Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.2 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.f.757.1 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41290 | + | 0.0608900i | −0.999073 | + | 0.0430557i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.99258 | − | 0.172063i | 0.996292 | − | 0.0860316i | ||||
\(5\) | 3.11390i | 1.39258i | 0.717760 | + | 0.696290i | \(0.245167\pi\) | ||||
−0.717760 | + | 0.696290i | \(0.754833\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.80485 | + | 0.364437i | −0.991664 | + | 0.128848i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.189605 | − | 4.39964i | −0.0599585 | − | 1.39129i | ||||
\(11\) | 2.37402i | 0.715793i | 0.933761 | + | 0.357897i | \(0.116506\pi\) | ||||
−0.933761 | + | 0.357897i | \(0.883494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.09044i | − | 0.302434i | −0.988501 | − | 0.151217i | \(-0.951681\pi\) | ||
0.988501 | − | 0.151217i | \(-0.0483192\pi\) | |||||||
\(14\) | −1.41290 | + | 0.0608900i | −0.377614 | + | 0.0162735i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.94079 | − | 0.685701i | 0.985197 | − | 0.171425i | ||||
\(17\) | 3.69300 | 0.895684 | 0.447842 | − | 0.894113i | \(-0.352193\pi\) | ||||
0.447842 | + | 0.894113i | \(0.352193\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.08263i | − | 0.248372i | −0.992259 | − | 0.124186i | \(-0.960368\pi\) | ||
0.992259 | − | 0.124186i | \(-0.0396320\pi\) | |||||||
\(20\) | 0.535788 | + | 6.20472i | 0.119806 | + | 1.38742i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.144554 | − | 3.35425i | −0.0308190 | − | 0.715129i | ||||
\(23\) | 4.87366 | 1.01623 | 0.508114 | − | 0.861290i | \(-0.330343\pi\) | ||||
0.508114 | + | 0.861290i | \(0.330343\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69640 | −0.939280 | ||||||||
\(26\) | 0.0663968 | + | 1.54068i | 0.0130215 | + | 0.302153i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.99258 | − | 0.172063i | 0.376563 | − | 0.0325169i | ||||
\(29\) | 1.59607i | 0.296382i | 0.988959 | + | 0.148191i | \(0.0473451\pi\) | ||||
−0.988959 | + | 0.148191i | \(0.952655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.45516 | 1.33899 | 0.669493 | − | 0.742818i | \(-0.266511\pi\) | ||||
0.669493 | + | 0.742818i | \(0.266511\pi\) | |||||||
\(32\) | −5.52620 | + | 1.20878i | −0.976903 | + | 0.213685i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.21785 | + | 0.224867i | −0.894853 | + | 0.0385643i | ||||
\(35\) | 3.11390i | 0.526346i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.61410i | 0.758554i | 0.925283 | + | 0.379277i | \(0.123827\pi\) | ||||
−0.925283 | + | 0.379277i | \(0.876173\pi\) | |||||||
\(38\) | 0.0659213 | + | 1.52965i | 0.0106938 | + | 0.248142i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.13482 | − | 8.73404i | −0.179431 | − | 1.38097i | ||||
\(41\) | −0.0380616 | −0.00594422 | −0.00297211 | − | 0.999996i | \(-0.500946\pi\) | ||||
−0.00297211 | + | 0.999996i | \(0.500946\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0608i | 1.68675i | 0.537323 | + | 0.843377i | \(0.319436\pi\) | ||||
−0.537323 | + | 0.843377i | \(0.680564\pi\) | |||||||
\(44\) | 0.408481 | + | 4.73043i | 0.0615808 | + | 0.713139i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.88600 | + | 0.296757i | −1.01529 | + | 0.0437544i | ||||
\(47\) | 0.337175 | 0.0491821 | 0.0245910 | − | 0.999698i | \(-0.492172\pi\) | ||||
0.0245910 | + | 0.999698i | \(0.492172\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.63555 | − | 0.285964i | 0.938409 | − | 0.0404413i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.187624 | − | 2.17279i | −0.0260188 | − | 0.301312i | ||||
\(53\) | − | 8.14672i | − | 1.11904i | −0.828818 | − | 0.559519i | \(-0.810986\pi\) | ||
0.828818 | − | 0.559519i | \(-0.189014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.39246 | −0.996799 | ||||||||
\(56\) | −2.80485 | + | 0.364437i | −0.374814 | + | 0.0486999i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0971845 | − | 2.25509i | −0.0127610 | − | 0.296108i | ||||
\(59\) | 15.0761i | 1.96274i | 0.192129 | + | 0.981370i | \(0.438461\pi\) | ||||
−0.192129 | + | 0.981370i | \(0.561539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.53745i | − | 0.708998i | −0.935056 | − | 0.354499i | \(-0.884651\pi\) | ||
0.935056 | − | 0.354499i | \(-0.115349\pi\) | |||||||
\(62\) | −10.5334 | + | 0.453944i | −1.33774 | + | 0.0576510i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.73437 | − | 2.04438i | 0.966796 | − | 0.255548i | ||||
\(65\) | 3.39553 | 0.421163 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.70421i | − | 0.941219i | −0.882342 | − | 0.470609i | \(-0.844034\pi\) | ||
0.882342 | − | 0.470609i | \(-0.155966\pi\) | |||||||
\(68\) | 7.35861 | − | 0.635429i | 0.892363 | − | 0.0770571i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.189605 | − | 4.39964i | −0.0226622 | − | 0.525858i | ||||
\(71\) | −13.5472 | −1.60776 | −0.803878 | − | 0.594794i | \(-0.797234\pi\) | ||||
−0.803878 | + | 0.594794i | \(0.797234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6727 | −1.71731 | −0.858656 | − | 0.512553i | \(-0.828700\pi\) | ||||
−0.858656 | + | 0.512553i | \(0.828700\pi\) | |||||||
\(74\) | −0.280953 | − | 6.51928i | −0.0326601 | − | 0.757851i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.186281 | − | 2.15723i | −0.0213679 | − | 0.247452i | ||||
\(77\) | 2.37402i | 0.270544i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.18122 | 0.582932 | 0.291466 | − | 0.956581i | \(-0.405857\pi\) | ||||
0.291466 | + | 0.956581i | \(0.405857\pi\) | |||||||
\(80\) | 2.13521 | + | 12.2712i | 0.238723 | + | 1.37197i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.0537773 | − | 0.00231757i | 0.00593870 | − | 0.000255932i | ||||
\(83\) | − | 0.138321i | − | 0.0151827i | −0.999971 | − | 0.00759136i | \(-0.997584\pi\) | ||
0.999971 | − | 0.00759136i | \(-0.00241643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4996i | 1.24731i | ||||||||
\(86\) | −0.673490 | − | 15.6278i | −0.0726243 | − | 1.68519i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.865179 | − | 6.65876i | −0.0922284 | − | 0.709826i | ||||
\(89\) | −11.9531 | −1.26703 | −0.633514 | − | 0.773731i | \(-0.718388\pi\) | ||||
−0.633514 | + | 0.773731i | \(0.718388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.09044i | − | 0.114309i | ||||||
\(92\) | 9.71118 | − | 0.838577i | 1.01246 | − | 0.0874277i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.476396 | + | 0.0205306i | −0.0491364 | + | 0.00211757i | ||||
\(95\) | 3.37121 | 0.345879 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.30202 | −0.538339 | −0.269169 | − | 0.963093i | \(-0.586749\pi\) | ||||
−0.269169 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(98\) | −1.41290 | + | 0.0608900i | −0.142725 | + | 0.00615081i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.35797 | + | 0.808077i | −0.935797 | + | 0.0808077i | ||||
\(101\) | 0.0753369i | 0.00749630i | 0.999993 | + | 0.00374815i | \(0.00119308\pi\) | ||||
−0.999993 | + | 0.00374815i | \(0.998807\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3347 | 1.51097 | 0.755487 | − | 0.655163i | \(-0.227400\pi\) | ||||
0.755487 | + | 0.655163i | \(0.227400\pi\) | |||||||
\(104\) | 0.397396 | + | 3.05852i | 0.0389679 | + | 0.299913i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.496053 | + | 11.5105i | 0.0481809 | + | 1.11800i | ||||
\(107\) | − | 4.03726i | − | 0.390297i | −0.980774 | − | 0.195148i | \(-0.937481\pi\) | ||
0.980774 | − | 0.195148i | \(-0.0625189\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2335i | 1.17176i | 0.810399 | + | 0.585879i | \(0.199251\pi\) | ||||
−0.810399 | + | 0.585879i | \(0.800749\pi\) | |||||||
\(110\) | 10.4448 | − | 0.450127i | 0.995875 | − | 0.0429179i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.94079 | − | 0.685701i | 0.372370 | − | 0.0647926i | ||||
\(113\) | −11.1934 | −1.05299 | −0.526495 | − | 0.850178i | \(-0.676494\pi\) | ||||
−0.526495 | + | 0.850178i | \(0.676494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.1761i | 1.41518i | ||||||||
\(116\) | 0.274624 | + | 3.18030i | 0.0254982 | + | 0.295284i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.917982 | − | 21.3010i | −0.0845071 | − | 1.96092i | ||||
\(119\) | 3.69300 | 0.338537 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.36404 | 0.487640 | ||||||||
\(122\) | 0.337175 | + | 7.82388i | 0.0305264 | + | 0.708340i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14.8550 | − | 1.28276i | 1.33402 | − | 0.115195i | ||||
\(125\) | 0.945386i | 0.0845579i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.43139 | −0.215751 | −0.107876 | − | 0.994164i | \(-0.534405\pi\) | ||||
−0.107876 | + | 0.994164i | \(0.534405\pi\) | |||||||
\(128\) | −10.8034 | + | 3.35946i | −0.954897 | + | 0.296937i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.79755 | + | 0.206753i | −0.420773 | + | 0.0181335i | ||||
\(131\) | 8.83723i | 0.772112i | 0.922475 | + | 0.386056i | \(0.126163\pi\) | ||||
−0.922475 | + | 0.386056i | \(0.873837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.08263i | − | 0.0938760i | ||||||
\(134\) | 0.469109 | + | 10.8853i | 0.0405248 | + | 0.940346i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.3583 | + | 1.34586i | −0.888218 | + | 0.115407i | ||||
\(137\) | 11.1478 | 0.952422 | 0.476211 | − | 0.879331i | \(-0.342010\pi\) | ||||
0.476211 | + | 0.879331i | \(0.342010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.2724i | 1.46502i | 0.680755 | + | 0.732511i | \(0.261652\pi\) | ||||
−0.680755 | + | 0.732511i | \(0.738348\pi\) | |||||||
\(140\) | 0.535788 | + | 6.20472i | 0.0452824 | + | 0.524394i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.1409 | − | 0.824888i | 1.60627 | − | 0.0692231i | ||||
\(143\) | 2.58872 | 0.216480 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.97000 | −0.412736 | ||||||||
\(146\) | 20.7311 | − | 0.893421i | 1.71572 | − | 0.0739400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.793917 | + | 9.19400i | 0.0652596 | + | 0.755742i | ||||
\(149\) | − | 13.7236i | − | 1.12428i | −0.827042 | − | 0.562140i | \(-0.809978\pi\) | ||
0.827042 | − | 0.562140i | \(-0.190022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8195 | −1.04324 | −0.521620 | − | 0.853178i | \(-0.674672\pi\) | ||||
−0.521620 | + | 0.853178i | \(0.674672\pi\) | |||||||
\(152\) | 0.394550 | + | 3.03662i | 0.0320023 | + | 0.246302i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.144554 | − | 3.35425i | −0.0116485 | − | 0.270293i | ||||
\(155\) | 23.2146i | 1.86465i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.1418i | 1.68730i | 0.536892 | + | 0.843651i | \(0.319598\pi\) | ||||
−0.536892 | + | 0.843651i | \(0.680402\pi\) | |||||||
\(158\) | −7.32055 | + | 0.315484i | −0.582392 | + | 0.0250986i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.76403 | − | 17.2080i | −0.297573 | − | 1.36042i | ||||
\(161\) | 4.87366 | 0.384098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.386568i | − | 0.0302784i | −0.999885 | − | 0.0151392i | \(-0.995181\pi\) | ||
0.999885 | − | 0.0151392i | \(-0.00481914\pi\) | |||||||
\(164\) | −0.0758409 | + | 0.00654899i | −0.00592218 | + | 0.000511390i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.00842236 | + | 0.195434i | 0.000653702 | + | 0.0151686i | ||||
\(167\) | −14.4336 | −1.11690 | −0.558451 | − | 0.829537i | \(-0.688604\pi\) | ||||
−0.558451 | + | 0.829537i | \(0.688604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8109 | 0.908534 | ||||||||
\(170\) | −0.700213 | − | 16.2479i | −0.0537039 | − | 1.24615i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.90315 | + | 22.0395i | 0.145114 | + | 1.68050i | ||||
\(173\) | − | 13.9493i | − | 1.06055i | −0.847826 | − | 0.530274i | \(-0.822089\pi\) | ||
0.847826 | − | 0.530274i | \(-0.177911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.69640 | −0.355014 | ||||||||
\(176\) | 1.62786 | + | 9.35550i | 0.122705 | + | 0.705197i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.8886 | − | 0.727825i | 1.26585 | − | 0.0545528i | ||||
\(179\) | 10.6569i | 0.796537i | 0.917269 | + | 0.398269i | \(0.130389\pi\) | ||||
−0.917269 | + | 0.398269i | \(0.869611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.63866i | 0.493448i | 0.969086 | + | 0.246724i | \(0.0793540\pi\) | ||||
−0.969086 | + | 0.246724i | \(0.920646\pi\) | |||||||
\(182\) | 0.0663968 | + | 1.54068i | 0.00492166 | + | 0.114203i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.6699 | + | 1.77614i | −1.00776 | + | 0.130939i | ||||
\(185\) | −14.3679 | −1.05635 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.76724i | 0.641124i | ||||||||
\(188\) | 0.671850 | − | 0.0580154i | 0.0489997 | − | 0.00423121i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.76319 | + | 0.205273i | −0.345558 | + | 0.0148920i | ||||
\(191\) | 9.81148 | 0.709934 | 0.354967 | − | 0.934879i | \(-0.384492\pi\) | ||||
0.354967 | + | 0.934879i | \(0.384492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4539 | 1.25636 | 0.628180 | − | 0.778068i | \(-0.283800\pi\) | ||||
0.628180 | + | 0.778068i | \(0.283800\pi\) | |||||||
\(194\) | 7.49124 | − | 0.322840i | 0.537839 | − | 0.0231785i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.99258 | − | 0.172063i | 0.142327 | − | 0.0122902i | ||||
\(197\) | − | 27.6871i | − | 1.97262i | −0.164888 | − | 0.986312i | \(-0.552726\pi\) | ||
0.164888 | − | 0.986312i | \(-0.447274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.29804 | 0.659121 | 0.329560 | − | 0.944134i | \(-0.393099\pi\) | ||||
0.329560 | + | 0.944134i | \(0.393099\pi\) | |||||||
\(200\) | 13.1727 | − | 1.71154i | 0.931450 | − | 0.121024i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.00458726 | − | 0.106444i | −0.000322759 | − | 0.00748935i | ||||
\(203\) | 1.59607i | 0.112022i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 0.118520i | − | 0.00827780i | ||||||
\(206\) | −21.6665 | + | 0.933730i | −1.50957 | + | 0.0650561i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.747715 | − | 4.29719i | −0.0518447 | − | 0.297957i | ||||
\(209\) | 2.57018 | 0.177783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.3068i | 1.12260i | 0.827611 | + | 0.561302i | \(0.189699\pi\) | ||||
−0.827611 | + | 0.561302i | \(0.810301\pi\) | |||||||
\(212\) | −1.40175 | − | 16.2330i | −0.0962725 | − | 1.11489i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.245829 | + | 5.70426i | 0.0168045 | + | 0.389935i | ||||
\(215\) | −34.4422 | −2.34894 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.45516 | 0.506089 | ||||||||
\(218\) | −0.744898 | − | 17.2848i | −0.0504509 | − | 1.17067i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −14.7301 | + | 1.27197i | −0.993103 | + | 0.0857562i | ||||
\(221\) | − | 4.02699i | − | 0.270885i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8846 | −1.26461 | −0.632304 | − | 0.774720i | \(-0.717891\pi\) | ||||
−0.632304 | + | 0.774720i | \(0.717891\pi\) | |||||||
\(224\) | −5.52620 | + | 1.20878i | −0.369235 | + | 0.0807652i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.8152 | − | 0.681568i | 1.05201 | − | 0.0453372i | ||||
\(227\) | 12.9709i | 0.860907i | 0.902613 | + | 0.430454i | \(0.141646\pi\) | ||||
−0.902613 | + | 0.430454i | \(0.858354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.92552i | − | 0.391569i | −0.980647 | − | 0.195785i | \(-0.937275\pi\) | ||
0.980647 | − | 0.195785i | \(-0.0627253\pi\) | |||||||
\(230\) | −0.924073 | − | 21.4424i | −0.0609315 | − | 1.41387i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.581666 | − | 4.47673i | −0.0381882 | − | 0.293912i | ||||
\(233\) | 12.2093 | 0.799861 | 0.399930 | − | 0.916546i | \(-0.369034\pi\) | ||||
0.399930 | + | 0.916546i | \(0.369034\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.04993i | 0.0684900i | ||||||||
\(236\) | 2.59404 | + | 30.0404i | 0.168858 | + | 1.95546i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.21785 | + | 0.224867i | −0.338223 | + | 0.0145759i | ||||
\(239\) | 22.5273 | 1.45717 | 0.728585 | − | 0.684956i | \(-0.240178\pi\) | ||||
0.728585 | + | 0.684956i | \(0.240178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1826 | −1.04241 | −0.521206 | − | 0.853431i | \(-0.674518\pi\) | ||||
−0.521206 | + | 0.853431i | \(0.674518\pi\) | |||||||
\(242\) | −7.57887 | + | 0.326616i | −0.487188 | + | 0.0209957i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.952791 | − | 11.0338i | −0.0609962 | − | 0.706369i | ||||
\(245\) | 3.11390i | 0.198940i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.18054 | −0.0751162 | ||||||||
\(248\) | −20.9106 | + | 2.71693i | −1.32782 | + | 0.172525i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.0575645 | − | 1.33574i | −0.00364070 | − | 0.0844794i | ||||
\(251\) | 6.88454i | 0.434548i | 0.976111 | + | 0.217274i | \(0.0697166\pi\) | ||||
−0.976111 | + | 0.217274i | \(0.930283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5702i | 0.727409i | ||||||||
\(254\) | 3.43532 | − | 0.148047i | 0.215551 | − | 0.00928932i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.0596 | − | 5.40440i | 0.941227 | − | 0.337775i | ||||
\(257\) | −2.70139 | −0.168508 | −0.0842541 | − | 0.996444i | \(-0.526851\pi\) | ||||
−0.0842541 | + | 0.996444i | \(0.526851\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.61410i | 0.286707i | ||||||||
\(260\) | 6.76587 | − | 0.584245i | 0.419602 | − | 0.0362333i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.538098 | − | 12.4861i | −0.0332438 | − | 0.771396i | ||||
\(263\) | 13.5500 | 0.835527 | 0.417763 | − | 0.908556i | \(-0.362814\pi\) | ||||
0.417763 | + | 0.908556i | \(0.362814\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.3681 | 1.55835 | ||||||||
\(266\) | 0.0659213 | + | 1.52965i | 0.00404190 | + | 0.0937889i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.32561 | − | 15.3513i | −0.0809745 | − | 0.937729i | ||||
\(269\) | − | 6.41522i | − | 0.391143i | −0.980689 | − | 0.195571i | \(-0.937344\pi\) | ||
0.980689 | − | 0.195571i | \(-0.0626562\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.5096 | −0.881397 | −0.440698 | − | 0.897655i | \(-0.645269\pi\) | ||||
−0.440698 | + | 0.897655i | \(0.645269\pi\) | |||||||
\(272\) | 14.5533 | − | 2.53229i | 0.882425 | − | 0.153543i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.7508 | + | 0.678790i | −0.951539 | + | 0.0410072i | ||||
\(275\) | − | 11.1493i | − | 0.672330i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 25.3175i | − | 1.52118i | −0.649231 | − | 0.760591i | \(-0.724909\pi\) | ||
0.649231 | − | 0.760591i | \(-0.275091\pi\) | |||||||
\(278\) | −1.05171 | − | 24.4042i | −0.0630776 | − | 1.46366i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.13482 | − | 8.73404i | −0.0678185 | − | 0.521958i | ||||
\(281\) | −0.719979 | −0.0429504 | −0.0214752 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214752 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3262i | 0.673275i | 0.941634 | + | 0.336637i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336637i | \(0.890710\pi\) | |||||||
\(284\) | −26.9939 | + | 2.33097i | −1.60180 | + | 0.138318i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.65761 | + | 0.157627i | −0.216279 | + | 0.00932069i | ||||
\(287\) | −0.0380616 | −0.00224670 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.36176 | −0.197751 | ||||||||
\(290\) | 7.02213 | − | 0.302623i | 0.412354 | − | 0.0177707i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.2366 | + | 2.52463i | −1.71094 | + | 0.147743i | ||||
\(293\) | − | 15.2567i | − | 0.891304i | −0.895206 | − | 0.445652i | \(-0.852972\pi\) | ||
0.895206 | − | 0.445652i | \(-0.147028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −46.9455 | −2.73327 | ||||||||
\(296\) | −1.68155 | − | 12.9419i | −0.0977381 | − | 0.752231i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.835628 | + | 19.3901i | 0.0484066 | + | 1.12324i | ||||
\(299\) | − | 5.31443i | − | 0.307342i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0608i | 0.637533i | ||||||||
\(302\) | 18.1128 | − | 0.780581i | 1.04227 | − | 0.0449174i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.742360 | − | 4.26642i | −0.0425773 | − | 0.244696i | ||||
\(305\) | 17.2431 | 0.987337 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.5497i | − | 1.45820i | −0.684409 | − | 0.729098i | \(-0.739940\pi\) | ||
0.684409 | − | 0.729098i | \(-0.260060\pi\) | |||||||
\(308\) | 0.408481 | + | 4.73043i | 0.0232753 | + | 0.269541i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.41354 | − | 32.8000i | −0.0802836 | − | 1.86292i | ||||
\(311\) | 3.00328 | 0.170300 | 0.0851501 | − | 0.996368i | \(-0.472863\pi\) | ||||
0.0851501 | + | 0.996368i | \(0.472863\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.53962 | −0.313118 | −0.156559 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156559 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(314\) | −1.28733 | − | 29.8713i | −0.0726480 | − | 1.68574i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.3240 | − | 0.891496i | 0.580771 | − | 0.0501506i | ||||
\(317\) | − | 32.1705i | − | 1.80688i | −0.428718 | − | 0.903439i | \(-0.641034\pi\) | ||
0.428718 | − | 0.903439i | \(-0.358966\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.78909 | −0.212148 | ||||||||
\(320\) | 6.36601 | + | 24.0841i | 0.355871 | + | 1.34634i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.88600 | + | 0.296757i | −0.383742 | + | 0.0165376i | ||||
\(323\) | − | 3.99815i | − | 0.222463i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.12114i | 0.284070i | ||||||||
\(326\) | 0.0235381 | + | 0.546183i | 0.00130366 | + | 0.0302503i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.106757 | − | 0.0138710i | 0.00589467 | − | 0.000765900i | ||||
\(329\) | 0.337175 | 0.0185891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.9617i | − | 1.37202i | −0.727592 | − | 0.686010i | \(-0.759361\pi\) | ||
0.727592 | − | 0.686010i | \(-0.240639\pi\) | |||||||
\(332\) | −0.0238000 | − | 0.275616i | −0.00130619 | − | 0.0151264i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.3932 | − | 0.878859i | 1.11587 | − | 0.0480890i | ||||
\(335\) | 23.9902 | 1.31072 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.7899 | 0.969076 | 0.484538 | − | 0.874770i | \(-0.338988\pi\) | ||||
0.484538 | + | 0.874770i | \(0.338988\pi\) | |||||||
\(338\) | −16.6877 | + | 0.719168i | −0.907691 | + | 0.0391176i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.97866 | + | 22.9140i | 0.107308 | + | 1.24269i | ||||
\(341\) | 17.6987i | 0.958437i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −4.03095 | − | 31.0238i | −0.217334 | − | 1.67269i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.849375 | + | 19.7091i | 0.0456627 | + | 1.05957i | ||||
\(347\) | 2.08108i | 0.111718i | 0.998439 | + | 0.0558591i | \(0.0177898\pi\) | ||||
−0.998439 | + | 0.0558591i | \(0.982210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.11683i | 0.380955i | 0.981692 | + | 0.190477i | \(0.0610036\pi\) | ||||
−0.981692 | + | 0.190477i | \(0.938996\pi\) | |||||||
\(350\) | 6.63555 | − | 0.285964i | 0.354685 | − | 0.0152854i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.86967 | − | 13.1193i | −0.152954 | − | 0.699260i | ||||
\(353\) | 28.9449 | 1.54058 | 0.770290 | − | 0.637694i | \(-0.220111\pi\) | ||||
0.770290 | + | 0.637694i | \(0.220111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 42.1847i | − | 2.23893i | ||||||
\(356\) | −23.8176 | + | 2.05669i | −1.26233 | + | 0.109004i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.648901 | − | 15.0572i | −0.0342955 | − | 0.795799i | ||||
\(359\) | −10.0190 | −0.528780 | −0.264390 | − | 0.964416i | \(-0.585171\pi\) | ||||
−0.264390 | + | 0.964416i | \(0.585171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8279 | 0.938311 | ||||||||
\(362\) | −0.404228 | − | 9.37977i | −0.0212457 | − | 0.492990i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.187624 | − | 2.17279i | −0.00983420 | − | 0.113885i | ||||
\(365\) | − | 45.6894i | − | 2.39149i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.4662 | 1.64252 | 0.821261 | − | 0.570552i | \(-0.193271\pi\) | ||||
0.821261 | + | 0.570552i | \(0.193271\pi\) | |||||||
\(368\) | 19.2061 | − | 3.34187i | 1.00119 | − | 0.174207i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.3004 | − | 0.874860i | 1.05537 | − | 0.0454818i | ||||
\(371\) | − | 8.14672i | − | 0.422956i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 31.8121i | − | 1.64717i | −0.567193 | − | 0.823585i | \(-0.691970\pi\) | ||
0.567193 | − | 0.823585i | \(-0.308030\pi\) | |||||||
\(374\) | −0.533837 | − | 12.3873i | −0.0276041 | − | 0.640530i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.945726 | + | 0.122879i | −0.0487721 | + | 0.00633700i | ||||
\(377\) | 1.74042 | 0.0896360 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.2806i | 0.784911i | 0.919771 | + | 0.392456i | \(0.128374\pi\) | ||||
−0.919771 | + | 0.392456i | \(0.871626\pi\) | |||||||
\(380\) | 6.71742 | − | 0.580060i | 0.344596 | − | 0.0297565i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.8627 | + | 0.597420i | −0.709275 | + | 0.0305667i | ||||
\(383\) | 19.0555 | 0.973691 | 0.486845 | − | 0.873488i | \(-0.338147\pi\) | ||||
0.486845 | + | 0.873488i | \(0.338147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.39246 | −0.376755 | ||||||||
\(386\) | −24.6607 | + | 1.06277i | −1.25520 | + | 0.0540935i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.5647 | + | 0.912282i | −0.536343 | + | 0.0463141i | ||||
\(389\) | 3.69055i | 0.187118i | 0.995614 | + | 0.0935591i | \(0.0298244\pi\) | ||||
−0.995614 | + | 0.0935591i | \(0.970176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.9984 | 0.910219 | ||||||||
\(392\) | −2.80485 | + | 0.364437i | −0.141666 | + | 0.0184068i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.68587 | + | 39.1192i | 0.0849327 | + | 1.97080i | ||||
\(395\) | 16.1338i | 0.811780i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 14.8184i | − | 0.743715i | −0.928290 | − | 0.371857i | \(-0.878721\pi\) | ||
0.928290 | − | 0.371857i | \(-0.121279\pi\) | |||||||
\(398\) | −13.1372 | + | 0.566157i | −0.658510 | + | 0.0283789i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.5075 | + | 3.22032i | −0.925376 | + | 0.161016i | ||||
\(401\) | −1.80006 | −0.0898908 | −0.0449454 | − | 0.998989i | \(-0.514311\pi\) | ||||
−0.0449454 | + | 0.998989i | \(0.514311\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.12940i | − | 0.404954i | ||||||
\(404\) | 0.0129627 | + | 0.150115i | 0.000644919 | + | 0.00746851i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0971845 | − | 2.25509i | −0.00482319 | − | 0.111918i | ||||
\(407\) | −10.9540 | −0.542968 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.6731 | −1.26945 | −0.634727 | − | 0.772736i | \(-0.718888\pi\) | ||||
−0.634727 | + | 0.772736i | \(0.718888\pi\) | |||||||
\(410\) | 0.00721668 | + | 0.167457i | 0.000356406 | + | 0.00827012i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 30.5557 | − | 2.63854i | 1.50537 | − | 0.129992i | ||||
\(413\) | 15.0761i | 0.741846i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.430719 | 0.0211431 | ||||||||
\(416\) | 1.31810 | + | 6.02599i | 0.0646254 | + | 0.295448i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.63142 | + | 0.156498i | −0.177618 | + | 0.00765458i | ||||
\(419\) | − | 17.3661i | − | 0.848392i | −0.905571 | − | 0.424196i | \(-0.860557\pi\) | ||
0.905571 | − | 0.424196i | \(-0.139443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4837i | 1.48568i | 0.669468 | + | 0.742841i | \(0.266522\pi\) | ||||
−0.669468 | + | 0.742841i | \(0.733478\pi\) | |||||||
\(422\) | −0.992918 | − | 23.0398i | −0.0483345 | − | 1.12156i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.96896 | + | 22.8503i | 0.144186 | + | 1.10971i | ||||
\(425\) | −17.3438 | −0.841298 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.53745i | − | 0.267976i | ||||||
\(428\) | −0.694664 | − | 8.04459i | −0.0335778 | − | 0.388850i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 48.6635 | − | 2.09718i | 2.34676 | − | 0.101135i | ||||
\(431\) | −9.49698 | −0.457453 | −0.228727 | − | 0.973491i | \(-0.573456\pi\) | ||||
−0.228727 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.6935 | 1.23475 | 0.617376 | − | 0.786668i | \(-0.288196\pi\) | ||||
0.617376 | + | 0.786668i | \(0.288196\pi\) | |||||||
\(434\) | −10.5334 | + | 0.453944i | −0.505620 | + | 0.0217900i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.10494 | + | 24.3763i | 0.100808 | + | 1.16741i | ||||
\(437\) | − | 5.27637i | − | 0.252403i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0047 | 0.525227 | 0.262614 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262614 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(440\) | 20.7347 | − | 2.69408i | 0.988490 | − | 0.128435i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.245203 | + | 5.68975i | 0.0116631 | + | 0.270634i | ||||
\(443\) | − | 32.0650i | − | 1.52346i | −0.647897 | − | 0.761728i | \(-0.724351\pi\) | ||
0.647897 | − | 0.761728i | \(-0.275649\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 37.2208i | − | 1.76444i | ||||||
\(446\) | 26.6821 | − | 1.14988i | 1.26344 | − | 0.0544486i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.73437 | − | 2.04438i | 0.365415 | − | 0.0965879i | ||||
\(449\) | 16.5474 | 0.780922 | 0.390461 | − | 0.920619i | \(-0.372316\pi\) | ||||
0.390461 | + | 0.920619i | \(0.372316\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 0.0903588i | − | 0.00425483i | ||||||
\(452\) | −22.3039 | + | 1.92598i | −1.04909 | + | 0.0905904i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.789796 | − | 18.3266i | −0.0370670 | − | 0.860109i | ||||
\(455\) | 3.39553 | 0.159185 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.9067 | −1.25864 | −0.629321 | − | 0.777145i | \(-0.716667\pi\) | ||||
−0.629321 | + | 0.777145i | \(0.716667\pi\) | |||||||
\(458\) | 0.360804 | + | 8.37217i | 0.0168593 | + | 0.391206i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.61125 | + | 30.2397i | 0.121750 | + | 1.40993i | ||||
\(461\) | − | 28.9351i | − | 1.34764i | −0.738895 | − | 0.673821i | \(-0.764652\pi\) | ||
0.738895 | − | 0.673821i | \(-0.235348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3287 | 0.480017 | 0.240009 | − | 0.970771i | \(-0.422850\pi\) | ||||
0.240009 | + | 0.970771i | \(0.422850\pi\) | |||||||
\(464\) | 1.09442 | + | 6.28977i | 0.0508074 | + | 0.291995i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.2506 | + | 0.743426i | −0.799119 | + | 0.0344386i | ||||
\(467\) | 22.1113i | 1.02319i | 0.859227 | + | 0.511595i | \(0.170945\pi\) | ||||
−0.859227 | + | 0.511595i | \(0.829055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.70421i | − | 0.355747i | ||||||
\(470\) | −0.0639303 | − | 1.48345i | −0.00294888 | − | 0.0684264i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.49428 | − | 42.2862i | −0.252895 | − | 1.94638i | ||||
\(473\) | −26.2585 | −1.20737 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.08446i | 0.233291i | ||||||||
\(476\) | 7.35861 | − | 0.635429i | 0.337281 | − | 0.0291248i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −31.8289 | + | 1.37169i | −1.45582 | + | 0.0627395i | ||||
\(479\) | −5.77499 | −0.263866 | −0.131933 | − | 0.991259i | \(-0.542118\pi\) | ||||
−0.131933 | + | 0.991259i | \(0.542118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.03140 | 0.229412 | ||||||||
\(482\) | 22.8644 | − | 0.985357i | 1.04145 | − | 0.0448818i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.6883 | − | 0.922954i | 0.485832 | − | 0.0419525i | ||||
\(485\) | − | 16.5100i | − | 0.749680i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5566 | 0.568993 | 0.284497 | − | 0.958677i | \(-0.408174\pi\) | ||||
0.284497 | + | 0.958677i | \(0.408174\pi\) | |||||||
\(488\) | 2.01805 | + | 15.5317i | 0.0913529 | + | 0.703088i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.189605 | − | 4.39964i | −0.00856550 | − | 0.198756i | ||||
\(491\) | 20.9548i | 0.945677i | 0.881149 | + | 0.472839i | \(0.156771\pi\) | ||||
−0.881149 | + | 0.472839i | \(0.843229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.89428i | 0.265465i | ||||||||
\(494\) | 1.66799 | − | 0.0718832i | 0.0750465 | − | 0.00323418i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29.3792 | − | 5.11201i | 1.31916 | − | 0.229536i | ||||
\(497\) | −13.5472 | −0.607675 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0152i | 0.582641i | 0.956626 | + | 0.291320i | \(0.0940946\pi\) | ||||
−0.956626 | + | 0.291320i | \(0.905905\pi\) | |||||||
\(500\) | 0.162666 | + | 1.88376i | 0.00727464 | + | 0.0842443i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.419200 | − | 9.72718i | −0.0187098 | − | 0.434146i | ||||
\(503\) | −22.9100 | −1.02150 | −0.510752 | − | 0.859728i | \(-0.670633\pi\) | ||||
−0.510752 | + | 0.859728i | \(0.670633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.234592 | −0.0104392 | ||||||||
\(506\) | −0.704506 | − | 16.3475i | −0.0313191 | − | 0.726735i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.84475 | + | 0.418353i | −0.214951 | + | 0.0185614i | ||||
\(509\) | 24.5703i | 1.08906i | 0.838741 | + | 0.544530i | \(0.183292\pi\) | ||||
−0.838741 | + | 0.544530i | \(0.816708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6727 | −0.649083 | ||||||||
\(512\) | −20.9487 | + | 8.55287i | −0.925811 | + | 0.377987i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.81680 | − | 0.164488i | 0.168352 | − | 0.00725524i | ||||
\(515\) | 47.7508i | 2.10415i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.800460i | 0.0352042i | ||||||||
\(518\) | −0.280953 | − | 6.51928i | −0.0123444 | − | 0.286441i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.52394 | + | 1.23745i | −0.417652 | + | 0.0542660i | ||||
\(521\) | 1.51316 | 0.0662929 | 0.0331465 | − | 0.999451i | \(-0.489447\pi\) | ||||
0.0331465 | + | 0.999451i | \(0.489447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.202190i | − | 0.00884117i | −0.999990 | − | 0.00442059i | \(-0.998593\pi\) | ||
0.999990 | − | 0.00442059i | \(-0.00140712\pi\) | |||||||
\(524\) | 1.52056 | + | 17.6089i | 0.0664260 | + | 0.769249i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1448 | + | 0.825057i | −0.834752 | + | 0.0359742i | ||||
\(527\) | 27.5319 | 1.19931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.752559 | 0.0327199 | ||||||||
\(530\) | −35.8426 | + | 1.54466i | −1.55690 | + | 0.0670958i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.186281 | − | 2.15723i | −0.00807629 | − | 0.0935279i | ||||
\(533\) | 0.0415038i | 0.00179773i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5716 | 0.543520 | ||||||||
\(536\) | 2.80770 | + | 21.6092i | 0.121274 | + | 0.933373i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.390623 | + | 9.06408i | 0.0168409 | + | 0.390780i | ||||
\(539\) | 2.37402i | 0.102256i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 28.5045i | − | 1.22550i | −0.790275 | − | 0.612752i | \(-0.790062\pi\) | ||
0.790275 | − | 0.612752i | \(-0.209938\pi\) | |||||||
\(542\) | 20.5007 | − | 0.883490i | 0.880580 | − | 0.0379492i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.4082 | + | 4.46403i | −0.874996 | + | 0.191394i | ||||
\(545\) | −38.0940 | −1.63177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 37.9150i | − | 1.62113i | −0.585648 | − | 0.810565i | \(-0.699160\pi\) | ||
0.585648 | − | 0.810565i | \(-0.300840\pi\) | |||||||
\(548\) | 22.2130 | − | 1.91813i | 0.948891 | − | 0.0819383i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.678882 | + | 15.7529i | 0.0289476 | + | 0.671706i | ||||
\(551\) | 1.72795 | 0.0736132 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.18122 | 0.220328 | ||||||||
\(554\) | 1.54158 | + | 35.7712i | 0.0654956 | + | 1.51977i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.97194 | + | 34.4166i | 0.126038 | + | 1.45959i | ||||
\(557\) | 16.6109i | 0.703828i | 0.936032 | + | 0.351914i | \(0.114469\pi\) | ||||
−0.936032 | + | 0.351914i | \(0.885531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0611 | 0.510131 | ||||||||
\(560\) | 2.13521 | + | 12.2712i | 0.0902289 | + | 0.518554i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.01726 | − | 0.0438395i | 0.0429105 | − | 0.00184926i | ||||
\(563\) | 6.84219i | 0.288364i | 0.989551 | + | 0.144182i | \(0.0460551\pi\) | ||||
−0.989551 | + | 0.144182i | \(0.953945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 34.8553i | − | 1.46637i | ||||||
\(566\) | −0.689654 | − | 16.0029i | −0.0289883 | − | 0.672651i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 37.9979 | − | 4.93710i | 1.59435 | − | 0.207156i | ||||
\(569\) | −15.3184 | −0.642180 | −0.321090 | − | 0.947049i | \(-0.604049\pi\) | ||||
−0.321090 | + | 0.947049i | \(0.604049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 36.6853i | − | 1.53523i | −0.640911 | − | 0.767616i | \(-0.721443\pi\) | ||
0.640911 | − | 0.767616i | \(-0.278557\pi\) | |||||||
\(572\) | 5.15825 | − | 0.445424i | 0.215677 | − | 0.0186241i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.0537773 | − | 0.00231757i | 0.00224462 | − | 9.67334e-5i | ||||
\(575\) | −22.8886 | −0.954523 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.9150 | −0.995596 | −0.497798 | − | 0.867293i | \(-0.665858\pi\) | ||||
−0.497798 | + | 0.867293i | \(0.665858\pi\) | |||||||
\(578\) | 4.74984 | − | 0.204697i | 0.197567 | − | 0.00851429i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.90315 | + | 0.855154i | −0.411206 | + | 0.0355083i | ||||
\(581\) | − | 0.138321i | − | 0.00573852i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.3404 | 0.800999 | ||||||||
\(584\) | 41.1548 | − | 5.34728i | 1.70300 | − | 0.221272i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.928978 | + | 21.5562i | 0.0383757 | + | 0.890477i | ||||
\(587\) | − | 45.0433i | − | 1.85914i | −0.368651 | − | 0.929568i | \(-0.620180\pi\) | ||
0.368651 | − | 0.929568i | \(-0.379820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.07118i | − | 0.332567i | ||||||
\(590\) | 66.3294 | − | 2.85851i | 2.73074 | − | 0.117683i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.16389 | + | 18.1832i | 0.130035 | + | 0.747325i | ||||
\(593\) | 13.4524 | 0.552425 | 0.276212 | − | 0.961097i | \(-0.410921\pi\) | ||||
0.276212 | + | 0.961097i | \(0.410921\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4996i | 0.471439i | ||||||||
\(596\) | −2.36132 | − | 27.3454i | −0.0967235 | − | 1.12011i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.323596 | + | 7.50877i | 0.0132328 | + | 0.307057i | ||||
\(599\) | −21.8377 | −0.892263 | −0.446132 | − | 0.894967i | \(-0.647199\pi\) | ||||
−0.446132 | + | 0.894967i | \(0.647199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.3704 | −0.667764 | −0.333882 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333882 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(602\) | −0.673490 | − | 15.6278i | −0.0274494 | − | 0.636942i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.5440 | + | 2.20577i | −1.03937 | + | 0.0897515i | ||||
\(605\) | 16.7031i | 0.679078i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.8256 | 1.17000 | 0.584998 | − | 0.811034i | \(-0.301095\pi\) | ||||
0.584998 | + | 0.811034i | \(0.301095\pi\) | |||||||
\(608\) | 1.30866 | + | 5.98283i | 0.0530734 | + | 0.242636i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.3628 | + | 1.04993i | −0.986421 | + | 0.0425105i | ||||
\(611\) | − | 0.367669i | − | 0.0148743i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.6397i | − | 1.39908i | −0.714592 | − | 0.699541i | \(-0.753388\pi\) | ||
0.714592 | − | 0.699541i | \(-0.246612\pi\) | |||||||
\(614\) | 1.55572 | + | 36.0992i | 0.0627837 | + | 1.45684i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.865179 | − | 6.65876i | −0.0348591 | − | 0.268289i | ||||
\(617\) | 38.6359 | 1.55542 | 0.777711 | − | 0.628622i | \(-0.216381\pi\) | ||||
0.777711 | + | 0.628622i | \(0.216381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.9642i | 1.04359i | 0.853071 | + | 0.521794i | \(0.174737\pi\) | ||||
−0.853071 | + | 0.521794i | \(0.825263\pi\) | |||||||
\(620\) | 3.99438 | + | 46.2571i | 0.160418 | + | 1.85773i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.24333 | + | 0.182869i | −0.170142 | + | 0.00733239i | ||||
\(623\) | −11.9531 | −0.478891 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.4258 | −1.05703 | ||||||||
\(626\) | 7.82694 | − | 0.337307i | 0.312828 | − | 0.0134815i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.63773 | + | 42.1269i | 0.145161 | + | 1.68105i | ||||
\(629\) | 17.0399i | 0.679425i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.94731 | 0.236759 | 0.118379 | − | 0.992968i | \(-0.462230\pi\) | ||||
0.118379 | + | 0.992968i | \(0.462230\pi\) | |||||||
\(632\) | −14.5325 | + | 1.88823i | −0.578073 | + | 0.0751096i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.95886 | + | 45.4538i | 0.0777964 | + | 1.80520i | ||||
\(635\) | − | 7.57112i | − | 0.300451i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.09044i | − | 0.0432048i | ||||||
\(638\) | 5.35362 | − | 0.230718i | 0.211952 | − | 0.00913420i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.4610 | − | 33.6408i | −0.413508 | − | 1.32977i | ||||
\(641\) | −41.7290 | −1.64820 | −0.824098 | − | 0.566447i | \(-0.808318\pi\) | ||||
−0.824098 | + | 0.566447i | \(0.808318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9825i | 1.45845i | 0.684275 | + | 0.729224i | \(0.260119\pi\) | ||||
−0.684275 | + | 0.729224i | \(0.739881\pi\) | |||||||
\(644\) | 9.71118 | − | 0.838577i | 0.382674 | − | 0.0330446i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.243447 | + | 5.64900i | 0.00957831 | + | 0.222257i | ||||
\(647\) | −2.39044 | −0.0939778 | −0.0469889 | − | 0.998895i | \(-0.514963\pi\) | ||||
−0.0469889 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.7909 | −1.40492 | ||||||||
\(650\) | −0.311826 | − | 7.23567i | −0.0122308 | − | 0.283806i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0665141 | − | 0.770270i | −0.00260489 | − | 0.0301661i | ||||
\(653\) | 27.1588i | 1.06280i | 0.847120 | + | 0.531402i | \(0.178335\pi\) | ||||
−0.847120 | + | 0.531402i | \(0.821665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.5183 | −1.07523 | ||||||||
\(656\) | −0.149993 | + | 0.0260988i | −0.00585623 | + | 0.00101899i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.476396 | + | 0.0205306i | −0.0185718 | + | 0.000800365i | ||||
\(659\) | 41.3343i | 1.61016i | 0.593169 | + | 0.805078i | \(0.297877\pi\) | ||||
−0.593169 | + | 0.805078i | \(0.702123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.44768i | 0.250786i | 0.992107 | + | 0.125393i | \(0.0400192\pi\) | ||||
−0.992107 | + | 0.125393i | \(0.959981\pi\) | |||||||
\(662\) | 1.51992 | + | 35.2684i | 0.0590733 | + | 1.37075i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0504093 | + | 0.387970i | 0.00195626 | + | 0.0150562i | ||||
\(665\) | 3.37121 | 0.130730 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.77869i | 0.301192i | ||||||||
\(668\) | −28.7601 | + | 2.48348i | −1.11276 | + | 0.0960889i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −33.8958 | + | 1.46076i | −1.30951 | + | 0.0564341i | ||||
\(671\) | 13.1460 | 0.507496 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.1564 | −1.39373 | −0.696863 | − | 0.717204i | \(-0.745421\pi\) | ||||
−0.696863 | + | 0.717204i | \(0.745421\pi\) | |||||||
\(674\) | −25.1354 | + | 1.08322i | −0.968178 | + | 0.0417243i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.5343 | − | 2.03223i | 0.905165 | − | 0.0781626i | ||||
\(677\) | 47.4088i | 1.82207i | 0.412330 | + | 0.911035i | \(0.364715\pi\) | ||||
−0.412330 | + | 0.911035i | \(0.635285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.30202 | −0.203473 | ||||||||
\(680\) | −4.19089 | − | 32.2548i | −0.160713 | − | 1.23691i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.07767 | − | 25.0065i | −0.0412662 | − | 0.957548i | ||||
\(683\) | 3.55646i | 0.136084i | 0.997682 | + | 0.0680420i | \(0.0216752\pi\) | ||||
−0.997682 | + | 0.0680420i | \(0.978325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.7132i | 1.32632i | ||||||||
\(686\) | −1.41290 | + | 0.0608900i | −0.0539449 | + | 0.00232479i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.58438 | + | 43.5882i | 0.289152 | + | 1.66178i | ||||
\(689\) | −8.88350 | −0.338435 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 41.6181i | − | 1.58323i | −0.611023 | − | 0.791613i | \(-0.709242\pi\) | ||
0.611023 | − | 0.791613i | \(-0.290758\pi\) | |||||||
\(692\) | −2.40017 | − | 27.7952i | −0.0912407 | − | 1.05662i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.126717 | − | 2.94036i | −0.00481010 | − | 0.111615i | ||||
\(695\) | −53.7845 | −2.04016 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.140561 | −0.00532414 | ||||||||
\(698\) | −0.433343 | − | 10.0554i | −0.0164023 | − | 0.380602i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.35797 | + | 0.808077i | −0.353698 | + | 0.0305424i | ||||
\(701\) | − | 34.8945i | − | 1.31795i | −0.752166 | − | 0.658973i | \(-0.770991\pi\) | ||
0.752166 | − | 0.658973i | \(-0.229009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.99537 | 0.188404 | ||||||||
\(704\) | 4.85340 | + | 18.3615i | 0.182919 | + | 0.692026i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.8963 | + | 1.76245i | −1.53915 | + | 0.0663308i | ||||
\(707\) | 0.0753369i | 0.00283334i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.2296i | 1.84886i | 0.381357 | + | 0.924428i | \(0.375457\pi\) | ||||
−0.381357 | + | 0.924428i | \(0.624543\pi\) | |||||||
\(710\) | 2.56862 | + | 59.6028i | 0.0963987 | + | 2.23685i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 33.5267 | − | 4.35615i | 1.25647 | − | 0.163254i | ||||
\(713\) | 36.3339 | 1.36072 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.06103i | 0.301466i | ||||||||
\(716\) | 1.83367 | + | 21.2349i | 0.0685274 | + | 0.793584i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.1558 | − | 0.610054i | 0.528290 | − | 0.0227670i | ||||
\(719\) | 10.9969 | 0.410117 | 0.205058 | − | 0.978750i | \(-0.434262\pi\) | ||||
0.205058 | + | 0.978750i | \(0.434262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3347 | 0.571095 | ||||||||
\(722\) | −25.1891 | + | 1.08554i | −0.937441 | + | 0.0403996i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.14227 | + | 13.2281i | 0.0424521 | + | 0.491618i | ||||
\(725\) | − | 7.49577i | − | 0.278386i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.03008 | 0.334907 | 0.167454 | − | 0.985880i | \(-0.446446\pi\) | ||||
0.167454 | + | 0.985880i | \(0.446446\pi\) | |||||||
\(728\) | 0.397396 | + | 3.05852i | 0.0147285 | + | 0.113356i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.78203 | + | 64.5547i | 0.102967 | + | 2.38928i | ||||
\(731\) | 40.8474i | 1.51080i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.6840i | 1.53963i | 0.638265 | + | 0.769817i | \(0.279653\pi\) | ||||
−0.638265 | + | 0.769817i | \(0.720347\pi\) | |||||||
\(734\) | −44.4587 | + | 1.91598i | −1.64100 | + | 0.0707200i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.9328 | + | 5.89119i | −0.992756 | + | 0.217152i | ||||
\(737\) | 18.2899 | 0.673718 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 34.7320i | − | 1.27764i | −0.769358 | − | 0.638818i | \(-0.779424\pi\) | ||
0.769358 | − | 0.638818i | \(-0.220576\pi\) | |||||||
\(740\) | −28.6292 | + | 2.47218i | −1.05243 | + | 0.0908792i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.496053 | + | 11.5105i | 0.0182107 | + | 0.422564i | ||||
\(743\) | 15.9173 | 0.583951 | 0.291975 | − | 0.956426i | \(-0.405687\pi\) | ||||
0.291975 | + | 0.956426i | \(0.405687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.7339 | 1.56565 | ||||||||
\(746\) | 1.93704 | + | 44.9474i | 0.0709201 | + | 1.64564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.50852 | + | 17.4695i | 0.0551569 | + | 0.638747i | ||||
\(749\) | − | 4.03726i | − | 0.147518i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.7001 | 0.499925 | 0.249963 | − | 0.968255i | \(-0.419582\pi\) | ||||
0.249963 | + | 0.968255i | \(0.419582\pi\) | |||||||
\(752\) | 1.32874 | − | 0.231201i | 0.0484540 | − | 0.00843104i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.45904 | + | 0.105974i | −0.0895529 | + | 0.00385934i | ||||
\(755\) | − | 39.9188i | − | 1.45279i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 27.3072i | − | 0.992496i | −0.868181 | − | 0.496248i | \(-0.834711\pi\) | ||
0.868181 | − | 0.496248i | \(-0.165289\pi\) | |||||||
\(758\) | −0.930435 | − | 21.5900i | −0.0337949 | − | 0.784183i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.45573 | + | 1.22859i | −0.342995 | + | 0.0445657i | ||||
\(761\) | 18.3078 | 0.663657 | 0.331829 | − | 0.943340i | \(-0.392334\pi\) | ||||
0.331829 | + | 0.943340i | \(0.392334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.2335i | 0.442883i | ||||||||
\(764\) | 19.5502 | − | 1.68819i | 0.707301 | − | 0.0610767i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.9236 | + | 1.16029i | −0.972788 | + | 0.0419229i | ||||
\(767\) | 16.4396 | 0.593598 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3631 | −0.481884 | −0.240942 | − | 0.970540i | \(-0.577456\pi\) | ||||
−0.240942 | + | 0.970540i | \(0.577456\pi\) | |||||||
\(770\) | 10.4448 | − | 0.450127i | 0.376405 | − | 0.0162214i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 34.7784 | − | 3.00317i | 1.25170 | − | 0.108087i | ||||
\(773\) | − | 39.3918i | − | 1.41682i | −0.705799 | − | 0.708412i | \(-0.749412\pi\) | ||
0.705799 | − | 0.708412i | \(-0.250588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.0124 | −1.25768 | ||||||||
\(776\) | 14.8714 | − | 1.93225i | 0.533851 | − | 0.0693638i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.224717 | − | 5.21438i | −0.00805651 | − | 0.186945i | ||||
\(779\) | 0.0412066i | 0.00147638i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 32.1613i | − | 1.15082i | ||||||
\(782\) | −25.4300 | + | 1.09592i | −0.909375 | + | 0.0391901i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.94079 | − | 0.685701i | 0.140742 | − | 0.0244893i | ||||
\(785\) | −65.8336 | −2.34970 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.3862i | − | 1.29703i | −0.761203 | − | 0.648514i | \(-0.775391\pi\) | ||
0.761203 | − | 0.648514i | \(-0.224609\pi\) | |||||||
\(788\) | −4.76393 | − | 55.1689i | −0.169708 | − | 1.96531i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.982387 | − | 22.7955i | −0.0349518 | − | 0.811027i | ||||
\(791\) | −11.1934 | −0.397993 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.03826 | −0.214425 | ||||||||
\(794\) | 0.902292 | + | 20.9370i | 0.0320212 | + | 0.743025i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.5271 | − | 1.59985i | 0.656677 | − | 0.0567052i | ||||
\(797\) | 33.1598i | 1.17458i | 0.809377 | + | 0.587290i | \(0.199805\pi\) | ||||
−0.809377 | + | 0.587290i | \(0.800195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.24519 | 0.0440516 | ||||||||
\(800\) | 25.9532 | − | 5.67692i | 0.917585 | − | 0.200710i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.54331 | − | 0.109606i | 0.0898074 | − | 0.00387031i | ||||
\(803\) | − | 34.8333i | − | 1.22924i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.1761i | 0.534888i | ||||||||
\(806\) | 0.494999 | + | 11.4860i | 0.0174356 | + | 0.404579i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.0274555 | − | 0.211309i | −0.000965883 | − | 0.00743382i | ||||
\(809\) | 44.9173 | 1.57921 | 0.789604 | − | 0.613616i | \(-0.210286\pi\) | ||||
0.789604 | + | 0.613616i | \(0.210286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5222i | 1.31758i | 0.752325 | + | 0.658792i | \(0.228932\pi\) | ||||
−0.752325 | + | 0.658792i | \(0.771068\pi\) | |||||||
\(812\) | 0.274624 | + | 3.18030i | 0.00963743 | + | 0.111607i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.4769 | − | 0.666986i | 0.542464 | − | 0.0233779i | ||||
\(815\) | 1.20374 | 0.0421650 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9747 | 0.418943 | ||||||||
\(818\) | 36.2736 | − | 1.56324i | 1.26828 | − | 0.0546573i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0203929 | − | 0.236161i | −0.000712152 | − | 0.00824711i | ||||
\(821\) | 0.214362i | 0.00748129i | 0.999993 | + | 0.00374065i | \(0.00119069\pi\) | ||||
−0.999993 | + | 0.00374065i | \(0.998809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.84153 | −0.168765 | −0.0843825 | − | 0.996433i | \(-0.526892\pi\) | ||||
−0.0843825 | + | 0.996433i | \(0.526892\pi\) | |||||||
\(824\) | −43.0116 | + | 5.58854i | −1.49838 | + | 0.194686i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.917982 | − | 21.3010i | −0.0319407 | − | 0.741158i | ||||
\(827\) | − | 9.13088i | − | 0.317512i | −0.987318 | − | 0.158756i | \(-0.949252\pi\) | ||
0.987318 | − | 0.158756i | \(-0.0507483\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 22.8115i | − | 0.792275i | −0.918191 | − | 0.396138i | \(-0.870350\pi\) | ||
0.918191 | − | 0.396138i | \(-0.129650\pi\) | |||||||
\(830\) | −0.608563 | + | 0.0262264i | −0.0211235 | + | 0.000910333i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.22927 | − | 8.43387i | −0.0772862 | − | 0.292392i | ||||
\(833\) | 3.69300 | 0.127955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 44.9447i | − | 1.55538i | ||||||
\(836\) | 5.12131 | − | 0.442234i | 0.177124 | − | 0.0152950i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.05742 | + | 24.5367i | 0.0365281 | + | 0.847605i | ||||
\(839\) | 37.9537 | 1.31031 | 0.655154 | − | 0.755496i | \(-0.272604\pi\) | ||||
0.655154 | + | 0.755496i | \(0.272604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4526 | 0.912157 | ||||||||
\(842\) | −1.85615 | − | 43.0704i | −0.0639671 | − | 1.48430i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.80579 | + | 32.4926i | 0.0965793 | + | 1.11844i | ||||
\(845\) | 36.7781i | 1.26521i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.36404 | 0.184311 | ||||||||
\(848\) | −5.58621 | − | 32.1045i | −0.191831 | − | 1.10247i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.5051 | − | 1.05606i | 0.840517 | − | 0.0362227i | ||||
\(851\) | 22.4876i | 0.770864i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.9465i | 1.23078i | 0.788221 | + | 0.615392i | \(0.211002\pi\) | ||||
−0.788221 | + | 0.615392i | \(0.788998\pi\) | |||||||
\(854\) | 0.337175 | + | 7.82388i | 0.0115379 | + | 0.267728i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.47133 | + | 11.3239i | 0.0502889 | + | 0.387043i | ||||
\(857\) | −36.9904 | −1.26357 | −0.631783 | − | 0.775145i | \(-0.717677\pi\) | ||||
−0.631783 | + | 0.775145i | \(0.717677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.924367i | 0.0315390i | 0.999876 | + | 0.0157695i | \(0.00501979\pi\) | ||||
−0.999876 | + | 0.0157695i | \(0.994980\pi\) | |||||||
\(860\) | −68.6290 | + | 5.92623i | −2.34023 | + | 0.202083i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.4183 | − | 0.578271i | 0.457029 | − | 0.0196960i | ||||
\(863\) | 11.2057 | 0.381445 | 0.190723 | − | 0.981644i | \(-0.438917\pi\) | ||||
0.190723 | + | 0.981644i | \(0.438917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.4369 | 1.47690 | ||||||||
\(866\) | −36.3024 | + | 1.56448i | −1.23361 | + | 0.0531631i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.8550 | − | 1.28276i | 0.504213 | − | 0.0435396i | ||||
\(869\) | 12.3003i | 0.417259i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.40098 | −0.284656 | ||||||||
\(872\) | −4.45834 | − | 34.3132i | −0.150978 | − | 1.16199i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.321278 | + | 7.45500i | 0.0108674 | + | 0.252169i | ||||
\(875\) | 0.945386i | 0.0319599i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 38.6354i | − | 1.30463i | −0.757950 | − | 0.652313i | \(-0.773799\pi\) | ||
0.757950 | − | 0.652313i | \(-0.226201\pi\) | |||||||
\(878\) | −15.5486 | + | 0.670078i | −0.524740 | + | 0.0226140i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −29.1321 | + | 5.06902i | −0.982044 | + | 0.170876i | ||||
\(881\) | 47.0860 | 1.58637 | 0.793184 | − | 0.608982i | \(-0.208422\pi\) | ||||
0.793184 | + | 0.608982i | \(0.208422\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.23864i | 0.0753362i | 0.999290 | + | 0.0376681i | \(0.0119930\pi\) | ||||
−0.999290 | + | 0.0376681i | \(0.988007\pi\) | |||||||
\(884\) | −0.692897 | − | 8.02413i | −0.0233046 | − | 0.269881i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.95244 | + | 45.3048i | 0.0655935 | + | 1.52204i | ||||
\(887\) | 56.5911 | 1.90014 | 0.950071 | − | 0.312032i | \(-0.101010\pi\) | ||||
0.950071 | + | 0.312032i | \(0.101010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.43139 | −0.0815463 | ||||||||
\(890\) | 2.26638 | + | 52.5894i | 0.0759691 | + | 1.76280i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.6292 | + | 3.24935i | −1.25992 | + | 0.108796i | ||||
\(893\) | − | 0.365036i | − | 0.0122155i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.1847 | −1.10924 | ||||||||
\(896\) | −10.8034 | + | 3.35946i | −0.360917 | + | 0.112232i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.3799 | + | 1.00757i | −0.780198 | + | 0.0336231i | ||||
\(899\) | 11.8989i | 0.396852i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 30.0858i | − | 1.00230i | ||||||
\(902\) | 0.00550194 | + | 0.127668i | 0.000183195 | + | 0.00425088i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31.3959 | − | 4.07930i | 1.04421 | − | 0.135676i | ||||
\(905\) | −20.6721 | −0.687165 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 37.0996i | − | 1.23187i | −0.787797 | − | 0.615935i | \(-0.788778\pi\) | ||
0.787797 | − | 0.615935i | \(-0.211222\pi\) | |||||||
\(908\) | 2.23181 | + | 25.8456i | 0.0740652 | + | 0.857715i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.79755 | + | 0.206753i | −0.159037 | + | 0.00685381i | ||||
\(911\) | 45.3701 | 1.50318 | 0.751589 | − | 0.659632i | \(-0.229288\pi\) | ||||
0.751589 | + | 0.659632i | \(0.229288\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.328377 | 0.0108677 | ||||||||
\(914\) | 38.0165 | − | 1.63835i | 1.25748 | − | 0.0541917i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.01956 | − | 11.8071i | −0.0336873 | − | 0.390117i | ||||
\(917\) | 8.83723i | 0.291831i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.8038 | 0.950148 | 0.475074 | − | 0.879946i | \(-0.342421\pi\) | ||||
0.475074 | + | 0.879946i | \(0.342421\pi\) | |||||||
\(920\) | −5.53073 | − | 42.5667i | −0.182343 | − | 1.40338i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.76186 | + | 40.8825i | 0.0580237 | + | 1.34639i | ||||
\(923\) | 14.7724i | 0.486240i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 21.6697i | − | 0.712495i | ||||||
\(926\) | −14.5935 | + | 0.628917i | −0.479572 | + | 0.0206675i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.92930 | − | 8.82019i | −0.0633323 | − | 0.289537i | ||||
\(929\) | 45.5518 | 1.49451 | 0.747254 | − | 0.664539i | \(-0.231372\pi\) | ||||
0.747254 | + | 0.664539i | \(0.231372\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.08263i | − | 0.0354818i | ||||||
\(932\) | 24.3282 | − | 2.10078i | 0.796895 | − | 0.0688133i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.34636 | − | 31.2411i | −0.0440541 | − | 1.02224i | ||||
\(935\) | −27.3003 | −0.892817 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.3973 | −1.41773 | −0.708864 | − | 0.705346i | \(-0.750792\pi\) | ||||
−0.708864 | + | 0.705346i | \(0.750792\pi\) | |||||||
\(938\) | 0.469109 | + | 10.8853i | 0.0153169 | + | 0.355417i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.180654 | + | 2.09208i | 0.00589230 | + | 0.0682360i | ||||
\(941\) | − | 17.5629i | − | 0.572534i | −0.958150 | − | 0.286267i | \(-0.907586\pi\) | ||
0.958150 | − | 0.286267i | \(-0.0924145\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.185499 | −0.00604068 | ||||||||
\(944\) | 10.3377 | + | 59.4117i | 0.336463 | + | 1.93369i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 37.1007 | − | 1.59888i | 1.20625 | − | 0.0519840i | ||||
\(947\) | − | 33.8968i | − | 1.10150i | −0.834671 | − | 0.550749i | \(-0.814342\pi\) | ||
0.834671 | − | 0.550749i | \(-0.185658\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.9997i | 0.519373i | ||||||||
\(950\) | −0.309593 | − | 7.18385i | −0.0100445 | − | 0.233075i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.3583 | + | 1.34586i | −0.335715 | + | 0.0436197i | ||||
\(953\) | 42.7021 | 1.38326 | 0.691628 | − | 0.722254i | \(-0.256894\pi\) | ||||
0.691628 | + | 0.722254i | \(0.256894\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.5520i | 0.988639i | ||||||||
\(956\) | 44.8875 | − | 3.87612i | 1.45177 | − | 0.125363i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.15950 | − | 0.351639i | 0.263621 | − | 0.0113609i | ||||
\(959\) | 11.1478 | 0.359982 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.5794 | 0.792883 | ||||||||
\(962\) | −7.10888 | + | 0.306362i | −0.229200 | + | 0.00987751i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −32.2452 | + | 2.78443i | −1.03855 | + | 0.0896804i | ||||
\(965\) | 54.3498i | 1.74958i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9796 | 0.771132 | 0.385566 | − | 0.922680i | \(-0.374006\pi\) | ||||
0.385566 | + | 0.922680i | \(0.374006\pi\) | |||||||
\(968\) | −15.0453 | + | 1.95485i | −0.483576 | + | 0.0628314i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.00529 | + | 23.3270i | 0.0322780 | + | 0.748985i | ||||
\(971\) | − | 13.2383i | − | 0.424837i | −0.977179 | − | 0.212418i | \(-0.931866\pi\) | ||
0.977179 | − | 0.212418i | \(-0.0681340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.2724i | 0.553726i | ||||||||
\(974\) | −17.7412 | + | 0.764570i | −0.568466 | + | 0.0244984i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.79703 | − | 21.8219i | −0.121540 | − | 0.698503i | ||||
\(977\) | −49.7224 | −1.59076 | −0.795380 | − | 0.606110i | \(-0.792729\pi\) | ||||
−0.795380 | + | 0.606110i | \(0.792729\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 28.3769i | − | 0.906929i | ||||||
\(980\) | 0.535788 | + | 6.20472i | 0.0171151 | + | 0.198202i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.27594 | − | 29.6071i | −0.0407168 | − | 0.944800i | ||||
\(983\) | −33.8135 | −1.07848 | −0.539241 | − | 0.842151i | \(-0.681289\pi\) | ||||
−0.539241 | + | 0.842151i | \(0.681289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 86.2150 | 2.74704 | ||||||||
\(986\) | −0.358902 | − | 8.32804i | −0.0114298 | − | 0.265219i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.35233 | + | 0.203128i | −0.0748377 | + | 0.00646236i | ||||
\(989\) | 53.9065i | 1.71413i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.2781 | 1.15241 | 0.576206 | − | 0.817304i | \(-0.304532\pi\) | ||||
0.576206 | + | 0.817304i | \(0.304532\pi\) | |||||||
\(992\) | −41.1987 | + | 9.01166i | −1.30806 | + | 0.286121i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.1409 | − | 0.824888i | 0.607111 | − | 0.0261639i | ||||
\(995\) | 28.9532i | 0.917879i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 22.7054i | − | 0.719088i | −0.933128 | − | 0.359544i | \(-0.882932\pi\) | ||
0.933128 | − | 0.359544i | \(-0.117068\pi\) | |||||||
\(998\) | −0.792496 | − | 18.3892i | −0.0250860 | − | 0.582101i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.c.f.757.2 | yes | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.f.757.23 | yes | 24 | |
4.3 | odd | 2 | 6048.2.c.g.3025.21 | 24 | |||
8.3 | odd | 2 | 6048.2.c.g.3025.4 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.f.757.1 | ✓ | 24 | |
12.11 | even | 2 | 6048.2.c.g.3025.3 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.f.757.24 | yes | 24 | |
24.11 | even | 2 | 6048.2.c.g.3025.22 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.1 | ✓ | 24 | 8.5 | even | 2 | inner | |
1512.2.c.f.757.2 | yes | 24 | 1.1 | even | 1 | trivial | |
1512.2.c.f.757.23 | yes | 24 | 3.2 | odd | 2 | inner | |
1512.2.c.f.757.24 | yes | 24 | 24.5 | odd | 2 | inner | |
6048.2.c.g.3025.3 | 24 | 12.11 | even | 2 | |||
6048.2.c.g.3025.4 | 24 | 8.3 | odd | 2 | |||
6048.2.c.g.3025.21 | 24 | 4.3 | odd | 2 | |||
6048.2.c.g.3025.22 | 24 | 24.11 | even | 2 |