Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(348,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("349.348");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.b (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: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 348.14 | ||
Character | \(\chi\) | \(=\) | 349.348 |
Dual form | 349.2.b.b.348.13 |
$q$-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 \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.719982i | 0.509104i | 0.967059 | + | 0.254552i | \(0.0819280\pi\) | ||||
−0.967059 | + | 0.254552i | \(0.918072\pi\) | |||||||
\(3\) | 1.92112 | 1.10916 | 0.554579 | − | 0.832131i | \(-0.312879\pi\) | ||||
0.554579 | + | 0.832131i | \(0.312879\pi\) | |||||||
\(4\) | 1.48163 | 0.740813 | ||||||||
\(5\) | 0.227297 | 0.101650 | 0.0508251 | − | 0.998708i | \(-0.483815\pi\) | ||||
0.0508251 | + | 0.998708i | \(0.483815\pi\) | |||||||
\(6\) | 1.38317i | 0.564677i | ||||||||
\(7\) | − | 2.96485i | − | 1.12061i | −0.828287 | − | 0.560304i | \(-0.810684\pi\) | ||
0.828287 | − | 0.560304i | \(-0.189316\pi\) | |||||||
\(8\) | 2.50671i | 0.886255i | ||||||||
\(9\) | 0.690697 | 0.230232 | ||||||||
\(10\) | 0.163649i | 0.0517505i | ||||||||
\(11\) | 3.61680i | 1.09050i | 0.838272 | + | 0.545252i | \(0.183566\pi\) | ||||
−0.838272 | + | 0.545252i | \(0.816434\pi\) | |||||||
\(12\) | 2.84638 | 0.821679 | ||||||||
\(13\) | − | 2.92669i | − | 0.811717i | −0.913936 | − | 0.405858i | \(-0.866973\pi\) | ||
0.913936 | − | 0.405858i | \(-0.133027\pi\) | |||||||
\(14\) | 2.13464 | 0.570506 | ||||||||
\(15\) | 0.436664 | 0.112746 | ||||||||
\(16\) | 1.15847 | 0.289618 | ||||||||
\(17\) | −1.57443 | −0.381855 | −0.190927 | − | 0.981604i | \(-0.561150\pi\) | ||||
−0.190927 | + | 0.981604i | \(0.561150\pi\) | |||||||
\(18\) | 0.497289i | 0.117212i | ||||||||
\(19\) | 1.16844 | 0.268058 | 0.134029 | − | 0.990977i | \(-0.457209\pi\) | ||||
0.134029 | + | 0.990977i | \(0.457209\pi\) | |||||||
\(20\) | 0.336769 | 0.0753038 | ||||||||
\(21\) | − | 5.69583i | − | 1.24293i | ||||||
\(22\) | −2.60403 | −0.555180 | ||||||||
\(23\) | −5.51662 | −1.15030 | −0.575148 | − | 0.818050i | \(-0.695055\pi\) | ||||
−0.575148 | + | 0.818050i | \(0.695055\pi\) | |||||||
\(24\) | 4.81568i | 0.982997i | ||||||||
\(25\) | −4.94834 | −0.989667 | ||||||||
\(26\) | 2.10716 | 0.413248 | ||||||||
\(27\) | −4.43645 | −0.853794 | ||||||||
\(28\) | − | 4.39280i | − | 0.830161i | ||||||
\(29\) | 7.55239 | 1.40244 | 0.701221 | − | 0.712944i | \(-0.252638\pi\) | ||||
0.701221 | + | 0.712944i | \(0.252638\pi\) | |||||||
\(30\) | 0.314390i | 0.0573995i | ||||||||
\(31\) | 0.298625 | 0.0536346 | 0.0268173 | − | 0.999640i | \(-0.491463\pi\) | ||||
0.0268173 | + | 0.999640i | \(0.491463\pi\) | |||||||
\(32\) | 5.84749i | 1.03370i | ||||||||
\(33\) | 6.94829i | 1.20954i | ||||||||
\(34\) | − | 1.13356i | − | 0.194404i | ||||||
\(35\) | − | 0.673900i | − | 0.113910i | ||||||
\(36\) | 1.02335 | 0.170559 | ||||||||
\(37\) | −1.62168 | −0.266603 | −0.133301 | − | 0.991076i | \(-0.542558\pi\) | ||||
−0.133301 | + | 0.991076i | \(0.542558\pi\) | |||||||
\(38\) | 0.841253i | 0.136469i | ||||||||
\(39\) | − | 5.62251i | − | 0.900322i | ||||||
\(40\) | 0.569766i | 0.0900879i | ||||||||
\(41\) | −2.90221 | −0.453249 | −0.226625 | − | 0.973982i | \(-0.572769\pi\) | ||||
−0.226625 | + | 0.973982i | \(0.572769\pi\) | |||||||
\(42\) | 4.10089 | 0.632781 | ||||||||
\(43\) | 5.41694i | 0.826076i | 0.910714 | + | 0.413038i | \(0.135532\pi\) | ||||
−0.910714 | + | 0.413038i | \(0.864468\pi\) | |||||||
\(44\) | 5.35874i | 0.807860i | ||||||||
\(45\) | 0.156993 | 0.0234031 | ||||||||
\(46\) | − | 3.97187i | − | 0.585620i | ||||||
\(47\) | − | 2.69771i | − | 0.393501i | −0.980454 | − | 0.196751i | \(-0.936961\pi\) | ||
0.980454 | − | 0.196751i | \(-0.0630390\pi\) | |||||||
\(48\) | 2.22556 | 0.321232 | ||||||||
\(49\) | −1.79033 | −0.255761 | ||||||||
\(50\) | − | 3.56271i | − | 0.503843i | ||||||
\(51\) | −3.02466 | −0.423537 | ||||||||
\(52\) | − | 4.33626i | − | 0.601330i | ||||||
\(53\) | 6.41377i | 0.880999i | 0.897753 | + | 0.440500i | \(0.145199\pi\) | ||||
−0.897753 | + | 0.440500i | \(0.854801\pi\) | |||||||
\(54\) | − | 3.19416i | − | 0.434670i | ||||||
\(55\) | 0.822085i | 0.110850i | ||||||||
\(56\) | 7.43201 | 0.993144 | ||||||||
\(57\) | 2.24470 | 0.297318 | ||||||||
\(58\) | 5.43758i | 0.713989i | ||||||||
\(59\) | − | 5.21837i | − | 0.679374i | −0.940539 | − | 0.339687i | \(-0.889679\pi\) | ||
0.940539 | − | 0.339687i | \(-0.110321\pi\) | |||||||
\(60\) | 0.646973 | 0.0835238 | ||||||||
\(61\) | 2.01219i | 0.257634i | 0.991668 | + | 0.128817i | \(0.0411180\pi\) | ||||
−0.991668 | + | 0.128817i | \(0.958882\pi\) | |||||||
\(62\) | 0.215004i | 0.0273056i | ||||||||
\(63\) | − | 2.04781i | − | 0.258000i | ||||||
\(64\) | −1.89314 | −0.236643 | ||||||||
\(65\) | − | 0.665226i | − | 0.0825111i | ||||||
\(66\) | −5.00264 | −0.615783 | ||||||||
\(67\) | 2.81322 | 0.343689 | 0.171845 | − | 0.985124i | \(-0.445027\pi\) | ||||
0.171845 | + | 0.985124i | \(0.445027\pi\) | |||||||
\(68\) | −2.33271 | −0.282883 | ||||||||
\(69\) | −10.5981 | −1.27586 | ||||||||
\(70\) | 0.485196 | 0.0579920 | ||||||||
\(71\) | − | 6.35775i | − | 0.754526i | −0.926106 | − | 0.377263i | \(-0.876865\pi\) | ||
0.926106 | − | 0.377263i | \(-0.123135\pi\) | |||||||
\(72\) | 1.73137i | 0.204044i | ||||||||
\(73\) | −13.8123 | −1.61661 | −0.808304 | − | 0.588766i | \(-0.799614\pi\) | ||||
−0.808304 | + | 0.588766i | \(0.799614\pi\) | |||||||
\(74\) | − | 1.16758i | − | 0.135728i | ||||||
\(75\) | −9.50634 | −1.09770 | ||||||||
\(76\) | 1.73119 | 0.198581 | ||||||||
\(77\) | 10.7233 | 1.22203 | ||||||||
\(78\) | 4.04810 | 0.458357 | ||||||||
\(79\) | 1.13066i | 0.127209i | 0.997975 | + | 0.0636044i | \(0.0202596\pi\) | ||||
−0.997975 | + | 0.0636044i | \(0.979740\pi\) | |||||||
\(80\) | 0.263317 | 0.0294397 | ||||||||
\(81\) | −10.5950 | −1.17723 | ||||||||
\(82\) | − | 2.08954i | − | 0.230751i | ||||||
\(83\) | 6.82981 | 0.749669 | 0.374834 | − | 0.927092i | \(-0.377700\pi\) | ||||
0.374834 | + | 0.927092i | \(0.377700\pi\) | |||||||
\(84\) | − | 8.43909i | − | 0.920780i | ||||||
\(85\) | −0.357862 | −0.0388156 | ||||||||
\(86\) | −3.90010 | −0.420558 | ||||||||
\(87\) | 14.5090 | 1.55553 | ||||||||
\(88\) | −9.06624 | −0.966465 | ||||||||
\(89\) | − | 0.406795i | − | 0.0431202i | −0.999768 | − | 0.0215601i | \(-0.993137\pi\) | ||
0.999768 | − | 0.0215601i | \(-0.00686333\pi\) | |||||||
\(90\) | 0.113032i | 0.0119146i | ||||||||
\(91\) | −8.67718 | −0.909616 | ||||||||
\(92\) | −8.17358 | −0.852154 | ||||||||
\(93\) | 0.573694 | 0.0594893 | ||||||||
\(94\) | 1.94230 | 0.200333 | ||||||||
\(95\) | 0.265582 | 0.0272481 | ||||||||
\(96\) | 11.2337i | 1.14654i | ||||||||
\(97\) | − | 8.19259i | − | 0.831831i | −0.909403 | − | 0.415916i | \(-0.863461\pi\) | ||
0.909403 | − | 0.415916i | \(-0.136539\pi\) | |||||||
\(98\) | − | 1.28900i | − | 0.130209i | ||||||
\(99\) | 2.49811i | 0.251069i | ||||||||
\(100\) | −7.33159 | −0.733159 | ||||||||
\(101\) | − | 13.2009i | − | 1.31354i | −0.754091 | − | 0.656770i | \(-0.771922\pi\) | ||
0.754091 | − | 0.656770i | \(-0.228078\pi\) | |||||||
\(102\) | − | 2.17770i | − | 0.215625i | ||||||
\(103\) | − | 20.2631i | − | 1.99658i | −0.0584352 | − | 0.998291i | \(-0.518611\pi\) | ||
0.0584352 | − | 0.998291i | \(-0.481389\pi\) | |||||||
\(104\) | 7.33634 | 0.719388 | ||||||||
\(105\) | − | 1.29464i | − | 0.126344i | ||||||
\(106\) | −4.61780 | −0.448520 | ||||||||
\(107\) | − | 11.9439i | − | 1.15466i | −0.816511 | − | 0.577331i | \(-0.804094\pi\) | ||
0.816511 | − | 0.577331i | \(-0.195906\pi\) | |||||||
\(108\) | −6.57316 | −0.632502 | ||||||||
\(109\) | 4.55295 | 0.436094 | 0.218047 | − | 0.975938i | \(-0.430031\pi\) | ||||
0.218047 | + | 0.975938i | \(0.430031\pi\) | |||||||
\(110\) | −0.591886 | −0.0564341 | ||||||||
\(111\) | −3.11544 | −0.295705 | ||||||||
\(112\) | − | 3.43469i | − | 0.324548i | ||||||
\(113\) | 6.06748i | 0.570780i | 0.958411 | + | 0.285390i | \(0.0921232\pi\) | ||||
−0.958411 | + | 0.285390i | \(0.907877\pi\) | |||||||
\(114\) | 1.61615i | 0.151366i | ||||||||
\(115\) | −1.25391 | −0.116928 | ||||||||
\(116\) | 11.1898 | 1.03895 | ||||||||
\(117\) | − | 2.02145i | − | 0.186883i | ||||||
\(118\) | 3.75713 | 0.345872 | ||||||||
\(119\) | 4.66794i | 0.427909i | ||||||||
\(120\) | 1.09459i | 0.0999218i | ||||||||
\(121\) | −2.08121 | −0.189201 | ||||||||
\(122\) | −1.44874 | −0.131163 | ||||||||
\(123\) | −5.57549 | −0.502725 | ||||||||
\(124\) | 0.442451 | 0.0397332 | ||||||||
\(125\) | −2.26122 | −0.202250 | ||||||||
\(126\) | 1.47439 | 0.131349 | ||||||||
\(127\) | 19.2080i | 1.70443i | 0.523190 | + | 0.852216i | \(0.324742\pi\) | ||||
−0.523190 | + | 0.852216i | \(0.675258\pi\) | |||||||
\(128\) | 10.3320i | 0.913224i | ||||||||
\(129\) | 10.4066i | 0.916249i | ||||||||
\(130\) | 0.478950 | 0.0420067 | ||||||||
\(131\) | 16.6511i | 1.45481i | 0.686208 | + | 0.727406i | \(0.259274\pi\) | ||||
−0.686208 | + | 0.727406i | \(0.740726\pi\) | |||||||
\(132\) | 10.2948i | 0.896045i | ||||||||
\(133\) | − | 3.46424i | − | 0.300388i | ||||||
\(134\) | 2.02546i | 0.174973i | ||||||||
\(135\) | −1.00839 | −0.0867883 | ||||||||
\(136\) | − | 3.94663i | − | 0.338421i | ||||||
\(137\) | 0.220208i | 0.0188137i | 0.999956 | + | 0.00940683i | \(0.00299433\pi\) | ||||
−0.999956 | + | 0.00940683i | \(0.997006\pi\) | |||||||
\(138\) | − | 7.63043i | − | 0.649545i | ||||||
\(139\) | 16.5090 | 1.40027 | 0.700137 | − | 0.714009i | \(-0.253122\pi\) | ||||
0.700137 | + | 0.714009i | \(0.253122\pi\) | |||||||
\(140\) | − | 0.998469i | − | 0.0843860i | ||||||
\(141\) | − | 5.18262i | − | 0.436455i | ||||||
\(142\) | 4.57746 | 0.384132 | ||||||||
\(143\) | 10.5852 | 0.885181 | ||||||||
\(144\) | 0.800152 | 0.0666793 | ||||||||
\(145\) | 1.71663 | 0.142559 | ||||||||
\(146\) | − | 9.94460i | − | 0.823021i | ||||||
\(147\) | −3.43944 | −0.283680 | ||||||||
\(148\) | −2.40273 | −0.197503 | ||||||||
\(149\) | 2.83961i | 0.232630i | 0.993212 | + | 0.116315i | \(0.0371081\pi\) | ||||
−0.993212 | + | 0.116315i | \(0.962892\pi\) | |||||||
\(150\) | − | 6.84439i | − | 0.558842i | ||||||
\(151\) | 2.71918 | 0.221284 | 0.110642 | − | 0.993860i | \(-0.464709\pi\) | ||||
0.110642 | + | 0.993860i | \(0.464709\pi\) | |||||||
\(152\) | 2.92893i | 0.237567i | ||||||||
\(153\) | −1.08745 | −0.0879153 | ||||||||
\(154\) | 7.72054i | 0.622139i | ||||||||
\(155\) | 0.0678764 | 0.00545197 | ||||||||
\(156\) | − | 8.33046i | − | 0.666971i | ||||||
\(157\) | 8.56005 | 0.683166 | 0.341583 | − | 0.939852i | \(-0.389037\pi\) | ||||
0.341583 | + | 0.939852i | \(0.389037\pi\) | |||||||
\(158\) | −0.814052 | −0.0647625 | ||||||||
\(159\) | 12.3216i | 0.977168i | ||||||||
\(160\) | 1.32912i | 0.105076i | ||||||||
\(161\) | 16.3560i | 1.28903i | ||||||||
\(162\) | − | 7.62822i | − | 0.599330i | ||||||
\(163\) | − | 12.6066i | − | 0.987427i | −0.869625 | − | 0.493713i | \(-0.835639\pi\) | ||
0.869625 | − | 0.493713i | \(-0.164361\pi\) | |||||||
\(164\) | −4.30000 | −0.335773 | ||||||||
\(165\) | 1.57932i | 0.122950i | ||||||||
\(166\) | 4.91734i | 0.381659i | ||||||||
\(167\) | 21.2390i | 1.64353i | 0.569829 | + | 0.821763i | \(0.307010\pi\) | ||||
−0.569829 | + | 0.821763i | \(0.692990\pi\) | |||||||
\(168\) | 14.2778 | 1.10155 | ||||||||
\(169\) | 4.43451 | 0.341116 | ||||||||
\(170\) | − | 0.257654i | − | 0.0197612i | ||||||
\(171\) | 0.807035 | 0.0617155 | ||||||||
\(172\) | 8.02589i | 0.611968i | ||||||||
\(173\) | − | 9.78902i | − | 0.744245i | −0.928184 | − | 0.372123i | \(-0.878630\pi\) | ||
0.928184 | − | 0.372123i | \(-0.121370\pi\) | |||||||
\(174\) | 10.4462i | 0.791927i | ||||||||
\(175\) | 14.6711i | 1.10903i | ||||||||
\(176\) | 4.18995i | 0.315829i | ||||||||
\(177\) | − | 10.0251i | − | 0.753533i | ||||||
\(178\) | 0.292885 | 0.0219527 | ||||||||
\(179\) | 9.70344i | 0.725269i | 0.931931 | + | 0.362635i | \(0.118123\pi\) | ||||
−0.931931 | + | 0.362635i | \(0.881877\pi\) | |||||||
\(180\) | 0.232605 | 0.0173374 | ||||||||
\(181\) | 20.2057 | 1.50188 | 0.750940 | − | 0.660371i | \(-0.229601\pi\) | ||||
0.750940 | + | 0.660371i | \(0.229601\pi\) | |||||||
\(182\) | − | 6.24741i | − | 0.463089i | ||||||
\(183\) | 3.86565i | 0.285757i | ||||||||
\(184\) | − | 13.8286i | − | 1.01945i | ||||||
\(185\) | −0.368603 | −0.0271002 | ||||||||
\(186\) | 0.413049i | 0.0302862i | ||||||||
\(187\) | − | 5.69438i | − | 0.416415i | ||||||
\(188\) | − | 3.99700i | − | 0.291511i | ||||||
\(189\) | 13.1534i | 0.956769i | ||||||||
\(190\) | 0.191214i | 0.0138721i | ||||||||
\(191\) | 2.75632 | 0.199441 | 0.0997203 | − | 0.995016i | \(-0.468205\pi\) | ||||
0.0997203 | + | 0.995016i | \(0.468205\pi\) | |||||||
\(192\) | −3.63695 | −0.262475 | ||||||||
\(193\) | − | 20.5656i | − | 1.48035i | −0.672416 | − | 0.740173i | \(-0.734744\pi\) | ||
0.672416 | − | 0.740173i | \(-0.265256\pi\) | |||||||
\(194\) | 5.89851 | 0.423488 | ||||||||
\(195\) | − | 1.27798i | − | 0.0915179i | ||||||
\(196\) | −2.65260 | −0.189472 | ||||||||
\(197\) | 22.5289i | 1.60512i | 0.596571 | + | 0.802560i | \(0.296529\pi\) | ||||
−0.596571 | + | 0.802560i | \(0.703471\pi\) | |||||||
\(198\) | −1.79859 | −0.127820 | ||||||||
\(199\) | 15.8099i | 1.12074i | 0.828244 | + | 0.560368i | \(0.189340\pi\) | ||||
−0.828244 | + | 0.560368i | \(0.810660\pi\) | |||||||
\(200\) | − | 12.4040i | − | 0.877097i | ||||||
\(201\) | 5.40452 | 0.381206 | ||||||||
\(202\) | 9.50442 | 0.668728 | ||||||||
\(203\) | − | 22.3917i | − | 1.57159i | ||||||
\(204\) | −4.48142 | −0.313762 | ||||||||
\(205\) | −0.659663 | −0.0460729 | ||||||||
\(206\) | 14.5891 | 1.01647 | ||||||||
\(207\) | −3.81031 | −0.264835 | ||||||||
\(208\) | − | 3.39048i | − | 0.235087i | ||||||
\(209\) | 4.22600i | 0.292318i | ||||||||
\(210\) | 0.932119 | 0.0643223 | ||||||||
\(211\) | 14.9620i | 1.03003i | 0.857182 | + | 0.515014i | \(0.172213\pi\) | ||||
−0.857182 | + | 0.515014i | \(0.827787\pi\) | |||||||
\(212\) | 9.50281i | 0.652656i | ||||||||
\(213\) | − | 12.2140i | − | 0.836889i | ||||||
\(214\) | 8.59939 | 0.587842 | ||||||||
\(215\) | 1.23125i | 0.0839708i | ||||||||
\(216\) | − | 11.1209i | − | 0.756679i | ||||||
\(217\) | − | 0.885378i | − | 0.0601034i | ||||||
\(218\) | 3.27804i | 0.222017i | ||||||||
\(219\) | −26.5351 | −1.79307 | ||||||||
\(220\) | 1.21802i | 0.0821191i | ||||||||
\(221\) | 4.60786i | 0.309958i | ||||||||
\(222\) | − | 2.24306i | − | 0.150544i | ||||||
\(223\) | −20.3450 | −1.36240 | −0.681200 | − | 0.732097i | \(-0.738542\pi\) | ||||
−0.681200 | + | 0.732097i | \(0.738542\pi\) | |||||||
\(224\) | 17.3369 | 1.15837 | ||||||||
\(225\) | −3.41780 | −0.227853 | ||||||||
\(226\) | −4.36847 | −0.290586 | ||||||||
\(227\) | 7.36520 | 0.488846 | 0.244423 | − | 0.969669i | \(-0.421401\pi\) | ||||
0.244423 | + | 0.969669i | \(0.421401\pi\) | |||||||
\(228\) | 3.32581 | 0.220257 | ||||||||
\(229\) | − | 16.7515i | − | 1.10697i | −0.832860 | − | 0.553484i | \(-0.813298\pi\) | ||
0.832860 | − | 0.553484i | \(-0.186702\pi\) | |||||||
\(230\) | − | 0.902792i | − | 0.0595283i | ||||||
\(231\) | 20.6006 | 1.35542 | ||||||||
\(232\) | 18.9316i | 1.24292i | ||||||||
\(233\) | −22.3820 | −1.46629 | −0.733147 | − | 0.680070i | \(-0.761949\pi\) | ||||
−0.733147 | + | 0.680070i | \(0.761949\pi\) | |||||||
\(234\) | 1.45541 | 0.0951430 | ||||||||
\(235\) | − | 0.613180i | − | 0.0399995i | ||||||
\(236\) | − | 7.73168i | − | 0.503289i | ||||||
\(237\) | 2.17212i | 0.141095i | ||||||||
\(238\) | −3.36083 | −0.217850 | ||||||||
\(239\) | 23.2227 | 1.50215 | 0.751077 | − | 0.660215i | \(-0.229535\pi\) | ||||
0.751077 | + | 0.660215i | \(0.229535\pi\) | |||||||
\(240\) | 0.505862 | 0.0326533 | ||||||||
\(241\) | −21.4469 | −1.38151 | −0.690757 | − | 0.723087i | \(-0.742723\pi\) | ||||
−0.690757 | + | 0.723087i | \(0.742723\pi\) | |||||||
\(242\) | − | 1.49843i | − | 0.0963227i | ||||||
\(243\) | −7.04497 | −0.451935 | ||||||||
\(244\) | 2.98131i | 0.190859i | ||||||||
\(245\) | −0.406936 | −0.0259982 | ||||||||
\(246\) | − | 4.01425i | − | 0.255939i | ||||||
\(247\) | − | 3.41965i | − | 0.217587i | ||||||
\(248\) | 0.748565i | 0.0475339i | ||||||||
\(249\) | 13.1209 | 0.831501 | ||||||||
\(250\) | − | 1.62804i | − | 0.102966i | ||||||
\(251\) | 3.80427i | 0.240123i | 0.992766 | + | 0.120062i | \(0.0383092\pi\) | ||||
−0.992766 | + | 0.120062i | \(0.961691\pi\) | |||||||
\(252\) | − | 3.03409i | − | 0.191130i | ||||||
\(253\) | − | 19.9525i | − | 1.25440i | ||||||
\(254\) | −13.8294 | −0.867733 | ||||||||
\(255\) | −0.687496 | −0.0430526 | ||||||||
\(256\) | −11.2251 | −0.701569 | ||||||||
\(257\) | 5.78099 | 0.360608 | 0.180304 | − | 0.983611i | \(-0.442292\pi\) | ||||
0.180304 | + | 0.983611i | \(0.442292\pi\) | |||||||
\(258\) | −7.49255 | −0.466466 | ||||||||
\(259\) | 4.80804i | 0.298757i | ||||||||
\(260\) | − | 0.985616i | − | 0.0611253i | ||||||
\(261\) | 5.21641 | 0.322887 | ||||||||
\(262\) | −11.9885 | −0.740650 | ||||||||
\(263\) | 28.3586 | 1.74867 | 0.874334 | − | 0.485325i | \(-0.161299\pi\) | ||||
0.874334 | + | 0.485325i | \(0.161299\pi\) | |||||||
\(264\) | −17.4173 | −1.07196 | ||||||||
\(265\) | 1.45783i | 0.0895537i | ||||||||
\(266\) | 2.49419 | 0.152928 | ||||||||
\(267\) | − | 0.781502i | − | 0.0478271i | ||||||
\(268\) | 4.16814 | 0.254609 | ||||||||
\(269\) | −14.7707 | −0.900588 | −0.450294 | − | 0.892880i | \(-0.648681\pi\) | ||||
−0.450294 | + | 0.892880i | \(0.648681\pi\) | |||||||
\(270\) | − | 0.726022i | − | 0.0441843i | ||||||
\(271\) | 12.3384 | 0.749502 | 0.374751 | − | 0.927125i | \(-0.377728\pi\) | ||||
0.374751 | + | 0.927125i | \(0.377728\pi\) | |||||||
\(272\) | −1.82393 | −0.110592 | ||||||||
\(273\) | −16.6699 | −1.00891 | ||||||||
\(274\) | −0.158546 | −0.00957810 | ||||||||
\(275\) | − | 17.8971i | − | 1.07924i | ||||||
\(276\) | −15.7024 | −0.945174 | ||||||||
\(277\) | 13.3371i | 0.801350i | 0.916220 | + | 0.400675i | \(0.131224\pi\) | ||||
−0.916220 | + | 0.400675i | \(0.868776\pi\) | |||||||
\(278\) | 11.8862i | 0.712885i | ||||||||
\(279\) | 0.206259 | 0.0123484 | ||||||||
\(280\) | 1.68927 | 0.100953 | ||||||||
\(281\) | −6.82202 | −0.406967 | −0.203484 | − | 0.979078i | \(-0.565226\pi\) | ||||
−0.203484 | + | 0.979078i | \(0.565226\pi\) | |||||||
\(282\) | 3.73139 | 0.222201 | ||||||||
\(283\) | 14.9414 | 0.888177 | 0.444088 | − | 0.895983i | \(-0.353528\pi\) | ||||
0.444088 | + | 0.895983i | \(0.353528\pi\) | |||||||
\(284\) | − | 9.41981i | − | 0.558963i | ||||||
\(285\) | 0.510214 | 0.0302225 | ||||||||
\(286\) | 7.62116i | 0.450649i | ||||||||
\(287\) | 8.60462i | 0.507915i | ||||||||
\(288\) | 4.03884i | 0.237991i | ||||||||
\(289\) | −14.5212 | −0.854187 | ||||||||
\(290\) | 1.23594i | 0.0725771i | ||||||||
\(291\) | − | 15.7389i | − | 0.922633i | ||||||
\(292\) | −20.4647 | −1.19760 | ||||||||
\(293\) | −17.2715 | −1.00901 | −0.504506 | − | 0.863408i | \(-0.668325\pi\) | ||||
−0.504506 | + | 0.863408i | \(0.668325\pi\) | |||||||
\(294\) | − | 2.47633i | − | 0.144423i | ||||||
\(295\) | − | 1.18612i | − | 0.0690585i | ||||||
\(296\) | − | 4.06508i | − | 0.236278i | ||||||
\(297\) | − | 16.0457i | − | 0.931067i | ||||||
\(298\) | −2.04446 | −0.118433 | ||||||||
\(299\) | 16.1454i | 0.933714i | ||||||||
\(300\) | −14.0848 | −0.813189 | ||||||||
\(301\) | 16.0604 | 0.925707 | ||||||||
\(302\) | 1.95776i | 0.112656i | ||||||||
\(303\) | − | 25.3605i | − | 1.45692i | ||||||
\(304\) | 1.35360 | 0.0776343 | ||||||||
\(305\) | 0.457364i | 0.0261886i | ||||||||
\(306\) | − | 0.782945i | − | 0.0447580i | ||||||
\(307\) | 26.9626 | 1.53884 | 0.769418 | − | 0.638746i | \(-0.220547\pi\) | ||||
0.769418 | + | 0.638746i | \(0.220547\pi\) | |||||||
\(308\) | 15.8879 | 0.905295 | ||||||||
\(309\) | − | 38.9278i | − | 2.21453i | ||||||
\(310\) | 0.0488698i | 0.00277562i | ||||||||
\(311\) | 13.8831i | 0.787240i | 0.919273 | + | 0.393620i | \(0.128777\pi\) | ||||
−0.919273 | + | 0.393620i | \(0.871223\pi\) | |||||||
\(312\) | 14.0940 | 0.797915 | ||||||||
\(313\) | 12.4262 | 0.702371 | 0.351185 | − | 0.936306i | \(-0.385779\pi\) | ||||
0.351185 | + | 0.936306i | \(0.385779\pi\) | |||||||
\(314\) | 6.16308i | 0.347802i | ||||||||
\(315\) | − | 0.465461i | − | 0.0262257i | ||||||
\(316\) | 1.67521i | 0.0942380i | ||||||||
\(317\) | − | 32.8113i | − | 1.84287i | −0.388534 | − | 0.921434i | \(-0.627019\pi\) | ||
0.388534 | − | 0.921434i | \(-0.372981\pi\) | |||||||
\(318\) | −8.87133 | −0.497480 | ||||||||
\(319\) | 27.3154i | 1.52937i | ||||||||
\(320\) | −0.430305 | −0.0240548 | ||||||||
\(321\) | − | 22.9457i | − | 1.28070i | ||||||
\(322\) | −11.7760 | −0.656250 | ||||||||
\(323\) | −1.83962 | −0.102359 | ||||||||
\(324\) | −15.6979 | −0.872104 | ||||||||
\(325\) | 14.4822i | 0.803329i | ||||||||
\(326\) | 9.07653 | 0.502703 | ||||||||
\(327\) | 8.74676 | 0.483697 | ||||||||
\(328\) | − | 7.27500i | − | 0.401694i | ||||||
\(329\) | −7.99830 | −0.440961 | ||||||||
\(330\) | −1.13708 | −0.0625944 | ||||||||
\(331\) | − | 14.6238i | − | 0.803797i | −0.915684 | − | 0.401898i | \(-0.868350\pi\) | ||
0.915684 | − | 0.401898i | \(-0.131650\pi\) | |||||||
\(332\) | 10.1192 | 0.555365 | ||||||||
\(333\) | −1.12009 | −0.0613805 | ||||||||
\(334\) | −15.2917 | −0.836726 | ||||||||
\(335\) | 0.639435 | 0.0349361 | ||||||||
\(336\) | − | 6.59845i | − | 0.359975i | ||||||
\(337\) | 15.0233 | 0.818370 | 0.409185 | − | 0.912451i | \(-0.365813\pi\) | ||||
0.409185 | + | 0.912451i | \(0.365813\pi\) | |||||||
\(338\) | 3.19277i | 0.173664i | ||||||||
\(339\) | 11.6563i | 0.633086i | ||||||||
\(340\) | −0.530218 | −0.0287551 | ||||||||
\(341\) | 1.08007i | 0.0584888i | ||||||||
\(342\) | 0.581050i | 0.0314196i | ||||||||
\(343\) | − | 15.4459i | − | 0.833999i | ||||||
\(344\) | −13.5787 | −0.732114 | ||||||||
\(345\) | −2.40891 | −0.129691 | ||||||||
\(346\) | 7.04791 | 0.378898 | ||||||||
\(347\) | 8.69561i | 0.466805i | 0.972380 | + | 0.233402i | \(0.0749859\pi\) | ||||
−0.972380 | + | 0.233402i | \(0.925014\pi\) | |||||||
\(348\) | 21.4970 | 1.15236 | ||||||||
\(349\) | −16.4065 | + | 8.93451i | −0.878222 | + | 0.478253i | ||||
\(350\) | −10.5629 | −0.564611 | ||||||||
\(351\) | 12.9841i | 0.693039i | ||||||||
\(352\) | −21.1492 | −1.12725 | ||||||||
\(353\) | −34.4982 | −1.83616 | −0.918078 | − | 0.396401i | \(-0.870259\pi\) | ||||
−0.918078 | + | 0.396401i | \(0.870259\pi\) | |||||||
\(354\) | 7.21789 | 0.383627 | ||||||||
\(355\) | − | 1.44509i | − | 0.0766977i | ||||||
\(356\) | − | 0.602719i | − | 0.0319440i | ||||||
\(357\) | 8.96767i | 0.474619i | ||||||||
\(358\) | −6.98630 | −0.369237 | ||||||||
\(359\) | − | 18.6713i | − | 0.985436i | −0.870189 | − | 0.492718i | \(-0.836003\pi\) | ||
0.870189 | − | 0.492718i | \(-0.163997\pi\) | |||||||
\(360\) | 0.393535i | 0.0207411i | ||||||||
\(361\) | −17.6348 | −0.928145 | ||||||||
\(362\) | 14.5477i | 0.764612i | ||||||||
\(363\) | −3.99824 | −0.209853 | ||||||||
\(364\) | −12.8563 | −0.673855 | ||||||||
\(365\) | −3.13949 | −0.164328 | ||||||||
\(366\) | −2.78320 | −0.145480 | ||||||||
\(367\) | 17.5618i | 0.916717i | 0.888767 | + | 0.458358i | \(0.151562\pi\) | ||||
−0.888767 | + | 0.458358i | \(0.848438\pi\) | |||||||
\(368\) | −6.39085 | −0.333146 | ||||||||
\(369\) | −2.00455 | −0.104353 | ||||||||
\(370\) | − | 0.265387i | − | 0.0137968i | ||||||
\(371\) | 19.0159 | 0.987254 | ||||||||
\(372\) | 0.850000 | 0.0440704 | ||||||||
\(373\) | 26.0464i | 1.34863i | 0.738443 | + | 0.674316i | \(0.235562\pi\) | ||||
−0.738443 | + | 0.674316i | \(0.764438\pi\) | |||||||
\(374\) | 4.09985 | 0.211998 | ||||||||
\(375\) | −4.34408 | −0.224327 | ||||||||
\(376\) | 6.76237 | 0.348742 | ||||||||
\(377\) | − | 22.1035i | − | 1.13839i | ||||||
\(378\) | −9.47020 | −0.487094 | ||||||||
\(379\) | 21.4445i | 1.10153i | 0.834660 | + | 0.550765i | \(0.185664\pi\) | ||||
−0.834660 | + | 0.550765i | \(0.814336\pi\) | |||||||
\(380\) | 0.393493 | 0.0201858 | ||||||||
\(381\) | 36.9008i | 1.89048i | ||||||||
\(382\) | 1.98450i | 0.101536i | ||||||||
\(383\) | 11.0196i | 0.563074i | 0.959550 | + | 0.281537i | \(0.0908442\pi\) | ||||
−0.959550 | + | 0.281537i | \(0.909156\pi\) | |||||||
\(384\) | 19.8489i | 1.01291i | ||||||||
\(385\) | 2.43736 | 0.124219 | ||||||||
\(386\) | 14.8069 | 0.753650 | ||||||||
\(387\) | 3.74146i | 0.190189i | ||||||||
\(388\) | − | 12.1384i | − | 0.616232i | ||||||
\(389\) | 4.80635i | 0.243691i | 0.992549 | + | 0.121846i | \(0.0388813\pi\) | ||||
−0.992549 | + | 0.121846i | \(0.961119\pi\) | |||||||
\(390\) | 0.920120 | 0.0465921 | ||||||||
\(391\) | 8.68553 | 0.439246 | ||||||||
\(392\) | − | 4.48783i | − | 0.226670i | ||||||
\(393\) | 31.9887i | 1.61362i | ||||||||
\(394\) | −16.2204 | −0.817173 | ||||||||
\(395\) | 0.256994i | 0.0129308i | ||||||||
\(396\) | 3.70126i | 0.185995i | ||||||||
\(397\) | −4.67721 | −0.234742 | −0.117371 | − | 0.993088i | \(-0.537447\pi\) | ||||
−0.117371 | + | 0.993088i | \(0.537447\pi\) | |||||||
\(398\) | −11.3828 | −0.570571 | ||||||||
\(399\) | − | 6.65521i | − | 0.333177i | ||||||
\(400\) | −5.73250 | −0.286625 | ||||||||
\(401\) | − | 10.4723i | − | 0.522962i | −0.965209 | − | 0.261481i | \(-0.915789\pi\) | ||
0.965209 | − | 0.261481i | \(-0.0842108\pi\) | |||||||
\(402\) | 3.89116i | 0.194073i | ||||||||
\(403\) | − | 0.873981i | − | 0.0435361i | ||||||
\(404\) | − | 19.5588i | − | 0.973088i | ||||||
\(405\) | −2.40821 | −0.119665 | ||||||||
\(406\) | 16.1216 | 0.800101 | ||||||||
\(407\) | − | 5.86529i | − | 0.290732i | ||||||
\(408\) | − | 7.58194i | − | 0.375362i | ||||||
\(409\) | 10.3473 | 0.511643 | 0.255822 | − | 0.966724i | \(-0.417654\pi\) | ||||
0.255822 | + | 0.966724i | \(0.417654\pi\) | |||||||
\(410\) | − | 0.474945i | − | 0.0234559i | ||||||
\(411\) | 0.423046i | 0.0208673i | ||||||||
\(412\) | − | 30.0223i | − | 1.47909i | ||||||
\(413\) | −15.4717 | −0.761312 | ||||||||
\(414\) | − | 2.74335i | − | 0.134829i | ||||||
\(415\) | 1.55239 | 0.0762040 | ||||||||
\(416\) | 17.1138 | 0.839072 | ||||||||
\(417\) | 31.7157 | 1.55313 | ||||||||
\(418\) | −3.04264 | −0.148820 | ||||||||
\(419\) | 17.4860 | 0.854245 | 0.427123 | − | 0.904194i | \(-0.359527\pi\) | ||||
0.427123 | + | 0.904194i | \(0.359527\pi\) | |||||||
\(420\) | − | 1.91818i | − | 0.0935974i | ||||||
\(421\) | − | 3.35844i | − | 0.163680i | −0.996645 | − | 0.0818401i | \(-0.973920\pi\) | ||
0.996645 | − | 0.0818401i | \(-0.0260797\pi\) | |||||||
\(422\) | −10.7724 | −0.524391 | ||||||||
\(423\) | − | 1.86330i | − | 0.0905967i | ||||||
\(424\) | −16.0774 | −0.780790 | ||||||||
\(425\) | 7.79080 | 0.377909 | ||||||||
\(426\) | 8.79384 | 0.426063 | ||||||||
\(427\) | 5.96583 | 0.288707 | ||||||||
\(428\) | − | 17.6964i | − | 0.855388i | ||||||
\(429\) | 20.3355 | 0.981806 | ||||||||
\(430\) | −0.886479 | −0.0427498 | ||||||||
\(431\) | − | 15.5444i | − | 0.748748i | −0.927278 | − | 0.374374i | \(-0.877858\pi\) | ||
0.927278 | − | 0.374374i | \(-0.122142\pi\) | |||||||
\(432\) | −5.13949 | −0.247274 | ||||||||
\(433\) | − | 4.89134i | − | 0.235063i | −0.993069 | − | 0.117531i | \(-0.962502\pi\) | ||
0.993069 | − | 0.117531i | \(-0.0374980\pi\) | |||||||
\(434\) | 0.637456 | 0.0305988 | ||||||||
\(435\) | 3.29785 | 0.158120 | ||||||||
\(436\) | 6.74577 | 0.323064 | ||||||||
\(437\) | −6.44582 | −0.308346 | ||||||||
\(438\) | − | 19.1048i | − | 0.912861i | ||||||
\(439\) | − | 1.35921i | − | 0.0648714i | −0.999474 | − | 0.0324357i | \(-0.989674\pi\) | ||
0.999474 | − | 0.0324357i | \(-0.0103264\pi\) | |||||||
\(440\) | −2.06073 | −0.0982413 | ||||||||
\(441\) | −1.23657 | −0.0588845 | ||||||||
\(442\) | −3.31757 | −0.157801 | ||||||||
\(443\) | −16.0173 | −0.761005 | −0.380503 | − | 0.924780i | \(-0.624249\pi\) | ||||
−0.380503 | + | 0.924780i | \(0.624249\pi\) | |||||||
\(444\) | −4.61592 | −0.219062 | ||||||||
\(445\) | − | 0.0924632i | − | 0.00438318i | ||||||
\(446\) | − | 14.6480i | − | 0.693603i | ||||||
\(447\) | 5.45522i | 0.258023i | ||||||||
\(448\) | 5.61289i | 0.265184i | ||||||||
\(449\) | −6.76249 | −0.319141 | −0.159571 | − | 0.987187i | \(-0.551011\pi\) | ||||
−0.159571 | + | 0.987187i | \(0.551011\pi\) | |||||||
\(450\) | − | 2.46075i | − | 0.116001i | ||||||
\(451\) | − | 10.4967i | − | 0.494271i | ||||||
\(452\) | 8.98973i | 0.422842i | ||||||||
\(453\) | 5.22386 | 0.245439 | ||||||||
\(454\) | 5.30281i | 0.248873i | ||||||||
\(455\) | −1.97229 | −0.0924626 | ||||||||
\(456\) | 5.62682i | 0.263500i | ||||||||
\(457\) | −2.63584 | −0.123300 | −0.0616498 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616498 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(458\) | 12.0607 | 0.563561 | ||||||||
\(459\) | 6.98486 | 0.326026 | ||||||||
\(460\) | −1.85783 | −0.0866216 | ||||||||
\(461\) | 10.5486i | 0.491296i | 0.969359 | + | 0.245648i | \(0.0790008\pi\) | ||||
−0.969359 | + | 0.245648i | \(0.920999\pi\) | |||||||
\(462\) | 14.8321i | 0.690051i | ||||||||
\(463\) | − | 6.55200i | − | 0.304497i | −0.988342 | − | 0.152249i | \(-0.951349\pi\) | ||
0.988342 | − | 0.152249i | \(-0.0486514\pi\) | |||||||
\(464\) | 8.74922 | 0.406172 | ||||||||
\(465\) | 0.130399 | 0.00604709 | ||||||||
\(466\) | − | 16.1146i | − | 0.746496i | ||||||
\(467\) | 10.0296 | 0.464116 | 0.232058 | − | 0.972702i | \(-0.425454\pi\) | ||||
0.232058 | + | 0.972702i | \(0.425454\pi\) | |||||||
\(468\) | − | 2.99504i | − | 0.138446i | ||||||
\(469\) | − | 8.34076i | − | 0.385141i | ||||||
\(470\) | 0.441478 | 0.0203639 | ||||||||
\(471\) | 16.4449 | 0.757739 | ||||||||
\(472\) | 13.0809 | 0.602098 | ||||||||
\(473\) | −19.5920 | −0.900840 | ||||||||
\(474\) | −1.56389 | −0.0718318 | ||||||||
\(475\) | −5.78182 | −0.265288 | ||||||||
\(476\) | 6.91615i | 0.317001i | ||||||||
\(477\) | 4.42997i | 0.202834i | ||||||||
\(478\) | 16.7199i | 0.764752i | ||||||||
\(479\) | 21.8304 | 0.997458 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(480\) | 2.55339i | 0.116546i | ||||||||
\(481\) | 4.74615i | 0.216406i | ||||||||
\(482\) | − | 15.4413i | − | 0.703334i | ||||||
\(483\) | 31.4217i | 1.42974i | ||||||||
\(484\) | −3.08357 | −0.140162 | ||||||||
\(485\) | − | 1.86215i | − | 0.0845558i | ||||||
\(486\) | − | 5.07225i | − | 0.230082i | ||||||
\(487\) | − | 26.4902i | − | 1.20038i | −0.799856 | − | 0.600192i | \(-0.795091\pi\) | ||
0.799856 | − | 0.600192i | \(-0.204909\pi\) | |||||||
\(488\) | −5.04397 | −0.228330 | ||||||||
\(489\) | − | 24.2188i | − | 1.09521i | ||||||
\(490\) | − | 0.292986i | − | 0.0132358i | ||||||
\(491\) | 7.03673 | 0.317563 | 0.158782 | − | 0.987314i | \(-0.449243\pi\) | ||||
0.158782 | + | 0.987314i | \(0.449243\pi\) | |||||||
\(492\) | −8.26080 | −0.372426 | ||||||||
\(493\) | −11.8907 | −0.535530 | ||||||||
\(494\) | 2.46208 | 0.110774 | ||||||||
\(495\) | 0.567812i | 0.0255212i | ||||||||
\(496\) | 0.345948 | 0.0155335 | ||||||||
\(497\) | −18.8498 | −0.845527 | ||||||||
\(498\) | 9.44679i | 0.423321i | ||||||||
\(499\) | − | 18.9065i | − | 0.846370i | −0.906043 | − | 0.423185i | \(-0.860912\pi\) | ||
0.906043 | − | 0.423185i | \(-0.139088\pi\) | |||||||
\(500\) | −3.35029 | −0.149829 | ||||||||
\(501\) | 40.8027i | 1.82293i | ||||||||
\(502\) | −2.73900 | −0.122248 | ||||||||
\(503\) | − | 23.0817i | − | 1.02916i | −0.857442 | − | 0.514581i | \(-0.827948\pi\) | ||
0.857442 | − | 0.514581i | \(-0.172052\pi\) | |||||||
\(504\) | 5.13326 | 0.228654 | ||||||||
\(505\) | − | 3.00052i | − | 0.133522i | ||||||
\(506\) | 14.3654 | 0.638621 | ||||||||
\(507\) | 8.51922 | 0.378352 | ||||||||
\(508\) | 28.4590i | 1.26267i | ||||||||
\(509\) | 16.8514i | 0.746925i | 0.927645 | + | 0.373463i | \(0.121830\pi\) | ||||
−0.927645 | + | 0.373463i | \(0.878170\pi\) | |||||||
\(510\) | − | 0.494984i | − | 0.0219183i | ||||||
\(511\) | 40.9514i | 1.81158i | ||||||||
\(512\) | 12.5820i | 0.556053i | ||||||||
\(513\) | −5.18371 | −0.228866 | ||||||||
\(514\) | 4.16221i | 0.183587i | ||||||||
\(515\) | − | 4.60573i | − | 0.202953i | ||||||
\(516\) | 15.4187i | 0.678770i | ||||||||
\(517\) | 9.75706 | 0.429115 | ||||||||
\(518\) | −3.46170 | −0.152098 | ||||||||
\(519\) | − | 18.8059i | − | 0.825486i | ||||||
\(520\) | 1.66753 | 0.0731259 | ||||||||
\(521\) | − | 13.5854i | − | 0.595189i | −0.954692 | − | 0.297595i | \(-0.903816\pi\) | ||
0.954692 | − | 0.297595i | \(-0.0961844\pi\) | |||||||
\(522\) | 3.75572i | 0.164383i | ||||||||
\(523\) | − | 25.0563i | − | 1.09563i | −0.836598 | − | 0.547817i | \(-0.815459\pi\) | ||
0.836598 | − | 0.547817i | \(-0.184541\pi\) | |||||||
\(524\) | 24.6707i | 1.07774i | ||||||||
\(525\) | 28.1849i | 1.23009i | ||||||||
\(526\) | 20.4177i | 0.890254i | ||||||||
\(527\) | −0.470163 | −0.0204806 | ||||||||
\(528\) | 8.04939i | 0.350305i | ||||||||
\(529\) | 7.43314 | 0.323180 | ||||||||
\(530\) | −1.04961 | −0.0455921 | ||||||||
\(531\) | − | 3.60431i | − | 0.156414i | ||||||
\(532\) | − | 5.13271i | − | 0.222531i | ||||||
\(533\) | 8.49386i | 0.367910i | ||||||||
\(534\) | 0.562667 | 0.0243490 | ||||||||
\(535\) | − | 2.71481i | − | 0.117371i | ||||||
\(536\) | 7.05191i | 0.304596i | ||||||||
\(537\) | 18.6415i | 0.804439i | ||||||||
\(538\) | − | 10.6347i | − | 0.458493i | ||||||
\(539\) | − | 6.47526i | − | 0.278909i | ||||||
\(540\) | −1.49406 | −0.0642939 | ||||||||
\(541\) | 9.12575 | 0.392347 | 0.196173 | − | 0.980569i | \(-0.437148\pi\) | ||||
0.196173 | + | 0.980569i | \(0.437148\pi\) | |||||||
\(542\) | 8.88340i | 0.381574i | ||||||||
\(543\) | 38.8176 | 1.66582 | ||||||||
\(544\) | − | 9.20645i | − | 0.394723i | ||||||
\(545\) | 1.03487 | 0.0443290 | ||||||||
\(546\) | − | 12.0020i | − | 0.513639i | ||||||
\(547\) | 17.3348 | 0.741182 | 0.370591 | − | 0.928796i | \(-0.379155\pi\) | ||||
0.370591 | + | 0.928796i | \(0.379155\pi\) | |||||||
\(548\) | 0.326266i | 0.0139374i | ||||||||
\(549\) | 1.38981i | 0.0593157i | ||||||||
\(550\) | 12.8856 | 0.549444 | ||||||||
\(551\) | 8.82448 | 0.375936 | ||||||||
\(552\) | − | 26.5663i | − | 1.13074i | ||||||
\(553\) | 3.35223 | 0.142551 | ||||||||
\(554\) | −9.60248 | −0.407970 | ||||||||
\(555\) | −0.708130 | −0.0300584 | ||||||||
\(556\) | 24.4601 | 1.03734 | ||||||||
\(557\) | − | 4.76111i | − | 0.201735i | −0.994900 | − | 0.100867i | \(-0.967838\pi\) | ||
0.994900 | − | 0.100867i | \(-0.0321618\pi\) | |||||||
\(558\) | 0.148503i | 0.00628662i | ||||||||
\(559\) | 15.8537 | 0.670540 | ||||||||
\(560\) | − | 0.780694i | − | 0.0329903i | ||||||
\(561\) | − | 10.9396i | − | 0.461870i | ||||||
\(562\) | − | 4.91173i | − | 0.207189i | ||||||
\(563\) | −38.3244 | −1.61518 | −0.807591 | − | 0.589743i | \(-0.799229\pi\) | ||||
−0.807591 | + | 0.589743i | \(0.799229\pi\) | |||||||
\(564\) | − | 7.67871i | − | 0.323332i | ||||||
\(565\) | 1.37912i | 0.0580199i | ||||||||
\(566\) | 10.7576i | 0.452174i | ||||||||
\(567\) | 31.4127i | 1.31921i | ||||||||
\(568\) | 15.9370 | 0.668702 | ||||||||
\(569\) | − | 26.9667i | − | 1.13050i | −0.824919 | − | 0.565251i | \(-0.808779\pi\) | ||
0.824919 | − | 0.565251i | \(-0.191221\pi\) | |||||||
\(570\) | 0.367345i | 0.0153864i | ||||||||
\(571\) | 44.8884i | 1.87852i | 0.343207 | + | 0.939260i | \(0.388487\pi\) | ||||
−0.343207 | + | 0.939260i | \(0.611513\pi\) | |||||||
\(572\) | 15.6833 | 0.655754 | ||||||||
\(573\) | 5.29523 | 0.221211 | ||||||||
\(574\) | −6.19517 | −0.258581 | ||||||||
\(575\) | 27.2981 | 1.13841 | ||||||||
\(576\) | −1.30759 | −0.0544828 | ||||||||
\(577\) | 6.68314 | 0.278223 | 0.139111 | − | 0.990277i | \(-0.455575\pi\) | ||||
0.139111 | + | 0.990277i | \(0.455575\pi\) | |||||||
\(578\) | − | 10.4550i | − | 0.434870i | ||||||
\(579\) | − | 39.5090i | − | 1.64194i | ||||||
\(580\) | 2.54341 | 0.105609 | ||||||||
\(581\) | − | 20.2494i | − | 0.840085i | ||||||
\(582\) | 11.3317 | 0.469716 | ||||||||
\(583\) | −23.1973 | −0.960734 | ||||||||
\(584\) | − | 34.6234i | − | 1.43273i | ||||||
\(585\) | − | 0.459469i | − | 0.0189967i | ||||||
\(586\) | − | 12.4352i | − | 0.513692i | ||||||
\(587\) | −17.9833 | −0.742250 | −0.371125 | − | 0.928583i | \(-0.621028\pi\) | ||||
−0.371125 | + | 0.928583i | \(0.621028\pi\) | |||||||
\(588\) | −5.09596 | −0.210154 | ||||||||
\(589\) | 0.348924 | 0.0143772 | ||||||||
\(590\) | 0.853983 | 0.0351579 | ||||||||
\(591\) | 43.2808i | 1.78033i | ||||||||
\(592\) | −1.87867 | −0.0772129 | ||||||||
\(593\) | − | 33.6245i | − | 1.38079i | −0.723432 | − | 0.690396i | \(-0.757436\pi\) | ||
0.723432 | − | 0.690396i | \(-0.242564\pi\) | |||||||
\(594\) | 11.5526 | 0.474010 | ||||||||
\(595\) | 1.06101i | 0.0434971i | ||||||||
\(596\) | 4.20724i | 0.172335i | ||||||||
\(597\) | 30.3727i | 1.24307i | ||||||||
\(598\) | −11.6244 | −0.475357 | ||||||||
\(599\) | 21.5246i | 0.879473i | 0.898127 | + | 0.439736i | \(0.144928\pi\) | ||||
−0.898127 | + | 0.439736i | \(0.855072\pi\) | |||||||
\(600\) | − | 23.8296i | − | 0.972840i | ||||||
\(601\) | − | 2.31490i | − | 0.0944267i | −0.998885 | − | 0.0472134i | \(-0.984966\pi\) | ||
0.998885 | − | 0.0472134i | \(-0.0150341\pi\) | |||||||
\(602\) | 11.5632i | 0.471281i | ||||||||
\(603\) | 1.94308 | 0.0791283 | ||||||||
\(604\) | 4.02881 | 0.163930 | ||||||||
\(605\) | −0.473051 | −0.0192323 | ||||||||
\(606\) | 18.2591 | 0.741726 | ||||||||
\(607\) | 22.3647 | 0.907754 | 0.453877 | − | 0.891064i | \(-0.350041\pi\) | ||||
0.453877 | + | 0.891064i | \(0.350041\pi\) | |||||||
\(608\) | 6.83242i | 0.277091i | ||||||||
\(609\) | − | 43.0171i | − | 1.74314i | ||||||
\(610\) | −0.329293 | −0.0133327 | ||||||||
\(611\) | −7.89535 | −0.319412 | ||||||||
\(612\) | −1.61120 | −0.0651288 | ||||||||
\(613\) | 10.9512 | 0.442314 | 0.221157 | − | 0.975238i | \(-0.429017\pi\) | ||||
0.221157 | + | 0.975238i | \(0.429017\pi\) | |||||||
\(614\) | 19.4126i | 0.783427i | ||||||||
\(615\) | −1.26729 | −0.0511021 | ||||||||
\(616\) | 26.8800i | 1.08303i | ||||||||
\(617\) | −35.1527 | −1.41519 | −0.707597 | − | 0.706616i | \(-0.750221\pi\) | ||||
−0.707597 | + | 0.706616i | \(0.750221\pi\) | |||||||
\(618\) | 28.0273 | 1.12742 | ||||||||
\(619\) | − | 35.8209i | − | 1.43976i | −0.694097 | − | 0.719882i | \(-0.744196\pi\) | ||
0.694097 | − | 0.719882i | \(-0.255804\pi\) | |||||||
\(620\) | 0.100568 | 0.00403889 | ||||||||
\(621\) | 24.4742 | 0.982116 | ||||||||
\(622\) | −9.99560 | −0.400787 | ||||||||
\(623\) | −1.20609 | −0.0483208 | ||||||||
\(624\) | − | 6.51351i | − | 0.260749i | ||||||
\(625\) | 24.2277 | 0.969109 | ||||||||
\(626\) | 8.94664i | 0.357580i | ||||||||
\(627\) | 8.11864i | 0.324227i | ||||||||
\(628\) | 12.6828 | 0.506099 | ||||||||
\(629\) | 2.55322 | 0.101804 | ||||||||
\(630\) | 0.335123 | 0.0133516 | ||||||||
\(631\) | −35.9978 | −1.43305 | −0.716525 | − | 0.697561i | \(-0.754268\pi\) | ||||
−0.716525 | + | 0.697561i | \(0.754268\pi\) | |||||||
\(632\) | −2.83422 | −0.112739 | ||||||||
\(633\) | 28.7438i | 1.14246i | ||||||||
\(634\) | 23.6236 | 0.938211 | ||||||||
\(635\) | 4.36591i | 0.173256i | ||||||||
\(636\) | 18.2560i | 0.723899i | ||||||||
\(637\) | 5.23973i | 0.207606i | ||||||||
\(638\) | −19.6666 | −0.778608 | ||||||||
\(639\) | − | 4.39127i | − | 0.173716i | ||||||
\(640\) | 2.34842i | 0.0928294i | ||||||||
\(641\) | 1.58340 | 0.0625407 | 0.0312704 | − | 0.999511i | \(-0.490045\pi\) | ||||
0.0312704 | + | 0.999511i | \(0.490045\pi\) | |||||||
\(642\) | 16.5205 | 0.652010 | ||||||||
\(643\) | − | 16.2454i | − | 0.640655i | −0.947307 | − | 0.320328i | \(-0.896207\pi\) | ||
0.947307 | − | 0.320328i | \(-0.103793\pi\) | |||||||
\(644\) | 24.2334i | 0.954931i | ||||||||
\(645\) | 2.36538i | 0.0931369i | ||||||||
\(646\) | − | 1.32449i | − | 0.0521114i | ||||||
\(647\) | −30.9792 | −1.21792 | −0.608958 | − | 0.793202i | \(-0.708412\pi\) | ||||
−0.608958 | + | 0.793202i | \(0.708412\pi\) | |||||||
\(648\) | − | 26.5586i | − | 1.04332i | ||||||
\(649\) | 18.8738 | 0.740860 | ||||||||
\(650\) | −10.4269 | −0.408978 | ||||||||
\(651\) | − | 1.70092i | − | 0.0666641i | ||||||
\(652\) | − | 18.6783i | − | 0.731499i | ||||||
\(653\) | −29.1806 | −1.14192 | −0.570962 | − | 0.820976i | \(-0.693430\pi\) | ||||
−0.570962 | + | 0.820976i | \(0.693430\pi\) | |||||||
\(654\) | 6.29750i | 0.246252i | ||||||||
\(655\) | 3.78473i | 0.147882i | ||||||||
\(656\) | −3.36213 | −0.131269 | ||||||||
\(657\) | −9.54011 | −0.372195 | ||||||||
\(658\) | − | 5.75863i | − | 0.224495i | ||||||
\(659\) | 11.2198i | 0.437063i | 0.975830 | + | 0.218531i | \(0.0701266\pi\) | ||||
−0.975830 | + | 0.218531i | \(0.929873\pi\) | |||||||
\(660\) | 2.33997i | 0.0910831i | ||||||||
\(661\) | 3.44171 | 0.133867 | 0.0669336 | − | 0.997757i | \(-0.478678\pi\) | ||||
0.0669336 | + | 0.997757i | \(0.478678\pi\) | |||||||
\(662\) | 10.5289 | 0.409216 | ||||||||
\(663\) | 8.85224i | 0.343792i | ||||||||
\(664\) | 17.1203i | 0.664398i | ||||||||
\(665\) | − | 0.787410i | − | 0.0305344i | ||||||
\(666\) | − | 0.806444i | − | 0.0312491i | ||||||
\(667\) | −41.6637 | −1.61322 | ||||||||
\(668\) | 31.4683i | 1.21755i | ||||||||
\(669\) | −39.0851 | −1.51112 | ||||||||
\(670\) | 0.460381i | 0.0177861i | ||||||||
\(671\) | −7.27767 | −0.280951 | ||||||||
\(672\) | 33.3063 | 1.28482 | ||||||||
\(673\) | −23.3596 | −0.900448 | −0.450224 | − | 0.892916i | \(-0.648656\pi\) | ||||
−0.450224 | + | 0.892916i | \(0.648656\pi\) | |||||||
\(674\) | 10.8165i | 0.416635i | ||||||||
\(675\) | 21.9530 | 0.844972 | ||||||||
\(676\) | 6.57029 | 0.252703 | ||||||||
\(677\) | − | 36.8091i | − | 1.41469i | −0.706869 | − | 0.707345i | \(-0.749893\pi\) | ||
0.706869 | − | 0.707345i | \(-0.250107\pi\) | |||||||
\(678\) | −8.39235 | −0.322306 | ||||||||
\(679\) | −24.2898 | −0.932156 | ||||||||
\(680\) | − | 0.897056i | − | 0.0344005i | ||||||
\(681\) | 14.1494 | 0.542207 | ||||||||
\(682\) | −0.777627 | −0.0297769 | ||||||||
\(683\) | −39.4358 | −1.50897 | −0.754485 | − | 0.656318i | \(-0.772113\pi\) | ||||
−0.754485 | + | 0.656318i | \(0.772113\pi\) | |||||||
\(684\) | 1.19572 | 0.0457197 | ||||||||
\(685\) | 0.0500526i | 0.00191241i | ||||||||
\(686\) | 11.1208 | 0.424592 | ||||||||
\(687\) | − | 32.1815i | − | 1.22780i | ||||||
\(688\) | 6.27537i | 0.239246i | ||||||||
\(689\) | 18.7711 | 0.715122 | ||||||||
\(690\) | − | 1.73437i | − | 0.0660264i | ||||||
\(691\) | 45.5476i | 1.73271i | 0.499427 | + | 0.866356i | \(0.333544\pi\) | ||||
−0.499427 | + | 0.866356i | \(0.666456\pi\) | |||||||
\(692\) | − | 14.5037i | − | 0.551347i | ||||||
\(693\) | 7.40651 | 0.281350 | ||||||||
\(694\) | −6.26068 | −0.237652 | ||||||||
\(695\) | 3.75244 | 0.142338 | ||||||||
\(696\) | 36.3699i | 1.37860i | ||||||||
\(697\) | 4.56932 | 0.173075 | ||||||||
\(698\) | −6.43268 | − | 11.8124i | −0.243481 | − | 0.447106i | ||||
\(699\) | −42.9985 | −1.62635 | ||||||||
\(700\) | 21.7370i | 0.821583i | ||||||||
\(701\) | −40.1238 | −1.51546 | −0.757728 | − | 0.652571i | \(-0.773690\pi\) | ||||
−0.757728 | + | 0.652571i | \(0.773690\pi\) | |||||||
\(702\) | −9.34830 | −0.352829 | ||||||||
\(703\) | −1.89483 | −0.0714649 | ||||||||
\(704\) | − | 6.84711i | − | 0.258060i | ||||||
\(705\) | − | 1.17799i | − | 0.0443657i | ||||||
\(706\) | − | 24.8381i | − | 0.934794i | ||||||
\(707\) | −39.1387 | −1.47196 | ||||||||
\(708\) | − | 14.8535i | − | 0.558227i | ||||||
\(709\) | − | 42.2100i | − | 1.58523i | −0.609722 | − | 0.792615i | \(-0.708719\pi\) | ||
0.609722 | − | 0.792615i | \(-0.291281\pi\) | |||||||
\(710\) | 1.04044 | 0.0390471 | ||||||||
\(711\) | 0.780940i | 0.0292876i | ||||||||
\(712\) | 1.01972 | 0.0382155 | ||||||||
\(713\) | −1.64740 | −0.0616957 | ||||||||
\(714\) | −6.45656 | −0.241631 | ||||||||
\(715\) | 2.40599 | 0.0899788 | ||||||||
\(716\) | 14.3769i | 0.537289i | ||||||||
\(717\) | 44.6136 | 1.66613 | ||||||||
\(718\) | 13.4430 | 0.501689 | ||||||||
\(719\) | 36.2471i | 1.35179i | 0.736998 | + | 0.675894i | \(0.236242\pi\) | ||||
−0.736998 | + | 0.675894i | \(0.763758\pi\) | |||||||
\(720\) | 0.181872 | 0.00677796 | ||||||||
\(721\) | −60.0770 | −2.23739 | ||||||||
\(722\) | − | 12.6967i | − | 0.472522i | ||||||
\(723\) | −41.2020 | −1.53232 | ||||||||
\(724\) | 29.9373 | 1.11261 | ||||||||
\(725\) | −37.3717 | −1.38795 | ||||||||
\(726\) | − | 2.87866i | − | 0.106837i | ||||||
\(727\) | 47.7872 | 1.77233 | 0.886165 | − | 0.463370i | \(-0.153360\pi\) | ||||
0.886165 | + | 0.463370i | \(0.153360\pi\) | |||||||
\(728\) | − | 21.7511i | − | 0.806151i | ||||||
\(729\) | 18.2509 | 0.675958 | ||||||||
\(730\) | − | 2.26037i | − | 0.0836602i | ||||||
\(731\) | − | 8.52859i | − | 0.315441i | ||||||
\(732\) | 5.72745i | 0.211693i | ||||||||
\(733\) | 44.7698i | 1.65361i | 0.562488 | + | 0.826805i | \(0.309844\pi\) | ||||
−0.562488 | + | 0.826805i | \(0.690156\pi\) | |||||||
\(734\) | −12.6441 | −0.466704 | ||||||||
\(735\) | −0.781772 | −0.0288361 | ||||||||
\(736\) | − | 32.2584i | − | 1.18906i | ||||||
\(737\) | 10.1748i | 0.374795i | ||||||||
\(738\) | − | 1.44324i | − | 0.0531263i | ||||||
\(739\) | −43.8350 | −1.61250 | −0.806249 | − | 0.591576i | \(-0.798506\pi\) | ||||
−0.806249 | + | 0.591576i | \(0.798506\pi\) | |||||||
\(740\) | −0.546132 | −0.0200762 | ||||||||
\(741\) | − | 6.56955i | − | 0.241338i | ||||||
\(742\) | 13.6911i | 0.502615i | ||||||||
\(743\) | −20.1179 | −0.738054 | −0.369027 | − | 0.929419i | \(-0.620309\pi\) | ||||
−0.369027 | + | 0.929419i | \(0.620309\pi\) | |||||||
\(744\) | 1.43808i | 0.0527227i | ||||||||
\(745\) | 0.645433i | 0.0236468i | ||||||||
\(746\) | −18.7529 | −0.686594 | ||||||||
\(747\) | 4.71732 | 0.172598 | ||||||||
\(748\) | − | 8.43695i | − | 0.308485i | ||||||
\(749\) | −35.4119 | −1.29392 | ||||||||
\(750\) | − | 3.12766i | − | 0.114206i | ||||||
\(751\) | − | 15.1066i | − | 0.551246i | −0.961266 | − | 0.275623i | \(-0.911116\pi\) | ||
0.961266 | − | 0.275623i | \(-0.0888842\pi\) | |||||||
\(752\) | − | 3.12522i | − | 0.113965i | ||||||
\(753\) | 7.30845i | 0.266335i | ||||||||
\(754\) | 15.9141 | 0.579557 | ||||||||
\(755\) | 0.618060 | 0.0224935 | ||||||||
\(756\) | 19.4884i | 0.708787i | ||||||||
\(757\) | − | 42.9205i | − | 1.55997i | −0.625796 | − | 0.779986i | \(-0.715226\pi\) | ||
0.625796 | − | 0.779986i | \(-0.284774\pi\) | |||||||
\(758\) | −15.4397 | −0.560794 | ||||||||
\(759\) | − | 38.3311i | − | 1.39133i | ||||||
\(760\) | 0.665735i | 0.0241488i | ||||||||
\(761\) | − | 32.6493i | − | 1.18354i | −0.806108 | − | 0.591768i | \(-0.798430\pi\) | ||
0.806108 | − | 0.591768i | \(-0.201570\pi\) | |||||||
\(762\) | −26.5679 | −0.962453 | ||||||||
\(763\) | − | 13.4988i | − | 0.488690i | ||||||
\(764\) | 4.08384 | 0.147748 | ||||||||
\(765\) | −0.247174 | −0.00893660 | ||||||||
\(766\) | −7.93389 | −0.286663 | ||||||||
\(767\) | −15.2725 | −0.551459 | ||||||||
\(768\) | −21.5648 | −0.778151 | ||||||||
\(769\) | − | 3.08282i | − | 0.111169i | −0.998454 | − | 0.0555847i | \(-0.982298\pi\) | ||
0.998454 | − | 0.0555847i | \(-0.0177023\pi\) | |||||||
\(770\) | 1.75485i | 0.0632405i | ||||||||
\(771\) | 11.1060 | 0.399972 | ||||||||
\(772\) | − | 30.4706i | − | 1.09666i | ||||||
\(773\) | 24.6690 | 0.887282 | 0.443641 | − | 0.896205i | \(-0.353687\pi\) | ||||
0.443641 | + | 0.896205i | \(0.353687\pi\) | |||||||
\(774\) | −2.69378 | −0.0968261 | ||||||||
\(775\) | −1.47770 | −0.0530804 | ||||||||
\(776\) | 20.5364 | 0.737214 | ||||||||
\(777\) | 9.23682i | 0.331369i | ||||||||
\(778\) | −3.46048 | −0.124064 | ||||||||
\(779\) | −3.39105 | −0.121497 | ||||||||
\(780\) | − | 1.89349i | − | 0.0677977i | ||||||
\(781\) | 22.9947 | 0.822814 | ||||||||
\(782\) | 6.25342i | 0.223622i | ||||||||
\(783\) | −33.5057 | −1.19740 | ||||||||
\(784\) | −2.07405 | −0.0740730 | ||||||||
\(785\) | 1.94567 | 0.0694439 | ||||||||
\(786\) | −23.0313 | −0.821498 | ||||||||
\(787\) | − | 9.44552i | − | 0.336696i | −0.985728 | − | 0.168348i | \(-0.946157\pi\) | ||
0.985728 | − | 0.168348i | \(-0.0538433\pi\) | |||||||
\(788\) | 33.3795i | 1.18909i | ||||||||
\(789\) | 54.4803 | 1.93955 | ||||||||
\(790\) | −0.185031 | −0.00658312 | ||||||||
\(791\) | 17.9892 | 0.639621 | ||||||||
\(792\) | −6.26202 | −0.222511 | ||||||||
\(793\) | 5.88904 | 0.209126 | ||||||||
\(794\) | − | 3.36750i | − | 0.119508i | ||||||
\(795\) | 2.80066i | 0.0993292i | ||||||||
\(796\) | 23.4244i | 0.830256i | ||||||||
\(797\) | − | 25.6341i | − | 0.908006i | −0.891000 | − | 0.454003i | \(-0.849996\pi\) | ||
0.891000 | − | 0.454003i | \(-0.150004\pi\) | |||||||
\(798\) | 4.79163 | 0.169622 | ||||||||
\(799\) | 4.24735i | 0.150260i | ||||||||
\(800\) | − | 28.9354i | − | 1.02302i | ||||||
\(801\) | − | 0.280972i | − | 0.00992766i | ||||||
\(802\) | 7.53986 | 0.266242 | ||||||||
\(803\) | − | 49.9563i | − | 1.76292i | ||||||
\(804\) | 8.00749 | 0.282402 | ||||||||
\(805\) | 3.71765i | 0.131030i | ||||||||
\(806\) | 0.629250 | 0.0221644 | ||||||||
\(807\) | −28.3764 | −0.998895 | ||||||||
\(808\) | 33.0908 | 1.16413 | ||||||||
\(809\) | −25.8850 | −0.910068 | −0.455034 | − | 0.890474i | \(-0.650373\pi\) | ||||
−0.455034 | + | 0.890474i | \(0.650373\pi\) | |||||||
\(810\) | − | 1.73387i | − | 0.0609220i | ||||||
\(811\) | − | 2.52277i | − | 0.0885864i | −0.999019 | − | 0.0442932i | \(-0.985896\pi\) | ||
0.999019 | − | 0.0442932i | \(-0.0141036\pi\) | |||||||
\(812\) | − | 33.1761i | − | 1.16425i | ||||||
\(813\) | 23.7035 | 0.831317 | ||||||||
\(814\) | 4.22290 | 0.148013 | ||||||||
\(815\) | − | 2.86544i | − | 0.100372i | ||||||
\(816\) | −3.50398 | −0.122664 | ||||||||
\(817\) | 6.32935i | 0.221436i | ||||||||
\(818\) | 7.44990i | 0.260480i | ||||||||
\(819\) | −5.99330 | −0.209423 | ||||||||
\(820\) | −0.977374 | −0.0341314 | ||||||||
\(821\) | −32.4133 | −1.13123 | −0.565616 | − | 0.824669i | \(-0.691362\pi\) | ||||
−0.565616 | + | 0.824669i | \(0.691362\pi\) | |||||||
\(822\) | −0.304585 | −0.0106236 | ||||||||
\(823\) | 20.7188 | 0.722213 | 0.361107 | − | 0.932525i | \(-0.382399\pi\) | ||||
0.361107 | + | 0.932525i | \(0.382399\pi\) | |||||||
\(824\) | 50.7936 | 1.76948 | ||||||||
\(825\) | − | 34.3825i | − | 1.19704i | ||||||
\(826\) | − | 11.1393i | − | 0.387587i | ||||||
\(827\) | − | 18.2348i | − | 0.634085i | −0.948411 | − | 0.317043i | \(-0.897310\pi\) | ||
0.948411 | − | 0.317043i | \(-0.102690\pi\) | |||||||
\(828\) | −5.64546 | −0.196193 | ||||||||
\(829\) | − | 38.0099i | − | 1.32014i | −0.751204 | − | 0.660070i | \(-0.770527\pi\) | ||
0.751204 | − | 0.660070i | \(-0.229473\pi\) | |||||||
\(830\) | 1.11769i | 0.0387957i | ||||||||
\(831\) | 25.6222i | 0.888824i | ||||||||
\(832\) | 5.54064i | 0.192087i | ||||||||
\(833\) | 2.81875 | 0.0976638 | ||||||||
\(834\) | 22.8347i | 0.790702i | ||||||||
\(835\) | 4.82756i | 0.167065i | ||||||||
\(836\) | 6.26135i | 0.216553i | ||||||||
\(837\) | −1.32483 | −0.0457929 | ||||||||
\(838\) | 12.5896i | 0.434899i | ||||||||
\(839\) | 18.7178i | 0.646210i | 0.946363 | + | 0.323105i | \(0.104727\pi\) | ||||
−0.946363 | + | 0.323105i | \(0.895273\pi\) | |||||||
\(840\) | 3.24529 | 0.111973 | ||||||||
\(841\) | 28.0385 | 0.966846 | ||||||||
\(842\) | 2.41801 | 0.0833302 | ||||||||
\(843\) | −13.1059 | −0.451391 | ||||||||
\(844\) | 22.1681i | 0.763058i | ||||||||
\(845\) | 1.00795 | 0.0346745 | ||||||||
\(846\) | 1.34154 | 0.0461231 | ||||||||
\(847\) | 6.17046i | 0.212020i | ||||||||
\(848\) | 7.43017i | 0.255153i | ||||||||
\(849\) | 28.7043 | 0.985128 | ||||||||
\(850\) | 5.60923i | 0.192395i | ||||||||
\(851\) | 8.94621 | 0.306672 | ||||||||
\(852\) | − | 18.0966i | − | 0.619978i | ||||||
\(853\) | −22.7361 | −0.778468 | −0.389234 | − | 0.921139i | \(-0.627260\pi\) | ||||
−0.389234 | + | 0.921139i | \(0.627260\pi\) | |||||||
\(854\) | 4.29529i | 0.146982i | ||||||||
\(855\) | 0.183436 | 0.00627339 | ||||||||
\(856\) | 29.9399 | 1.02332 | ||||||||
\(857\) | 37.7022i | 1.28788i | 0.765074 | + | 0.643942i | \(0.222702\pi\) | ||||
−0.765074 | + | 0.643942i | \(0.777298\pi\) | |||||||
\(858\) | 14.6412i | 0.499841i | ||||||||
\(859\) | 7.14352i | 0.243734i | 0.992546 | + | 0.121867i | \(0.0388881\pi\) | ||||
−0.992546 | + | 0.121867i | \(0.961112\pi\) | |||||||
\(860\) | 1.82426i | 0.0622067i | ||||||||
\(861\) | 16.5305i | 0.563358i | ||||||||
\(862\) | 11.1917 | 0.381190 | ||||||||
\(863\) | 6.29022i | 0.214121i | 0.994252 | + | 0.107061i | \(0.0341439\pi\) | ||||
−0.994252 | + | 0.107061i | \(0.965856\pi\) | |||||||
\(864\) | − | 25.9421i | − | 0.882567i | ||||||
\(865\) | − | 2.22501i | − | 0.0756527i | ||||||
\(866\) | 3.52167 | 0.119671 | ||||||||
\(867\) | −27.8969 | −0.947428 | ||||||||
\(868\) | − | 1.31180i | − | 0.0445254i | ||||||
\(869\) | −4.08935 | −0.138722 | ||||||||
\(870\) | 2.37439i | 0.0804995i | ||||||||
\(871\) | − | 8.23340i | − | 0.278978i | ||||||
\(872\) | 11.4129i | 0.386490i | ||||||||
\(873\) | − | 5.65859i | − | 0.191514i | ||||||
\(874\) | − | 4.64087i | − | 0.156980i | ||||||
\(875\) | 6.70419i | 0.226643i | ||||||||
\(876\) | −39.3151 | −1.32833 | ||||||||
\(877\) | 36.4226i | 1.22990i | 0.788565 | + | 0.614951i | \(0.210824\pi\) | ||||
−0.788565 | + | 0.614951i | \(0.789176\pi\) | |||||||
\(878\) | 0.978604 | 0.0330263 | ||||||||
\(879\) | −33.1806 | −1.11915 | ||||||||
\(880\) | 0.952362i | 0.0321041i | ||||||||
\(881\) | 40.4785i | 1.36376i | 0.731466 | + | 0.681878i | \(0.238837\pi\) | ||||
−0.731466 | + | 0.681878i | \(0.761163\pi\) | |||||||
\(882\) | − | 0.890311i | − | 0.0299783i | ||||||
\(883\) | −5.99811 | −0.201852 | −0.100926 | − | 0.994894i | \(-0.532181\pi\) | ||||
−0.100926 | + | 0.994894i | \(0.532181\pi\) | |||||||
\(884\) | 6.82712i | 0.229621i | ||||||||
\(885\) | − | 2.27867i | − | 0.0765968i | ||||||
\(886\) | − | 11.5322i | − | 0.387431i | ||||||
\(887\) | 1.36885i | 0.0459616i | 0.999736 | + | 0.0229808i | \(0.00731566\pi\) | ||||
−0.999736 | + | 0.0229808i | \(0.992684\pi\) | |||||||
\(888\) | − | 7.80950i | − | 0.262070i | ||||||
\(889\) | 56.9487 | 1.91000 | ||||||||
\(890\) | 0.0665718 | 0.00223149 | ||||||||
\(891\) | − | 38.3200i | − | 1.28377i | ||||||
\(892\) | −30.1437 | −1.00928 | ||||||||
\(893\) | − | 3.15210i | − | 0.105481i | ||||||
\(894\) | −3.92766 | −0.131360 | ||||||||
\(895\) | 2.20556i | 0.0737238i | ||||||||
\(896\) | 30.6327 | 1.02337 | ||||||||
\(897\) | 31.0173i | 1.03564i | ||||||||
\(898\) | − | 4.86886i | − | 0.162476i | ||||||
\(899\) | 2.25533 | 0.0752195 | ||||||||
\(900\) | −5.06390 | −0.168797 | ||||||||
\(901\) | − | 10.0980i | − | 0.336414i | ||||||
\(902\) | 7.55744 | 0.251635 | ||||||||
\(903\) | 30.8540 | 1.02676 | ||||||||
\(904\) | −15.2094 | −0.505857 | ||||||||
\(905\) | 4.59269 | 0.152666 | ||||||||
\(906\) | 3.76109i | 0.124954i | ||||||||
\(907\) | 40.1750i | 1.33399i | 0.745063 | + | 0.666994i | \(0.232419\pi\) | ||||
−0.745063 | + | 0.666994i | \(0.767581\pi\) | |||||||
\(908\) | 10.9125 | 0.362143 | ||||||||
\(909\) | − | 9.11783i | − | 0.302419i | ||||||
\(910\) | − | 1.42002i | − | 0.0470731i | ||||||
\(911\) | − | 45.9632i | − | 1.52283i | −0.648265 | − | 0.761415i | \(-0.724505\pi\) | ||
0.648265 | − | 0.761415i | \(-0.275495\pi\) | |||||||
\(912\) | 2.60043 | 0.0861087 | ||||||||
\(913\) | 24.7020i | 0.817517i | ||||||||
\(914\) | − | 1.89776i | − | 0.0627723i | ||||||
\(915\) | 0.878650i | 0.0290473i | ||||||||
\(916\) | − | 24.8194i | − | 0.820056i | ||||||
\(917\) | 49.3679 | 1.63027 | ||||||||
\(918\) | 5.02897i | 0.165981i | ||||||||
\(919\) | 32.3909i | 1.06848i | 0.845334 | + | 0.534238i | \(0.179401\pi\) | ||||
−0.845334 | + | 0.534238i | \(0.820599\pi\) | |||||||
\(920\) | − | 3.14318i | − | 0.103628i | ||||||
\(921\) | 51.7983 | 1.70681 | ||||||||
\(922\) | −7.59478 | −0.250121 | ||||||||
\(923\) | −18.6071 | −0.612461 | ||||||||
\(924\) | 30.5225 | 1.00412 | ||||||||
\(925\) | 8.02463 | 0.263848 | ||||||||
\(926\) | 4.71732 | 0.155021 | ||||||||
\(927\) | − | 13.9957i | − | 0.459677i | ||||||
\(928\) | 44.1625i | 1.44971i | ||||||||
\(929\) | −12.7665 | −0.418854 | −0.209427 | − | 0.977824i | \(-0.567160\pi\) | ||||
−0.209427 | + | 0.977824i | \(0.567160\pi\) | |||||||
\(930\) | 0.0938846i | 0.00307860i | ||||||||
\(931\) | −2.09189 | −0.0685588 | ||||||||
\(932\) | −33.1618 | −1.08625 | ||||||||
\(933\) | 26.6711i | 0.873174i | ||||||||
\(934\) | 7.22115i | 0.236283i | ||||||||
\(935\) | − | 1.29431i | − | 0.0423286i | ||||||
\(936\) | 5.06719 | 0.165626 | ||||||||
\(937\) | −19.4848 | −0.636541 | −0.318270 | − | 0.948000i | \(-0.603102\pi\) | ||||
−0.318270 | + | 0.948000i | \(0.603102\pi\) | |||||||
\(938\) | 6.00520 | 0.196077 | ||||||||
\(939\) | 23.8722 | 0.779041 | ||||||||
\(940\) | − | 0.908504i | − | 0.0296321i | ||||||
\(941\) | 21.6860 | 0.706945 | 0.353472 | − | 0.935445i | \(-0.385001\pi\) | ||||
0.353472 | + | 0.935445i | \(0.385001\pi\) | |||||||
\(942\) | 11.8400i | 0.385768i | ||||||||
\(943\) | 16.0104 | 0.521371 | ||||||||
\(944\) | − | 6.04533i | − | 0.196759i | ||||||
\(945\) | 2.98972i | 0.0972557i | ||||||||
\(946\) | − | 14.1059i | − | 0.458621i | ||||||
\(947\) | −50.6863 | −1.64708 | −0.823541 | − | 0.567257i | \(-0.808005\pi\) | ||||
−0.823541 | + | 0.567257i | \(0.808005\pi\) | |||||||
\(948\) | 3.21828i | 0.104525i | ||||||||
\(949\) | 40.4243i | 1.31223i | ||||||||
\(950\) | − | 4.16280i | − | 0.135059i | ||||||
\(951\) | − | 63.0345i | − | 2.04403i | ||||||
\(952\) | −11.7012 | −0.379237 | ||||||||
\(953\) | −0.0601424 | −0.00194820 | −0.000974102 | − | 1.00000i | \(-0.500310\pi\) | ||||
−0.000974102 | 1.00000i | \(0.500310\pi\) | ||||||||
\(954\) | −3.18950 | −0.103264 | ||||||||
\(955\) | 0.626503 | 0.0202732 | ||||||||
\(956\) | 34.4074 | 1.11282 | ||||||||
\(957\) | 52.4762i | 1.69631i | ||||||||
\(958\) | 15.7175i | 0.507809i | ||||||||
\(959\) | 0.652884 | 0.0210827 | ||||||||
\(960\) | −0.826667 | −0.0266806 | ||||||||
\(961\) | −30.9108 | −0.997123 | ||||||||
\(962\) | −3.41714 | −0.110173 | ||||||||
\(963\) | − | 8.24962i | − | 0.265840i | ||||||
\(964\) | −31.7763 | −1.02344 | ||||||||
\(965\) | − | 4.67450i | − | 0.150477i | ||||||
\(966\) | −22.6231 | −0.727885 | ||||||||
\(967\) | 35.3304 | 1.13615 | 0.568074 | − | 0.822978i | \(-0.307689\pi\) | ||||
0.568074 | + | 0.822978i | \(0.307689\pi\) | |||||||
\(968\) | − | 5.21697i | − | 0.167680i | ||||||
\(969\) | −3.53413 | −0.113532 | ||||||||
\(970\) | 1.34071 | 0.0430477 | ||||||||
\(971\) | 4.65749 | 0.149466 | 0.0747329 | − | 0.997204i | \(-0.476190\pi\) | ||||
0.0747329 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(972\) | −10.4380 | −0.334799 | ||||||||
\(973\) | − | 48.9466i | − | 1.56916i | ||||||
\(974\) | 19.0724 | 0.611120 | ||||||||
\(975\) | 27.8221i | 0.891019i | ||||||||
\(976\) | 2.33106i | 0.0746155i | ||||||||
\(977\) | 42.8303 | 1.37026 | 0.685131 | − | 0.728420i | \(-0.259745\pi\) | ||||
0.685131 | + | 0.728420i | \(0.259745\pi\) | |||||||
\(978\) | 17.4371 | 0.557577 | ||||||||
\(979\) | 1.47129 | 0.0470228 | ||||||||
\(980\) | −0.602927 | −0.0192598 | ||||||||
\(981\) | 3.14471 | 0.100403 | ||||||||
\(982\) | 5.06631i | 0.161673i | ||||||||
\(983\) | 20.5074 | 0.654084 | 0.327042 | − | 0.945010i | \(-0.393948\pi\) | ||||
0.327042 | + | 0.945010i | \(0.393948\pi\) | |||||||
\(984\) | − | 13.9761i | − | 0.445543i | ||||||
\(985\) | 5.12075i | 0.163161i | ||||||||
\(986\) | − | 8.56107i | − | 0.272640i | ||||||
\(987\) | −15.3657 | −0.489095 | ||||||||
\(988\) | − | 5.06664i | − | 0.161191i | ||||||
\(989\) | − | 29.8832i | − | 0.950232i | ||||||
\(990\) | −0.408814 | −0.0129930 | ||||||||
\(991\) | 44.6137 | 1.41720 | 0.708600 | − | 0.705611i | \(-0.249327\pi\) | ||||
0.708600 | + | 0.705611i | \(0.249327\pi\) | |||||||
\(992\) | 1.74621i | 0.0554421i | ||||||||
\(993\) | − | 28.0941i | − | 0.891538i | ||||||
\(994\) | − | 13.5715i | − | 0.430461i | ||||||
\(995\) | 3.59354i | 0.113923i | ||||||||
\(996\) | 19.4402 | 0.615987 | ||||||||
\(997\) | − | 9.03393i | − | 0.286107i | −0.989715 | − | 0.143054i | \(-0.954308\pi\) | ||
0.989715 | − | 0.143054i | \(-0.0456922\pi\) | |||||||
\(998\) | 13.6123 | 0.430890 | ||||||||
\(999\) | 7.19450 | 0.227624 |
(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 | 349.2.b.b.348.14 | yes | 26 | |
349.348 | even | 2 | inner | 349.2.b.b.348.13 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.b.b.348.13 | ✓ | 26 | 349.348 | even | 2 | inner | |
349.2.b.b.348.14 | yes | 26 | 1.1 | even | 1 | trivial |