Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(17,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.n (of order \(6\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.13 | ||
Character | \(\chi\) | \(=\) | 224.145 |
Dual form | 224.3.n.a.17.13 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.94818 | + | 3.37434i | 0.649392 | + | 1.12478i | 0.983268 | + | 0.182163i | \(0.0583098\pi\) |
−0.333876 | + | 0.942617i | \(0.608357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.42985 | + | 7.67272i | −0.885969 | + | 1.53454i | −0.0413705 | + | 0.999144i | \(0.513172\pi\) |
−0.844599 | + | 0.535400i | \(0.820161\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.92329 | − | 1.03347i | 0.989041 | − | 0.147638i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.09078 | + | 5.35338i | −0.343420 | + | 0.594820i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.15749 | − | 1.82298i | 0.287045 | − | 0.165725i | −0.349564 | − | 0.936913i | \(-0.613670\pi\) |
0.636608 | + | 0.771187i | \(0.280337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.79378 | −0.599522 | −0.299761 | − | 0.954014i | \(-0.596907\pi\) | ||||
−0.299761 | + | 0.954014i | \(0.596907\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −34.5205 | −2.30136 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9.07152 | + | 5.23744i | −0.533619 | + | 0.308085i | −0.742489 | − | 0.669858i | \(-0.766355\pi\) |
0.208870 | + | 0.977943i | \(0.433021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.39264 | + | 9.34032i | −0.283823 | + | 0.491596i | −0.972323 | − | 0.233640i | \(-0.924936\pi\) |
0.688500 | + | 0.725236i | \(0.258269\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.9751 | + | 21.3482i | 0.808336 | + | 1.01658i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.45553 | + | 11.1813i | −0.280675 | + | 0.486144i | −0.971551 | − | 0.236829i | \(-0.923892\pi\) |
0.690876 | + | 0.722973i | \(0.257225\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26.7471 | − | 46.3273i | −1.06988 | − | 1.85309i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.9817 | 0.406728 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 17.2327i | − | 0.594231i | −0.954842 | − | 0.297115i | \(-0.903975\pi\) | ||
0.954842 | − | 0.297115i | \(-0.0960246\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.1797 | − | 15.1148i | 0.844505 | − | 0.487575i | −0.0142878 | − | 0.999898i | \(-0.504548\pi\) |
0.858793 | + | 0.512323i | \(0.171215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.3027 | + | 7.10296i | 0.372809 | + | 0.215241i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −22.7396 | + | 57.6986i | −0.649703 | + | 1.64853i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.2810 | + | 19.7922i | 0.926515 | + | 0.534924i | 0.885708 | − | 0.464244i | \(-0.153674\pi\) |
0.0408071 | + | 0.999167i | \(0.487007\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.1837 | − | 26.2989i | −0.389324 | − | 0.674330i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 73.6801i | 1.79707i | 0.438897 | + | 0.898537i | \(0.355369\pi\) | ||||
−0.438897 | + | 0.898537i | \(0.644631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 40.8501i | − | 0.950002i | −0.879985 | − | 0.475001i | \(-0.842448\pi\) | ||
0.879985 | − | 0.475001i | \(-0.157552\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −27.3833 | − | 47.4293i | −0.608518 | − | 1.05398i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 36.2025 | + | 20.9015i | 0.770266 | + | 0.444713i | 0.832969 | − | 0.553319i | \(-0.186639\pi\) |
−0.0627038 | + | 0.998032i | \(0.519972\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 46.8639 | − | 14.3100i | 0.956406 | − | 0.292041i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −35.3458 | − | 20.4069i | −0.693055 | − | 0.400136i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.55272 | + | 3.20586i | −0.104768 | + | 0.0604880i | −0.551469 | − | 0.834196i | \(-0.685932\pi\) |
0.446700 | + | 0.894684i | \(0.352599\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 32.3020i | 0.587310i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −42.0232 | −0.737249 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.95742 | + | 13.7827i | 0.134871 | + | 0.233604i | 0.925548 | − | 0.378629i | \(-0.123605\pi\) |
−0.790677 | + | 0.612234i | \(0.790271\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.07848 | + | 10.5282i | −0.0996472 | + | 0.172594i | −0.911539 | − | 0.411214i | \(-0.865105\pi\) |
0.811891 | + | 0.583808i | \(0.198438\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.8658 | + | 40.2572i | −0.251838 | + | 0.639004i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 34.5253 | − | 59.7995i | 0.531158 | − | 0.919992i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.75274 | + | 3.89870i | −0.100787 | + | 0.0581895i | −0.549546 | − | 0.835463i | \(-0.685199\pi\) |
0.448759 | + | 0.893653i | \(0.351866\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −50.3060 | −0.729073 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 41.3627 | 0.582574 | 0.291287 | − | 0.956636i | \(-0.405917\pi\) | ||||
0.291287 | + | 0.956636i | \(0.405917\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77.6038 | − | 44.8046i | 1.06307 | − | 0.613761i | 0.136787 | − | 0.990601i | \(-0.456322\pi\) |
0.926279 | + | 0.376839i | \(0.122989\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 104.216 | − | 180.507i | 1.38955 | − | 2.40677i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.9762 | − | 15.8842i | 0.259432 | − | 0.206288i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35.3975 | − | 61.3103i | 0.448070 | − | 0.776080i | −0.550191 | − | 0.835039i | \(-0.685445\pi\) |
0.998260 | + | 0.0589594i | \(0.0187783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 49.2112 | + | 85.2363i | 0.607546 | + | 1.05230i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 60.8673 | 0.733341 | 0.366671 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366671 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 92.8043i | − | 1.09182i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 58.1489 | − | 33.5723i | 0.668379 | − | 0.385889i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −23.4004 | − | 13.5102i | −0.262926 | − | 0.151800i | 0.362743 | − | 0.931889i | \(-0.381840\pi\) |
−0.625668 | + | 0.780089i | \(0.715174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −53.9586 | + | 8.05463i | −0.592952 | + | 0.0885124i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 102.005 | + | 58.8927i | 1.09683 | + | 0.633255i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −47.7771 | − | 82.7524i | −0.502917 | − | 0.871078i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.26608i | − | 0.0336710i | −0.999858 | − | 0.0168355i | \(-0.994641\pi\) | ||
0.999858 | − | 0.0168355i | \(-0.00535916\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 22.5377i | 0.227653i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −68.8571 | − | 119.264i | −0.681754 | − | 1.18083i | −0.974445 | − | 0.224625i | \(-0.927884\pi\) |
0.292691 | − | 0.956207i | \(-0.405449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −86.3243 | − | 49.8393i | −0.838100 | − | 0.483877i | 0.0185182 | − | 0.999829i | \(-0.494105\pi\) |
−0.856618 | + | 0.515952i | \(0.827438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −238.995 | + | 35.6758i | −2.27615 | + | 0.339770i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 81.4157 | + | 47.0054i | 0.760894 | + | 0.439302i | 0.829617 | − | 0.558333i | \(-0.188559\pi\) |
−0.0687226 | + | 0.997636i | \(0.521892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −169.697 | + | 97.9745i | −1.55685 | + | 0.898849i | −0.559297 | + | 0.828967i | \(0.688929\pi\) |
−0.997555 | + | 0.0698815i | \(0.977738\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 154.234i | 1.38950i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 101.873 | 0.901527 | 0.450763 | − | 0.892643i | \(-0.351152\pi\) | ||||
0.450763 | + | 0.892643i | \(0.351152\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −57.1940 | − | 99.0629i | −0.497339 | − | 0.861417i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24.0888 | − | 41.7231i | 0.205887 | − | 0.356608i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −57.3920 | + | 45.6355i | −0.482286 | + | 0.383491i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.8535 | + | 93.2770i | −0.445070 | + | 0.770884i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −248.622 | + | 143.542i | −2.02131 | + | 1.16701i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 252.449 | 2.01960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 139.079 | 1.09511 | 0.547554 | − | 0.836770i | \(-0.315559\pi\) | ||||
0.547554 | + | 0.836770i | \(0.315559\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 137.842 | − | 79.5831i | 1.06854 | − | 0.616924i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −45.8526 | + | 79.4190i | −0.350020 | + | 0.606252i | −0.986252 | − | 0.165245i | \(-0.947158\pi\) |
0.636233 | + | 0.771497i | \(0.280492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −27.6819 | + | 70.2389i | −0.208134 | + | 0.528112i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −48.6471 | + | 84.2592i | −0.360349 | + | 0.624142i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −99.7904 | − | 172.842i | −0.728397 | − | 1.26162i | −0.957560 | − | 0.288233i | \(-0.906932\pi\) |
0.229163 | − | 0.973388i | \(-0.426401\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 39.4768 | 0.284006 | 0.142003 | − | 0.989866i | \(-0.454646\pi\) | ||||
0.142003 | + | 0.989866i | \(0.454646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 162.879i | 1.15517i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.6088 | + | 14.2079i | −0.172089 | + | 0.0993559i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 132.222 | + | 76.3382i | 0.911873 | + | 0.526470i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 139.586 | + | 130.256i | 0.949564 | + | 0.886097i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 82.0846 | + | 47.3916i | 0.550903 | + | 0.318064i | 0.749486 | − | 0.662020i | \(-0.230301\pi\) |
−0.198583 | + | 0.980084i | \(0.563634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 33.2843 | + | 57.6501i | 0.220426 | + | 0.381789i | 0.954937 | − | 0.296807i | \(-0.0959220\pi\) |
−0.734511 | + | 0.678596i | \(0.762589\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 64.7511i | − | 0.423210i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 267.826i | 1.72791i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7597 | − | 22.1004i | −0.0812720 | − | 0.140767i | 0.822525 | − | 0.568730i | \(-0.192565\pi\) |
−0.903797 | + | 0.427962i | \(0.859232\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.6353 | − | 12.4912i | −0.136071 | − | 0.0785608i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.1380 | + | 84.0830i | −0.205826 | + | 0.522255i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −166.364 | − | 96.0504i | −1.02064 | − | 0.589267i | −0.106350 | − | 0.994329i | \(-0.533917\pi\) |
−0.914289 | + | 0.405062i | \(0.867250\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −108.998 | + | 62.9301i | −0.660594 | + | 0.381394i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 184.150i | − | 1.10269i | −0.834276 | − | 0.551346i | \(-0.814114\pi\) | ||
0.834276 | − | 0.551346i | \(-0.185886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −108.257 | −0.640574 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −33.3349 | − | 57.7377i | −0.194941 | − | 0.337647i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −34.9519 | + | 60.5384i | −0.202034 | + | 0.349933i | −0.949184 | − | 0.314723i | \(-0.898088\pi\) |
0.747150 | + | 0.664656i | \(0.231422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −233.056 | − | 293.095i | −1.33175 | − | 1.67483i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −31.0049 | + | 53.7021i | −0.175169 | + | 0.303401i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 207.251 | − | 119.657i | 1.15783 | − | 0.668473i | 0.207047 | − | 0.978331i | \(-0.433615\pi\) |
0.950783 | + | 0.309858i | \(0.100281\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 36.2834 | 0.200461 | 0.100230 | − | 0.994964i | \(-0.468042\pi\) | ||||
0.100230 | + | 0.994964i | \(0.468042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −47.3678 | −0.258840 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −303.720 | + | 175.353i | −1.64173 | + | 0.947852i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.0955 | + | 33.0744i | −0.102115 | + | 0.176868i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 76.0292 | − | 11.3492i | 0.402271 | − | 0.0600487i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −162.622 | + | 281.669i | −0.851422 | + | 1.47471i | 0.0285024 | + | 0.999594i | \(0.490926\pi\) |
−0.879925 | + | 0.475113i | \(0.842407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −99.8198 | − | 172.893i | −0.517201 | − | 0.895818i | −0.999800 | − | 0.0199772i | \(-0.993641\pi\) |
0.482599 | − | 0.875841i | \(-0.339693\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 269.045 | 1.37972 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.5053i | − | 0.0787071i | −0.999225 | − | 0.0393536i | \(-0.987470\pi\) | ||
0.999225 | − | 0.0393536i | \(-0.0125299\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 48.6375 | − | 28.0809i | 0.244409 | − | 0.141110i | −0.372792 | − | 0.927915i | \(-0.621600\pi\) |
0.617202 | + | 0.786805i | \(0.288266\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.3110 | − | 15.1907i | −0.130901 | − | 0.0755756i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.8094 | − | 119.307i | −0.0877312 | − | 0.587719i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −565.326 | − | 326.391i | −2.75769 | − | 1.59215i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −39.9052 | − | 69.1178i | −0.192779 | − | 0.333903i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 39.3226i | 0.188147i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 370.470i | − | 1.75578i | −0.478859 | − | 0.877892i | \(-0.658949\pi\) | ||
0.478859 | − | 0.877892i | \(-0.341051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 80.5819 | + | 139.572i | 0.378319 | + | 0.655267i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 313.431 | + | 180.960i | 1.45782 | + | 0.841673i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 165.629 | − | 131.700i | 0.763266 | − | 0.606914i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 302.372 | + | 174.574i | 1.38069 | + | 0.797143i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 70.7014 | − | 40.8195i | 0.319916 | − | 0.184704i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.78533i | − | 0.0304275i | −0.999884 | − | 0.0152137i | \(-0.995157\pi\) | ||
0.999884 | − | 0.0152137i | \(-0.00484287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 330.677 | 1.46968 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −148.309 | − | 256.879i | −0.653344 | − | 1.13163i | −0.982306 | − | 0.187282i | \(-0.940032\pi\) |
0.328962 | − | 0.944343i | \(-0.393301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 89.0964 | − | 154.320i | 0.389067 | − | 0.673885i | −0.603257 | − | 0.797547i | \(-0.706131\pi\) |
0.992324 | + | 0.123662i | \(0.0394640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 92.5158 | + | 36.4614i | 0.400501 | + | 0.157842i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −58.9011 | + | 102.020i | −0.252795 | + | 0.437853i | −0.964294 | − | 0.264833i | \(-0.914683\pi\) |
0.711500 | + | 0.702687i | \(0.248016\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −320.743 | + | 185.181i | −1.36486 | + | 0.788004i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 275.842 | 1.16389 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −46.3543 | −0.193951 | −0.0969755 | − | 0.995287i | \(-0.530917\pi\) | ||||
−0.0969755 | + | 0.995287i | \(0.530917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 317.501 | − | 183.309i | 1.31743 | − | 0.760619i | 0.334115 | − | 0.942532i | \(-0.391562\pi\) |
0.983315 | + | 0.181914i | \(0.0582291\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −142.327 | + | 246.517i | −0.585706 | + | 1.01447i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −97.8032 | + | 422.965i | −0.399197 | + | 1.72639i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.0290 | − | 72.7964i | 0.170158 | − | 0.294722i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 118.580 | + | 205.387i | 0.476226 | + | 0.824847i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −129.896 | −0.517513 | −0.258756 | − | 0.965943i | \(-0.583313\pi\) | ||||
−0.258756 | + | 0.965943i | \(0.583313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 47.0732i | 0.186060i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 313.153 | − | 180.799i | 1.22805 | − | 0.709016i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 232.394 | + | 134.173i | 0.904256 | + | 0.522073i | 0.878579 | − | 0.477598i | \(-0.158492\pi\) |
0.0256776 | + | 0.999670i | \(0.491826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 257.792 | + | 101.599i | 0.995337 | + | 0.392272i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 92.2532 | + | 53.2624i | 0.353460 | + | 0.204070i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −117.691 | − | 203.847i | −0.447495 | − | 0.775085i | 0.550727 | − | 0.834685i | \(-0.314351\pi\) |
−0.998222 | + | 0.0596008i | \(0.981017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 56.8059i | − | 0.214362i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 105.281i | − | 0.394311i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −177.348 | − | 307.175i | −0.659285 | − | 1.14192i | −0.980801 | − | 0.195011i | \(-0.937526\pi\) |
0.321516 | − | 0.946904i | \(-0.395808\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 365.350 | + | 210.935i | 1.34816 | + | 0.778358i | 0.987988 | − | 0.154529i | \(-0.0493861\pi\) |
0.360168 | + | 0.932888i | \(0.382719\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −132.300 | − | 166.383i | −0.484615 | − | 0.609461i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −168.907 | − | 97.5186i | −0.614208 | − | 0.354613i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 319.155 | − | 184.264i | 1.15218 | − | 0.665214i | 0.202766 | − | 0.979227i | \(-0.435007\pi\) |
0.949419 | + | 0.314013i | \(0.101674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 186.866i | 0.669772i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −35.2868 | −0.125576 | −0.0627879 | − | 0.998027i | \(-0.519999\pi\) | ||||
−0.0627879 | + | 0.998027i | \(0.519999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −98.3087 | − | 170.276i | −0.347380 | − | 0.601681i | 0.638403 | − | 0.769702i | \(-0.279595\pi\) |
−0.985783 | + | 0.168022i | \(0.946262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 186.156 | − | 322.432i | 0.653180 | − | 1.13134i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 76.1460 | + | 510.108i | 0.265317 | + | 1.77738i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −89.6384 | + | 155.258i | −0.310167 | + | 0.537226i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.0209 | − | 6.36291i | 0.0378724 | − | 0.0218657i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −317.573 | −1.08387 | −0.541933 | − | 0.840421i | \(-0.682307\pi\) | ||||
−0.541933 | + | 0.840421i | \(0.682307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −141.001 | −0.477968 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 34.6745 | − | 20.0193i | 0.116749 | − | 0.0674051i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 50.3130 | − | 87.1447i | 0.168271 | − | 0.291454i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −42.2173 | − | 282.817i | −0.140257 | − | 0.939591i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 268.292 | − | 464.695i | 0.885451 | − | 1.53365i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −53.8535 | − | 93.2769i | −0.176569 | − | 0.305826i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −132.193 | −0.430596 | −0.215298 | − | 0.976548i | \(-0.569072\pi\) | ||||
−0.215298 | + | 0.976548i | \(0.569072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 388.383i | − | 1.25690i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −400.453 | + | 231.202i | −1.28763 | + | 0.743414i | −0.978231 | − | 0.207518i | \(-0.933462\pi\) |
−0.309400 | + | 0.950932i | \(0.600128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −490.206 | − | 283.021i | −1.56615 | − | 0.904220i | −0.996611 | − | 0.0822589i | \(-0.973787\pi\) |
−0.569544 | − | 0.821961i | \(-0.692880\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −238.599 | − | 300.067i | −0.757458 | − | 0.952594i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 153.315 | + | 88.5163i | 0.483643 | + | 0.279231i | 0.721933 | − | 0.691963i | \(-0.243254\pi\) |
−0.238291 | + | 0.971194i | \(0.576587\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.4148 | − | 54.4120i | −0.0984790 | − | 0.170571i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 366.299i | 1.14112i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 112.975i | − | 0.349766i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 208.461 | + | 361.065i | 0.641418 | + | 1.11097i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −661.199 | − | 381.743i | −2.02201 | − | 1.16741i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 272.241 | + | 107.293i | 0.827481 | + | 0.326119i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 429.688 | + | 248.080i | 1.29815 | + | 0.749487i | 0.980084 | − | 0.198582i | \(-0.0636335\pi\) |
0.318065 | + | 0.948069i | \(0.396967\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −211.910 | + | 122.346i | −0.636367 | + | 0.367406i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 69.0825i | − | 0.206216i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −206.191 | −0.611843 | −0.305922 | − | 0.952057i | \(-0.598965\pi\) | ||||
−0.305922 | + | 0.952057i | \(0.598965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 198.466 | + | 343.752i | 0.585444 | + | 1.01402i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.1080 | − | 95.4499i | 0.161607 | − | 0.279912i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 309.663 | − | 147.505i | 0.902809 | − | 0.430043i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 222.848 | − | 385.984i | 0.645936 | − | 1.11879i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 524.976 | − | 303.095i | 1.51290 | − | 0.873472i | 0.513013 | − | 0.858381i | \(-0.328529\pi\) |
0.999886 | − | 0.0150913i | \(-0.00480389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −136.343 | −0.390669 | −0.195335 | − | 0.980737i | \(-0.562579\pi\) | ||||
−0.195335 | + | 0.980737i | \(0.562579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −85.5887 | −0.243842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.72457 | + | 5.03713i | −0.0247155 | + | 0.0142695i | −0.512307 | − | 0.858802i | \(-0.671209\pi\) |
0.487591 | + | 0.873072i | \(0.337876\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −183.231 | + | 317.365i | −0.516143 | + | 0.893985i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −265.799 | − | 104.754i | −0.744536 | − | 0.293429i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 197.808 | − | 342.613i | 0.550997 | − | 0.954354i | −0.447206 | − | 0.894431i | \(-0.647581\pi\) |
0.998203 | − | 0.0599236i | \(-0.0190857\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 122.339 | + | 211.897i | 0.338889 | + | 0.586973i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −419.664 | −1.15610 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 793.909i | 2.17509i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −164.486 | + | 94.9661i | −0.448191 | + | 0.258763i | −0.707066 | − | 0.707148i | \(-0.749982\pi\) |
0.258875 | + | 0.965911i | \(0.416648\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −394.438 | − | 227.729i | −1.06894 | − | 0.617151i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.1299 | + | 27.9337i | −0.0946898 | + | 0.0752930i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 311.859 | + | 180.052i | 0.836083 | + | 0.482713i | 0.855931 | − | 0.517090i | \(-0.172985\pi\) |
−0.0198479 | + | 0.999803i | \(0.506318\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 491.816 | + | 851.850i | 1.31151 | + | 2.27160i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 134.308i | 0.356254i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2929i | 0.0297966i | 0.999889 | + | 0.0148983i | \(0.00474246\pi\) | ||||
−0.999889 | + | 0.0148983i | \(0.995258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 270.950 | + | 469.299i | 0.711154 | + | 1.23176i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −376.075 | − | 217.127i | −0.981918 | − | 0.566910i | −0.0790692 | − | 0.996869i | \(-0.525195\pi\) |
−0.902849 | + | 0.429959i | \(0.858528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33.3831 | + | 223.636i | 0.0867095 | + | 0.580874i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 218.686 | + | 126.258i | 0.565080 | + | 0.326249i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −37.3803 | + | 21.5816i | −0.0960934 | + | 0.0554796i | −0.547277 | − | 0.836952i | \(-0.684335\pi\) |
0.451183 | + | 0.892431i | \(0.351002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 135.242i | − | 0.345887i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −357.315 | −0.909199 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 313.611 | + | 543.190i | 0.793952 | + | 1.37517i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −243.395 | + | 421.573i | −0.613086 | + | 1.06190i | 0.377631 | + | 0.925956i | \(0.376739\pi\) |
−0.990717 | + | 0.135940i | \(0.956595\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −290.939 | + | 43.4297i | −0.729170 | + | 0.108846i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 273.457 | − | 473.641i | 0.681938 | − | 1.18115i | −0.292451 | − | 0.956280i | \(-0.594471\pi\) |
0.974389 | − | 0.224870i | \(-0.0721958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −204.039 | + | 117.802i | −0.506299 | + | 0.292312i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −871.992 | −2.15307 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 144.323 | 0.354601 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 57.8217 | − | 33.3834i | 0.141373 | − | 0.0816220i | −0.427645 | − | 0.903947i | \(-0.640657\pi\) |
0.569018 | + | 0.822325i | \(0.307323\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 388.819 | − | 673.453i | 0.946030 | − | 1.63857i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 69.3354 | + | 87.1976i | 0.167882 | + | 0.211132i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −269.633 | + | 467.018i | −0.649718 | + | 1.12534i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 76.9077 | + | 133.208i | 0.184431 | + | 0.319444i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −550.169 | −1.31305 | −0.656527 | − | 0.754303i | \(-0.727975\pi\) | ||||
−0.656527 | + | 0.754303i | \(0.727975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 579.599i | − | 1.37672i | −0.725369 | − | 0.688360i | \(-0.758331\pi\) | ||
0.725369 | − | 0.688360i | \(-0.241669\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −223.788 | + | 129.204i | −0.529049 | + | 0.305446i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 485.273 | + | 280.173i | 1.14182 | + | 0.659230i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.2025 | + | 79.1719i | −0.0730737 | + | 0.185414i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −95.8845 | − | 55.3589i | −0.223507 | − | 0.129042i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −215.935 | − | 374.010i | −0.501009 | − | 0.867773i | −0.999999 | − | 0.00116534i | \(-0.999629\pi\) |
0.498990 | − | 0.866607i | \(-0.333704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.143463i | 0.000331322i | 1.00000 | 0.000165661i | \(5.27316e-5\pi\) | |||||
−1.00000 | 0.000165661i | \(0.999947\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 594.881i | 1.36754i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −69.6247 | − | 120.593i | −0.159324 | − | 0.275958i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 165.713 | + | 95.6744i | 0.377478 | + | 0.217937i | 0.676721 | − | 0.736240i | \(-0.263401\pi\) |
−0.299242 | + | 0.954177i | \(0.596734\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −68.2389 | + | 295.109i | −0.154737 | + | 0.669182i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −340.782 | − | 196.751i | −0.769260 | − | 0.444133i | 0.0633505 | − | 0.997991i | \(-0.479821\pi\) |
−0.832611 | + | 0.553859i | \(0.813155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 207.320 | − | 119.696i | 0.465888 | − | 0.268981i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 369.308i | 0.826193i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −725.831 | −1.61655 | −0.808275 | − | 0.588805i | \(-0.799598\pi\) | ||||
−0.808275 | + | 0.588805i | \(0.799598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 134.317 | + | 232.644i | 0.297821 | + | 0.515841i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −129.687 | + | 224.625i | −0.286286 | + | 0.495861i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 177.227 | − | 449.690i | 0.389511 | − | 0.988330i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.6713 | − | 60.0525i | 0.0758673 | − | 0.131406i | −0.825596 | − | 0.564262i | \(-0.809161\pi\) |
0.901463 | + | 0.432856i | \(0.142494\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −99.6203 | + | 57.5158i | −0.217038 | + | 0.125307i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 768.006 | 1.66596 | 0.832978 | − | 0.553306i | \(-0.186634\pi\) | ||||
0.832978 | + | 0.553306i | \(0.186634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −215.717 | −0.465911 | −0.232956 | − | 0.972487i | \(-0.574840\pi\) | ||||
−0.232956 | + | 0.972487i | \(0.574840\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −903.734 | + | 521.771i | −1.94351 | + | 1.12209i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.4688 | + | 25.0607i | −0.0309824 | + | 0.0536631i | −0.881101 | − | 0.472928i | \(-0.843197\pi\) |
0.850118 | + | 0.526592i | \(0.176530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.7220 | + | 33.9705i | −0.0910917 | + | 0.0724319i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 49.7163 | − | 86.1111i | 0.105555 | − | 0.182826i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −74.4688 | − | 128.984i | −0.157439 | − | 0.272693i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 576.949 | 1.21463 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 39.6344i | − | 0.0830911i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 695.377 | − | 401.476i | 1.45173 | − | 0.838154i | 0.453146 | − | 0.891436i | \(-0.350302\pi\) |
0.998580 | + | 0.0532818i | \(0.0169682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −267.179 | − | 154.256i | −0.555466 | − | 0.320698i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −348.283 | + | 51.9897i | −0.721083 | + | 0.107639i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.0598 | + | 14.4683i | 0.0516696 | + | 0.0298315i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.96197 | + | 17.2546i | 0.0204558 | + | 0.0354305i | 0.876072 | − | 0.482180i | \(-0.160155\pi\) |
−0.855616 | + | 0.517611i | \(0.826822\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 748.493i | − | 1.53066i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 76.2017i | 0.155197i | 0.996985 | + | 0.0775985i | \(0.0247252\pi\) | ||||
−0.996985 | + | 0.0775985i | \(0.975275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 90.2552 | + | 156.327i | 0.183073 | + | 0.317093i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −172.925 | − | 99.8384i | −0.349344 | − | 0.201694i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 286.366 | − | 42.7471i | 0.576190 | − | 0.0860102i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −452.819 | − | 261.435i | −0.907454 | − | 0.523919i | −0.0278428 | − | 0.999612i | \(-0.508864\pi\) |
−0.879611 | + | 0.475694i | \(0.842197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 621.384 | − | 358.756i | 1.24029 | − | 0.716080i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 132.060i | − | 0.262545i | −0.991346 | − | 0.131273i | \(-0.958094\pi\) | ||
0.991346 | − | 0.131273i | \(-0.0419064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1220.11 | 2.41605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −210.904 | − | 365.296i | −0.415983 | − | 0.720504i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −155.079 | + | 268.604i | −0.304673 | + | 0.527709i | −0.977189 | − | 0.212374i | \(-0.931881\pi\) |
0.672515 | + | 0.740083i | \(0.265214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 490.969 | − | 390.396i | 0.960801 | − | 0.763984i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −59.2201 | + | 102.572i | −0.115439 | + | 0.199946i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 764.806 | − | 441.561i | 1.48506 | − | 0.857400i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 152.412 | 0.294801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −272.369 | −0.524797 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 52.9121 | − | 30.5488i | 0.101559 | − | 0.0586349i | −0.448360 | − | 0.893853i | \(-0.647992\pi\) |
0.549919 | + | 0.835218i | \(0.314659\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −256.923 | + | 445.004i | −0.491249 | + | 0.850868i | −0.999949 | − | 0.0100759i | \(-0.996793\pi\) |
0.508701 | + | 0.860944i | \(0.330126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 534.969 | − | 1357.41i | 1.01899 | − | 2.58554i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −158.326 | + | 274.229i | −0.300429 | + | 0.520359i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 181.152 | + | 313.765i | 0.342443 | + | 0.593128i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −98.3784 | −0.185270 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 574.246i | − | 1.07739i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −721.318 | + | 416.453i | −1.34826 | + | 0.778417i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 807.525 | + | 466.225i | 1.50377 | + | 0.868202i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 121.885 | − | 130.616i | 0.226133 | − | 0.242329i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −92.7322 | − | 53.5390i | −0.171409 | − | 0.0989630i | 0.411841 | − | 0.911256i | \(-0.364886\pi\) |
−0.583250 | + | 0.812293i | \(0.698219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 70.6863 | + | 122.432i | 0.130177 | + | 0.225474i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1736.05i | − | 3.18541i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.3240i | − | 0.0792030i | −0.999216 | − | 0.0396015i | \(-0.987391\pi\) | ||
0.999216 | − | 0.0396015i | \(-0.0126088\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −37.5744 | − | 65.0808i | −0.0684416 | − | 0.118544i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 160.959 | + | 92.9296i | 0.292121 | + | 0.168656i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 181.705 | − | 461.051i | 0.328581 | − | 0.833727i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1183.40 | − | 683.235i | −2.13225 | − | 1.23105i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −62.7878 | + | 36.2506i | −0.112725 | + | 0.0650818i | −0.555302 | − | 0.831648i | \(-0.687397\pi\) |
0.442577 | + | 0.896730i | \(0.354064\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 318.377i | 0.569547i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −148.805 | −0.265250 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 292.471 | + | 506.575i | 0.519487 | + | 0.899779i | 0.999743 | + | 0.0226503i | \(0.00721043\pi\) |
−0.480256 | + | 0.877128i | \(0.659456\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −451.280 | + | 781.639i | −0.798725 | + | 1.38343i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 428.792 | + | 539.257i | 0.756247 | + | 0.951071i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −371.765 | + | 643.915i | −0.653365 | + | 1.13166i | 0.328936 | + | 0.944352i | \(0.393310\pi\) |
−0.982301 | + | 0.187309i | \(0.940023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 893.793 | − | 516.031i | 1.56531 | − | 0.903733i | 0.568607 | − | 0.822609i | \(-0.307483\pi\) |
0.996704 | − | 0.0811234i | \(-0.0258508\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1267.26 | −2.21163 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 690.666 | 1.20116 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −825.404 | + | 476.547i | −1.43051 | + | 0.825905i | −0.997159 | − | 0.0753213i | \(-0.976002\pi\) |
−0.433350 | + | 0.901226i | \(0.642668\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 388.933 | − | 673.652i | 0.671732 | − | 1.16347i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 421.402 | − | 62.9044i | 0.725305 | − | 0.108269i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.6884 | + | 20.2450i | −0.0200488 | + | 0.0347255i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 213.420 | + | 369.654i | 0.364820 | + | 0.631887i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −96.2876 | −0.164033 | −0.0820167 | − | 0.996631i | \(-0.526136\pi\) | ||||
−0.0820167 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 326.035i | 0.553540i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 52.3201 | − | 30.2071i | 0.0885282 | − | 0.0511118i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.1840 | + | 25.5096i | 0.0745092 | + | 0.0430179i | 0.536792 | − | 0.843715i | \(-0.319636\pi\) |
−0.462283 | + | 0.886733i | \(0.652969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −95.9103 | − | 642.511i | −0.161194 | − | 1.07985i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 189.509 | + | 109.413i | 0.317435 | + | 0.183271i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 451.118 | + | 781.359i | 0.753119 | + | 1.30444i | 0.946304 | + | 0.323277i | \(0.104785\pi\) |
−0.193186 | + | 0.981162i | \(0.561882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 903.595i | 1.50349i | 0.659456 | + | 0.751743i | \(0.270787\pi\) | ||||
−0.659456 | + | 0.751743i | \(0.729213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 48.2000i | − | 0.0799337i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −477.125 | − | 826.406i | −0.788637 | − | 1.36596i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 306.928 | + | 177.205i | 0.505648 | + | 0.291936i | 0.731043 | − | 0.682332i | \(-0.239034\pi\) |
−0.225395 | + | 0.974267i | \(0.572367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 367.886 | − | 292.526i | 0.604082 | − | 0.480338i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −282.154 | − | 162.902i | −0.461791 | − | 0.266615i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 290.984 | − | 168.000i | 0.474688 | − | 0.274061i | −0.243512 | − | 0.969898i | \(-0.578300\pi\) |
0.718200 | + | 0.695837i | \(0.244966\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 2543.47i | − | 4.13573i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 223.359 | 0.362008 | 0.181004 | − | 0.983482i | \(-0.442065\pi\) | ||||
0.181004 | + | 0.983482i | \(0.442065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 363.026 | + | 628.780i | 0.586472 | + | 1.01580i | 0.994690 | + | 0.102915i | \(0.0328170\pi\) |
−0.408218 | + | 0.912885i | \(0.633850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −70.8925 | + | 122.789i | −0.114159 | + | 0.197728i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −175.970 | − | 69.3516i | −0.282456 | − | 0.111319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −449.635 | + | 778.791i | −0.719416 | + | 1.24607i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −132.688 | + | 76.6074i | −0.211623 | + | 0.122181i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −414.642 | −0.659208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 326.157 | 0.516888 | 0.258444 | − | 0.966026i | \(-0.416790\pi\) | ||||
0.258444 | + | 0.966026i | \(0.416790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1250.09 | − | 721.741i | 1.97487 | − | 1.14019i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −616.097 | + | 1067.11i | −0.970232 | + | 1.68049i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −365.247 | + | 111.529i | −0.573386 | + | 0.175085i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −127.843 | + | 221.431i | −0.200067 | + | 0.346527i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 299.187 | + | 518.208i | 0.466751 | + | 0.808436i | 0.999279 | − | 0.0379764i | \(-0.0120912\pi\) |
−0.532528 | + | 0.846413i | \(0.678758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1008.20 | 1.56796 | 0.783979 | − | 0.620787i | \(-0.213187\pi\) | ||||
0.783979 | + | 0.620787i | \(0.213187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1410.16i | 2.18630i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −574.378 | + | 331.617i | −0.887756 | + | 0.512546i | −0.873208 | − | 0.487348i | \(-0.837964\pi\) |
−0.0145481 | + | 0.999894i | \(0.504631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.2509 | + | 29.0124i | 0.0774283 | + | 0.0447032i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 767.075 | + | 302.312i | 1.17830 | + | 0.464381i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −857.892 | − | 495.304i | −1.31377 | − | 0.758506i | −0.331052 | − | 0.943612i | \(-0.607404\pi\) |
−0.982718 | + | 0.185107i | \(0.940737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −406.240 | − | 703.628i | −0.620213 | − | 1.07424i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 553.924i | 0.843110i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 82.2318i | 0.124783i | 0.998052 | + | 0.0623914i | \(0.0198727\pi\) | ||||
−0.998052 | + | 0.0623914i | \(0.980127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 313.110 | + | 542.322i | 0.473691 | + | 0.820457i | 0.999546 | − | 0.0301171i | \(-0.00958802\pi\) |
−0.525855 | + | 0.850574i | \(0.676255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 275.478 | + | 159.047i | 0.415502 | + | 0.239890i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −416.297 | − | 523.543i | −0.626010 | − | 0.787282i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 192.684 | + | 111.246i | 0.288882 | + | 0.166786i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.8960 | − | 13.2190i | 0.0342242 | − | 0.0197594i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.3237i | 0.0660562i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −150.211 | −0.223196 | −0.111598 | − | 0.993753i | \(-0.535597\pi\) | ||||
−0.111598 | + | 0.993753i | \(0.535597\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −293.727 | − | 508.751i | −0.435152 | − | 0.753705i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 278.207 | − | 481.869i | 0.410941 | − | 0.711771i | −0.584052 | − | 0.811716i | \(-0.698533\pi\) |
0.994993 | + | 0.0999455i | \(0.0318668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.37540 | − | 22.6121i | −0.00497113 | − | 0.0333020i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 577.865 | − | 1000.89i | 0.848553 | − | 1.46974i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −685.334 | + | 395.678i | −1.00342 | + | 0.579323i | −0.909258 | − | 0.416234i | \(-0.863350\pi\) |
−0.0941597 | + | 0.995557i | \(0.530016\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1768.22 | 2.58135 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 694.302 | 1.01063 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.2767 | − | 24.9858i | 0.0628109 | − | 0.0362639i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 488.267 | − | 845.703i | 0.706609 | − | 1.22388i | −0.259499 | − | 0.965743i | \(-0.583557\pi\) |
0.966108 | − | 0.258139i | \(-0.0831093\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.2920 | + | 156.035i | 0.0336103 | + | 0.225158i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −174.876 | + | 302.894i | −0.251620 | + | 0.435819i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −385.895 | − | 668.390i | −0.553652 | − | 0.958953i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −458.999 | −0.656651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 855.098i | − | 1.21983i | −0.792468 | − | 0.609913i | \(-0.791204\pi\) | ||
0.792468 | − | 0.609913i | \(-0.208796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −369.730 | + | 213.464i | −0.525932 | + | 0.303647i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1249.73 | − | 721.530i | −1.77266 | − | 1.02345i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −599.974 | − | 754.538i | −0.848619 | − | 1.06724i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 288.794 | + | 166.735i | 0.407326 | + | 0.235170i | 0.689640 | − | 0.724152i | \(-0.257769\pi\) |
−0.282314 | + | 0.959322i | \(0.591102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 218.812 | + | 378.993i | 0.307752 | + | 0.533042i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 390.297i | 0.547401i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 251.755i | − | 0.352105i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −90.3063 | − | 156.415i | −0.125950 | − | 0.218152i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.4877 | + | 19.9115i | 0.0479662 | + | 0.0276933i | 0.523791 | − | 0.851847i | \(-0.324517\pi\) |
−0.475825 | + | 0.879540i | \(0.657850\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −649.155 | − | 255.839i | −0.900354 | − | 0.354839i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1237.09 | + | 714.237i | 1.71106 | + | 0.987879i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −798.344 | + | 460.924i | −1.10116 | + | 0.635757i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 489.402i | 0.673180i | 0.941651 | + | 0.336590i | \(0.109274\pi\) | ||||
−0.941651 | + | 0.336590i | \(0.890726\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −223.307 | −0.306320 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 213.950 | + | 370.572i | 0.292681 | + | 0.506939i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −89.1592 | + | 154.428i | −0.121636 | + | 0.210680i | −0.920413 | − | 0.390948i | \(-0.872147\pi\) |
0.798777 | + | 0.601627i | \(0.205481\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1617.76 | + | 493.988i | −2.20104 | + | 0.672093i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.2145 | + | 24.6202i | −0.0192869 | + | 0.0334060i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −764.182 | + | 441.200i | −1.03408 | + | 0.597024i | −0.918149 | − | 0.396234i | \(-0.870317\pi\) |
−0.115926 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 327.520 | 0.441997 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1404.00 | −1.88964 | −0.944819 | − | 0.327591i | \(-0.893763\pi\) | ||||
−0.944819 | + | 0.327591i | \(0.893763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −727.244 | + | 419.875i | −0.976167 | + | 0.563590i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −188.127 | + | 325.846i | −0.251844 | + | 0.436206i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 612.243 | + | 241.291i | 0.817414 | + | 0.322151i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 102.840 | − | 178.124i | 0.136938 | − | 0.237183i | −0.789398 | − | 0.613881i | \(-0.789607\pi\) |
0.926336 | + | 0.376698i | \(0.122941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −253.060 | − | 438.312i | −0.336069 | − | 0.582088i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −589.777 | −0.781162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 15.0345i | − | 0.0198606i | −0.999951 | − | 0.00993032i | \(-0.996839\pi\) | ||
0.999951 | − | 0.00993032i | \(-0.00316097\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −158.841 | + | 91.7068i | −0.209276 | + | 0.120826i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −544.290 | − | 314.246i | −0.715229 | − | 0.412938i | 0.0977649 | − | 0.995210i | \(-0.468831\pi\) |
−0.812994 | + | 0.582272i | \(0.802164\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1073.61 | + | 853.682i | −1.40709 | + | 1.11885i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 496.817 | + | 286.837i | 0.649434 | + | 0.374951i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −62.0184 | − | 107.419i | −0.0808584 | − | 0.140051i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 442.918i | 0.575967i | 0.957635 | + | 0.287983i | \(0.0929848\pi\) | ||||
−0.957635 | + | 0.287983i | \(0.907015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1045.57i | 1.35612i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 84.5990 | + | 146.530i | 0.109442 | + | 0.189560i | 0.915545 | − | 0.402217i | \(-0.131760\pi\) |
−0.806102 | + | 0.591777i | \(0.798427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1400.46 | − | 808.555i | −1.80704 | − | 1.04330i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 159.396 | + | 1067.81i | 0.205143 | + | 1.37427i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −688.196 | − | 397.330i | −0.883435 | − | 0.510051i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 130.602 | − | 75.4034i | 0.167225 | − | 0.0965472i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 189.244i | − | 0.241690i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 226.094 | 0.288018 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.2437 | − | 40.2593i | −0.0295346 | − | 0.0511554i | 0.850880 | − | 0.525360i | \(-0.176069\pi\) |
−0.880415 | + | 0.474204i | \(0.842736\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 458.567 | − | 794.261i | 0.581200 | − | 1.00667i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 705.293 | − | 105.282i | 0.891647 | − | 0.133100i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.3743 | − | 82.0548i | 0.0597407 | − | 0.103474i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 191.683 | − | 110.668i | 0.241110 | − | 0.139205i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1351.86 | −1.69618 | −0.848092 | − | 0.529850i | \(-0.822248\pi\) | ||||
−0.848092 | + | 0.529850i | \(0.822248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −437.882 | −0.548038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 144.651 | − | 83.5141i | 0.180588 | − | 0.104262i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 163.355 | − | 282.940i | 0.203431 | − | 0.352354i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −498.349 | − | 626.733i | −0.619067 | − | 0.778551i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 691.009 | − | 1196.86i | 0.856269 | − | 1.48310i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 701.563 | + | 1215.14i | 0.867198 | + | 1.50203i | 0.864848 | + | 0.502034i | \(0.167415\pi\) |
0.00235012 | + | 0.999997i | \(0.499252\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 689.037 | 0.849614 | 0.424807 | − | 0.905284i | \(-0.360342\pi\) | ||||
0.424807 | + | 0.905284i | \(0.360342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1643.75i | 2.02184i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1473.94 | − | 850.977i | 1.80851 | − | 1.04414i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 381.553 | + | 220.290i | 0.467017 | + | 0.269632i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 123.655 | − | 313.756i | 0.150982 | − | 0.383097i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.3490 | + | 11.1711i | 0.0235675 | + | 0.0136067i | 0.511737 | − | 0.859142i | \(-0.329002\pi\) |
−0.488170 | + | 0.872749i | \(0.662335\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 512.111 | + | 887.003i | 0.622249 | + | 1.07777i | 0.989066 | + | 0.147474i | \(0.0471144\pi\) |
−0.366816 | + | 0.930293i | \(0.619552\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 759.934i | − | 0.921132i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 466.377i | 0.563938i | 0.959424 | + | 0.281969i | \(0.0909875\pi\) | ||||
−0.959424 | + | 0.281969i | \(0.909012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 750.350 | + | 1299.64i | 0.905126 | + | 1.56773i | 0.820747 | + | 0.571291i | \(0.193557\pi\) |
0.0843791 | + | 0.996434i | \(0.473109\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1243.54 | + | 717.958i | 1.49644 | + | 0.863969i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −350.179 | + | 375.260i | −0.420383 | + | 0.450493i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1412.93 | + | 815.755i | 1.69213 | + | 0.976952i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 287.496 | − | 165.986i | 0.343484 | − | 0.198311i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1068.18i | 1.27316i | 0.771212 | + | 0.636579i | \(0.219651\pi\) | ||||
−0.771212 | + | 0.636579i | \(0.780349\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 544.034 | 0.646890 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −68.7449 | − | 119.070i | −0.0815479 | − | 0.141245i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 479.562 | − | 830.625i | 0.567529 | − | 0.982988i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −276.445 | + | 701.440i | −0.326381 | + | 0.828146i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 383.045 | − | 663.453i | 0.451172 | − | 0.781453i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −442.605 | + | 255.538i | −0.520100 | + | 0.300280i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −918.640 | −1.07695 | −0.538476 | − | 0.842641i | \(-0.681000\pi\) | ||||
−0.538476 | + | 0.842641i | \(0.681000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 590.673 | 0.690846 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −438.167 | + | 252.976i | −0.511280 | + | 0.295188i | −0.733360 | − | 0.679841i | \(-0.762049\pi\) |
0.222080 | + | 0.975029i | \(0.428716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −688.516 | + | 1192.54i | −0.801532 | + | 1.38829i | 0.117075 | + | 0.993123i | \(0.462648\pi\) |
−0.918607 | + | 0.395171i | \(0.870685\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1572.93 | + | 1250.72i | −1.82687 | + | 1.45264i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 458.817 | − | 794.695i | 0.531654 | − | 0.920852i | −0.467663 | − | 0.883907i | \(-0.654904\pi\) |
0.999317 | − | 0.0369450i | \(-0.0117626\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −309.663 | − | 536.352i | −0.357992 | − | 0.620060i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −698.525 | −0.805681 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 258.116i | − | 0.297026i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.6294 | − | 30.3856i | 0.0604241 | − | 0.0348859i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.4846 | + | 10.0947i | 0.0200282 | + | 0.0115633i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1747.78 | − | 260.898i | 1.99746 | − | 0.298170i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 606.173 | + | 349.974i | 0.691189 | + | 0.399058i | 0.804057 | − | 0.594552i | \(-0.202671\pi\) |
−0.112868 | + | 0.993610i | \(0.536004\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −618.688 | − | 1071.60i | −0.703854 | − | 1.21911i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.37652i | − | 0.00723783i | −0.999993 | − | 0.00361891i | \(-0.998848\pi\) | ||
0.999993 | − | 0.00361891i | \(-0.00115194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1548.35i | − | 1.75351i | −0.480935 | − | 0.876756i | \(-0.659703\pi\) | ||
0.480935 | − | 0.876756i | \(-0.340297\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −274.694 | − | 475.784i | −0.310389 | − | 0.537609i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −634.250 | − | 366.185i | −0.715051 | − | 0.412835i | 0.0978774 | − | 0.995198i | \(-0.468795\pi\) |
−0.812928 | + | 0.582364i | \(0.802128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 962.882 | − | 143.733i | 1.08311 | − | 0.161680i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 310.768 | + | 179.422i | 0.348785 | + | 0.201371i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −390.454 | + | 225.429i | −0.437238 | + | 0.252440i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2120.24i | 2.36899i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 392.074 | 0.437095 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −260.469 | − | 451.146i | −0.289732 | − | 0.501831i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.5811 | − | 58.1641i | 0.0372709 | − | 0.0645551i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 872.074 | − | 693.433i | 0.965752 | − | 0.767921i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −160.730 | + | 278.392i | −0.177602 | + | 0.307615i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 626.862 | − | 361.919i | 0.691138 | − | 0.399029i | −0.112900 | − | 0.993606i | \(-0.536014\pi\) |
0.804038 | + | 0.594578i | \(0.202681\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 851.288 | 0.936511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1600.04 | −1.75636 | −0.878179 | − | 0.478332i | \(-0.841242\pi\) | ||||
−0.878179 | + | 0.478332i | \(0.841242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 192.188 | − | 110.960i | 0.210502 | − | 0.121533i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 209.832 | − | 363.440i | 0.229325 | − | 0.397202i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −235.374 | + | 597.228i | −0.256678 | + | 0.651284i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −262.042 | + | 453.871i | −0.285139 | + | 0.493875i | −0.972643 | − | 0.232306i | \(-0.925373\pi\) |
0.687504 | + | 0.726180i | \(0.258706\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −257.535 | − | 446.064i | −0.279626 | − | 0.484326i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −322.372 | −0.349266 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2117.53i | − | 2.28922i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 533.618 | − | 308.084i | 0.575640 | − | 0.332346i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 551.791 | + | 318.577i | 0.593962 | + | 0.342924i | 0.766663 | − | 0.642050i | \(-0.221916\pi\) |
−0.172700 | + | 0.984974i | \(0.555249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −119.060 | + | 514.892i | −0.127884 | + | 0.553053i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1560.31 | − | 900.844i | −1.67235 | − | 0.965534i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −169.180 | − | 293.029i | −0.180941 | − | 0.313400i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 383.587i | − | 0.409378i | −0.978827 | − | 0.204689i | \(-0.934382\pi\) | ||
0.978827 | − | 0.204689i | \(-0.0656182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2205.50i | − | 2.34877i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 130.295 | + | 225.678i | 0.138465 | + | 0.239828i | 0.926916 | − | 0.375270i | \(-0.122450\pi\) |
−0.788451 | + | 0.615098i | \(0.789117\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −823.840 | − | 475.644i | −0.873637 | − | 0.504394i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −249.719 | + | 633.626i | −0.264252 | + | 0.670504i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 851.444 | + | 491.581i | 0.899096 | + | 0.519093i | 0.876907 | − | 0.480660i | \(-0.159603\pi\) |
0.0221894 | + | 0.999754i | \(0.492936\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −604.827 | + | 349.197i | −0.637331 | + | 0.367963i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 689.781i | 0.725322i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1137.60 | −1.19370 | −0.596851 | − | 0.802352i | \(-0.703582\pi\) | ||||
−0.596851 | + | 0.802352i | \(0.703582\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1440.78 | − | 2495.50i | −1.50867 | − | 2.61309i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 122.403 | − | 212.008i | 0.127903 | − | 0.221534i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −869.505 | − | 1093.51i | −0.906679 | − | 1.14026i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5835 | + | 40.8479i | −0.0245406 | + | 0.0425056i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −503.275 | + | 290.566i | −0.522612 | + | 0.301730i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1768.75 | 1.83290 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1296.35 | 1.34059 | 0.670297 | − | 0.742093i | \(-0.266167\pi\) | ||||
0.670297 | + | 0.742093i | \(0.266167\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 381.214 | − | 220.094i | 0.393410 | − | 0.227135i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 665.237 | − | 1152.22i | 0.685105 | − | 1.18664i | −0.288299 | − | 0.957540i | \(-0.593090\pi\) |
0.973404 | − | 0.229096i | \(-0.0735768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 273.309 | − | 40.7980i | 0.280893 | − | 0.0419301i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −812.237 | + | 1406.84i | −0.833063 | + | 1.44291i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −693.081 | − | 1200.45i | −0.709397 | − | 1.22871i | −0.965081 | − | 0.261952i | \(-0.915634\pi\) |
0.255684 | − | 0.966760i | \(-0.417699\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −98.5153 | −0.100629 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1211.27i | − | 1.23473i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 601.161 | − | 347.081i | 0.611558 | − | 0.353083i | −0.162017 | − | 0.986788i | \(-0.551800\pi\) |
0.773575 | + | 0.633705i | \(0.218467\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 118.968 | + | 68.6861i | 0.120780 | + | 0.0697321i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 168.331 | + | 1127.66i | 0.170548 | + | 1.14251i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 456.757 | + | 263.709i | 0.461838 | + | 0.266642i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −467.257 | − | 809.312i | −0.471500 | − | 0.816662i | 0.527968 | − | 0.849264i | \(-0.322954\pi\) |
−0.999468 | + | 0.0326018i | \(0.989621\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1933.22i | 1.94684i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 497.576i | 0.500076i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −769.103 | − | 1332.12i | −0.771417 | − | 1.33613i | −0.936786 | − | 0.349902i | \(-0.886215\pi\) |
0.165370 | − | 0.986232i | \(-0.447118\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 376.463 | + | 217.351i | 0.376840 | + | 0.217568i |
(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 | 224.3.n.a.145.13 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.5.1 | ✓ | 28 | ||
7.2 | even | 3 | 1568.3.h.a.881.4 | 28 | |||
7.3 | odd | 6 | inner | 224.3.n.a.17.2 | 28 | ||
7.5 | odd | 6 | 1568.3.h.a.881.26 | 28 | |||
8.3 | odd | 2 | 56.3.j.a.5.10 | yes | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.145.2 | 28 | ||
28.3 | even | 6 | 56.3.j.a.45.10 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.325.10 | 28 | |||
28.19 | even | 6 | 392.3.h.a.293.19 | 28 | |||
28.23 | odd | 6 | 392.3.h.a.293.20 | 28 | |||
28.27 | even | 2 | 392.3.j.e.117.1 | 28 | |||
56.3 | even | 6 | 56.3.j.a.45.1 | yes | 28 | ||
56.5 | odd | 6 | 1568.3.h.a.881.3 | 28 | |||
56.11 | odd | 6 | 392.3.j.e.325.1 | 28 | |||
56.19 | even | 6 | 392.3.h.a.293.18 | 28 | |||
56.27 | even | 2 | 392.3.j.e.117.10 | 28 | |||
56.37 | even | 6 | 1568.3.h.a.881.25 | 28 | |||
56.45 | odd | 6 | inner | 224.3.n.a.17.13 | 28 | ||
56.51 | odd | 6 | 392.3.h.a.293.17 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.1 | ✓ | 28 | 4.3 | odd | 2 | ||
56.3.j.a.5.10 | yes | 28 | 8.3 | odd | 2 | ||
56.3.j.a.45.1 | yes | 28 | 56.3 | even | 6 | ||
56.3.j.a.45.10 | yes | 28 | 28.3 | even | 6 | ||
224.3.n.a.17.2 | 28 | 7.3 | odd | 6 | inner | ||
224.3.n.a.17.13 | 28 | 56.45 | odd | 6 | inner | ||
224.3.n.a.145.2 | 28 | 8.5 | even | 2 | inner | ||
224.3.n.a.145.13 | 28 | 1.1 | even | 1 | trivial | ||
392.3.h.a.293.17 | 28 | 56.51 | odd | 6 | |||
392.3.h.a.293.18 | 28 | 56.19 | even | 6 | |||
392.3.h.a.293.19 | 28 | 28.19 | even | 6 | |||
392.3.h.a.293.20 | 28 | 28.23 | odd | 6 | |||
392.3.j.e.117.1 | 28 | 28.27 | even | 2 | |||
392.3.j.e.117.10 | 28 | 56.27 | even | 2 | |||
392.3.j.e.325.1 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.325.10 | 28 | 28.11 | odd | 6 | |||
1568.3.h.a.881.3 | 28 | 56.5 | odd | 6 | |||
1568.3.h.a.881.4 | 28 | 7.2 | even | 3 | |||
1568.3.h.a.881.25 | 28 | 56.37 | even | 6 | |||
1568.3.h.a.881.26 | 28 | 7.5 | odd | 6 |