Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(66.1241179138\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1183) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36142 | −0.962672 | −0.481336 | − | 0.876536i | \(-0.659848\pi\) | ||||
−0.481336 | + | 0.876536i | \(0.659848\pi\) | |||||||
\(3\) | −1.31293 | −0.758020 | −0.379010 | − | 0.925393i | \(-0.623735\pi\) | ||||
−0.379010 | + | 0.925393i | \(0.623735\pi\) | |||||||
\(4\) | −0.146524 | −0.0732621 | ||||||||
\(5\) | −3.05867 | −1.36788 | −0.683939 | − | 0.729539i | \(-0.739735\pi\) | ||||
−0.683939 | + | 0.729539i | \(0.739735\pi\) | |||||||
\(6\) | 1.78745 | 0.729725 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.92233 | 1.03320 | ||||||||
\(9\) | −1.27622 | −0.425405 | ||||||||
\(10\) | 4.16415 | 1.31682 | ||||||||
\(11\) | 1.55093 | 0.467623 | 0.233812 | − | 0.972282i | \(-0.424880\pi\) | ||||
0.233812 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(12\) | 0.192376 | 0.0555342 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.01582 | 1.03688 | ||||||||
\(16\) | −3.68548 | −0.921371 | ||||||||
\(17\) | 5.82376 | 1.41247 | 0.706235 | − | 0.707977i | \(-0.250392\pi\) | ||||
0.706235 | + | 0.707977i | \(0.250392\pi\) | |||||||
\(18\) | 1.73747 | 0.409526 | ||||||||
\(19\) | 1.44521 | 0.331554 | 0.165777 | − | 0.986163i | \(-0.446987\pi\) | ||||
0.165777 | + | 0.986163i | \(0.446987\pi\) | |||||||
\(20\) | 0.448169 | 0.100214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.11147 | −0.450168 | ||||||||
\(23\) | 6.27773 | 1.30900 | 0.654498 | − | 0.756063i | \(-0.272880\pi\) | ||||
0.654498 | + | 0.756063i | \(0.272880\pi\) | |||||||
\(24\) | −3.83681 | −0.783186 | ||||||||
\(25\) | 4.35546 | 0.871092 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61437 | 1.08049 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.88196 | −1.83503 | −0.917517 | − | 0.397698i | \(-0.869809\pi\) | ||||
−0.917517 | + | 0.397698i | \(0.869809\pi\) | |||||||
\(30\) | −5.46723 | −0.998176 | ||||||||
\(31\) | 1.52667 | 0.274199 | 0.137099 | − | 0.990557i | \(-0.456222\pi\) | ||||
0.137099 | + | 0.990557i | \(0.456222\pi\) | |||||||
\(32\) | −0.827155 | −0.146222 | ||||||||
\(33\) | −2.03626 | −0.354468 | ||||||||
\(34\) | −7.92861 | −1.35975 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.186996 | 0.0311661 | ||||||||
\(37\) | 7.75148 | 1.27434 | 0.637168 | − | 0.770725i | \(-0.280106\pi\) | ||||
0.637168 | + | 0.770725i | \(0.280106\pi\) | |||||||
\(38\) | −1.96754 | −0.319178 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.93844 | −1.41329 | ||||||||
\(41\) | 7.17386 | 1.12037 | 0.560184 | − | 0.828368i | \(-0.310730\pi\) | ||||
0.560184 | + | 0.828368i | \(0.310730\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.03082 | 0.767194 | 0.383597 | − | 0.923501i | \(-0.374685\pi\) | ||||
0.383597 | + | 0.923501i | \(0.374685\pi\) | |||||||
\(44\) | −0.227249 | −0.0342590 | ||||||||
\(45\) | 3.90352 | 0.581903 | ||||||||
\(46\) | −8.54665 | −1.26013 | ||||||||
\(47\) | 5.21844 | 0.761188 | 0.380594 | − | 0.924742i | \(-0.375720\pi\) | ||||
0.380594 | + | 0.924742i | \(0.375720\pi\) | |||||||
\(48\) | 4.83878 | 0.698418 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.92963 | −0.838576 | ||||||||
\(51\) | −7.64619 | −1.07068 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.77747 | 1.06832 | 0.534159 | − | 0.845384i | \(-0.320628\pi\) | ||||
0.534159 | + | 0.845384i | \(0.320628\pi\) | |||||||
\(54\) | −7.64354 | −1.04015 | ||||||||
\(55\) | −4.74378 | −0.639652 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.89746 | −0.251325 | ||||||||
\(58\) | 13.4535 | 1.76654 | ||||||||
\(59\) | 2.79061 | 0.363306 | 0.181653 | − | 0.983363i | \(-0.441855\pi\) | ||||
0.181653 | + | 0.983363i | \(0.441855\pi\) | |||||||
\(60\) | −0.588415 | −0.0759640 | ||||||||
\(61\) | 13.7572 | 1.76143 | 0.880714 | − | 0.473649i | \(-0.157063\pi\) | ||||
0.880714 | + | 0.473649i | \(0.157063\pi\) | |||||||
\(62\) | −2.07845 | −0.263964 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.49707 | 1.06213 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.77222 | 0.341236 | ||||||||
\(67\) | −0.683026 | −0.0834449 | −0.0417225 | − | 0.999129i | \(-0.513285\pi\) | ||||
−0.0417225 | + | 0.999129i | \(0.513285\pi\) | |||||||
\(68\) | −0.853322 | −0.103481 | ||||||||
\(69\) | −8.24222 | −0.992246 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.582838 | −0.0691702 | −0.0345851 | − | 0.999402i | \(-0.511011\pi\) | ||||
−0.0345851 | + | 0.999402i | \(0.511011\pi\) | |||||||
\(72\) | −3.72952 | −0.439529 | ||||||||
\(73\) | 4.32488 | 0.506189 | 0.253095 | − | 0.967441i | \(-0.418552\pi\) | ||||
0.253095 | + | 0.967441i | \(0.418552\pi\) | |||||||
\(74\) | −10.5531 | −1.22677 | ||||||||
\(75\) | −5.71842 | −0.660306 | ||||||||
\(76\) | −0.211758 | −0.0242903 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.41818 | 0.722102 | 0.361051 | − | 0.932546i | \(-0.382418\pi\) | ||||
0.361051 | + | 0.932546i | \(0.382418\pi\) | |||||||
\(80\) | 11.2727 | 1.26032 | ||||||||
\(81\) | −3.54263 | −0.393625 | ||||||||
\(82\) | −9.76667 | −1.07855 | ||||||||
\(83\) | 14.7890 | 1.62331 | 0.811653 | − | 0.584140i | \(-0.198568\pi\) | ||||
0.811653 | + | 0.584140i | \(0.198568\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.8130 | −1.93209 | ||||||||
\(86\) | −6.84909 | −0.738556 | ||||||||
\(87\) | 12.9743 | 1.39099 | ||||||||
\(88\) | 4.53233 | 0.483148 | ||||||||
\(89\) | −2.06579 | −0.218973 | −0.109487 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109487 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(90\) | −5.31435 | −0.560182 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.919839 | −0.0958999 | ||||||||
\(93\) | −2.00442 | −0.207848 | ||||||||
\(94\) | −7.10451 | −0.732774 | ||||||||
\(95\) | −4.42042 | −0.453526 | ||||||||
\(96\) | 1.08600 | 0.110839 | ||||||||
\(97\) | 5.78897 | 0.587781 | 0.293890 | − | 0.955839i | \(-0.405050\pi\) | ||||
0.293890 | + | 0.955839i | \(0.405050\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.97932 | −0.198929 | ||||||||
\(100\) | −0.638181 | −0.0638181 | ||||||||
\(101\) | −16.8223 | −1.67388 | −0.836942 | − | 0.547291i | \(-0.815659\pi\) | ||||
−0.836942 | + | 0.547291i | \(0.815659\pi\) | |||||||
\(102\) | 10.4097 | 1.03071 | ||||||||
\(103\) | −0.532797 | −0.0524980 | −0.0262490 | − | 0.999655i | \(-0.508356\pi\) | ||||
−0.0262490 | + | 0.999655i | \(0.508356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.5884 | −1.02844 | ||||||||
\(107\) | −15.6549 | −1.51341 | −0.756707 | − | 0.653754i | \(-0.773193\pi\) | ||||
−0.756707 | + | 0.653754i | \(0.773193\pi\) | |||||||
\(108\) | −0.822641 | −0.0791587 | ||||||||
\(109\) | −5.85539 | −0.560844 | −0.280422 | − | 0.959877i | \(-0.590474\pi\) | ||||
−0.280422 | + | 0.959877i | \(0.590474\pi\) | |||||||
\(110\) | 6.45830 | 0.615775 | ||||||||
\(111\) | −10.1771 | −0.965972 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.38603 | −0.600747 | −0.300373 | − | 0.953822i | \(-0.597111\pi\) | ||||
−0.300373 | + | 0.953822i | \(0.597111\pi\) | |||||||
\(114\) | 2.58325 | 0.241943 | ||||||||
\(115\) | −19.2015 | −1.79055 | ||||||||
\(116\) | 1.44795 | 0.134438 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.79920 | −0.349745 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 11.7355 | 1.07130 | ||||||||
\(121\) | −8.59462 | −0.781329 | ||||||||
\(122\) | −18.7294 | −1.69568 | ||||||||
\(123\) | −9.41877 | −0.849262 | ||||||||
\(124\) | −0.223695 | −0.0200884 | ||||||||
\(125\) | 1.97143 | 0.176330 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.2760 | −1.35552 | −0.677762 | − | 0.735281i | \(-0.737050\pi\) | ||||
−0.677762 | + | 0.735281i | \(0.737050\pi\) | |||||||
\(128\) | −9.91381 | −0.876265 | ||||||||
\(129\) | −6.60512 | −0.581548 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.60251 | −0.751605 | −0.375802 | − | 0.926700i | \(-0.622633\pi\) | ||||
−0.375802 | + | 0.926700i | \(0.622633\pi\) | |||||||
\(132\) | 0.298362 | 0.0259691 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.929889 | 0.0803301 | ||||||||
\(135\) | −17.1725 | −1.47797 | ||||||||
\(136\) | 17.0190 | 1.45936 | ||||||||
\(137\) | 8.80304 | 0.752094 | 0.376047 | − | 0.926601i | \(-0.377283\pi\) | ||||
0.376047 | + | 0.926601i | \(0.377283\pi\) | |||||||
\(138\) | 11.2212 | 0.955208 | ||||||||
\(139\) | −9.68708 | −0.821647 | −0.410824 | − | 0.911715i | \(-0.634759\pi\) | ||||
−0.410824 | + | 0.911715i | \(0.634759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.85145 | −0.576996 | ||||||||
\(142\) | 0.793490 | 0.0665882 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.70347 | 0.391956 | ||||||||
\(145\) | 30.2256 | 2.51010 | ||||||||
\(146\) | −5.88800 | −0.487295 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.13578 | −0.0933605 | ||||||||
\(149\) | 0.447444 | 0.0366561 | 0.0183280 | − | 0.999832i | \(-0.494166\pi\) | ||||
0.0183280 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(150\) | 7.78519 | 0.635658 | ||||||||
\(151\) | −14.2769 | −1.16184 | −0.580918 | − | 0.813962i | \(-0.697306\pi\) | ||||
−0.580918 | + | 0.813962i | \(0.697306\pi\) | |||||||
\(152\) | 4.22338 | 0.342561 | ||||||||
\(153\) | −7.43238 | −0.600872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.66959 | −0.375071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.97329 | 0.556529 | 0.278265 | − | 0.960504i | \(-0.410241\pi\) | ||||
0.278265 | + | 0.960504i | \(0.410241\pi\) | |||||||
\(158\) | −8.73787 | −0.695147 | ||||||||
\(159\) | −10.2113 | −0.809807 | ||||||||
\(160\) | 2.52999 | 0.200014 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.82302 | 0.378932 | ||||||||
\(163\) | 22.6114 | 1.77106 | 0.885530 | − | 0.464582i | \(-0.153796\pi\) | ||||
0.885530 | + | 0.464582i | \(0.153796\pi\) | |||||||
\(164\) | −1.05114 | −0.0820806 | ||||||||
\(165\) | 6.22825 | 0.484869 | ||||||||
\(166\) | −20.1341 | −1.56271 | ||||||||
\(167\) | 5.44039 | 0.420990 | 0.210495 | − | 0.977595i | \(-0.432492\pi\) | ||||
0.210495 | + | 0.977595i | \(0.432492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 24.2510 | 1.85997 | ||||||||
\(171\) | −1.84440 | −0.141045 | ||||||||
\(172\) | −0.737138 | −0.0562062 | ||||||||
\(173\) | 18.6522 | 1.41810 | 0.709049 | − | 0.705159i | \(-0.249125\pi\) | ||||
0.709049 | + | 0.705159i | \(0.249125\pi\) | |||||||
\(174\) | −17.6635 | −1.33907 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.71593 | −0.430854 | ||||||||
\(177\) | −3.66387 | −0.275393 | ||||||||
\(178\) | 2.81241 | 0.210799 | ||||||||
\(179\) | 1.43984 | 0.107618 | 0.0538092 | − | 0.998551i | \(-0.482864\pi\) | ||||
0.0538092 | + | 0.998551i | \(0.482864\pi\) | |||||||
\(180\) | −0.571960 | −0.0426314 | ||||||||
\(181\) | 1.93813 | 0.144060 | 0.0720300 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720300 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.0622 | −1.33520 | ||||||||
\(184\) | 18.3456 | 1.35246 | ||||||||
\(185\) | −23.7092 | −1.74314 | ||||||||
\(186\) | 2.72886 | 0.200090 | ||||||||
\(187\) | 9.03225 | 0.660504 | ||||||||
\(188\) | −0.764628 | −0.0557662 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.01807 | 0.436596 | ||||||||
\(191\) | 5.13781 | 0.371759 | 0.185879 | − | 0.982573i | \(-0.440487\pi\) | ||||
0.185879 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(192\) | −11.1561 | −0.805119 | ||||||||
\(193\) | −8.66938 | −0.624035 | −0.312018 | − | 0.950076i | \(-0.601005\pi\) | ||||
−0.312018 | + | 0.950076i | \(0.601005\pi\) | |||||||
\(194\) | −7.88124 | −0.565840 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.2707 | −1.23049 | −0.615243 | − | 0.788337i | \(-0.710942\pi\) | ||||
−0.615243 | + | 0.788337i | \(0.710942\pi\) | |||||||
\(198\) | 2.69470 | 0.191504 | ||||||||
\(199\) | −10.2717 | −0.728141 | −0.364071 | − | 0.931371i | \(-0.618613\pi\) | ||||
−0.364071 | + | 0.931371i | \(0.618613\pi\) | |||||||
\(200\) | 12.7281 | 0.900012 | ||||||||
\(201\) | 0.896766 | 0.0632530 | ||||||||
\(202\) | 22.9023 | 1.61140 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.12035 | 0.0784403 | ||||||||
\(205\) | −21.9425 | −1.53253 | ||||||||
\(206\) | 0.725362 | 0.0505384 | ||||||||
\(207\) | −8.01174 | −0.556854 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.24142 | 0.155042 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.7889 | −1.91307 | −0.956535 | − | 0.291618i | \(-0.905806\pi\) | ||||
−0.956535 | + | 0.291618i | \(0.905806\pi\) | |||||||
\(212\) | −1.13959 | −0.0782672 | ||||||||
\(213\) | 0.765226 | 0.0524324 | ||||||||
\(214\) | 21.3129 | 1.45692 | ||||||||
\(215\) | −15.3876 | −1.04943 | ||||||||
\(216\) | 16.4070 | 1.11636 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.97167 | 0.539909 | ||||||||
\(219\) | −5.67827 | −0.383702 | ||||||||
\(220\) | 0.695079 | 0.0468622 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 13.8554 | 0.929915 | ||||||||
\(223\) | 20.2750 | 1.35771 | 0.678856 | − | 0.734271i | \(-0.262476\pi\) | ||||
0.678856 | + | 0.734271i | \(0.262476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.55851 | −0.370567 | ||||||||
\(226\) | 8.69409 | 0.578322 | ||||||||
\(227\) | 1.79509 | 0.119144 | 0.0595720 | − | 0.998224i | \(-0.481026\pi\) | ||||
0.0595720 | + | 0.998224i | \(0.481026\pi\) | |||||||
\(228\) | 0.278024 | 0.0184126 | ||||||||
\(229\) | 4.81218 | 0.317998 | 0.158999 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.158999 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(230\) | 26.1414 | 1.72371 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −28.8783 | −1.89596 | ||||||||
\(233\) | 12.8778 | 0.843651 | 0.421826 | − | 0.906677i | \(-0.361389\pi\) | ||||
0.421826 | + | 0.906677i | \(0.361389\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.9615 | −1.04121 | ||||||||
\(236\) | −0.408891 | −0.0266166 | ||||||||
\(237\) | −8.42662 | −0.547368 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.97163 | 0.645011 | 0.322505 | − | 0.946568i | \(-0.395475\pi\) | ||||
0.322505 | + | 0.946568i | \(0.395475\pi\) | |||||||
\(240\) | −14.8002 | −0.955351 | ||||||||
\(241\) | 23.5714 | 1.51836 | 0.759182 | − | 0.650878i | \(-0.225599\pi\) | ||||
0.759182 | + | 0.650878i | \(0.225599\pi\) | |||||||
\(242\) | 11.7009 | 0.752163 | ||||||||
\(243\) | −12.1919 | −0.782110 | ||||||||
\(244\) | −2.01576 | −0.129046 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.8229 | 0.817561 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.46145 | 0.283302 | ||||||||
\(249\) | −19.4169 | −1.23050 | ||||||||
\(250\) | −2.68395 | −0.169748 | ||||||||
\(251\) | −12.5979 | −0.795175 | −0.397587 | − | 0.917564i | \(-0.630152\pi\) | ||||
−0.397587 | + | 0.917564i | \(0.630152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.73632 | 0.612117 | ||||||||
\(254\) | 20.7971 | 1.30493 | ||||||||
\(255\) | 23.3872 | 1.46456 | ||||||||
\(256\) | −3.49724 | −0.218578 | ||||||||
\(257\) | −5.97339 | −0.372610 | −0.186305 | − | 0.982492i | \(-0.559651\pi\) | ||||
−0.186305 | + | 0.982492i | \(0.559651\pi\) | |||||||
\(258\) | 8.99237 | 0.559840 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.6115 | 0.780633 | ||||||||
\(262\) | 11.7117 | 0.723549 | ||||||||
\(263\) | 29.2598 | 1.80424 | 0.902118 | − | 0.431489i | \(-0.142012\pi\) | ||||
0.902118 | + | 0.431489i | \(0.142012\pi\) | |||||||
\(264\) | −5.95063 | −0.366236 | ||||||||
\(265\) | −23.7887 | −1.46133 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.71224 | 0.165986 | ||||||||
\(268\) | 0.100080 | 0.00611335 | ||||||||
\(269\) | 3.44421 | 0.209997 | 0.104999 | − | 0.994472i | \(-0.466516\pi\) | ||||
0.104999 | + | 0.994472i | \(0.466516\pi\) | |||||||
\(270\) | 23.3791 | 1.42280 | ||||||||
\(271\) | −31.2275 | −1.89694 | −0.948468 | − | 0.316873i | \(-0.897367\pi\) | ||||
−0.948468 | + | 0.316873i | \(0.897367\pi\) | |||||||
\(272\) | −21.4634 | −1.30141 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.9847 | −0.724020 | ||||||||
\(275\) | 6.75502 | 0.407343 | ||||||||
\(276\) | 1.20768 | 0.0726940 | ||||||||
\(277\) | 23.2363 | 1.39613 | 0.698067 | − | 0.716032i | \(-0.254044\pi\) | ||||
0.698067 | + | 0.716032i | \(0.254044\pi\) | |||||||
\(278\) | 13.1882 | 0.790977 | ||||||||
\(279\) | −1.94837 | −0.116646 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.30362 | 0.316387 | 0.158194 | − | 0.987408i | \(-0.449433\pi\) | ||||
0.158194 | + | 0.987408i | \(0.449433\pi\) | |||||||
\(282\) | 9.32772 | 0.555458 | ||||||||
\(283\) | 9.79277 | 0.582120 | 0.291060 | − | 0.956705i | \(-0.405992\pi\) | ||||
0.291060 | + | 0.956705i | \(0.405992\pi\) | |||||||
\(284\) | 0.0853999 | 0.00506755 | ||||||||
\(285\) | 5.80370 | 0.343782 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.05563 | 0.0622035 | ||||||||
\(289\) | 16.9162 | 0.995072 | ||||||||
\(290\) | −41.1499 | −2.41641 | ||||||||
\(291\) | −7.60051 | −0.445550 | ||||||||
\(292\) | −0.633700 | −0.0370845 | ||||||||
\(293\) | 24.2189 | 1.41488 | 0.707441 | − | 0.706772i | \(-0.249849\pi\) | ||||
0.707441 | + | 0.706772i | \(0.249849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.53555 | −0.496959 | ||||||||
\(296\) | 22.6524 | 1.31664 | ||||||||
\(297\) | 8.70750 | 0.505260 | ||||||||
\(298\) | −0.609161 | −0.0352878 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.837886 | 0.0483754 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.4369 | 1.11847 | ||||||||
\(303\) | 22.0865 | 1.26884 | ||||||||
\(304\) | −5.32630 | −0.305484 | ||||||||
\(305\) | −42.0787 | −2.40942 | ||||||||
\(306\) | 10.1186 | 0.578443 | ||||||||
\(307\) | 6.52654 | 0.372490 | 0.186245 | − | 0.982503i | \(-0.440368\pi\) | ||||
0.186245 | + | 0.982503i | \(0.440368\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.699524 | 0.0397946 | ||||||||
\(310\) | 6.35730 | 0.361070 | ||||||||
\(311\) | −1.71314 | −0.0971430 | −0.0485715 | − | 0.998820i | \(-0.515467\pi\) | ||||
−0.0485715 | + | 0.998820i | \(0.515467\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.07898 | −0.230558 | −0.115279 | − | 0.993333i | \(-0.536776\pi\) | ||||
−0.115279 | + | 0.993333i | \(0.536776\pi\) | |||||||
\(314\) | −9.49360 | −0.535755 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.940419 | −0.0529027 | ||||||||
\(317\) | −0.497659 | −0.0279513 | −0.0139756 | − | 0.999902i | \(-0.504449\pi\) | ||||
−0.0139756 | + | 0.999902i | \(0.504449\pi\) | |||||||
\(318\) | 13.9019 | 0.779579 | ||||||||
\(319\) | −15.3262 | −0.858104 | ||||||||
\(320\) | −25.9897 | −1.45287 | ||||||||
\(321\) | 20.5538 | 1.14720 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.41656 | 0.468310 | ||||||||
\(324\) | 0.519081 | 0.0288378 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.7837 | −1.70495 | ||||||||
\(327\) | 7.68771 | 0.425131 | ||||||||
\(328\) | 20.9644 | 1.15756 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.47930 | −0.466770 | ||||||||
\(331\) | −10.0544 | −0.552638 | −0.276319 | − | 0.961066i | \(-0.589115\pi\) | ||||
−0.276319 | + | 0.961066i | \(0.589115\pi\) | |||||||
\(332\) | −2.16695 | −0.118927 | ||||||||
\(333\) | −9.89256 | −0.542109 | ||||||||
\(334\) | −7.40668 | −0.405275 | ||||||||
\(335\) | 2.08915 | 0.114143 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4206 | −1.11238 | −0.556189 | − | 0.831056i | \(-0.687737\pi\) | ||||
−0.556189 | + | 0.831056i | \(0.687737\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.38440 | 0.455378 | ||||||||
\(340\) | 2.61003 | 0.141549 | ||||||||
\(341\) | 2.36777 | 0.128222 | ||||||||
\(342\) | 2.51101 | 0.135780 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.7017 | 0.792664 | ||||||||
\(345\) | 25.2102 | 1.35727 | ||||||||
\(346\) | −25.3935 | −1.36516 | ||||||||
\(347\) | −27.3668 | −1.46912 | −0.734562 | − | 0.678541i | \(-0.762613\pi\) | ||||
−0.734562 | + | 0.678541i | \(0.762613\pi\) | |||||||
\(348\) | −1.90105 | −0.101907 | ||||||||
\(349\) | −22.2070 | −1.18871 | −0.594356 | − | 0.804202i | \(-0.702593\pi\) | ||||
−0.594356 | + | 0.804202i | \(0.702593\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.28286 | −0.0683767 | ||||||||
\(353\) | 27.8506 | 1.48234 | 0.741168 | − | 0.671319i | \(-0.234272\pi\) | ||||
0.741168 | + | 0.671319i | \(0.234272\pi\) | |||||||
\(354\) | 4.98808 | 0.265114 | ||||||||
\(355\) | 1.78271 | 0.0946164 | ||||||||
\(356\) | 0.302688 | 0.0160424 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.96023 | −0.103601 | ||||||||
\(359\) | 20.8005 | 1.09781 | 0.548904 | − | 0.835885i | \(-0.315045\pi\) | ||||
0.548904 | + | 0.835885i | \(0.315045\pi\) | |||||||
\(360\) | 11.4074 | 0.601222 | ||||||||
\(361\) | −16.9114 | −0.890072 | ||||||||
\(362\) | −2.63862 | −0.138683 | ||||||||
\(363\) | 11.2841 | 0.592263 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.2284 | −0.692406 | ||||||||
\(366\) | 24.5903 | 1.28536 | ||||||||
\(367\) | −15.7858 | −0.824012 | −0.412006 | − | 0.911181i | \(-0.635172\pi\) | ||||
−0.412006 | + | 0.911181i | \(0.635172\pi\) | |||||||
\(368\) | −23.1365 | −1.20607 | ||||||||
\(369\) | −9.15539 | −0.476611 | ||||||||
\(370\) | 32.2783 | 1.67807 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.293695 | 0.0152274 | ||||||||
\(373\) | 9.01000 | 0.466520 | 0.233260 | − | 0.972414i | \(-0.425061\pi\) | ||||
0.233260 | + | 0.972414i | \(0.425061\pi\) | |||||||
\(374\) | −12.2967 | −0.635849 | ||||||||
\(375\) | −2.58835 | −0.133662 | ||||||||
\(376\) | 15.2500 | 0.786459 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6146 | 0.596603 | 0.298301 | − | 0.954472i | \(-0.403580\pi\) | ||||
0.298301 | + | 0.954472i | \(0.403580\pi\) | |||||||
\(380\) | 0.647698 | 0.0332262 | ||||||||
\(381\) | 20.0563 | 1.02752 | ||||||||
\(382\) | −6.99474 | −0.357882 | ||||||||
\(383\) | 4.33633 | 0.221576 | 0.110788 | − | 0.993844i | \(-0.464663\pi\) | ||||
0.110788 | + | 0.993844i | \(0.464663\pi\) | |||||||
\(384\) | 13.0161 | 0.664227 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.8027 | 0.600742 | ||||||||
\(387\) | −6.42042 | −0.326368 | ||||||||
\(388\) | −0.848224 | −0.0430621 | ||||||||
\(389\) | 6.81733 | 0.345653 | 0.172826 | − | 0.984952i | \(-0.444710\pi\) | ||||
0.172826 | + | 0.984952i | \(0.444710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.5600 | 1.84892 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.2945 | 0.569732 | ||||||||
\(394\) | 23.5128 | 1.18456 | ||||||||
\(395\) | −19.6311 | −0.987748 | ||||||||
\(396\) | 0.290018 | 0.0145740 | ||||||||
\(397\) | −24.8275 | −1.24605 | −0.623027 | − | 0.782200i | \(-0.714097\pi\) | ||||
−0.623027 | + | 0.782200i | \(0.714097\pi\) | |||||||
\(398\) | 13.9841 | 0.700961 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.0520 | −0.802599 | ||||||||
\(401\) | −10.6211 | −0.530393 | −0.265197 | − | 0.964194i | \(-0.585437\pi\) | ||||
−0.265197 | + | 0.964194i | \(0.585437\pi\) | |||||||
\(402\) | −1.22088 | −0.0608919 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.46488 | 0.122632 | ||||||||
\(405\) | 10.8357 | 0.538432 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0220 | 0.595909 | ||||||||
\(408\) | −22.3447 | −1.10623 | ||||||||
\(409\) | 10.6699 | 0.527592 | 0.263796 | − | 0.964579i | \(-0.415025\pi\) | ||||
0.263796 | + | 0.964579i | \(0.415025\pi\) | |||||||
\(410\) | 29.8730 | 1.47532 | ||||||||
\(411\) | −11.5578 | −0.570103 | ||||||||
\(412\) | 0.0780676 | 0.00384611 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 10.9074 | 0.536068 | ||||||||
\(415\) | −45.2347 | −2.22049 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.7185 | 0.622825 | ||||||||
\(418\) | −3.05152 | −0.149255 | ||||||||
\(419\) | −8.54940 | −0.417666 | −0.208833 | − | 0.977951i | \(-0.566966\pi\) | ||||
−0.208833 | + | 0.977951i | \(0.566966\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.523234 | 0.0255009 | 0.0127504 | − | 0.999919i | \(-0.495941\pi\) | ||||
0.0127504 | + | 0.999919i | \(0.495941\pi\) | |||||||
\(422\) | 37.8325 | 1.84166 | ||||||||
\(423\) | −6.65985 | −0.323813 | ||||||||
\(424\) | 22.7283 | 1.10379 | ||||||||
\(425\) | 25.3652 | 1.23039 | ||||||||
\(426\) | −1.04180 | −0.0504752 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.29382 | 0.110876 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.9491 | 1.01026 | ||||||||
\(431\) | 26.6501 | 1.28369 | 0.641846 | − | 0.766834i | \(-0.278169\pi\) | ||||
0.641846 | + | 0.766834i | \(0.278169\pi\) | |||||||
\(432\) | −20.6917 | −0.995528 | ||||||||
\(433\) | 13.2489 | 0.636700 | 0.318350 | − | 0.947973i | \(-0.396871\pi\) | ||||
0.318350 | + | 0.947973i | \(0.396871\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −39.6841 | −1.90271 | ||||||||
\(436\) | 0.857956 | 0.0410886 | ||||||||
\(437\) | 9.07264 | 0.434003 | ||||||||
\(438\) | 7.73053 | 0.369379 | ||||||||
\(439\) | −7.90856 | −0.377455 | −0.188728 | − | 0.982029i | \(-0.560436\pi\) | ||||
−0.188728 | + | 0.982029i | \(0.560436\pi\) | |||||||
\(440\) | −13.8629 | −0.660888 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.741911 | 0.0352493 | 0.0176246 | − | 0.999845i | \(-0.494390\pi\) | ||||
0.0176246 | + | 0.999845i | \(0.494390\pi\) | |||||||
\(444\) | 1.49120 | 0.0707692 | ||||||||
\(445\) | 6.31857 | 0.299529 | ||||||||
\(446\) | −27.6028 | −1.30703 | ||||||||
\(447\) | −0.587463 | −0.0277860 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.1281 | −1.23306 | −0.616530 | − | 0.787332i | \(-0.711462\pi\) | ||||
−0.616530 | + | 0.787332i | \(0.711462\pi\) | |||||||
\(450\) | 7.56749 | 0.356735 | ||||||||
\(451\) | 11.1262 | 0.523910 | ||||||||
\(452\) | 0.935707 | 0.0440120 | ||||||||
\(453\) | 18.7445 | 0.880695 | ||||||||
\(454\) | −2.44387 | −0.114697 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.54500 | −0.259668 | ||||||||
\(457\) | −2.95826 | −0.138381 | −0.0691907 | − | 0.997603i | \(-0.522042\pi\) | ||||
−0.0691907 | + | 0.997603i | \(0.522042\pi\) | |||||||
\(458\) | −6.55142 | −0.306128 | ||||||||
\(459\) | 32.6968 | 1.52615 | ||||||||
\(460\) | 2.81348 | 0.131179 | ||||||||
\(461\) | −0.916982 | −0.0427081 | −0.0213541 | − | 0.999772i | \(-0.506798\pi\) | ||||
−0.0213541 | + | 0.999772i | \(0.506798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.1773 | 0.472981 | 0.236490 | − | 0.971634i | \(-0.424003\pi\) | ||||
0.236490 | + | 0.971634i | \(0.424003\pi\) | |||||||
\(464\) | 36.4198 | 1.69075 | ||||||||
\(465\) | 6.13085 | 0.284311 | ||||||||
\(466\) | −17.5321 | −0.812160 | ||||||||
\(467\) | −27.2677 | −1.26180 | −0.630900 | − | 0.775864i | \(-0.717314\pi\) | ||||
−0.630900 | + | 0.775864i | \(0.717314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 21.7304 | 1.00235 | ||||||||
\(471\) | −9.15544 | −0.421860 | ||||||||
\(472\) | 8.15507 | 0.375368 | ||||||||
\(473\) | 7.80246 | 0.358757 | ||||||||
\(474\) | 11.4722 | 0.526936 | ||||||||
\(475\) | 6.29456 | 0.288814 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.92573 | −0.454468 | ||||||||
\(478\) | −13.5756 | −0.620934 | ||||||||
\(479\) | 33.4296 | 1.52744 | 0.763720 | − | 0.645548i | \(-0.223371\pi\) | ||||
0.763720 | + | 0.645548i | \(0.223371\pi\) | |||||||
\(480\) | −3.32171 | −0.151614 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −32.0906 | −1.46169 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.25932 | 0.0572418 | ||||||||
\(485\) | −17.7065 | −0.804013 | ||||||||
\(486\) | 16.5983 | 0.752916 | ||||||||
\(487\) | 36.6328 | 1.65999 | 0.829996 | − | 0.557769i | \(-0.188342\pi\) | ||||
0.829996 | + | 0.557769i | \(0.188342\pi\) | |||||||
\(488\) | 40.2030 | 1.81991 | ||||||||
\(489\) | −29.6871 | −1.34250 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.1049 | 0.591415 | 0.295708 | − | 0.955278i | \(-0.404445\pi\) | ||||
0.295708 | + | 0.955278i | \(0.404445\pi\) | |||||||
\(492\) | 1.38008 | 0.0622187 | ||||||||
\(493\) | −57.5502 | −2.59193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.05409 | 0.272111 | ||||||||
\(496\) | −5.62653 | −0.252639 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 26.4347 | 1.18457 | ||||||||
\(499\) | −4.17391 | −0.186850 | −0.0934250 | − | 0.995626i | \(-0.529782\pi\) | ||||
−0.0934250 | + | 0.995626i | \(0.529782\pi\) | |||||||
\(500\) | −0.288862 | −0.0129183 | ||||||||
\(501\) | −7.14285 | −0.319119 | ||||||||
\(502\) | 17.1511 | 0.765492 | ||||||||
\(503\) | 18.9926 | 0.846838 | 0.423419 | − | 0.905934i | \(-0.360830\pi\) | ||||
0.423419 | + | 0.905934i | \(0.360830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 51.4540 | 2.28967 | ||||||||
\(506\) | −13.2553 | −0.589268 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.23830 | 0.0993086 | ||||||||
\(509\) | −4.25731 | −0.188702 | −0.0943509 | − | 0.995539i | \(-0.530078\pi\) | ||||
−0.0943509 | + | 0.995539i | \(0.530078\pi\) | |||||||
\(510\) | −31.8399 | −1.40989 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.5889 | 1.08668 | ||||||||
\(513\) | 8.11394 | 0.358239 | ||||||||
\(514\) | 8.13232 | 0.358701 | ||||||||
\(515\) | 1.62965 | 0.0718109 | ||||||||
\(516\) | 0.967810 | 0.0426054 | ||||||||
\(517\) | 8.09344 | 0.355949 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.4890 | −1.07495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.35828 | −0.103318 | −0.0516590 | − | 0.998665i | \(-0.516451\pi\) | ||||
−0.0516590 | + | 0.998665i | \(0.516451\pi\) | |||||||
\(522\) | −17.1696 | −0.751493 | ||||||||
\(523\) | 5.57416 | 0.243741 | 0.121870 | − | 0.992546i | \(-0.461111\pi\) | ||||
0.121870 | + | 0.992546i | \(0.461111\pi\) | |||||||
\(524\) | 1.26048 | 0.0550641 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −39.8350 | −1.73689 | ||||||||
\(527\) | 8.89099 | 0.387298 | ||||||||
\(528\) | 7.50461 | 0.326596 | ||||||||
\(529\) | 16.4099 | 0.713473 | ||||||||
\(530\) | 32.3865 | 1.40678 | ||||||||
\(531\) | −3.56142 | −0.154552 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.69250 | −0.159790 | ||||||||
\(535\) | 47.8831 | 2.07017 | ||||||||
\(536\) | −1.99603 | −0.0862153 | ||||||||
\(537\) | −1.89040 | −0.0815769 | ||||||||
\(538\) | −4.68904 | −0.202159 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.51619 | 0.108279 | ||||||||
\(541\) | −4.64124 | −0.199542 | −0.0997712 | − | 0.995010i | \(-0.531811\pi\) | ||||
−0.0997712 | + | 0.995010i | \(0.531811\pi\) | |||||||
\(542\) | 42.5139 | 1.82613 | ||||||||
\(543\) | −2.54463 | −0.109200 | ||||||||
\(544\) | −4.81716 | −0.206534 | ||||||||
\(545\) | 17.9097 | 0.767167 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.82685 | −0.334652 | −0.167326 | − | 0.985902i | \(-0.553513\pi\) | ||||
−0.167326 | + | 0.985902i | \(0.553513\pi\) | |||||||
\(548\) | −1.28986 | −0.0551000 | ||||||||
\(549\) | −17.5571 | −0.749321 | ||||||||
\(550\) | −9.19644 | −0.392138 | ||||||||
\(551\) | −14.2815 | −0.608412 | ||||||||
\(552\) | −24.0865 | −1.02519 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −31.6345 | −1.34402 | ||||||||
\(555\) | 31.1285 | 1.32133 | ||||||||
\(556\) | 1.41939 | 0.0601956 | ||||||||
\(557\) | 34.0460 | 1.44258 | 0.721288 | − | 0.692635i | \(-0.243550\pi\) | ||||
0.721288 | + | 0.692635i | \(0.243550\pi\) | |||||||
\(558\) | 2.65255 | 0.112291 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.8587 | −0.500675 | ||||||||
\(562\) | −7.22048 | −0.304577 | ||||||||
\(563\) | −4.13227 | −0.174154 | −0.0870772 | − | 0.996202i | \(-0.527753\pi\) | ||||
−0.0870772 | + | 0.996202i | \(0.527753\pi\) | |||||||
\(564\) | 1.00390 | 0.0422719 | ||||||||
\(565\) | 19.5327 | 0.821749 | ||||||||
\(566\) | −13.3321 | −0.560390 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.70325 | −0.0714666 | ||||||||
\(569\) | 10.0458 | 0.421142 | 0.210571 | − | 0.977579i | \(-0.432468\pi\) | ||||
0.210571 | + | 0.977579i | \(0.432468\pi\) | |||||||
\(570\) | −7.90130 | −0.330949 | ||||||||
\(571\) | 10.7360 | 0.449289 | 0.224645 | − | 0.974441i | \(-0.427878\pi\) | ||||
0.224645 | + | 0.974441i | \(0.427878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.74558 | −0.281801 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.3424 | 1.14026 | ||||||||
\(576\) | −10.8441 | −0.451837 | ||||||||
\(577\) | 42.5070 | 1.76959 | 0.884795 | − | 0.465980i | \(-0.154298\pi\) | ||||
0.884795 | + | 0.465980i | \(0.154298\pi\) | |||||||
\(578\) | −23.0302 | −0.957928 | ||||||||
\(579\) | 11.3823 | 0.473032 | ||||||||
\(580\) | −4.42879 | −0.183895 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.3475 | 0.428918 | ||||||||
\(583\) | 12.0623 | 0.499570 | ||||||||
\(584\) | 12.6387 | 0.522995 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.9722 | −1.36207 | ||||||||
\(587\) | 18.8276 | 0.777098 | 0.388549 | − | 0.921428i | \(-0.372976\pi\) | ||||
0.388549 | + | 0.921428i | \(0.372976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.20637 | 0.0909117 | ||||||||
\(590\) | 11.6205 | 0.478408 | ||||||||
\(591\) | 22.6752 | 0.932734 | ||||||||
\(592\) | −28.5679 | −1.17414 | ||||||||
\(593\) | 8.45175 | 0.347072 | 0.173536 | − | 0.984828i | \(-0.444481\pi\) | ||||
0.173536 | + | 0.984828i | \(0.444481\pi\) | |||||||
\(594\) | −11.8546 | −0.486400 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.0655614 | −0.00268550 | ||||||||
\(597\) | 13.4860 | 0.551946 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.7524 | 1.41994 | 0.709972 | − | 0.704230i | \(-0.248707\pi\) | ||||
0.709972 | + | 0.704230i | \(0.248707\pi\) | |||||||
\(600\) | −16.7111 | −0.682228 | ||||||||
\(601\) | 33.2606 | 1.35673 | 0.678364 | − | 0.734726i | \(-0.262689\pi\) | ||||
0.678364 | + | 0.734726i | \(0.262689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.871689 | 0.0354979 | ||||||||
\(604\) | 2.09191 | 0.0851185 | ||||||||
\(605\) | 26.2881 | 1.06876 | ||||||||
\(606\) | −30.0692 | −1.22148 | ||||||||
\(607\) | −26.6989 | −1.08367 | −0.541837 | − | 0.840484i | \(-0.682271\pi\) | ||||
−0.541837 | + | 0.840484i | \(0.682271\pi\) | |||||||
\(608\) | −1.19541 | −0.0484804 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 57.2870 | 2.31948 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.08902 | 0.0440212 | ||||||||
\(613\) | −21.0806 | −0.851438 | −0.425719 | − | 0.904855i | \(-0.639979\pi\) | ||||
−0.425719 | + | 0.904855i | \(0.639979\pi\) | |||||||
\(614\) | −8.88539 | −0.358585 | ||||||||
\(615\) | 28.8089 | 1.16169 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.37659 | −0.256712 | −0.128356 | − | 0.991728i | \(-0.540970\pi\) | ||||
−0.128356 | + | 0.991728i | \(0.540970\pi\) | |||||||
\(618\) | −0.952349 | −0.0383091 | ||||||||
\(619\) | −39.0440 | −1.56931 | −0.784656 | − | 0.619931i | \(-0.787160\pi\) | ||||
−0.784656 | + | 0.619931i | \(0.787160\pi\) | |||||||
\(620\) | 0.684208 | 0.0274785 | ||||||||
\(621\) | 35.2455 | 1.41435 | ||||||||
\(622\) | 2.33230 | 0.0935169 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.8073 | −1.11229 | ||||||||
\(626\) | 5.55323 | 0.221952 | ||||||||
\(627\) | −2.94283 | −0.117525 | ||||||||
\(628\) | −1.02176 | −0.0407725 | ||||||||
\(629\) | 45.1428 | 1.79996 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.7857 | −0.469181 | −0.234590 | − | 0.972094i | \(-0.575375\pi\) | ||||
−0.234590 | + | 0.972094i | \(0.575375\pi\) | |||||||
\(632\) | 18.7560 | 0.746075 | ||||||||
\(633\) | 36.4849 | 1.45015 | ||||||||
\(634\) | 0.677524 | 0.0269079 | ||||||||
\(635\) | 46.7242 | 1.85419 | ||||||||
\(636\) | 1.49620 | 0.0593281 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.8655 | 0.826073 | ||||||||
\(639\) | 0.743827 | 0.0294254 | ||||||||
\(640\) | 30.3231 | 1.19862 | ||||||||
\(641\) | 0.620887 | 0.0245236 | 0.0122618 | − | 0.999925i | \(-0.496097\pi\) | ||||
0.0122618 | + | 0.999925i | \(0.496097\pi\) | |||||||
\(642\) | −27.9824 | −1.10438 | ||||||||
\(643\) | 6.61337 | 0.260806 | 0.130403 | − | 0.991461i | \(-0.458373\pi\) | ||||
0.130403 | + | 0.991461i | \(0.458373\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.2029 | 0.795488 | ||||||||
\(646\) | −11.4585 | −0.450829 | ||||||||
\(647\) | 6.45338 | 0.253709 | 0.126854 | − | 0.991921i | \(-0.459512\pi\) | ||||
0.126854 | + | 0.991921i | \(0.459512\pi\) | |||||||
\(648\) | −10.3527 | −0.406693 | ||||||||
\(649\) | 4.32804 | 0.169890 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.31311 | −0.129752 | ||||||||
\(653\) | −4.52898 | −0.177233 | −0.0886164 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886164 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(654\) | −10.4662 | −0.409262 | ||||||||
\(655\) | 26.3122 | 1.02810 | ||||||||
\(656\) | −26.4391 | −1.03227 | ||||||||
\(657\) | −5.51949 | −0.215336 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.2666 | −1.06216 | −0.531078 | − | 0.847323i | \(-0.678213\pi\) | ||||
−0.531078 | + | 0.847323i | \(0.678213\pi\) | |||||||
\(660\) | −0.912590 | −0.0355225 | ||||||||
\(661\) | 3.89031 | 0.151315 | 0.0756577 | − | 0.997134i | \(-0.475894\pi\) | ||||
0.0756577 | + | 0.997134i | \(0.475894\pi\) | |||||||
\(662\) | 13.6883 | 0.532009 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 43.2184 | 1.67720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.4680 | 0.521873 | ||||||||
\(667\) | −62.0362 | −2.40205 | ||||||||
\(668\) | −0.797148 | −0.0308426 | ||||||||
\(669\) | −26.6196 | −1.02917 | ||||||||
\(670\) | −2.84422 | −0.109882 | ||||||||
\(671\) | 21.3364 | 0.823684 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.18325 | −0.161253 | −0.0806263 | − | 0.996744i | \(-0.525692\pi\) | ||||
−0.0806263 | + | 0.996744i | \(0.525692\pi\) | |||||||
\(674\) | 27.8010 | 1.07086 | ||||||||
\(675\) | 24.4532 | 0.941203 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.5653 | 1.67435 | 0.837175 | − | 0.546935i | \(-0.184205\pi\) | ||||
0.837175 | + | 0.546935i | \(0.184205\pi\) | |||||||
\(678\) | −11.4147 | −0.438380 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −52.0554 | −1.99623 | ||||||||
\(681\) | −2.35682 | −0.0903136 | ||||||||
\(682\) | −3.22353 | −0.123435 | ||||||||
\(683\) | −14.7994 | −0.566283 | −0.283142 | − | 0.959078i | \(-0.591377\pi\) | ||||
−0.283142 | + | 0.959078i | \(0.591377\pi\) | |||||||
\(684\) | 0.270249 | 0.0103332 | ||||||||
\(685\) | −26.9256 | −1.02877 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.31806 | −0.241049 | ||||||||
\(688\) | −18.5410 | −0.706870 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −34.3218 | −1.30661 | ||||||||
\(691\) | −4.73188 | −0.180009 | −0.0900047 | − | 0.995941i | \(-0.528688\pi\) | ||||
−0.0900047 | + | 0.995941i | \(0.528688\pi\) | |||||||
\(692\) | −2.73299 | −0.103893 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 37.2578 | 1.41429 | ||||||||
\(695\) | 29.6296 | 1.12391 | ||||||||
\(696\) | 37.9152 | 1.43717 | ||||||||
\(697\) | 41.7789 | 1.58249 | ||||||||
\(698\) | 30.2331 | 1.14434 | ||||||||
\(699\) | −16.9076 | −0.639505 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.8398 | 1.39142 | 0.695709 | − | 0.718324i | \(-0.255090\pi\) | ||||
0.695709 | + | 0.718324i | \(0.255090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.2025 | 0.422511 | ||||||||
\(704\) | 13.1784 | 0.496678 | ||||||||
\(705\) | 20.9563 | 0.789260 | ||||||||
\(706\) | −37.9164 | −1.42700 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.536846 | 0.0201759 | ||||||||
\(709\) | −17.0716 | −0.641136 | −0.320568 | − | 0.947225i | \(-0.603874\pi\) | ||||
−0.320568 | + | 0.947225i | \(0.603874\pi\) | |||||||
\(710\) | −2.42702 | −0.0910846 | ||||||||
\(711\) | −8.19098 | −0.307186 | ||||||||
\(712\) | −6.03692 | −0.226243 | ||||||||
\(713\) | 9.58405 | 0.358925 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.210971 | −0.00788435 | ||||||||
\(717\) | −13.0920 | −0.488931 | ||||||||
\(718\) | −28.3183 | −1.05683 | ||||||||
\(719\) | 22.2490 | 0.829747 | 0.414874 | − | 0.909879i | \(-0.363826\pi\) | ||||
0.414874 | + | 0.909879i | \(0.363826\pi\) | |||||||
\(720\) | −14.3864 | −0.536148 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 23.0235 | 0.856848 | ||||||||
\(723\) | −30.9475 | −1.15095 | ||||||||
\(724\) | −0.283983 | −0.0105541 | ||||||||
\(725\) | −43.0405 | −1.59848 | ||||||||
\(726\) | −15.3625 | −0.570155 | ||||||||
\(727\) | −47.9699 | −1.77910 | −0.889552 | − | 0.456833i | \(-0.848984\pi\) | ||||
−0.889552 | + | 0.456833i | \(0.848984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.6350 | 0.986481 | ||||||||
\(730\) | 18.0095 | 0.666560 | ||||||||
\(731\) | 29.2983 | 1.08364 | ||||||||
\(732\) | 2.64655 | 0.0978194 | ||||||||
\(733\) | −37.9957 | −1.40340 | −0.701701 | − | 0.712471i | \(-0.747576\pi\) | ||||
−0.701701 | + | 0.712471i | \(0.747576\pi\) | |||||||
\(734\) | 21.4912 | 0.793254 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.19266 | −0.191404 | ||||||||
\(737\) | −1.05933 | −0.0390208 | ||||||||
\(738\) | 12.4644 | 0.458820 | ||||||||
\(739\) | −34.5887 | −1.27237 | −0.636184 | − | 0.771538i | \(-0.719488\pi\) | ||||
−0.636184 | + | 0.771538i | \(0.719488\pi\) | |||||||
\(740\) | 3.47397 | 0.127706 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1252 | −0.921752 | −0.460876 | − | 0.887464i | \(-0.652465\pi\) | ||||
−0.460876 | + | 0.887464i | \(0.652465\pi\) | |||||||
\(744\) | −5.85757 | −0.214749 | ||||||||
\(745\) | −1.36858 | −0.0501410 | ||||||||
\(746\) | −12.2664 | −0.449106 | ||||||||
\(747\) | −18.8740 | −0.690563 | ||||||||
\(748\) | −1.32344 | −0.0483899 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.52384 | 0.128672 | ||||||||
\(751\) | −10.5969 | −0.386685 | −0.193343 | − | 0.981131i | \(-0.561933\pi\) | ||||
−0.193343 | + | 0.981131i | \(0.561933\pi\) | |||||||
\(752\) | −19.2325 | −0.701336 | ||||||||
\(753\) | 16.5402 | 0.602758 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.6682 | 1.58925 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.4219 | 0.742248 | 0.371124 | − | 0.928583i | \(-0.378972\pi\) | ||||
0.371124 | + | 0.928583i | \(0.378972\pi\) | |||||||
\(758\) | −15.8124 | −0.574333 | ||||||||
\(759\) | −12.7831 | −0.463997 | ||||||||
\(760\) | −12.9179 | −0.468582 | ||||||||
\(761\) | 8.57045 | 0.310678 | 0.155339 | − | 0.987861i | \(-0.450353\pi\) | ||||
0.155339 | + | 0.987861i | \(0.450353\pi\) | |||||||
\(762\) | −27.3051 | −0.989160 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.752813 | −0.0272358 | ||||||||
\(765\) | 22.7332 | 0.821920 | ||||||||
\(766\) | −5.90358 | −0.213305 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.59164 | 0.165686 | ||||||||
\(769\) | 14.8952 | 0.537133 | 0.268567 | − | 0.963261i | \(-0.413450\pi\) | ||||
0.268567 | + | 0.963261i | \(0.413450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.84264 | 0.282446 | ||||||||
\(772\) | 1.27027 | 0.0457181 | ||||||||
\(773\) | −49.2303 | −1.77069 | −0.885345 | − | 0.464935i | \(-0.846078\pi\) | ||||
−0.885345 | + | 0.464935i | \(0.846078\pi\) | |||||||
\(774\) | 8.74091 | 0.314186 | ||||||||
\(775\) | 6.64937 | 0.238853 | ||||||||
\(776\) | 16.9173 | 0.607295 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.28128 | −0.332750 | ||||||||
\(779\) | 10.3677 | 0.371463 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.903942 | −0.0323456 | ||||||||
\(782\) | −49.7737 | −1.77990 | ||||||||
\(783\) | −55.4810 | −1.98273 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3290 | −0.761264 | ||||||||
\(786\) | −15.3766 | −0.548465 | ||||||||
\(787\) | 18.8851 | 0.673180 | 0.336590 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336590 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(788\) | 2.53058 | 0.0901480 | ||||||||
\(789\) | −38.4160 | −1.36765 | ||||||||
\(790\) | 26.7263 | 0.950877 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.78423 | −0.205534 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 33.8007 | 1.19954 | ||||||||
\(795\) | 31.2329 | 1.10772 | ||||||||
\(796\) | 1.50505 | 0.0533451 | ||||||||
\(797\) | 11.8478 | 0.419672 | 0.209836 | − | 0.977737i | \(-0.432707\pi\) | ||||
0.209836 | + | 0.977737i | \(0.432707\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.3910 | 1.07515 | ||||||||
\(800\) | −3.60264 | −0.127373 | ||||||||
\(801\) | 2.63639 | 0.0931523 | ||||||||
\(802\) | 14.4599 | 0.510595 | ||||||||
\(803\) | 6.70759 | 0.236706 | ||||||||
\(804\) | −0.131398 | −0.00463404 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.52201 | −0.159182 | ||||||||
\(808\) | −49.1604 | −1.72946 | ||||||||
\(809\) | −23.3622 | −0.821371 | −0.410686 | − | 0.911777i | \(-0.634711\pi\) | ||||
−0.410686 | + | 0.911777i | \(0.634711\pi\) | |||||||
\(810\) | −14.7520 | −0.518333 | ||||||||
\(811\) | −17.8384 | −0.626390 | −0.313195 | − | 0.949689i | \(-0.601399\pi\) | ||||
−0.313195 | + | 0.949689i | \(0.601399\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 40.9995 | 1.43792 | ||||||||
\(814\) | −16.3671 | −0.573665 | ||||||||
\(815\) | −69.1607 | −2.42259 | ||||||||
\(816\) | 28.1799 | 0.986494 | ||||||||
\(817\) | 7.27060 | 0.254366 | ||||||||
\(818\) | −14.5262 | −0.507898 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.21510 | 0.112276 | ||||||||
\(821\) | −27.0060 | −0.942516 | −0.471258 | − | 0.881996i | \(-0.656200\pi\) | ||||
−0.471258 | + | 0.881996i | \(0.656200\pi\) | |||||||
\(822\) | 15.7350 | 0.548822 | ||||||||
\(823\) | −49.8512 | −1.73770 | −0.868852 | − | 0.495072i | \(-0.835142\pi\) | ||||
−0.868852 | + | 0.495072i | \(0.835142\pi\) | |||||||
\(824\) | −1.55701 | −0.0542409 | ||||||||
\(825\) | −8.86886 | −0.308774 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.2002 | −1.01539 | −0.507695 | − | 0.861537i | \(-0.669502\pi\) | ||||
−0.507695 | + | 0.861537i | \(0.669502\pi\) | |||||||
\(828\) | 1.17391 | 0.0407963 | ||||||||
\(829\) | 15.3988 | 0.534822 | 0.267411 | − | 0.963583i | \(-0.413832\pi\) | ||||
0.267411 | + | 0.963583i | \(0.413832\pi\) | |||||||
\(830\) | 61.5837 | 2.13760 | ||||||||
\(831\) | −30.5076 | −1.05830 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.3152 | −0.599577 | ||||||||
\(835\) | −16.6404 | −0.575863 | ||||||||
\(836\) | −0.328422 | −0.0113587 | ||||||||
\(837\) | 8.57132 | 0.296268 | ||||||||
\(838\) | 11.6394 | 0.402075 | ||||||||
\(839\) | 29.6007 | 1.02193 | 0.510966 | − | 0.859601i | \(-0.329288\pi\) | ||||
0.510966 | + | 0.859601i | \(0.329288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 68.6530 | 2.36735 | ||||||||
\(842\) | −0.712343 | −0.0245490 | ||||||||
\(843\) | −6.96328 | −0.239828 | ||||||||
\(844\) | 4.07175 | 0.140156 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.06689 | 0.311726 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −28.6637 | −0.984317 | ||||||||
\(849\) | −12.8572 | −0.441258 | ||||||||
\(850\) | −34.5328 | −1.18446 | ||||||||
\(851\) | 48.6617 | 1.66810 | ||||||||
\(852\) | −0.112124 | −0.00384131 | ||||||||
\(853\) | −27.5135 | −0.942046 | −0.471023 | − | 0.882121i | \(-0.656115\pi\) | ||||
−0.471023 | + | 0.882121i | \(0.656115\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.64141 | 0.192932 | ||||||||
\(856\) | −45.7487 | −1.56366 | ||||||||
\(857\) | 13.3991 | 0.457706 | 0.228853 | − | 0.973461i | \(-0.426503\pi\) | ||||
0.228853 | + | 0.973461i | \(0.426503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.4736 | 1.51742 | 0.758710 | − | 0.651429i | \(-0.225830\pi\) | ||||
0.758710 | + | 0.651429i | \(0.225830\pi\) | |||||||
\(860\) | 2.25466 | 0.0768833 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.2821 | −1.23577 | ||||||||
\(863\) | 27.5554 | 0.937996 | 0.468998 | − | 0.883199i | \(-0.344615\pi\) | ||||
0.468998 | + | 0.883199i | \(0.344615\pi\) | |||||||
\(864\) | −4.64396 | −0.157991 | ||||||||
\(865\) | −57.0508 | −1.93979 | ||||||||
\(866\) | −18.0373 | −0.612934 | ||||||||
\(867\) | −22.2098 | −0.754285 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.95415 | 0.337672 | ||||||||
\(870\) | 54.0269 | 1.83169 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17.1114 | −0.579464 | ||||||||
\(873\) | −7.38797 | −0.250045 | ||||||||
\(874\) | −12.3517 | −0.417803 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.832004 | 0.0281108 | ||||||||
\(877\) | 19.4434 | 0.656558 | 0.328279 | − | 0.944581i | \(-0.393531\pi\) | ||||
0.328279 | + | 0.944581i | \(0.393531\pi\) | |||||||
\(878\) | 10.7669 | 0.363366 | ||||||||
\(879\) | −31.7977 | −1.07251 | ||||||||
\(880\) | 17.4831 | 0.589356 | ||||||||
\(881\) | 5.21331 | 0.175641 | 0.0878205 | − | 0.996136i | \(-0.472010\pi\) | ||||
0.0878205 | + | 0.996136i | \(0.472010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.9305 | −0.872632 | −0.436316 | − | 0.899793i | \(-0.643717\pi\) | ||||
−0.436316 | + | 0.899793i | \(0.643717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.2066 | 0.376705 | ||||||||
\(886\) | −1.01006 | −0.0339335 | ||||||||
\(887\) | 19.5294 | 0.655732 | 0.327866 | − | 0.944724i | \(-0.393670\pi\) | ||||
0.327866 | + | 0.944724i | \(0.393670\pi\) | |||||||
\(888\) | −29.7410 | −0.998042 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.60225 | −0.288348 | ||||||||
\(891\) | −5.49437 | −0.184068 | ||||||||
\(892\) | −2.97077 | −0.0994688 | ||||||||
\(893\) | 7.54174 | 0.252375 | ||||||||
\(894\) | 0.799786 | 0.0267488 | ||||||||
\(895\) | −4.40398 | −0.147209 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 35.5714 | 1.18703 | ||||||||
\(899\) | −15.0865 | −0.503164 | ||||||||
\(900\) | 0.814456 | 0.0271485 | ||||||||
\(901\) | 45.2942 | 1.50897 | ||||||||
\(902\) | −15.1474 | −0.504354 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.6621 | −0.620691 | ||||||||
\(905\) | −5.92810 | −0.197057 | ||||||||
\(906\) | −25.5192 | −0.847820 | ||||||||
\(907\) | −27.8808 | −0.925766 | −0.462883 | − | 0.886419i | \(-0.653185\pi\) | ||||
−0.462883 | + | 0.886419i | \(0.653185\pi\) | |||||||
\(908\) | −0.263023 | −0.00872874 | ||||||||
\(909\) | 21.4689 | 0.712079 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.1656 | 0.866906 | 0.433453 | − | 0.901176i | \(-0.357295\pi\) | ||||
0.433453 | + | 0.901176i | \(0.357295\pi\) | |||||||
\(912\) | 6.99305 | 0.231563 | ||||||||
\(913\) | 22.9367 | 0.759095 | ||||||||
\(914\) | 4.02744 | 0.133216 | ||||||||
\(915\) | 55.2464 | 1.82639 | ||||||||
\(916\) | −0.705101 | −0.0232972 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −44.5142 | −1.46919 | ||||||||
\(919\) | −27.3730 | −0.902951 | −0.451476 | − | 0.892283i | \(-0.649102\pi\) | ||||
−0.451476 | + | 0.892283i | \(0.649102\pi\) | |||||||
\(920\) | −56.1131 | −1.84999 | ||||||||
\(921\) | −8.56889 | −0.282355 | ||||||||
\(922\) | 1.24840 | 0.0411139 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.7613 | 1.11006 | ||||||||
\(926\) | −13.8557 | −0.455325 | ||||||||
\(927\) | 0.679963 | 0.0223329 | ||||||||
\(928\) | 8.17391 | 0.268322 | ||||||||
\(929\) | −9.86006 | −0.323498 | −0.161749 | − | 0.986832i | \(-0.551714\pi\) | ||||
−0.161749 | + | 0.986832i | \(0.551714\pi\) | |||||||
\(930\) | −8.34668 | −0.273699 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.88691 | −0.0618077 | ||||||||
\(933\) | 2.24923 | 0.0736364 | ||||||||
\(934\) | 37.1230 | 1.21470 | ||||||||
\(935\) | −27.6267 | −0.903489 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.2540 | −1.57639 | −0.788194 | − | 0.615426i | \(-0.788984\pi\) | ||||
−0.788194 | + | 0.615426i | \(0.788984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.35542 | 0.174767 | ||||||||
\(940\) | 2.33874 | 0.0762814 | ||||||||
\(941\) | 2.42957 | 0.0792018 | 0.0396009 | − | 0.999216i | \(-0.487391\pi\) | ||||
0.0396009 | + | 0.999216i | \(0.487391\pi\) | |||||||
\(942\) | 12.4644 | 0.406113 | ||||||||
\(943\) | 45.0355 | 1.46656 | ||||||||
\(944\) | −10.2847 | −0.334740 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.6225 | −0.345366 | ||||||||
\(947\) | −0.696419 | −0.0226306 | −0.0113153 | − | 0.999936i | \(-0.503602\pi\) | ||||
−0.0113153 | + | 0.999936i | \(0.503602\pi\) | |||||||
\(948\) | 1.23470 | 0.0401013 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.56956 | −0.278033 | ||||||||
\(951\) | 0.653391 | 0.0211876 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.9112 | 1.13088 | 0.565442 | − | 0.824788i | \(-0.308706\pi\) | ||||
0.565442 | + | 0.824788i | \(0.308706\pi\) | |||||||
\(954\) | 13.5131 | 0.437504 | ||||||||
\(955\) | −15.7149 | −0.508521 | ||||||||
\(956\) | −1.46108 | −0.0472549 | ||||||||
\(957\) | 20.1223 | 0.650460 | ||||||||
\(958\) | −45.5119 | −1.47042 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 34.1227 | 1.10131 | ||||||||
\(961\) | −28.6693 | −0.924815 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.9790 | 0.643814 | ||||||||
\(964\) | −3.45377 | −0.111239 | ||||||||
\(965\) | 26.5168 | 0.853605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1384 | −0.390345 | −0.195172 | − | 0.980769i | \(-0.562527\pi\) | ||||
−0.195172 | + | 0.980769i | \(0.562527\pi\) | |||||||
\(968\) | −25.1163 | −0.807269 | ||||||||
\(969\) | −11.0504 | −0.354988 | ||||||||
\(970\) | 24.1061 | 0.774001 | ||||||||
\(971\) | −33.1210 | −1.06290 | −0.531451 | − | 0.847089i | \(-0.678353\pi\) | ||||
−0.531451 | + | 0.847089i | \(0.678353\pi\) | |||||||
\(972\) | 1.78641 | 0.0572990 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −49.8728 | −1.59803 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −50.7019 | −1.62293 | ||||||||
\(977\) | −43.1916 | −1.38182 | −0.690911 | − | 0.722940i | \(-0.742790\pi\) | ||||
−0.690911 | + | 0.722940i | \(0.742790\pi\) | |||||||
\(978\) | 40.4168 | 1.29239 | ||||||||
\(979\) | −3.20389 | −0.102397 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.47274 | 0.238586 | ||||||||
\(982\) | −17.8413 | −0.569339 | ||||||||
\(983\) | 39.1839 | 1.24977 | 0.624887 | − | 0.780716i | \(-0.285145\pi\) | ||||
0.624887 | + | 0.780716i | \(0.285145\pi\) | |||||||
\(984\) | −27.5248 | −0.877457 | ||||||||
\(985\) | 52.8254 | 1.68316 | ||||||||
\(986\) | 78.3502 | 2.49518 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.5822 | 1.00425 | ||||||||
\(990\) | −8.24219 | −0.261954 | ||||||||
\(991\) | 8.45729 | 0.268655 | 0.134327 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134327 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(992\) | −1.26280 | −0.0400938 | ||||||||
\(993\) | 13.2007 | 0.418911 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.4177 | 0.996009 | ||||||||
\(996\) | 2.84505 | 0.0901489 | ||||||||
\(997\) | −29.7433 | −0.941980 | −0.470990 | − | 0.882139i | \(-0.656103\pi\) | ||||
−0.470990 | + | 0.882139i | \(0.656103\pi\) | |||||||
\(998\) | 5.68247 | 0.179875 | ||||||||
\(999\) | 43.5197 | 1.37690 |
(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 | 8281.2.a.cu.1.7 | 24 | ||
7.2 | even | 3 | 1183.2.e.l.508.18 | yes | 48 | ||
7.4 | even | 3 | 1183.2.e.l.170.18 | yes | 48 | ||
7.6 | odd | 2 | 8281.2.a.ct.1.7 | 24 | |||
13.12 | even | 2 | 8281.2.a.cv.1.18 | 24 | |||
91.25 | even | 6 | 1183.2.e.k.170.7 | ✓ | 48 | ||
91.51 | even | 6 | 1183.2.e.k.508.7 | yes | 48 | ||
91.90 | odd | 2 | 8281.2.a.cw.1.18 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.e.k.170.7 | ✓ | 48 | 91.25 | even | 6 | ||
1183.2.e.k.508.7 | yes | 48 | 91.51 | even | 6 | ||
1183.2.e.l.170.18 | yes | 48 | 7.4 | even | 3 | ||
1183.2.e.l.508.18 | yes | 48 | 7.2 | even | 3 | ||
8281.2.a.ct.1.7 | 24 | 7.6 | odd | 2 | |||
8281.2.a.cu.1.7 | 24 | 1.1 | even | 1 | trivial | ||
8281.2.a.cv.1.18 | 24 | 13.12 | even | 2 | |||
8281.2.a.cw.1.18 | 24 | 91.90 | odd | 2 |