Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(207,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.207");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.s (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 207.3 | ||
Character | \(\chi\) | \(=\) | 1600.207 |
Dual form | 1600.2.s.e.943.3 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.35800 | −1.36139 | −0.680697 | − | 0.732565i | \(-0.738323\pi\) | ||||
−0.680697 | + | 0.732565i | \(0.738323\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.66357 | − | 2.66357i | −1.00674 | − | 1.00674i | −0.999977 | − | 0.00675825i | \(-0.997849\pi\) |
−0.00675825 | − | 0.999977i | \(-0.502151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.56018 | 0.853392 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20666 | − | 2.20666i | 0.665333 | − | 0.665333i | −0.291299 | − | 0.956632i | \(-0.594087\pi\) |
0.956632 | + | 0.291299i | \(0.0940873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.16154i | − | 1.15420i | −0.816672 | − | 0.577102i | \(-0.804183\pi\) | ||
0.816672 | − | 0.577102i | \(-0.195817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.69084 | − | 1.69084i | −0.410088 | − | 0.410088i | 0.471681 | − | 0.881769i | \(-0.343647\pi\) |
−0.881769 | + | 0.471681i | \(0.843647\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.74110 | + | 4.74110i | −1.08768 | + | 1.08768i | −0.0919157 | + | 0.995767i | \(0.529299\pi\) |
−0.995767 | + | 0.0919157i | \(0.970701\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.28071 | + | 6.28071i | 1.37056 | + | 1.37056i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.70658 | − | 3.70658i | 0.772875 | − | 0.772875i | −0.205733 | − | 0.978608i | \(-0.565958\pi\) |
0.978608 | + | 0.205733i | \(0.0659580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.03710 | 0.199591 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65701 | + | 3.65701i | 0.679089 | + | 0.679089i | 0.959794 | − | 0.280705i | \(-0.0905683\pi\) |
−0.280705 | + | 0.959794i | \(0.590568\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.90069i | − | 1.23940i | −0.784839 | − | 0.619700i | \(-0.787254\pi\) | ||
0.784839 | − | 0.619700i | \(-0.212746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.20331 | + | 5.20331i | −0.905781 | + | 0.905781i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.10092i | − | 0.180989i | −0.995897 | − | 0.0904947i | \(-0.971155\pi\) | ||
0.995897 | − | 0.0904947i | \(-0.0288448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.81293i | 1.57133i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.85512i | − | 1.53911i | −0.638579 | − | 0.769556i | \(-0.720478\pi\) | ||
0.638579 | − | 0.769556i | \(-0.279522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0944i | 1.53938i | 0.638417 | + | 0.769691i | \(0.279590\pi\) | ||||
−0.638417 | + | 0.769691i | \(0.720410\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.90722 | + | 3.90722i | −0.569927 | + | 0.569927i | −0.932108 | − | 0.362181i | \(-0.882032\pi\) |
0.362181 | + | 0.932108i | \(0.382032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.18923i | 1.02703i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.98700 | + | 3.98700i | 0.558291 | + | 0.558291i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.19464 | −0.850899 | −0.425450 | − | 0.904982i | \(-0.639884\pi\) | ||||
−0.425450 | + | 0.904982i | \(0.639884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1795 | − | 11.1795i | 1.48076 | − | 1.48076i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.42978 | − | 3.42978i | −0.446519 | − | 0.446519i | 0.447677 | − | 0.894196i | \(-0.352252\pi\) |
−0.894196 | + | 0.447677i | \(0.852252\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.57442 | + | 4.57442i | −0.585694 | + | 0.585694i | −0.936462 | − | 0.350768i | \(-0.885920\pi\) |
0.350768 | + | 0.936462i | \(0.385920\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.81921 | − | 6.81921i | −0.859140 | − | 0.859140i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.37605i | 0.778958i | 0.921035 | + | 0.389479i | \(0.127345\pi\) | ||||
−0.921035 | + | 0.389479i | \(0.872655\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.74012 | + | 8.74012i | −1.05219 | + | 1.05219i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.03776 | 0.123160 | 0.0615800 | − | 0.998102i | \(-0.480386\pi\) | ||||
0.0615800 | + | 0.998102i | \(0.480386\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.70822 | − | 4.70822i | −0.551056 | − | 0.551056i | 0.375690 | − | 0.926746i | \(-0.377406\pi\) |
−0.926746 | + | 0.375690i | \(0.877406\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.7552 | −1.33963 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.54448 | −0.286277 | −0.143138 | − | 0.989703i | \(-0.545719\pi\) | ||||
−0.143138 | + | 0.989703i | \(0.545719\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1260 | −1.12511 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.65615 | −0.840371 | −0.420186 | − | 0.907438i | \(-0.638035\pi\) | ||||
−0.420186 | + | 0.907438i | \(0.638035\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.62323 | − | 8.62323i | −0.924507 | − | 0.924507i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.77392 | −0.188036 | −0.0940178 | − | 0.995571i | \(-0.529971\pi\) | ||||
−0.0940178 | + | 0.995571i | \(0.529971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.0846 | + | 11.0846i | −1.16198 | + | 1.16198i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.2718i | 1.68731i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.16560 | − | 1.16560i | −0.118349 | − | 0.118349i | 0.645452 | − | 0.763801i | \(-0.276669\pi\) |
−0.763801 | + | 0.645452i | \(0.776669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.64944 | − | 5.64944i | 0.567790 | − | 0.567790i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.20347 | + | 8.20347i | 0.816275 | + | 0.816275i | 0.985566 | − | 0.169291i | \(-0.0541477\pi\) |
−0.169291 | + | 0.985566i | \(0.554148\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.71614 | + | 9.71614i | −0.957359 | + | 0.957359i | −0.999127 | − | 0.0417680i | \(-0.986701\pi\) |
0.0417680 | + | 0.999127i | \(0.486701\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.37605 | 0.616396 | 0.308198 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308198 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.651659 | − | 0.651659i | −0.0624176 | − | 0.0624176i | 0.675209 | − | 0.737627i | \(-0.264053\pi\) |
−0.737627 | + | 0.675209i | \(0.764053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.59596i | 0.246398i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.86164 | + | 8.86164i | −0.833633 | + | 0.833633i | −0.988012 | − | 0.154378i | \(-0.950662\pi\) |
0.154378 | + | 0.988012i | \(0.450662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 10.6543i | − | 0.984989i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.00732i | 0.825700i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.26129i | 0.114663i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 23.2384i | 2.09534i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.95966 | − | 5.95966i | 0.528834 | − | 0.528834i | −0.391391 | − | 0.920225i | \(-0.628006\pi\) |
0.920225 | + | 0.391391i | \(0.128006\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 23.8026i | − | 2.09570i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.32406 | + | 1.32406i | 0.115683 | + | 0.115683i | 0.762579 | − | 0.646895i | \(-0.223933\pi\) |
−0.646895 | + | 0.762579i | \(0.723933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.2565 | 2.19002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.4807 | + | 15.4807i | −1.32260 | + | 1.32260i | −0.410943 | + | 0.911661i | \(0.634801\pi\) |
−0.911661 | + | 0.410943i | \(0.865199\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.97722 | − | 5.97722i | −0.506981 | − | 0.506981i | 0.406617 | − | 0.913599i | \(-0.366708\pi\) |
−0.913599 | + | 0.406617i | \(0.866708\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.21324 | − | 9.21324i | 0.775895 | − | 0.775895i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.18312 | − | 9.18312i | −0.767931 | − | 0.767931i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 16.9522i | − | 1.39820i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.16964 | + | 3.16964i | −0.259667 | + | 0.259667i | −0.824919 | − | 0.565252i | \(-0.808779\pi\) |
0.565252 | + | 0.824919i | \(0.308779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1344 | 0.906103 | 0.453051 | − | 0.891484i | \(-0.350335\pi\) | ||||
0.453051 | + | 0.891484i | \(0.350335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.32884 | − | 4.32884i | −0.349966 | − | 0.349966i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4517 | 1.07356 | 0.536781 | − | 0.843722i | \(-0.319640\pi\) | ||||
0.536781 | + | 0.843722i | \(0.319640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.6070 | 1.15841 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7455 | −1.55616 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.01486 | 0.0794896 | 0.0397448 | − | 0.999210i | \(-0.487346\pi\) | ||||
0.0397448 | + | 0.999210i | \(0.487346\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.83926 | + | 5.83926i | 0.451855 | + | 0.451855i | 0.895970 | − | 0.444115i | \(-0.146482\pi\) |
−0.444115 | + | 0.895970i | \(0.646482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.31844 | −0.332188 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.1380 | + | 12.1380i | −0.928220 | + | 0.928220i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.55812i | − | 0.498605i | −0.968426 | − | 0.249302i | \(-0.919799\pi\) | ||
0.968426 | − | 0.249302i | \(-0.0802013\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.08743 | + | 8.08743i | 0.607888 | + | 0.607888i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.45256 | + | 5.45256i | −0.407543 | + | 0.407543i | −0.880881 | − | 0.473338i | \(-0.843049\pi\) |
0.473338 | + | 0.880881i | \(0.343049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.39320 | − | 5.39320i | −0.400873 | − | 0.400873i | 0.477667 | − | 0.878541i | \(-0.341482\pi\) |
−0.878541 | + | 0.477667i | \(0.841482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.7865 | − | 10.7865i | 0.797360 | − | 0.797360i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.46221 | −0.545691 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.76240 | − | 2.76240i | −0.200935 | − | 0.200935i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.78551i | − | 0.635698i | −0.948141 | − | 0.317849i | \(-0.897040\pi\) | ||
0.948141 | − | 0.317849i | \(-0.102960\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.7474 | + | 11.7474i | −0.845598 | + | 0.845598i | −0.989580 | − | 0.143982i | \(-0.954009\pi\) |
0.143982 | + | 0.989580i | \(0.454009\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.9577i | 1.06569i | 0.846212 | + | 0.532846i | \(0.178877\pi\) | ||||
−0.846212 | + | 0.532846i | \(0.821123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.9644i | − | 0.777245i | −0.921397 | − | 0.388623i | \(-0.872951\pi\) | ||
0.921397 | − | 0.388623i | \(-0.127049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 15.0347i | − | 1.06047i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 19.4814i | − | 1.36733i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.48949 | − | 9.48949i | 0.659565 | − | 0.659565i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.9240i | 1.44734i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.1093 | − | 14.1093i | −0.971326 | − | 0.971326i | 0.0282740 | − | 0.999600i | \(-0.490999\pi\) |
−0.999600 | + | 0.0282740i | \(0.990999\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.44705 | −0.167669 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.3805 | + | 18.3805i | −1.24775 | + | 1.24775i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1020 | + | 11.1020i | 0.750204 | + | 0.750204i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.03649 | + | 7.03649i | −0.473325 | + | 0.473325i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.1252 | + | 14.1252i | 0.945897 | + | 0.945897i | 0.998610 | − | 0.0527131i | \(-0.0167869\pi\) |
−0.0527131 | + | 0.998610i | \(0.516787\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 8.40121i | − | 0.557608i | −0.960348 | − | 0.278804i | \(-0.910062\pi\) | ||
0.960348 | − | 0.278804i | \(-0.0899379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.9755 | + | 15.9755i | −1.05569 | + | 1.05569i | −0.0573343 | + | 0.998355i | \(0.518260\pi\) |
−0.998355 | + | 0.0573343i | \(0.981740\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 27.7188 | 1.82376 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8176 | − | 10.8176i | −0.708684 | − | 0.708684i | 0.257574 | − | 0.966258i | \(-0.417077\pi\) |
−0.966258 | + | 0.257574i | \(0.917077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.99990 | 0.389735 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.7033 | 0.821706 | 0.410853 | − | 0.911702i | \(-0.365231\pi\) | ||||
0.410853 | + | 0.911702i | \(0.365231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.1860 | 1.88004 | 0.940019 | − | 0.341122i | \(-0.110807\pi\) | ||||
0.940019 | + | 0.341122i | \(0.110807\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.7659 | 1.33213 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.7303 | + | 19.7303i | 1.25541 | + | 1.25541i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0532 | 1.14408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.59622 | + | 7.59622i | −0.479469 | + | 0.479469i | −0.904962 | − | 0.425493i | \(-0.860101\pi\) |
0.425493 | + | 0.904962i | \(0.360101\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.3583i | − | 1.02844i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.72143 | − | 4.72143i | −0.294515 | − | 0.294515i | 0.544346 | − | 0.838861i | \(-0.316778\pi\) |
−0.838861 | + | 0.544346i | \(0.816778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.93237 | + | 2.93237i | −0.182208 | + | 0.182208i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.36258 | + | 9.36258i | 0.579529 | + | 0.579529i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6431 | − | 15.6431i | 0.964594 | − | 0.964594i | −0.0348001 | − | 0.999394i | \(-0.511079\pi\) |
0.999394 | + | 0.0348001i | \(0.0110795\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.18292 | 0.255991 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.1216 | − | 11.1216i | −0.678096 | − | 0.678096i | 0.281473 | − | 0.959569i | \(-0.409177\pi\) |
−0.959569 | + | 0.281473i | \(0.909177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.7962i | − | 1.02030i | −0.860086 | − | 0.510148i | \(-0.829590\pi\) | ||
0.860086 | − | 0.510148i | \(-0.170410\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 26.1374 | − | 26.1374i | 1.58191 | − | 1.58191i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.5871i | − | 0.756287i | −0.925747 | − | 0.378144i | \(-0.876563\pi\) | ||
0.925747 | − | 0.378144i | \(-0.123437\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 17.6670i | − | 1.05769i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.3713i | 1.87146i | 0.352722 | + | 0.935728i | \(0.385256\pi\) | ||||
−0.352722 | + | 0.935728i | \(0.614744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.58242i | − | 0.450728i | −0.974275 | − | 0.225364i | \(-0.927643\pi\) | ||
0.974275 | − | 0.225364i | \(-0.0723571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.2498 | + | 26.2498i | −1.54948 | + | 1.54948i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 11.2821i | − | 0.663656i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.74849 | + | 2.74849i | 0.161119 | + | 0.161119i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.6053 | 1.55430 | 0.777149 | − | 0.629317i | \(-0.216665\pi\) | ||||
0.777149 | + | 0.629317i | \(0.216665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.28854 | − | 2.28854i | 0.132794 | − | 0.132794i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.4251 | − | 15.4251i | −0.892055 | − | 0.892055i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8871 | − | 26.8871i | 1.54975 | − | 1.54975i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.3438 | − | 19.3438i | −1.11127 | − | 1.11127i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.78617i | 0.159015i | 0.996834 | + | 0.0795075i | \(0.0253347\pi\) | ||||
−0.996834 | + | 0.0795075i | \(0.974665\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.9107 | − | 22.9107i | 1.30334 | − | 1.30334i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.97594 | −0.282159 | −0.141080 | − | 0.989998i | \(-0.545057\pi\) | ||||
−0.141080 | + | 0.989998i | \(0.545057\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.76254 | + | 6.76254i | 0.382241 | + | 0.382241i | 0.871909 | − | 0.489668i | \(-0.162882\pi\) |
−0.489668 | + | 0.871909i | \(0.662882\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.81211 | 0.101778 | 0.0508892 | − | 0.998704i | \(-0.483794\pi\) | ||||
0.0508892 | + | 0.998704i | \(0.483794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.1395 | 0.903641 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0347 | −0.839157 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0328 | 0.892091 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.53661 | + | 1.53661i | 0.0849749 | + | 0.0849749i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.8143 | 1.14753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.35992 | − | 1.35992i | 0.0747482 | − | 0.0747482i | −0.668744 | − | 0.743492i | \(-0.733168\pi\) |
0.743492 | + | 0.668744i | \(0.233168\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.81854i | − | 0.154455i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.83330 | + | 3.83330i | 0.208813 | + | 0.208813i | 0.803763 | − | 0.594950i | \(-0.202828\pi\) |
−0.594950 | + | 0.803763i | \(0.702828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.8958 | − | 20.8958i | 1.13490 | − | 1.13490i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.2275 | − | 15.2275i | −0.824614 | − | 0.824614i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.504019 | − | 0.504019i | 0.0272144 | − | 0.0272144i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.4284 | −1.15034 | −0.575169 | − | 0.818035i | \(-0.695064\pi\) | ||||
−0.575169 | + | 0.818035i | \(0.695064\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.63033 | + | 2.63033i | 0.140798 | + | 0.140798i | 0.773993 | − | 0.633195i | \(-0.218257\pi\) |
−0.633195 | + | 0.773993i | \(0.718257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.31595i | − | 0.230369i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.754635 | − | 0.754635i | 0.0401651 | − | 0.0401651i | −0.686739 | − | 0.726904i | \(-0.740958\pi\) |
0.726904 | + | 0.686739i | \(0.240958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 21.2393i | − | 1.12410i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.0363i | 0.899140i | 0.893245 | + | 0.449570i | \(0.148423\pi\) | ||||
−0.893245 | + | 0.449570i | \(0.851577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 25.9560i | − | 1.36611i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.97412i | − | 0.156101i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.86375 | − | 4.86375i | 0.253886 | − | 0.253886i | −0.568676 | − | 0.822562i | \(-0.692544\pi\) |
0.822562 | + | 0.568676i | \(0.192544\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 25.2309i | − | 1.31347i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4999 | + | 16.4999i | 0.856631 | + | 0.856631i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.2209 | 0.788109 | 0.394055 | − | 0.919087i | \(-0.371072\pi\) | ||||
0.394055 | + | 0.919087i | \(0.371072\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.2188 | − | 15.2188i | 0.783807 | − | 0.783807i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.75236 | − | 2.75236i | −0.141379 | − | 0.141379i | 0.632875 | − | 0.774254i | \(-0.281875\pi\) |
−0.774254 | + | 0.632875i | \(0.781875\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.0529 | + | 14.0529i | −0.719951 | + | 0.719951i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6326 | + | 13.6326i | 0.696591 | + | 0.696591i | 0.963674 | − | 0.267083i | \(-0.0860596\pi\) |
−0.267083 | + | 0.963674i | \(0.586060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.8434i | 1.31370i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.9333 | − | 15.9333i | 0.807850 | − | 0.807850i | −0.176459 | − | 0.984308i | \(-0.556464\pi\) |
0.984308 | + | 0.176459i | \(0.0564641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.5344 | −0.633893 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.12213 | − | 3.12213i | −0.157491 | − | 0.157491i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4837 | 0.576353 | 0.288176 | − | 0.957577i | \(-0.406951\pi\) | ||||
0.288176 | + | 0.957577i | \(0.406951\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −59.5549 | −2.98147 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.56979 | −0.328080 | −0.164040 | − | 0.986454i | \(-0.552453\pi\) | ||||
−0.164040 | + | 0.986454i | \(0.552453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.7175 | −1.43052 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.42935 | − | 2.42935i | −0.120418 | − | 0.120418i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3172 | −1.05407 | −0.527034 | − | 0.849844i | \(-0.676696\pi\) | ||||
−0.527034 | + | 0.849844i | \(0.676696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.5035 | − | 36.5035i | 1.80058 | − | 1.80058i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.2709i | 0.899053i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.0943 | + | 14.0943i | 0.690201 | + | 0.690201i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.25496 | − | 8.25496i | 0.403281 | − | 0.403281i | −0.476106 | − | 0.879388i | \(-0.657952\pi\) |
0.879388 | + | 0.476106i | \(0.157952\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.52333 | + | 3.52333i | 0.171717 | + | 0.171717i | 0.787733 | − | 0.616017i | \(-0.211255\pi\) |
−0.616017 | + | 0.787733i | \(0.711255\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.0032 | + | 10.0032i | −0.486371 | + | 0.486371i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.3686 | 1.17928 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.6538 | + | 21.6538i | 1.04546 | + | 1.04546i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.8672i | 1.63133i | 0.578526 | + | 0.815664i | \(0.303628\pi\) | ||||
−0.578526 | + | 0.815664i | \(0.696372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.7321 | − | 18.7321i | 0.900206 | − | 0.900206i | −0.0952478 | − | 0.995454i | \(-0.530364\pi\) |
0.995454 | + | 0.0952478i | \(0.0303643\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 35.1465i | 1.68128i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 21.5595i | − | 1.02898i | −0.857497 | − | 0.514489i | \(-0.827982\pi\) | ||
0.857497 | − | 0.514489i | \(-0.172018\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4057i | 0.876461i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 0.517182i | − | 0.0245721i | −0.999925 | − | 0.0122860i | \(-0.996089\pi\) | ||
0.999925 | − | 0.0122860i | \(-0.00391086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.47402 | − | 7.47402i | 0.353509 | − | 0.353509i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.34582i | − | 0.252285i | −0.992012 | − | 0.126142i | \(-0.959740\pi\) | ||
0.992012 | − | 0.126142i | \(-0.0402597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.7469 | − | 21.7469i | −1.02402 | − | 1.02402i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −26.2549 | −1.23356 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5862 | − | 20.5862i | 0.962982 | − | 0.962982i | −0.0363565 | − | 0.999339i | \(-0.511575\pi\) |
0.999339 | + | 0.0363565i | \(0.0115752\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.75357 | − | 1.75357i | −0.0818498 | − | 0.0818498i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.6538 | + | 20.6538i | −0.961943 | + | 0.961943i | −0.999302 | − | 0.0373593i | \(-0.988105\pi\) |
0.0373593 | + | 0.999302i | \(0.488105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.94042 | + | 9.94042i | 0.461971 | + | 0.461971i | 0.899301 | − | 0.437330i | \(-0.144076\pi\) |
−0.437330 | + | 0.899301i | \(0.644076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.1108i | 1.62473i | 0.583146 | + | 0.812367i | \(0.301821\pi\) | ||||
−0.583146 | + | 0.812367i | \(0.698179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.9831 | − | 16.9831i | 0.784205 | − | 0.784205i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.7191 | −1.46154 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.2749 | + | 22.2749i | 1.02420 | + | 1.02420i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.8594 | −0.726151 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.4324 | −0.842198 | −0.421099 | − | 0.907015i | \(-0.638356\pi\) | ||||
−0.421099 | + | 0.907015i | \(0.638356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.58151 | −0.208899 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 46.5599 | 2.11855 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.6160 | − | 24.6160i | −1.11546 | − | 1.11546i | −0.992400 | − | 0.123057i | \(-0.960730\pi\) |
−0.123057 | − | 0.992400i | \(-0.539270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.39303 | −0.108217 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0271 | + | 19.0271i | −0.858683 | + | 0.858683i | −0.991183 | − | 0.132500i | \(-0.957700\pi\) |
0.132500 | + | 0.991183i | \(0.457700\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.3668i | − | 0.556972i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.76416 | − | 2.76416i | −0.123989 | − | 0.123989i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.2817 | + | 30.2817i | −1.35560 | + | 1.35560i | −0.476328 | + | 0.879268i | \(0.658032\pi\) |
−0.879268 | + | 0.476328i | \(0.841968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.7690 | − | 13.7690i | −0.615153 | − | 0.615153i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.491214 | + | 0.491214i | −0.0219021 | + | 0.0219021i | −0.717973 | − | 0.696071i | \(-0.754930\pi\) |
0.696071 | + | 0.717973i | \(0.254930\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1829 | 0.452238 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.5506 | − | 24.5506i | −1.08819 | − | 1.08819i | −0.995715 | − | 0.0924714i | \(-0.970523\pi\) |
−0.0924714 | − | 0.995715i | \(-0.529477\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.0814i | 1.10953i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.91701 | + | 4.91701i | −0.217091 | + | 0.217091i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.2438i | 0.758383i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.4641i | 0.678797i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4988i | 0.722826i | 0.932406 | + | 0.361413i | \(0.117706\pi\) | ||||
−0.932406 | + | 0.361413i | \(0.882294\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 10.9746i | − | 0.479887i | −0.970787 | − | 0.239943i | \(-0.922871\pi\) | ||
0.970787 | − | 0.239943i | \(-0.0771289\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.6679 | + | 11.6679i | −0.508263 | + | 0.508263i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 4.47742i | − | 0.194670i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.78084 | − | 8.78084i | −0.381056 | − | 0.381056i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.0125 | −1.77645 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.8571 | − | 12.8571i | 0.554827 | − | 0.554827i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.8642 | + | 15.8642i | 0.683319 | + | 0.683319i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8026 | + | 21.8026i | −0.937368 | + | 0.937368i | −0.998151 | − | 0.0607833i | \(-0.980640\pi\) |
0.0607833 | + | 0.998151i | \(0.480640\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.7172 | + | 12.7172i | 0.545746 | + | 0.545746i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5619i | 0.836408i | 0.908353 | + | 0.418204i | \(0.137340\pi\) | ||||
−0.908353 | + | 0.418204i | \(0.862660\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.7113 | + | 11.7113i | −0.499827 | + | 0.499827i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.6764 | −1.47727 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.77741 | + | 6.77741i | 0.288205 | + | 0.288205i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.8550 | −1.01077 | −0.505385 | − | 0.862894i | \(-0.668649\pi\) | ||||
−0.505385 | + | 0.862894i | \(0.668649\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 42.0083 | 1.77676 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.5959 | 0.742900 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.6435 | −1.50220 | −0.751098 | − | 0.660191i | \(-0.770475\pi\) | ||||
−0.751098 | + | 0.660191i | \(0.770475\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.9714 | + | 26.9714i | 1.13269 | + | 1.13269i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.4354 | −0.898619 | −0.449310 | − | 0.893376i | \(-0.648330\pi\) | ||||
−0.449310 | + | 0.893376i | \(0.648330\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.26872 | − | 7.26872i | 0.304186 | − | 0.304186i | −0.538463 | − | 0.842649i | \(-0.680995\pi\) |
0.842649 | + | 0.538463i | \(0.180995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.7163i | 0.865434i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0903 | − | 15.0903i | −0.628219 | − | 0.628219i | 0.319401 | − | 0.947620i | \(-0.396518\pi\) |
−0.947620 | + | 0.319401i | \(0.896518\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.7004 | − | 27.7004i | 1.15119 | − | 1.15119i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.3927 | + | 20.3927i | 0.846031 | + | 0.846031i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.6695 | + | 13.6695i | −0.566132 | + | 0.566132i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0083 | −0.495637 | −0.247818 | − | 0.968806i | \(-0.579714\pi\) | ||||
−0.247818 | + | 0.968806i | \(0.579714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.7168 | + | 32.7168i | 1.34807 | + | 1.34807i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 35.2703i | − | 1.45083i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.67491 | + | 8.67491i | −0.356236 | + | 0.356236i | −0.862423 | − | 0.506188i | \(-0.831054\pi\) |
0.506188 | + | 0.862423i | \(0.331054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.8541i | 1.05814i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 48.1944i | − | 1.96917i | −0.174908 | − | 0.984585i | \(-0.555963\pi\) | ||
0.174908 | − | 0.984585i | \(-0.444037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.1744i | − | 1.47559i | −0.675028 | − | 0.737793i | \(-0.735868\pi\) | ||
0.675028 | − | 0.737793i | \(-0.264132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.3238i | 0.664757i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.43441 | − | 4.43441i | 0.179987 | − | 0.179987i | −0.611363 | − | 0.791350i | \(-0.709379\pi\) |
0.791350 | + | 0.611363i | \(0.209379\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 45.9372i | 1.86147i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.2601 | + | 16.2601i | 0.657812 | + | 0.657812i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.5740 | −1.47721 | −0.738605 | − | 0.674139i | \(-0.764515\pi\) | ||||
−0.738605 | + | 0.674139i | \(0.764515\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.61726 | + | 8.61726i | −0.346918 | + | 0.346918i | −0.858960 | − | 0.512042i | \(-0.828889\pi\) |
0.512042 | + | 0.858960i | \(0.328889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.4732 | − | 16.4732i | −0.662113 | − | 0.662113i | 0.293765 | − | 0.955878i | \(-0.405092\pi\) |
−0.955878 | + | 0.293765i | \(0.905092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.84411 | − | 3.84411i | 0.154259 | − | 0.154259i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.72498 | + | 4.72498i | 0.189302 | + | 0.189302i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 49.3388i | − | 1.97040i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.86147 | + | 1.86147i | −0.0742216 | + | 0.0742216i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4406 | −1.01277 | −0.506387 | − | 0.862306i | \(-0.669019\pi\) | ||||
−0.506387 | + | 0.862306i | \(0.669019\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.2698 | + | 33.2698i | 1.32236 | + | 1.32236i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.9183 | 1.18541 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.65686 | 0.105104 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.6124 | 1.13012 | 0.565060 | − | 0.825050i | \(-0.308853\pi\) | ||||
0.565060 | + | 0.825050i | \(0.308853\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.55384 | 0.219022 | 0.109511 | − | 0.993986i | \(-0.465072\pi\) | ||||
0.109511 | + | 0.993986i | \(0.465072\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.4355 | − | 33.4355i | −1.31448 | − | 1.31448i | −0.918073 | − | 0.396410i | \(-0.870256\pi\) |
−0.396410 | − | 0.918073i | \(-0.629744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.1367 | −0.594168 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 43.3412 | − | 43.3412i | 1.69868 | − | 1.69868i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 47.7786i | − | 1.86972i | −0.355017 | − | 0.934860i | \(-0.615525\pi\) | ||
0.355017 | − | 0.934860i | \(-0.384475\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.0539 | − | 12.0539i | −0.470267 | − | 0.470267i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.3273 | + | 11.3273i | −0.441249 | + | 0.441249i | −0.892432 | − | 0.451183i | \(-0.851002\pi\) |
0.451183 | + | 0.892432i | \(0.351002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.24123 | − | 4.24123i | −0.164965 | − | 0.164965i | 0.619797 | − | 0.784762i | \(-0.287215\pi\) |
−0.784762 | + | 0.619797i | \(0.787215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.5921 | − | 16.5921i | 0.644382 | − | 0.644382i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.1099 | 1.04970 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.3074 | − | 33.3074i | −1.28774 | − | 1.28774i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.1884i | 0.779364i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.48193 | + | 3.48193i | −0.134218 | + | 0.134218i | −0.771024 | − | 0.636806i | \(-0.780255\pi\) |
0.636806 | + | 0.771024i | \(0.280255\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 28.3010i | − | 1.08769i | −0.839184 | − | 0.543847i | \(-0.816967\pi\) | ||
0.839184 | − | 0.543847i | \(-0.183033\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.20932i | 0.238292i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8101i | 0.759123i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 26.0075i | − | 0.995151i | −0.867421 | − | 0.497575i | \(-0.834224\pi\) | ||
0.867421 | − | 0.497575i | \(-0.165776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.6702 | − | 37.6702i | 1.43721 | − | 1.43721i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.7793i | 0.982112i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2570 | + | 27.2570i | 1.03690 | + | 1.03690i | 0.999292 | + | 0.0376109i | \(0.0119747\pi\) |
0.0376109 | + | 0.999292i | \(0.488025\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −30.0954 | −1.14323 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.6634 | + | 16.6634i | −0.631171 | + | 0.631171i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.5079 | + | 25.5079i | 0.964798 | + | 0.964798i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0047 | − | 14.0047i | 0.528949 | − | 0.528949i | −0.391310 | − | 0.920259i | \(-0.627978\pi\) |
0.920259 | + | 0.391310i | \(0.127978\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.21955 | + | 5.21955i | 0.196859 | + | 0.196859i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 43.7010i | − | 1.64355i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.2686 | − | 24.2686i | 0.911428 | − | 0.911428i | −0.0849564 | − | 0.996385i | \(-0.527075\pi\) |
0.996385 | + | 0.0849564i | \(0.0270751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.51432 | −0.244306 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.5779 | − | 25.5779i | −0.957901 | − | 0.957901i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.9543 | −1.11867 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.2093 | −0.790973 | −0.395487 | − | 0.918472i | \(-0.629424\pi\) | ||||
−0.395487 | + | 0.918472i | \(0.629424\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.7592 | 1.92762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −68.8208 | −2.55947 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.4304 | − | 24.4304i | −0.906073 | − | 0.906073i | 0.0898798 | − | 0.995953i | \(-0.471352\pi\) |
−0.995953 | + | 0.0898798i | \(0.971352\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.5879 | −0.688442 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.0680 | − | 17.0680i | 0.631282 | − | 0.631282i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.5318i | 0.462872i | 0.972850 | + | 0.231436i | \(0.0743423\pi\) | ||||
−0.972850 | + | 0.231436i | \(0.925658\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.0698 | + | 14.0698i | 0.518267 | + | 0.518267i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.46558 | + | 8.46558i | −0.311411 | + | 0.311411i | −0.845456 | − | 0.534045i | \(-0.820671\pi\) |
0.534045 | + | 0.845456i | \(0.320671\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46.5241 | − | 46.5241i | −1.70910 | − | 1.70910i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.7929 | + | 23.7929i | −0.872876 | + | 0.872876i | −0.992785 | − | 0.119909i | \(-0.961740\pi\) |
0.119909 | + | 0.992785i | \(0.461740\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.6011 | −0.717166 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.9831 | − | 16.9831i | −0.620548 | − | 0.620548i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.8257i | 1.30730i | 0.756797 | + | 0.653650i | \(0.226763\pi\) | ||||
−0.756797 | + | 0.653650i | \(0.773237\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.9119 | − | 17.9119i | 0.652746 | − | 0.652746i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7730i | 0.391552i | 0.980649 | + | 0.195776i | \(0.0627226\pi\) | ||||
−0.980649 | + | 0.195776i | \(0.937277\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 38.5730i | 1.40011i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.3935i | 0.666765i | 0.942792 | + | 0.333383i | \(0.108190\pi\) | ||||
−0.942792 | + | 0.333383i | \(0.891810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.47148i | 0.125676i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.2732 | + | 14.2732i | −0.515374 | + | 0.515374i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.2512i | 1.12695i | 0.826135 | + | 0.563473i | \(0.190535\pi\) | ||||
−0.826135 | + | 0.563473i | \(0.809465\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1331 | + | 11.1331i | 0.400951 | + | 0.400951i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.9433 | 0.501504 | 0.250752 | − | 0.968051i | \(-0.419322\pi\) | ||||
0.250752 | + | 0.968051i | \(0.419322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.91453 | − | 6.91453i | 0.248057 | − | 0.248057i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.7241 | + | 46.7241i | 1.67407 | + | 1.67407i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.28999 | − | 2.28999i | 0.0819424 | − | 0.0819424i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.79270 | + | 3.79270i | 0.135540 | + | 0.135540i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.23076i | − | 0.329041i | −0.986374 | − | 0.164520i | \(-0.947392\pi\) | ||
0.986374 | − | 0.164520i | \(-0.0526077\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.8864 | + | 36.8864i | −1.31319 | + | 1.31319i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 47.2072 | 1.67850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.0366 | + | 19.0366i | 0.676011 | + | 0.676011i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.2806 | −1.10801 | −0.554007 | − | 0.832512i | \(-0.686902\pi\) | ||||
−0.554007 | + | 0.832512i | \(0.686902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2129 | 0.467440 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.54156 | −0.160468 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.7789 | −0.733272 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.2247 | + | 26.2247i | 0.923155 | + | 0.923155i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.5905 | 1.53256 | 0.766280 | − | 0.642507i | \(-0.222106\pi\) | ||||
0.766280 | + | 0.642507i | \(0.222106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3324 | − | 13.3324i | 0.468164 | − | 0.468164i | −0.433155 | − | 0.901319i | \(-0.642600\pi\) |
0.901319 | + | 0.433155i | \(0.142600\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.6055i | 1.38903i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.8585 | − | 47.8585i | −1.67436 | − | 1.67436i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.3785 | + | 28.3785i | −0.991623 | + | 0.991623i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.8302 | − | 22.8302i | −0.796779 | − | 0.796779i | 0.185807 | − | 0.982586i | \(-0.440510\pi\) |
−0.982586 | + | 0.185807i | \(0.940510\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.70575 | − | 6.70575i | 0.233748 | − | 0.233748i | −0.580507 | − | 0.814255i | \(-0.697146\pi\) |
0.814255 | + | 0.580507i | \(0.197146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.9746 | −1.00755 | −0.503773 | − | 0.863836i | \(-0.668055\pi\) | ||||
−0.503773 | + | 0.863836i | \(0.668055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.6348 | + | 16.6348i | 0.577749 | + | 0.577749i | 0.934282 | − | 0.356534i | \(-0.116041\pi\) |
−0.356534 | + | 0.934282i | \(0.616041\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.6805i | 1.02960i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.1558 | − | 12.1558i | 0.421174 | − | 0.421174i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7.15673i | − | 0.247373i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 56.4946i | 1.95041i | 0.221300 | + | 0.975206i | \(0.428970\pi\) | ||||
−0.221300 | + | 0.975206i | \(0.571030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2.25262i | − | 0.0776766i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 73.9737i | − | 2.54779i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.35953 | − | 3.35953i | 0.115435 | − | 0.115435i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.8794i | 0.613618i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.08063 | − | 4.08063i | −0.139882 | − | 0.139882i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.13309 | −0.175754 | −0.0878768 | − | 0.996131i | \(-0.528008\pi\) | ||||
−0.0878768 | + | 0.996131i | \(0.528008\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.91389 | + | 9.91389i | −0.338652 | + | 0.338652i | −0.855860 | − | 0.517208i | \(-0.826971\pi\) |
0.517208 | + | 0.855860i | \(0.326971\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.1068 | + | 21.1068i | 0.720154 | + | 0.720154i | 0.968636 | − | 0.248482i | \(-0.0799317\pi\) |
−0.248482 | + | 0.968636i | \(0.579932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 61.8972 | − | 61.8972i | 2.10945 | − | 2.10945i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.72724 | − | 4.72724i | −0.160917 | − | 0.160917i | 0.622056 | − | 0.782973i | \(-0.286298\pi\) |
−0.782973 | + | 0.622056i | \(0.786298\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.6033i | 0.903497i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.61481 | + | 5.61481i | −0.190469 | + | 0.190469i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.5342 | 0.899077 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.98414 | − | 2.98414i | −0.100998 | − | 0.100998i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.8569 | 1.78485 | 0.892425 | − | 0.451195i | \(-0.149002\pi\) | ||||
0.892425 | + | 0.451195i | \(0.149002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −62.7353 | −2.11601 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1635 | −1.04993 | −0.524963 | − | 0.851125i | \(-0.675921\pi\) | ||||
−0.524963 | + | 0.851125i | \(0.675921\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.8593 | 1.27407 | 0.637033 | − | 0.770837i | \(-0.280162\pi\) | ||||
0.637033 | + | 0.770837i | \(0.280162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.4782 | + | 34.4782i | 1.15766 | + | 1.15766i | 0.984976 | + | 0.172688i | \(0.0552454\pi\) |
0.172688 | + | 0.984976i | \(0.444755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.7479 | −1.06479 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.3447 | + | 22.3447i | −0.748576 | + | 0.748576i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 37.0491i | − | 1.23980i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 36.3724 | + | 36.3724i | 1.21444 | + | 1.21444i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.2359 | − | 25.2359i | 0.841663 | − | 0.841663i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.4741 | + | 10.4741i | 0.348944 | + | 0.348944i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −63.4000 | + | 63.4000i | −2.10982 | + | 2.10982i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.44928 | 0.214145 | 0.107072 | − | 0.994251i | \(-0.465852\pi\) | ||||
0.107072 | + | 0.994251i | \(0.465852\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.0023 | + | 21.0023i | 0.696603 | + | 0.696603i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.53662i | 0.0509105i | 0.999676 | + | 0.0254553i | \(0.00810353\pi\) | ||||
−0.999676 | + | 0.0254553i | \(0.991896\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.8945 | + | 16.8945i | −0.559127 | + | 0.559127i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.05344i | − | 0.232925i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 55.6116i | − | 1.83446i | −0.398361 | − | 0.917229i | \(-0.630421\pi\) | ||
0.398361 | − | 0.917229i | \(-0.369579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.56979i | − | 0.216482i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 4.31870i | − | 0.142152i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.8750 | + | 24.8750i | −0.817003 | + | 0.817003i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.19045i | − | 0.235911i | −0.993019 | − | 0.117955i | \(-0.962366\pi\) | ||
0.993019 | − | 0.117955i | \(-0.0376340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.0848 | − | 34.0848i | −1.11709 | − | 1.11709i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.7333 | 0.384130 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.71397 | − | 4.71397i | 0.153999 | − | 0.153999i | −0.625903 | − | 0.779901i | \(-0.715269\pi\) |
0.779901 | + | 0.625903i | \(0.215269\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.9461 | − | 15.9461i | −0.520381 | − | 0.520381i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.36011 | + | 5.36011i | −0.174735 | + | 0.174735i | −0.789056 | − | 0.614321i | \(-0.789430\pi\) |
0.614321 | + | 0.789056i | \(0.289430\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.5288 | − | 36.5288i | −1.18954 | − | 1.18954i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 21.9071i | − | 0.711886i | −0.934508 | − | 0.355943i | \(-0.884160\pi\) | ||
0.934508 | − | 0.355943i | \(-0.115840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.5935 | + | 19.5935i | −0.636031 | + | 0.636031i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.27297 | −0.138560 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.3690 | − | 43.3690i | −1.40486 | − | 1.40486i | −0.783620 | − | 0.621241i | \(-0.786629\pi\) |
−0.621241 | − | 0.783620i | \(-0.713371\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −38.0571 | −1.23021 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 82.4678 | 2.66302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.6195 | −0.536113 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.3238 | 0.526028 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.5130 | − | 11.5130i | −0.370232 | − | 0.370232i | 0.497330 | − | 0.867562i | \(-0.334314\pi\) |
−0.867562 | + | 0.497330i | \(0.834314\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −37.8055 | −1.21449 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.2567 | + | 25.2567i | −0.810524 | + | 0.810524i | −0.984712 | − | 0.174188i | \(-0.944270\pi\) |
0.174188 | + | 0.984712i | \(0.444270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.8415i | 1.02079i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.59728 | + | 5.59728i | 0.179073 | + | 0.179073i | 0.790952 | − | 0.611879i | \(-0.209586\pi\) |
−0.611879 | + | 0.790952i | \(0.709586\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.91445 | + | 3.91445i | −0.125106 | + | 0.125106i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.66836 | − | 1.66836i | −0.0532667 | − | 0.0532667i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.9203 | + | 20.9203i | −0.667255 | + | 0.667255i | −0.957080 | − | 0.289825i | \(-0.906403\pi\) |
0.289825 | + | 0.957080i | \(0.406403\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −49.0803 | −1.56224 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.4157 | + | 37.4157i | 1.18975 | + | 1.18975i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 35.6265i | − | 1.13171i | −0.824503 | − | 0.565857i | \(-0.808545\pi\) | ||
0.824503 | − | 0.565857i | \(-0.191455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.20671 | + | 3.20671i | −0.101762 | + | 0.101762i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 44.8208i | − | 1.41949i | −0.704459 | − | 0.709745i | \(-0.748810\pi\) | ||
0.704459 | − | 0.709745i | \(-0.251190\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 1.14176i | − | 0.0361238i |
(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 | 1600.2.s.e.207.3 | 24 | ||
4.3 | odd | 2 | 400.2.s.e.107.7 | yes | 24 | ||
5.2 | odd | 4 | 1600.2.j.e.143.10 | 24 | |||
5.3 | odd | 4 | 1600.2.j.e.143.3 | 24 | |||
5.4 | even | 2 | inner | 1600.2.s.e.207.10 | 24 | ||
16.3 | odd | 4 | 1600.2.j.e.1007.10 | 24 | |||
16.13 | even | 4 | 400.2.j.e.307.12 | yes | 24 | ||
20.3 | even | 4 | 400.2.j.e.43.12 | yes | 24 | ||
20.7 | even | 4 | 400.2.j.e.43.1 | ✓ | 24 | ||
20.19 | odd | 2 | 400.2.s.e.107.6 | yes | 24 | ||
80.3 | even | 4 | inner | 1600.2.s.e.943.3 | 24 | ||
80.13 | odd | 4 | 400.2.s.e.243.7 | yes | 24 | ||
80.19 | odd | 4 | 1600.2.j.e.1007.3 | 24 | |||
80.29 | even | 4 | 400.2.j.e.307.1 | yes | 24 | ||
80.67 | even | 4 | inner | 1600.2.s.e.943.10 | 24 | ||
80.77 | odd | 4 | 400.2.s.e.243.6 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.e.43.1 | ✓ | 24 | 20.7 | even | 4 | ||
400.2.j.e.43.12 | yes | 24 | 20.3 | even | 4 | ||
400.2.j.e.307.1 | yes | 24 | 80.29 | even | 4 | ||
400.2.j.e.307.12 | yes | 24 | 16.13 | even | 4 | ||
400.2.s.e.107.6 | yes | 24 | 20.19 | odd | 2 | ||
400.2.s.e.107.7 | yes | 24 | 4.3 | odd | 2 | ||
400.2.s.e.243.6 | yes | 24 | 80.77 | odd | 4 | ||
400.2.s.e.243.7 | yes | 24 | 80.13 | odd | 4 | ||
1600.2.j.e.143.3 | 24 | 5.3 | odd | 4 | |||
1600.2.j.e.143.10 | 24 | 5.2 | odd | 4 | |||
1600.2.j.e.1007.3 | 24 | 80.19 | odd | 4 | |||
1600.2.j.e.1007.10 | 24 | 16.3 | odd | 4 | |||
1600.2.s.e.207.3 | 24 | 1.1 | even | 1 | trivial | ||
1600.2.s.e.207.10 | 24 | 5.4 | even | 2 | inner | ||
1600.2.s.e.943.3 | 24 | 80.3 | even | 4 | inner | ||
1600.2.s.e.943.10 | 24 | 80.67 | even | 4 | inner |