Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,7,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (of order \(2\), degree \(1\), 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: | \(13.8032450172\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.5 | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.7.c.a.31.6 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53904 | − | 7.17462i | −0.442379 | − | 0.896828i | ||||
\(3\) | − | 15.5885i | − | 0.577350i | ||||||
\(4\) | −38.9505 | + | 50.7825i | −0.608601 | + | 0.793477i | ||||
\(5\) | 55.9017 | 0.447214 | ||||||||
\(6\) | −111.841 | + | 55.1681i | −0.517784 | + | 0.255408i | ||||
\(7\) | 99.9522i | 0.291406i | 0.989328 | + | 0.145703i | \(0.0465444\pi\) | ||||
−0.989328 | + | 0.145703i | \(0.953456\pi\) | |||||||
\(8\) | 502.192 | + | 99.7338i | 0.980844 | + | 0.194793i | ||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | −197.838 | − | 401.074i | −0.197838 | − | 0.401074i | ||||
\(11\) | 2399.27i | 1.80261i | 0.433186 | + | 0.901304i | \(0.357389\pi\) | ||||
−0.433186 | + | 0.901304i | \(0.642611\pi\) | |||||||
\(12\) | 791.621 | + | 607.177i | 0.458114 | + | 0.351376i | ||||
\(13\) | 3619.28 | 1.64737 | 0.823687 | − | 0.567045i | \(-0.191913\pi\) | ||||
0.823687 | + | 0.567045i | \(0.191913\pi\) | |||||||
\(14\) | 717.119 | − | 353.734i | 0.261341 | − | 0.128912i | ||||
\(15\) | − | 871.421i | − | 0.258199i | ||||||
\(16\) | −1061.72 | − | 3956.00i | −0.259210 | − | 0.965821i | ||||
\(17\) | −927.422 | −0.188769 | −0.0943845 | − | 0.995536i | \(-0.530088\pi\) | ||||
−0.0943845 | + | 0.995536i | \(0.530088\pi\) | |||||||
\(18\) | 859.986 | + | 1743.43i | 0.147460 | + | 0.298943i | ||||
\(19\) | − | 773.488i | − | 0.112770i | −0.998409 | − | 0.0563849i | \(-0.982043\pi\) | ||
0.998409 | − | 0.0563849i | \(-0.0179574\pi\) | |||||||
\(20\) | −2177.40 | + | 2838.83i | −0.272175 | + | 0.354854i | ||||
\(21\) | 1558.10 | 0.168243 | ||||||||
\(22\) | 17213.9 | − | 8491.11i | 1.61663 | − | 0.797437i | ||||
\(23\) | − | 12221.5i | − | 1.00448i | −0.864728 | − | 0.502241i | \(-0.832509\pi\) | ||
0.864728 | − | 0.502241i | \(-0.167491\pi\) | |||||||
\(24\) | 1554.70 | − | 7828.40i | 0.112464 | − | 0.566291i | ||||
\(25\) | 3125.00 | 0.200000 | ||||||||
\(26\) | −12808.8 | − | 25967.0i | −0.728764 | − | 1.47741i | ||||
\(27\) | 3788.00i | 0.192450i | ||||||||
\(28\) | −5075.82 | − | 3893.18i | −0.231224 | − | 0.177350i | ||||
\(29\) | 29029.7 | 1.19028 | 0.595139 | − | 0.803623i | \(-0.297097\pi\) | ||||
0.595139 | + | 0.803623i | \(0.297097\pi\) | |||||||
\(30\) | −6252.12 | + | 3083.99i | −0.231560 | + | 0.114222i | ||||
\(31\) | − | 9560.97i | − | 0.320935i | −0.987041 | − | 0.160467i | \(-0.948700\pi\) | ||
0.987041 | − | 0.160467i | \(-0.0513002\pi\) | |||||||
\(32\) | −24625.3 | + | 21617.9i | −0.751506 | + | 0.659726i | ||||
\(33\) | 37401.0 | 1.04074 | ||||||||
\(34\) | 3282.18 | + | 6653.91i | 0.0835076 | + | 0.169293i | ||||
\(35\) | 5587.50i | 0.130321i | ||||||||
\(36\) | 9464.96 | − | 12340.1i | 0.202867 | − | 0.264492i | ||||
\(37\) | 88644.4 | 1.75003 | 0.875016 | − | 0.484093i | \(-0.160851\pi\) | ||||
0.875016 | + | 0.484093i | \(0.160851\pi\) | |||||||
\(38\) | −5549.49 | + | 2737.40i | −0.101135 | + | 0.0498870i | ||||
\(39\) | − | 56419.0i | − | 0.951112i | ||||||
\(40\) | 28073.4 | + | 5575.29i | 0.438647 | + | 0.0871139i | ||||
\(41\) | −53763.7 | −0.780077 | −0.390039 | − | 0.920799i | \(-0.627538\pi\) | ||||
−0.390039 | + | 0.920799i | \(0.627538\pi\) | |||||||
\(42\) | −5514.17 | − | 11178.8i | −0.0744273 | − | 0.150885i | ||||
\(43\) | 140348.i | 1.76522i | 0.470103 | + | 0.882612i | \(0.344217\pi\) | ||||
−0.470103 | + | 0.882612i | \(0.655783\pi\) | |||||||
\(44\) | −121841. | − | 93452.8i | −1.43033 | − | 1.09707i | ||||
\(45\) | −13584.1 | −0.149071 | ||||||||
\(46\) | −87684.9 | + | 43252.5i | −0.900848 | + | 0.444362i | ||||
\(47\) | 105555.i | 1.01668i | 0.861157 | + | 0.508339i | \(0.169740\pi\) | ||||
−0.861157 | + | 0.508339i | \(0.830260\pi\) | |||||||
\(48\) | −61668.0 | + | 16550.6i | −0.557617 | + | 0.149655i | ||||
\(49\) | 107659. | 0.915083 | ||||||||
\(50\) | −11059.5 | − | 22420.7i | −0.0884759 | − | 0.179366i | ||||
\(51\) | 14457.1i | 0.108986i | ||||||||
\(52\) | −140973. | + | 183796.i | −1.00259 | + | 1.30715i | ||||
\(53\) | −80965.8 | −0.543844 | −0.271922 | − | 0.962319i | \(-0.587659\pi\) | ||||
−0.271922 | + | 0.962319i | \(0.587659\pi\) | |||||||
\(54\) | 27177.4 | − | 13405.9i | 0.172595 | − | 0.0851360i | ||||
\(55\) | 134123.i | 0.806151i | ||||||||
\(56\) | −9968.61 | + | 50195.2i | −0.0567637 | + | 0.285824i | ||||
\(57\) | −12057.5 | −0.0651077 | ||||||||
\(58\) | −102737. | − | 208277.i | −0.526555 | − | 1.06747i | ||||
\(59\) | − | 59057.3i | − | 0.287553i | −0.989610 | − | 0.143776i | \(-0.954075\pi\) | ||
0.989610 | − | 0.143776i | \(-0.0459246\pi\) | |||||||
\(60\) | 44252.9 | + | 33942.3i | 0.204875 | + | 0.157140i | ||||
\(61\) | 116330. | 0.512508 | 0.256254 | − | 0.966609i | \(-0.417512\pi\) | ||||
0.256254 | + | 0.966609i | \(0.417512\pi\) | |||||||
\(62\) | −68596.4 | + | 33836.6i | −0.287823 | + | 0.141975i | ||||
\(63\) | − | 24288.4i | − | 0.0971353i | ||||||
\(64\) | 242250. | + | 100171.i | 0.924112 | + | 0.382122i | ||||
\(65\) | 202324. | 0.736728 | ||||||||
\(66\) | −132363. | − | 268338.i | −0.460401 | − | 0.933362i | ||||
\(67\) | 134450.i | 0.447029i | 0.974701 | + | 0.223514i | \(0.0717529\pi\) | ||||
−0.974701 | + | 0.223514i | \(0.928247\pi\) | |||||||
\(68\) | 36123.5 | − | 47096.8i | 0.114885 | − | 0.149784i | ||||
\(69\) | −190515. | −0.579938 | ||||||||
\(70\) | 40088.2 | − | 19774.4i | 0.116875 | − | 0.0576512i | ||||
\(71\) | 468387.i | 1.30867i | 0.756206 | + | 0.654334i | \(0.227051\pi\) | ||||
−0.756206 | + | 0.654334i | \(0.772949\pi\) | |||||||
\(72\) | −122033. | − | 24235.3i | −0.326948 | − | 0.0649308i | ||||
\(73\) | 79504.8 | 0.204373 | 0.102187 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102187 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(74\) | −313716. | − | 635990.i | −0.774178 | − | 1.56948i | ||||
\(75\) | − | 48713.9i | − | 0.115470i | ||||||
\(76\) | 39279.7 | + | 30127.7i | 0.0894802 | + | 0.0686318i | ||||
\(77\) | −239813. | −0.525291 | ||||||||
\(78\) | −404785. | + | 199669.i | −0.852984 | + | 0.420752i | ||||
\(79\) | − | 670660.i | − | 1.36026i | −0.733093 | − | 0.680129i | \(-0.761924\pi\) | ||
0.733093 | − | 0.680129i | \(-0.238076\pi\) | |||||||
\(80\) | −59352.2 | − | 221147.i | −0.115922 | − | 0.431928i | ||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 190272. | + | 385734.i | 0.345090 | + | 0.699595i | ||||
\(83\) | − | 549656.i | − | 0.961296i | −0.876914 | − | 0.480648i | \(-0.840402\pi\) | ||
0.876914 | − | 0.480648i | \(-0.159598\pi\) | |||||||
\(84\) | −60688.7 | + | 79124.2i | −0.102393 | + | 0.133497i | ||||
\(85\) | −51844.5 | −0.0844201 | ||||||||
\(86\) | 1.00694e6 | − | 496695.i | 1.58310 | − | 0.780899i | ||||
\(87\) | − | 452528.i | − | 0.687207i | ||||||
\(88\) | −239288. | + | 1.20490e6i | −0.351135 | + | 1.76808i | ||||
\(89\) | 785334. | 1.11400 | 0.556999 | − | 0.830513i | \(-0.311953\pi\) | ||||
0.556999 | + | 0.830513i | \(0.311953\pi\) | |||||||
\(90\) | 48074.7 | + | 97460.9i | 0.0659460 | + | 0.133691i | ||||
\(91\) | 361755.i | 0.480054i | ||||||||
\(92\) | 620640. | + | 476034.i | 0.797033 | + | 0.611329i | ||||
\(93\) | −149041. | −0.185292 | ||||||||
\(94\) | 757314. | − | 373561.i | 0.911785 | − | 0.449757i | ||||
\(95\) | − | 43239.3i | − | 0.0504322i | ||||||
\(96\) | 336990. | + | 383871.i | 0.380893 | + | 0.433882i | ||||
\(97\) | 664400. | 0.727972 | 0.363986 | − | 0.931404i | \(-0.381416\pi\) | ||||
0.363986 | + | 0.931404i | \(0.381416\pi\) | |||||||
\(98\) | −381007. | − | 772410.i | −0.404814 | − | 0.820672i | ||||
\(99\) | − | 583023.i | − | 0.600870i | ||||||
\(100\) | −121720. | + | 158695.i | −0.121720 | + | 0.158695i | ||||
\(101\) | −1.49801e6 | −1.45396 | −0.726978 | − | 0.686661i | \(-0.759076\pi\) | ||||
−0.726978 | + | 0.686661i | \(0.759076\pi\) | |||||||
\(102\) | 103724. | − | 51164.1i | 0.0977416 | − | 0.0482131i | ||||
\(103\) | 799842.i | 0.731968i | 0.930621 | + | 0.365984i | \(0.119268\pi\) | ||||
−0.930621 | + | 0.365984i | \(0.880732\pi\) | |||||||
\(104\) | 1.81758e6 | + | 360965.i | 1.61582 | + | 0.320896i | ||||
\(105\) | 87100.5 | 0.0752406 | ||||||||
\(106\) | 286541. | + | 580899.i | 0.240585 | + | 0.487734i | ||||
\(107\) | 349292.i | 0.285126i | 0.989786 | + | 0.142563i | \(0.0455344\pi\) | ||||
−0.989786 | + | 0.142563i | \(0.954466\pi\) | |||||||
\(108\) | −192364. | − | 147544.i | −0.152705 | − | 0.117125i | ||||
\(109\) | 680148. | 0.525199 | 0.262599 | − | 0.964905i | \(-0.415420\pi\) | ||||
0.262599 | + | 0.964905i | \(0.415420\pi\) | |||||||
\(110\) | 962285. | − | 474668.i | 0.722979 | − | 0.356625i | ||||
\(111\) | − | 1.38183e6i | − | 1.01038i | ||||||
\(112\) | 395411. | − | 106122.i | 0.281446 | − | 0.0755353i | ||||
\(113\) | −1.68229e6 | −1.16591 | −0.582955 | − | 0.812505i | \(-0.698104\pi\) | ||||
−0.582955 | + | 0.812505i | \(0.698104\pi\) | |||||||
\(114\) | 42671.9 | + | 86507.9i | 0.0288023 | + | 0.0583904i | ||||
\(115\) | − | 683205.i | − | 0.449218i | ||||||
\(116\) | −1.13072e6 | + | 1.47420e6i | −0.724404 | + | 0.944458i | ||||
\(117\) | −879485. | −0.549125 | ||||||||
\(118\) | −423714. | + | 209006.i | −0.257886 | + | 0.127208i | ||||
\(119\) | − | 92697.9i | − | 0.0550084i | ||||||
\(120\) | 86910.1 | − | 437621.i | 0.0502952 | − | 0.253253i | ||||
\(121\) | −3.98495e6 | −2.24940 | ||||||||
\(122\) | −411695. | − | 834621.i | −0.226723 | − | 0.459632i | ||||
\(123\) | 838093.i | 0.450378i | ||||||||
\(124\) | 485530. | + | 372404.i | 0.254654 | + | 0.195321i | ||||
\(125\) | 174693. | 0.0894427 | ||||||||
\(126\) | −174260. | + | 85957.4i | −0.0871136 | + | 0.0429706i | ||||
\(127\) | − | 2.92911e6i | − | 1.42996i | −0.699145 | − | 0.714980i | \(-0.746436\pi\) | ||
0.699145 | − | 0.714980i | \(-0.253564\pi\) | |||||||
\(128\) | −138643. | − | 2.09256e6i | −0.0661101 | − | 0.997812i | ||||
\(129\) | 2.18780e6 | 1.01915 | ||||||||
\(130\) | −716032. | − | 1.45160e6i | −0.325913 | − | 0.660718i | ||||
\(131\) | 1.57652e6i | 0.701272i | 0.936512 | + | 0.350636i | \(0.114035\pi\) | ||||
−0.936512 | + | 0.350636i | \(0.885965\pi\) | |||||||
\(132\) | −1.45678e6 | + | 1.89931e6i | −0.633393 | + | 0.825800i | ||||
\(133\) | 77311.8 | 0.0328618 | ||||||||
\(134\) | 964626. | − | 475822.i | 0.400908 | − | 0.197756i | ||||
\(135\) | 211755.i | 0.0860663i | ||||||||
\(136\) | −465744. | − | 92495.3i | −0.185153 | − | 0.0367708i | ||||
\(137\) | −3.34075e6 | −1.29922 | −0.649609 | − | 0.760269i | \(-0.725067\pi\) | ||||
−0.649609 | + | 0.760269i | \(0.725067\pi\) | |||||||
\(138\) | 674239. | + | 1.36687e6i | 0.256553 | + | 0.520105i | ||||
\(139\) | − | 857823.i | − | 0.319413i | −0.987165 | − | 0.159707i | \(-0.948945\pi\) | ||
0.987165 | − | 0.159707i | \(-0.0510549\pi\) | |||||||
\(140\) | −283747. | − | 217636.i | −0.103406 | − | 0.0793132i | ||||
\(141\) | 1.64543e6 | 0.586979 | ||||||||
\(142\) | 3.36050e6 | − | 1.65764e6i | 1.17365 | − | 0.578928i | ||||
\(143\) | 8.68364e6i | 2.96957i | ||||||||
\(144\) | 257999. | + | 961309.i | 0.0864034 | + | 0.321940i | ||||
\(145\) | 1.62281e6 | 0.532309 | ||||||||
\(146\) | −281370. | − | 570417.i | −0.0904106 | − | 0.183288i | ||||
\(147\) | − | 1.67823e6i | − | 0.528323i | ||||||
\(148\) | −3.45274e6 | + | 4.50158e6i | −1.06507 | + | 1.38861i | ||||
\(149\) | −4.93323e6 | −1.49133 | −0.745663 | − | 0.666323i | \(-0.767867\pi\) | ||||
−0.745663 | + | 0.666323i | \(0.767867\pi\) | |||||||
\(150\) | −349504. | + | 172400.i | −0.103557 | + | 0.0510816i | ||||
\(151\) | − | 2.17991e6i | − | 0.633151i | −0.948567 | − | 0.316575i | \(-0.897467\pi\) | ||
0.948567 | − | 0.316575i | \(-0.102533\pi\) | |||||||
\(152\) | 77142.9 | − | 388440.i | 0.0219667 | − | 0.110610i | ||||
\(153\) | 225364. | 0.0629230 | ||||||||
\(154\) | 848705. | + | 1.72056e6i | 0.232378 | + | 0.471095i | ||||
\(155\) | − | 534475.i | − | 0.143526i | ||||||
\(156\) | 2.86510e6 | + | 2.19755e6i | 0.754685 | + | 0.578847i | ||||
\(157\) | −561357. | −0.145058 | −0.0725288 | − | 0.997366i | \(-0.523107\pi\) | ||||
−0.0725288 | + | 0.997366i | \(0.523107\pi\) | |||||||
\(158\) | −4.81173e6 | + | 2.37349e6i | −1.21992 | + | 0.601750i | ||||
\(159\) | 1.26213e6i | 0.313988i | ||||||||
\(160\) | −1.37660e6 | + | 1.20848e6i | −0.336084 | + | 0.295039i | ||||
\(161\) | 1.22157e6 | 0.292712 | ||||||||
\(162\) | −208977. | − | 423654.i | −0.0491533 | − | 0.0996476i | ||||
\(163\) | − | 3.42959e6i | − | 0.791915i | −0.918269 | − | 0.395958i | \(-0.870413\pi\) | ||
0.918269 | − | 0.395958i | \(-0.129587\pi\) | |||||||
\(164\) | 2.09412e6 | − | 2.73025e6i | 0.474756 | − | 0.618973i | ||||
\(165\) | 2.09078e6 | 0.465432 | ||||||||
\(166\) | −3.94358e6 | + | 1.94525e6i | −0.862117 | + | 0.425257i | ||||
\(167\) | 4.96116e6i | 1.06521i | 0.846365 | + | 0.532603i | \(0.178786\pi\) | ||||
−0.846365 | + | 0.532603i | \(0.821214\pi\) | |||||||
\(168\) | 782466. | + | 155395.i | 0.165020 | + | 0.0327725i | ||||
\(169\) | 8.27239e6 | 1.71384 | ||||||||
\(170\) | 183479. | + | 371965.i | 0.0373457 | + | 0.0757103i | ||||
\(171\) | 187958.i | 0.0375899i | ||||||||
\(172\) | −7.12720e6 | − | 5.46660e6i | −1.40066 | − | 1.07432i | ||||
\(173\) | 1.02232e7 | 1.97447 | 0.987235 | − | 0.159271i | \(-0.0509144\pi\) | ||||
0.987235 | + | 0.159271i | \(0.0509144\pi\) | |||||||
\(174\) | −3.24672e6 | + | 1.60151e6i | −0.616307 | + | 0.304006i | ||||
\(175\) | 312351.i | 0.0582812i | ||||||||
\(176\) | 9.49153e6 | − | 2.54737e6i | 1.74100 | − | 0.467254i | ||||
\(177\) | −920613. | −0.166019 | ||||||||
\(178\) | −2.77932e6 | − | 5.63447e6i | −0.492810 | − | 0.999064i | ||||
\(179\) | 162204.i | 0.0282815i | 0.999900 | + | 0.0141407i | \(0.00450128\pi\) | ||||
−0.999900 | + | 0.0141407i | \(0.995499\pi\) | |||||||
\(180\) | 529107. | − | 689835.i | 0.0907249 | − | 0.118285i | ||||
\(181\) | −6.54734e6 | −1.10415 | −0.552076 | − | 0.833794i | \(-0.686164\pi\) | ||||
−0.552076 | + | 0.833794i | \(0.686164\pi\) | |||||||
\(182\) | 2.59546e6 | − | 1.28026e6i | 0.430526 | − | 0.212366i | ||||
\(183\) | − | 1.81340e6i | − | 0.295897i | ||||||
\(184\) | 1.21890e6 | − | 6.13756e6i | 0.195666 | − | 0.985241i | ||||
\(185\) | 4.95537e6 | 0.782638 | ||||||||
\(186\) | 527461. | + | 1.06931e6i | 0.0819693 | + | 0.166175i | ||||
\(187\) | − | 2.22514e6i | − | 0.340277i | ||||||
\(188\) | −5.36032e6 | − | 4.11140e6i | −0.806710 | − | 0.618751i | ||||
\(189\) | −378618. | −0.0560811 | ||||||||
\(190\) | −310226. | + | 153025.i | −0.0452290 | + | 0.0223102i | ||||
\(191\) | − | 3.54149e6i | − | 0.508260i | −0.967170 | − | 0.254130i | \(-0.918211\pi\) | ||
0.967170 | − | 0.254130i | \(-0.0817891\pi\) | |||||||
\(192\) | 1.56151e6 | − | 3.77631e6i | 0.220618 | − | 0.533536i | ||||
\(193\) | 8.80294e6 | 1.22449 | 0.612246 | − | 0.790667i | \(-0.290266\pi\) | ||||
0.612246 | + | 0.790667i | \(0.290266\pi\) | |||||||
\(194\) | −2.35134e6 | − | 4.76682e6i | −0.322040 | − | 0.652865i | ||||
\(195\) | − | 3.15392e6i | − | 0.425350i | ||||||
\(196\) | −4.19335e6 | + | 5.46717e6i | −0.556920 | + | 0.726097i | ||||
\(197\) | 3.09941e6 | 0.405397 | 0.202698 | − | 0.979241i | \(-0.435029\pi\) | ||||
0.202698 | + | 0.979241i | \(0.435029\pi\) | |||||||
\(198\) | −4.18297e6 | + | 2.06334e6i | −0.538877 | + | 0.265812i | ||||
\(199\) | 852821.i | 0.108218i | 0.998535 | + | 0.0541089i | \(0.0172318\pi\) | ||||
−0.998535 | + | 0.0541089i | \(0.982768\pi\) | |||||||
\(200\) | 1.56935e6 | + | 311668.i | 0.196169 | + | 0.0389585i | ||||
\(201\) | 2.09586e6 | 0.258092 | ||||||||
\(202\) | 5.30152e6 | + | 1.07477e7i | 0.643200 | + | 1.30395i | ||||
\(203\) | 2.90158e6i | 0.346854i | ||||||||
\(204\) | −734167. | − | 563110.i | −0.0864777 | − | 0.0663289i | ||||
\(205\) | −3.00548e6 | −0.348861 | ||||||||
\(206\) | 5.73856e6 | − | 2.83067e6i | 0.656450 | − | 0.323808i | ||||
\(207\) | 2.96983e6i | 0.334827i | ||||||||
\(208\) | −3.84268e6 | − | 1.43179e7i | −0.427016 | − | 1.59107i | ||||
\(209\) | 1.85581e6 | 0.203280 | ||||||||
\(210\) | −308252. | − | 624913.i | −0.0332849 | − | 0.0674779i | ||||
\(211\) | − | 1.07917e7i | − | 1.14880i | −0.818576 | − | 0.574399i | \(-0.805236\pi\) | ||
0.818576 | − | 0.574399i | \(-0.194764\pi\) | |||||||
\(212\) | 3.15366e6 | − | 4.11165e6i | 0.330984 | − | 0.431527i | ||||
\(213\) | 7.30142e6 | 0.755560 | ||||||||
\(214\) | 2.50604e6 | − | 1.23616e6i | 0.255709 | − | 0.126134i | ||||
\(215\) | 7.84567e6i | 0.789432i | ||||||||
\(216\) | −377791. | + | 1.90230e6i | −0.0374878 | + | 0.188764i | ||||
\(217\) | 955640. | 0.0935223 | ||||||||
\(218\) | −2.40707e6 | − | 4.87980e6i | −0.232337 | − | 0.471013i | ||||
\(219\) | − | 1.23936e6i | − | 0.117995i | ||||||
\(220\) | −6.81112e6 | − | 5.22417e6i | −0.639662 | − | 0.490624i | ||||
\(221\) | −3.35660e6 | −0.310973 | ||||||||
\(222\) | −9.91411e6 | + | 4.89034e6i | −0.906139 | + | 0.446972i | ||||
\(223\) | 1.42777e7i | 1.28749i | 0.765240 | + | 0.643745i | \(0.222620\pi\) | ||||
−0.765240 | + | 0.643745i | \(0.777380\pi\) | |||||||
\(224\) | −2.16076e6 | − | 2.46136e6i | −0.192248 | − | 0.218993i | ||||
\(225\) | −759375. | −0.0666667 | ||||||||
\(226\) | 5.95368e6 | + | 1.20698e7i | 0.515774 | + | 1.04562i | ||||
\(227\) | 1.14371e7i | 0.977776i | 0.872347 | + | 0.488888i | \(0.162597\pi\) | ||||
−0.872347 | + | 0.488888i | \(0.837403\pi\) | |||||||
\(228\) | 469644. | − | 612309.i | 0.0396246 | − | 0.0516614i | ||||
\(229\) | −1.28721e7 | −1.07187 | −0.535936 | − | 0.844258i | \(-0.680041\pi\) | ||||
−0.535936 | + | 0.844258i | \(0.680041\pi\) | |||||||
\(230\) | −4.90174e6 | + | 2.41789e6i | −0.402871 | + | 0.198725i | ||||
\(231\) | 3.73831e6i | 0.303277i | ||||||||
\(232\) | 1.45785e7 | + | 2.89524e6i | 1.16748 | + | 0.231857i | ||||
\(233\) | −9.25991e6 | −0.732047 | −0.366023 | − | 0.930606i | \(-0.619281\pi\) | ||||
−0.366023 | + | 0.930606i | \(0.619281\pi\) | |||||||
\(234\) | 3.11253e6 | + | 6.30998e6i | 0.242921 | + | 0.492470i | ||||
\(235\) | 5.90068e6i | 0.454672i | ||||||||
\(236\) | 2.99908e6 | + | 2.30031e6i | 0.228167 | + | 0.175005i | ||||
\(237\) | −1.04546e7 | −0.785345 | ||||||||
\(238\) | −665073. | + | 328061.i | −0.0493331 | + | 0.0243346i | ||||
\(239\) | − | 4.26361e6i | − | 0.312308i | −0.987733 | − | 0.156154i | \(-0.950090\pi\) | ||
0.987733 | − | 0.156154i | \(-0.0499097\pi\) | |||||||
\(240\) | −3.44734e6 | + | 925209.i | −0.249374 | + | 0.0669278i | ||||
\(241\) | −1.13558e7 | −0.811271 | −0.405636 | − | 0.914035i | \(-0.632950\pi\) | ||||
−0.405636 | + | 0.914035i | \(0.632950\pi\) | |||||||
\(242\) | 1.41029e7 | + | 2.85905e7i | 0.995088 | + | 2.01732i | ||||
\(243\) | − | 920483.i | − | 0.0641500i | ||||||
\(244\) | −4.53109e6 | + | 5.90751e6i | −0.311913 | + | 0.406663i | ||||
\(245\) | 6.01830e6 | 0.409237 | ||||||||
\(246\) | 6.01300e6 | − | 2.96604e6i | 0.403911 | − | 0.199238i | ||||
\(247\) | − | 2.79947e6i | − | 0.185774i | ||||||
\(248\) | 953552. | − | 4.80145e6i | 0.0625157 | − | 0.314787i | ||||
\(249\) | −8.56829e6 | −0.555004 | ||||||||
\(250\) | −618244. | − | 1.25336e6i | −0.0395676 | − | 0.0802147i | ||||
\(251\) | − | 2.40153e7i | − | 1.51868i | −0.650692 | − | 0.759342i | \(-0.725521\pi\) | ||
0.650692 | − | 0.759342i | \(-0.274479\pi\) | |||||||
\(252\) | 1.23342e6 | + | 946043.i | 0.0770746 | + | 0.0591166i | ||||
\(253\) | 2.93228e7 | 1.81069 | ||||||||
\(254\) | −2.10152e7 | + | 1.03662e7i | −1.28243 | + | 0.632585i | ||||
\(255\) | 808176.i | 0.0487400i | ||||||||
\(256\) | −1.45227e7 | + | 8.40037e6i | −0.865620 | + | 0.500701i | ||||
\(257\) | −7.77314e6 | −0.457928 | −0.228964 | − | 0.973435i | \(-0.573534\pi\) | ||||
−0.228964 | + | 0.973435i | \(0.573534\pi\) | |||||||
\(258\) | −7.74271e6 | − | 1.56967e7i | −0.450852 | − | 0.914004i | ||||
\(259\) | 8.86020e6i | 0.509970i | ||||||||
\(260\) | −7.88061e6 | + | 1.02745e7i | −0.448373 | + | 0.584576i | ||||
\(261\) | −7.05421e6 | −0.396759 | ||||||||
\(262\) | 1.13110e7 | − | 5.57938e6i | 0.628921 | − | 0.310229i | ||||
\(263\) | − | 2.33758e7i | − | 1.28499i | −0.766292 | − | 0.642493i | \(-0.777900\pi\) | ||
0.766292 | − | 0.642493i | \(-0.222100\pi\) | |||||||
\(264\) | 1.87825e7 | + | 3.73014e6i | 1.02080 | + | 0.202728i | ||||
\(265\) | −4.52613e6 | −0.243214 | ||||||||
\(266\) | −273609. | − | 554683.i | −0.0145374 | − | 0.0294714i | ||||
\(267\) | − | 1.22421e7i | − | 0.643167i | ||||||
\(268\) | −6.82769e6 | − | 5.23687e6i | −0.354707 | − | 0.272062i | ||||
\(269\) | −2.52755e7 | −1.29850 | −0.649252 | − | 0.760573i | \(-0.724918\pi\) | ||||
−0.649252 | + | 0.760573i | \(0.724918\pi\) | |||||||
\(270\) | 1.51927e6 | − | 749410.i | 0.0771867 | − | 0.0380740i | ||||
\(271\) | 1.98065e7i | 0.995175i | 0.867414 | + | 0.497588i | \(0.165781\pi\) | ||||
−0.867414 | + | 0.497588i | \(0.834219\pi\) | |||||||
\(272\) | 984667. | + | 3.66889e6i | 0.0489308 | + | 0.182317i | ||||
\(273\) | 5.63920e6 | 0.277159 | ||||||||
\(274\) | 1.18230e7 | + | 2.39686e7i | 0.574747 | + | 1.16517i | ||||
\(275\) | 7.49773e6i | 0.360522i | ||||||||
\(276\) | 7.42064e6 | − | 9.67482e6i | 0.352951 | − | 0.460167i | ||||
\(277\) | −1.96620e6 | −0.0925101 | −0.0462551 | − | 0.998930i | \(-0.514729\pi\) | ||||
−0.0462551 | + | 0.998930i | \(0.514729\pi\) | |||||||
\(278\) | −6.15456e6 | + | 3.03587e6i | −0.286459 | + | 0.141302i | ||||
\(279\) | 2.32332e6i | 0.106978i | ||||||||
\(280\) | −557262. | + | 2.80600e6i | −0.0253855 | + | 0.127824i | ||||
\(281\) | −3.71366e7 | −1.67372 | −0.836862 | − | 0.547414i | \(-0.815612\pi\) | ||||
−0.836862 | + | 0.547414i | \(0.815612\pi\) | |||||||
\(282\) | −5.82325e6 | − | 1.18054e7i | −0.259668 | − | 0.526419i | ||||
\(283\) | − | 1.30641e7i | − | 0.576395i | −0.957571 | − | 0.288197i | \(-0.906944\pi\) | ||
0.957571 | − | 0.288197i | \(-0.0930559\pi\) | |||||||
\(284\) | −2.37858e7 | − | 1.82439e7i | −1.03840 | − | 0.796456i | ||||
\(285\) | −674034. | −0.0291170 | ||||||||
\(286\) | 6.23019e7 | − | 3.07317e7i | 2.66319 | − | 1.31368i | ||||
\(287\) | − | 5.37380e6i | − | 0.227319i | ||||||
\(288\) | 5.98396e6 | − | 5.25315e6i | 0.250502 | − | 0.219909i | ||||
\(289\) | −2.32775e7 | −0.964366 | ||||||||
\(290\) | −5.74318e6 | − | 1.16430e7i | −0.235482 | − | 0.477389i | ||||
\(291\) | − | 1.03570e7i | − | 0.420295i | ||||||
\(292\) | −3.09675e6 | + | 4.03745e6i | −0.124382 | + | 0.162166i | ||||
\(293\) | 2.99876e7 | 1.19217 | 0.596085 | − | 0.802921i | \(-0.296722\pi\) | ||||
0.596085 | + | 0.802921i | \(0.296722\pi\) | |||||||
\(294\) | −1.20407e7 | + | 5.93932e6i | −0.473815 | + | 0.233719i | ||||
\(295\) | − | 3.30141e6i | − | 0.128598i | ||||||
\(296\) | 4.45165e7 | + | 8.84084e6i | 1.71651 | + | 0.340893i | ||||
\(297\) | −9.08843e6 | −0.346912 | ||||||||
\(298\) | 1.74589e7 | + | 3.53941e7i | 0.659732 | + | 1.33746i | ||||
\(299\) | − | 4.42332e7i | − | 1.65476i | ||||||
\(300\) | 2.47382e6 | + | 1.89743e6i | 0.0916228 | + | 0.0702752i | ||||
\(301\) | −1.40281e7 | −0.514396 | ||||||||
\(302\) | −1.56400e7 | + | 7.71477e6i | −0.567827 | + | 0.280093i | ||||
\(303\) | 2.33517e7i | 0.839442i | ||||||||
\(304\) | −3.05992e6 | + | 821231.i | −0.108915 | + | 0.0292311i | ||||
\(305\) | 6.50302e6 | 0.229201 | ||||||||
\(306\) | −797570. | − | 1.61690e6i | −0.0278359 | − | 0.0564311i | ||||
\(307\) | − | 2.02161e7i | − | 0.698688i | −0.936995 | − | 0.349344i | \(-0.886404\pi\) | ||
0.936995 | − | 0.349344i | \(-0.113596\pi\) | |||||||
\(308\) | 9.34081e6 | − | 1.21783e7i | 0.319692 | − | 0.416806i | ||||
\(309\) | 1.24683e7 | 0.422602 | ||||||||
\(310\) | −3.83465e6 | + | 1.89152e6i | −0.128719 | + | 0.0634932i | ||||
\(311\) | 2.22851e6i | 0.0740856i | 0.999314 | + | 0.0370428i | \(0.0117938\pi\) | ||||
−0.999314 | + | 0.0370428i | \(0.988206\pi\) | |||||||
\(312\) | 5.62688e6 | − | 2.83332e7i | 0.185269 | − | 0.932893i | ||||
\(313\) | 5.08300e7 | 1.65763 | 0.828814 | − | 0.559525i | \(-0.189016\pi\) | ||||
0.828814 | + | 0.559525i | \(0.189016\pi\) | |||||||
\(314\) | 1.98666e6 | + | 4.02753e6i | 0.0641705 | + | 0.130092i | ||||
\(315\) | − | 1.35776e6i | − | 0.0434402i | ||||||
\(316\) | 3.40578e7 | + | 2.61225e7i | 1.07933 | + | 0.827854i | ||||
\(317\) | 2.26114e7 | 0.709821 | 0.354911 | − | 0.934900i | \(-0.384511\pi\) | ||||
0.354911 | + | 0.934900i | \(0.384511\pi\) | |||||||
\(318\) | 9.05533e6 | − | 4.46673e6i | 0.281594 | − | 0.138902i | ||||
\(319\) | 6.96501e7i | 2.14561i | ||||||||
\(320\) | 1.35422e7 | + | 5.59973e6i | 0.413275 | + | 0.170890i | ||||
\(321\) | 5.44492e6 | 0.164618 | ||||||||
\(322\) | −4.32318e6 | − | 8.76430e6i | −0.129490 | − | 0.262512i | ||||
\(323\) | 717350.i | 0.0212874i | ||||||||
\(324\) | −2.29999e6 | + | 2.99866e6i | −0.0676223 | + | 0.0881641i | ||||
\(325\) | 1.13103e7 | 0.329475 | ||||||||
\(326\) | −2.46060e7 | + | 1.21374e7i | −0.710212 | + | 0.350327i | ||||
\(327\) | − | 1.06025e7i | − | 0.303224i | ||||||
\(328\) | −2.69997e7 | − | 5.36206e6i | −0.765134 | − | 0.151953i | ||||
\(329\) | −1.05504e7 | −0.296266 | ||||||||
\(330\) | −7.39933e6 | − | 1.50005e7i | −0.205897 | − | 0.417412i | ||||
\(331\) | − | 2.54747e7i | − | 0.702467i | −0.936288 | − | 0.351233i | \(-0.885762\pi\) | ||
0.936288 | − | 0.351233i | \(-0.114238\pi\) | |||||||
\(332\) | 2.79129e7 | + | 2.14094e7i | 0.762766 | + | 0.585045i | ||||
\(333\) | −2.15406e7 | −0.583344 | ||||||||
\(334\) | 3.55945e7 | − | 1.75577e7i | 0.955307 | − | 0.471225i | ||||
\(335\) | 7.51596e6i | 0.199917i | ||||||||
\(336\) | −1.65427e6 | − | 6.16385e6i | −0.0436103 | − | 0.162493i | ||||
\(337\) | −6.19868e7 | −1.61961 | −0.809803 | − | 0.586702i | \(-0.800426\pi\) | ||||
−0.809803 | + | 0.586702i | \(0.800426\pi\) | |||||||
\(338\) | −2.92763e7 | − | 5.93513e7i | −0.758168 | − | 1.53702i | ||||
\(339\) | 2.62243e7i | 0.673138i | ||||||||
\(340\) | 2.01937e6 | − | 2.63279e6i | 0.0513781 | − | 0.0669854i | ||||
\(341\) | 2.29394e7 | 0.578520 | ||||||||
\(342\) | 1.34852e6 | − | 665189.i | 0.0337117 | − | 0.0166290i | ||||
\(343\) | 2.25200e7i | 0.558066i | ||||||||
\(344\) | −1.39974e7 | + | 7.04815e7i | −0.343852 | + | 1.73141i | ||||
\(345\) | −1.06501e7 | −0.259356 | ||||||||
\(346\) | −3.61804e7 | − | 7.33479e7i | −0.873465 | − | 1.77076i | ||||
\(347\) | − | 5.60089e7i | − | 1.34051i | −0.742133 | − | 0.670253i | \(-0.766186\pi\) | ||
0.742133 | − | 0.670253i | \(-0.233814\pi\) | |||||||
\(348\) | 2.29805e7 | + | 1.76262e7i | 0.545283 | + | 0.418235i | ||||
\(349\) | 4.87021e7 | 1.14570 | 0.572850 | − | 0.819660i | \(-0.305838\pi\) | ||||
0.572850 | + | 0.819660i | \(0.305838\pi\) | |||||||
\(350\) | 2.24100e6 | − | 1.10542e6i | 0.0522682 | − | 0.0257824i | ||||
\(351\) | 1.37098e7i | 0.317037i | ||||||||
\(352\) | −5.18673e7 | − | 5.90829e7i | −1.18923 | − | 1.35467i | ||||
\(353\) | 4.35162e7 | 0.989297 | 0.494649 | − | 0.869093i | \(-0.335297\pi\) | ||||
0.494649 | + | 0.869093i | \(0.335297\pi\) | |||||||
\(354\) | 3.25808e6 | + | 6.60505e6i | 0.0734433 | + | 0.148890i | ||||
\(355\) | 2.61836e7i | 0.585254i | ||||||||
\(356\) | −3.05891e7 | + | 3.98812e7i | −0.677980 | + | 0.883931i | ||||
\(357\) | −1.44502e6 | −0.0317591 | ||||||||
\(358\) | 1.16375e6 | − | 574045.i | 0.0253636 | − | 0.0125111i | ||||
\(359\) | − | 1.34201e7i | − | 0.290049i | −0.989428 | − | 0.145025i | \(-0.953674\pi\) | ||
0.989428 | − | 0.145025i | \(-0.0463261\pi\) | |||||||
\(360\) | −6.82184e6 | − | 1.35479e6i | −0.146216 | − | 0.0290380i | ||||
\(361\) | 4.64476e7 | 0.987283 | ||||||||
\(362\) | 2.31713e7 | + | 4.69747e7i | 0.488454 | + | 0.990235i | ||||
\(363\) | 6.21192e7i | 1.29869i | ||||||||
\(364\) | −1.83708e7 | − | 1.40905e7i | −0.380912 | − | 0.292161i | ||||
\(365\) | 4.44445e6 | 0.0913986 | ||||||||
\(366\) | −1.30105e7 | + | 6.41768e6i | −0.265368 | + | 0.130899i | ||||
\(367\) | − | 2.34709e7i | − | 0.474823i | −0.971409 | − | 0.237411i | \(-0.923701\pi\) | ||
0.971409 | − | 0.237411i | \(-0.0762989\pi\) | |||||||
\(368\) | −4.83484e7 | + | 1.29759e7i | −0.970150 | + | 0.260372i | ||||
\(369\) | 1.30646e7 | 0.260026 | ||||||||
\(370\) | −1.75372e7 | − | 3.55529e7i | −0.346223 | − | 0.701892i | ||||
\(371\) | − | 8.09271e6i | − | 0.158479i | ||||||
\(372\) | 5.80521e6 | − | 7.56867e6i | 0.112769 | − | 0.147025i | ||||
\(373\) | −5.34360e7 | −1.02969 | −0.514847 | − | 0.857282i | \(-0.672151\pi\) | ||||
−0.514847 | + | 0.857282i | \(0.672151\pi\) | |||||||
\(374\) | −1.59645e7 | + | 7.87485e6i | −0.305170 | + | 0.150531i | ||||
\(375\) | − | 2.72319e6i | − | 0.0516398i | ||||||
\(376\) | −1.05274e7 | + | 5.30087e7i | −0.198041 | + | 0.997203i | ||||
\(377\) | 1.05067e8 | 1.96083 | ||||||||
\(378\) | 1.33994e6 | + | 2.71644e6i | 0.0248091 | + | 0.0502951i | ||||
\(379\) | 2.02671e7i | 0.372285i | 0.982523 | + | 0.186142i | \(0.0595985\pi\) | ||||
−0.982523 | + | 0.186142i | \(0.940401\pi\) | |||||||
\(380\) | 2.19580e6 | + | 1.68419e6i | 0.0400168 | + | 0.0306931i | ||||
\(381\) | −4.56602e7 | −0.825588 | ||||||||
\(382\) | −2.54089e7 | + | 1.25335e7i | −0.455822 | + | 0.224844i | ||||
\(383\) | − | 5.58252e6i | − | 0.0993651i | −0.998765 | − | 0.0496826i | \(-0.984179\pi\) | ||
0.998765 | − | 0.0496826i | \(-0.0158210\pi\) | |||||||
\(384\) | −3.26198e7 | + | 2.16123e6i | −0.576087 | + | 0.0381687i | ||||
\(385\) | −1.34059e7 | −0.234917 | ||||||||
\(386\) | −3.11539e7 | − | 6.31578e7i | −0.541690 | − | 1.09816i | ||||
\(387\) | − | 3.41045e7i | − | 0.588408i | ||||||
\(388\) | −2.58787e7 | + | 3.37399e7i | −0.443044 | + | 0.577629i | ||||
\(389\) | −1.05876e7 | −0.179865 | −0.0899327 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899327 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(390\) | −2.26282e7 | + | 1.11618e7i | −0.381466 | + | 0.188166i | ||||
\(391\) | 1.13345e7i | 0.189615i | ||||||||
\(392\) | 5.40653e7 | + | 1.07372e7i | 0.897554 | + | 0.178251i | ||||
\(393\) | 2.45756e7 | 0.404880 | ||||||||
\(394\) | −1.09689e7 | − | 2.22371e7i | −0.179339 | − | 0.363571i | ||||
\(395\) | − | 3.74910e7i | − | 0.608326i | ||||||
\(396\) | 2.96074e7 | + | 2.27090e7i | 0.476776 | + | 0.365690i | ||||
\(397\) | −1.89692e7 | −0.303164 | −0.151582 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151582 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(398\) | 6.11867e6 | − | 3.01817e6i | 0.0970528 | − | 0.0478734i | ||||
\(399\) | − | 1.20517e6i | − | 0.0189728i | ||||||
\(400\) | −3.31789e6 | − | 1.23625e7i | −0.0518420 | − | 0.193164i | ||||
\(401\) | 9.20319e6 | 0.142727 | 0.0713634 | − | 0.997450i | \(-0.477265\pi\) | ||||
0.0713634 | + | 0.997450i | \(0.477265\pi\) | |||||||
\(402\) | −7.41733e6 | − | 1.50370e7i | −0.114175 | − | 0.231464i | ||||
\(403\) | − | 3.46038e7i | − | 0.528700i | ||||||
\(404\) | 5.83482e7 | − | 7.60728e7i | 0.884879 | − | 1.15368i | ||||
\(405\) | 3.30094e6 | 0.0496904 | ||||||||
\(406\) | 2.08178e7 | − | 1.02688e7i | 0.311068 | − | 0.153441i | ||||
\(407\) | 2.12682e8i | 3.15462i | ||||||||
\(408\) | −1.44186e6 | + | 7.26024e6i | −0.0212296 | + | 0.106898i | ||||
\(409\) | −6.63022e7 | −0.969076 | −0.484538 | − | 0.874770i | \(-0.661012\pi\) | ||||
−0.484538 | + | 0.874770i | \(0.661012\pi\) | |||||||
\(410\) | 1.06365e7 | + | 2.15632e7i | 0.154329 | + | 0.312868i | ||||
\(411\) | 5.20771e7i | 0.750103i | ||||||||
\(412\) | −4.06180e7 | − | 3.11542e7i | −0.580800 | − | 0.445477i | ||||
\(413\) | 5.90291e6 | 0.0837946 | ||||||||
\(414\) | 2.13074e7 | − | 1.05103e7i | 0.300283 | − | 0.148121i | ||||
\(415\) | − | 3.07267e7i | − | 0.429904i | ||||||
\(416\) | −8.91261e7 | + | 7.82413e7i | −1.23801 | + | 1.08682i | ||||
\(417\) | −1.33721e7 | −0.184413 | ||||||||
\(418\) | −6.56777e6 | − | 1.33147e7i | −0.0899268 | − | 0.182307i | ||||
\(419\) | − | 1.06809e8i | − | 1.45200i | −0.687696 | − | 0.725999i | \(-0.741378\pi\) | ||
0.687696 | − | 0.725999i | \(-0.258622\pi\) | |||||||
\(420\) | −3.39260e6 | + | 4.42318e6i | −0.0457915 | + | 0.0597017i | ||||
\(421\) | −3.11843e7 | −0.417916 | −0.208958 | − | 0.977925i | \(-0.567007\pi\) | ||||
−0.208958 | + | 0.977925i | \(0.567007\pi\) | |||||||
\(422\) | −7.74266e7 | + | 3.81923e7i | −1.03027 | + | 0.508204i | ||||
\(423\) | − | 2.56498e7i | − | 0.338893i | ||||||
\(424\) | −4.06604e7 | − | 8.07503e6i | −0.533426 | − | 0.105937i | ||||
\(425\) | −2.89820e6 | −0.0377538 | ||||||||
\(426\) | −2.58400e7 | − | 5.23850e7i | −0.334244 | − | 0.677607i | ||||
\(427\) | 1.16274e7i | 0.149348i | ||||||||
\(428\) | −1.77379e7 | − | 1.36051e7i | −0.226241 | − | 0.173528i | ||||
\(429\) | 1.35365e8 | 1.71448 | ||||||||
\(430\) | 5.62897e7 | − | 2.77661e7i | 0.707985 | − | 0.349228i | ||||
\(431\) | 9.72310e7i | 1.21443i | 0.794537 | + | 0.607215i | \(0.207714\pi\) | ||||
−0.794537 | + | 0.607215i | \(0.792286\pi\) | |||||||
\(432\) | 1.49853e7 | − | 4.02181e6i | 0.185872 | − | 0.0498850i | ||||
\(433\) | −6.52726e7 | −0.804021 | −0.402010 | − | 0.915635i | \(-0.631688\pi\) | ||||
−0.402010 | + | 0.915635i | \(0.631688\pi\) | |||||||
\(434\) | −3.38204e6 | − | 6.85636e6i | −0.0413723 | − | 0.0838734i | ||||
\(435\) | − | 2.52971e7i | − | 0.307328i | ||||||
\(436\) | −2.64921e7 | + | 3.45396e7i | −0.319636 | + | 0.416733i | ||||
\(437\) | −9.45321e6 | −0.113275 | ||||||||
\(438\) | −8.89192e6 | + | 4.38613e6i | −0.105821 | + | 0.0521986i | ||||
\(439\) | 8.96022e7i | 1.05907i | 0.848288 | + | 0.529536i | \(0.177634\pi\) | ||||
−0.848288 | + | 0.529536i | \(0.822366\pi\) | |||||||
\(440\) | −1.33766e7 | + | 6.73558e7i | −0.157032 | + | 0.790709i | ||||
\(441\) | −2.61610e7 | −0.305028 | ||||||||
\(442\) | 1.18791e7 | + | 2.40824e7i | 0.137568 | + | 0.278890i | ||||
\(443\) | − | 5.37278e7i | − | 0.617999i | −0.951062 | − | 0.309000i | \(-0.900006\pi\) | ||
0.951062 | − | 0.309000i | \(-0.0999942\pi\) | |||||||
\(444\) | 7.01728e7 | + | 5.38229e7i | 0.801714 | + | 0.614919i | ||||
\(445\) | 4.39015e7 | 0.498195 | ||||||||
\(446\) | 1.02437e8 | − | 5.05293e7i | 1.15466 | − | 0.569560i | ||||
\(447\) | 7.69015e7i | 0.861018i | ||||||||
\(448\) | −1.00123e7 | + | 2.42135e7i | −0.111353 | + | 0.269292i | ||||
\(449\) | 1.07640e8 | 1.18914 | 0.594571 | − | 0.804043i | \(-0.297322\pi\) | ||||
0.594571 | + | 0.804043i | \(0.297322\pi\) | |||||||
\(450\) | 2.68746e6 | + | 5.44823e6i | 0.0294920 | + | 0.0597885i | ||||
\(451\) | − | 1.28994e8i | − | 1.40617i | ||||||
\(452\) | 6.55259e7 | − | 8.54308e7i | 0.709573 | − | 0.925122i | ||||
\(453\) | −3.39814e7 | −0.365550 | ||||||||
\(454\) | 8.20571e7 | − | 4.04764e7i | 0.876897 | − | 0.432548i | ||||
\(455\) | 2.02227e7i | 0.214687i | ||||||||
\(456\) | −6.05518e6 | − | 1.20254e6i | −0.0638605 | − | 0.0126825i | ||||
\(457\) | 5.35694e7 | 0.561266 | 0.280633 | − | 0.959815i | \(-0.409456\pi\) | ||||
0.280633 | + | 0.959815i | \(0.409456\pi\) | |||||||
\(458\) | 4.55548e7 | + | 9.23525e7i | 0.474174 | + | 0.961285i | ||||
\(459\) | − | 3.51307e6i | − | 0.0363286i | ||||||
\(460\) | 3.46948e7 | + | 2.66111e7i | 0.356444 | + | 0.273395i | ||||
\(461\) | −5.79532e7 | −0.591528 | −0.295764 | − | 0.955261i | \(-0.595574\pi\) | ||||
−0.295764 | + | 0.955261i | \(0.595574\pi\) | |||||||
\(462\) | 2.68209e7 | − | 1.32300e7i | 0.271987 | − | 0.134163i | ||||
\(463\) | 5.12513e6i | 0.0516371i | 0.999667 | + | 0.0258185i | \(0.00821921\pi\) | ||||
−0.999667 | + | 0.0258185i | \(0.991781\pi\) | |||||||
\(464\) | −3.08215e7 | − | 1.14842e8i | −0.308532 | − | 1.14960i | ||||
\(465\) | −8.33164e6 | −0.0828651 | ||||||||
\(466\) | 3.27711e7 | + | 6.64364e7i | 0.323843 | + | 0.656520i | ||||
\(467\) | 2.52747e7i | 0.248162i | 0.992272 | + | 0.124081i | \(0.0395983\pi\) | ||||
−0.992272 | + | 0.124081i | \(0.960402\pi\) | |||||||
\(468\) | 3.42563e7 | − | 4.46625e7i | 0.334198 | − | 0.435718i | ||||
\(469\) | −1.34385e7 | −0.130267 | ||||||||
\(470\) | 4.23352e7 | − | 2.08827e7i | 0.407763 | − | 0.201138i | ||||
\(471\) | 8.75069e6i | 0.0837490i | ||||||||
\(472\) | 5.89001e6 | − | 2.96581e7i | 0.0560132 | − | 0.282045i | ||||
\(473\) | −3.36732e8 | −3.18201 | ||||||||
\(474\) | 3.69991e7 | + | 7.50075e7i | 0.347421 | + | 0.704320i | ||||
\(475\) | − | 2.41715e6i | − | 0.0225540i | ||||||
\(476\) | 4.70743e6 | + | 3.61062e6i | 0.0436479 | + | 0.0334782i | ||||
\(477\) | 1.96747e7 | 0.181281 | ||||||||
\(478\) | −3.05898e7 | + | 1.50891e7i | −0.280087 | + | 0.138159i | ||||
\(479\) | − | 1.83052e8i | − | 1.66559i | −0.553583 | − | 0.832794i | \(-0.686740\pi\) | ||
0.553583 | − | 0.832794i | \(-0.313260\pi\) | |||||||
\(480\) | 1.88383e7 | + | 2.14591e7i | 0.170341 | + | 0.194038i | ||||
\(481\) | 3.20829e8 | 2.88296 | ||||||||
\(482\) | 4.01885e7 | + | 8.14735e7i | 0.358890 | + | 0.727571i | ||||
\(483\) | − | 1.90424e7i | − | 0.168997i | ||||||
\(484\) | 1.55216e8 | − | 2.02366e8i | 1.36899 | − | 1.78485i | ||||
\(485\) | 3.71411e7 | 0.325559 | ||||||||
\(486\) | −6.60412e6 | + | 3.25762e6i | −0.0575315 | + | 0.0283787i | ||||
\(487\) | − | 7.19456e7i | − | 0.622899i | −0.950263 | − | 0.311449i | \(-0.899186\pi\) | ||
0.950263 | − | 0.311449i | \(-0.100814\pi\) | |||||||
\(488\) | 5.84198e7 | + | 1.16020e7i | 0.502691 | + | 0.0998327i | ||||
\(489\) | −5.34619e7 | −0.457213 | ||||||||
\(490\) | −2.12990e7 | − | 4.31790e7i | −0.181038 | − | 0.367016i | ||||
\(491\) | − | 5.86205e7i | − | 0.495227i | −0.968859 | − | 0.247614i | \(-0.920354\pi\) | ||
0.968859 | − | 0.247614i | \(-0.0796464\pi\) | |||||||
\(492\) | −4.25605e7 | − | 3.26441e7i | −0.357364 | − | 0.274100i | ||||
\(493\) | −2.69228e7 | −0.224688 | ||||||||
\(494\) | −2.00851e7 | + | 9.90743e6i | −0.166607 | + | 0.0821826i | ||||
\(495\) | − | 3.25920e7i | − | 0.268717i | ||||||
\(496\) | −3.78232e7 | + | 1.01511e7i | −0.309966 | + | 0.0831896i | ||||
\(497\) | −4.68163e7 | −0.381353 | ||||||||
\(498\) | 3.03235e7 | + | 6.14743e7i | 0.245522 | + | 0.497743i | ||||
\(499\) | − | 2.37768e8i | − | 1.91360i | −0.290743 | − | 0.956801i | \(-0.593902\pi\) | ||
0.290743 | − | 0.956801i | \(-0.406098\pi\) | |||||||
\(500\) | −6.80436e6 | + | 8.87134e6i | −0.0544349 | + | 0.0709707i | ||||
\(501\) | 7.73368e7 | 0.614997 | ||||||||
\(502\) | −1.72301e8 | + | 8.49911e7i | −1.36200 | + | 0.671834i | ||||
\(503\) | 2.08303e8i | 1.63678i | 0.574660 | + | 0.818392i | \(0.305134\pi\) | ||||
−0.574660 | + | 0.818392i | \(0.694866\pi\) | |||||||
\(504\) | 2.42237e6 | − | 1.21974e7i | 0.0189212 | − | 0.0952746i | ||||
\(505\) | −8.37414e7 | −0.650229 | ||||||||
\(506\) | −1.03774e8 | − | 2.10380e8i | −0.801012 | − | 1.62388i | ||||
\(507\) | − | 1.28954e8i | − | 0.989487i | ||||||
\(508\) | 1.48747e8 | + | 1.14090e8i | 1.13464 | + | 0.870275i | ||||
\(509\) | −6.06760e7 | −0.460112 | −0.230056 | − | 0.973177i | \(-0.573891\pi\) | ||||
−0.230056 | + | 0.973177i | \(0.573891\pi\) | |||||||
\(510\) | 5.79836e6 | − | 2.86016e6i | 0.0437114 | − | 0.0215616i | ||||
\(511\) | 7.94667e6i | 0.0595556i | ||||||||
\(512\) | 1.11666e8 | + | 7.44657e7i | 0.831975 | + | 0.554813i | ||||
\(513\) | 2.92997e6 | 0.0217026 | ||||||||
\(514\) | 2.75094e7 | + | 5.57693e7i | 0.202578 | + | 0.410682i | ||||
\(515\) | 4.47125e7i | 0.327346i | ||||||||
\(516\) | −8.52159e7 | + | 1.11102e8i | −0.620257 | + | 0.808673i | ||||
\(517\) | −2.53254e8 | −1.83267 | ||||||||
\(518\) | 6.35686e7 | − | 3.13566e7i | 0.457355 | − | 0.225600i | ||||
\(519\) | − | 1.59365e8i | − | 1.13996i | ||||||
\(520\) | 1.01606e8 | + | 2.01785e7i | 0.722616 | + | 0.143509i | ||||
\(521\) | −4.23437e7 | −0.299416 | −0.149708 | − | 0.988730i | \(-0.547833\pi\) | ||||
−0.149708 | + | 0.988730i | \(0.547833\pi\) | |||||||
\(522\) | 2.49651e7 | + | 5.06113e7i | 0.175518 | + | 0.355825i | ||||
\(523\) | − | 2.64065e8i | − | 1.84589i | −0.384928 | − | 0.922947i | \(-0.625774\pi\) | ||
0.384928 | − | 0.922947i | \(-0.374226\pi\) | |||||||
\(524\) | −8.00598e7 | − | 6.14063e7i | −0.556443 | − | 0.426795i | ||||
\(525\) | 4.86906e6 | 0.0336486 | ||||||||
\(526\) | −1.67712e8 | + | 8.27276e7i | −1.15241 | + | 0.568451i | ||||
\(527\) | 8.86706e6i | 0.0605826i | ||||||||
\(528\) | −3.97095e7 | − | 1.47958e8i | −0.269769 | − | 1.00517i | ||||
\(529\) | −1.33004e6 | −0.00898459 | ||||||||
\(530\) | 1.60181e7 | + | 3.24733e7i | 0.107593 | + | 0.218121i | ||||
\(531\) | 1.43509e7i | 0.0958510i | ||||||||
\(532\) | −3.01133e6 | + | 3.92609e6i | −0.0199997 | + | 0.0260750i | ||||
\(533\) | −1.94586e8 | −1.28508 | ||||||||
\(534\) | −8.78327e7 | + | 4.33254e7i | −0.576810 | + | 0.284524i | ||||
\(535\) | 1.95260e7i | 0.127512i | ||||||||
\(536\) | −1.34092e7 | + | 6.75196e7i | −0.0870778 | + | 0.438465i | ||||
\(537\) | 2.52851e6 | 0.0163283 | ||||||||
\(538\) | 8.94510e7 | + | 1.81342e8i | 0.574432 | + | 1.16454i | ||||
\(539\) | 2.58302e8i | 1.64954i | ||||||||
\(540\) | −1.07535e7 | − | 8.24797e6i | −0.0682916 | − | 0.0523800i | ||||
\(541\) | −4.99745e7 | −0.315614 | −0.157807 | − | 0.987470i | \(-0.550442\pi\) | ||||
−0.157807 | + | 0.987470i | \(0.550442\pi\) | |||||||
\(542\) | 1.42104e8 | − | 7.00958e7i | 0.892501 | − | 0.440245i | ||||
\(543\) | 1.02063e8i | 0.637483i | ||||||||
\(544\) | 2.28381e7 | − | 2.00489e7i | 0.141861 | − | 0.124536i | ||||
\(545\) | 3.80214e7 | 0.234876 | ||||||||
\(546\) | −1.99573e7 | − | 4.04592e7i | −0.122610 | − | 0.248564i | ||||
\(547\) | 2.70311e8i | 1.65159i | 0.563971 | + | 0.825795i | \(0.309273\pi\) | ||||
−0.563971 | + | 0.825795i | \(0.690727\pi\) | |||||||
\(548\) | 1.30124e8 | − | 1.69651e8i | 0.790705 | − | 1.03090i | ||||
\(549\) | −2.82681e7 | −0.170836 | ||||||||
\(550\) | 5.37934e7 | − | 2.65347e7i | 0.323326 | − | 0.159487i | ||||
\(551\) | − | 2.24541e7i | − | 0.134227i | ||||||
\(552\) | −9.56751e7 | − | 1.90008e7i | −0.568829 | − | 0.112968i | ||||
\(553\) | 6.70339e7 | 0.396387 | ||||||||
\(554\) | 6.95846e6 | + | 1.41068e7i | 0.0409246 | + | 0.0829656i | ||||
\(555\) | − | 7.72466e7i | − | 0.451856i | ||||||
\(556\) | 4.35624e7 | + | 3.34126e7i | 0.253447 | + | 0.194395i | ||||
\(557\) | 1.75087e8 | 1.01319 | 0.506593 | − | 0.862185i | \(-0.330905\pi\) | ||||
0.506593 | + | 0.862185i | \(0.330905\pi\) | |||||||
\(558\) | 1.66689e7 | − | 8.22230e6i | 0.0959412 | − | 0.0473250i | ||||
\(559\) | 5.07957e8i | 2.90798i | ||||||||
\(560\) | 2.21042e7 | − | 5.93238e6i | 0.125866 | − | 0.0337804i | ||||
\(561\) | −3.46865e7 | −0.196459 | ||||||||
\(562\) | 1.31428e8 | + | 2.66441e8i | 0.740421 | + | 1.50104i | ||||
\(563\) | − | 1.20097e7i | − | 0.0672989i | −0.999434 | − | 0.0336495i | \(-0.989287\pi\) | ||
0.999434 | − | 0.0336495i | \(-0.0107130\pi\) | |||||||
\(564\) | −6.40904e7 | + | 8.35592e7i | −0.357236 | + | 0.465754i | ||||
\(565\) | −9.40427e7 | −0.521411 | ||||||||
\(566\) | −9.37299e7 | + | 4.62343e7i | −0.516927 | + | 0.254985i | ||||
\(567\) | 5.90208e6i | 0.0323784i | ||||||||
\(568\) | −4.67140e7 | + | 2.35220e8i | −0.254919 | + | 1.28360i | ||||
\(569\) | 1.60968e8 | 0.873781 | 0.436891 | − | 0.899515i | \(-0.356080\pi\) | ||||
0.436891 | + | 0.899515i | \(0.356080\pi\) | |||||||
\(570\) | 2.38543e6 | + | 4.83594e6i | 0.0128808 | + | 0.0261130i | ||||
\(571\) | 3.01355e8i | 1.61871i | 0.587319 | + | 0.809356i | \(0.300184\pi\) | ||||
−0.587319 | + | 0.809356i | \(0.699816\pi\) | |||||||
\(572\) | −4.40977e8 | − | 3.38232e8i | −2.35629 | − | 1.80728i | ||||
\(573\) | −5.52064e7 | −0.293444 | ||||||||
\(574\) | −3.85550e7 | + | 1.90181e7i | −0.203866 | + | 0.100561i | ||||
\(575\) | − | 3.81923e7i | − | 0.200896i | ||||||
\(576\) | −5.88668e7 | − | 2.43416e7i | −0.308037 | − | 0.127374i | ||||
\(577\) | 3.49901e8 | 1.82145 | 0.910726 | − | 0.413012i | \(-0.135523\pi\) | ||||
0.910726 | + | 0.413012i | \(0.135523\pi\) | |||||||
\(578\) | 8.23798e7 | + | 1.67007e8i | 0.426616 | + | 0.864871i | ||||
\(579\) | − | 1.37224e8i | − | 0.706961i | ||||||
\(580\) | −6.32091e7 | + | 8.24103e7i | −0.323963 | + | 0.422374i | ||||
\(581\) | 5.49393e7 | 0.280127 | ||||||||
\(582\) | −7.43074e7 | + | 3.66537e7i | −0.376932 | + | 0.185930i | ||||
\(583\) | − | 1.94259e8i | − | 0.980338i | ||||||
\(584\) | 3.99267e7 | + | 7.92931e6i | 0.200459 | + | 0.0398104i | ||||
\(585\) | −4.91647e7 | −0.245576 | ||||||||
\(586\) | −1.06127e8 | − | 2.15149e8i | −0.527392 | − | 1.06917i | ||||
\(587\) | 3.88340e7i | 0.191998i | 0.995381 | + | 0.0959992i | \(0.0306046\pi\) | ||||
−0.995381 | + | 0.0959992i | \(0.969395\pi\) | |||||||
\(588\) | 8.52248e7 | + | 6.53679e7i | 0.419212 | + | 0.321538i | ||||
\(589\) | −7.39530e6 | −0.0361918 | ||||||||
\(590\) | −2.36863e7 | + | 1.16838e7i | −0.115330 | + | 0.0568889i | ||||
\(591\) | − | 4.83150e7i | − | 0.234056i | ||||||
\(592\) | −9.41159e7 | − | 3.50677e8i | −0.453626 | − | 1.69022i | ||||
\(593\) | −1.76851e8 | −0.848091 | −0.424046 | − | 0.905641i | \(-0.639390\pi\) | ||||
−0.424046 | + | 0.905641i | \(0.639390\pi\) | |||||||
\(594\) | 3.21643e7 | + | 6.52061e7i | 0.153467 | + | 0.311121i | ||||
\(595\) | − | 5.18197e6i | − | 0.0246005i | ||||||
\(596\) | 1.92152e8 | − | 2.50522e8i | 0.907622 | − | 1.18333i | ||||
\(597\) | 1.32942e7 | 0.0624796 | ||||||||
\(598\) | −3.17356e8 | + | 1.56543e8i | −1.48403 | + | 0.732031i | ||||
\(599\) | − | 1.77934e8i | − | 0.827900i | −0.910300 | − | 0.413950i | \(-0.864149\pi\) | ||
0.910300 | − | 0.413950i | \(-0.135851\pi\) | |||||||
\(600\) | 4.85842e6 | − | 2.44638e7i | 0.0224927 | − | 0.113258i | ||||
\(601\) | −1.37416e8 | −0.633016 | −0.316508 | − | 0.948590i | \(-0.602510\pi\) | ||||
−0.316508 | + | 0.948590i | \(0.602510\pi\) | |||||||
\(602\) | 4.96458e7 | + | 1.00646e8i | 0.227558 | + | 0.461325i | ||||
\(603\) | − | 3.26713e7i | − | 0.149010i | ||||||
\(604\) | 1.10701e8 | + | 8.49084e7i | 0.502390 | + | 0.385336i | ||||
\(605\) | −2.22765e8 | −1.00596 | ||||||||
\(606\) | 1.67540e8 | − | 8.26425e7i | 0.752835 | − | 0.371352i | ||||
\(607\) | − | 3.25760e8i | − | 1.45657i | −0.685275 | − | 0.728284i | \(-0.740318\pi\) | ||
0.685275 | − | 0.728284i | \(-0.259682\pi\) | |||||||
\(608\) | 1.67212e7 | + | 1.90474e7i | 0.0743972 | + | 0.0847472i | ||||
\(609\) | 4.52312e7 | 0.200256 | ||||||||
\(610\) | −2.30144e7 | − | 4.66567e7i | −0.101394 | − | 0.205553i | ||||
\(611\) | 3.82032e8i | 1.67485i | ||||||||
\(612\) | −8.77802e6 | + | 1.14445e7i | −0.0382950 | + | 0.0499279i | ||||
\(613\) | 1.79249e8 | 0.778173 | 0.389087 | − | 0.921201i | \(-0.372791\pi\) | ||||
0.389087 | + | 0.921201i | \(0.372791\pi\) | |||||||
\(614\) | −1.45043e8 | + | 7.15457e7i | −0.626603 | + | 0.309085i | ||||
\(615\) | 4.68508e7i | 0.201415i | ||||||||
\(616\) | −1.20432e8 | − | 2.39174e7i | −0.515228 | − | 0.102323i | ||||
\(617\) | −4.40621e7 | −0.187590 | −0.0937951 | − | 0.995592i | \(-0.529900\pi\) | ||||
−0.0937951 | + | 0.995592i | \(0.529900\pi\) | |||||||
\(618\) | −4.41257e7 | − | 8.94553e7i | −0.186951 | − | 0.379001i | ||||
\(619\) | 3.99677e8i | 1.68515i | 0.538582 | + | 0.842573i | \(0.318960\pi\) | ||||
−0.538582 | + | 0.842573i | \(0.681040\pi\) | |||||||
\(620\) | 2.71420e7 | + | 2.08180e7i | 0.113885 | + | 0.0873503i | ||||
\(621\) | 4.62951e7 | 0.193313 | ||||||||
\(622\) | 1.59887e7 | − | 7.88678e6i | 0.0664420 | − | 0.0327739i | ||||
\(623\) | 7.84958e7i | 0.324625i | ||||||||
\(624\) | −2.23194e8 | + | 5.99014e7i | −0.918604 | + | 0.246538i | ||||
\(625\) | 9.76562e6 | 0.0400000 | ||||||||
\(626\) | −1.79889e8 | − | 3.64686e8i | −0.733300 | − | 1.48661i | ||||
\(627\) | − | 2.89292e7i | − | 0.117364i | ||||||
\(628\) | 2.18651e7 | − | 2.85071e7i | 0.0882821 | − | 0.115100i | ||||
\(629\) | −8.22108e7 | −0.330352 | ||||||||
\(630\) | −9.74143e6 | + | 4.80517e6i | −0.0389584 | + | 0.0192171i | ||||
\(631\) | − | 1.34075e8i | − | 0.533654i | −0.963744 | − | 0.266827i | \(-0.914025\pi\) | ||
0.963744 | − | 0.266827i | \(-0.0859753\pi\) | |||||||
\(632\) | 6.68875e7 | − | 3.36800e8i | 0.264968 | − | 1.33420i | ||||
\(633\) | −1.68226e8 | −0.663258 | ||||||||
\(634\) | −8.00224e7 | − | 1.62228e8i | −0.314010 | − | 0.636587i | ||||
\(635\) | − | 1.63742e8i | − | 0.639498i | ||||||
\(636\) | −6.40942e7 | − | 4.91606e7i | −0.249142 | − | 0.191094i | ||||
\(637\) | 3.89647e8 | 1.50748 | ||||||||
\(638\) | 4.99714e8 | − | 2.46494e8i | 1.92424 | − | 0.949172i | ||||
\(639\) | − | 1.13818e8i | − | 0.436223i | ||||||
\(640\) | −7.75038e6 | − | 1.16978e8i | −0.0295653 | − | 0.446235i | ||||
\(641\) | 4.99004e8 | 1.89466 | 0.947328 | − | 0.320266i | \(-0.103772\pi\) | ||||
0.947328 | + | 0.320266i | \(0.103772\pi\) | |||||||
\(642\) | −1.92698e7 | − | 3.90653e7i | −0.0728235 | − | 0.147634i | ||||
\(643\) | − | 4.27044e8i | − | 1.60635i | −0.595745 | − | 0.803174i | \(-0.703143\pi\) | ||
0.595745 | − | 0.803174i | \(-0.296857\pi\) | |||||||
\(644\) | −4.75807e7 | + | 6.20343e7i | −0.178145 | + | 0.232260i | ||||
\(645\) | 1.22302e8 | 0.455779 | ||||||||
\(646\) | 5.14672e6 | − | 2.53873e6i | 0.0190912 | − | 0.00941713i | ||||
\(647\) | − | 2.61812e7i | − | 0.0966666i | −0.998831 | − | 0.0483333i | \(-0.984609\pi\) | ||
0.998831 | − | 0.0483333i | \(-0.0153910\pi\) | |||||||
\(648\) | 2.96540e7 | + | 5.88918e6i | 0.108983 | + | 0.0216436i | ||||
\(649\) | 1.41695e8 | 0.518346 | ||||||||
\(650\) | −4.00274e7 | − | 8.11468e7i | −0.145753 | − | 0.295482i | ||||
\(651\) | − | 1.48970e7i | − | 0.0539951i | ||||||
\(652\) | 1.74163e8 | + | 1.33584e8i | 0.628366 | + | 0.481960i | ||||
\(653\) | 4.83197e8 | 1.73534 | 0.867671 | − | 0.497139i | \(-0.165616\pi\) | ||||
0.867671 | + | 0.497139i | \(0.165616\pi\) | |||||||
\(654\) | −7.60686e7 | + | 3.75225e7i | −0.271939 | + | 0.134140i | ||||
\(655\) | 8.81304e7i | 0.313619i | ||||||||
\(656\) | 5.70822e7 | + | 2.12689e8i | 0.202204 | + | 0.753415i | ||||
\(657\) | −1.93197e7 | −0.0681245 | ||||||||
\(658\) | 3.73383e7 | + | 7.56952e7i | 0.131062 | + | 0.265700i | ||||
\(659\) | − | 2.51071e6i | − | 0.00877283i | −0.999990 | − | 0.00438642i | \(-0.998604\pi\) | ||
0.999990 | − | 0.00438642i | \(-0.00139624\pi\) | |||||||
\(660\) | −8.14367e7 | + | 1.06175e8i | −0.283262 | + | 0.369309i | ||||
\(661\) | 4.38678e8 | 1.51894 | 0.759472 | − | 0.650540i | \(-0.225458\pi\) | ||||
0.759472 | + | 0.650540i | \(0.225458\pi\) | |||||||
\(662\) | −1.82772e8 | + | 9.01560e7i | −0.629992 | + | 0.310757i | ||||
\(663\) | 5.23243e7i | 0.179540i | ||||||||
\(664\) | 5.48193e7 | − | 2.76033e8i | 0.187253 | − | 0.942881i | ||||
\(665\) | 4.32186e6 | 0.0146962 | ||||||||
\(666\) | 7.62329e7 | + | 1.54546e8i | 0.258059 | + | 0.523159i | ||||
\(667\) | − | 3.54787e8i | − | 1.19561i | ||||||
\(668\) | −2.51940e8 | − | 1.93239e8i | −0.845216 | − | 0.648285i | ||||
\(669\) | 2.22568e8 | 0.743333 | ||||||||
\(670\) | 5.39242e7 | − | 2.65993e7i | 0.179291 | − | 0.0884393i | ||||
\(671\) | 2.79106e8i | 0.923852i | ||||||||
\(672\) | −3.83688e7 | + | 3.36829e7i | −0.126436 | + | 0.110994i | ||||
\(673\) | −1.98183e8 | −0.650160 | −0.325080 | − | 0.945686i | \(-0.605391\pi\) | ||||
−0.325080 | + | 0.945686i | \(0.605391\pi\) | |||||||
\(674\) | 2.19373e8 | + | 4.44732e8i | 0.716480 | + | 1.45251i | ||||
\(675\) | 1.18375e7i | 0.0384900i | ||||||||
\(676\) | −3.22213e8 | + | 4.20092e8i | −1.04305 | + | 1.35989i | ||||
\(677\) | −1.73607e8 | −0.559500 | −0.279750 | − | 0.960073i | \(-0.590252\pi\) | ||||
−0.279750 | + | 0.960073i | \(0.590252\pi\) | |||||||
\(678\) | 1.88149e8 | − | 9.28086e7i | 0.603689 | − | 0.297783i | ||||
\(679\) | 6.64082e7i | 0.212135i | ||||||||
\(680\) | −2.60359e7 | − | 5.17065e6i | −0.0828030 | − | 0.0164444i | ||||
\(681\) | 1.78287e8 | 0.564519 | ||||||||
\(682\) | −8.11833e7 | − | 1.64581e8i | −0.255925 | − | 0.518833i | ||||
\(683\) | 1.59479e8i | 0.500544i | 0.968176 | + | 0.250272i | \(0.0805200\pi\) | ||||
−0.968176 | + | 0.250272i | \(0.919480\pi\) | |||||||
\(684\) | −9.54496e6 | − | 7.32103e6i | −0.0298267 | − | 0.0228773i | ||||
\(685\) | −1.86753e8 | −0.581028 | ||||||||
\(686\) | 1.61572e8 | − | 7.96990e7i | 0.500489 | − | 0.246877i | ||||
\(687\) | 2.00656e8i | 0.618846i | ||||||||
\(688\) | 5.55216e8 | − | 1.49011e8i | 1.70489 | − | 0.457564i | ||||
\(689\) | −2.93038e8 | −0.895914 | ||||||||
\(690\) | 3.76911e7 | + | 7.64105e7i | 0.114734 | + | 0.232598i | ||||
\(691\) | − | 3.01483e8i | − | 0.913753i | −0.889530 | − | 0.456877i | \(-0.848968\pi\) | ||
0.889530 | − | 0.456877i | \(-0.151032\pi\) | |||||||
\(692\) | −3.98200e8 | + | 5.19162e8i | −1.20166 | + | 1.56670i | ||||
\(693\) | 5.82744e7 | 0.175097 | ||||||||
\(694\) | −4.01843e8 | + | 1.98218e8i | −1.20220 | + | 0.593012i | ||||
\(695\) | − | 4.79538e7i | − | 0.142846i | ||||||
\(696\) | 4.51323e7 | − | 2.27256e8i | 0.133863 | − | 0.674044i | ||||
\(697\) | 4.98617e7 | 0.147254 | ||||||||
\(698\) | −1.72358e8 | − | 3.49419e8i | −0.506834 | − | 1.02750i | ||||
\(699\) | 1.44348e8i | 0.422647i | ||||||||
\(700\) | −1.58619e7 | − | 1.21662e7i | −0.0462447 | − | 0.0354700i | ||||
\(701\) | 1.33555e8 | 0.387710 | 0.193855 | − | 0.981030i | \(-0.437901\pi\) | ||||
0.193855 | + | 0.981030i | \(0.437901\pi\) | |||||||
\(702\) | 9.83628e7 | − | 4.85195e7i | 0.284328 | − | 0.140251i | ||||
\(703\) | − | 6.85654e7i | − | 0.197351i | ||||||
\(704\) | −2.40338e8 | + | 5.81225e8i | −0.688817 | + | 1.66581i | ||||
\(705\) | 9.19825e7 | 0.262505 | ||||||||
\(706\) | −1.54005e8 | − | 3.12212e8i | −0.437645 | − | 0.887229i | ||||
\(707\) | − | 1.49730e8i | − | 0.423691i | ||||||
\(708\) | 3.58583e7 | − | 4.67510e7i | 0.101039 | − | 0.131732i | ||||
\(709\) | −6.26975e8 | −1.75919 | −0.879593 | − | 0.475728i | \(-0.842185\pi\) | ||||
−0.879593 | + | 0.475728i | \(0.842185\pi\) | |||||||
\(710\) | 1.87858e8 | − | 9.26647e7i | 0.524872 | − | 0.258904i | ||||
\(711\) | 1.62970e8i | 0.453419i | ||||||||
\(712\) | 3.94389e8 | + | 7.83243e7i | 1.09266 | + | 0.216998i | ||||
\(713\) | −1.16850e8 | −0.322373 | ||||||||
\(714\) | 5.11397e6 | + | 1.03675e7i | 0.0140496 | + | 0.0284825i | ||||
\(715\) | 4.85430e8i | 1.32803i | ||||||||
\(716\) | −8.23711e6 | − | 6.31791e6i | −0.0224407 | − | 0.0172121i | ||||
\(717\) | −6.64631e7 | −0.180311 | ||||||||
\(718\) | −9.62840e7 | + | 4.74941e7i | −0.260124 | + | 0.128312i | ||||
\(719\) | 1.61719e8i | 0.435084i | 0.976051 | + | 0.217542i | \(0.0698039\pi\) | ||||
−0.976051 | + | 0.217542i | \(0.930196\pi\) | |||||||
\(720\) | 1.44226e7 | + | 5.37388e7i | 0.0386408 | + | 0.143976i | ||||
\(721\) | −7.99459e7 | −0.213300 | ||||||||
\(722\) | −1.64380e8 | − | 3.33244e8i | −0.436754 | − | 0.885423i | ||||
\(723\) | 1.77019e8i | 0.468388i | ||||||||
\(724\) | 2.55022e8 | − | 3.32490e8i | 0.671988 | − | 0.876119i | ||||
\(725\) | 9.07178e7 | 0.238056 | ||||||||
\(726\) | 4.45682e8 | − | 2.19842e8i | 1.16470 | − | 0.574514i | ||||
\(727\) | 2.51088e8i | 0.653466i | 0.945117 | + | 0.326733i | \(0.105948\pi\) | ||||
−0.945117 | + | 0.326733i | \(0.894052\pi\) | |||||||
\(728\) | −3.60792e7 | + | 1.81671e8i | −0.0935110 | + | 0.470859i | ||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | −1.57291e7 | − | 3.18873e7i | −0.0404329 | − | 0.0819688i | ||||
\(731\) | − | 1.30162e8i | − | 0.333220i | ||||||
\(732\) | 9.20889e7 | + | 7.06327e7i | 0.234787 | + | 0.180083i | ||||
\(733\) | 1.62811e8 | 0.413400 | 0.206700 | − | 0.978404i | \(-0.433728\pi\) | ||||
0.206700 | + | 0.978404i | \(0.433728\pi\) | |||||||
\(734\) | −1.68395e8 | + | 8.30643e7i | −0.425834 | + | 0.210052i | ||||
\(735\) | − | 9.38160e7i | − | 0.236273i | ||||||
\(736\) | 2.64204e8 | + | 3.00960e8i | 0.662683 | + | 0.754874i | ||||
\(737\) | −3.22581e8 | −0.805818 | ||||||||
\(738\) | −4.62360e7 | − | 9.37334e7i | −0.115030 | − | 0.233198i | ||||
\(739\) | 1.02236e8i | 0.253320i | 0.991946 | + | 0.126660i | \(0.0404257\pi\) | ||||
−0.991946 | + | 0.126660i | \(0.959574\pi\) | |||||||
\(740\) | −1.93014e8 | + | 2.51646e8i | −0.476314 | + | 0.621005i | ||||
\(741\) | −4.36394e7 | −0.107257 | ||||||||
\(742\) | −5.80622e7 | + | 2.86404e7i | −0.142129 | + | 0.0701080i | ||||
\(743\) | − | 4.84447e8i | − | 1.18108i | −0.807008 | − | 0.590540i | \(-0.798915\pi\) | ||
0.807008 | − | 0.590540i | \(-0.201085\pi\) | |||||||
\(744\) | −7.48472e7 | − | 1.48644e7i | −0.181743 | − | 0.0360935i | ||||
\(745\) | −2.75776e8 | −0.666941 | ||||||||
\(746\) | 1.89112e8 | + | 3.83384e8i | 0.455515 | + | 0.923458i | ||||
\(747\) | 1.33566e8i | 0.320432i | ||||||||
\(748\) | 1.12998e8 | + | 8.66702e7i | 0.270002 | + | 0.207093i | ||||
\(749\) | −3.49125e7 | −0.0830874 | ||||||||
\(750\) | −1.95379e7 | + | 9.63747e6i | −0.0463120 | + | 0.0228444i | ||||
\(751\) | − | 5.03888e8i | − | 1.18964i | −0.803860 | − | 0.594818i | \(-0.797224\pi\) | ||
0.803860 | − | 0.594818i | \(-0.202776\pi\) | |||||||
\(752\) | 4.17574e8 | − | 1.12070e8i | 0.981929 | − | 0.263533i | ||||
\(753\) | −3.74362e8 | −0.876812 | ||||||||
\(754\) | −3.71834e8 | − | 7.53813e8i | −0.867432 | − | 1.75853i | ||||
\(755\) | − | 1.21861e8i | − | 0.283154i | ||||||
\(756\) | 1.47474e7 | − | 1.92272e7i | 0.0341310 | − | 0.0444990i | ||||
\(757\) | −1.36114e8 | −0.313772 | −0.156886 | − | 0.987617i | \(-0.550145\pi\) | ||||
−0.156886 | + | 0.987617i | \(0.550145\pi\) | |||||||
\(758\) | 1.45409e8 | − | 7.17262e7i | 0.333875 | − | 0.164691i | ||||
\(759\) | − | 4.57097e8i | − | 1.04540i | ||||||
\(760\) | 4.31242e6 | − | 2.17144e7i | 0.00982381 | − | 0.0494661i | ||||
\(761\) | −6.36763e8 | −1.44485 | −0.722426 | − | 0.691448i | \(-0.756973\pi\) | ||||
−0.722426 | + | 0.691448i | \(0.756973\pi\) | |||||||
\(762\) | 1.61593e8 | + | 3.27595e8i | 0.365223 | + | 0.740410i | ||||
\(763\) | 6.79822e7i | 0.153046i | ||||||||
\(764\) | 1.79846e8 | + | 1.37943e8i | 0.403292 | + | 0.309328i | ||||
\(765\) | 1.25982e7 | 0.0281400 | ||||||||
\(766\) | −4.00525e7 | + | 1.97567e7i | −0.0891134 | + | 0.0439571i | ||||
\(767\) | − | 2.13745e8i | − | 0.473707i | ||||||
\(768\) | 1.30949e8 | + | 2.26386e8i | 0.289080 | + | 0.499766i | ||||
\(769\) | −3.95443e8 | −0.869570 | −0.434785 | − | 0.900534i | \(-0.643176\pi\) | ||||
−0.434785 | + | 0.900534i | \(0.643176\pi\) | |||||||
\(770\) | 4.74441e7 | + | 9.61825e7i | 0.103923 | + | 0.210680i | ||||
\(771\) | 1.21171e8i | 0.264385i | ||||||||
\(772\) | −3.42879e8 | + | 4.47035e8i | −0.745227 | + | 0.971606i | ||||
\(773\) | 4.24812e8 | 0.919725 | 0.459863 | − | 0.887990i | \(-0.347899\pi\) | ||||
0.459863 | + | 0.887990i | \(0.347899\pi\) | |||||||
\(774\) | −2.44687e8 | + | 1.20697e8i | −0.527701 | + | 0.260300i | ||||
\(775\) | − | 2.98780e7i | − | 0.0641870i | ||||||
\(776\) | 3.33657e8 | + | 6.62631e7i | 0.714027 | + | 0.141803i | ||||
\(777\) | 1.38117e8 | 0.294431 | ||||||||
\(778\) | 3.74698e7 | + | 7.59618e7i | 0.0795687 | + | 0.161308i | ||||
\(779\) | 4.15856e7i | 0.0879691i | ||||||||
\(780\) | 1.60164e8 | + | 1.22847e8i | 0.337505 | + | 0.258868i | ||||
\(781\) | −1.12379e9 | −2.35902 | ||||||||
\(782\) | 8.13210e7 | − | 4.01133e7i | 0.170052 | − | 0.0838819i | ||||
\(783\) | 1.09964e8i | 0.229069i | ||||||||
\(784\) | −1.14304e8 | − | 4.25898e8i | −0.237199 | − | 0.883806i | ||||
\(785\) | −3.13808e7 | −0.0648717 | ||||||||
\(786\) | −8.69739e7 | − | 1.76321e8i | −0.179111 | − | 0.363108i | ||||
\(787\) | 7.13202e8i | 1.46315i | 0.681762 | + | 0.731574i | \(0.261214\pi\) | ||||
−0.681762 | + | 0.731574i | \(0.738786\pi\) | |||||||
\(788\) | −1.20723e8 | + | 1.57396e8i | −0.246725 | + | 0.321673i | ||||
\(789\) | −3.64392e8 | −0.741887 | ||||||||
\(790\) | −2.68984e8 | + | 1.32682e8i | −0.545564 | + | 0.269111i | ||||
\(791\) | − | 1.68148e8i | − | 0.339753i | ||||||
\(792\) | 5.81471e7 | − | 2.92790e8i | 0.117045 | − | 0.589360i | ||||
\(793\) | 4.21029e8 | 0.844293 | ||||||||
\(794\) | 6.71328e7 | + | 1.36097e8i | 0.134114 | + | 0.271886i | ||||
\(795\) | 7.05554e7i | 0.140420i | ||||||||
\(796\) | −4.33084e7 | − | 3.32178e7i | −0.0858683 | − | 0.0658615i | ||||
\(797\) | −4.19593e8 | −0.828807 | −0.414404 | − | 0.910093i | \(-0.636010\pi\) | ||||
−0.414404 | + | 0.910093i | \(0.636010\pi\) | |||||||
\(798\) | −8.64665e6 | + | 4.26515e6i | −0.0170153 | + | 0.00839316i | ||||
\(799\) | − | 9.78937e7i | − | 0.191917i | ||||||
\(800\) | −7.69542e7 | + | 6.75560e7i | −0.150301 | + | 0.131945i | ||||
\(801\) | −1.90836e8 | −0.371332 | ||||||||
\(802\) | −3.25704e7 | − | 6.60294e7i | −0.0631394 | − | 0.128001i | ||||
\(803\) | 1.90754e8i | 0.368405i | ||||||||
\(804\) | −8.16348e7 | + | 1.06433e8i | −0.157075 | + | 0.204790i | ||||
\(805\) | 6.82878e7 | 0.130905 | ||||||||
\(806\) | −2.48270e8 | + | 1.22464e8i | −0.474153 | + | 0.233886i | ||||
\(807\) | 3.94007e8i | 0.749692i | ||||||||
\(808\) | −7.52290e8 | − | 1.49402e8i | −1.42610 | − | 0.283220i | ||||
\(809\) | 8.33070e8 | 1.57339 | 0.786695 | − | 0.617342i | \(-0.211791\pi\) | ||||
0.786695 | + | 0.617342i | \(0.211791\pi\) | |||||||
\(810\) | −1.16821e7 | − | 2.36830e7i | −0.0219820 | − | 0.0445637i | ||||
\(811\) | − | 3.54040e8i | − | 0.663727i | −0.943327 | − | 0.331864i | \(-0.892323\pi\) | ||
0.943327 | − | 0.331864i | \(-0.107677\pi\) | |||||||
\(812\) | −1.47350e8 | − | 1.13018e8i | −0.275220 | − | 0.211096i | ||||
\(813\) | 3.08752e8 | 0.574565 | ||||||||
\(814\) | 1.52591e9 | − | 7.52689e8i | 2.82916 | − | 1.39554i | ||||
\(815\) | − | 1.91720e8i | − | 0.354155i | ||||||
\(816\) | 5.71923e7 | − | 1.53494e7i | 0.105261 | − | 0.0282502i | ||||
\(817\) | 1.08557e8 | 0.199064 | ||||||||
\(818\) | 2.34646e8 | + | 4.75693e8i | 0.428699 | + | 0.869094i | ||||
\(819\) | − | 8.79065e7i | − | 0.160018i | ||||||
\(820\) | 1.17065e8 | − | 1.52626e8i | 0.212317 | − | 0.276813i | ||||
\(821\) | 1.14351e8 | 0.206638 | 0.103319 | − | 0.994648i | \(-0.467054\pi\) | ||||
0.103319 | + | 0.994648i | \(0.467054\pi\) | |||||||
\(822\) | 3.73633e8 | − | 1.84303e8i | 0.672714 | − | 0.331830i | ||||
\(823\) | − | 8.23571e8i | − | 1.47741i | −0.674028 | − | 0.738706i | \(-0.735437\pi\) | ||
0.674028 | − | 0.738706i | \(-0.264563\pi\) | |||||||
\(824\) | −7.97712e7 | + | 4.01674e8i | −0.142582 | + | 0.717947i | ||||
\(825\) | 1.16878e8 | 0.208147 | ||||||||
\(826\) | −2.08906e7 | − | 4.23512e7i | −0.0370690 | − | 0.0751493i | ||||
\(827\) | − | 1.96296e7i | − | 0.0347053i | −0.999849 | − | 0.0173526i | \(-0.994476\pi\) | ||
0.999849 | − | 0.0173526i | \(-0.00552379\pi\) | |||||||
\(828\) | −1.50816e8 | − | 1.15676e8i | −0.265678 | − | 0.203776i | ||||
\(829\) | −8.54284e8 | −1.49947 | −0.749737 | − | 0.661736i | \(-0.769820\pi\) | ||||
−0.749737 | + | 0.661736i | \(0.769820\pi\) | |||||||
\(830\) | −2.20453e8 | + | 1.08743e8i | −0.385550 | + | 0.190181i | ||||
\(831\) | 3.06501e7i | 0.0534107i | ||||||||
\(832\) | 8.76772e8 | + | 3.62547e8i | 1.52236 | + | 0.629498i | ||||
\(833\) | −9.98450e7 | −0.172739 | ||||||||
\(834\) | 4.73245e7 | + | 9.59400e7i | 0.0815807 | + | 0.165387i | ||||
\(835\) | 2.77337e8i | 0.476375i | ||||||||
\(836\) | −7.22846e7 | + | 9.42426e7i | −0.123716 | + | 0.161298i | ||||
\(837\) | 3.62169e7 | 0.0617640 | ||||||||
\(838\) | −7.66314e8 | + | 3.78001e8i | −1.30219 | + | 0.642334i | ||||
\(839\) | − | 6.38615e8i | − | 1.08132i | −0.841242 | − | 0.540659i | \(-0.818175\pi\) | ||
0.841242 | − | 0.540659i | \(-0.181825\pi\) | |||||||
\(840\) | 4.37412e7 | + | 8.68686e6i | 0.0737994 | + | 0.0146563i | ||||
\(841\) | 2.47900e8 | 0.416762 | ||||||||
\(842\) | 1.10362e8 | + | 2.23735e8i | 0.184877 | + | 0.374799i | ||||
\(843\) | 5.78903e8i | 0.966325i | ||||||||
\(844\) | 5.48031e8 | + | 4.20343e8i | 0.911544 | + | 0.699159i | ||||
\(845\) | 4.62440e8 | 0.766453 | ||||||||
\(846\) | −1.84027e8 | + | 9.07754e7i | −0.303928 | + | 0.149919i | ||||
\(847\) | − | 3.98304e8i | − | 0.655488i | ||||||
\(848\) | 8.59634e7 | + | 3.20301e8i | 0.140970 | + | 0.525256i | ||||
\(849\) | −2.03649e8 | −0.332782 | ||||||||
\(850\) | 1.02568e7 | + | 2.07935e7i | 0.0167015 | + | 0.0338587i | ||||
\(851\) | − | 1.08337e9i | − | 1.75788i | ||||||
\(852\) | −2.84394e8 | + | 3.70785e8i | −0.459834 | + | 0.599519i | ||||
\(853\) | −8.91021e7 | −0.143562 | −0.0717812 | − | 0.997420i | \(-0.522868\pi\) | ||||
−0.0717812 | + | 0.997420i | \(0.522868\pi\) | |||||||
\(854\) | 8.34222e7 | − | 4.11498e7i | 0.133939 | − | 0.0660684i | ||||
\(855\) | 1.05071e7i | 0.0168107i | ||||||||
\(856\) | −3.48362e7 | + | 1.75412e8i | −0.0555404 | + | 0.279664i | ||||
\(857\) | 1.62561e8 | 0.258269 | 0.129135 | − | 0.991627i | \(-0.458780\pi\) | ||||
0.129135 | + | 0.991627i | \(0.458780\pi\) | |||||||
\(858\) | −4.79060e8 | − | 9.71190e8i | −0.758452 | − | 1.53760i | ||||
\(859\) | 8.52772e8i | 1.34541i | 0.739913 | + | 0.672703i | \(0.234867\pi\) | ||||
−0.739913 | + | 0.672703i | \(0.765133\pi\) | |||||||
\(860\) | −3.98423e8 | − | 3.05592e8i | −0.626396 | − | 0.480449i | ||||
\(861\) | −8.37692e7 | −0.131243 | ||||||||
\(862\) | 6.97596e8 | − | 3.44104e8i | 1.08914 | − | 0.537239i | ||||
\(863\) | 5.82925e8i | 0.906944i | 0.891271 | + | 0.453472i | \(0.149815\pi\) | ||||
−0.891271 | + | 0.453472i | \(0.850185\pi\) | |||||||
\(864\) | −8.18885e7 | − | 9.32807e7i | −0.126964 | − | 0.144627i | ||||
\(865\) | 5.71497e8 | 0.883010 | ||||||||
\(866\) | 2.31002e8 | + | 4.68307e8i | 0.355682 | + | 0.721069i | ||||
\(867\) | 3.62860e8i | 0.556777i | ||||||||
\(868\) | −3.72226e7 | + | 4.85298e7i | −0.0569178 | + | 0.0742078i | ||||
\(869\) | 1.60910e9 | 2.45201 | ||||||||
\(870\) | −1.81497e8 | + | 8.95273e7i | −0.275621 | + | 0.135956i | ||||
\(871\) | 4.86611e8i | 0.736423i | ||||||||
\(872\) | 3.41565e8 | + | 6.78337e7i | 0.515138 | + | 0.102305i | ||||
\(873\) | −1.61449e8 | −0.242657 | ||||||||
\(874\) | 3.34553e7 | + | 6.78232e7i | 0.0501106 | + | 0.101588i | ||||
\(875\) | 1.74609e7i | 0.0260641i | ||||||||
\(876\) | 6.29376e7 | + | 4.82735e7i | 0.0936263 | + | 0.0718119i | ||||
\(877\) | −1.43231e8 | −0.212343 | −0.106172 | − | 0.994348i | \(-0.533859\pi\) | ||||
−0.106172 | + | 0.994348i | \(0.533859\pi\) | |||||||
\(878\) | 6.42862e8 | − | 3.17106e8i | 0.949805 | − | 0.468511i | ||||
\(879\) | − | 4.67460e8i | − | 0.688300i | ||||||
\(880\) | 5.30593e8 | − | 1.42402e8i | 0.778598 | − | 0.208963i | ||||
\(881\) | 1.71050e8 | 0.250147 | 0.125073 | − | 0.992147i | \(-0.460083\pi\) | ||||
0.125073 | + | 0.992147i | \(0.460083\pi\) | |||||||
\(882\) | 9.25848e7 | + | 1.87696e8i | 0.134938 | + | 0.273557i | ||||
\(883\) | − | 1.32995e8i | − | 0.193177i | −0.995324 | − | 0.0965883i | \(-0.969207\pi\) | ||
0.995324 | − | 0.0965883i | \(-0.0307930\pi\) | |||||||
\(884\) | 1.30741e8 | − | 1.70457e8i | 0.189259 | − | 0.246750i | ||||
\(885\) | −5.14638e7 | −0.0742459 | ||||||||
\(886\) | −3.85477e8 | + | 1.90145e8i | −0.554239 | + | 0.273390i | ||||
\(887\) | − | 1.22634e9i | − | 1.75727i | −0.477492 | − | 0.878636i | \(-0.658454\pi\) | ||
0.477492 | − | 0.878636i | \(-0.341546\pi\) | |||||||
\(888\) | 1.37815e8 | − | 6.93944e8i | 0.196815 | − | 0.991027i | ||||
\(889\) | 2.92770e8 | 0.416699 | ||||||||
\(890\) | −1.55369e8 | − | 3.14977e8i | −0.220391 | − | 0.446795i | ||||
\(891\) | 1.41675e8i | 0.200290i | ||||||||
\(892\) | −7.25058e8 | − | 5.56124e8i | −1.02159 | − | 0.783568i | ||||
\(893\) | 8.16452e7 | 0.114651 | ||||||||
\(894\) | 5.51739e8 | − | 2.72157e8i | 0.772185 | − | 0.380897i | ||||
\(895\) | 9.06746e6i | 0.0126479i | ||||||||
\(896\) | 2.09156e8 | − | 1.38577e7i | 0.290768 | − | 0.0192649i | ||||
\(897\) | −6.89527e8 | −0.955375 | ||||||||
\(898\) | −3.80941e8 | − | 7.72275e8i | −0.526052 | − | 1.06646i | ||||
\(899\) | − | 2.77552e8i | − | 0.382002i | ||||||
\(900\) | 2.95780e7 | − | 3.85630e7i | 0.0405734 | − | 0.0528984i | ||||
\(901\) | 7.50895e7 | 0.102661 | ||||||||
\(902\) | −9.25482e8 | + | 4.56514e8i | −1.26110 | + | 0.622063i | ||||
\(903\) | 2.18676e8i | 0.296987i | ||||||||
\(904\) | −8.44832e8 | − | 1.67781e8i | −1.14358 | − | 0.227110i | ||||
\(905\) | −3.66007e8 | −0.493792 | ||||||||
\(906\) | 1.20261e8 | + | 2.43804e8i | 0.161712 | + | 0.327835i | ||||
\(907\) | 8.14503e8i | 1.09162i | 0.837910 | + | 0.545809i | \(0.183778\pi\) | ||||
−0.837910 | + | 0.545809i | \(0.816222\pi\) | |||||||
\(908\) | −5.80806e8 | − | 4.45481e8i | −0.775842 | − | 0.595075i | ||||
\(909\) | 3.64017e8 | 0.484652 | ||||||||
\(910\) | 1.45090e8 | − | 7.15689e7i | 0.192537 | − | 0.0949730i | ||||
\(911\) | 1.69872e8i | 0.224681i | 0.993670 | + | 0.112341i | \(0.0358348\pi\) | ||||
−0.993670 | + | 0.112341i | \(0.964165\pi\) | |||||||
\(912\) | 1.28017e7 | + | 4.76994e7i | 0.0168766 | + | 0.0628823i | ||||
\(913\) | 1.31878e9 | 1.73284 | ||||||||
\(914\) | −1.89584e8 | − | 3.84341e8i | −0.248292 | − | 0.503359i | ||||
\(915\) | − | 1.01372e8i | − | 0.132329i | ||||||
\(916\) | 5.01374e8 | − | 6.53678e8i | 0.652342 | − | 0.850506i | ||||
\(917\) | −1.57577e8 | −0.204355 | ||||||||
\(918\) | −2.52050e7 | + | 1.24329e7i | −0.0325805 | + | 0.0160710i | ||||
\(919\) | − | 5.97220e7i | − | 0.0769464i | −0.999260 | − | 0.0384732i | \(-0.987751\pi\) | ||
0.999260 | − | 0.0384732i | \(-0.0122494\pi\) | |||||||
\(920\) | 6.81386e7 | − | 3.43100e8i | 0.0875043 | − | 0.440613i | ||||
\(921\) | −3.15139e8 | −0.403388 | ||||||||
\(922\) | 2.05099e8 | + | 4.15793e8i | 0.261680 | + | 0.530498i | ||||
\(923\) | 1.69522e9i | 2.15587i | ||||||||
\(924\) | −1.89841e8 | − | 1.45609e8i | −0.240643 | − | 0.184574i | ||||
\(925\) | 2.77014e8 | 0.350007 | ||||||||
\(926\) | 3.67709e7 | − | 1.81380e7i | 0.0463096 | − | 0.0228432i | ||||
\(927\) | − | 1.94362e8i | − | 0.243989i | ||||||
\(928\) | −7.14866e8 | + | 6.27561e8i | −0.894501 | + | 0.785258i | ||||
\(929\) | −7.77993e8 | −0.970351 | −0.485175 | − | 0.874417i | \(-0.661244\pi\) | ||||
−0.485175 | + | 0.874417i | \(0.661244\pi\) | |||||||
\(930\) | 2.94860e7 | + | 5.97764e7i | 0.0366578 | + | 0.0743157i | ||||
\(931\) | − | 8.32726e7i | − | 0.103194i | ||||||
\(932\) | 3.60678e8 | − | 4.70241e8i | 0.445524 | − | 0.580862i | ||||
\(933\) | 3.47391e7 | 0.0427733 | ||||||||
\(934\) | 1.81337e8 | − | 8.94482e7i | 0.222559 | − | 0.109782i | ||||
\(935\) | − | 1.24389e8i | − | 0.152176i | ||||||
\(936\) | −4.41671e8 | − | 8.77144e7i | −0.538606 | − | 0.106965i | ||||
\(937\) | 5.16472e8 | 0.627810 | 0.313905 | − | 0.949454i | \(-0.398363\pi\) | ||||
0.313905 | + | 0.949454i | \(0.398363\pi\) | |||||||
\(938\) | 4.75595e7 | + | 9.64164e7i | 0.0576273 | + | 0.116827i | ||||
\(939\) | − | 7.92361e8i | − | 0.957032i | ||||||
\(940\) | −2.99651e8 | − | 2.29834e8i | −0.360772 | − | 0.276714i | ||||
\(941\) | −8.72197e8 | −1.04676 | −0.523379 | − | 0.852100i | \(-0.675329\pi\) | ||||
−0.523379 | + | 0.852100i | \(0.675329\pi\) | |||||||
\(942\) | 6.27829e7 | − | 3.09690e7i | 0.0751084 | − | 0.0370488i | ||||
\(943\) | 6.57075e8i | 0.783574i | ||||||||
\(944\) | −2.33631e8 | + | 6.27026e7i | −0.277725 | + | 0.0745366i | ||||
\(945\) | −2.11654e7 | −0.0250802 | ||||||||
\(946\) | 1.19171e9 | + | 2.41593e9i | 1.40765 | + | 2.85371i | ||||
\(947\) | − | 9.56619e8i | − | 1.12639i | −0.826324 | − | 0.563195i | \(-0.809572\pi\) | ||
0.826324 | − | 0.563195i | \(-0.190428\pi\) | |||||||
\(948\) | 4.07210e8 | − | 5.30909e8i | 0.477962 | − | 0.623153i | ||||
\(949\) | 2.87750e8 | 0.336680 | ||||||||
\(950\) | −1.73421e7 | + | 8.55438e6i | −0.0202270 | + | 0.00997741i | ||||
\(951\) | − | 3.52476e8i | − | 0.409815i | ||||||
\(952\) | 9.24511e6 | − | 4.65522e7i | 0.0107152 | − | 0.0539547i | ||||
\(953\) | 2.31699e8 | 0.267699 | 0.133849 | − | 0.991002i | \(-0.457266\pi\) | ||||
0.133849 | + | 0.991002i | \(0.457266\pi\) | |||||||
\(954\) | −6.96295e7 | − | 1.41159e8i | −0.0801951 | − | 0.162578i | ||||
\(955\) | − | 1.97975e8i | − | 0.227301i | ||||||
\(956\) | 2.16517e8 | + | 1.66070e8i | 0.247809 | + | 0.190071i | ||||
\(957\) | 1.08574e9 | 1.23877 | ||||||||
\(958\) | −1.31333e9 | + | 6.47827e8i | −1.49375 | + | 0.736822i | ||||
\(959\) | − | 3.33915e8i | − | 0.378599i | ||||||
\(960\) | 8.72912e7 | − | 2.11102e8i | 0.0986636 | − | 0.238605i | ||||
\(961\) | 7.96091e8 | 0.897001 | ||||||||
\(962\) | −1.13543e9 | − | 2.30183e9i | −1.27536 | − | 2.58552i | ||||
\(963\) | − | 8.48779e7i | − | 0.0950421i | ||||||
\(964\) | 4.42313e8 | − | 5.76675e8i | 0.493740 | − | 0.643725i | ||||
\(965\) | 4.92099e8 | 0.547609 | ||||||||
\(966\) | −1.36622e8 | + | 6.73917e7i | −0.151562 | + | 0.0747609i | ||||
\(967\) | 6.25565e8i | 0.691820i | 0.938268 | + | 0.345910i | \(0.112430\pi\) | ||||
−0.938268 | + | 0.345910i | \(0.887570\pi\) | |||||||
\(968\) | −2.00121e9 | − | 3.97434e8i | −2.20631 | − | 0.438166i | ||||
\(969\) | 1.11824e7 | 0.0122903 | ||||||||
\(970\) | −1.31444e8 | − | 2.66473e8i | −0.144021 | − | 0.291970i | ||||
\(971\) | 5.82254e8i | 0.635997i | 0.948091 | + | 0.317999i | \(0.103011\pi\) | ||||
−0.948091 | + | 0.317999i | \(0.896989\pi\) | |||||||
\(972\) | 4.67444e7 | + | 3.58532e7i | 0.0509015 | + | 0.0390418i | ||||
\(973\) | 8.57413e7 | 0.0930789 | ||||||||
\(974\) | −5.16183e8 | + | 2.54618e8i | −0.558633 | + | 0.275558i | ||||
\(975\) | − | 1.76309e8i | − | 0.190222i | ||||||
\(976\) | −1.23510e8 | − | 4.60200e8i | −0.132847 | − | 0.494991i | ||||
\(977\) | −9.44037e8 | −1.01229 | −0.506145 | − | 0.862448i | \(-0.668930\pi\) | ||||
−0.506145 | + | 0.862448i | \(0.668930\pi\) | |||||||
\(978\) | 1.89204e8 | + | 3.83569e8i | 0.202261 | + | 0.410041i | ||||
\(979\) | 1.88423e9i | 2.00810i | ||||||||
\(980\) | −2.34415e8 | + | 3.05624e8i | −0.249062 | + | 0.324720i | ||||
\(981\) | −1.65276e8 | −0.175066 | ||||||||
\(982\) | −4.20580e8 | + | 2.07460e8i | −0.444134 | + | 0.219078i | ||||
\(983\) | 7.66179e8i | 0.806621i | 0.915063 | + | 0.403311i | \(0.132141\pi\) | ||||
−0.915063 | + | 0.403311i | \(0.867859\pi\) | |||||||
\(984\) | −8.35862e7 | + | 4.20884e8i | −0.0877302 | + | 0.441751i | ||||
\(985\) | 1.73262e8 | 0.181299 | ||||||||
\(986\) | 9.52807e7 | + | 1.93161e8i | 0.0993972 | + | 0.201506i | ||||
\(987\) | 1.64465e8i | 0.171049i | ||||||||
\(988\) | 1.42164e8 | + | 1.09041e8i | 0.147407 | + | 0.113062i | ||||
\(989\) | 1.71526e9 | 1.77314 | ||||||||
\(990\) | −2.33835e8 | + | 1.15344e8i | −0.240993 | + | 0.118875i | ||||
\(991\) | 3.33236e8i | 0.342398i | 0.985236 | + | 0.171199i | \(0.0547641\pi\) | ||||
−0.985236 | + | 0.171199i | \(0.945236\pi\) | |||||||
\(992\) | 2.06688e8 | + | 2.35442e8i | 0.211729 | + | 0.241185i | ||||
\(993\) | −3.97112e8 | −0.405569 | ||||||||
\(994\) | 1.65684e8 | + | 3.35889e8i | 0.168703 | + | 0.342008i | ||||
\(995\) | 4.76742e7i | 0.0483965i | ||||||||
\(996\) | 3.33739e8 | − | 4.35119e8i | 0.337776 | − | 0.440383i | ||||
\(997\) | −1.69413e9 | −1.70947 | −0.854737 | − | 0.519062i | \(-0.826281\pi\) | ||||
−0.854737 | + | 0.519062i | \(0.826281\pi\) | |||||||
\(998\) | −1.70590e9 | + | 8.41469e8i | −1.71617 | + | 0.846538i | ||||
\(999\) | 3.35785e8i | 0.336794i |
(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 | 60.7.c.a.31.5 | ✓ | 24 | |
3.2 | odd | 2 | 180.7.c.b.91.20 | 24 | |||
4.3 | odd | 2 | inner | 60.7.c.a.31.6 | yes | 24 | |
12.11 | even | 2 | 180.7.c.b.91.19 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.c.a.31.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
60.7.c.a.31.6 | yes | 24 | 4.3 | odd | 2 | inner | |
180.7.c.b.91.19 | 24 | 12.11 | even | 2 | |||
180.7.c.b.91.20 | 24 | 3.2 | odd | 2 |