | 864.2.s.a.287.9 | 24 | |||
72.5 | odd | 6 | 576.2.s.g.383.7 | 24 | |||
72.11 | even | 6 | 5184.2.c.m.5183.7 | 24 | |||
72.13 | even | 6 | 1728.2.s.g.1151.4 | 24 | |||
72.29 | odd | 6 | 5184.2.c.m.5183.8 | 24 | |||
72.43 | odd | 6 | 5184.2.c.m.5183.17 | 24 | |||
72.59 | even | 6 | 576.2.s.g.383.6 | 24 | |||
72.61 | even | 6 | 5184.2.c.m.5183.18 | 24 | |||
72.67 | odd | 6 | 1728.2.s.g.1151.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.s.a.95.6 | ✓ | 24 | 9.5 | odd | 6 | inner | |
288.2.s.a.95.7 | yes | 24 | 36.23 | even | 6 | inner | |
288.2.s.a.191.6 | yes | 24 | 4.3 | odd | 2 | inner | |
288.2.s.a.191.7 | yes | 24 | 1.1 | even | 1 | trivial | |
576.2.s.g.191.6 | 24 | 8.5 | even | 2 | |||
576.2.s.g.191.7 | 24 | 8.3 | odd | 2 | |||
576.2.s.g.383.6 | 24 | 72.59 | even | 6 | |||
576.2.s.g.383.7 | 24 | 72.5 | odd | 6 | |||
864.2.s.a.287.9 | 24 | 36.31 | odd | 6 | |||
864.2.s.a.287.10 | 24 | 9.4 | even | 3 | |||
864.2.s.a.575.9 | 24 | 3.2 | odd | 2 | |||
864.2.s.a.575.10 | 24 | 12.11 | even | 2 | |||
1728.2.s.g.575.3 | 24 | 24.5 | odd | 2 | |||
1728.2.s.g.575.4 | 24 | 24.11 | even | 2 | |||
1728.2.s.g.1151.3 | 24 | 72.67 | odd | 6 | |||
1728.2.s.g.1151.4 | 24 | 72.13 | even | 6 | |||
2592.2.c.c.2591.7 | 24 | 36.7 | odd | 6 | |||
2592.2.c.c.2591.8 | 24 | 9.7 | even | 3 | |||
2592.2.c.c.2591.17 | 24 | 36.11 | even | 6 | |||
2592.2.c.c.2591.18 | 24 | 9.2 | odd | 6 | |||
5184.2.c.m.5183.7 | 24 | 72.11 | even | 6 | |||
5184.2.c.m.5183.8 | 24 | 72.29 | odd | 6 | |||
5184.2.c.m.5183.17 | 24 | 72.43 | odd | 6 | |||
5184.2.c.m.5183.18 | 24 | 72.61 | even | 6 |