Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,3,Mod(209,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.209");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.l (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: | \(12.2071158433\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 433.22 | ||
Character | \(\chi\) | \(=\) | 448.433 |
Dual form | 448.3.l.b.209.22 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 2.28266 | + | 2.28266i | 0.760885 | + | 0.760885i | 0.976482 | − | 0.215597i | \(-0.0691697\pi\) |
−0.215597 | + | 0.976482i | \(0.569170\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.90674 | + | 2.90674i | −0.581348 | + | 0.581348i | −0.935274 | − | 0.353925i | \(-0.884847\pi\) |
0.353925 | + | 0.935274i | \(0.384847\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.26451 | − | 6.62359i | −0.323501 | − | 0.946228i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.42104i | 0.157893i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.96314 | − | 9.96314i | −0.905740 | − | 0.905740i | 0.0901854 | − | 0.995925i | \(-0.471254\pi\) |
−0.995925 | + | 0.0901854i | \(0.971254\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.5346 | − | 15.5346i | −1.19497 | − | 1.19497i | −0.975655 | − | 0.219310i | \(-0.929619\pi\) |
−0.219310 | − | 0.975655i | \(-0.570381\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.2702 | −0.884679 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 32.2316i | 1.89597i | 0.318309 | + | 0.947987i | \(0.396885\pi\) | ||||
−0.318309 | + | 0.947987i | \(0.603115\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.4296 | − | 14.4296i | −0.759454 | − | 0.759454i | 0.216769 | − | 0.976223i | \(-0.430448\pi\) |
−0.976223 | + | 0.216769i | \(0.930448\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.95030 | − | 20.2885i | 0.473824 | − | 0.966118i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 16.0348i | − | 0.697165i | −0.937278 | − | 0.348583i | \(-0.886663\pi\) | ||
0.937278 | − | 0.348583i | \(-0.113337\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.10171i | 0.324068i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.3002 | − | 17.3002i | 0.640747 | − | 0.640747i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0884 | + | 10.0884i | −0.347877 | + | 0.347877i | −0.859318 | − | 0.511441i | \(-0.829112\pi\) |
0.511441 | + | 0.859318i | \(0.329112\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.11658i | − | 0.100535i | −0.998736 | − | 0.0502674i | \(-0.983993\pi\) | ||
0.998736 | − | 0.0502674i | \(-0.0160073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 45.4848i | − | 1.37833i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 25.8354 | + | 12.6707i | 0.738155 | + | 0.362021i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −36.8766 | − | 36.8766i | −0.996664 | − | 0.996664i | 0.00333020 | − | 0.999994i | \(-0.498940\pi\) |
−0.999994 | + | 0.00333020i | \(0.998940\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 70.9201i | − | 1.81846i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 39.5924 | 0.965668 | 0.482834 | − | 0.875712i | \(-0.339607\pi\) | ||||
0.482834 | + | 0.875712i | \(0.339607\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.5881 | + | 19.5881i | 0.455536 | + | 0.455536i | 0.897187 | − | 0.441651i | \(-0.145607\pi\) |
−0.441651 | + | 0.897187i | \(0.645607\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.13060 | − | 4.13060i | −0.0917910 | − | 0.0917910i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20.9684i | 0.446136i | 0.974803 | + | 0.223068i | \(0.0716072\pi\) | ||||
−0.974803 | + | 0.223068i | \(0.928393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −38.7440 | + | 29.9984i | −0.790694 | + | 0.612211i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −73.5736 | + | 73.5736i | −1.44262 | + | 1.44262i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −18.6330 | − | 18.6330i | −0.351567 | − | 0.351567i | 0.509126 | − | 0.860692i | \(-0.329969\pi\) |
−0.860692 | + | 0.509126i | \(0.829969\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 57.9205 | 1.05310 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 65.8758i | − | 1.15572i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 21.7777 | − | 21.7777i | 0.369113 | − | 0.369113i | −0.498040 | − | 0.867154i | \(-0.665947\pi\) |
0.867154 | + | 0.498040i | \(0.165947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.5695 | + | 23.5695i | 0.386386 | + | 0.386386i | 0.873396 | − | 0.487010i | \(-0.161913\pi\) |
−0.487010 | + | 0.873396i | \(0.661913\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.41240 | − | 3.21796i | 0.149403 | − | 0.0510787i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 90.3098 | 1.38938 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.0012 | + | 14.0012i | −0.208974 | + | 0.208974i | −0.803831 | − | 0.594858i | \(-0.797208\pi\) |
0.594858 | + | 0.803831i | \(0.297208\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 36.6019 | − | 36.6019i | 0.530463 | − | 0.530463i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.39288i | − | 0.0337026i | −0.999858 | − | 0.0168513i | \(-0.994636\pi\) | ||
0.999858 | − | 0.0168513i | \(-0.00536418\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −22.2579 | −0.304903 | −0.152451 | − | 0.988311i | \(-0.548717\pi\) | ||||
−0.152451 | + | 0.988311i | \(0.548717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.4934 | + | 18.4934i | −0.246579 | + | 0.246579i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −43.4302 | + | 88.5534i | −0.564028 | + | 1.15004i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −67.0638 | −0.848908 | −0.424454 | − | 0.905449i | \(-0.639534\pi\) | ||||
−0.424454 | + | 0.905449i | \(0.639534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 91.7700 | 1.13296 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −82.2869 | − | 82.2869i | −0.991409 | − | 0.991409i | 0.00855454 | − | 0.999963i | \(-0.497277\pi\) |
−0.999963 | + | 0.00855454i | \(0.997277\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −93.6888 | − | 93.6888i | −1.10222 | − | 1.10222i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −46.0569 | −0.529390 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −103.252 | −1.16014 | −0.580069 | − | 0.814567i | \(-0.696975\pi\) | ||||
−0.580069 | + | 0.814567i | \(0.696975\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −67.7165 | + | 138.073i | −0.744137 | + | 1.51728i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.11407 | − | 7.11407i | 0.0764954 | − | 0.0764954i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 83.8864 | 0.883015 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.8468i | − | 0.194297i | −0.995270 | − | 0.0971486i | \(-0.969028\pi\) | ||
0.995270 | − | 0.0971486i | \(-0.0309722\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.1580 | − | 14.1580i | 0.143010 | − | 0.143010i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.2491 | + | 17.2491i | −0.170783 | + | 0.170783i | −0.787323 | − | 0.616540i | \(-0.788534\pi\) |
0.616540 | + | 0.787323i | \(0.288534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −52.8655 | −0.513258 | −0.256629 | − | 0.966510i | \(-0.582612\pi\) | ||||
−0.256629 | + | 0.966510i | \(0.582612\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.0504 | + | 87.8963i | 0.286195 | + | 0.837108i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7578 | − | 14.7578i | −0.137923 | − | 0.137923i | 0.634774 | − | 0.772697i | \(-0.281093\pi\) |
−0.772697 | + | 0.634774i | \(0.781093\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.7521 | − | 16.7521i | 0.153689 | − | 0.153689i | −0.626075 | − | 0.779763i | \(-0.715339\pi\) |
0.779763 | + | 0.626075i | \(0.215339\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 168.353i | − | 1.51669i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 113.623 | 1.00552 | 0.502758 | − | 0.864427i | \(-0.332319\pi\) | ||||
0.502758 | + | 0.864427i | \(0.332319\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 46.6090 | + | 46.6090i | 0.405296 | + | 0.405296i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22.0752 | − | 22.0752i | 0.188677 | − | 0.188677i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 213.489 | − | 72.9886i | 1.79402 | − | 0.613350i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 77.5281i | 0.640728i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 90.3758 | + | 90.3758i | 0.734763 | + | 0.734763i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −96.2181 | − | 96.2181i | −0.769745 | − | 0.769745i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 174.458 | 1.37369 | 0.686843 | − | 0.726805i | \(-0.258996\pi\) | ||||
0.686843 | + | 0.726805i | \(0.258996\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 89.4256i | 0.693222i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 28.5604 | + | 28.5604i | 0.218018 | + | 0.218018i | 0.807663 | − | 0.589644i | \(-0.200732\pi\) |
−0.589644 | + | 0.807663i | \(0.700732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −62.9000 | + | 128.252i | −0.472932 | + | 0.964301i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 100.574i | 0.744994i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 113.638i | − | 0.829475i | −0.909941 | − | 0.414737i | \(-0.863873\pi\) | ||
0.909941 | − | 0.414737i | \(-0.136127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −103.663 | + | 103.663i | −0.745780 | + | 0.745780i | −0.973684 | − | 0.227904i | \(-0.926813\pi\) |
0.227904 | + | 0.973684i | \(0.426813\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −47.8636 | + | 47.8636i | −0.339458 | + | 0.339458i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 309.546i | 2.16466i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 58.6490i | − | 0.404476i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −156.915 | − | 19.9633i | −1.06745 | − | 0.135805i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 145.889 | + | 145.889i | 0.979123 | + | 0.979123i | 0.999786 | − | 0.0206638i | \(-0.00657795\pi\) |
−0.0206638 | + | 0.999786i | \(0.506578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 138.380i | − | 0.916422i | −0.888844 | − | 0.458211i | \(-0.848490\pi\) | ||
0.888844 | − | 0.458211i | \(-0.151510\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −45.8023 | −0.299362 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.05908 | + | 9.05908i | 0.0584457 | + | 0.0584457i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.59938 | − | 3.59938i | −0.0229260 | − | 0.0229260i | 0.695551 | − | 0.718477i | \(-0.255160\pi\) |
−0.718477 | + | 0.695551i | \(0.755160\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 85.0656i | − | 0.535004i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −106.208 | + | 36.3109i | −0.659677 | + | 0.225534i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −87.4226 | + | 87.4226i | −0.536335 | + | 0.536335i | −0.922450 | − | 0.386116i | \(-0.873817\pi\) |
0.386116 | + | 0.922450i | \(0.373817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 132.213 | + | 132.213i | 0.801289 | + | 0.801289i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −29.9561 | −0.179378 | −0.0896889 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896889 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 313.645i | 1.85589i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.5051 | − | 20.5051i | 0.119913 | − | 0.119913i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 191.004 | + | 191.004i | 1.10407 | + | 1.10407i | 0.993914 | + | 0.110158i | \(0.0351356\pi\) |
0.110158 | + | 0.993914i | \(0.464864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53.6625 | − | 18.3464i | 0.306643 | − | 0.104837i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 99.4219 | 0.561706 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 114.979 | − | 114.979i | 0.642340 | − | 0.642340i | −0.308790 | − | 0.951130i | \(-0.599924\pi\) |
0.951130 | + | 0.308790i | \(0.0999240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 71.2709 | − | 71.2709i | 0.393762 | − | 0.393762i | −0.482264 | − | 0.876026i | \(-0.660185\pi\) |
0.876026 | + | 0.482264i | \(0.160185\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 107.602i | 0.587991i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 214.381 | 1.15882 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 321.127 | − | 321.127i | 1.71726 | − | 1.71726i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −153.766 | − | 75.4129i | −0.813575 | − | 0.399010i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −300.815 | −1.57495 | −0.787474 | − | 0.616347i | \(-0.788612\pi\) | ||||
−0.787474 | + | 0.616347i | \(0.788612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −35.0743 | −0.181732 | −0.0908660 | − | 0.995863i | \(-0.528963\pi\) | ||||
−0.0908660 | + | 0.995863i | \(0.528963\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 206.146 | + | 206.146i | 1.05716 | + | 1.05716i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −39.3549 | − | 39.3549i | −0.199771 | − | 0.199771i | 0.600131 | − | 0.799902i | \(-0.295115\pi\) |
−0.799902 | + | 0.600131i | \(0.795115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −123.196 | −0.619077 | −0.309539 | − | 0.950887i | \(-0.600175\pi\) | ||||
−0.309539 | + | 0.950887i | \(0.600175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −63.9200 | −0.318010 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 89.6671 | + | 43.9764i | 0.441710 | + | 0.216633i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −115.085 | + | 115.085i | −0.561389 | + | 0.561389i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.7861 | 0.110078 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 287.529i | 1.37574i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 270.885 | − | 270.885i | 1.28381 | − | 1.28381i | 0.345335 | − | 0.938479i | \(-0.387765\pi\) |
0.938479 | − | 0.345335i | \(-0.112235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.46213 | − | 5.46213i | 0.0256438 | − | 0.0256438i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −113.875 | −0.529651 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.6429 | + | 7.05751i | −0.0951287 | + | 0.0325231i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −50.8071 | − | 50.8071i | −0.231996 | − | 0.231996i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 500.703 | − | 500.703i | 2.26562 | − | 2.26562i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 152.745i | 0.684956i | 0.939526 | + | 0.342478i | \(0.111266\pi\) | ||||
−0.939526 | + | 0.342478i | \(0.888734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.5129 | −0.0511683 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −123.736 | − | 123.736i | −0.545094 | − | 0.545094i | 0.379924 | − | 0.925018i | \(-0.375950\pi\) |
−0.925018 | + | 0.379924i | \(0.875950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −111.719 | + | 111.719i | −0.487855 | + | 0.487855i | −0.907629 | − | 0.419774i | \(-0.862109\pi\) |
0.419774 | + | 0.907629i | \(0.362109\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −301.273 | + | 103.001i | −1.30421 | + | 0.445891i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 68.8807i | − | 0.295625i | −0.989015 | − | 0.147813i | \(-0.952777\pi\) | ||
0.989015 | − | 0.147813i | \(-0.0472232\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −60.9497 | − | 60.9497i | −0.259360 | − | 0.259360i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −153.084 | − | 153.084i | −0.645922 | − | 0.645922i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 32.0400 | 0.134059 | 0.0670293 | − | 0.997751i | \(-0.478648\pi\) | ||||
0.0670293 | + | 0.997751i | \(0.478648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 288.635i | − | 1.19765i | −0.800878 | − | 0.598827i | \(-0.795634\pi\) | ||
0.800878 | − | 0.598827i | \(-0.204366\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 53.7779 | + | 53.7779i | 0.221308 | + | 0.221308i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.4213 | − | 199.816i | 0.103761 | − | 0.815577i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 448.316i | 1.81504i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 375.666i | − | 1.50870i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.3592 | + | 18.3592i | −0.0731441 | + | 0.0731441i | −0.742732 | − | 0.669588i | \(-0.766471\pi\) |
0.669588 | + | 0.742732i | \(0.266471\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −159.757 | + | 159.757i | −0.631450 | + | 0.631450i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 427.719i | − | 1.67733i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 334.673i | − | 1.30223i | −0.758980 | − | 0.651114i | \(-0.774302\pi\) | ||
0.758980 | − | 0.651114i | \(-0.225698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −160.748 | + | 327.763i | −0.620649 | + | 1.26549i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.3361 | − | 14.3361i | −0.0549275 | − | 0.0549275i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 157.697i | − | 0.599607i | −0.954001 | − | 0.299803i | \(-0.903079\pi\) | ||
0.954001 | − | 0.299803i | \(-0.0969210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 108.323 | 0.408765 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −235.690 | − | 235.690i | −0.882732 | − | 0.882732i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −36.7111 | − | 36.7111i | −0.136473 | − | 0.136473i | 0.635570 | − | 0.772043i | \(-0.280765\pi\) |
−0.772043 | + | 0.635570i | \(0.780765\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 520.390i | 1.92026i | 0.279558 | + | 0.960129i | \(0.409812\pi\) | ||||
−0.279558 | + | 0.960129i | \(0.590188\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −469.746 | + | 160.599i | −1.72068 | + | 0.588275i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 80.7185 | − | 80.7185i | 0.293522 | − | 0.293522i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.7640 | + | 27.7640i | 0.100231 | + | 0.100231i | 0.755444 | − | 0.655213i | \(-0.227421\pi\) |
−0.655213 | + | 0.755444i | \(0.727421\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.42878 | 0.0158738 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 383.880i | − | 1.36612i | −0.730361 | − | 0.683061i | \(-0.760648\pi\) | ||
0.730361 | − | 0.683061i | \(-0.239352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 41.4810 | − | 41.4810i | 0.146576 | − | 0.146576i | −0.630011 | − | 0.776587i | \(-0.716949\pi\) |
0.776587 | + | 0.630011i | \(0.216949\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 191.484 | + | 191.484i | 0.671873 | + | 0.671873i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −89.6572 | − | 262.244i | −0.312395 | − | 0.913742i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −749.873 | −2.59472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 43.0208 | − | 43.0208i | 0.147838 | − | 0.147838i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −213.203 | + | 213.203i | −0.727655 | + | 0.727655i | −0.970152 | − | 0.242497i | \(-0.922034\pi\) |
0.242497 | + | 0.970152i | \(0.422034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 126.604i | 0.429167i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −344.728 | −1.16070 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −249.093 | + | 249.093i | −0.833089 | + | 0.833089i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 85.3861 | − | 174.101i | 0.283675 | − | 0.578408i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −78.7473 | −0.259892 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −137.021 | −0.449250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −326.956 | − | 326.956i | −1.06500 | − | 1.06500i | −0.997735 | − | 0.0672699i | \(-0.978571\pi\) |
−0.0672699 | − | 0.997735i | \(-0.521429\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −120.674 | − | 120.674i | −0.390530 | − | 0.390530i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 221.386 | 0.711851 | 0.355926 | − | 0.934514i | \(-0.384166\pi\) | ||||
0.355926 | + | 0.934514i | \(0.384166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 195.538 | 0.624722 | 0.312361 | − | 0.949963i | \(-0.398880\pi\) | ||||
0.312361 | + | 0.949963i | \(0.398880\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.0056 | + | 36.7132i | −0.0571607 | + | 0.116550i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.4658 | − | 32.4658i | 0.102416 | − | 0.102416i | −0.654042 | − | 0.756458i | \(-0.726928\pi\) |
0.756458 | + | 0.654042i | \(0.226928\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 201.025 | 0.630173 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 67.3738i | − | 0.209887i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 465.089 | − | 465.089i | 1.43991 | − | 1.43991i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 125.856 | − | 125.856i | 0.387251 | − | 0.387251i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 76.4784 | 0.233879 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 138.886 | − | 47.4831i | 0.422146 | − | 0.144325i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −198.058 | − | 198.058i | −0.598364 | − | 0.598364i | 0.341513 | − | 0.939877i | \(-0.389061\pi\) |
−0.939877 | + | 0.341513i | \(0.889061\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 52.4031 | − | 52.4031i | 0.157367 | − | 0.157367i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 81.3959i | − | 0.242973i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 306.746 | 0.910225 | 0.455112 | − | 0.890434i | \(-0.349599\pi\) | ||||
0.455112 | + | 0.890434i | \(0.349599\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 259.363 | + | 259.363i | 0.765083 | + | 0.765083i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.0509 | + | 31.0509i | −0.0910583 | + | 0.0910583i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 286.433 | + | 188.693i | 0.835082 | + | 0.550126i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 212.785i | 0.616767i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −91.7162 | − | 91.7162i | −0.264312 | − | 0.264312i | 0.562491 | − | 0.826803i | \(-0.309843\pi\) |
−0.826803 | + | 0.562491i | \(0.809843\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 395.328 | + | 395.328i | 1.13274 | + | 1.13274i | 0.989719 | + | 0.143025i | \(0.0456828\pi\) |
0.143025 | + | 0.989719i | \(0.454317\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −537.500 | −1.53134 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 164.022i | − | 0.464650i | −0.972638 | − | 0.232325i | \(-0.925367\pi\) | ||
0.972638 | − | 0.232325i | \(-0.0746333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.95549 | + | 6.95549i | 0.0195929 | + | 0.0195929i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 653.929 | + | 320.714i | 1.83173 | + | 0.898357i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 93.5104i | − | 0.260475i | −0.991483 | − | 0.130237i | \(-0.958426\pi\) | ||
0.991483 | − | 0.130237i | \(-0.0415739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.4285i | 0.153541i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −176.970 | + | 176.970i | −0.487521 | + | 0.487521i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 64.6979 | − | 64.6979i | 0.177255 | − | 0.177255i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 412.826i | − | 1.12487i | −0.826843 | − | 0.562433i | \(-0.809866\pi\) | ||
0.826843 | − | 0.562433i | \(-0.190134\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 56.2624i | 0.152473i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −81.2230 | + | 165.612i | −0.218930 | + | 0.446394i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −340.213 | − | 340.213i | −0.912099 | − | 0.912099i | 0.0843379 | − | 0.996437i | \(-0.473122\pi\) |
−0.996437 | + | 0.0843379i | \(0.973122\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 439.266i | − | 1.17138i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 313.439 | 0.831403 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −450.626 | − | 450.626i | −1.18899 | − | 1.18899i | −0.977348 | − | 0.211640i | \(-0.932119\pi\) |
−0.211640 | − | 0.977348i | \(-0.567881\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 398.228 | + | 398.228i | 1.04522 | + | 1.04522i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 374.094i | − | 0.976745i | −0.872635 | − | 0.488373i | \(-0.837591\pi\) | ||
0.872635 | − | 0.488373i | \(-0.162409\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −131.161 | − | 383.642i | −0.340679 | − | 0.996473i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.8354 | + | 27.8354i | −0.0719262 | + | 0.0719262i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 295.277 | + | 295.277i | 0.759067 | + | 0.759067i | 0.976153 | − | 0.217085i | \(-0.0696550\pi\) |
−0.217085 | + | 0.976153i | \(0.569655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 516.827 | 1.32181 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 130.387i | 0.331774i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 194.937 | − | 194.937i | 0.493511 | − | 0.493511i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −531.600 | − | 531.600i | −1.33904 | − | 1.33904i | −0.896989 | − | 0.442053i | \(-0.854250\pi\) |
−0.442053 | − | 0.896989i | \(-0.645750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −436.334 | + | 149.176i | −1.09357 | + | 0.373875i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 671.156 | 1.67371 | 0.836853 | − | 0.547428i | \(-0.184393\pi\) | ||||
0.836853 | + | 0.547428i | \(0.184393\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.4146 | + | 48.4146i | −0.120136 | + | 0.120136i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −266.752 | + | 266.752i | −0.658646 | + | 0.658646i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 734.813i | 1.80544i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −379.027 | −0.926717 | −0.463358 | − | 0.886171i | \(-0.653356\pi\) | ||||
−0.463358 | + | 0.886171i | \(0.653356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 259.397 | − | 259.397i | 0.631135 | − | 0.631135i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −193.562 | − | 94.9308i | −0.468674 | − | 0.229857i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 478.374 | 1.15271 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −473.256 | −1.13491 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 426.017 | + | 426.017i | 1.01675 | + | 1.01675i | 0.999857 | + | 0.0168902i | \(0.00537657\pi\) |
0.0168902 | + | 0.999857i | \(0.494623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.05175 | − | 8.05175i | −0.0191253 | − | 0.0191253i | 0.697479 | − | 0.716605i | \(-0.254305\pi\) |
−0.716605 | + | 0.697479i | \(0.754305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.7969 | −0.0704419 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −261.131 | −0.614425 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 102.742 | − | 209.489i | 0.240613 | − | 0.490605i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −706.586 | + | 706.586i | −1.64705 | + | 1.64705i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 389.916 | 0.904677 | 0.452338 | − | 0.891846i | \(-0.350590\pi\) | ||||
0.452338 | + | 0.891846i | \(0.350590\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 158.384i | − | 0.365782i | −0.983133 | − | 0.182891i | \(-0.941454\pi\) | ||
0.983133 | − | 0.182891i | \(-0.0585456\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 133.875 | − | 133.875i | 0.307760 | − | 0.307760i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −231.376 | + | 231.376i | −0.529465 | + | 0.529465i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −764.403 | −1.74124 | −0.870618 | − | 0.491960i | \(-0.836281\pi\) | ||||
−0.870618 | + | 0.491960i | \(0.836281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.6289 | − | 55.0568i | −0.0966641 | − | 0.124845i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 119.551 | + | 119.551i | 0.269867 | + | 0.269867i | 0.829047 | − | 0.559180i | \(-0.188884\pi\) |
−0.559180 | + | 0.829047i | \(0.688884\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 300.128 | − | 300.128i | 0.674444 | − | 0.674444i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 666.030i | 1.49000i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 652.600 | 1.45345 | 0.726726 | − | 0.686927i | \(-0.241041\pi\) | ||||
0.726726 | + | 0.686927i | \(0.241041\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −394.464 | − | 394.464i | −0.874643 | − | 0.874643i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 315.873 | − | 315.873i | 0.697292 | − | 0.697292i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −204.507 | − | 598.176i | −0.449467 | − | 1.31467i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 719.580i | 1.57457i | 0.616588 | + | 0.787286i | \(0.288515\pi\) | ||||
−0.616588 | + | 0.787286i | \(0.711485\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 557.611 | + | 557.611i | 1.21484 | + | 1.21484i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 323.632 | + | 323.632i | 0.702022 | + | 0.702022i | 0.964844 | − | 0.262822i | \(-0.0846532\pi\) |
−0.262822 | + | 0.964844i | \(0.584653\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 65.5977 | 0.141680 | 0.0708399 | − | 0.997488i | \(-0.477432\pi\) | ||||
0.0708399 | + | 0.997488i | \(0.477432\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 41.3575i | 0.0889409i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.7847 | + | 11.7847i | 0.0252349 | + | 0.0252349i | 0.719612 | − | 0.694377i | \(-0.244320\pi\) |
−0.694377 | + | 0.719612i | \(0.744320\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 124.444 | + | 61.0326i | 0.265340 | + | 0.130133i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 16.4323i | − | 0.0348881i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 390.317i | − | 0.825195i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 116.905 | − | 116.905i | 0.246115 | − | 0.246115i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.4783 | − | 26.4783i | 0.0555101 | − | 0.0555101i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 475.079i | 0.991814i | 0.868376 | + | 0.495907i | \(0.165164\pi\) | ||||
−0.868376 | + | 0.495907i | \(0.834836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1145.72i | 2.38196i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −325.322 | − | 159.551i | −0.673544 | − | 0.330333i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 54.7829 | + | 54.7829i | 0.112954 | + | 0.112954i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 524.310i | − | 1.07661i | −0.842750 | − | 0.538306i | \(-0.819065\pi\) | ||
0.842750 | − | 0.538306i | \(-0.180935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −399.111 | −0.816179 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 335.136 | + | 335.136i | 0.682558 | + | 0.682558i | 0.960576 | − | 0.278018i | \(-0.0896774\pi\) |
−0.278018 | + | 0.960576i | \(0.589677\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −325.166 | − | 325.166i | −0.659566 | − | 0.659566i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 82.3074i | 0.166278i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.8495 | + | 5.41870i | −0.0318903 | + | 0.0109028i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −56.5874 | + | 56.5874i | −0.113402 | + | 0.113402i | −0.761531 | − | 0.648129i | \(-0.775552\pi\) |
0.648129 | + | 0.761531i | \(0.275552\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −68.3795 | − | 68.3795i | −0.136486 | − | 0.136486i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −458.739 | −0.912006 | −0.456003 | − | 0.889978i | \(-0.650719\pi\) | ||||
−0.456003 | + | 0.889978i | \(0.650719\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 100.277i | − | 0.198568i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −715.943 | + | 715.943i | −1.41212 | + | 1.41212i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −154.189 | − | 154.189i | −0.302926 | − | 0.302926i | 0.539232 | − | 0.842157i | \(-0.318715\pi\) |
−0.842157 | + | 0.539232i | \(0.818715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.4032 | + | 147.427i | 0.0986363 | + | 0.288507i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −499.270 | −0.973236 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 153.666 | − | 153.666i | 0.298381 | − | 0.298381i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 208.911 | − | 208.911i | 0.404083 | − | 0.404083i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 871.995i | 1.68014i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 328.373 | 0.630274 | 0.315137 | − | 0.949046i | \(-0.397950\pi\) | ||||
0.315137 | + | 0.949046i | \(0.397950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −285.071 | + | 285.071i | −0.545068 | + | 0.545068i | −0.925010 | − | 0.379942i | \(-0.875944\pi\) |
0.379942 | + | 0.925010i | \(0.375944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 164.371 | + | 80.6144i | 0.313088 | + | 0.153551i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 100.452 | 0.190611 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 271.885 | 0.513960 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.9470 | + | 30.9470i | 0.0582805 | + | 0.0582805i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −615.050 | − | 615.050i | −1.15394 | − | 1.15394i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 85.7940 | 0.160363 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 524.915 | 0.977495 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 684.890 | + | 87.1341i | 1.27067 | + | 0.161659i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 434.228 | − | 434.228i | 0.802640 | − | 0.802640i | −0.180868 | − | 0.983507i | \(-0.557891\pi\) |
0.983507 | + | 0.180868i | \(0.0578906\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 325.374 | 0.599215 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 97.3878i | 0.178693i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −693.945 | + | 693.945i | −1.26864 | + | 1.26864i | −0.321846 | + | 0.946792i | \(0.604303\pi\) |
−0.946792 | + | 0.321846i | \(0.895697\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.4933 | + | 33.4933i | −0.0610078 | + | 0.0610078i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 291.145 | 0.528394 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 151.866 | + | 444.203i | 0.274623 | + | 0.803261i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 489.359 | + | 489.359i | 0.881728 | + | 0.881728i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −257.121 | + | 257.121i | −0.461618 | + | 0.461618i | −0.899186 | − | 0.437568i | \(-0.855840\pi\) |
0.437568 | + | 0.899186i | \(0.355840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 608.584i | − | 1.08870i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1466.05 | 2.61327 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −62.8920 | − | 62.8920i | −0.111709 | − | 0.111709i | 0.649043 | − | 0.760752i | \(-0.275170\pi\) |
−0.760752 | + | 0.649043i | \(0.775170\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −330.274 | + | 330.274i | −0.584555 | + | 0.584555i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −207.814 | − | 607.847i | −0.366515 | − | 1.07204i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 333.590i | − | 0.586274i | −0.956070 | − | 0.293137i | \(-0.905301\pi\) | ||
0.956070 | − | 0.293137i | \(-0.0946992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 221.941 | + | 221.941i | 0.388688 | + | 0.388688i | 0.874219 | − | 0.485531i | \(-0.161374\pi\) |
−0.485531 | + | 0.874219i | \(0.661374\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −686.658 | − | 686.658i | −1.19836 | − | 1.19836i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 129.909 | 0.225929 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 73.1448i | 0.126767i | 0.997989 | + | 0.0633837i | \(0.0201892\pi\) | ||||
−0.997989 | + | 0.0633837i | \(0.979811\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −80.0625 | − | 80.0625i | −0.138277 | − | 0.138277i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −358.696 | + | 731.375i | −0.617377 | + | 1.25882i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 371.287i | 0.636856i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 128.334i | 0.219374i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 339.824 | − | 339.824i | 0.578917 | − | 0.578917i | −0.355688 | − | 0.934605i | \(-0.615753\pi\) |
0.934605 | + | 0.355688i | \(0.115753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.9710 | + | 44.9710i | −0.0763515 | + | 0.0763515i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 179.667i | − | 0.304006i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 96.6120i | − | 0.162921i | −0.996677 | − | 0.0814604i | \(-0.974042\pi\) | ||
0.996677 | − | 0.0814604i | \(-0.0259584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −408.398 | + | 832.716i | −0.686382 | + | 1.39952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −281.215 | − | 281.215i | −0.471047 | − | 0.471047i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 754.853i | − | 1.26019i | −0.776519 | − | 0.630094i | \(-0.783016\pi\) | ||
0.776519 | − | 0.630094i | \(-0.216984\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −678.470 | −1.12890 | −0.564451 | − | 0.825467i | \(-0.690912\pi\) | ||||
−0.564451 | + | 0.825467i | \(0.690912\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.8963 | − | 19.8963i | −0.0329955 | − | 0.0329955i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −225.354 | − | 225.354i | −0.372486 | − | 0.372486i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2945i | 0.0169596i | 0.999964 | + | 0.00847980i | \(0.00269924\pi\) | ||||
−0.999964 | + | 0.00847980i | \(0.997301\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 104.296 | + | 305.062i | 0.171258 | + | 0.500923i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 325.734 | − | 325.734i | 0.533117 | − | 0.533117i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 442.295 | + | 442.295i | 0.721525 | + | 0.721525i | 0.968916 | − | 0.247390i | \(-0.0795730\pi\) |
−0.247390 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −525.398 | −0.854306 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 531.027i | 0.860660i | 0.902672 | + | 0.430330i | \(0.141603\pi\) | ||||
−0.902672 | + | 0.430330i | \(0.858397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 207.632 | − | 207.632i | 0.335432 | − | 0.335432i | −0.519213 | − | 0.854645i | \(-0.673775\pi\) |
0.854645 | + | 0.519213i | \(0.173775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −277.405 | − | 277.405i | −0.446706 | − | 0.446706i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 233.816 | + | 683.901i | 0.375306 | + | 1.09776i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 356.819 | 0.570911 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −656.329 | + | 656.329i | −1.04678 | + | 1.04678i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1188.59 | − | 1188.59i | 1.88965 | − | 1.88965i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0278i | 0.0396637i | 0.999803 | + | 0.0198319i | \(0.00631309\pi\) | ||||
−0.999803 | + | 0.0198319i | \(0.993687\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1236.67 | 1.95367 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −507.105 | + | 507.105i | −0.798590 | + | 0.798590i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1067.88 | + | 135.860i | 1.67642 | + | 0.213281i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.40038 | 0.00532141 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −702.170 | −1.09543 | −0.547715 | − | 0.836665i | \(-0.684502\pi\) | ||||
−0.547715 | + | 0.836665i | \(0.684502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −356.339 | − | 356.339i | −0.554182 | − | 0.554182i | 0.373463 | − | 0.927645i | \(-0.378170\pi\) |
−0.927645 | + | 0.373463i | \(0.878170\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −259.937 | − | 259.937i | −0.403003 | − | 0.403003i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 663.547 | 1.02557 | 0.512787 | − | 0.858516i | \(-0.328613\pi\) | ||||
0.512787 | + | 0.858516i | \(0.328613\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −433.948 | −0.668641 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −63.2306 | − | 31.0109i | −0.0971284 | − | 0.0476357i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −749.238 | + | 749.238i | −1.14738 | + | 1.14738i | −0.160311 | + | 0.987066i | \(0.551250\pi\) |
−0.987066 | + | 0.160311i | \(0.948750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −166.035 | −0.253489 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 31.6294i | − | 0.0481421i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 183.052 | − | 183.052i | 0.277773 | − | 0.277773i | −0.554446 | − | 0.832219i | \(-0.687070\pi\) |
0.832219 | + | 0.554446i | \(0.187070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 488.925 | − | 488.925i | 0.739674 | − | 0.739674i | −0.232841 | − | 0.972515i | \(-0.574802\pi\) |
0.972515 | + | 0.232841i | \(0.0748021\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2285.86 | 3.44776 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −189.961 | − | 555.629i | −0.285656 | − | 0.835533i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 161.766 | + | 161.766i | 0.242528 | + | 0.242528i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −348.665 | + | 348.665i | −0.521173 | + | 0.521173i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 469.653i | − | 0.699930i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 722.532 | 1.07360 | 0.536800 | − | 0.843710i | \(-0.319633\pi\) | ||||
0.536800 | + | 0.843710i | \(0.319633\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 140.161 | + | 140.161i | 0.207646 | + | 0.207646i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 85.6013 | − | 85.6013i | 0.126442 | − | 0.126442i | −0.641054 | − | 0.767496i | \(-0.721502\pi\) |
0.767496 | + | 0.641054i | \(0.221502\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −124.834 | + | 42.6788i | −0.183849 | + | 0.0628554i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 564.895i | − | 0.829508i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −118.436 | − | 118.436i | −0.173406 | − | 0.173406i | 0.615068 | − | 0.788474i | \(-0.289129\pi\) |
−0.788474 | + | 0.615068i | \(0.789129\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 330.316 | + | 330.316i | 0.482214 | + | 0.482214i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −510.031 | −0.742403 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 578.912i | 0.840220i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −412.838 | − | 412.838i | −0.597450 | − | 0.597450i | 0.342183 | − | 0.939633i | \(-0.388834\pi\) |
−0.939633 | + | 0.342183i | \(0.888834\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −125.838 | − | 61.7160i | −0.181584 | − | 0.0890563i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 602.645i | − | 0.867115i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1276.12i | 1.83088i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 157.231 | − | 157.231i | 0.224937 | − | 0.224937i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −264.725 | + | 264.725i | −0.377639 | + | 0.377639i | −0.870250 | − | 0.492611i | \(-0.836043\pi\) |
0.492611 | + | 0.870250i | \(0.336043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1064.23i | 1.51384i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 278.254i | − | 0.394687i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 153.311 | + | 75.1901i | 0.216848 | + | 0.106351i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −416.810 | − | 416.810i | −0.587885 | − | 0.587885i | 0.349173 | − | 0.937058i | \(-0.386462\pi\) |
−0.937058 | + | 0.349173i | \(0.886462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 95.3003i | − | 0.134037i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −49.9737 | −0.0700893 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −899.769 | − | 899.769i | −1.25842 | − | 1.25842i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 73.1363 | + | 73.1363i | 0.102003 | + | 0.102003i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1253.20i | − | 1.74298i | −0.490412 | − | 0.871491i | \(-0.663154\pi\) | ||
0.490412 | − | 0.871491i | \(-0.336846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 119.714 | + | 350.160i | 0.166039 | + | 0.485659i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 658.854 | − | 658.854i | 0.911278 | − | 0.911278i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −81.7337 | − | 81.7337i | −0.112736 | − | 0.112736i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −673.130 | −0.925901 | −0.462950 | − | 0.886384i | \(-0.653209\pi\) | ||||
−0.462950 | + | 0.886384i | \(0.653209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 580.417i | − | 0.796182i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −631.354 | + | 631.354i | −0.863685 | + | 0.863685i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 495.647 | + | 495.647i | 0.676189 | + | 0.676189i | 0.959136 | − | 0.282946i | \(-0.0913119\pi\) |
−0.282946 | + | 0.959136i | \(0.591312\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 514.140 | − | 398.084i | 0.699510 | − | 0.541611i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 278.992 | 0.378551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −730.041 | + | 730.041i | −0.987876 | + | 0.987876i | −0.999927 | − | 0.0120510i | \(-0.996164\pi\) |
0.0120510 | + | 0.999927i | \(0.496164\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1023.35 | + | 1023.35i | −1.38104 | + | 1.38104i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 362.785i | − | 0.488271i | −0.969741 | − | 0.244135i | \(-0.921496\pi\) | ||
0.969741 | − | 0.244135i | \(-0.0785041\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −848.125 | −1.13842 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 116.933 | − | 116.933i | 0.156537 | − | 0.156537i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −64.3304 | + | 131.168i | −0.0858883 | + | 0.175125i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 352.201 | 0.468976 | 0.234488 | − | 0.972119i | \(-0.424659\pi\) | ||||
0.234488 | + | 0.972119i | \(0.424659\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −83.8153 | −0.111308 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 402.234 | + | 402.234i | 0.532760 | + | 0.532760i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1010.20 | − | 1010.20i | −1.33447 | − | 1.33447i | −0.901321 | − | 0.433151i | \(-0.857402\pi\) |
−0.433151 | − | 0.901321i | \(-0.642598\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −729.340 | −0.960923 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1065.18 | 1.39971 | 0.699855 | − | 0.714285i | \(-0.253248\pi\) | ||||
0.699855 | + | 0.714285i | \(0.253248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −148.894 | − | 73.0237i | −0.195143 | − | 0.0957060i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 133.136 | − | 133.136i | 0.174033 | − | 0.174033i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −676.613 | −0.882155 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1415.77i | − | 1.84105i | −0.390680 | − | 0.920527i | \(-0.627760\pi\) | ||
0.390680 | − | 0.920527i | \(-0.372240\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 763.943 | − | 763.943i | 0.990847 | − | 0.990847i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −363.001 | + | 363.001i | −0.469600 | + | 0.469600i | −0.901785 | − | 0.432185i | \(-0.857743\pi\) |
0.432185 | + | 0.901785i | \(0.357743\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.2496 | 0.0325801 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1115.10 | + | 381.237i | −1.43514 | + | 0.490652i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −571.303 | − | 571.303i | −0.733380 | − | 0.733380i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.8406 | + | 23.8406i | −0.0305257 | + | 0.0305257i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 349.063i | 0.445802i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.9249 | 0.0266560 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 464.183 | + | 464.183i | 0.589814 | + | 0.589814i | 0.937581 | − | 0.347767i | \(-0.113060\pi\) |
−0.347767 | + | 0.937581i | \(0.613060\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 359.967 | − | 359.967i | 0.456232 | − | 0.456232i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −257.301 | − | 752.595i | −0.325286 | − | 0.951448i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 732.285i | − | 0.923436i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 247.264 | + | 247.264i | 0.311024 | + | 0.311024i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 252.417 | + | 252.417i | 0.316708 | + | 0.316708i | 0.847501 | − | 0.530793i | \(-0.178106\pi\) |
−0.530793 | + | 0.847501i | \(0.678106\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −675.844 | −0.845862 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 146.726i | − | 0.183178i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 221.758 | + | 221.758i | 0.276162 | + | 0.276162i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 203.173 | − | 414.266i | 0.252389 | − | 0.514616i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 167.598i | − | 0.207680i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 332.184i | − | 0.410611i | −0.978698 | − | 0.205306i | \(-0.934181\pi\) | ||
0.978698 | − | 0.205306i | \(-0.0658188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 566.768 | − | 566.768i | 0.698851 | − | 0.698851i | −0.265311 | − | 0.964163i | \(-0.585475\pi\) |
0.964163 | + | 0.265311i | \(0.0854748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1187.87 | + | 1187.87i | −1.46110 | + | 1.46110i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 508.230i | − | 0.623595i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 565.297i | − | 0.691918i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −196.207 | − | 96.2278i | −0.239569 | − | 0.117494i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 380.824 | + | 380.824i | 0.463854 | + | 0.463854i | 0.899916 | − | 0.436063i | \(-0.143627\pi\) |
−0.436063 | + | 0.899916i | \(0.643627\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 275.483i | − | 0.334730i | −0.985895 | − | 0.167365i | \(-0.946474\pi\) | ||
0.985895 | − | 0.167365i | \(-0.0535259\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 368.505 | 0.446673 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.5616 | + | 13.5616i | 0.0163986 | + | 0.0163986i | 0.715259 | − | 0.698860i | \(-0.246309\pi\) |
−0.698860 | + | 0.715259i | \(0.746309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 260.673 | + | 260.673i | 0.314443 | + | 0.314443i | 0.846628 | − | 0.532185i | \(-0.178629\pi\) |
−0.532185 | + | 0.846628i | \(0.678629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 126.751i | 0.152528i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −966.894 | − | 1248.78i | −1.16074 | − | 1.49914i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 87.0746 | − | 87.0746i | 0.104281 | − | 0.104281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −53.9173 | − | 53.9173i | −0.0644173 | − | 0.0644173i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 795.591 | 0.948261 | 0.474130 | − | 0.880455i | \(-0.342763\pi\) | ||||
0.474130 | + | 0.880455i | \(0.342763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 637.447i | 0.757963i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 876.267 | − | 876.267i | 1.03946 | − | 1.03946i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −911.684 | − | 911.684i | −1.07892 | − | 1.07892i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 513.515 | − | 175.563i | 0.606275 | − | 0.207276i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 189.374 | 0.223055 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −591.309 | + | 591.309i | −0.694840 | + | 0.694840i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −397.199 | + | 397.199i | −0.465650 | + | 0.465650i | −0.900502 | − | 0.434852i | \(-0.856801\pi\) |
0.434852 | + | 0.900502i | \(0.356801\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 119.206i | 0.139422i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1328.76 | −1.55048 | −0.775239 | − | 0.631668i | \(-0.782371\pi\) | ||||
−0.775239 | + | 0.631668i | \(0.782371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −889.815 | + | 889.815i | −1.03587 | + | 1.03587i | −0.0365413 | + | 0.999332i | \(0.511634\pi\) |
−0.999332 | + | 0.0365413i | \(0.988366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 393.956 | − | 803.269i | 0.457556 | − | 0.932949i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −951.400 | −1.10243 | −0.551216 | − | 0.834362i | \(-0.685836\pi\) | ||||
−0.551216 | + | 0.834362i | \(0.685836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1110.40 | −1.28370 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1711.70 | − | 1711.70i | −1.97428 | − | 1.97428i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 668.165 | + | 668.165i | 0.768890 | + | 0.768890i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 435.006 | 0.499432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26.7821 | 0.0306782 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −419.423 | + | 855.196i | −0.479341 | + | 0.977367i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1165.54 | − | 1165.54i | 1.32901 | − | 1.32901i | 0.422767 | − | 0.906239i | \(-0.361059\pi\) |
0.906239 | − | 0.422767i | \(-0.138941\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −973.338 | −1.10732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 107.367i | − | 0.121870i | −0.998142 | − | 0.0609349i | \(-0.980592\pi\) | ||
0.998142 | − | 0.0609349i | \(-0.0194082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 473.801 | − | 473.801i | 0.536581 | − | 0.536581i | −0.385942 | − | 0.922523i | \(-0.626123\pi\) |
0.922523 | + | 0.385942i | \(0.126123\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −288.994 | + | 288.994i | −0.326547 | + | 0.326547i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −410.161 | −0.462414 | −0.231207 | − | 0.972905i | \(-0.574267\pi\) | ||||
−0.231207 | + | 0.972905i | \(0.574267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −395.062 | − | 1155.54i | −0.444389 | − | 1.29982i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −914.317 | − | 914.317i | −1.02617 | − | 1.02617i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 302.566 | − | 302.566i | 0.338820 | − | 0.338820i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 668.428i | 0.746847i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1137.19 | −1.26777 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.4414 | + | 31.4414i | 0.0349737 | + | 0.0349737i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 600.572 | − | 600.572i | 0.666561 | − | 0.666561i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 592.319 | − | 202.505i | 0.655946 | − | 0.224258i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 414.332i | 0.457826i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −725.905 | − | 725.905i | −0.800337 | − | 0.800337i | 0.182811 | − | 0.983148i | \(-0.441480\pi\) |
−0.983148 | + | 0.182811i | \(0.941480\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.5116 | − | 24.5116i | −0.0269655 | − | 0.0269655i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1068.94 | 1.17337 | 0.586684 | − | 0.809816i | \(-0.300433\pi\) | ||||
0.586684 | + | 0.809816i | \(0.300433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1639.67i | 1.79592i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −312.772 | − | 312.772i | −0.341828 | − | 0.341828i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 124.497 | − | 253.848i | 0.135766 | − | 0.276824i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 166.789i | 0.181489i | 0.995874 | + | 0.0907447i | \(0.0289247\pi\) | ||||
−0.995874 | + | 0.0907447i | \(0.971075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1492.66i | − | 1.62069i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.1723 | + | 37.1723i | −0.0402734 | + | 0.0402734i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 298.763 | − | 298.763i | 0.322987 | − | 0.322987i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 75.1241i | − | 0.0810400i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1609.29i | 1.73228i | 0.499798 | + | 0.866142i | \(0.333407\pi\) | ||||
−0.499798 | + | 0.866142i | \(0.666593\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 991.927 | + | 126.196i | 1.06544 | + | 0.135549i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 505.348 | + | 505.348i | 0.541637 | + | 0.541637i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1866.87i | 1.99665i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1185.02 | 1.26470 | 0.632348 | − | 0.774684i | \(-0.282091\pi\) | ||||
0.632348 | + | 0.774684i | \(0.282091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 446.346 | + | 446.346i | 0.475342 | + | 0.475342i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.79618 | − | 8.79618i | −0.00934770 | − | 0.00934770i | 0.702417 | − | 0.711765i | \(-0.252104\pi\) |
−0.711765 | + | 0.702417i | \(0.752104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 634.856i | − | 0.673230i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 666.163 | − | 227.751i | 0.704934 | − | 0.241006i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −670.227 | + | 670.227i | −0.707737 | + | 0.707737i | −0.966059 | − | 0.258322i | \(-0.916831\pi\) |
0.258322 | + | 0.966059i | \(0.416831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 345.766 | + | 345.766i | 0.364348 | + | 0.364348i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 148.217 | 0.155853 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 777.795i | 0.816154i | 0.912947 | + | 0.408077i | \(0.133801\pi\) | ||||
−0.912947 | + | 0.408077i | \(0.866199\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 874.392 | − | 874.392i | 0.915594 | − | 0.915594i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 458.871 | + | 458.871i | 0.479489 | + | 0.479489i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −752.692 | + | 257.334i | −0.784872 | + | 0.268336i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 951.287 | 0.989893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.9714 | − | 20.9714i | 0.0217771 | − | 0.0217771i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 101.952 | − | 101.952i | 0.105650 | − | 0.105650i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 980.179i | 1.01363i | 0.862055 | + | 0.506815i | \(0.169177\pi\) | ||||
−0.862055 | + | 0.506815i | \(0.830823\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2123.28 | 2.19121 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 631.690 | − | 631.690i | 0.650556 | − | 0.650556i | −0.302571 | − | 0.953127i | \(-0.597845\pi\) |
0.953127 | + | 0.302571i | \(0.0978449\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 921.370 | + | 451.878i | 0.946938 | + | 0.464417i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 574.574 | 0.589307 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1150.81 | −1.17790 | −0.588949 | − | 0.808170i | \(-0.700458\pi\) | ||||
−0.588949 | + | 0.808170i | \(0.700458\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1028.72 | + | 1028.72i | 1.05078 | + | 1.05078i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.8053 | + | 23.8053i | 0.0242664 | + | 0.0242664i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1733.07 | −1.76304 | −0.881520 | − | 0.472147i | \(-0.843479\pi\) | ||||
−0.881520 | + | 0.472147i | \(0.843479\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 228.789 | 0.232273 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 425.417 | + | 208.642i | 0.431020 | + | 0.211390i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 314.091 | − | 314.091i | 0.317584 | − | 0.317584i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 918.372 | 0.926713 | 0.463356 | − | 0.886172i | \(-0.346645\pi\) | ||||
0.463356 | + | 0.886172i | \(0.346645\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 904.198i | − | 0.910572i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 358.100 | − | 358.100i | 0.359900 | − | 0.359900i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 505.584 | − | 505.584i | 0.507105 | − | 0.507105i | −0.406532 | − | 0.913637i | \(-0.633262\pi\) |
0.913637 | + | 0.406532i | \(0.133262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1275.94 | −1.27722 |
(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 | 448.3.l.b.433.22 | 56 | ||
4.3 | odd | 2 | 112.3.l.b.69.9 | yes | 56 | ||
7.6 | odd | 2 | inner | 448.3.l.b.433.7 | 56 | ||
16.3 | odd | 4 | 112.3.l.b.13.10 | yes | 56 | ||
16.13 | even | 4 | inner | 448.3.l.b.209.7 | 56 | ||
28.27 | even | 2 | 112.3.l.b.69.10 | yes | 56 | ||
112.13 | odd | 4 | inner | 448.3.l.b.209.22 | 56 | ||
112.83 | even | 4 | 112.3.l.b.13.9 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.3.l.b.13.9 | ✓ | 56 | 112.83 | even | 4 | ||
112.3.l.b.13.10 | yes | 56 | 16.3 | odd | 4 | ||
112.3.l.b.69.9 | yes | 56 | 4.3 | odd | 2 | ||
112.3.l.b.69.10 | yes | 56 | 28.27 | even | 2 | ||
448.3.l.b.209.7 | 56 | 16.13 | even | 4 | inner | ||
448.3.l.b.209.22 | 56 | 112.13 | odd | 4 | inner | ||
448.3.l.b.433.7 | 56 | 7.6 | odd | 2 | inner | ||
448.3.l.b.433.22 | 56 | 1.1 | even | 1 | trivial |