Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(474,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.474");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 474.18 | ||
Character | \(\chi\) | \(=\) | 475.474 |
Dual form | 475.3.d.c.474.17 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.88109 | 0.940545 | 0.470273 | − | 0.882521i | \(-0.344156\pi\) | ||||
0.470273 | + | 0.882521i | \(0.344156\pi\) | |||||||
\(3\) | 0.840697 | 0.280232 | 0.140116 | − | 0.990135i | \(-0.455252\pi\) | ||||
0.140116 | + | 0.990135i | \(0.455252\pi\) | |||||||
\(4\) | −0.461500 | −0.115375 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.58143 | 0.263571 | ||||||||
\(7\) | − | 2.31342i | − | 0.330488i | −0.986253 | − | 0.165244i | \(-0.947159\pi\) | ||
0.986253 | − | 0.165244i | \(-0.0528411\pi\) | |||||||
\(8\) | −8.39248 | −1.04906 | ||||||||
\(9\) | −8.29323 | −0.921470 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.28979 | −0.753617 | −0.376808 | − | 0.926291i | \(-0.622979\pi\) | ||||
−0.376808 | + | 0.926291i | \(0.622979\pi\) | |||||||
\(12\) | −0.387981 | −0.0323318 | ||||||||
\(13\) | −7.20783 | −0.554448 | −0.277224 | − | 0.960805i | \(-0.589414\pi\) | ||||
−0.277224 | + | 0.960805i | \(0.589414\pi\) | |||||||
\(14\) | − | 4.35174i | − | 0.310839i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −13.9410 | −0.871314 | ||||||||
\(17\) | 6.37730i | 0.375136i | 0.982252 | + | 0.187568i | \(0.0600604\pi\) | ||||
−0.982252 | + | 0.187568i | \(0.939940\pi\) | |||||||
\(18\) | −15.6003 | −0.866684 | ||||||||
\(19\) | −8.31075 | + | 17.0860i | −0.437408 | + | 0.899263i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 1.94488i | − | 0.0926134i | ||||||
\(22\) | −15.5938 | −0.708811 | ||||||||
\(23\) | − | 14.5958i | − | 0.634601i | −0.948325 | − | 0.317300i | \(-0.897224\pi\) | ||
0.948325 | − | 0.317300i | \(-0.102776\pi\) | |||||||
\(24\) | −7.05554 | −0.293981 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.5586 | −0.521484 | ||||||||
\(27\) | −14.5384 | −0.538458 | ||||||||
\(28\) | 1.06764i | 0.0381300i | ||||||||
\(29\) | 16.9209i | 0.583478i | 0.956498 | + | 0.291739i | \(0.0942339\pi\) | ||||
−0.956498 | + | 0.291739i | \(0.905766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 39.5651i | − | 1.27629i | −0.769915 | − | 0.638146i | \(-0.779701\pi\) | ||
0.769915 | − | 0.638146i | \(-0.220299\pi\) | |||||||
\(32\) | 7.34562 | 0.229551 | ||||||||
\(33\) | −6.96920 | −0.211188 | ||||||||
\(34\) | 11.9963i | 0.352832i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82732 | 0.106314 | ||||||||
\(37\) | −8.68586 | −0.234753 | −0.117377 | − | 0.993087i | \(-0.537448\pi\) | ||||
−0.117377 | + | 0.993087i | \(0.537448\pi\) | |||||||
\(38\) | −15.6333 | + | 32.1403i | −0.411402 | + | 0.845798i | ||||
\(39\) | −6.05960 | −0.155374 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 41.6193i | − | 1.01510i | −0.861621 | − | 0.507552i | \(-0.830550\pi\) | ||
0.861621 | − | 0.507552i | \(-0.169450\pi\) | |||||||
\(42\) | − | 3.65850i | − | 0.0871071i | ||||||
\(43\) | − | 3.51015i | − | 0.0816313i | −0.999167 | − | 0.0408157i | \(-0.987004\pi\) | ||
0.999167 | − | 0.0408157i | \(-0.0129956\pi\) | |||||||
\(44\) | 3.82573 | 0.0869485 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 27.4560i | − | 0.596871i | ||||||
\(47\) | 68.8086i | 1.46401i | 0.681298 | + | 0.732006i | \(0.261416\pi\) | ||||
−0.681298 | + | 0.732006i | \(0.738584\pi\) | |||||||
\(48\) | −11.7202 | −0.244170 | ||||||||
\(49\) | 43.6481 | 0.890778 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.36138i | 0.105125i | ||||||||
\(52\) | 3.32641 | 0.0639694 | ||||||||
\(53\) | −89.1014 | −1.68116 | −0.840579 | − | 0.541688i | \(-0.817785\pi\) | ||||
−0.840579 | + | 0.541688i | \(0.817785\pi\) | |||||||
\(54\) | −27.3480 | −0.506444 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.4153i | 0.346702i | ||||||||
\(57\) | −6.98682 | + | 14.3642i | −0.122576 | + | 0.252003i | ||||
\(58\) | 31.8297i | 0.548788i | ||||||||
\(59\) | − | 95.2910i | − | 1.61510i | −0.589798 | − | 0.807551i | \(-0.700793\pi\) | ||
0.589798 | − | 0.807551i | \(-0.299207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.8583 | −0.210792 | −0.105396 | − | 0.994430i | \(-0.533611\pi\) | ||||
−0.105396 | + | 0.994430i | \(0.533611\pi\) | |||||||
\(62\) | − | 74.4255i | − | 1.20041i | ||||||
\(63\) | 19.1857i | 0.304535i | ||||||||
\(64\) | 69.5818 | 1.08722 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.1097 | −0.198632 | ||||||||
\(67\) | −65.8457 | −0.982772 | −0.491386 | − | 0.870942i | \(-0.663510\pi\) | ||||
−0.491386 | + | 0.870942i | \(0.663510\pi\) | |||||||
\(68\) | − | 2.94312i | − | 0.0432812i | ||||||
\(69\) | − | 12.2707i | − | 0.177836i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.56645i | 0.0361471i | 0.999837 | + | 0.0180736i | \(0.00575331\pi\) | ||||
−0.999837 | + | 0.0180736i | \(0.994247\pi\) | |||||||
\(72\) | 69.6008 | 0.966677 | ||||||||
\(73\) | 98.0969i | 1.34379i | 0.740645 | + | 0.671897i | \(0.234520\pi\) | ||||
−0.740645 | + | 0.671897i | \(0.765480\pi\) | |||||||
\(74\) | −16.3389 | −0.220796 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.83541 | − | 7.88518i | 0.0504659 | − | 0.103752i | ||||
\(77\) | 19.1777i | 0.249061i | ||||||||
\(78\) | −11.3987 | −0.146137 | ||||||||
\(79\) | 27.1569i | 0.343758i | 0.985118 | + | 0.171879i | \(0.0549838\pi\) | ||||
−0.985118 | + | 0.171879i | \(0.945016\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 62.4167 | 0.770576 | ||||||||
\(82\) | − | 78.2896i | − | 0.954751i | ||||||
\(83\) | 12.4242i | 0.149689i | 0.997195 | + | 0.0748445i | \(0.0238460\pi\) | ||||
−0.997195 | + | 0.0748445i | \(0.976154\pi\) | |||||||
\(84\) | 0.897562i | 0.0106853i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.60290i | − | 0.0767780i | ||||||
\(87\) | 14.2253i | 0.163510i | ||||||||
\(88\) | 69.5719 | 0.790590 | ||||||||
\(89\) | − | 25.1923i | − | 0.283060i | −0.989934 | − | 0.141530i | \(-0.954798\pi\) | ||
0.989934 | − | 0.141530i | \(-0.0452022\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.6747i | 0.183238i | ||||||||
\(92\) | 6.73596i | 0.0732170i | ||||||||
\(93\) | − | 33.2623i | − | 0.357659i | ||||||
\(94\) | 129.435i | 1.37697i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.17544 | 0.0643275 | ||||||||
\(97\) | 62.6956 | 0.646346 | 0.323173 | − | 0.946340i | \(-0.395250\pi\) | ||||
0.323173 | + | 0.946340i | \(0.395250\pi\) | |||||||
\(98\) | 82.1060 | 0.837817 | ||||||||
\(99\) | 68.7491 | 0.694435 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 138.987 | 1.37611 | 0.688055 | − | 0.725658i | \(-0.258465\pi\) | ||||
0.688055 | + | 0.725658i | \(0.258465\pi\) | |||||||
\(102\) | 10.0852i | 0.0988749i | ||||||||
\(103\) | 97.7629 | 0.949155 | 0.474577 | − | 0.880214i | \(-0.342601\pi\) | ||||
0.474577 | + | 0.880214i | \(0.342601\pi\) | |||||||
\(104\) | 60.4916 | 0.581650 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −167.608 | −1.58121 | ||||||||
\(107\) | −88.3158 | −0.825381 | −0.412691 | − | 0.910871i | \(-0.635411\pi\) | ||||
−0.412691 | + | 0.910871i | \(0.635411\pi\) | |||||||
\(108\) | 6.70945 | 0.0621245 | ||||||||
\(109\) | − | 130.713i | − | 1.19920i | −0.800301 | − | 0.599599i | \(-0.795327\pi\) | ||
0.800301 | − | 0.599599i | \(-0.204673\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.30218 | −0.0657854 | ||||||||
\(112\) | 32.2514i | 0.287959i | ||||||||
\(113\) | −74.9095 | −0.662916 | −0.331458 | − | 0.943470i | \(-0.607541\pi\) | ||||
−0.331458 | + | 0.943470i | \(0.607541\pi\) | |||||||
\(114\) | −13.1428 | + | 27.0203i | −0.115288 | + | 0.237020i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 7.80897i | − | 0.0673187i | ||||||
\(117\) | 59.7762 | 0.510907 | ||||||||
\(118\) | − | 179.251i | − | 1.51908i | ||||||
\(119\) | 14.7534 | 0.123978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −52.2794 | −0.432062 | ||||||||
\(122\) | −24.1876 | −0.198259 | ||||||||
\(123\) | − | 34.9892i | − | 0.284465i | ||||||
\(124\) | 18.2593i | 0.147252i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 36.0900i | 0.286429i | ||||||||
\(127\) | −67.5562 | −0.531938 | −0.265969 | − | 0.963982i | \(-0.585692\pi\) | ||||
−0.265969 | + | 0.963982i | \(0.585692\pi\) | |||||||
\(128\) | 101.507 | 0.793026 | ||||||||
\(129\) | − | 2.95097i | − | 0.0228758i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 87.9131 | 0.671093 | 0.335546 | − | 0.942024i | \(-0.391079\pi\) | ||||
0.335546 | + | 0.942024i | \(0.391079\pi\) | |||||||
\(132\) | 3.21628 | 0.0243658 | ||||||||
\(133\) | 39.5270 | + | 19.2262i | 0.297196 | + | 0.144558i | ||||
\(134\) | −123.862 | −0.924342 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 53.5214i | − | 0.393540i | ||||||
\(137\) | 112.209i | 0.819040i | 0.912301 | + | 0.409520i | \(0.134304\pi\) | ||||
−0.912301 | + | 0.409520i | \(0.865696\pi\) | |||||||
\(138\) | − | 23.0822i | − | 0.167263i | ||||||
\(139\) | −162.255 | −1.16731 | −0.583653 | − | 0.812003i | \(-0.698377\pi\) | ||||
−0.583653 | + | 0.812003i | \(0.698377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 57.8472i | 0.410264i | ||||||||
\(142\) | 4.82772i | 0.0339980i | ||||||||
\(143\) | 59.7513 | 0.417842 | ||||||||
\(144\) | 115.616 | 0.802889 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 184.529i | 1.26390i | ||||||||
\(147\) | 36.6948 | 0.249625 | ||||||||
\(148\) | 4.00852 | 0.0270846 | ||||||||
\(149\) | −142.097 | −0.953671 | −0.476836 | − | 0.878992i | \(-0.658216\pi\) | ||||
−0.476836 | + | 0.878992i | \(0.658216\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 258.564i | 1.71234i | 0.516692 | + | 0.856172i | \(0.327163\pi\) | ||||
−0.516692 | + | 0.856172i | \(0.672837\pi\) | |||||||
\(152\) | 69.7478 | − | 143.394i | 0.458867 | − | 0.943381i | ||||
\(153\) | − | 52.8884i | − | 0.345676i | ||||||
\(154\) | 36.0750i | 0.234253i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.79650 | 0.0179263 | ||||||||
\(157\) | − | 179.201i | − | 1.14141i | −0.821155 | − | 0.570705i | \(-0.806670\pi\) | ||
0.821155 | − | 0.570705i | \(-0.193330\pi\) | |||||||
\(158\) | 51.0846i | 0.323320i | ||||||||
\(159\) | −74.9073 | −0.471115 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.7662 | −0.209728 | ||||||||
\(162\) | 117.411 | 0.724762 | ||||||||
\(163\) | − | 207.556i | − | 1.27335i | −0.771132 | − | 0.636675i | \(-0.780309\pi\) | ||
0.771132 | − | 0.636675i | \(-0.219691\pi\) | |||||||
\(164\) | 19.2073i | 0.117118i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.3710i | 0.140789i | ||||||||
\(167\) | 65.8665 | 0.394410 | 0.197205 | − | 0.980362i | \(-0.436814\pi\) | ||||
0.197205 | + | 0.980362i | \(0.436814\pi\) | |||||||
\(168\) | 16.3224i | 0.0971571i | ||||||||
\(169\) | −117.047 | −0.692587 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 68.9229 | − | 141.698i | 0.403058 | − | 0.828644i | ||||
\(172\) | 1.61993i | 0.00941821i | ||||||||
\(173\) | 75.7872 | 0.438076 | 0.219038 | − | 0.975716i | \(-0.429708\pi\) | ||||
0.219038 | + | 0.975716i | \(0.429708\pi\) | |||||||
\(174\) | 26.7591i | 0.153788i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 115.568 | 0.656637 | ||||||||
\(177\) | − | 80.1109i | − | 0.452604i | ||||||
\(178\) | − | 47.3890i | − | 0.266231i | ||||||
\(179\) | − | 148.451i | − | 0.829338i | −0.909972 | − | 0.414669i | \(-0.863897\pi\) | ||
0.909972 | − | 0.414669i | \(-0.136103\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 293.213i | 1.61996i | 0.586455 | + | 0.809981i | \(0.300523\pi\) | ||||
−0.586455 | + | 0.809981i | \(0.699477\pi\) | |||||||
\(182\) | 31.3666i | 0.172344i | ||||||||
\(183\) | −10.8099 | −0.0590707 | ||||||||
\(184\) | 122.495i | 0.665735i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 62.5693i | − | 0.336394i | ||||||
\(187\) | − | 52.8665i | − | 0.282708i | ||||||
\(188\) | − | 31.7551i | − | 0.168910i | ||||||
\(189\) | 33.6333i | 0.177954i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.0781 | −0.0894139 | −0.0447070 | − | 0.999000i | \(-0.514235\pi\) | ||||
−0.0447070 | + | 0.999000i | \(0.514235\pi\) | |||||||
\(192\) | 58.4973 | 0.304673 | ||||||||
\(193\) | −227.915 | −1.18091 | −0.590453 | − | 0.807072i | \(-0.701051\pi\) | ||||
−0.590453 | + | 0.807072i | \(0.701051\pi\) | |||||||
\(194\) | 117.936 | 0.607918 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.1436 | −0.102773 | ||||||||
\(197\) | 364.907i | 1.85232i | 0.377130 | + | 0.926160i | \(0.376911\pi\) | ||||
−0.377130 | + | 0.926160i | \(0.623089\pi\) | |||||||
\(198\) | 129.323 | 0.653148 | ||||||||
\(199\) | 76.8411 | 0.386136 | 0.193068 | − | 0.981185i | \(-0.438156\pi\) | ||||
0.193068 | + | 0.981185i | \(0.438156\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −55.3563 | −0.275405 | ||||||||
\(202\) | 261.447 | 1.29429 | ||||||||
\(203\) | 39.1450 | 0.192833 | ||||||||
\(204\) | − | 2.47428i | − | 0.0121288i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 183.901 | 0.892723 | ||||||||
\(207\) | 121.046i | 0.584765i | ||||||||
\(208\) | 100.484 | 0.483098 | ||||||||
\(209\) | 68.8943 | − | 141.639i | 0.329638 | − | 0.677700i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 178.990i | − | 0.848293i | −0.905594 | − | 0.424146i | \(-0.860574\pi\) | ||
0.905594 | − | 0.424146i | \(-0.139426\pi\) | |||||||
\(212\) | 41.1203 | 0.193964 | ||||||||
\(213\) | 2.15761i | 0.0101296i | ||||||||
\(214\) | −166.130 | −0.776308 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 122.013 | 0.564875 | ||||||||
\(217\) | −91.5305 | −0.421799 | ||||||||
\(218\) | − | 245.882i | − | 1.12790i | ||||||
\(219\) | 82.4698i | 0.376575i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 45.9665i | − | 0.207993i | ||||||
\(222\) | −13.7361 | −0.0618742 | ||||||||
\(223\) | 46.2665 | 0.207473 | 0.103736 | − | 0.994605i | \(-0.466920\pi\) | ||||
0.103736 | + | 0.994605i | \(0.466920\pi\) | |||||||
\(224\) | − | 16.9935i | − | 0.0758637i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −140.912 | −0.623502 | ||||||||
\(227\) | −353.533 | −1.55741 | −0.778707 | − | 0.627388i | \(-0.784124\pi\) | ||||
−0.778707 | + | 0.627388i | \(0.784124\pi\) | |||||||
\(228\) | 3.22442 | − | 6.62905i | 0.0141422 | − | 0.0290748i | ||||
\(229\) | −15.5586 | −0.0679415 | −0.0339707 | − | 0.999423i | \(-0.510815\pi\) | ||||
−0.0339707 | + | 0.999423i | \(0.510815\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.1227i | 0.0697950i | ||||||||
\(232\) | − | 142.008i | − | 0.612104i | ||||||
\(233\) | 110.847i | 0.475738i | 0.971297 | + | 0.237869i | \(0.0764489\pi\) | ||||
−0.971297 | + | 0.237869i | \(0.923551\pi\) | |||||||
\(234\) | 112.444 | 0.480531 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 43.9767i | 0.186342i | ||||||||
\(237\) | 22.8307i | 0.0963322i | ||||||||
\(238\) | 27.7524 | 0.116607 | ||||||||
\(239\) | 231.840 | 0.970040 | 0.485020 | − | 0.874503i | \(-0.338812\pi\) | ||||
0.485020 | + | 0.874503i | \(0.338812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.2261i | − | 0.104673i | −0.998630 | − | 0.0523364i | \(-0.983333\pi\) | ||
0.998630 | − | 0.0523364i | \(-0.0166668\pi\) | |||||||
\(242\) | −98.3423 | −0.406373 | ||||||||
\(243\) | 183.319 | 0.754399 | ||||||||
\(244\) | 5.93410 | 0.0243201 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 65.8179i | − | 0.267552i | ||||||
\(247\) | 59.9024 | − | 123.153i | 0.242520 | − | 0.498595i | ||||
\(248\) | 332.049i | 1.33891i | ||||||||
\(249\) | 10.4450i | 0.0419477i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −302.298 | −1.20438 | −0.602188 | − | 0.798355i | \(-0.705704\pi\) | ||||
−0.602188 | + | 0.798355i | \(0.705704\pi\) | |||||||
\(252\) | − | 8.85418i | − | 0.0351356i | ||||||
\(253\) | 120.996i | 0.478246i | ||||||||
\(254\) | −127.079 | −0.500312 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −87.3831 | −0.341340 | ||||||||
\(257\) | −482.042 | −1.87565 | −0.937826 | − | 0.347107i | \(-0.887164\pi\) | ||||
−0.937826 | + | 0.347107i | \(0.887164\pi\) | |||||||
\(258\) | − | 5.55104i | − | 0.0215157i | ||||||
\(259\) | 20.0940i | 0.0775830i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 140.329i | − | 0.537658i | ||||||
\(262\) | 165.373 | 0.631193 | ||||||||
\(263\) | − | 14.9627i | − | 0.0568925i | −0.999595 | − | 0.0284462i | \(-0.990944\pi\) | ||
0.999595 | − | 0.0284462i | \(-0.00905594\pi\) | |||||||
\(264\) | 58.4889 | 0.221549 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 74.3539 | + | 36.1662i | 0.279526 | + | 0.135963i | ||||
\(267\) | − | 21.1791i | − | 0.0793226i | ||||||
\(268\) | 30.3878 | 0.113387 | ||||||||
\(269\) | − | 333.769i | − | 1.24078i | −0.784294 | − | 0.620389i | \(-0.786975\pi\) | ||
0.784294 | − | 0.620389i | \(-0.213025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −111.309 | −0.410735 | −0.205368 | − | 0.978685i | \(-0.565839\pi\) | ||||
−0.205368 | + | 0.978685i | \(0.565839\pi\) | |||||||
\(272\) | − | 88.9061i | − | 0.326861i | ||||||
\(273\) | 14.0184i | 0.0513494i | ||||||||
\(274\) | 211.074i | 0.770345i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.66291i | 0.0205178i | ||||||||
\(277\) | − | 245.520i | − | 0.886355i | −0.896434 | − | 0.443178i | \(-0.853851\pi\) | ||
0.896434 | − | 0.443178i | \(-0.146149\pi\) | |||||||
\(278\) | −305.217 | −1.09790 | ||||||||
\(279\) | 328.122i | 1.17607i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 483.657i | − | 1.72120i | −0.509281 | − | 0.860600i | \(-0.670089\pi\) | ||
0.509281 | − | 0.860600i | \(-0.329911\pi\) | |||||||
\(282\) | 108.816i | 0.385872i | ||||||||
\(283\) | 510.891i | 1.80527i | 0.430407 | + | 0.902635i | \(0.358370\pi\) | ||||
−0.430407 | + | 0.902635i | \(0.641630\pi\) | |||||||
\(284\) | − | 1.18441i | − | 0.00417047i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 112.398 | 0.392999 | ||||||||
\(287\) | −96.2827 | −0.335480 | ||||||||
\(288\) | −60.9189 | −0.211524 | ||||||||
\(289\) | 248.330 | 0.859273 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 52.7080 | 0.181127 | ||||||||
\(292\) | − | 45.2717i | − | 0.155040i | ||||||
\(293\) | −459.172 | −1.56714 | −0.783570 | − | 0.621303i | \(-0.786603\pi\) | ||||
−0.783570 | + | 0.621303i | \(0.786603\pi\) | |||||||
\(294\) | 69.0263 | 0.234783 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 72.8960 | 0.246270 | ||||||||
\(297\) | 120.520 | 0.405791 | ||||||||
\(298\) | −267.297 | −0.896971 | ||||||||
\(299\) | 105.204i | 0.351853i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.12043 | −0.0269782 | ||||||||
\(302\) | 486.382i | 1.61054i | ||||||||
\(303\) | 116.846 | 0.385631 | ||||||||
\(304\) | 115.860 | − | 238.196i | 0.381119 | − | 0.783540i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 99.4879i | − | 0.325124i | ||||||
\(307\) | 560.721 | 1.82645 | 0.913227 | − | 0.407452i | \(-0.133583\pi\) | ||||
0.913227 | + | 0.407452i | \(0.133583\pi\) | |||||||
\(308\) | − | 8.85051i | − | 0.0287354i | ||||||
\(309\) | 82.1890 | 0.265984 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −63.4058 | −0.203877 | −0.101939 | − | 0.994791i | \(-0.532505\pi\) | ||||
−0.101939 | + | 0.994791i | \(0.532505\pi\) | |||||||
\(312\) | 50.8551 | 0.162997 | ||||||||
\(313\) | 185.259i | 0.591881i | 0.955206 | + | 0.295940i | \(0.0956330\pi\) | ||||
−0.955206 | + | 0.295940i | \(0.904367\pi\) | |||||||
\(314\) | − | 337.094i | − | 1.07355i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 12.5329i | − | 0.0396611i | ||||||
\(317\) | −362.734 | −1.14427 | −0.572135 | − | 0.820159i | \(-0.693885\pi\) | ||||
−0.572135 | + | 0.820159i | \(0.693885\pi\) | |||||||
\(318\) | −140.907 | −0.443105 | ||||||||
\(319\) | − | 140.270i | − | 0.439719i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −74.2469 | −0.231299 | ||||||||
\(322\) | −63.5172 | −0.197259 | ||||||||
\(323\) | −108.963 | − | 53.0002i | −0.337346 | − | 0.164087i | ||||
\(324\) | −28.8053 | −0.0889052 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 390.432i | − | 1.19764i | ||||||
\(327\) | − | 109.890i | − | 0.336054i | ||||||
\(328\) | 349.289i | 1.06491i | ||||||||
\(329\) | 159.183 | 0.483838 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 368.904i | 1.11451i | 0.830341 | + | 0.557256i | \(0.188146\pi\) | ||||
−0.830341 | + | 0.557256i | \(0.811854\pi\) | |||||||
\(332\) | − | 5.73375i | − | 0.0172703i | ||||||
\(333\) | 72.0338 | 0.216318 | ||||||||
\(334\) | 123.901 | 0.370961 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 27.1136i | 0.0806954i | ||||||||
\(337\) | −233.994 | −0.694345 | −0.347173 | − | 0.937801i | \(-0.612858\pi\) | ||||
−0.347173 | + | 0.937801i | \(0.612858\pi\) | |||||||
\(338\) | −220.176 | −0.651409 | ||||||||
\(339\) | −62.9762 | −0.185771 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 327.986i | 0.961836i | ||||||||
\(342\) | 129.650 | − | 266.547i | 0.379094 | − | 0.779377i | ||||
\(343\) | − | 214.334i | − | 0.624879i | ||||||
\(344\) | 29.4589i | 0.0856362i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 142.563 | 0.412031 | ||||||||
\(347\) | 377.811i | 1.08879i | 0.838828 | + | 0.544396i | \(0.183241\pi\) | ||||
−0.838828 | + | 0.544396i | \(0.816759\pi\) | |||||||
\(348\) | − | 6.56498i | − | 0.0188649i | ||||||
\(349\) | −281.791 | −0.807425 | −0.403712 | − | 0.914886i | \(-0.632280\pi\) | ||||
−0.403712 | + | 0.914886i | \(0.632280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 104.790 | 0.298547 | ||||||||
\(352\) | −60.8936 | −0.172993 | ||||||||
\(353\) | − | 92.5752i | − | 0.262253i | −0.991366 | − | 0.131126i | \(-0.958141\pi\) | ||
0.991366 | − | 0.131126i | \(-0.0418593\pi\) | |||||||
\(354\) | − | 150.696i | − | 0.425694i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.6262i | 0.0326580i | ||||||||
\(357\) | 12.4031 | 0.0347426 | ||||||||
\(358\) | − | 279.251i | − | 0.780030i | ||||||
\(359\) | −443.170 | −1.23446 | −0.617228 | − | 0.786785i | \(-0.711744\pi\) | ||||
−0.617228 | + | 0.786785i | \(0.711744\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −222.863 | − | 283.995i | −0.617349 | − | 0.786690i | ||||
\(362\) | 551.561i | 1.52365i | ||||||||
\(363\) | −43.9512 | −0.121078 | ||||||||
\(364\) | − | 7.69536i | − | 0.0211411i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.3345 | −0.0555587 | ||||||||
\(367\) | − | 576.621i | − | 1.57117i | −0.618751 | − | 0.785587i | \(-0.712361\pi\) | ||
0.618751 | − | 0.785587i | \(-0.287639\pi\) | |||||||
\(368\) | 203.481i | 0.552936i | ||||||||
\(369\) | 345.158i | 0.935388i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 206.129i | 0.555603i | ||||||||
\(372\) | 15.3505i | 0.0412648i | ||||||||
\(373\) | −291.370 | −0.781153 | −0.390577 | − | 0.920570i | \(-0.627724\pi\) | ||||
−0.390577 | + | 0.920570i | \(0.627724\pi\) | |||||||
\(374\) | − | 99.4466i | − | 0.265900i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 577.475i | − | 1.53584i | ||||||
\(377\) | − | 121.963i | − | 0.323509i | ||||||
\(378\) | 63.2672i | 0.167374i | ||||||||
\(379\) | − | 208.089i | − | 0.549048i | −0.961580 | − | 0.274524i | \(-0.911480\pi\) | ||
0.961580 | − | 0.274524i | \(-0.0885204\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −56.7943 | −0.149066 | ||||||||
\(382\) | −32.1254 | −0.0840978 | ||||||||
\(383\) | −19.9700 | −0.0521410 | −0.0260705 | − | 0.999660i | \(-0.508299\pi\) | ||||
−0.0260705 | + | 0.999660i | \(0.508299\pi\) | |||||||
\(384\) | 85.3369 | 0.222231 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −428.729 | −1.11070 | ||||||||
\(387\) | 29.1105i | 0.0752208i | ||||||||
\(388\) | −28.9340 | −0.0745721 | ||||||||
\(389\) | −389.050 | −1.00013 | −0.500065 | − | 0.865988i | \(-0.666690\pi\) | ||||
−0.500065 | + | 0.865988i | \(0.666690\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 93.0820 | 0.238061 | ||||||||
\(392\) | −366.316 | −0.934480 | ||||||||
\(393\) | 73.9083 | 0.188062 | ||||||||
\(394\) | 686.423i | 1.74219i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −31.7277 | −0.0801204 | ||||||||
\(397\) | 292.277i | 0.736213i | 0.929784 | + | 0.368107i | \(0.119994\pi\) | ||||
−0.929784 | + | 0.368107i | \(0.880006\pi\) | |||||||
\(398\) | 144.545 | 0.363178 | ||||||||
\(399\) | 33.2303 | + | 16.1634i | 0.0832839 | + | 0.0405098i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 720.767i | − | 1.79742i | −0.438540 | − | 0.898712i | \(-0.644504\pi\) | ||
0.438540 | − | 0.898712i | \(-0.355496\pi\) | |||||||
\(402\) | −104.130 | −0.259031 | ||||||||
\(403\) | 285.178i | 0.707638i | ||||||||
\(404\) | −64.1425 | −0.158769 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 73.6353 | 0.181368 | ||||||||
\(407\) | 72.0039 | 0.176914 | ||||||||
\(408\) | − | 44.9953i | − | 0.110283i | ||||||
\(409\) | 310.253i | 0.758564i | 0.925281 | + | 0.379282i | \(0.123829\pi\) | ||||
−0.925281 | + | 0.379282i | \(0.876171\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 94.3334i | 0.229522i | ||||||||
\(412\) | −45.1175 | −0.109509 | ||||||||
\(413\) | −220.448 | −0.533772 | ||||||||
\(414\) | 227.699i | 0.549998i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −52.9459 | −0.127274 | ||||||||
\(417\) | −136.408 | −0.327117 | ||||||||
\(418\) | 129.596 | − | 266.436i | 0.310039 | − | 0.637407i | ||||
\(419\) | −251.699 | −0.600713 | −0.300357 | − | 0.953827i | \(-0.597106\pi\) | ||||
−0.300357 | + | 0.953827i | \(0.597106\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 256.848i | − | 0.610090i | −0.952338 | − | 0.305045i | \(-0.901328\pi\) | ||
0.952338 | − | 0.305045i | \(-0.0986715\pi\) | |||||||
\(422\) | − | 336.696i | − | 0.797858i | ||||||
\(423\) | − | 570.645i | − | 1.34904i | ||||||
\(424\) | 747.782 | 1.76364 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.05865i | 0.00952735i | ||||||||
\(427\) | 29.7466i | 0.0696641i | ||||||||
\(428\) | 40.7577 | 0.0952283 | ||||||||
\(429\) | 50.2328 | 0.117093 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 734.747i | 1.70475i | 0.522931 | + | 0.852375i | \(0.324839\pi\) | ||||
−0.522931 | + | 0.852375i | \(0.675161\pi\) | |||||||
\(432\) | 202.680 | 0.469166 | ||||||||
\(433\) | 87.4830 | 0.202039 | 0.101020 | − | 0.994884i | \(-0.467790\pi\) | ||||
0.101020 | + | 0.994884i | \(0.467790\pi\) | |||||||
\(434\) | −172.177 | −0.396721 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 60.3238i | 0.138357i | ||||||||
\(437\) | 249.384 | + | 121.302i | 0.570673 | + | 0.277579i | ||||
\(438\) | 155.133i | 0.354185i | ||||||||
\(439\) | − | 340.926i | − | 0.776598i | −0.921534 | − | 0.388299i | \(-0.873063\pi\) | ||
0.921534 | − | 0.388299i | \(-0.126937\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −361.984 | −0.820825 | ||||||||
\(442\) | − | 86.4671i | − | 0.195627i | ||||||
\(443\) | − | 573.891i | − | 1.29546i | −0.761868 | − | 0.647732i | \(-0.775718\pi\) | ||
0.761868 | − | 0.647732i | \(-0.224282\pi\) | |||||||
\(444\) | 3.36995 | 0.00758999 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 87.0314 | 0.195138 | ||||||||
\(447\) | −119.461 | −0.267250 | ||||||||
\(448\) | − | 160.972i | − | 0.359312i | ||||||
\(449\) | 650.271i | 1.44826i | 0.689661 | + | 0.724132i | \(0.257760\pi\) | ||||
−0.689661 | + | 0.724132i | \(0.742240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 345.015i | 0.765000i | ||||||||
\(452\) | 34.5707 | 0.0764838 | ||||||||
\(453\) | 217.374i | 0.479854i | ||||||||
\(454\) | −665.027 | −1.46482 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 58.6368 | − | 120.551i | 0.128589 | − | 0.264366i | ||||
\(457\) | 743.048i | 1.62593i | 0.582315 | + | 0.812963i | \(0.302147\pi\) | ||||
−0.582315 | + | 0.812963i | \(0.697853\pi\) | |||||||
\(458\) | −29.2671 | −0.0639020 | ||||||||
\(459\) | − | 92.7156i | − | 0.201995i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −279.048 | −0.605310 | −0.302655 | − | 0.953100i | \(-0.597873\pi\) | ||||
−0.302655 | + | 0.953100i | \(0.597873\pi\) | |||||||
\(462\) | 30.3282i | 0.0656454i | ||||||||
\(463\) | − | 399.848i | − | 0.863603i | −0.901969 | − | 0.431801i | \(-0.857878\pi\) | ||
0.901969 | − | 0.431801i | \(-0.142122\pi\) | |||||||
\(464\) | − | 235.894i | − | 0.508393i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 208.513i | 0.447453i | ||||||||
\(467\) | − | 902.196i | − | 1.93190i | −0.258733 | − | 0.965949i | \(-0.583305\pi\) | ||
0.258733 | − | 0.965949i | \(-0.416695\pi\) | |||||||
\(468\) | −27.5867 | −0.0589459 | ||||||||
\(469\) | 152.329i | 0.324794i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 150.654i | − | 0.319860i | ||||||
\(472\) | 799.728i | 1.69434i | ||||||||
\(473\) | 29.0984i | 0.0615188i | ||||||||
\(474\) | 42.9467i | 0.0906048i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.80867 | −0.0143039 | ||||||||
\(477\) | 738.938 | 1.54914 | ||||||||
\(478\) | 436.111 | 0.912367 | ||||||||
\(479\) | −138.417 | −0.288971 | −0.144485 | − | 0.989507i | \(-0.546153\pi\) | ||||
−0.144485 | + | 0.989507i | \(0.546153\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 62.6062 | 0.130158 | ||||||||
\(482\) | − | 47.4527i | − | 0.0984495i | ||||||
\(483\) | −28.3871 | −0.0587725 | ||||||||
\(484\) | 24.1269 | 0.0498490 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 344.839 | 0.709546 | ||||||||
\(487\) | 533.362 | 1.09520 | 0.547600 | − | 0.836740i | \(-0.315542\pi\) | ||||
0.547600 | + | 0.836740i | \(0.315542\pi\) | |||||||
\(488\) | 107.913 | 0.221133 | ||||||||
\(489\) | − | 174.492i | − | 0.356834i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 538.259 | 1.09625 | 0.548125 | − | 0.836396i | \(-0.315342\pi\) | ||||
0.548125 | + | 0.836396i | \(0.315342\pi\) | |||||||
\(492\) | 16.1475i | 0.0328201i | ||||||||
\(493\) | −107.910 | −0.218883 | ||||||||
\(494\) | 112.682 | − | 231.662i | 0.228101 | − | 0.468951i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 551.578i | 1.11205i | ||||||||
\(497\) | 5.93726 | 0.0119462 | ||||||||
\(498\) | 19.6479i | 0.0394537i | ||||||||
\(499\) | 714.752 | 1.43237 | 0.716184 | − | 0.697911i | \(-0.245887\pi\) | ||||
0.716184 | + | 0.697911i | \(0.245887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 55.3738 | 0.110527 | ||||||||
\(502\) | −568.650 | −1.13277 | ||||||||
\(503\) | 475.580i | 0.945487i | 0.881200 | + | 0.472744i | \(0.156736\pi\) | ||||
−0.881200 | + | 0.472744i | \(0.843264\pi\) | |||||||
\(504\) | − | 161.015i | − | 0.319475i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 227.605i | 0.449812i | ||||||||
\(507\) | −98.4013 | −0.194085 | ||||||||
\(508\) | 31.1771 | 0.0613723 | ||||||||
\(509\) | − | 817.149i | − | 1.60540i | −0.596382 | − | 0.802701i | \(-0.703396\pi\) | ||
0.596382 | − | 0.802701i | \(-0.296604\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 226.939 | 0.444107 | ||||||||
\(512\) | −570.404 | −1.11407 | ||||||||
\(513\) | 120.825 | − | 248.403i | 0.235526 | − | 0.484216i | ||||
\(514\) | −906.765 | −1.76413 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.36187i | 0.00263929i | ||||||||
\(517\) | − | 570.409i | − | 1.10330i | ||||||
\(518\) | 37.7986i | 0.0729704i | ||||||||
\(519\) | 63.7141 | 0.122763 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 56.3140i | 0.108088i | 0.998539 | + | 0.0540441i | \(0.0172112\pi\) | ||||
−0.998539 | + | 0.0540441i | \(0.982789\pi\) | |||||||
\(522\) | − | 263.971i | − | 0.505691i | ||||||
\(523\) | 419.732 | 0.802547 | 0.401274 | − | 0.915958i | \(-0.368568\pi\) | ||||
0.401274 | + | 0.915958i | \(0.368568\pi\) | |||||||
\(524\) | −40.5719 | −0.0774272 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 28.1462i | − | 0.0535099i | ||||||
\(527\) | 252.319 | 0.478783 | ||||||||
\(528\) | 97.1578 | 0.184011 | ||||||||
\(529\) | 315.962 | 0.597282 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 790.270i | 1.48827i | ||||||||
\(532\) | −18.2417 | − | 8.87289i | −0.0342889 | − | 0.0166784i | ||||
\(533\) | 299.985i | 0.562823i | ||||||||
\(534\) | − | 39.8398i | − | 0.0746065i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 552.609 | 1.03099 | ||||||||
\(537\) | − | 124.803i | − | 0.232407i | ||||||
\(538\) | − | 627.850i | − | 1.16701i | ||||||
\(539\) | −361.834 | −0.671305 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 168.063 | 0.310652 | 0.155326 | − | 0.987863i | \(-0.450357\pi\) | ||||
0.155326 | + | 0.987863i | \(0.450357\pi\) | |||||||
\(542\) | −209.383 | −0.386315 | ||||||||
\(543\) | 246.504i | 0.453966i | ||||||||
\(544\) | 46.8452i | 0.0861125i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 26.3698i | 0.0482964i | ||||||||
\(547\) | 974.400 | 1.78135 | 0.890676 | − | 0.454638i | \(-0.150232\pi\) | ||||
0.890676 | + | 0.454638i | \(0.150232\pi\) | |||||||
\(548\) | − | 51.7842i | − | 0.0944967i | ||||||
\(549\) | 106.637 | 0.194238 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −289.110 | − | 140.625i | −0.524701 | − | 0.255218i | ||||
\(552\) | 102.981i | 0.186560i | ||||||||
\(553\) | 62.8252 | 0.113608 | ||||||||
\(554\) | − | 461.846i | − | 0.833657i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 74.8808 | 0.134678 | ||||||||
\(557\) | − | 497.467i | − | 0.893119i | −0.894754 | − | 0.446560i | \(-0.852649\pi\) | ||
0.894754 | − | 0.446560i | \(-0.147351\pi\) | |||||||
\(558\) | 617.228i | 1.10614i | ||||||||
\(559\) | 25.3005i | 0.0452604i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 44.4447i | − | 0.0792241i | ||||||
\(562\) | − | 909.803i | − | 1.61887i | ||||||
\(563\) | 550.233 | 0.977323 | 0.488661 | − | 0.872473i | \(-0.337485\pi\) | ||||
0.488661 | + | 0.872473i | \(0.337485\pi\) | |||||||
\(564\) | − | 26.6965i | − | 0.0473341i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 961.033i | 1.69794i | ||||||||
\(567\) | − | 144.396i | − | 0.254666i | ||||||
\(568\) | − | 21.5389i | − | 0.0379205i | ||||||
\(569\) | 862.576i | 1.51595i | 0.652283 | + | 0.757975i | \(0.273811\pi\) | ||||
−0.652283 | + | 0.757975i | \(0.726189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 372.995 | 0.653230 | 0.326615 | − | 0.945157i | \(-0.394092\pi\) | ||||
0.326615 | + | 0.945157i | \(0.394092\pi\) | |||||||
\(572\) | −27.5752 | −0.0482084 | ||||||||
\(573\) | −14.3575 | −0.0250567 | ||||||||
\(574\) | −181.116 | −0.315534 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −577.058 | −1.00184 | ||||||||
\(577\) | 796.258i | 1.38000i | 0.723811 | + | 0.689999i | \(0.242389\pi\) | ||||
−0.723811 | + | 0.689999i | \(0.757611\pi\) | |||||||
\(578\) | 467.131 | 0.808185 | ||||||||
\(579\) | −191.608 | −0.330928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.7423 | 0.0494704 | ||||||||
\(582\) | 99.1486 | 0.170358 | ||||||||
\(583\) | 738.632 | 1.26695 | ||||||||
\(584\) | − | 823.277i | − | 1.40972i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −863.744 | −1.47397 | ||||||||
\(587\) | 469.946i | 0.800590i | 0.916386 | + | 0.400295i | \(0.131092\pi\) | ||||
−0.916386 | + | 0.400295i | \(0.868908\pi\) | |||||||
\(588\) | −16.9347 | −0.0288004 | ||||||||
\(589\) | 676.009 | + | 328.815i | 1.14772 | + | 0.558260i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 306.777i | 0.519080i | ||||||||
\(592\) | 121.090 | 0.204544 | ||||||||
\(593\) | − | 242.100i | − | 0.408263i | −0.978943 | − | 0.204131i | \(-0.934563\pi\) | ||
0.978943 | − | 0.204131i | \(-0.0654370\pi\) | |||||||
\(594\) | 226.709 | 0.381665 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 65.5777 | 0.110030 | ||||||||
\(597\) | 64.6001 | 0.108208 | ||||||||
\(598\) | 197.898i | 0.330934i | ||||||||
\(599\) | 209.810i | 0.350268i | 0.984545 | + | 0.175134i | \(0.0560358\pi\) | ||||
−0.984545 | + | 0.175134i | \(0.943964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 782.856i | − | 1.30259i | −0.758825 | − | 0.651294i | \(-0.774226\pi\) | ||
0.758825 | − | 0.651294i | \(-0.225774\pi\) | |||||||
\(602\) | −15.2753 | −0.0253742 | ||||||||
\(603\) | 546.074 | 0.905595 | ||||||||
\(604\) | − | 119.327i | − | 0.197561i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 219.798 | 0.362703 | ||||||||
\(607\) | 110.135 | 0.181442 | 0.0907210 | − | 0.995876i | \(-0.471083\pi\) | ||||
0.0907210 | + | 0.995876i | \(0.471083\pi\) | |||||||
\(608\) | −61.0476 | + | 125.507i | −0.100407 | + | 0.206426i | ||||
\(609\) | 32.9091 | 0.0540379 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 495.960i | − | 0.811719i | ||||||
\(612\) | 24.4080i | 0.0398823i | ||||||||
\(613\) | − | 793.645i | − | 1.29469i | −0.762197 | − | 0.647345i | \(-0.775879\pi\) | ||
0.762197 | − | 0.647345i | \(-0.224121\pi\) | |||||||
\(614\) | 1054.77 | 1.71786 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 160.949i | − | 0.261280i | ||||||
\(617\) | − | 243.961i | − | 0.395398i | −0.980263 | − | 0.197699i | \(-0.936653\pi\) | ||
0.980263 | − | 0.197699i | \(-0.0633469\pi\) | |||||||
\(618\) | 154.605 | 0.250170 | ||||||||
\(619\) | 1163.97 | 1.88041 | 0.940205 | − | 0.340610i | \(-0.110633\pi\) | ||||
0.940205 | + | 0.340610i | \(0.110633\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 212.199i | 0.341706i | ||||||||
\(622\) | −119.272 | −0.191756 | ||||||||
\(623\) | −58.2803 | −0.0935479 | ||||||||
\(624\) | 84.4770 | 0.135380 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 348.488i | 0.556691i | ||||||||
\(627\) | 57.9193 | − | 119.076i | 0.0923752 | − | 0.189914i | ||||
\(628\) | 82.7014i | 0.131690i | ||||||||
\(629\) | − | 55.3924i | − | 0.0880642i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1244.64 | 1.97249 | 0.986244 | − | 0.165297i | \(-0.0528581\pi\) | ||||
0.986244 | + | 0.165297i | \(0.0528581\pi\) | |||||||
\(632\) | − | 227.914i | − | 0.360623i | ||||||
\(633\) | − | 150.476i | − | 0.237719i | ||||||
\(634\) | −682.335 | −1.07624 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 34.5697 | 0.0543549 | ||||||||
\(637\) | −314.608 | −0.493890 | ||||||||
\(638\) | − | 263.861i | − | 0.413576i | ||||||
\(639\) | − | 21.2841i | − | 0.0333085i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 123.441i | 0.192575i | 0.995354 | + | 0.0962877i | \(0.0306969\pi\) | ||||
−0.995354 | + | 0.0962877i | \(0.969303\pi\) | |||||||
\(642\) | −139.665 | −0.217547 | ||||||||
\(643\) | − | 97.0311i | − | 0.150904i | −0.997149 | − | 0.0754519i | \(-0.975960\pi\) | ||
0.997149 | − | 0.0754519i | \(-0.0240399\pi\) | |||||||
\(644\) | 15.5831 | 0.0241973 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −204.969 | − | 99.6981i | −0.317289 | − | 0.154331i | ||||
\(647\) | 988.138i | 1.52726i | 0.645653 | + | 0.763631i | \(0.276585\pi\) | ||||
−0.645653 | + | 0.763631i | \(0.723415\pi\) | |||||||
\(648\) | −523.831 | −0.808381 | ||||||||
\(649\) | 789.942i | 1.21717i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −76.9494 | −0.118202 | ||||||||
\(652\) | 95.7871i | 0.146913i | ||||||||
\(653\) | 1068.01i | 1.63554i | 0.575546 | + | 0.817770i | \(0.304790\pi\) | ||||
−0.575546 | + | 0.817770i | \(0.695210\pi\) | |||||||
\(654\) | − | 206.712i | − | 0.316074i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 580.215i | 0.884474i | ||||||||
\(657\) | − | 813.540i | − | 1.23827i | ||||||
\(658\) | 299.437 | 0.455072 | ||||||||
\(659\) | − | 515.122i | − | 0.781672i | −0.920460 | − | 0.390836i | \(-0.872186\pi\) | ||
0.920460 | − | 0.390836i | \(-0.127814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 778.350i | − | 1.17753i | −0.808303 | − | 0.588767i | \(-0.799613\pi\) | ||
0.808303 | − | 0.588767i | \(-0.200387\pi\) | |||||||
\(662\) | 693.941i | 1.04825i | ||||||||
\(663\) | − | 38.6439i | − | 0.0582864i | ||||||
\(664\) | − | 104.270i | − | 0.157033i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 135.502 | 0.203457 | ||||||||
\(667\) | 246.974 | 0.370276 | ||||||||
\(668\) | −30.3974 | −0.0455050 | ||||||||
\(669\) | 38.8961 | 0.0581406 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 106.593 | 0.158856 | ||||||||
\(672\) | − | 14.2864i | − | 0.0212595i | ||||||
\(673\) | 781.412 | 1.16109 | 0.580544 | − | 0.814229i | \(-0.302840\pi\) | ||||
0.580544 | + | 0.814229i | \(0.302840\pi\) | |||||||
\(674\) | −440.164 | −0.653063 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 54.0172 | 0.0799072 | ||||||||
\(677\) | −848.810 | −1.25378 | −0.626891 | − | 0.779107i | \(-0.715673\pi\) | ||||
−0.626891 | + | 0.779107i | \(0.715673\pi\) | |||||||
\(678\) | −118.464 | −0.174726 | ||||||||
\(679\) | − | 145.041i | − | 0.213610i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −297.214 | −0.436438 | ||||||||
\(682\) | 616.971i | 0.904650i | ||||||||
\(683\) | 238.270 | 0.348859 | 0.174429 | − | 0.984670i | \(-0.444192\pi\) | ||||
0.174429 | + | 0.984670i | \(0.444192\pi\) | |||||||
\(684\) | −31.8079 | + | 65.3936i | −0.0465028 | + | 0.0956047i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 403.181i | − | 0.587727i | ||||||
\(687\) | −13.0801 | −0.0190394 | ||||||||
\(688\) | 48.9350i | 0.0711265i | ||||||||
\(689\) | 642.228 | 0.932116 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 147.763 | 0.213840 | 0.106920 | − | 0.994268i | \(-0.465901\pi\) | ||||
0.106920 | + | 0.994268i | \(0.465901\pi\) | |||||||
\(692\) | −34.9758 | −0.0505430 | ||||||||
\(693\) | − | 159.045i | − | 0.229502i | ||||||
\(694\) | 710.696i | 1.02406i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 119.386i | − | 0.171531i | ||||||
\(697\) | 265.419 | 0.380802 | ||||||||
\(698\) | −530.075 | −0.759419 | ||||||||
\(699\) | 93.1887i | 0.133317i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 742.215 | 1.05879 | 0.529397 | − | 0.848374i | \(-0.322418\pi\) | ||||
0.529397 | + | 0.848374i | \(0.322418\pi\) | |||||||
\(702\) | 197.120 | 0.280797 | ||||||||
\(703\) | 72.1860 | − | 148.407i | 0.102683 | − | 0.211105i | ||||
\(704\) | −576.819 | −0.819345 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 174.142i | − | 0.246660i | ||||||
\(707\) | − | 321.535i | − | 0.454788i | ||||||
\(708\) | 36.9711i | 0.0522191i | ||||||||
\(709\) | 233.821 | 0.329790 | 0.164895 | − | 0.986311i | \(-0.447271\pi\) | ||||
0.164895 | + | 0.986311i | \(0.447271\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 225.218i | − | 0.316763i | ||||||
\(712\) | 211.426i | 0.296947i | ||||||||
\(713\) | −577.485 | −0.809936 | ||||||||
\(714\) | 23.3314 | 0.0326770 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 68.5103i | 0.0956848i | ||||||||
\(717\) | 194.907 | 0.271837 | ||||||||
\(718\) | −833.642 | −1.16106 | ||||||||
\(719\) | −544.422 | −0.757193 | −0.378596 | − | 0.925562i | \(-0.623593\pi\) | ||||
−0.378596 | + | 0.925562i | \(0.623593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 226.166i | − | 0.313684i | ||||||
\(722\) | −419.225 | − | 534.220i | −0.580644 | − | 0.739917i | ||||
\(723\) | − | 21.2076i | − | 0.0293327i | ||||||
\(724\) | − | 135.318i | − | 0.186903i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −82.6762 | −0.113879 | ||||||||
\(727\) | − | 239.420i | − | 0.329326i | −0.986350 | − | 0.164663i | \(-0.947346\pi\) | ||
0.986350 | − | 0.164663i | \(-0.0526537\pi\) | |||||||
\(728\) | − | 139.942i | − | 0.192228i | ||||||
\(729\) | −407.634 | −0.559169 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.3853 | 0.0306228 | ||||||||
\(732\) | 4.98878 | 0.00681528 | ||||||||
\(733\) | 322.159i | 0.439507i | 0.975555 | + | 0.219754i | \(0.0705253\pi\) | ||||
−0.975555 | + | 0.219754i | \(0.929475\pi\) | |||||||
\(734\) | − | 1084.68i | − | 1.47776i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 107.215i | − | 0.145673i | ||||||
\(737\) | 545.847 | 0.740634 | ||||||||
\(738\) | 649.274i | 0.879775i | ||||||||
\(739\) | −1055.17 | −1.42784 | −0.713921 | − | 0.700227i | \(-0.753082\pi\) | ||||
−0.713921 | + | 0.700227i | \(0.753082\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50.3598 | − | 103.534i | 0.0679620 | − | 0.139722i | ||||
\(742\) | 387.746i | 0.522569i | ||||||||
\(743\) | 485.597 | 0.653562 | 0.326781 | − | 0.945100i | \(-0.394036\pi\) | ||||
0.326781 | + | 0.945100i | \(0.394036\pi\) | |||||||
\(744\) | 279.153i | 0.375206i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −548.094 | −0.734710 | ||||||||
\(747\) | − | 103.037i | − | 0.137934i | ||||||
\(748\) | 24.3979i | 0.0326175i | ||||||||
\(749\) | 204.311i | 0.272779i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 912.769i | 1.21540i | 0.794165 | + | 0.607702i | \(0.207909\pi\) | ||||
−0.794165 | + | 0.607702i | \(0.792091\pi\) | |||||||
\(752\) | − | 959.262i | − | 1.27561i | ||||||
\(753\) | −254.141 | −0.337505 | ||||||||
\(754\) | − | 229.423i | − | 0.304274i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 15.5217i | − | 0.0205314i | ||||||
\(757\) | 737.208i | 0.973855i | 0.873442 | + | 0.486928i | \(0.161882\pi\) | ||||
−0.873442 | + | 0.486928i | \(0.838118\pi\) | |||||||
\(758\) | − | 391.435i | − | 0.516405i | ||||||
\(759\) | 101.721i | 0.134020i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −990.845 | −1.30203 | −0.651015 | − | 0.759065i | \(-0.725656\pi\) | ||||
−0.651015 | + | 0.759065i | \(0.725656\pi\) | |||||||
\(762\) | −106.835 | −0.140204 | ||||||||
\(763\) | −302.392 | −0.396320 | ||||||||
\(764\) | 7.88152 | 0.0103161 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.5654 | −0.0490410 | ||||||||
\(767\) | 686.841i | 0.895490i | ||||||||
\(768\) | −73.4627 | −0.0956546 | ||||||||
\(769\) | 331.509 | 0.431091 | 0.215545 | − | 0.976494i | \(-0.430847\pi\) | ||||
0.215545 | + | 0.976494i | \(0.430847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −405.252 | −0.525618 | ||||||||
\(772\) | 105.183 | 0.136247 | ||||||||
\(773\) | −1418.41 | −1.83494 | −0.917468 | − | 0.397809i | \(-0.869771\pi\) | ||||
−0.917468 | + | 0.397809i | \(0.869771\pi\) | |||||||
\(774\) | 54.7594i | 0.0707486i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −526.172 | −0.678056 | ||||||||
\(777\) | 16.8930i | 0.0217413i | ||||||||
\(778\) | −731.839 | −0.940667 | ||||||||
\(779\) | 711.107 | + | 345.887i | 0.912846 | + | 0.444015i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 21.2753i | − | 0.0272411i | ||||||
\(782\) | 175.096 | 0.223907 | ||||||||
\(783\) | − | 246.002i | − | 0.314179i | ||||||
\(784\) | −608.499 | −0.776147 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 139.028 | 0.176881 | ||||||||
\(787\) | 268.008 | 0.340543 | 0.170272 | − | 0.985397i | \(-0.445535\pi\) | ||||
0.170272 | + | 0.985397i | \(0.445535\pi\) | |||||||
\(788\) | − | 168.405i | − | 0.213711i | ||||||
\(789\) | − | 12.5791i | − | 0.0159431i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 173.297i | 0.219086i | ||||||||
\(792\) | −576.976 | −0.728505 | ||||||||
\(793\) | 92.6804 | 0.116873 | ||||||||
\(794\) | 549.799i | 0.692442i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −35.4621 | −0.0445504 | ||||||||
\(797\) | −106.821 | −0.134029 | −0.0670147 | − | 0.997752i | \(-0.521347\pi\) | ||||
−0.0670147 | + | 0.997752i | \(0.521347\pi\) | |||||||
\(798\) | 62.5091 | + | 30.4049i | 0.0783322 | + | 0.0381013i | ||||
\(799\) | −438.813 | −0.549203 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 208.926i | 0.260831i | ||||||||
\(802\) | − | 1355.83i | − | 1.69056i | ||||||
\(803\) | − | 813.203i | − | 1.01271i | ||||||
\(804\) | 25.5469 | 0.0317748 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 536.446i | 0.665566i | ||||||||
\(807\) | − | 280.599i | − | 0.347706i | ||||||
\(808\) | −1166.45 | −1.44362 | ||||||||
\(809\) | −235.725 | −0.291378 | −0.145689 | − | 0.989330i | \(-0.546540\pi\) | ||||
−0.145689 | + | 0.989330i | \(0.546540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 953.232i | − | 1.17538i | −0.809087 | − | 0.587689i | \(-0.800038\pi\) | ||
0.809087 | − | 0.587689i | \(-0.199962\pi\) | |||||||
\(812\) | −18.0654 | −0.0222480 | ||||||||
\(813\) | −93.5774 | −0.115101 | ||||||||
\(814\) | 135.446 | 0.166395 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 74.7431i | − | 0.0915970i | ||||||
\(817\) | 59.9744 | + | 29.1720i | 0.0734081 | + | 0.0357062i | ||||
\(818\) | 583.614i | 0.713464i | ||||||||
\(819\) | − | 138.287i | − | 0.168849i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1229.40 | −1.49745 | −0.748723 | − | 0.662883i | \(-0.769333\pi\) | ||||
−0.748723 | + | 0.662883i | \(0.769333\pi\) | |||||||
\(822\) | 177.450i | 0.215876i | ||||||||
\(823\) | − | 625.946i | − | 0.760566i | −0.924870 | − | 0.380283i | \(-0.875827\pi\) | ||
0.924870 | − | 0.380283i | \(-0.124173\pi\) | |||||||
\(824\) | −820.474 | −0.995721 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −414.682 | −0.502036 | ||||||||
\(827\) | 573.760 | 0.693785 | 0.346892 | − | 0.937905i | \(-0.387237\pi\) | ||||
0.346892 | + | 0.937905i | \(0.387237\pi\) | |||||||
\(828\) | − | 55.8629i | − | 0.0674672i | ||||||
\(829\) | − | 651.345i | − | 0.785700i | −0.919603 | − | 0.392850i | \(-0.871489\pi\) | ||
0.919603 | − | 0.392850i | \(-0.128511\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 206.408i | − | 0.248385i | ||||||
\(832\) | −501.534 | −0.602805 | ||||||||
\(833\) | 278.357i | 0.334162i | ||||||||
\(834\) | −256.595 | −0.307668 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −31.7947 | + | 65.3665i | −0.0380319 | + | 0.0781896i | ||||
\(837\) | 575.212i | 0.687230i | ||||||||
\(838\) | −473.468 | −0.564998 | ||||||||
\(839\) | 737.524i | 0.879051i | 0.898230 | + | 0.439525i | \(0.144853\pi\) | ||||
−0.898230 | + | 0.439525i | \(0.855147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 554.684 | 0.659553 | ||||||||
\(842\) | − | 483.154i | − | 0.573817i | ||||||
\(843\) | − | 406.610i | − | 0.482336i | ||||||
\(844\) | 82.6037i | 0.0978717i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 1073.44i | − | 1.26884i | ||||||
\(847\) | 120.944i | 0.142791i | ||||||||
\(848\) | 1242.16 | 1.46482 | ||||||||
\(849\) | 429.505i | 0.505895i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 126.777i | 0.148974i | ||||||||
\(852\) | − | 0.995734i | − | 0.00116870i | ||||||
\(853\) | 1181.14i | 1.38469i | 0.721567 | + | 0.692345i | \(0.243422\pi\) | ||||
−0.721567 | + | 0.692345i | \(0.756578\pi\) | |||||||
\(854\) | 55.9560i | 0.0655223i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 741.189 | 0.865875 | ||||||||
\(857\) | −626.333 | −0.730844 | −0.365422 | − | 0.930842i | \(-0.619075\pi\) | ||||
−0.365422 | + | 0.930842i | \(0.619075\pi\) | |||||||
\(858\) | 94.4924 | 0.110131 | ||||||||
\(859\) | 191.158 | 0.222536 | 0.111268 | − | 0.993790i | \(-0.464509\pi\) | ||||
0.111268 | + | 0.993790i | \(0.464509\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −80.9446 | −0.0940123 | ||||||||
\(862\) | 1382.13i | 1.60339i | ||||||||
\(863\) | −831.146 | −0.963089 | −0.481544 | − | 0.876422i | \(-0.659924\pi\) | ||||
−0.481544 | + | 0.876422i | \(0.659924\pi\) | |||||||
\(864\) | −106.793 | −0.123603 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 164.563 | 0.190027 | ||||||||
\(867\) | 208.770 | 0.240796 | ||||||||
\(868\) | 42.2413 | 0.0486651 | ||||||||
\(869\) | − | 225.125i | − | 0.259062i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 474.605 | 0.544896 | ||||||||
\(872\) | 1097.00i | 1.25803i | ||||||||
\(873\) | −519.949 | −0.595589 | ||||||||
\(874\) | 469.114 | + | 228.180i | 0.536744 | + | 0.261076i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 38.0598i | − | 0.0434472i | ||||||
\(877\) | −185.869 | −0.211937 | −0.105968 | − | 0.994369i | \(-0.533794\pi\) | ||||
−0.105968 | + | 0.994369i | \(0.533794\pi\) | |||||||
\(878\) | − | 641.313i | − | 0.730425i | ||||||
\(879\) | −386.025 | −0.439163 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −397.804 | −0.451537 | −0.225768 | − | 0.974181i | \(-0.572489\pi\) | ||||
−0.225768 | + | 0.974181i | \(0.572489\pi\) | |||||||
\(882\) | −680.924 | −0.772023 | ||||||||
\(883\) | 978.520i | 1.10818i | 0.832458 | + | 0.554088i | \(0.186933\pi\) | ||||
−0.832458 | + | 0.554088i | \(0.813067\pi\) | |||||||
\(884\) | 21.2135i | 0.0239972i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 1079.54i | − | 1.21844i | ||||||
\(887\) | −128.464 | −0.144830 | −0.0724151 | − | 0.997375i | \(-0.523071\pi\) | ||||
−0.0724151 | + | 0.997375i | \(0.523071\pi\) | |||||||
\(888\) | 61.2834 | 0.0690129 | ||||||||
\(889\) | 156.285i | 0.175799i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −517.421 | −0.580719 | ||||||||
\(892\) | −21.3519 | −0.0239372 | ||||||||
\(893\) | −1175.66 | − | 571.851i | −1.31653 | − | 0.640371i | ||||
\(894\) | −224.716 | −0.251360 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 234.828i | − | 0.262085i | ||||||
\(897\) | 88.4448i | 0.0986007i | ||||||||
\(898\) | 1223.22i | 1.36216i | ||||||||
\(899\) | 669.476 | 0.744689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 568.227i | − | 0.630662i | ||||||
\(902\) | 649.004i | 0.719517i | ||||||||
\(903\) | −6.82682 | −0.00756016 | ||||||||
\(904\) | 628.677 | 0.695439 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 408.900i | 0.451324i | ||||||||
\(907\) | −885.139 | −0.975897 | −0.487949 | − | 0.872872i | \(-0.662255\pi\) | ||||
−0.487949 | + | 0.872872i | \(0.662255\pi\) | |||||||
\(908\) | 163.155 | 0.179686 | ||||||||
\(909\) | −1152.65 | −1.26804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1542.51i | − | 1.69320i | −0.532228 | − | 0.846601i | \(-0.678645\pi\) | ||
0.532228 | − | 0.846601i | \(-0.321355\pi\) | |||||||
\(912\) | 97.4034 | − | 200.251i | 0.106802 | − | 0.219573i | ||||
\(913\) | − | 102.994i | − | 0.112808i | ||||||
\(914\) | 1397.74i | 1.52926i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.18028 | 0.00783874 | ||||||||
\(917\) | − | 203.380i | − | 0.221788i | ||||||
\(918\) | − | 174.406i | − | 0.189985i | ||||||
\(919\) | 1242.28 | 1.35178 | 0.675889 | − | 0.737003i | \(-0.263760\pi\) | ||||
0.675889 | + | 0.737003i | \(0.263760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 471.397 | 0.511831 | ||||||||
\(922\) | −524.915 | −0.569322 | ||||||||
\(923\) | − | 18.4985i | − | 0.0200417i | ||||||
\(924\) | − | 7.44060i | − | 0.00805260i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 752.151i | − | 0.812258i | ||||||
\(927\) | −810.770 | −0.874617 | ||||||||
\(928\) | 124.294i | 0.133938i | ||||||||
\(929\) | −1276.20 | −1.37373 | −0.686866 | − | 0.726785i | \(-0.741014\pi\) | ||||
−0.686866 | + | 0.726785i | \(0.741014\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −362.748 | + | 745.772i | −0.389633 | + | 0.801044i | ||||
\(932\) | − | 51.1558i | − | 0.0548882i | ||||||
\(933\) | −53.3051 | −0.0571330 | ||||||||
\(934\) | − | 1697.11i | − | 1.81704i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −501.670 | −0.535973 | ||||||||
\(937\) | − | 1537.08i | − | 1.64042i | −0.572060 | − | 0.820212i | \(-0.693855\pi\) | ||
0.572060 | − | 0.820212i | \(-0.306145\pi\) | |||||||
\(938\) | 286.544i | 0.305484i | ||||||||
\(939\) | 155.747i | 0.165864i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 571.078i | − | 0.606884i | −0.952850 | − | 0.303442i | \(-0.901864\pi\) | ||
0.952850 | − | 0.303442i | \(-0.0981359\pi\) | |||||||
\(942\) | − | 283.394i | − | 0.300843i | ||||||
\(943\) | −607.467 | −0.644186 | ||||||||
\(944\) | 1328.45i | 1.40726i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 54.7367i | 0.0578612i | ||||||||
\(947\) | − | 578.957i | − | 0.611359i | −0.952135 | − | 0.305679i | \(-0.901116\pi\) | ||
0.952135 | − | 0.305679i | \(-0.0988836\pi\) | |||||||
\(948\) | − | 10.5364i | − | 0.0111143i | ||||||
\(949\) | − | 707.066i | − | 0.745064i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −304.949 | −0.320662 | ||||||||
\(952\) | −123.817 | −0.130060 | ||||||||
\(953\) | −621.530 | −0.652182 | −0.326091 | − | 0.945338i | \(-0.605732\pi\) | ||||
−0.326091 | + | 0.945338i | \(0.605732\pi\) | |||||||
\(954\) | 1390.01 | 1.45703 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −106.994 | −0.111918 | ||||||||
\(957\) | − | 117.925i | − | 0.123224i | ||||||
\(958\) | −260.375 | −0.271790 | ||||||||
\(959\) | 259.585 | 0.270683 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −604.396 | −0.628924 | ||||||||
\(962\) | 117.768 | 0.122420 | ||||||||
\(963\) | 732.423 | 0.760564 | ||||||||
\(964\) | 11.6419i | 0.0120766i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −53.3988 | −0.0552782 | ||||||||
\(967\) | 1198.21i | 1.23910i | 0.784955 | + | 0.619552i | \(0.212686\pi\) | ||||
−0.784955 | + | 0.619552i | \(0.787314\pi\) | |||||||
\(968\) | 438.754 | 0.453259 | ||||||||
\(969\) | −91.6046 | − | 44.5571i | −0.0945352 | − | 0.0459826i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 448.776i | − | 0.462179i | −0.972932 | − | 0.231090i | \(-0.925771\pi\) | ||
0.972932 | − | 0.231090i | \(-0.0742290\pi\) | |||||||
\(972\) | −84.6016 | −0.0870387 | ||||||||
\(973\) | 375.364i | 0.385780i | ||||||||
\(974\) | 1003.30 | 1.03008 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 179.258 | 0.183666 | ||||||||
\(977\) | 369.963 | 0.378673 | 0.189336 | − | 0.981912i | \(-0.439366\pi\) | ||||
0.189336 | + | 0.981912i | \(0.439366\pi\) | |||||||
\(978\) | − | 328.235i | − | 0.335619i | ||||||
\(979\) | 208.839i | 0.213319i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1084.03i | 1.10502i | ||||||||
\(982\) | 1012.51 | 1.03107 | ||||||||
\(983\) | 972.897 | 0.989723 | 0.494861 | − | 0.868972i | \(-0.335219\pi\) | ||||
0.494861 | + | 0.868972i | \(0.335219\pi\) | |||||||
\(984\) | 293.646i | 0.298421i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −202.988 | −0.205870 | ||||||||
\(987\) | 133.825 | 0.135587 | ||||||||
\(988\) | −27.6449 | + | 56.8350i | −0.0279807 | + | 0.0575253i | ||||
\(989\) | −51.2335 | −0.0518033 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1332.05i | 1.34415i | 0.740485 | + | 0.672073i | \(0.234596\pi\) | ||||
−0.740485 | + | 0.672073i | \(0.765404\pi\) | |||||||
\(992\) | − | 290.630i | − | 0.292974i | ||||||
\(993\) | 310.136i | 0.312323i | ||||||||
\(994\) | 11.1685 | 0.0112359 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 4.82035i | − | 0.00483971i | ||||||
\(997\) | 719.460i | 0.721625i | 0.932638 | + | 0.360813i | \(0.117501\pi\) | ||||
−0.932638 | + | 0.360813i | \(0.882499\pi\) | |||||||
\(998\) | 1344.51 | 1.34721 | ||||||||
\(999\) | 126.278 | 0.126405 |
(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 | 475.3.d.c.474.18 | 24 | ||
5.2 | odd | 4 | 95.3.c.a.56.9 | yes | 12 | ||
5.3 | odd | 4 | 475.3.c.g.151.4 | 12 | |||
5.4 | even | 2 | inner | 475.3.d.c.474.7 | 24 | ||
15.2 | even | 4 | 855.3.e.a.721.4 | 12 | |||
19.18 | odd | 2 | inner | 475.3.d.c.474.8 | 24 | ||
20.7 | even | 4 | 1520.3.h.a.721.7 | 12 | |||
95.18 | even | 4 | 475.3.c.g.151.9 | 12 | |||
95.37 | even | 4 | 95.3.c.a.56.4 | ✓ | 12 | ||
95.94 | odd | 2 | inner | 475.3.d.c.474.17 | 24 | ||
285.227 | odd | 4 | 855.3.e.a.721.9 | 12 | |||
380.227 | odd | 4 | 1520.3.h.a.721.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.3.c.a.56.4 | ✓ | 12 | 95.37 | even | 4 | ||
95.3.c.a.56.9 | yes | 12 | 5.2 | odd | 4 | ||
475.3.c.g.151.4 | 12 | 5.3 | odd | 4 | |||
475.3.c.g.151.9 | 12 | 95.18 | even | 4 | |||
475.3.d.c.474.7 | 24 | 5.4 | even | 2 | inner | ||
475.3.d.c.474.8 | 24 | 19.18 | odd | 2 | inner | ||
475.3.d.c.474.17 | 24 | 95.94 | odd | 2 | inner | ||
475.3.d.c.474.18 | 24 | 1.1 | even | 1 | trivial | ||
855.3.e.a.721.4 | 12 | 15.2 | even | 4 | |||
855.3.e.a.721.9 | 12 | 285.227 | odd | 4 | |||
1520.3.h.a.721.6 | 12 | 380.227 | odd | 4 | |||
1520.3.h.a.721.7 | 12 | 20.7 | even | 4 |