Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (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 | 143.10 | ||
Character | \(\chi\) | \(=\) | 1600.143 |
Dual form | 1600.2.j.e.1007.3 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 2.35800i | 1.36139i | 0.732565 | + | 0.680697i | \(0.238323\pi\) | ||||
−0.732565 | + | 0.680697i | \(0.761677\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.66357 | − | 2.66357i | 1.00674 | − | 1.00674i | 0.00675825 | − | 0.999977i | \(-0.497849\pi\) |
0.999977 | − | 0.00675825i | \(-0.00215123\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −4.16154 | −1.15420 | −0.577102 | − | 0.816672i | \(-0.695817\pi\) | ||||
−0.577102 | + | 0.816672i | \(0.695817\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.69084 | − | 1.69084i | 0.410088 | − | 0.410088i | −0.471681 | − | 0.881769i | \(-0.656353\pi\) |
0.881769 | + | 0.471681i | \(0.156353\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.74110 | − | 4.74110i | 1.08768 | − | 1.08768i | 0.0919157 | − | 0.995767i | \(-0.470701\pi\) |
0.995767 | − | 0.0919157i | \(-0.0292990\pi\) | |||||||
\(20\) | 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 | \(-0.434042\pi\) |
−0.978608 | + | 0.205733i | \(0.934042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.03710i | 0.199591i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.65701 | − | 3.65701i | −0.679089 | − | 0.679089i | 0.280705 | − | 0.959794i | \(-0.409432\pi\) |
−0.959794 | + | 0.280705i | \(0.909432\pi\) | |||||||
\(30\) | 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 | ||||||||
\(37\) | 1.10092 | 0.180989 | 0.0904947 | − | 0.995897i | \(-0.471155\pi\) | ||||
0.0904947 | + | 0.995897i | \(0.471155\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 10.0944 | 1.53938 | 0.769691 | − | 0.638417i | \(-0.220410\pi\) | ||||
0.769691 | + | 0.638417i | \(0.220410\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.90722 | − | 3.90722i | −0.569927 | − | 0.569927i | 0.362181 | − | 0.932108i | \(-0.382032\pi\) |
−0.932108 | + | 0.362181i | \(0.882032\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 7.18923i | − | 1.02703i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.98700 | + | 3.98700i | 0.558291 | + | 0.558291i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.19464i | 0.850899i | 0.904982 | + | 0.425450i | \(0.139884\pi\) | ||||
−0.904982 | + | 0.425450i | \(0.860116\pi\) | |||||||
\(54\) | 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 | 0.894196 | − | 0.447677i | \(-0.147748\pi\) |
−0.447677 | + | 0.894196i | \(0.647748\pi\) | |||||||
\(60\) | 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 | ||||||||
\(67\) | −6.37605 | −0.778958 | −0.389479 | − | 0.921035i | \(-0.627345\pi\) | ||||
−0.389479 | + | 0.921035i | \(0.627345\pi\) | |||||||
\(68\) | 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 | −0.926746 | − | 0.375690i | \(-0.877406\pi\) |
0.375690 | + | 0.926746i | \(0.377406\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 11.7552i | − | 1.33963i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.54448 | 0.286277 | 0.143138 | − | 0.989703i | \(-0.454281\pi\) | ||||
0.143138 | + | 0.989703i | \(0.454281\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1260 | −1.12511 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.65615i | 0.840371i | 0.907438 | + | 0.420186i | \(0.138035\pi\) | ||||
−0.907438 | + | 0.420186i | \(0.861965\pi\) | |||||||
\(84\) | 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 | \(-0.470029\pi\) | ||||
0.0940178 | + | 0.995571i | \(0.470029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.0846 | + | 11.0846i | −1.16198 | + | 1.16198i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.2718 | 1.68731 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.16560 | − | 1.16560i | 0.118349 | − | 0.118349i | −0.645452 | − | 0.763801i | \(-0.723331\pi\) |
0.763801 | + | 0.645452i | \(0.223331\pi\) | |||||||
\(98\) | 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 | \(-0.0132990\pi\) |
−0.0417680 | + | 0.999127i | \(0.513299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.37605i | 0.616396i | 0.951322 | + | 0.308198i | \(0.0997259\pi\) | ||||
−0.951322 | + | 0.308198i | \(0.900274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.651659 | + | 0.651659i | 0.0624176 | + | 0.0624176i | 0.737627 | − | 0.675209i | \(-0.235947\pi\) |
−0.675209 | + | 0.737627i | \(0.735947\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.59596i | 0.246398i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.86164 | + | 8.86164i | 0.833633 | + | 0.833633i | 0.988012 | − | 0.154378i | \(-0.0493375\pi\) |
−0.154378 | + | 0.988012i | \(0.549338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.6543 | 0.984989 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.00732i | − | 0.825700i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.26129i | 0.114663i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 23.2384 | 2.09534 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.95966 | + | 5.95966i | 0.528834 | + | 0.528834i | 0.920225 | − | 0.391391i | \(-0.128006\pi\) |
−0.391391 | + | 0.920225i | \(0.628006\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | − | 25.2565i | − | 2.19002i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.4807 | − | 15.4807i | −1.32260 | − | 1.32260i | −0.911661 | − | 0.410943i | \(-0.865199\pi\) |
−0.410943 | − | 0.911661i | \(-0.634801\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.97722 | + | 5.97722i | 0.506981 | + | 0.506981i | 0.913599 | − | 0.406617i | \(-0.133292\pi\) |
−0.406617 | + | 0.913599i | \(0.633292\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 16.9522 | 1.39820 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.16964 | − | 3.16964i | 0.259667 | − | 0.259667i | −0.565252 | − | 0.824919i | \(-0.691221\pi\) |
0.824919 | + | 0.565252i | \(0.191221\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | 13.4517i | 1.07356i | 0.843722 | + | 0.536781i | \(0.180360\pi\) | ||||
−0.843722 | + | 0.536781i | \(0.819640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.6070 | −1.15841 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7455 | −1.55616 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.01486i | − | 0.0794896i | −0.999210 | − | 0.0397448i | \(-0.987346\pi\) | ||
0.999210 | − | 0.0397448i | \(-0.0126545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.83926 | + | 5.83926i | −0.451855 | + | 0.451855i | −0.895970 | − | 0.444115i | \(-0.853518\pi\) |
0.444115 | + | 0.895970i | \(0.353518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.31844 | 0.332188 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.1380 | + | 12.1380i | −0.928220 | + | 0.928220i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.55812 | −0.498605 | −0.249302 | − | 0.968426i | \(-0.580201\pi\) | ||||
−0.249302 | + | 0.968426i | \(0.580201\pi\) | |||||||
\(174\) | 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 | −0.473338 | − | 0.880881i | \(-0.656951\pi\) |
0.880881 | + | 0.473338i | \(0.156951\pi\) | |||||||
\(180\) | 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 | ||||||||
\(187\) | − | 7.46221i | − | 0.545691i | ||||||
\(188\) | 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 | \(-0.0459909\pi\) |
−0.143982 | + | 0.989580i | \(0.545991\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9577 | −1.06569 | −0.532846 | − | 0.846212i | \(-0.678877\pi\) | ||||
−0.532846 | + | 0.846212i | \(0.678877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.9644i | 0.777245i | 0.921397 | + | 0.388623i | \(0.127049\pi\) | ||||
−0.921397 | + | 0.388623i | \(0.872951\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 15.0347i | − | 1.06047i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.4814 | −1.36733 | ||||||||
\(204\) | 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 | ||||||||
\(213\) | 2.44705i | 0.167669i | ||||||||
\(214\) | 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 | −0.0527131 | − | 0.998610i | \(-0.516787\pi\) |
0.998610 | + | 0.0527131i | \(0.0167869\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.40121 | 0.557608 | 0.278804 | − | 0.960348i | \(-0.410062\pi\) | ||||
0.278804 | + | 0.960348i | \(0.410062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.9755 | − | 15.9755i | 1.05569 | − | 1.05569i | 0.0573343 | − | 0.998355i | \(-0.481740\pi\) |
0.998355 | − | 0.0573343i | \(-0.0182601\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 27.7188 | 1.82376 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.8176 | + | 10.8176i | −0.708684 | + | 0.708684i | −0.966258 | − | 0.257574i | \(-0.917077\pi\) |
0.257574 | + | 0.966258i | \(0.417077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.99990i | 0.389735i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.7033 | −0.821706 | −0.410853 | − | 0.911702i | \(-0.634769\pi\) | ||||
−0.410853 | + | 0.911702i | \(0.634769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.1860 | 1.88004 | 0.940019 | − | 0.341122i | \(-0.110807\pi\) | ||||
0.940019 | + | 0.341122i | \(0.110807\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 20.7659i | − | 1.33213i | ||||||
\(244\) | 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 | ||||||||
\(253\) | −16.3583 | −1.02844 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.72143 | − | 4.72143i | 0.294515 | − | 0.294515i | −0.544346 | − | 0.838861i | \(-0.683222\pi\) |
0.838861 | + | 0.544346i | \(0.183222\pi\) | |||||||
\(258\) | 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 | \(-0.488921\pi\) |
−0.999394 | + | 0.0348001i | \(0.988921\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.18292i | 0.255991i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1216 | + | 11.1216i | 0.678096 | + | 0.678096i | 0.959569 | − | 0.281473i | \(-0.0908231\pi\) |
−0.281473 | + | 0.959569i | \(0.590823\pi\) | |||||||
\(270\) | 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 | ||||||||
\(277\) | 12.5871 | 0.756287 | 0.378144 | − | 0.925747i | \(-0.376563\pi\) | ||||
0.378144 | + | 0.925747i | \(0.376563\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −7.58242 | −0.450728 | −0.225364 | − | 0.974275i | \(-0.572357\pi\) | ||||
−0.225364 | + | 0.974275i | \(0.572357\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | − | 26.6053i | − | 1.55430i | −0.629317 | − | 0.777149i | \(-0.716665\pi\) | ||
0.629317 | − | 0.777149i | \(-0.283335\pi\) | |||||||
\(294\) | 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 | ||||||||
\(307\) | −2.78617 | −0.159015 | −0.0795075 | − | 0.996834i | \(-0.525335\pi\) | ||||
−0.0795075 | + | 0.996834i | \(0.525335\pi\) | |||||||
\(308\) | 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 | −0.489668 | − | 0.871909i | \(-0.662882\pi\) |
0.871909 | + | 0.489668i | \(0.162882\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.81211i | 0.101778i | 0.998704 | + | 0.0508892i | \(0.0162055\pi\) | ||||
−0.998704 | + | 0.0508892i | \(0.983794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.1395 | −0.903641 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0347 | −0.839157 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 16.0328i | − | 0.892091i | ||||||
\(324\) | 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 | ||||||||
\(333\) | −2.81854 | −0.154455 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.83330 | + | 3.83330i | −0.208813 | + | 0.208813i | −0.803763 | − | 0.594950i | \(-0.797172\pi\) |
0.594950 | + | 0.803763i | \(0.297172\pi\) | |||||||
\(338\) | 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 | ||||||||
\(347\) | − | 21.4284i | − | 1.15034i | −0.818035 | − | 0.575169i | \(-0.804936\pi\) | ||
0.818035 | − | 0.575169i | \(-0.195064\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.63033 | − | 2.63033i | −0.140798 | − | 0.140798i | 0.633195 | − | 0.773993i | \(-0.281743\pi\) |
−0.773993 | + | 0.633195i | \(0.781743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.31595i | − | 0.230369i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.754635 | − | 0.754635i | −0.0401651 | − | 0.0401651i | 0.686739 | − | 0.726904i | \(-0.259042\pi\) |
−0.726904 | + | 0.686739i | \(0.759042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.2393 | 1.12410 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.0363i | − | 0.899140i | −0.893245 | − | 0.449570i | \(-0.851577\pi\) | ||
0.893245 | − | 0.449570i | \(-0.148423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 25.9560i | − | 1.36611i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.97412 | −0.156101 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.86375 | + | 4.86375i | 0.253886 | + | 0.253886i | 0.822562 | − | 0.568676i | \(-0.192544\pi\) |
−0.568676 | + | 0.822562i | \(0.692544\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.2309i | 1.31347i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4999 | + | 16.4999i | 0.856631 | + | 0.856631i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.2209i | − | 0.788109i | −0.919087 | − | 0.394055i | \(-0.871072\pi\) | ||
0.919087 | − | 0.394055i | \(-0.128928\pi\) | |||||||
\(374\) | 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 | 0.774254 | − | 0.632875i | \(-0.218125\pi\) |
−0.632875 | + | 0.774254i | \(0.718125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.0529 | + | 14.0529i | −0.719951 | + | 0.719951i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.6326 | − | 13.6326i | 0.696591 | − | 0.696591i | −0.267083 | − | 0.963674i | \(-0.586060\pi\) |
0.963674 | + | 0.267083i | \(0.0860596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.8434 | −1.31370 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.9333 | + | 15.9333i | −0.807850 | + | 0.807850i | −0.984308 | − | 0.176459i | \(-0.943536\pi\) |
0.176459 | + | 0.984308i | \(0.443536\pi\) | |||||||
\(390\) | 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 | ||||||||
\(397\) | 11.4837i | 0.576353i | 0.957577 | + | 0.288176i | \(0.0930489\pi\) | ||||
−0.957577 | + | 0.288176i | \(0.906951\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 28.7175i | 1.43052i | ||||||||
\(404\) | 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 | \(-0.323304\pi\) | ||||
0.527034 | + | 0.849844i | \(0.323304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.5035 | − | 36.5035i | 1.80058 | − | 1.80058i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.2709 | 0.899053 | ||||||||
\(414\) | 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 | −0.879388 | − | 0.476106i | \(-0.842048\pi\) |
0.476106 | + | 0.879388i | \(0.342048\pi\) | |||||||
\(420\) | 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 | ||||||||
\(427\) | 24.3686i | 1.17928i | ||||||||
\(428\) | 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 | \(-0.469636\pi\) |
−0.995454 | + | 0.0952478i | \(0.969636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.1465 | −1.68128 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.5595i | 1.02898i | 0.857497 | + | 0.514489i | \(0.172018\pi\) | ||||
−0.857497 | + | 0.514489i | \(0.827982\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.4057i | 0.876461i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.517182 | −0.0245721 | −0.0122860 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122860 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(444\) | 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 | \(0.0402597\pi\) | ||||
−0.992012 | + | 0.126142i | \(0.959740\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.7469 | − | 21.7469i | −1.02402 | − | 1.02402i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.2549i | 1.23356i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5862 | + | 20.5862i | 0.962982 | + | 0.962982i | 0.999339 | − | 0.0363565i | \(-0.0115752\pi\) |
−0.0363565 | + | 0.999339i | \(0.511575\pi\) | |||||||
\(458\) | 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 | −0.437330 | − | 0.899301i | \(-0.644076\pi\) |
0.899301 | + | 0.437330i | \(0.144076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.1108 | −1.62473 | −0.812367 | − | 0.583146i | \(-0.801821\pi\) | ||||
−0.812367 | + | 0.583146i | \(0.801821\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | − | 15.8594i | − | 0.726151i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.4324 | 0.842198 | 0.421099 | − | 0.907015i | \(-0.361644\pi\) | ||||
0.421099 | + | 0.907015i | \(0.361644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.58151 | −0.208899 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 46.5599i | − | 2.11855i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.6160 | − | 24.6160i | 1.11546 | − | 1.11546i | 0.123057 | − | 0.992400i | \(-0.460730\pi\) |
0.992400 | − | 0.123057i | \(-0.0392699\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | −12.3668 | −0.556972 | ||||||||
\(494\) | 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 | \(-0.341968\pi\) |
0.879268 | − | 0.476328i | \(-0.158032\pi\) | |||||||
\(500\) | 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 | \(-0.245070\pi\) |
−0.696071 | + | 0.717973i | \(0.745070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1829i | 0.452238i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.5506 | + | 24.5506i | 1.08819 | + | 1.08819i | 0.995715 | + | 0.0924714i | \(0.0294767\pi\) |
0.0924714 | + | 0.995715i | \(0.470523\pi\) | |||||||
\(510\) | 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 | ||||||||
\(517\) | −17.2438 | −0.758383 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | −10.9746 | −0.479887 | −0.239943 | − | 0.970787i | \(-0.577129\pi\) | ||||
−0.239943 | + | 0.970787i | \(0.577129\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | 41.0125i | 1.77645i | ||||||||
\(534\) | 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 | ||||||||
\(547\) | −19.5619 | −0.836408 | −0.418204 | − | 0.908353i | \(-0.637340\pi\) | ||||
−0.418204 | + | 0.908353i | \(0.637340\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | − | 23.8550i | − | 1.01077i | −0.862894 | − | 0.505385i | \(-0.831351\pi\) | ||
0.862894 | − | 0.505385i | \(-0.168649\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.0083 | −1.77676 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.5959 | 0.742900 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.6435i | 1.50220i | 0.660191 | + | 0.751098i | \(0.270475\pi\) | ||||
−0.660191 | + | 0.751098i | \(0.729525\pi\) | |||||||
\(564\) | 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 | \(-0.351670\pi\) | ||||
0.449310 | + | 0.893376i | \(0.351670\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 20.7163 | 0.865434 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.0903 | − | 15.0903i | 0.628219 | − | 0.628219i | −0.319401 | − | 0.947620i | \(-0.603482\pi\) |
0.947620 | + | 0.319401i | \(0.103482\pi\) | |||||||
\(578\) | 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 | ||||||||
\(587\) | − | 12.0083i | − | 0.495637i | −0.968806 | − | 0.247818i | \(-0.920286\pi\) | ||
0.968806 | − | 0.247818i | \(-0.0797137\pi\) | |||||||
\(588\) | 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 | \(-0.168946\pi\) |
−0.506188 | + | 0.862423i | \(0.668946\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.8541 | −1.05814 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 48.1944i | 1.96917i | 0.174908 | + | 0.984585i | \(0.444037\pi\) | ||||
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.1744i | − | 1.47559i | −0.675028 | − | 0.737793i | \(-0.735868\pi\) | ||
0.675028 | − | 0.737793i | \(-0.264132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.3238 | 0.664757 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.43441 | + | 4.43441i | 0.179987 | + | 0.179987i | 0.791350 | − | 0.611363i | \(-0.209379\pi\) |
−0.611363 | + | 0.791350i | \(0.709379\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 45.9372i | − | 1.86147i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.2601 | + | 16.2601i | 0.657812 | + | 0.657812i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.5740i | 1.47721i | 0.674139 | + | 0.738605i | \(0.264515\pi\) | ||||
−0.674139 | + | 0.738605i | \(0.735485\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.61726 | − | 8.61726i | −0.346918 | − | 0.346918i | 0.512042 | − | 0.858960i | \(-0.328889\pi\) |
−0.858960 | + | 0.512042i | \(0.828889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.4732 | + | 16.4732i | 0.662113 | + | 0.662113i | 0.955878 | − | 0.293765i | \(-0.0949082\pi\) |
−0.293765 | + | 0.955878i | \(0.594908\pi\) | |||||||
\(620\) | 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 | ||||||||
\(627\) | 49.3388 | 1.97040 | ||||||||
\(628\) | 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 | ||||||||
\(637\) | 29.9183i | 1.18541i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − | 5.55384i | − | 0.219022i | −0.993986 | − | 0.109511i | \(-0.965072\pi\) | ||
0.993986 | − | 0.109511i | \(-0.0349285\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.4355 | − | 33.4355i | 1.31448 | − | 1.31448i | 0.396410 | − | 0.918073i | \(-0.370256\pi\) |
0.918073 | − | 0.396410i | \(-0.129744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.1367 | 0.594168 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 43.3412 | − | 43.3412i | 1.69868 | − | 1.69868i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.7786 | −1.86972 | −0.934860 | − | 0.355017i | \(-0.884475\pi\) | ||||
−0.934860 | + | 0.355017i | \(0.884475\pi\) | |||||||
\(654\) | 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 | −0.451183 | − | 0.892432i | \(-0.648998\pi\) |
0.892432 | + | 0.451183i | \(0.148998\pi\) | |||||||
\(660\) | 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 | ||||||||
\(667\) | 27.1099i | 1.04970i | ||||||||
\(668\) | 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 | \(-0.219745\pi\) |
−0.636806 | + | 0.771024i | \(0.719745\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.3010 | 1.08769 | 0.543847 | − | 0.839184i | \(-0.316967\pi\) | ||||
0.543847 | + | 0.839184i | \(0.316967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 6.20932i | − | 0.238292i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8101i | 0.759123i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.0075 | −0.995151 | −0.497575 | − | 0.867421i | \(-0.665776\pi\) | ||||
−0.497575 | + | 0.867421i | \(0.665776\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | 30.0954i | 1.14323i | ||||||||
\(694\) | 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 | ||||||||
\(707\) | 43.7010 | 1.64355 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.2686 | + | 24.2686i | −0.911428 | + | 0.911428i | −0.996385 | − | 0.0849564i | \(-0.972925\pi\) |
0.0849564 | + | 0.996385i | \(0.472925\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | − | 29.9543i | − | 1.11867i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.2093 | 0.790973 | 0.395487 | − | 0.918472i | \(-0.370576\pi\) | ||||
0.395487 | + | 0.918472i | \(0.370576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.7592 | 1.92762 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 68.8208i | 2.55947i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.4304 | − | 24.4304i | 0.906073 | − | 0.906073i | −0.0898798 | − | 0.995953i | \(-0.528648\pi\) |
0.995953 | + | 0.0898798i | \(0.0286483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.5879 | 0.688442 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.0680 | − | 17.0680i | 0.631282 | − | 0.631282i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.5318 | 0.462872 | 0.231436 | − | 0.972850i | \(-0.425658\pi\) | ||||
0.231436 | + | 0.972850i | \(0.425658\pi\) | |||||||
\(734\) | 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 | −0.534045 | − | 0.845456i | \(-0.679329\pi\) |
0.845456 | + | 0.534045i | \(0.179329\pi\) | |||||||
\(740\) | 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 | \(-0.0382603\pi\) |
−0.119909 | + | 0.992785i | \(0.538260\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.6011i | − | 0.717166i | ||||||
\(748\) | 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 | ||||||||
\(757\) | −10.7730 | −0.391552 | −0.195776 | − | 0.980649i | \(-0.562723\pi\) | ||||
−0.195776 | + | 0.980649i | \(0.562723\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 3.47148 | 0.125676 | ||||||||
\(764\) | 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 | \(-0.809465\pi\) | ||
0.826135 | − | 0.563473i | \(-0.190535\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.1331 | + | 11.1331i | 0.400951 | + | 0.400951i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 13.9433i | − | 0.501504i | −0.968051 | − | 0.250752i | \(-0.919322\pi\) | ||
0.968051 | − | 0.250752i | \(-0.0806779\pi\) | |||||||
\(774\) | 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 | ||||||||
\(787\) | 9.23076 | 0.329041 | 0.164520 | − | 0.986374i | \(-0.447392\pi\) | ||||
0.164520 | + | 0.986374i | \(0.447392\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | − | 31.2806i | − | 1.10801i | −0.832512 | − | 0.554007i | \(-0.813098\pi\) | ||
0.832512 | − | 0.554007i | \(-0.186902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.2129 | −0.467440 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.54156 | −0.160468 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.7789i | 0.733272i | ||||||||
\(804\) | 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 | \(-0.777894\pi\) | ||||
−0.766280 | + | 0.642507i | \(0.777894\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 39.6055 | 1.38903 | ||||||||
\(814\) | 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 | \(-0.302854\pi\) |
−0.814255 | + | 0.580507i | \(0.802854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28.9746i | − | 1.00755i | −0.863836 | − | 0.503773i | \(-0.831945\pi\) | ||
0.863836 | − | 0.503773i | \(-0.168055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.6348 | − | 16.6348i | −0.577749 | − | 0.577749i | 0.356534 | − | 0.934282i | \(-0.383959\pi\) |
−0.934282 | + | 0.356534i | \(0.883959\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | 7.15673 | 0.247373 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 56.4946i | − | 1.95041i | −0.221300 | − | 0.975206i | \(-0.571030\pi\) | ||
0.221300 | − | 0.975206i | \(-0.428970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2.25262i | − | 0.0776766i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −73.9737 | −2.54779 | ||||||||
\(844\) | 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 | ||||||||
\(853\) | 5.13309i | 0.175754i | 0.996131 | + | 0.0878768i | \(0.0280082\pi\) | ||||
−0.996131 | + | 0.0878768i | \(0.971992\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.91389 | − | 9.91389i | −0.338652 | − | 0.338652i | 0.517208 | − | 0.855860i | \(-0.326971\pi\) |
−0.855860 | + | 0.517208i | \(0.826971\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.1068 | − | 21.1068i | −0.720154 | − | 0.720154i | 0.248482 | − | 0.968636i | \(-0.420068\pi\) |
−0.968636 | + | 0.248482i | \(0.920068\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 61.8972 | − | 61.8972i | 2.10945 | − | 2.10945i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.72724 | + | 4.72724i | −0.160917 | + | 0.160917i | −0.782973 | − | 0.622056i | \(-0.786298\pi\) |
0.622056 | + | 0.782973i | \(0.286298\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.6033 | −0.903497 | ||||||||
\(868\) | 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 | ||||||||
\(877\) | 52.8569i | 1.78485i | 0.451195 | + | 0.892425i | \(0.350998\pi\) | ||||
−0.451195 | + | 0.892425i | \(0.649002\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 37.8593i | − | 1.27407i | −0.770837 | − | 0.637033i | \(-0.780162\pi\) | ||
0.770837 | − | 0.637033i | \(-0.219838\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.4782 | + | 34.4782i | −1.15766 | + | 1.15766i | −0.172688 | + | 0.984976i | \(0.555245\pi\) |
−0.984976 | + | 0.172688i | \(0.944755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.7479 | 1.06479 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.3447 | + | 22.3447i | −0.748576 | + | 0.748576i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −37.0491 | −1.23980 | ||||||||
\(894\) | 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 | ||||||||
\(907\) | 6.44928i | 0.214145i | 0.994251 | + | 0.107072i | \(0.0341477\pi\) | ||||
−0.994251 | + | 0.107072i | \(0.965852\pi\) | |||||||
\(908\) | 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 | ||||||||
\(917\) | 7.05344 | 0.232925 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.6116i | 1.83446i | 0.398361 | + | 0.917229i | \(0.369579\pi\) | ||||
−0.398361 | + | 0.917229i | \(0.630421\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.56979i | − | 0.216482i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.31870 | −0.142152 | ||||||||
\(924\) | 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 | \(0.0376340\pi\) | ||||
−0.993019 | + | 0.117955i | \(0.962366\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.0848 | − | 34.0848i | −1.11709 | − | 1.11709i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 11.7333i | − | 0.384130i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.71397 | + | 4.71397i | 0.153999 | + | 0.153999i | 0.779901 | − | 0.625903i | \(-0.215269\pi\) |
−0.625903 | + | 0.779901i | \(0.715269\pi\) | |||||||
\(938\) | 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 | ||||||||
\(947\) | 21.9071 | 0.711886 | 0.355943 | − | 0.934508i | \(-0.384160\pi\) | ||||
0.355943 | + | 0.934508i | \(0.384160\pi\) | |||||||
\(948\) | 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 | −0.621241 | + | 0.783620i | \(0.713371\pi\) |
−0.783620 | + | 0.621241i | \(0.786629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 38.0571i | − | 1.23021i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −82.4678 | −2.66302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.6195 | −0.536113 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 16.3238i | − | 0.526028i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.5130 | − | 11.5130i | 0.370232 | − | 0.370232i | −0.497330 | − | 0.867562i | \(-0.665686\pi\) |
0.867562 | + | 0.497330i | \(0.165686\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 31.8415 | 1.02079 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.59728 | + | 5.59728i | −0.179073 | + | 0.179073i | −0.790952 | − | 0.611879i | \(-0.790414\pi\) |
0.611879 | + | 0.790952i | \(0.290414\pi\) | |||||||
\(978\) | 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 | \(-0.0935970\pi\) |
−0.289825 | + | 0.957080i | \(0.593597\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 49.0803i | − | 1.56224i | ||||||
\(988\) | 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 | ||||||||
\(997\) | 44.8208 | 1.41949 | 0.709745 | − | 0.704459i | \(-0.248810\pi\) | ||||
0.709745 | + | 0.704459i | \(0.248810\pi\) | |||||||
\(998\) | 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.j.e.143.10 | 24 | ||
4.3 | odd | 2 | 400.2.j.e.43.1 | ✓ | 24 | ||
5.2 | odd | 4 | 1600.2.s.e.207.10 | 24 | |||
5.3 | odd | 4 | 1600.2.s.e.207.3 | 24 | |||
5.4 | even | 2 | inner | 1600.2.j.e.143.3 | 24 | ||
16.3 | odd | 4 | 1600.2.s.e.943.10 | 24 | |||
16.13 | even | 4 | 400.2.s.e.243.6 | yes | 24 | ||
20.3 | even | 4 | 400.2.s.e.107.7 | yes | 24 | ||
20.7 | even | 4 | 400.2.s.e.107.6 | yes | 24 | ||
20.19 | odd | 2 | 400.2.j.e.43.12 | yes | 24 | ||
80.3 | even | 4 | inner | 1600.2.j.e.1007.10 | 24 | ||
80.13 | odd | 4 | 400.2.j.e.307.12 | yes | 24 | ||
80.19 | odd | 4 | 1600.2.s.e.943.3 | 24 | |||
80.29 | even | 4 | 400.2.s.e.243.7 | yes | 24 | ||
80.67 | even | 4 | inner | 1600.2.j.e.1007.3 | 24 | ||
80.77 | odd | 4 | 400.2.j.e.307.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.e.43.1 | ✓ | 24 | 4.3 | odd | 2 | ||
400.2.j.e.43.12 | yes | 24 | 20.19 | odd | 2 | ||
400.2.j.e.307.1 | yes | 24 | 80.77 | odd | 4 | ||
400.2.j.e.307.12 | yes | 24 | 80.13 | odd | 4 | ||
400.2.s.e.107.6 | yes | 24 | 20.7 | even | 4 | ||
400.2.s.e.107.7 | yes | 24 | 20.3 | even | 4 | ||
400.2.s.e.243.6 | yes | 24 | 16.13 | even | 4 | ||
400.2.s.e.243.7 | yes | 24 | 80.29 | even | 4 | ||
1600.2.j.e.143.3 | 24 | 5.4 | even | 2 | inner | ||
1600.2.j.e.143.10 | 24 | 1.1 | even | 1 | trivial | ||
1600.2.j.e.1007.3 | 24 | 80.67 | even | 4 | inner | ||
1600.2.j.e.1007.10 | 24 | 80.3 | even | 4 | inner | ||
1600.2.s.e.207.3 | 24 | 5.3 | odd | 4 | |||
1600.2.s.e.207.10 | 24 | 5.2 | odd | 4 | |||
1600.2.s.e.943.3 | 24 | 80.19 | odd | 4 | |||
1600.2.s.e.943.10 | 24 | 16.3 | odd | 4 |