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 | 433.25 | ||
Character | \(\chi\) | \(=\) | 448.433 |
Dual form | 448.3.l.b.209.25 |
$q$-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 | ||||||||
\(3\) | 3.31524 | + | 3.31524i | 1.10508 | + | 1.10508i | 0.993788 | + | 0.111293i | \(0.0354991\pi\) |
0.111293 | + | 0.993788i | \(0.464501\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.66000 | + | 4.66000i | −0.932001 | + | 0.932001i | −0.997831 | − | 0.0658299i | \(-0.979031\pi\) |
0.0658299 | + | 0.997831i | \(0.479031\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.13987 | + | 6.66491i | 0.305695 | + | 0.952129i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 12.9816i | 1.44241i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.29514 | − | 8.29514i | −0.754103 | − | 0.754103i | 0.221139 | − | 0.975242i | \(-0.429023\pi\) |
−0.975242 | + | 0.221139i | \(0.929023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.1395 | + | 13.1395i | 1.01073 | + | 1.01073i | 0.999942 | + | 0.0107894i | \(0.00343445\pi\) |
0.0107894 | + | 0.999942i | \(0.496566\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.8981 | −2.05987 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 11.5210i | − | 0.677705i | −0.940839 | − | 0.338853i | \(-0.889961\pi\) | ||
0.940839 | − | 0.338853i | \(-0.110039\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.21978 | − | 5.21978i | −0.274725 | − | 0.274725i | 0.556274 | − | 0.830999i | \(-0.312231\pi\) |
−0.830999 | + | 0.556274i | \(0.812231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −15.0016 | + | 29.1899i | −0.714362 | + | 1.39000i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 20.5622i | − | 0.894007i | −0.894532 | − | 0.447003i | \(-0.852491\pi\) | ||
0.894532 | − | 0.447003i | \(-0.147509\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 18.4313i | − | 0.737251i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.2001 | + | 13.2001i | −0.488893 | + | 0.488893i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −39.7028 | + | 39.7028i | −1.36906 | + | 1.36906i | −0.507283 | + | 0.861780i | \(0.669350\pi\) |
−0.861780 | + | 0.507283i | \(0.830650\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.7004i | 0.409691i | 0.978794 | + | 0.204846i | \(0.0656693\pi\) | ||||
−0.978794 | + | 0.204846i | \(0.934331\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 55.0008i | − | 1.66669i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −41.0303 | − | 21.0867i | −1.17229 | − | 0.602477i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.59936 | + | 5.59936i | 0.151334 | + | 0.151334i | 0.778714 | − | 0.627380i | \(-0.215873\pi\) |
−0.627380 | + | 0.778714i | \(0.715873\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 87.1213i | 2.23388i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 22.7338 | 0.554482 | 0.277241 | − | 0.960800i | \(-0.410580\pi\) | ||||
0.277241 | + | 0.960800i | \(0.410580\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22.2151 | + | 22.2151i | 0.516631 | + | 0.516631i | 0.916550 | − | 0.399920i | \(-0.130962\pi\) |
−0.399920 | + | 0.916550i | \(0.630962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −60.4945 | − | 60.4945i | −1.34432 | − | 1.34432i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 75.1143i | − | 1.59818i | −0.601213 | − | 0.799089i | \(-0.705316\pi\) | ||
0.601213 | − | 0.799089i | \(-0.294684\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −39.8419 | + | 28.5240i | −0.813101 | + | 0.582123i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 38.1949 | − | 38.1949i | 0.748919 | − | 0.748919i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 33.8972 | + | 33.8972i | 0.639570 | + | 0.639570i | 0.950449 | − | 0.310880i | \(-0.100624\pi\) |
−0.310880 | + | 0.950449i | \(0.600624\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 77.3108 | 1.40565 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 34.6097i | − | 0.607187i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.18100 | − | 2.18100i | 0.0369662 | − | 0.0369662i | −0.688382 | − | 0.725348i | \(-0.741679\pi\) |
0.725348 | + | 0.688382i | \(0.241679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42.9938 | + | 42.9938i | 0.704816 | + | 0.704816i | 0.965440 | − | 0.260624i | \(-0.0839283\pi\) |
−0.260624 | + | 0.965440i | \(0.583928\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −86.5215 | + | 27.7790i | −1.37336 | + | 0.440936i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −122.460 | −1.88400 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.01453 | − | 2.01453i | 0.0300676 | − | 0.0300676i | −0.691913 | − | 0.721981i | \(-0.743232\pi\) |
0.721981 | + | 0.691913i | \(0.243232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 68.1685 | − | 68.1685i | 0.987950 | − | 0.987950i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.2019i | 0.566224i | 0.959087 | + | 0.283112i | \(0.0913668\pi\) | ||||
−0.959087 | + | 0.283112i | \(0.908633\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −53.0564 | −0.726799 | −0.363400 | − | 0.931633i | \(-0.618384\pi\) | ||||
−0.363400 | + | 0.931633i | \(0.618384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 61.1042 | − | 61.1042i | 0.814722 | − | 0.814722i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 37.5358 | − | 73.0368i | 0.487478 | − | 0.948530i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −36.5862 | −0.463117 | −0.231558 | − | 0.972821i | \(-0.574382\pi\) | ||||
−0.231558 | + | 0.972821i | \(0.574382\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.3116 | 0.361872 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 90.3415 | + | 90.3415i | 1.08845 | + | 1.08845i | 0.995688 | + | 0.0927635i | \(0.0295700\pi\) |
0.0927635 | + | 0.995688i | \(0.470430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 53.6879 | + | 53.6879i | 0.631622 | + | 0.631622i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −263.249 | −3.02585 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 99.6505 | 1.11967 | 0.559834 | − | 0.828605i | \(-0.310865\pi\) | ||||
0.559834 | + | 0.828605i | \(0.310865\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −59.4568 | + | 115.690i | −0.653371 | + | 1.27132i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −42.1050 | + | 42.1050i | −0.452742 | + | 0.452742i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 48.6484 | 0.512089 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 161.684i | 1.66685i | 0.552633 | + | 0.833425i | \(0.313623\pi\) | ||||
−0.552633 | + | 0.833425i | \(0.686377\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 107.685 | − | 107.685i | 1.08772 | − | 1.08772i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.7670 | − | 19.7670i | 0.195713 | − | 0.195713i | −0.602446 | − | 0.798159i | \(-0.705807\pi\) |
0.798159 | + | 0.602446i | \(0.205807\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −51.6767 | −0.501716 | −0.250858 | − | 0.968024i | \(-0.580713\pi\) | ||||
−0.250858 | + | 0.968024i | \(0.580713\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −66.1177 | − | 205.933i | −0.629693 | − | 1.96126i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −20.4315 | − | 20.4315i | −0.190949 | − | 0.190949i | 0.605157 | − | 0.796106i | \(-0.293110\pi\) |
−0.796106 | + | 0.605157i | \(0.793110\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −85.8458 | + | 85.8458i | −0.787576 | + | 0.787576i | −0.981096 | − | 0.193520i | \(-0.938009\pi\) |
0.193520 | + | 0.981096i | \(0.438009\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 37.1265i | 0.334473i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 43.1097 | 0.381502 | 0.190751 | − | 0.981638i | \(-0.438908\pi\) | ||||
0.190751 | + | 0.981638i | \(0.438908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 95.8198 | + | 95.8198i | 0.833215 | + | 0.833215i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −170.572 | + | 170.572i | −1.45788 | + | 1.45788i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 76.7863 | − | 24.6534i | 0.645263 | − | 0.207171i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6186i | 0.137344i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 75.3679 | + | 75.3679i | 0.612747 | + | 0.612747i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −30.6102 | − | 30.6102i | −0.244882 | − | 0.244882i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −32.1368 | −0.253046 | −0.126523 | − | 0.991964i | \(-0.540382\pi\) | ||||
−0.126523 | + | 0.991964i | \(0.540382\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 147.297i | 1.14184i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 125.429 | + | 125.429i | 0.957471 | + | 0.957471i | 0.999132 | − | 0.0416609i | \(-0.0132649\pi\) |
−0.0416609 | + | 0.999132i | \(0.513265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.6197 | − | 45.9590i | 0.177592 | − | 0.345556i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 123.025i | − | 0.911298i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 53.1819i | − | 0.388189i | −0.980983 | − | 0.194095i | \(-0.937823\pi\) | ||
0.980983 | − | 0.194095i | \(-0.0621769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 113.897 | − | 113.897i | 0.819401 | − | 0.819401i | −0.166620 | − | 0.986021i | \(-0.553285\pi\) |
0.986021 | + | 0.166620i | \(0.0532853\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 249.022 | − | 249.022i | 1.76611 | − | 1.76611i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 217.988i | − | 1.52439i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 370.031i | − | 2.55193i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −226.650 | − | 37.5217i | −1.54183 | − | 0.255250i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.75799 | − | 6.75799i | −0.0453556 | − | 0.0453556i | 0.684065 | − | 0.729421i | \(-0.260210\pi\) |
−0.729421 | + | 0.684065i | \(0.760210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 165.702i | − | 1.09736i | −0.836032 | − | 0.548681i | \(-0.815130\pi\) | ||
0.836032 | − | 0.548681i | \(-0.184870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 149.561 | 0.977526 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −59.1841 | − | 59.1841i | −0.381833 | − | 0.381833i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 82.7381 | + | 82.7381i | 0.526994 | + | 0.526994i | 0.919675 | − | 0.392681i | \(-0.128452\pi\) |
−0.392681 | + | 0.919675i | \(0.628452\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 224.755i | 1.41355i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 137.045 | − | 44.0003i | 0.851210 | − | 0.273294i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 198.331 | − | 198.331i | 1.21675 | − | 1.21675i | 0.247989 | − | 0.968763i | \(-0.420230\pi\) |
0.968763 | − | 0.247989i | \(-0.0797696\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 256.304 | + | 256.304i | 1.55336 | + | 1.55336i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 234.300 | 1.40299 | 0.701497 | − | 0.712673i | \(-0.252516\pi\) | ||||
0.701497 | + | 0.712673i | \(0.252516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 176.293i | 1.04316i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 67.7614 | − | 67.7614i | 0.396265 | − | 0.396265i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 113.853 | + | 113.853i | 0.658112 | + | 0.658112i | 0.954933 | − | 0.296821i | \(-0.0959264\pi\) |
−0.296821 | + | 0.954933i | \(0.595926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 122.843 | − | 39.4405i | 0.701959 | − | 0.225374i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.4611 | 0.0817012 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 54.7105 | − | 54.7105i | 0.305645 | − | 0.305645i | −0.537572 | − | 0.843218i | \(-0.680659\pi\) |
0.843218 | + | 0.537572i | \(0.180659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 137.091 | − | 137.091i | 0.757406 | − | 0.757406i | −0.218443 | − | 0.975850i | \(-0.570098\pi\) |
0.975850 | + | 0.218443i | \(0.0700979\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 285.070i | 1.55776i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −52.1861 | −0.282087 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −95.5682 | + | 95.5682i | −0.511060 | + | 0.511060i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −116.224 | − | 59.7311i | −0.614942 | − | 0.316038i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −40.7416 | −0.213307 | −0.106653 | − | 0.994296i | \(-0.534014\pi\) | ||||
−0.106653 | + | 0.994296i | \(0.534014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 81.8084 | 0.423878 | 0.211939 | − | 0.977283i | \(-0.432022\pi\) | ||||
0.211939 | + | 0.977283i | \(0.432022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −405.985 | − | 405.985i | −2.08198 | − | 2.08198i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −254.441 | − | 254.441i | −1.29158 | − | 1.29158i | −0.933810 | − | 0.357768i | \(-0.883538\pi\) |
−0.357768 | − | 0.933810i | \(-0.616462\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 201.967 | 1.01491 | 0.507455 | − | 0.861678i | \(-0.330586\pi\) | ||||
0.507455 | + | 0.861678i | \(0.330586\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.3573 | 0.0664542 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −349.574 | − | 179.657i | −1.72204 | − | 0.885009i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −105.939 | + | 105.939i | −0.516778 | + | 0.516778i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 266.931 | 1.28952 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 86.5976i | 0.414343i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −162.003 | + | 162.003i | −0.767785 | + | 0.767785i | −0.977716 | − | 0.209932i | \(-0.932676\pi\) |
0.209932 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −133.279 | + | 133.279i | −0.625723 | + | 0.625723i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −207.045 | −0.963000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −84.6472 | + | 27.1772i | −0.390079 | + | 0.125241i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −175.895 | − | 175.895i | −0.803172 | − | 0.803172i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 151.380 | − | 151.380i | 0.684978 | − | 0.684978i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 16.8442i | − | 0.0755344i | −0.999287 | − | 0.0377672i | \(-0.987975\pi\) | ||
0.999287 | − | 0.0377672i | \(-0.0120245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 239.268 | 1.06342 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −84.3452 | − | 84.3452i | −0.371565 | − | 0.371565i | 0.496482 | − | 0.868047i | \(-0.334625\pi\) |
−0.868047 | + | 0.496482i | \(0.834625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −153.690 | + | 153.690i | −0.671136 | + | 0.671136i | −0.957978 | − | 0.286842i | \(-0.907395\pi\) |
0.286842 | + | 0.957978i | \(0.407395\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 366.575 | − | 117.694i | 1.58690 | − | 0.509499i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 268.552i | − | 1.15258i | −0.817245 | − | 0.576291i | \(-0.804499\pi\) | ||
0.817245 | − | 0.576291i | \(-0.195501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 350.033 | + | 350.033i | 1.48950 | + | 1.48950i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −121.292 | − | 121.292i | −0.511781 | − | 0.511781i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −223.803 | −0.936414 | −0.468207 | − | 0.883619i | \(-0.655100\pi\) | ||||
−0.468207 | + | 0.883619i | \(0.655100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 103.352i | − | 0.428846i | −0.976741 | − | 0.214423i | \(-0.931213\pi\) | ||
0.976741 | − | 0.214423i | \(-0.0687872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 215.976 | + | 215.976i | 0.888791 | + | 0.888791i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 52.7417 | − | 318.586i | 0.215272 | − | 1.30035i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 137.171i | − | 0.555347i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 599.008i | 2.40565i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −332.455 | + | 332.455i | −1.32452 | + | 1.32452i | −0.414450 | + | 0.910072i | \(0.636026\pi\) |
−0.910072 | + | 0.414450i | \(0.863974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −170.566 | + | 170.566i | −0.674174 | + | 0.674174i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 355.977i | 1.39599i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 90.4052i | 0.351771i | 0.984411 | + | 0.175886i | \(0.0562789\pi\) | ||||
−0.984411 | + | 0.175886i | \(0.943721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.3373 | + | 49.3011i | −0.0978276 | + | 0.190352i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −515.408 | − | 515.408i | −1.97474 | − | 1.97474i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 197.271i | 0.750079i | 0.927009 | + | 0.375040i | \(0.122371\pi\) | ||||
−0.927009 | + | 0.375040i | \(0.877629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −315.922 | −1.19216 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 330.365 | + | 330.365i | 1.23732 | + | 1.23732i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 75.0832 | + | 75.0832i | 0.279120 | + | 0.279120i | 0.832758 | − | 0.553638i | \(-0.186761\pi\) |
−0.553638 | + | 0.832758i | \(0.686761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 157.382i | − | 0.580747i | −0.956913 | − | 0.290373i | \(-0.906220\pi\) | ||
0.956913 | − | 0.290373i | \(-0.0937795\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −580.655 | + | 186.428i | −2.12694 | + | 0.682886i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −152.890 | + | 152.890i | −0.555964 | + | 0.555964i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 107.714 | + | 107.714i | 0.388859 | + | 0.388859i | 0.874280 | − | 0.485421i | \(-0.161334\pi\) |
−0.485421 | + | 0.874280i | \(0.661334\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −164.873 | −0.590941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 141.437i | 0.503335i | 0.967814 | + | 0.251667i | \(0.0809789\pi\) | ||||
−0.967814 | + | 0.251667i | \(0.919021\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.9231 | + | 26.9231i | −0.0951347 | + | 0.0951347i | −0.753072 | − | 0.657938i | \(-0.771429\pi\) |
0.657938 | + | 0.753072i | \(0.271429\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 161.281 | + | 161.281i | 0.565899 | + | 0.565899i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48.6472 | + | 151.518i | 0.169502 | + | 0.527939i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 156.267 | 0.540715 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −536.023 | + | 536.023i | −1.84200 | + | 1.84200i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.0487 | + | 32.0487i | −0.109381 | + | 0.109381i | −0.759679 | − | 0.650298i | \(-0.774644\pi\) |
0.650298 | + | 0.759679i | \(0.274644\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.3270i | 0.0689050i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 218.994 | 0.737352 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 270.177 | − | 270.177i | 0.903601 | − | 0.903601i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −100.524 | + | 195.599i | −0.333968 | + | 0.649831i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 131.065 | 0.432558 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −400.703 | −1.31378 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 90.4013 | + | 90.4013i | 0.294467 | + | 0.294467i | 0.838842 | − | 0.544375i | \(-0.183233\pi\) |
−0.544375 | + | 0.838842i | \(0.683233\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −171.321 | − | 171.321i | −0.554436 | − | 0.554436i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −84.3194 | −0.271123 | −0.135562 | − | 0.990769i | \(-0.543284\pi\) | ||||
−0.135562 | + | 0.990769i | \(0.543284\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −172.576 | −0.551362 | −0.275681 | − | 0.961249i | \(-0.588903\pi\) | ||||
−0.275681 | + | 0.961249i | \(0.588903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 273.740 | − | 532.641i | 0.869017 | − | 1.69092i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −59.8683 | + | 59.8683i | −0.188859 | + | 0.188859i | −0.795203 | − | 0.606344i | \(-0.792636\pi\) |
0.606344 | + | 0.795203i | \(0.292636\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 658.681 | 2.06483 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 135.471i | − | 0.422027i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −60.1371 | + | 60.1371i | −0.186183 | + | 0.186183i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 242.178 | − | 242.178i | 0.745163 | − | 0.745163i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −569.199 | −1.74067 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 500.630 | − | 160.735i | 1.52167 | − | 0.488555i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −186.575 | − | 186.575i | −0.563672 | − | 0.563672i | 0.366677 | − | 0.930348i | \(-0.380496\pi\) |
−0.930348 | + | 0.366677i | \(0.880496\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −72.6889 | + | 72.6889i | −0.218285 | + | 0.218285i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.7754i | 0.0560461i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 505.780 | 1.50083 | 0.750416 | − | 0.660966i | \(-0.229853\pi\) | ||||
0.750416 | + | 0.660966i | \(0.229853\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 142.919 | + | 142.919i | 0.421590 | + | 0.421590i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 105.352 | − | 105.352i | 0.308950 | − | 0.308950i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −275.366 | − | 204.505i | −0.802817 | − | 0.596225i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 635.331i | 1.84154i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −347.916 | − | 347.916i | −1.00264 | − | 1.00264i | −0.999997 | − | 0.00264331i | \(-0.999159\pi\) |
−0.00264331 | − | 0.999997i | \(-0.500841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −279.398 | − | 279.398i | −0.800567 | − | 0.800567i | 0.182617 | − | 0.983184i | \(-0.441543\pi\) |
−0.983184 | + | 0.182617i | \(0.941543\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −346.886 | −0.988280 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 428.422i | − | 1.21366i | −0.794832 | − | 0.606830i | \(-0.792441\pi\) | ||
0.794832 | − | 0.606830i | \(-0.207559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −187.341 | − | 187.341i | −0.527721 | − | 0.527721i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 336.297 | + | 172.833i | 0.942009 | + | 0.484127i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.80972i | − | 0.0161831i | −0.999967 | − | 0.00809154i | \(-0.997424\pi\) | ||
0.999967 | − | 0.00809154i | \(-0.00257564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 306.508i | − | 0.849052i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −55.0947 | + | 55.0947i | −0.151776 | + | 0.151776i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 247.243 | − | 247.243i | 0.677378 | − | 0.677378i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 99.5445i | − | 0.271238i | −0.990761 | − | 0.135619i | \(-0.956698\pi\) | ||
0.990761 | − | 0.135619i | \(-0.0433024\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 295.122i | 0.799788i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −153.386 | + | 298.457i | −0.413440 | + | 0.804467i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 239.494 | + | 239.494i | 0.642076 | + | 0.642076i | 0.951065 | − | 0.308990i | \(-0.0999908\pi\) |
−0.308990 | + | 0.951065i | \(0.599991\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 202.961i | − | 0.541228i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1043.35 | −2.76751 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 120.835 | + | 120.835i | 0.318825 | + | 0.318825i | 0.848316 | − | 0.529491i | \(-0.177617\pi\) |
−0.529491 | + | 0.848316i | \(0.677617\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −106.541 | − | 106.541i | −0.279636 | − | 0.279636i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 715.292i | − | 1.86760i | −0.357792 | − | 0.933801i | \(-0.616470\pi\) | ||
0.357792 | − | 0.933801i | \(-0.383530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 165.435 | + | 515.269i | 0.429700 | + | 1.33836i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −288.389 | + | 288.389i | −0.745191 | + | 0.745191i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 234.994 | + | 234.994i | 0.604096 | + | 0.604096i | 0.941397 | − | 0.337301i | \(-0.109514\pi\) |
−0.337301 | + | 0.941397i | \(0.609514\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −236.896 | −0.605873 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 831.653i | 2.11616i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 170.492 | − | 170.492i | 0.431625 | − | 0.431625i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −463.022 | − | 463.022i | −1.16630 | − | 1.16630i | −0.983069 | − | 0.183234i | \(-0.941343\pi\) |
−0.183234 | − | 0.983069i | \(-0.558657\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 230.670 | − | 74.0601i | 0.578121 | − | 0.185614i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −379.791 | −0.947111 | −0.473555 | − | 0.880764i | \(-0.657030\pi\) | ||||
−0.473555 | + | 0.880764i | \(0.657030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −166.877 | + | 166.877i | −0.414088 | + | 0.414088i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −136.592 | + | 136.592i | −0.337265 | + | 0.337265i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 92.8950i | − | 0.228243i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 489.166 | 1.19601 | 0.598003 | − | 0.801494i | \(-0.295961\pi\) | ||||
0.598003 | + | 0.801494i | \(0.295961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 176.311 | − | 176.311i | 0.428980 | − | 0.428980i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.2032 | + | 9.86913i | 0.0464969 | + | 0.0238962i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −841.983 | −2.02888 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 755.191 | 1.81101 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.0850 | − | 26.0850i | −0.0622553 | − | 0.0622553i | 0.675294 | − | 0.737549i | \(-0.264017\pi\) |
−0.737549 | + | 0.675294i | \(0.764017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −355.644 | − | 355.644i | −0.844760 | − | 0.844760i | 0.144714 | − | 0.989474i | \(-0.453774\pi\) |
−0.989474 | + | 0.144714i | \(0.953774\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 975.108 | 2.30522 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −212.347 | −0.499639 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −194.549 | + | 378.551i | −0.455617 | + | 0.886535i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 722.683 | − | 722.683i | 1.68458 | − | 1.68458i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −90.4146 | −0.209779 | −0.104889 | − | 0.994484i | \(-0.533449\pi\) | ||||
−0.104889 | + | 0.994484i | \(0.533449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 359.503i | 0.830262i | 0.909762 | + | 0.415131i | \(0.136264\pi\) | ||||
−0.909762 | + | 0.415131i | \(0.863736\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1226.74 | − | 1226.74i | 2.82009 | − | 2.82009i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −107.330 | + | 107.330i | −0.245606 | + | 0.245606i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 427.544 | 0.973904 | 0.486952 | − | 0.873429i | \(-0.338109\pi\) | ||||
0.486952 | + | 0.873429i | \(0.338109\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −370.289 | − | 517.214i | −0.839657 | − | 1.17282i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 216.567 | + | 216.567i | 0.488865 | + | 0.488865i | 0.907948 | − | 0.419083i | \(-0.137648\pi\) |
−0.419083 | + | 0.907948i | \(0.637648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −464.372 | + | 464.372i | −1.04353 | + | 1.04353i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 44.8087i | − | 0.100243i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −167.920 | −0.373987 | −0.186994 | − | 0.982361i | \(-0.559874\pi\) | ||||
−0.186994 | + | 0.982361i | \(0.559874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −188.580 | − | 188.580i | −0.418137 | − | 0.418137i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 549.341 | − | 549.341i | 1.21267 | − | 1.21267i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −262.049 | − | 816.187i | −0.575931 | − | 1.79382i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 509.760i | − | 1.11545i | −0.830026 | − | 0.557725i | \(-0.811675\pi\) | ||
0.830026 | − | 0.557725i | \(-0.188325\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 152.079 | + | 152.079i | 0.331326 | + | 0.331326i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 604.068 | + | 604.068i | 1.31034 | + | 1.31034i | 0.921161 | + | 0.389181i | \(0.127242\pi\) |
0.389181 | + | 0.921161i | \(0.372758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 248.442 | 0.536592 | 0.268296 | − | 0.963336i | \(-0.413539\pi\) | ||||
0.268296 | + | 0.963336i | \(0.413539\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 392.419i | − | 0.843912i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −241.814 | − | 241.814i | −0.517802 | − | 0.517802i | 0.399103 | − | 0.916906i | \(-0.369321\pi\) |
−0.916906 | + | 0.399103i | \(0.869321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.7375 | + | 9.11582i | 0.0378198 | + | 0.0194367i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 548.594i | 1.16474i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 368.555i | − | 0.779186i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −96.2073 | + | 96.2073i | −0.202542 | + | 0.202542i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −440.041 | + | 440.041i | −0.922519 | + | 0.922519i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 747.728i | 1.56102i | 0.625144 | + | 0.780509i | \(0.285040\pi\) | ||||
−0.625144 | + | 0.780509i | \(0.714960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 147.146i | 0.305916i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 600.208 | + | 308.465i | 1.24267 | + | 0.638645i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −753.450 | − | 753.450i | −1.55351 | − | 1.55351i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 479.744i | 0.985100i | 0.870284 | + | 0.492550i | \(0.163935\pi\) | ||||
−0.870284 | + | 0.492550i | \(0.836065\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1315.03 | 2.68922 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −515.730 | − | 515.730i | −1.05037 | − | 1.05037i | −0.998663 | − | 0.0517031i | \(-0.983535\pi\) |
−0.0517031 | − | 0.998663i | \(-0.516465\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 457.416 | + | 457.416i | 0.927821 | + | 0.927821i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1003.62i | 2.02752i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −267.942 | + | 86.0266i | −0.539118 | + | 0.173092i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −113.064 | + | 113.064i | −0.226581 | + | 0.226581i | −0.811263 | − | 0.584682i | \(-0.801219\pi\) |
0.584682 | + | 0.811263i | \(0.301219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 776.760 | + | 776.760i | 1.55042 | + | 1.55042i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 91.7304 | 0.182367 | 0.0911833 | − | 0.995834i | \(-0.470935\pi\) | ||||
0.0911833 | + | 0.995834i | \(0.470935\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 184.229i | 0.364810i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −584.455 | + | 584.455i | −1.15277 | + | 1.15277i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −282.406 | − | 282.406i | −0.554826 | − | 0.554826i | 0.373004 | − | 0.927830i | \(-0.378328\pi\) |
−0.927830 | + | 0.373004i | \(0.878328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −113.533 | − | 353.616i | −0.222179 | − | 0.692007i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 137.804 | 0.268623 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 240.814 | − | 240.814i | 0.467599 | − | 0.467599i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −623.084 | + | 623.084i | −1.20519 | + | 1.20519i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 754.903i | 1.45453i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −258.579 | −0.496313 | −0.248156 | − | 0.968720i | \(-0.579825\pi\) | ||||
−0.248156 | + | 0.968720i | \(0.579825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −533.576 | + | 533.576i | −1.02022 | + | 1.02022i | −0.0204296 | + | 0.999791i | \(0.506503\pi\) |
−0.999791 | + | 0.0204296i | \(0.993497\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 538.008 | + | 276.499i | 1.02478 | + | 0.526664i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 146.322 | 0.277650 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 106.198 | 0.200752 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.3130 | + | 28.3130i | 0.0533202 | + | 0.0533202i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 298.711 | + | 298.711i | 0.560432 | + | 0.560432i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 190.422 | 0.355928 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 362.757 | 0.675525 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 567.105 | + | 93.8839i | 1.05214 | + | 0.174182i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 318.101 | − | 318.101i | 0.587987 | − | 0.587987i | −0.349099 | − | 0.937086i | \(-0.613512\pi\) |
0.937086 | + | 0.349099i | \(0.113512\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 908.976 | 1.67399 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 800.084i | − | 1.46804i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 591.111 | − | 591.111i | 1.08064 | − | 1.08064i | 0.0841918 | − | 0.996450i | \(-0.473169\pi\) |
0.996450 | − | 0.0841918i | \(-0.0268308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −558.130 | + | 558.130i | −1.01663 | + | 1.01663i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 414.480 | 0.752233 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −78.2896 | − | 243.844i | −0.141572 | − | 0.440947i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −173.010 | − | 173.010i | −0.311729 | − | 0.311729i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 337.829 | − | 337.829i | 0.606516 | − | 0.606516i | −0.335518 | − | 0.942034i | \(-0.608911\pi\) |
0.942034 | + | 0.335518i | \(0.108911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 583.791i | 1.04435i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −633.663 | −1.12952 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −531.679 | − | 531.679i | −0.944368 | − | 0.944368i | 0.0541639 | − | 0.998532i | \(-0.482751\pi\) |
−0.998532 | + | 0.0541639i | \(0.982751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −200.891 | + | 200.891i | −0.355560 | + | 0.355560i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 62.7230 | + | 195.359i | 0.110623 | + | 0.344549i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 464.888i | − | 0.817026i | −0.912753 | − | 0.408513i | \(-0.866048\pi\) | ||
0.912753 | − | 0.408513i | \(-0.133952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 354.278 | + | 354.278i | 0.620453 | + | 0.620453i | 0.945647 | − | 0.325195i | \(-0.105430\pi\) |
−0.325195 | + | 0.945647i | \(0.605430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −135.068 | − | 135.068i | −0.235721 | − | 0.235721i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −378.987 | −0.659108 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 477.529i | 0.827606i | 0.910366 | + | 0.413803i | \(0.135800\pi\) | ||||
−0.910366 | + | 0.413803i | \(0.864200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 271.215 | + | 271.215i | 0.468419 | + | 0.468419i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −408.799 | + | 795.436i | −0.703613 | + | 1.36908i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 562.364i | − | 0.964603i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 1589.74i | − | 2.71750i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 407.567 | − | 407.567i | 0.694322 | − | 0.694322i | −0.268858 | − | 0.963180i | \(-0.586646\pi\) |
0.963180 | + | 0.268858i | \(0.0866463\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 66.2935 | − | 66.2935i | 0.112553 | − | 0.112553i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 1687.07i | − | 2.85460i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 293.102i | − | 0.494269i | −0.968981 | − | 0.247135i | \(-0.920511\pi\) | ||
0.968981 | − | 0.247135i | \(-0.0794890\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −242.940 | + | 472.710i | −0.408302 | + | 0.794470i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 669.570 | + | 669.570i | 1.12156 | + | 1.12156i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 29.9752i | − | 0.0500420i | −0.999687 | − | 0.0250210i | \(-0.992035\pi\) | ||
0.999687 | − | 0.0250210i | \(-0.00796526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 770.010 | 1.28121 | 0.640607 | − | 0.767869i | \(-0.278683\pi\) | ||||
0.640607 | + | 0.767869i | \(0.278683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.1519 | + | 26.1519i | 0.0433697 | + | 0.0433697i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −77.4428 | − | 77.4428i | −0.128005 | − | 0.128005i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 374.183i | − | 0.616447i | −0.951314 | − | 0.308223i | \(-0.900266\pi\) | ||
0.951314 | − | 0.308223i | \(-0.0997344\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −563.317 | − | 1754.53i | −0.924987 | − | 2.88100i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 986.965 | − | 986.965i | 1.61533 | − | 1.61533i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −523.959 | − | 523.959i | −0.854746 | − | 0.854746i | 0.135968 | − | 0.990713i | \(-0.456586\pi\) |
−0.990713 | + | 0.135968i | \(0.956586\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −702.430 | −1.14216 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 599.458i | 0.971569i | 0.874079 | + | 0.485785i | \(0.161466\pi\) | ||||
−0.874079 | + | 0.485785i | \(0.838534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 135.489 | − | 135.489i | 0.218883 | − | 0.218883i | −0.589145 | − | 0.808028i | \(-0.700535\pi\) |
0.808028 | + | 0.589145i | \(0.200535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 271.423 | + | 271.423i | 0.437074 | + | 0.437074i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 213.239 | + | 664.161i | 0.342277 | + | 1.06607i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 746.070 | 1.19371 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −287.092 | + | 287.092i | −0.457882 | + | 0.457882i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 64.5102 | − | 64.5102i | 0.102560 | − | 0.102560i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 317.510i | − | 0.503186i | −0.967833 | − | 0.251593i | \(-0.919046\pi\) | ||
0.967833 | − | 0.251593i | \(-0.0809544\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1074.15 | −1.69693 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 149.758 | − | 149.758i | 0.235839 | − | 0.235839i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −898.295 | − | 148.712i | −1.41020 | − | 0.233457i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −521.887 | −0.816724 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −294.765 | −0.459852 | −0.229926 | − | 0.973208i | \(-0.573848\pi\) | ||||
−0.229926 | + | 0.973208i | \(0.573848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 596.748 | + | 596.748i | 0.928068 | + | 0.928068i | 0.997581 | − | 0.0695126i | \(-0.0221444\pi\) |
−0.0695126 | + | 0.997581i | \(0.522144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −686.404 | − | 686.404i | −1.06419 | − | 1.06419i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −958.028 | −1.48072 | −0.740362 | − | 0.672208i | \(-0.765346\pi\) | ||||
−0.740362 | + | 0.672208i | \(0.765346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.1835 | −0.0557526 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −370.725 | − | 190.527i | −0.569470 | − | 0.292668i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −418.776 | + | 418.776i | −0.641310 | + | 0.641310i | −0.950878 | − | 0.309567i | \(-0.899816\pi\) |
0.309567 | + | 0.950878i | \(0.399816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1169.00 | −1.78473 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 688.759i | − | 1.04834i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 359.378 | − | 359.378i | 0.545338 | − | 0.545338i | −0.379750 | − | 0.925089i | \(-0.623990\pi\) |
0.925089 | + | 0.379750i | \(0.123990\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 286.993 | − | 286.993i | 0.434181 | − | 0.434181i | −0.455867 | − | 0.890048i | \(-0.650671\pi\) |
0.890048 | + | 0.455867i | \(0.150671\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1003.72 | 1.51391 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 104.101 | + | 324.237i | 0.156543 | + | 0.487575i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 816.375 | + | 816.375i | 1.22395 | + | 1.22395i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 55.8425 | − | 55.8425i | 0.0834716 | − | 0.0834716i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 713.279i | − | 1.06301i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1166.76 | 1.73367 | 0.866837 | − | 0.498591i | \(-0.166149\pi\) | ||||
0.866837 | + | 0.498591i | \(0.166149\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 243.295 | + | 243.295i | 0.360437 | + | 0.360437i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 950.932 | − | 950.932i | 1.40463 | − | 1.40463i | 0.620117 | − | 0.784509i | \(-0.287085\pi\) |
0.784509 | − | 0.620117i | \(-0.212915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1077.61 | + | 345.983i | −1.58706 | + | 0.509548i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 559.250i | − | 0.821218i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −598.548 | − | 598.548i | −0.876351 | − | 0.876351i | 0.116804 | − | 0.993155i | \(-0.462735\pi\) |
−0.993155 | + | 0.116804i | \(0.962735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 247.828 | + | 247.828i | 0.361793 | + | 0.361793i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1019.04 | −1.48332 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 890.785i | 1.29287i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −758.106 | − | 758.106i | −1.09711 | − | 1.09711i | −0.994747 | − | 0.102368i | \(-0.967358\pi\) |
−0.102368 | − | 0.994747i | \(-0.532642\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 948.138 | + | 487.277i | 1.36816 | + | 0.703141i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1061.52i | 1.52737i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 261.916i | − | 0.375776i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 890.313 | − | 890.313i | 1.27370 | − | 1.27370i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −149.764 | + | 149.764i | −0.213643 | + | 0.213643i | −0.805813 | − | 0.592170i | \(-0.798271\pi\) |
0.592170 | + | 0.805813i | \(0.298271\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 58.4549i | − | 0.0831507i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2320.89i | 3.29204i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 174.044 | + | 89.4467i | 0.246173 | + | 0.126516i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 938.869 | + | 938.869i | 1.32422 | + | 1.32422i | 0.910328 | + | 0.413888i | \(0.135830\pi\) |
0.413888 | + | 0.910328i | \(0.364170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 474.949i | − | 0.668002i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 261.148 | 0.366267 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1015.83 | + | 1015.83i | 1.42073 | + | 1.42073i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −741.961 | − | 741.961i | −1.03481 | − | 1.03481i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 524.039i | 0.728844i | 0.931234 | + | 0.364422i | \(0.118733\pi\) | ||||
−0.931234 | + | 0.364422i | \(0.881267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −110.581 | − | 344.420i | −0.153372 | − | 0.477698i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 342.637 | − | 342.637i | 0.473910 | − | 0.473910i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 731.774 | + | 731.774i | 1.00934 | + | 1.00934i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 550.877 | 0.757739 | 0.378870 | − | 0.925450i | \(-0.376313\pi\) | ||||
0.378870 | + | 0.925450i | \(0.376313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1168.22i | 1.60250i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 255.940 | − | 255.940i | 0.350123 | − | 0.350123i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −106.728 | − | 106.728i | −0.145604 | − | 0.145604i | 0.630547 | − | 0.776151i | \(-0.282831\pi\) |
−0.776151 | + | 0.630547i | \(0.782831\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1231.04 | − | 881.337i | 1.67488 | − | 1.19910i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.4216 | −0.0453482 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −788.242 | + | 788.242i | −1.06663 | + | 1.06663i | −0.0690175 | + | 0.997615i | \(0.521986\pi\) |
−0.997615 | + | 0.0690175i | \(0.978014\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 454.754 | − | 454.754i | 0.613703 | − | 0.613703i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.36550i | − | 0.00856729i | −0.999991 | − | 0.00428365i | \(-0.998636\pi\) | ||
0.999991 | − | 0.00428365i | \(-0.00136353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 62.9845 | 0.0845430 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1172.78 | + | 1172.78i | −1.56999 | + | 1.56999i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 92.4533 | − | 179.895i | 0.123436 | − | 0.240180i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −738.817 | −0.983778 | −0.491889 | − | 0.870658i | \(-0.663693\pi\) | ||||
−0.491889 | + | 0.870658i | \(0.663693\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2204.34 | −2.92741 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 772.171 | + | 772.171i | 1.02274 | + | 1.02274i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −538.649 | − | 538.649i | −0.711557 | − | 0.711557i | 0.255304 | − | 0.966861i | \(-0.417824\pi\) |
−0.966861 | + | 0.255304i | \(0.917824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1130.93 | −1.49003 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 304.961 | 0.400737 | 0.200369 | − | 0.979721i | \(-0.435786\pi\) | ||||
0.200369 | + | 0.979721i | \(0.435786\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −755.853 | − | 388.456i | −0.990633 | − | 0.509116i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −696.957 | + | 696.957i | −0.911055 | + | 0.911055i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 57.3146 | 0.0747257 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.4537i | 0.0539059i | 0.999637 | + | 0.0269530i | \(0.00858043\pi\) | ||||
−0.999637 | + | 0.0269530i | \(0.991420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −299.715 | + | 299.715i | −0.388735 | + | 0.388735i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 500.899 | − | 500.899i | 0.647993 | − | 0.647993i | −0.304514 | − | 0.952508i | \(-0.598494\pi\) |
0.952508 | + | 0.304514i | \(0.0984942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 234.085 | 0.302046 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −247.444 | + | 79.4457i | −0.318461 | + | 0.102247i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −118.665 | − | 118.665i | −0.152330 | − | 0.152330i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 333.480 | − | 333.480i | 0.426991 | − | 0.426991i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1048.16i | − | 1.33865i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −771.120 | −0.982318 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 328.763 | + | 328.763i | 0.417742 | + | 0.417742i | 0.884425 | − | 0.466683i | \(-0.154551\pi\) |
−0.466683 | + | 0.884425i | \(0.654551\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −654.001 | + | 654.001i | −0.828898 | + | 0.828898i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 92.2489 | + | 287.322i | 0.116623 | + | 0.363239i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1129.83i | 1.42476i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1047.36 | − | 1047.36i | −1.31743 | − | 1.31743i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 350.489 | + | 350.489i | 0.439760 | + | 0.439760i | 0.891931 | − | 0.452171i | \(-0.149350\pi\) |
−0.452171 | + | 0.891931i | \(0.649350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −865.392 | −1.08309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1293.63i | 1.61502i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 440.110 | + | 440.110i | 0.548082 | + | 0.548082i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −433.588 | + | 843.671i | −0.538619 | + | 1.04804i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 497.838i | 0.616900i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 499.525i | 0.617460i | 0.951150 | + | 0.308730i | \(0.0999039\pi\) | ||||
−0.951150 | + | 0.308730i | \(0.900096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 458.310 | − | 458.310i | 0.565117 | − | 0.565117i | −0.365639 | − | 0.930757i | \(-0.619150\pi\) |
0.930757 | + | 0.365639i | \(0.119150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 521.761 | − | 521.761i | 0.641772 | − | 0.641772i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1848.44i | 2.26803i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 231.916i | − | 0.283863i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1501.85 | − | 771.847i | −1.83376 | − | 0.942426i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −799.288 | − | 799.288i | −0.973554 | − | 0.973554i | 0.0261048 | − | 0.999659i | \(-0.491690\pi\) |
−0.999659 | + | 0.0261048i | \(0.991690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1017.99i | − | 1.23693i | −0.785812 | − | 0.618465i | \(-0.787755\pi\) | ||
0.785812 | − | 0.618465i | \(-0.212245\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1013.73 | −1.22877 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −135.830 | − | 135.830i | −0.164245 | − | 0.164245i | 0.620199 | − | 0.784444i | \(-0.287052\pi\) |
−0.784444 | + | 0.620199i | \(0.787052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −240.155 | − | 240.155i | −0.289693 | − | 0.289693i | 0.547266 | − | 0.836959i | \(-0.315669\pi\) |
−0.836959 | + | 0.547266i | \(0.815669\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 714.195i | 0.859441i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 328.625 | + | 459.019i | 0.394508 | + | 0.551043i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1091.84 | + | 1091.84i | −1.30759 | + | 1.30759i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −167.647 | − | 167.647i | −0.200295 | − | 0.200295i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.3581 | −0.0337999 | −0.0168999 | − | 0.999857i | \(-0.505380\pi\) | ||||
−0.0168999 | + | 0.999857i | \(0.505380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2311.63i | − | 2.74866i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −468.898 | + | 468.898i | −0.556225 | + | 0.556225i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −821.527 | − | 821.527i | −0.972222 | − | 0.972222i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −110.762 | + | 35.5616i | −0.130769 | + | 0.0419854i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −178.513 | −0.210263 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 115.135 | − | 115.135i | 0.135294 | − | 0.135294i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 351.304 | − | 351.304i | 0.411846 | − | 0.411846i | −0.470535 | − | 0.882381i | \(-0.655939\pi\) |
0.882381 | + | 0.470535i | \(0.155939\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 631.537i | 0.738640i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 847.908 | 0.989391 | 0.494696 | − | 0.869066i | \(-0.335280\pi\) | ||||
0.494696 | + | 0.869066i | \(0.335280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 578.524 | − | 578.524i | 0.673486 | − | 0.673486i | −0.285032 | − | 0.958518i | \(-0.592004\pi\) |
0.958518 | + | 0.285032i | \(0.0920043\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −341.043 | + | 663.597i | −0.396101 | + | 0.770729i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1082.66 | 1.25453 | 0.627266 | − | 0.778805i | \(-0.284174\pi\) | ||||
0.627266 | + | 0.778805i | \(0.284174\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1061.11 | −1.22672 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 518.062 | + | 518.062i | 0.597534 | + | 0.597534i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 303.488 | + | 303.488i | 0.349238 | + | 0.349238i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.9398 | 0.0607805 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2098.93 | −2.40427 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 138.513 | − | 269.516i | 0.158300 | − | 0.308018i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −378.296 | + | 378.296i | −0.431353 | + | 0.431353i | −0.889088 | − | 0.457736i | \(-0.848661\pi\) |
0.457736 | + | 0.889088i | \(0.348661\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −212.498 | −0.241750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 348.803i | 0.395917i | 0.980210 | + | 0.197958i | \(0.0634311\pi\) | ||||
−0.980210 | + | 0.197958i | \(0.936569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 93.9565 | − | 93.9565i | 0.106406 | − | 0.106406i | −0.651899 | − | 0.758305i | \(-0.726028\pi\) |
0.758305 | + | 0.651899i | \(0.226028\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −67.3888 | + | 67.3888i | −0.0761456 | + | 0.0761456i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1418.82 | 1.59957 | 0.799784 | − | 0.600288i | \(-0.204947\pi\) | ||||
0.799784 | + | 0.600288i | \(0.204947\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −68.7685 | − | 214.189i | −0.0773549 | − | 0.240932i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −243.144 | − | 243.144i | −0.272889 | − | 0.272889i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −392.081 | + | 392.081i | −0.439060 | + | 0.439060i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 509.902i | 0.569723i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1791.40 | 1.99710 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −504.243 | − | 504.243i | −0.560893 | − | 0.560893i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 390.529 | − | 390.529i | 0.433440 | − | 0.433440i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −981.720 | + | 315.196i | −1.08718 | + | 0.349054i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1277.69i | 1.41181i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1066.03 | + | 1066.03i | 1.17533 | + | 1.17533i | 0.980920 | + | 0.194414i | \(0.0622804\pi\) |
0.194414 | + | 0.980920i | \(0.437720\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 256.609 | + | 256.609i | 0.282298 | + | 0.282298i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −526.652 | −0.578103 | −0.289051 | − | 0.957314i | \(-0.593340\pi\) | ||||
−0.289051 | + | 0.957314i | \(0.593340\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1498.79i | − | 1.64161i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1328.43 | − | 1328.43i | −1.45183 | − | 1.45183i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −567.570 | + | 1104.37i | −0.618942 | + | 1.20433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 306.233i | − | 0.333224i | −0.986023 | − | 0.166612i | \(-0.946717\pi\) | ||
0.986023 | − | 0.166612i | \(-0.0532828\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 599.404i | 0.650819i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −528.233 | + | 528.233i | −0.572300 | + | 0.572300i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 103.203 | − | 103.203i | 0.111571 | − | 0.111571i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 670.849i | − | 0.723677i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 644.517i | − | 0.693776i | −0.937907 | − | 0.346888i | \(-0.887238\pi\) | ||
0.937907 | − | 0.346888i | \(-0.112762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 356.855 | + | 59.0772i | 0.383303 | + | 0.0634556i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −279.539 | − | 279.539i | −0.299613 | − | 0.299613i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 890.697i | − | 0.952617i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 707.989 | 0.755591 | 0.377796 | − | 0.925889i | \(-0.376682\pi\) | ||||
0.377796 | + | 0.925889i | \(0.376682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −572.132 | − | 572.132i | −0.609299 | − | 0.609299i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −895.058 | − | 895.058i | −0.951177 | − | 0.951177i | 0.0476851 | − | 0.998862i | \(-0.484816\pi\) |
−0.998862 | + | 0.0476851i | \(0.984816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 467.455i | − | 0.495711i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 819.952 | − | 263.258i | 0.867674 | − | 0.278579i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −622.940 | + | 622.940i | −0.657804 | + | 0.657804i | −0.954860 | − | 0.297056i | \(-0.903995\pi\) |
0.297056 | + | 0.954860i | \(0.403995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −697.134 | − | 697.134i | −0.734599 | − | 0.734599i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −396.956 | −0.417409 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1574.91i | 1.65258i | 0.563243 | + | 0.826291i | \(0.309553\pi\) | ||||
−0.563243 | + | 0.826291i | \(0.690447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 189.856 | − | 189.856i | 0.198802 | − | 0.198802i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2183.68 | + | 2183.68i | 2.28180 | + | 2.28180i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 354.452 | − | 113.802i | 0.369606 | − | 0.118668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 799.699 | 0.832153 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 265.234 | − | 265.234i | 0.275425 | − | 0.275425i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −381.227 | + | 381.227i | −0.395054 | + | 0.395054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 114.443i | − | 0.118348i | −0.998248 | − | 0.0591741i | \(-0.981153\pi\) | ||
0.998248 | − | 0.0591741i | \(-0.0188467\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −398.738 | −0.411494 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −693.409 | + | 693.409i | −0.714118 | + | 0.714118i | −0.967394 | − | 0.253276i | \(-0.918492\pi\) |
0.253276 | + | 0.967394i | \(0.418492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1002.84 | + | 515.388i | 1.03066 | + | 0.529689i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1605.76 | 1.64693 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1198.67 | 1.22689 | 0.613446 | − | 0.789736i | \(-0.289783\pi\) | ||||
0.613446 | + | 0.789736i | \(0.289783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −826.615 | − | 826.615i | −0.844346 | − | 0.844346i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1114.42 | − | 1114.42i | −1.13600 | − | 1.13600i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −381.555 | −0.388153 | −0.194077 | − | 0.980986i | \(-0.562171\pi\) | ||||
−0.194077 | + | 0.980986i | \(0.562171\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2371.39 | 2.40751 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2192.58 | + | 1126.84i | 2.22146 | + | 1.14168i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 456.791 | − | 456.791i | 0.461871 | − | 0.461871i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 472.063 | 0.476350 | 0.238175 | − | 0.971222i | \(-0.423451\pi\) | ||||
0.238175 | + | 0.971222i | \(0.423451\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1237.08i | − | 1.24581i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −941.168 | + | 941.168i | −0.945898 | + | 0.945898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1090.50 | − | 1090.50i | 1.09378 | − | 1.09378i | 0.0986584 | − | 0.995121i | \(-0.468545\pi\) |
0.995121 | − | 0.0986584i | \(-0.0314551\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −147.825 | −0.147973 |
(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.433.25 | 56 | ||
4.3 | odd | 2 | 112.3.l.b.69.1 | yes | 56 | ||
7.6 | odd | 2 | inner | 448.3.l.b.433.4 | 56 | ||
16.3 | odd | 4 | 112.3.l.b.13.2 | yes | 56 | ||
16.13 | even | 4 | inner | 448.3.l.b.209.4 | 56 | ||
28.27 | even | 2 | 112.3.l.b.69.2 | yes | 56 | ||
112.13 | odd | 4 | inner | 448.3.l.b.209.25 | 56 | ||
112.83 | even | 4 | 112.3.l.b.13.1 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.3.l.b.13.1 | ✓ | 56 | 112.83 | even | 4 | ||
112.3.l.b.13.2 | yes | 56 | 16.3 | odd | 4 | ||
112.3.l.b.69.1 | yes | 56 | 4.3 | odd | 2 | ||
112.3.l.b.69.2 | yes | 56 | 28.27 | even | 2 | ||
448.3.l.b.209.4 | 56 | 16.13 | even | 4 | inner | ||
448.3.l.b.209.25 | 56 | 112.13 | odd | 4 | inner | ||
448.3.l.b.433.4 | 56 | 7.6 | odd | 2 | inner | ||
448.3.l.b.433.25 | 56 | 1.1 | even | 1 | trivial |