Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(20,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.20");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.o (of order \(6\), degree \(2\), 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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.9 | ||
Character | \(\chi\) | \(=\) | 63.41 |
Dual form | 63.4.o.a.20.9 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10556 | + | 0.638294i | −0.390874 | + | 0.225671i | −0.682539 | − | 0.730849i | \(-0.739124\pi\) |
0.291665 | + | 0.956521i | \(0.405791\pi\) | |||||||
\(3\) | −0.213646 | − | 5.19176i | −0.0411161 | − | 0.999154i | ||||
\(4\) | −3.18516 | + | 5.51686i | −0.398145 | + | 0.689607i | ||||
\(5\) | 1.59510 | − | 2.76280i | 0.142670 | − | 0.247112i | −0.785831 | − | 0.618441i | \(-0.787764\pi\) |
0.928501 | + | 0.371329i | \(0.121098\pi\) | |||||||
\(6\) | 3.55007 | + | 5.60342i | 0.241552 | + | 0.381265i | ||||
\(7\) | −13.1775 | − | 13.0136i | −0.711519 | − | 0.702667i | ||||
\(8\) | − | 18.3450i | − | 0.810742i | ||||||
\(9\) | −26.9087 | + | 2.21839i | −0.996619 | + | 0.0821627i | ||||
\(10\) | 4.07258i | 0.128786i | ||||||||
\(11\) | −38.0908 | + | 21.9917i | −1.04407 | + | 0.602795i | −0.920984 | − | 0.389600i | \(-0.872613\pi\) |
−0.123088 | + | 0.992396i | \(0.539280\pi\) | |||||||
\(12\) | 29.3227 | + | 15.3579i | 0.705394 | + | 0.369454i | ||||
\(13\) | −65.6143 | − | 37.8824i | −1.39986 | − | 0.808208i | −0.405480 | − | 0.914104i | \(-0.632895\pi\) |
−0.994377 | + | 0.105896i | \(0.966229\pi\) | |||||||
\(14\) | 22.8750 | + | 5.97614i | 0.436686 | + | 0.114085i | ||||
\(15\) | −14.6846 | − | 7.69113i | −0.252769 | − | 0.132389i | ||||
\(16\) | −13.7718 | − | 23.8534i | −0.215184 | − | 0.372710i | ||||
\(17\) | 104.977 | 1.49769 | 0.748843 | − | 0.662748i | \(-0.230610\pi\) | ||||
0.748843 | + | 0.662748i | \(0.230610\pi\) | |||||||
\(18\) | 28.3332 | − | 19.6282i | 0.371011 | − | 0.257023i | ||||
\(19\) | − | 74.7068i | − | 0.902048i | −0.892512 | − | 0.451024i | \(-0.851059\pi\) | ||
0.892512 | − | 0.451024i | \(-0.148941\pi\) | |||||||
\(20\) | 10.1613 | + | 17.5999i | 0.113607 | + | 0.196773i | ||||
\(21\) | −64.7481 | + | 71.1947i | −0.672818 | + | 0.739808i | ||||
\(22\) | 28.0744 | − | 48.6262i | 0.272067 | − | 0.471234i | ||||
\(23\) | 46.6533 | + | 26.9353i | 0.422952 | + | 0.244191i | 0.696339 | − | 0.717713i | \(-0.254811\pi\) |
−0.273388 | + | 0.961904i | \(0.588144\pi\) | |||||||
\(24\) | −95.2428 | + | 3.91933i | −0.810056 | + | 0.0333346i | ||||
\(25\) | 57.4113 | + | 99.4393i | 0.459290 | + | 0.795514i | ||||
\(26\) | 96.7206 | 0.729557 | ||||||||
\(27\) | 17.2663 | + | 139.230i | 0.123070 | + | 0.992398i | ||||
\(28\) | 113.767 | − | 31.2481i | 0.767852 | − | 0.210905i | ||||
\(29\) | −26.3321 | + | 15.2028i | −0.168612 | + | 0.0973481i | −0.581931 | − | 0.813238i | \(-0.697703\pi\) |
0.413319 | + | 0.910586i | \(0.364369\pi\) | |||||||
\(30\) | 21.1439 | − | 0.870089i | 0.128677 | − | 0.00529519i | ||||
\(31\) | −111.231 | − | 64.2193i | −0.644441 | − | 0.372068i | 0.141882 | − | 0.989884i | \(-0.454685\pi\) |
−0.786323 | + | 0.617815i | \(0.788018\pi\) | |||||||
\(32\) | 157.549 | + | 90.9609i | 0.870343 | + | 0.502493i | ||||
\(33\) | 122.314 | + | 193.060i | 0.645214 | + | 1.01840i | ||||
\(34\) | −116.058 | + | 67.0062i | −0.585406 | + | 0.337984i | ||||
\(35\) | −56.9734 | + | 15.6488i | −0.275150 | + | 0.0755751i | ||||
\(36\) | 73.4700 | − | 155.518i | 0.340139 | − | 0.719989i | ||||
\(37\) | 46.1138 | 0.204894 | 0.102447 | − | 0.994738i | \(-0.467333\pi\) | ||||
0.102447 | + | 0.994738i | \(0.467333\pi\) | |||||||
\(38\) | 47.6849 | + | 82.5928i | 0.203566 | + | 0.352587i | ||||
\(39\) | −182.658 | + | 348.747i | −0.749968 | + | 1.43190i | ||||
\(40\) | −50.6835 | − | 29.2621i | −0.200344 | − | 0.115669i | ||||
\(41\) | 213.104 | − | 369.107i | 0.811738 | − | 1.40597i | −0.0999082 | − | 0.994997i | \(-0.531855\pi\) |
0.911647 | − | 0.410975i | \(-0.134812\pi\) | |||||||
\(42\) | 26.1396 | − | 120.038i | 0.0960338 | − | 0.441007i | ||||
\(43\) | −166.003 | − | 287.526i | −0.588728 | − | 1.01971i | −0.994399 | − | 0.105687i | \(-0.966296\pi\) |
0.405672 | − | 0.914019i | \(-0.367038\pi\) | |||||||
\(44\) | − | 280.188i | − | 0.960000i | ||||||
\(45\) | −36.7932 | + | 77.8819i | −0.121884 | + | 0.257999i | ||||
\(46\) | −68.7706 | −0.220428 | ||||||||
\(47\) | −170.147 | − | 294.704i | −0.528054 | − | 0.914616i | −0.999465 | − | 0.0327026i | \(-0.989589\pi\) |
0.471411 | − | 0.881913i | \(-0.343745\pi\) | |||||||
\(48\) | −120.899 | + | 76.5959i | −0.363547 | + | 0.230326i | ||||
\(49\) | 4.29341 | + | 342.973i | 0.0125172 | + | 0.999922i | ||||
\(50\) | −126.943 | − | 73.2906i | −0.359049 | − | 0.207297i | ||||
\(51\) | −22.4279 | − | 545.015i | −0.0615790 | − | 1.49642i | ||||
\(52\) | 417.984 | − | 241.323i | 1.11469 | − | 0.643568i | ||||
\(53\) | 235.233i | 0.609654i | 0.952408 | + | 0.304827i | \(0.0985987\pi\) | ||||
−0.952408 | + | 0.304827i | \(0.901401\pi\) | |||||||
\(54\) | −107.958 | − | 142.905i | −0.272061 | − | 0.360129i | ||||
\(55\) | 140.316i | 0.344004i | ||||||||
\(56\) | −238.734 | + | 241.741i | −0.569682 | + | 0.576858i | ||||
\(57\) | −387.860 | + | 15.9608i | −0.901286 | + | 0.0370887i | ||||
\(58\) | 19.4078 | − | 33.6152i | 0.0439373 | − | 0.0761017i | ||||
\(59\) | −272.093 | + | 471.279i | −0.600398 | + | 1.03992i | 0.392363 | + | 0.919811i | \(0.371658\pi\) |
−0.992761 | + | 0.120109i | \(0.961676\pi\) | |||||||
\(60\) | 89.2036 | − | 56.5152i | 0.191936 | − | 0.121601i | ||||
\(61\) | −321.478 | + | 185.606i | −0.674772 | + | 0.389580i | −0.797882 | − | 0.602813i | \(-0.794046\pi\) |
0.123110 | + | 0.992393i | \(0.460713\pi\) | |||||||
\(62\) | 163.963 | 0.335861 | ||||||||
\(63\) | 383.459 | + | 320.946i | 0.766846 | + | 0.641831i | ||||
\(64\) | −11.8909 | −0.0232244 | ||||||||
\(65\) | −209.323 | + | 120.853i | −0.399436 | + | 0.230614i | ||||
\(66\) | −258.454 | − | 135.367i | −0.482022 | − | 0.252462i | ||||
\(67\) | −53.3481 | + | 92.4017i | −0.0972763 | + | 0.168487i | −0.910556 | − | 0.413385i | \(-0.864346\pi\) |
0.813280 | + | 0.581872i | \(0.197680\pi\) | |||||||
\(68\) | −334.368 | + | 579.143i | −0.596296 | + | 1.03282i | ||||
\(69\) | 129.874 | − | 247.967i | 0.226595 | − | 0.432634i | ||||
\(70\) | 52.9988 | − | 53.6665i | 0.0904939 | − | 0.0916338i | ||||
\(71\) | − | 974.682i | − | 1.62920i | −0.580020 | − | 0.814602i | \(-0.696955\pi\) | ||
0.580020 | − | 0.814602i | \(-0.303045\pi\) | |||||||
\(72\) | 40.6964 | + | 493.640i | 0.0666128 | + | 0.808001i | ||||
\(73\) | − | 576.299i | − | 0.923982i | −0.886885 | − | 0.461991i | \(-0.847135\pi\) | ||
0.886885 | − | 0.461991i | \(-0.152865\pi\) | |||||||
\(74\) | −50.9815 | + | 29.4342i | −0.0800876 | + | 0.0462386i | ||||
\(75\) | 503.999 | − | 319.310i | 0.775957 | − | 0.491610i | ||||
\(76\) | 412.147 | + | 237.953i | 0.622059 | + | 0.359146i | ||||
\(77\) | 788.132 | + | 205.901i | 1.16644 | + | 0.304735i | ||||
\(78\) | −20.6639 | − | 502.150i | −0.0299965 | − | 0.728940i | ||||
\(79\) | −10.6691 | − | 18.4794i | −0.0151945 | − | 0.0263176i | 0.858328 | − | 0.513101i | \(-0.171503\pi\) |
−0.873523 | + | 0.486783i | \(0.838170\pi\) | |||||||
\(80\) | −87.8696 | −0.122801 | ||||||||
\(81\) | 719.157 | − | 119.388i | 0.986499 | − | 0.163770i | ||||
\(82\) | 544.093i | 0.732744i | ||||||||
\(83\) | −168.669 | − | 292.143i | −0.223058 | − | 0.386348i | 0.732677 | − | 0.680576i | \(-0.238271\pi\) |
−0.955735 | + | 0.294229i | \(0.904937\pi\) | |||||||
\(84\) | −186.538 | − | 583.973i | −0.242298 | − | 0.758531i | ||||
\(85\) | 167.449 | − | 290.030i | 0.213675 | − | 0.370096i | ||||
\(86\) | 367.053 | + | 211.918i | 0.460237 | + | 0.265718i | ||||
\(87\) | 84.5552 | + | 133.462i | 0.104198 | + | 0.164467i | ||||
\(88\) | 403.438 | + | 698.775i | 0.488711 | + | 0.846473i | ||||
\(89\) | −1024.06 | −1.21967 | −0.609834 | − | 0.792529i | \(-0.708764\pi\) | ||||
−0.609834 | + | 0.792529i | \(0.708764\pi\) | |||||||
\(90\) | −9.03458 | − | 109.588i | −0.0105814 | − | 0.128351i | ||||
\(91\) | 371.647 | + | 1353.07i | 0.428123 | + | 1.55869i | ||||
\(92\) | −297.197 | + | 171.586i | −0.336792 | + | 0.194447i | ||||
\(93\) | −309.647 | + | 591.205i | −0.345257 | + | 0.659195i | ||||
\(94\) | 376.216 | + | 217.208i | 0.412805 | + | 0.238333i | ||||
\(95\) | −206.400 | − | 119.165i | −0.222907 | − | 0.128695i | ||||
\(96\) | 438.587 | − | 837.389i | 0.466283 | − | 0.890267i | ||||
\(97\) | 63.5527 | − | 36.6922i | 0.0665237 | − | 0.0384075i | −0.466369 | − | 0.884590i | \(-0.654438\pi\) |
0.532893 | + | 0.846183i | \(0.321105\pi\) | |||||||
\(98\) | −223.664 | − | 376.436i | −0.230546 | − | 0.388019i | ||||
\(99\) | 976.187 | − | 676.269i | 0.991015 | − | 0.686541i | ||||
\(100\) | −731.457 | −0.731457 | ||||||||
\(101\) | 442.380 | + | 766.224i | 0.435826 | + | 0.754873i | 0.997363 | − | 0.0725790i | \(-0.0231229\pi\) |
−0.561537 | + | 0.827452i | \(0.689790\pi\) | |||||||
\(102\) | 372.675 | + | 588.230i | 0.361768 | + | 0.571015i | ||||
\(103\) | −38.7086 | − | 22.3484i | −0.0370299 | − | 0.0213792i | 0.481371 | − | 0.876517i | \(-0.340139\pi\) |
−0.518401 | + | 0.855138i | \(0.673472\pi\) | |||||||
\(104\) | −694.953 | + | 1203.69i | −0.655248 | + | 1.13492i | ||||
\(105\) | 93.4169 | + | 292.449i | 0.0868243 | + | 0.271810i | ||||
\(106\) | −150.148 | − | 260.063i | −0.137581 | − | 0.238298i | ||||
\(107\) | − | 517.187i | − | 0.467274i | −0.972324 | − | 0.233637i | \(-0.924937\pi\) | ||
0.972324 | − | 0.233637i | \(-0.0750628\pi\) | |||||||
\(108\) | −823.106 | − | 348.213i | −0.733365 | − | 0.310248i | ||||
\(109\) | −39.6511 | −0.0348430 | −0.0174215 | − | 0.999848i | \(-0.505546\pi\) | ||||
−0.0174215 | + | 0.999848i | \(0.505546\pi\) | |||||||
\(110\) | −89.5630 | − | 155.128i | −0.0776318 | − | 0.134462i | ||||
\(111\) | −9.85202 | − | 239.412i | −0.00842443 | − | 0.204720i | ||||
\(112\) | −128.941 | + | 493.549i | −0.108783 | + | 0.416393i | ||||
\(113\) | 627.942 | + | 362.542i | 0.522759 | + | 0.301815i | 0.738063 | − | 0.674732i | \(-0.235741\pi\) |
−0.215304 | + | 0.976547i | \(0.569074\pi\) | |||||||
\(114\) | 418.614 | − | 265.214i | 0.343919 | − | 0.217891i | ||||
\(115\) | 148.834 | − | 85.9291i | 0.120685 | − | 0.0696777i | ||||
\(116\) | − | 193.694i | − | 0.155035i | ||||||
\(117\) | 1849.63 | + | 873.809i | 1.46153 | + | 0.690459i | ||||
\(118\) | − | 694.701i | − | 0.541970i | ||||||
\(119\) | −1383.33 | − | 1366.13i | −1.06563 | − | 1.05237i | ||||
\(120\) | −141.094 | + | 269.388i | −0.107334 | + | 0.204931i | ||||
\(121\) | 301.771 | − | 522.682i | 0.226725 | − | 0.392699i | ||||
\(122\) | 236.942 | − | 410.396i | 0.175834 | − | 0.304553i | ||||
\(123\) | −1961.84 | − | 1027.53i | −1.43816 | − | 0.753244i | ||||
\(124\) | 708.577 | − | 409.097i | 0.513162 | − | 0.296274i | ||||
\(125\) | 765.083 | 0.547449 | ||||||||
\(126\) | −628.794 | − | 110.065i | −0.444583 | − | 0.0778201i | ||||
\(127\) | −567.501 | −0.396516 | −0.198258 | − | 0.980150i | \(-0.563528\pi\) | ||||
−0.198258 | + | 0.980150i | \(0.563528\pi\) | |||||||
\(128\) | −1247.24 | + | 720.097i | −0.861265 | + | 0.497251i | ||||
\(129\) | −1457.30 | + | 923.279i | −0.994638 | + | 0.630156i | ||||
\(130\) | 154.279 | − | 267.220i | 0.104086 | − | 0.180282i | ||||
\(131\) | 603.074 | − | 1044.55i | 0.402220 | − | 0.696665i | −0.591774 | − | 0.806104i | \(-0.701572\pi\) |
0.993994 | + | 0.109439i | \(0.0349055\pi\) | |||||||
\(132\) | −1454.67 | + | 59.8611i | −0.959188 | + | 0.0394715i | ||||
\(133\) | −972.203 | + | 984.450i | −0.633840 | + | 0.641824i | ||||
\(134\) | − | 136.207i | − | 0.0878098i | ||||||
\(135\) | 412.205 | + | 174.382i | 0.262792 | + | 0.111174i | ||||
\(136\) | − | 1925.80i | − | 1.21424i | ||||||
\(137\) | 522.414 | − | 301.616i | 0.325787 | − | 0.188093i | −0.328182 | − | 0.944615i | \(-0.606436\pi\) |
0.653969 | + | 0.756521i | \(0.273103\pi\) | |||||||
\(138\) | 14.6925 | + | 357.040i | 0.00906313 | + | 0.220241i | ||||
\(139\) | 298.587 | + | 172.389i | 0.182200 | + | 0.105193i | 0.588326 | − | 0.808624i | \(-0.299787\pi\) |
−0.406126 | + | 0.913817i | \(0.633121\pi\) | |||||||
\(140\) | 95.1371 | − | 364.158i | 0.0574325 | − | 0.219835i | ||||
\(141\) | −1493.68 | + | 946.326i | −0.892131 | + | 0.565213i | ||||
\(142\) | 622.134 | + | 1077.57i | 0.367665 | + | 0.636814i | ||||
\(143\) | 3332.40 | 1.94874 | ||||||||
\(144\) | 423.497 | + | 611.313i | 0.245079 | + | 0.353769i | ||||
\(145\) | 97.0003i | 0.0555547i | ||||||||
\(146\) | 367.848 | + | 637.132i | 0.208516 | + | 0.361160i | ||||
\(147\) | 1779.72 | − | 95.5651i | 0.998561 | − | 0.0536195i | ||||
\(148\) | −146.880 | + | 254.403i | −0.0815774 | + | 0.141296i | ||||
\(149\) | 197.969 | + | 114.298i | 0.108847 | + | 0.0628431i | 0.553435 | − | 0.832892i | \(-0.313317\pi\) |
−0.444588 | + | 0.895735i | \(0.646650\pi\) | |||||||
\(150\) | −353.386 | + | 674.716i | −0.192359 | + | 0.367269i | ||||
\(151\) | −1697.35 | − | 2939.90i | −0.914758 | − | 1.58441i | −0.807256 | − | 0.590202i | \(-0.799048\pi\) |
−0.107502 | − | 0.994205i | \(-0.534285\pi\) | |||||||
\(152\) | −1370.50 | −0.731328 | ||||||||
\(153\) | −2824.79 | + | 232.880i | −1.49262 | + | 0.123054i | ||||
\(154\) | −1002.75 | + | 275.425i | −0.524702 | + | 0.144119i | ||||
\(155\) | −354.850 | + | 204.873i | −0.183885 | + | 0.106166i | ||||
\(156\) | −1342.19 | − | 2118.52i | −0.688855 | − | 1.08729i | ||||
\(157\) | −2829.60 | − | 1633.67i | −1.43838 | − | 0.830452i | −0.440647 | − | 0.897680i | \(-0.645251\pi\) |
−0.997738 | + | 0.0672287i | \(0.978584\pi\) | |||||||
\(158\) | 23.5905 | + | 13.6200i | 0.0118782 | + | 0.00685791i | ||||
\(159\) | 1221.27 | − | 50.2564i | 0.609139 | − | 0.0250666i | ||||
\(160\) | 502.613 | − | 290.184i | 0.248344 | − | 0.143382i | ||||
\(161\) | −264.250 | − | 962.067i | −0.129353 | − | 0.470941i | ||||
\(162\) | −718.866 | + | 591.025i | −0.348638 | + | 0.286638i | ||||
\(163\) | 689.462 | 0.331306 | 0.165653 | − | 0.986184i | \(-0.447027\pi\) | ||||
0.165653 | + | 0.986184i | \(0.447027\pi\) | |||||||
\(164\) | 1357.54 | + | 2351.33i | 0.646379 | + | 1.11956i | ||||
\(165\) | 728.487 | − | 29.9779i | 0.343713 | − | 0.0141441i | ||||
\(166\) | 372.946 | + | 215.321i | 0.174375 | + | 0.100675i | ||||
\(167\) | 683.829 | − | 1184.43i | 0.316864 | − | 0.548824i | −0.662968 | − | 0.748648i | \(-0.730703\pi\) |
0.979832 | + | 0.199823i | \(0.0640368\pi\) | |||||||
\(168\) | 1306.07 | + | 1187.80i | 0.599793 | + | 0.545482i | ||||
\(169\) | 1771.66 | + | 3068.60i | 0.806399 | + | 1.39672i | ||||
\(170\) | 427.527i | 0.192881i | ||||||||
\(171\) | 165.729 | + | 2010.26i | 0.0741147 | + | 0.898998i | ||||
\(172\) | 2114.99 | 0.937596 | ||||||||
\(173\) | −613.500 | − | 1062.61i | −0.269616 | − | 0.466988i | 0.699147 | − | 0.714978i | \(-0.253563\pi\) |
−0.968763 | + | 0.247990i | \(0.920230\pi\) | |||||||
\(174\) | −178.669 | − | 93.5787i | −0.0778438 | − | 0.0407712i | ||||
\(175\) | 537.523 | − | 2057.49i | 0.232188 | − | 0.888751i | ||||
\(176\) | 1049.15 | + | 605.730i | 0.449335 | + | 0.259424i | ||||
\(177\) | 2504.90 | + | 1311.95i | 1.06373 | + | 0.557133i | ||||
\(178\) | 1132.16 | − | 653.654i | 0.476737 | − | 0.275244i | ||||
\(179\) | 1597.37i | 0.667002i | 0.942750 | + | 0.333501i | \(0.108230\pi\) | ||||
−0.942750 | + | 0.333501i | \(0.891770\pi\) | |||||||
\(180\) | −312.471 | − | 451.049i | −0.129390 | − | 0.186773i | ||||
\(181\) | − | 549.998i | − | 0.225862i | −0.993603 | − | 0.112931i | \(-0.963976\pi\) | ||
0.993603 | − | 0.112931i | \(-0.0360239\pi\) | |||||||
\(182\) | −1274.54 | − | 1258.68i | −0.519093 | − | 0.512636i | ||||
\(183\) | 1032.30 | + | 1629.38i | 0.416994 | + | 0.658183i | ||||
\(184\) | 494.128 | − | 855.855i | 0.197976 | − | 0.342905i | ||||
\(185\) | 73.5562 | − | 127.403i | 0.0292322 | − | 0.0506317i | ||||
\(186\) | −35.0300 | − | 851.258i | −0.0138093 | − | 0.335577i | ||||
\(187\) | −3998.65 | + | 2308.62i | −1.56369 | + | 0.902798i | ||||
\(188\) | 2167.79 | 0.840968 | ||||||||
\(189\) | 1584.35 | − | 2059.40i | 0.609759 | − | 0.792587i | ||||
\(190\) | 304.249 | 0.116171 | ||||||||
\(191\) | 3253.62 | − | 1878.48i | 1.23258 | − | 0.711633i | 0.265017 | − | 0.964244i | \(-0.414622\pi\) |
0.967568 | + | 0.252611i | \(0.0812891\pi\) | |||||||
\(192\) | 2.54044 | + | 61.7346i | 0.000954897 | + | 0.0232047i | ||||
\(193\) | −1311.43 | + | 2271.46i | −0.489111 | + | 0.847165i | −0.999922 | − | 0.0125280i | \(-0.996012\pi\) |
0.510810 | + | 0.859693i | \(0.329345\pi\) | |||||||
\(194\) | −46.8408 | + | 81.1307i | −0.0173349 | + | 0.0300250i | ||||
\(195\) | 672.159 | + | 1060.94i | 0.246843 | + | 0.389616i | ||||
\(196\) | −1905.81 | − | 1068.74i | −0.694537 | − | 0.389482i | ||||
\(197\) | 4603.93i | 1.66506i | 0.553982 | + | 0.832528i | \(0.313107\pi\) | ||||
−0.553982 | + | 0.832528i | \(0.686893\pi\) | |||||||
\(198\) | −647.573 | + | 1370.75i | −0.232429 | + | 0.491995i | ||||
\(199\) | − | 3145.00i | − | 1.12032i | −0.828385 | − | 0.560158i | \(-0.810740\pi\) | ||
0.828385 | − | 0.560158i | \(-0.189260\pi\) | |||||||
\(200\) | 1824.21 | − | 1053.21i | 0.644957 | − | 0.372366i | ||||
\(201\) | 491.125 | + | 257.229i | 0.172345 | + | 0.0902665i | ||||
\(202\) | −978.154 | − | 564.737i | −0.340706 | − | 0.196707i | ||||
\(203\) | 544.834 | + | 142.339i | 0.188374 | + | 0.0492131i | ||||
\(204\) | 3078.21 | + | 1612.23i | 1.05646 | + | 0.553326i | ||||
\(205\) | −679.846 | − | 1177.53i | −0.231622 | − | 0.401181i | ||||
\(206\) | 57.0596 | 0.0192987 | ||||||||
\(207\) | −1315.13 | − | 621.299i | −0.441585 | − | 0.208615i | ||||
\(208\) | 2086.83i | 0.695653i | ||||||||
\(209\) | 1642.93 | + | 2845.64i | 0.543751 | + | 0.941804i | ||||
\(210\) | −289.946 | − | 263.692i | −0.0952771 | − | 0.0866498i | ||||
\(211\) | 341.927 | − | 592.236i | 0.111560 | − | 0.193228i | −0.804839 | − | 0.593493i | \(-0.797748\pi\) |
0.916400 | + | 0.400265i | \(0.131082\pi\) | |||||||
\(212\) | −1297.74 | − | 749.253i | −0.420422 | − | 0.242731i | ||||
\(213\) | −5060.32 | + | 208.237i | −1.62783 | + | 0.0669866i | ||||
\(214\) | 330.118 | + | 571.780i | 0.105450 | + | 0.182645i | ||||
\(215\) | −1059.17 | −0.335976 | ||||||||
\(216\) | 2554.17 | − | 316.750i | 0.804578 | − | 0.0997783i | ||||
\(217\) | 630.025 | + | 2293.76i | 0.197092 | + | 0.717562i | ||||
\(218\) | 43.8366 | − | 25.3091i | 0.0136192 | − | 0.00786307i | ||||
\(219\) | −2992.00 | + | 123.124i | −0.923200 | + | 0.0379906i | ||||
\(220\) | −774.104 | − | 446.929i | −0.237228 | − | 0.136963i | ||||
\(221\) | −6887.99 | − | 3976.78i | −2.09655 | − | 1.21044i | ||||
\(222\) | 163.707 | + | 258.395i | 0.0494924 | + | 0.0781187i | ||||
\(223\) | 2030.24 | − | 1172.16i | 0.609664 | − | 0.351990i | −0.163170 | − | 0.986598i | \(-0.552172\pi\) |
0.772834 | + | 0.634608i | \(0.218839\pi\) | |||||||
\(224\) | −892.374 | − | 3248.91i | −0.266180 | − | 0.969094i | ||||
\(225\) | −1765.46 | − | 2548.42i | −0.523099 | − | 0.755088i | ||||
\(226\) | −925.635 | −0.272444 | ||||||||
\(227\) | 1536.15 | + | 2660.69i | 0.449154 | + | 0.777958i | 0.998331 | − | 0.0577480i | \(-0.0183920\pi\) |
−0.549177 | + | 0.835706i | \(0.685059\pi\) | |||||||
\(228\) | 1147.34 | − | 2190.61i | 0.333266 | − | 0.636300i | ||||
\(229\) | 1213.76 | + | 700.766i | 0.350252 | + | 0.202218i | 0.664796 | − | 0.747025i | \(-0.268518\pi\) |
−0.314544 | + | 0.949243i | \(0.601852\pi\) | |||||||
\(230\) | −109.696 | + | 189.999i | −0.0314485 | + | 0.0544704i | ||||
\(231\) | 900.609 | − | 4135.78i | 0.256518 | − | 1.17798i | ||||
\(232\) | 278.896 | + | 483.062i | 0.0789242 | + | 0.136701i | ||||
\(233\) | 5201.59i | 1.46252i | 0.682098 | + | 0.731261i | \(0.261068\pi\) | ||||
−0.682098 | + | 0.731261i | \(0.738932\pi\) | |||||||
\(234\) | −2602.63 | + | 214.564i | −0.727090 | + | 0.0599424i | ||||
\(235\) | −1085.61 | −0.301350 | ||||||||
\(236\) | −1733.32 | − | 3002.20i | −0.478091 | − | 0.828078i | ||||
\(237\) | −93.6609 | + | 59.3392i | −0.0256706 | + | 0.0162637i | ||||
\(238\) | 2401.35 | + | 627.358i | 0.654018 | + | 0.170864i | ||||
\(239\) | −1811.86 | − | 1046.08i | −0.490373 | − | 0.283117i | 0.234356 | − | 0.972151i | \(-0.424702\pi\) |
−0.724729 | + | 0.689034i | \(0.758035\pi\) | |||||||
\(240\) | 18.7730 | + | 456.198i | 0.00504912 | + | 0.122698i | ||||
\(241\) | 6077.25 | − | 3508.70i | 1.62436 | − | 0.937823i | 0.638622 | − | 0.769520i | \(-0.279505\pi\) |
0.985735 | − | 0.168303i | \(-0.0538287\pi\) | |||||||
\(242\) | 770.474i | 0.204661i | ||||||||
\(243\) | −773.480 | − | 3708.19i | −0.204192 | − | 0.978931i | ||||
\(244\) | − | 2364.73i | − | 0.620437i | ||||||
\(245\) | 954.414 | + | 535.215i | 0.248879 | + | 0.139566i | ||||
\(246\) | 2824.80 | − | 116.243i | 0.732124 | − | 0.0301276i | ||||
\(247\) | −2830.08 | + | 4901.84i | −0.729042 | + | 1.26274i | ||||
\(248\) | −1178.10 | + | 2040.53i | −0.301651 | + | 0.522476i | ||||
\(249\) | −1480.70 | + | 938.103i | −0.376850 | + | 0.238754i | ||||
\(250\) | −845.844 | + | 488.348i | −0.213984 | + | 0.123543i | ||||
\(251\) | −7255.60 | −1.82458 | −0.912290 | − | 0.409545i | \(-0.865687\pi\) | ||||
−0.912290 | + | 0.409545i | \(0.865687\pi\) | |||||||
\(252\) | −2991.99 | + | 1093.23i | −0.747928 | + | 0.273281i | ||||
\(253\) | −2369.41 | −0.588789 | ||||||||
\(254\) | 627.406 | − | 362.233i | 0.154988 | − | 0.0894823i | ||||
\(255\) | −1541.54 | − | 807.391i | −0.378569 | − | 0.198278i | ||||
\(256\) | 966.831 | − | 1674.60i | 0.236043 | − | 0.408838i | ||||
\(257\) | 505.462 | − | 875.487i | 0.122684 | − | 0.212496i | −0.798141 | − | 0.602471i | \(-0.794183\pi\) |
0.920825 | + | 0.389975i | \(0.127516\pi\) | |||||||
\(258\) | 1021.81 | − | 1950.93i | 0.246570 | − | 0.470773i | ||||
\(259\) | −607.665 | − | 600.106i | −0.145786 | − | 0.143972i | ||||
\(260\) | − | 1539.74i | − | 0.367272i | ||||||
\(261\) | 674.836 | − | 467.503i | 0.160043 | − | 0.110873i | ||||
\(262\) | 1539.75i | 0.363078i | ||||||||
\(263\) | 2754.95 | − | 1590.57i | 0.645921 | − | 0.372923i | −0.140971 | − | 0.990014i | \(-0.545022\pi\) |
0.786892 | + | 0.617091i | \(0.211689\pi\) | |||||||
\(264\) | 3541.68 | − | 2243.84i | 0.825663 | − | 0.523102i | ||||
\(265\) | 649.900 | + | 375.220i | 0.150653 | + | 0.0869795i | ||||
\(266\) | 446.459 | − | 1708.92i | 0.102910 | − | 0.393912i | ||||
\(267\) | 218.787 | + | 5316.69i | 0.0501480 | + | 1.21864i | ||||
\(268\) | −339.845 | − | 588.628i | −0.0774601 | − | 0.134165i | ||||
\(269\) | 1227.12 | 0.278137 | 0.139069 | − | 0.990283i | \(-0.455589\pi\) | ||||
0.139069 | + | 0.990283i | \(0.455589\pi\) | |||||||
\(270\) | −567.024 | + | 70.3184i | −0.127807 | + | 0.0158498i | ||||
\(271\) | 7222.65i | 1.61898i | 0.587131 | + | 0.809492i | \(0.300257\pi\) | ||||
−0.587131 | + | 0.809492i | \(0.699743\pi\) | |||||||
\(272\) | −1445.72 | − | 2504.06i | −0.322278 | − | 0.558202i | ||||
\(273\) | 6945.43 | − | 2218.58i | 1.53977 | − | 0.491848i | ||||
\(274\) | −385.039 | + | 666.908i | −0.0848945 | + | 0.147042i | ||||
\(275\) | −4373.68 | − | 2525.15i | −0.959065 | − | 0.553716i | ||||
\(276\) | 954.330 | + | 1506.31i | 0.208130 | + | 0.328512i | ||||
\(277\) | −1132.04 | − | 1960.75i | −0.245551 | − | 0.425306i | 0.716736 | − | 0.697345i | \(-0.245635\pi\) |
−0.962286 | + | 0.272039i | \(0.912302\pi\) | |||||||
\(278\) | −440.141 | −0.0949564 | ||||||||
\(279\) | 3135.55 | + | 1481.30i | 0.672833 | + | 0.317861i | ||||
\(280\) | 287.077 | + | 1045.18i | 0.0612719 | + | 0.223076i | ||||
\(281\) | 859.806 | − | 496.409i | 0.182533 | − | 0.105385i | −0.405949 | − | 0.913896i | \(-0.633059\pi\) |
0.588482 | + | 0.808510i | \(0.299726\pi\) | |||||||
\(282\) | 1047.32 | − | 1999.63i | 0.221159 | − | 0.422255i | ||||
\(283\) | 4936.03 | + | 2849.82i | 1.03681 | + | 0.598601i | 0.918927 | − | 0.394427i | \(-0.129057\pi\) |
0.117880 | + | 0.993028i | \(0.462390\pi\) | |||||||
\(284\) | 5377.19 | + | 3104.52i | 1.12351 | + | 0.648660i | ||||
\(285\) | −574.580 | + | 1097.04i | −0.119422 | + | 0.228010i | ||||
\(286\) | −3684.16 | + | 2127.05i | −0.761710 | + | 0.439773i | ||||
\(287\) | −7611.59 | + | 2090.66i | −1.56550 | + | 0.429993i | ||||
\(288\) | −4441.22 | − | 2098.13i | −0.908686 | − | 0.429284i | ||||
\(289\) | 6107.16 | 1.24306 | ||||||||
\(290\) | −61.9147 | − | 107.239i | −0.0125371 | − | 0.0217149i | ||||
\(291\) | −204.075 | − | 322.111i | −0.0411102 | − | 0.0648883i | ||||
\(292\) | 3179.36 | + | 1835.60i | 0.637185 | + | 0.367879i | ||||
\(293\) | −1110.55 | + | 1923.52i | −0.221429 | + | 0.383527i | −0.955242 | − | 0.295825i | \(-0.904406\pi\) |
0.733813 | + | 0.679352i | \(0.237739\pi\) | |||||||
\(294\) | −1906.58 | + | 1241.64i | −0.378211 | + | 0.246305i | ||||
\(295\) | 868.032 | + | 1503.48i | 0.171318 | + | 0.296731i | ||||
\(296\) | − | 845.958i | − | 0.166116i | ||||||
\(297\) | −3719.58 | − | 4923.65i | −0.726707 | − | 0.961949i | ||||
\(298\) | −291.822 | −0.0567275 | ||||||||
\(299\) | −2040.75 | − | 3534.68i | −0.394714 | − | 0.683665i | ||||
\(300\) | 156.273 | + | 3797.55i | 0.0300747 | + | 0.730838i | ||||
\(301\) | −1554.24 | + | 5949.18i | −0.297624 | + | 1.13922i | ||||
\(302\) | 3753.04 | + | 2166.82i | 0.715110 | + | 0.412869i | ||||
\(303\) | 3883.54 | − | 2460.43i | 0.736315 | − | 0.466495i | ||||
\(304\) | −1782.01 | + | 1028.85i | −0.336202 | + | 0.194106i | ||||
\(305\) | 1184.24i | 0.222326i | ||||||||
\(306\) | 2974.33 | − | 2060.51i | 0.555657 | − | 0.384940i | ||||
\(307\) | 3006.91i | 0.559002i | 0.960145 | + | 0.279501i | \(0.0901690\pi\) | ||||
−0.960145 | + | 0.279501i | \(0.909831\pi\) | |||||||
\(308\) | −3646.26 | + | 3692.19i | −0.674561 | + | 0.683058i | ||||
\(309\) | −107.758 | + | 205.741i | −0.0198386 | + | 0.0378776i | ||||
\(310\) | 261.538 | − | 452.997i | 0.0479173 | − | 0.0829952i | ||||
\(311\) | −1269.29 | + | 2198.47i | −0.231430 | + | 0.400848i | −0.958229 | − | 0.286002i | \(-0.907674\pi\) |
0.726799 | + | 0.686850i | \(0.241007\pi\) | |||||||
\(312\) | 6397.76 | + | 3350.86i | 1.16090 | + | 0.608030i | ||||
\(313\) | 4916.75 | − | 2838.69i | 0.887895 | − | 0.512627i | 0.0146418 | − | 0.999893i | \(-0.495339\pi\) |
0.873253 | + | 0.487266i | \(0.162006\pi\) | |||||||
\(314\) | 4171.05 | 0.749636 | ||||||||
\(315\) | 1498.36 | − | 547.478i | 0.268010 | − | 0.0979267i | ||||
\(316\) | 135.931 | 0.0241984 | ||||||||
\(317\) | 6662.61 | − | 3846.66i | 1.18047 | − | 0.681545i | 0.224347 | − | 0.974509i | \(-0.427975\pi\) |
0.956123 | + | 0.292964i | \(0.0946416\pi\) | |||||||
\(318\) | −1318.11 | + | 835.092i | −0.232440 | + | 0.147263i | ||||
\(319\) | 668.672 | − | 1158.17i | 0.117362 | − | 0.203277i | ||||
\(320\) | −18.9672 | + | 32.8521i | −0.00331343 | + | 0.00573903i | ||||
\(321\) | −2685.11 | + | 110.495i | −0.466879 | + | 0.0192125i | ||||
\(322\) | 906.225 | + | 894.952i | 0.156838 | + | 0.154887i | ||||
\(323\) | − | 7842.50i | − | 1.35098i | ||||||
\(324\) | −1631.98 | + | 4347.76i | −0.279833 | + | 0.745501i | ||||
\(325\) | − | 8699.52i | − | 1.48481i | ||||||
\(326\) | −762.240 | + | 440.080i | −0.129499 | + | 0.0747661i | ||||
\(327\) | 8.47129 | + | 205.859i | 0.00143261 | + | 0.0348136i | ||||
\(328\) | −6771.27 | − | 3909.39i | −1.13988 | − | 0.658110i | ||||
\(329\) | −1593.03 | + | 6097.69i | −0.266951 | + | 1.02181i | ||||
\(330\) | −786.251 | + | 498.132i | −0.131157 | + | 0.0830947i | ||||
\(331\) | 852.222 | + | 1476.09i | 0.141518 | + | 0.245116i | 0.928068 | − | 0.372410i | \(-0.121468\pi\) |
−0.786551 | + | 0.617526i | \(0.788135\pi\) | |||||||
\(332\) | 2148.95 | 0.355238 | ||||||||
\(333\) | −1240.86 | + | 102.299i | −0.204201 | + | 0.0168346i | ||||
\(334\) | 1745.94i | 0.286028i | ||||||||
\(335\) | 170.191 | + | 294.780i | 0.0277569 | + | 0.0480763i | ||||
\(336\) | 2589.93 | + | 563.984i | 0.420513 | + | 0.0915710i | ||||
\(337\) | 3770.46 | − | 6530.62i | 0.609466 | − | 1.05563i | −0.381863 | − | 0.924219i | \(-0.624717\pi\) |
0.991329 | − | 0.131407i | \(-0.0419493\pi\) | |||||||
\(338\) | −3917.35 | − | 2261.68i | −0.630401 | − | 0.363962i | ||||
\(339\) | 1748.08 | − | 3337.58i | 0.280066 | − | 0.534727i | ||||
\(340\) | 1066.70 | + | 1847.59i | 0.170147 | + | 0.294704i | ||||
\(341\) | 5649.17 | 0.897125 | ||||||||
\(342\) | −1466.36 | − | 2116.68i | −0.231848 | − | 0.334670i | ||||
\(343\) | 4406.73 | − | 4575.40i | 0.693706 | − | 0.720258i | ||||
\(344\) | −5274.67 | + | 3045.33i | −0.826718 | + | 0.477306i | ||||
\(345\) | −477.921 | − | 754.350i | −0.0745808 | − | 0.117718i | ||||
\(346\) | 1356.52 | + | 783.188i | 0.210772 | + | 0.121689i | ||||
\(347\) | −1623.73 | − | 937.459i | −0.251199 | − | 0.145030i | 0.369114 | − | 0.929384i | \(-0.379661\pi\) |
−0.620313 | + | 0.784354i | \(0.712995\pi\) | |||||||
\(348\) | −1005.61 | + | 41.3818i | −0.154904 | + | 0.00637442i | ||||
\(349\) | 1501.48 | − | 866.879i | 0.230293 | − | 0.132960i | −0.380414 | − | 0.924816i | \(-0.624219\pi\) |
0.610707 | + | 0.791856i | \(0.290885\pi\) | |||||||
\(350\) | 719.020 | + | 2617.77i | 0.109809 | + | 0.399788i | ||||
\(351\) | 4141.44 | − | 9789.54i | 0.629783 | − | 1.48868i | ||||
\(352\) | −8001.54 | −1.21160 | ||||||||
\(353\) | 4678.78 | + | 8103.88i | 0.705457 | + | 1.22189i | 0.966526 | + | 0.256567i | \(0.0825914\pi\) |
−0.261070 | + | 0.965320i | \(0.584075\pi\) | |||||||
\(354\) | −3606.72 | + | 148.420i | −0.541512 | + | 0.0222837i | ||||
\(355\) | −2692.85 | − | 1554.72i | −0.402596 | − | 0.232439i | ||||
\(356\) | 3261.81 | − | 5649.61i | 0.485605 | − | 0.841092i | ||||
\(357\) | −6797.05 | + | 7473.81i | −1.00767 | + | 1.10800i | ||||
\(358\) | −1019.60 | − | 1765.99i | −0.150523 | − | 0.260714i | ||||
\(359\) | 11558.3i | 1.69923i | 0.527401 | + | 0.849616i | \(0.323167\pi\) | ||||
−0.527401 | + | 0.849616i | \(0.676833\pi\) | |||||||
\(360\) | 1428.74 | + | 674.970i | 0.209170 | + | 0.0988169i | ||||
\(361\) | 1277.89 | 0.186309 | ||||||||
\(362\) | 351.061 | + | 608.055i | 0.0509706 | + | 0.0882836i | ||||
\(363\) | −2778.11 | − | 1455.05i | −0.401689 | − | 0.210387i | ||||
\(364\) | −8648.47 | − | 2259.43i | −1.24534 | − | 0.325347i | ||||
\(365\) | −1592.20 | − | 919.255i | −0.228327 | − | 0.131825i | ||||
\(366\) | −2181.30 | − | 1142.47i | −0.311525 | − | 0.163163i | ||||
\(367\) | −7156.41 | + | 4131.76i | −1.01788 | + | 0.587673i | −0.913489 | − | 0.406864i | \(-0.866622\pi\) |
−0.104390 | + | 0.994536i | \(0.533289\pi\) | |||||||
\(368\) | − | 1483.79i | − | 0.210184i | ||||||
\(369\) | −4915.53 | + | 10404.9i | −0.693475 | + | 1.46791i | ||||
\(370\) | 187.802i | 0.0263875i | ||||||||
\(371\) | 3061.22 | − | 3099.78i | 0.428384 | − | 0.433780i | ||||
\(372\) | −2275.32 | − | 3591.36i | −0.317123 | − | 0.500547i | ||||
\(373\) | 4591.28 | − | 7952.33i | 0.637339 | − | 1.10390i | −0.348676 | − | 0.937243i | \(-0.613369\pi\) |
0.986014 | − | 0.166660i | \(-0.0532981\pi\) | |||||||
\(374\) | 2947.16 | − | 5104.64i | 0.407471 | − | 0.705761i | ||||
\(375\) | −163.457 | − | 3972.13i | −0.0225090 | − | 0.546986i | ||||
\(376\) | −5406.34 | + | 3121.35i | −0.741517 | + | 0.428115i | ||||
\(377\) | 2303.68 | 0.314710 | ||||||||
\(378\) | −437.090 | + | 3288.06i | −0.0594748 | + | 0.447407i | ||||
\(379\) | −9297.03 | −1.26004 | −0.630022 | − | 0.776577i | \(-0.716954\pi\) | ||||
−0.630022 | + | 0.776577i | \(0.716954\pi\) | |||||||
\(380\) | 1314.83 | − | 759.119i | 0.177499 | − | 0.102479i | ||||
\(381\) | 121.244 | + | 2946.33i | 0.0163032 | + | 0.396181i | ||||
\(382\) | −2398.05 | + | 4153.54i | −0.321190 | + | 0.556318i | ||||
\(383\) | 3674.74 | − | 6364.84i | 0.490262 | − | 0.849159i | −0.509675 | − | 0.860367i | \(-0.670234\pi\) |
0.999937 | + | 0.0112079i | \(0.00356767\pi\) | |||||||
\(384\) | 4005.04 | + | 6321.55i | 0.532243 | + | 0.840091i | ||||
\(385\) | 1826.02 | − | 1849.02i | 0.241720 | − | 0.244765i | ||||
\(386\) | − | 3348.30i | − | 0.441513i | ||||||
\(387\) | 5104.79 | + | 7368.70i | 0.670519 | + | 0.967887i | ||||
\(388\) | 467.482i | 0.0611670i | ||||||||
\(389\) | −4531.66 | + | 2616.35i | −0.590653 | + | 0.341014i | −0.765356 | − | 0.643607i | \(-0.777437\pi\) |
0.174702 | + | 0.984621i | \(0.444104\pi\) | |||||||
\(390\) | −1420.30 | − | 743.890i | −0.184410 | − | 0.0965855i | ||||
\(391\) | 4897.52 | + | 2827.59i | 0.633448 | + | 0.365722i | ||||
\(392\) | 6291.84 | − | 78.7625i | 0.810678 | − | 0.0101482i | ||||
\(393\) | −5551.92 | − | 2907.85i | −0.712614 | − | 0.373235i | ||||
\(394\) | −2938.66 | − | 5089.91i | −0.375755 | − | 0.650827i | ||||
\(395\) | −68.0730 | −0.00867120 | ||||||||
\(396\) | 621.568 | + | 7539.51i | 0.0788762 | + | 0.956754i | ||||
\(397\) | − | 10045.1i | − | 1.26990i | −0.772554 | − | 0.634949i | \(-0.781021\pi\) | ||
0.772554 | − | 0.634949i | \(-0.218979\pi\) | |||||||
\(398\) | 2007.44 | + | 3476.98i | 0.252823 | + | 0.437903i | ||||
\(399\) | 5318.73 | + | 4837.12i | 0.667342 | + | 0.606915i | ||||
\(400\) | 1581.31 | − | 2738.91i | 0.197664 | − | 0.342364i | ||||
\(401\) | −6480.01 | − | 3741.24i | −0.806974 | − | 0.465906i | 0.0389302 | − | 0.999242i | \(-0.487605\pi\) |
−0.845904 | + | 0.533335i | \(0.820938\pi\) | |||||||
\(402\) | −707.155 | + | 29.1001i | −0.0877356 | + | 0.00361040i | ||||
\(403\) | 4865.57 | + | 8427.41i | 0.601417 | + | 1.04169i | ||||
\(404\) | −5636.20 | −0.694088 | ||||||||
\(405\) | 817.284 | − | 2177.32i | 0.100275 | − | 0.267141i | ||||
\(406\) | −693.201 | + | 190.400i | −0.0847364 | + | 0.0232744i | ||||
\(407\) | −1756.51 | + | 1014.12i | −0.213924 | + | 0.123509i | ||||
\(408\) | −9998.30 | + | 411.439i | −1.21321 | + | 0.0499247i | ||||
\(409\) | −9878.34 | − | 5703.26i | −1.19426 | − | 0.689506i | −0.234990 | − | 0.971998i | \(-0.575506\pi\) |
−0.959270 | + | 0.282491i | \(0.908839\pi\) | |||||||
\(410\) | 1503.22 | + | 867.883i | 0.181070 | + | 0.104541i | ||||
\(411\) | −1677.53 | − | 2647.81i | −0.201329 | − | 0.317778i | ||||
\(412\) | 246.587 | − | 142.367i | 0.0294865 | − | 0.0170240i | ||||
\(413\) | 9718.53 | − | 2669.38i | 1.15791 | − | 0.318042i | ||||
\(414\) | 1850.53 | − | 152.560i | 0.219682 | − | 0.0181109i | ||||
\(415\) | −1076.18 | −0.127295 | ||||||||
\(416\) | −6891.64 | − | 11936.7i | −0.812237 | − | 1.40684i | ||||
\(417\) | 831.212 | − | 1587.02i | 0.0976130 | − | 0.186371i | ||||
\(418\) | −3632.71 | − | 2097.35i | −0.425076 | − | 0.245418i | ||||
\(419\) | −3027.27 | + | 5243.38i | −0.352964 | + | 0.611351i | −0.986767 | − | 0.162143i | \(-0.948159\pi\) |
0.633804 | + | 0.773494i | \(0.281493\pi\) | |||||||
\(420\) | −1910.95 | − | 416.128i | −0.222011 | − | 0.0483452i | ||||
\(421\) | −3434.60 | − | 5948.91i | −0.397606 | − | 0.688674i | 0.595824 | − | 0.803115i | \(-0.296826\pi\) |
−0.993430 | + | 0.114441i | \(0.963492\pi\) | |||||||
\(422\) | 873.002i | 0.100704i | ||||||||
\(423\) | 5232.21 | + | 7552.64i | 0.601416 | + | 0.868137i | ||||
\(424\) | 4315.34 | 0.494272 | ||||||||
\(425\) | 6026.86 | + | 10438.8i | 0.687873 | + | 1.19143i | ||||
\(426\) | 5461.56 | − | 3460.19i | 0.621158 | − | 0.393537i | ||||
\(427\) | 6651.68 | + | 1737.77i | 0.753858 | + | 0.196947i | ||||
\(428\) | 2853.25 | + | 1647.32i | 0.322236 | + | 0.186043i | ||||
\(429\) | −711.953 | − | 17301.0i | −0.0801245 | − | 1.94709i | ||||
\(430\) | 1170.97 | − | 676.062i | 0.131324 | − | 0.0758200i | ||||
\(431\) | 7761.64i | 0.867436i | 0.901049 | + | 0.433718i | \(0.142799\pi\) | ||||
−0.901049 | + | 0.433718i | \(0.857201\pi\) | |||||||
\(432\) | 3083.31 | − | 2329.30i | 0.343393 | − | 0.259418i | ||||
\(433\) | − | 7474.70i | − | 0.829586i | −0.909916 | − | 0.414793i | \(-0.863854\pi\) | ||
0.909916 | − | 0.414793i | \(-0.136146\pi\) | |||||||
\(434\) | −2160.63 | − | 2133.75i | −0.238971 | − | 0.235998i | ||||
\(435\) | 503.602 | − | 20.7237i | 0.0555077 | − | 0.00228420i | ||||
\(436\) | 126.295 | − | 218.750i | 0.0138726 | − | 0.0240280i | ||||
\(437\) | 2012.25 | − | 3485.32i | 0.220272 | − | 0.381523i | ||||
\(438\) | 3229.25 | − | 2045.90i | 0.352282 | − | 0.223189i | ||||
\(439\) | 804.050 | − | 464.219i | 0.0874151 | − | 0.0504691i | −0.455655 | − | 0.890156i | \(-0.650595\pi\) |
0.543070 | + | 0.839687i | \(0.317262\pi\) | |||||||
\(440\) | 2574.10 | 0.278898 | ||||||||
\(441\) | −876.379 | − | 9219.44i | −0.0946312 | − | 0.995512i | ||||
\(442\) | 10153.4 | 1.09265 | ||||||||
\(443\) | 4799.04 | − | 2770.72i | 0.514693 | − | 0.297158i | −0.220068 | − | 0.975485i | \(-0.570628\pi\) |
0.734761 | + | 0.678326i | \(0.237294\pi\) | |||||||
\(444\) | 1352.18 | + | 708.213i | 0.144531 | + | 0.0756988i | ||||
\(445\) | −1633.49 | + | 2829.28i | −0.174010 | + | 0.301395i | ||||
\(446\) | −1496.37 | + | 2591.78i | −0.158868 | + | 0.275167i | ||||
\(447\) | 551.110 | − | 1052.23i | 0.0583146 | − | 0.111339i | ||||
\(448\) | 156.692 | + | 154.743i | 0.0165246 | + | 0.0163190i | ||||
\(449\) | − | 13088.2i | − | 1.37566i | −0.725873 | − | 0.687829i | \(-0.758564\pi\) | ||
0.725873 | − | 0.687829i | \(-0.241436\pi\) | |||||||
\(450\) | 3578.46 | + | 1690.55i | 0.374867 | + | 0.177096i | ||||
\(451\) | 18746.1i | 1.95725i | ||||||||
\(452\) | −4000.19 | + | 2309.51i | −0.416268 | + | 0.240332i | ||||
\(453\) | −14900.6 | + | 9440.33i | −1.54546 | + | 0.979129i | ||||
\(454\) | −3396.61 | − | 1961.04i | −0.351126 | − | 0.202722i | ||||
\(455\) | 4331.08 | + | 1131.51i | 0.446251 | + | 0.116584i | ||||
\(456\) | 292.801 | + | 7115.28i | 0.0300694 | + | 0.730710i | ||||
\(457\) | 5771.25 | + | 9996.10i | 0.590739 | + | 1.02319i | 0.994133 | + | 0.108164i | \(0.0344971\pi\) |
−0.403394 | + | 0.915026i | \(0.632170\pi\) | |||||||
\(458\) | −1789.18 | −0.182539 | ||||||||
\(459\) | 1812.56 | + | 14615.9i | 0.184321 | + | 1.48630i | ||||
\(460\) | 1094.79i | 0.110967i | ||||||||
\(461\) | −4557.29 | − | 7893.46i | −0.460421 | − | 0.797473i | 0.538561 | − | 0.842587i | \(-0.318968\pi\) |
−0.998982 | + | 0.0451139i | \(0.985635\pi\) | |||||||
\(462\) | 1644.17 | + | 5147.20i | 0.165571 | + | 0.518332i | ||||
\(463\) | −1592.53 | + | 2758.34i | −0.159851 | + | 0.276871i | −0.934815 | − | 0.355135i | \(-0.884435\pi\) |
0.774964 | + | 0.632006i | \(0.217768\pi\) | |||||||
\(464\) | 725.279 | + | 418.740i | 0.0725651 | + | 0.0418955i | ||||
\(465\) | 1139.46 | + | 1798.52i | 0.113637 | + | 0.179365i | ||||
\(466\) | −3320.15 | − | 5750.66i | −0.330049 | − | 0.571662i | ||||
\(467\) | 995.144 | 0.0986077 | 0.0493038 | − | 0.998784i | \(-0.484300\pi\) | ||||
0.0493038 | + | 0.998784i | \(0.484300\pi\) | |||||||
\(468\) | −10712.1 | + | 7420.95i | −1.05805 | + | 0.732978i | ||||
\(469\) | 1905.47 | − | 523.373i | 0.187605 | − | 0.0515291i | ||||
\(470\) | 1200.20 | − | 692.938i | 0.117790 | − | 0.0680061i | ||||
\(471\) | −7877.08 | + | 15039.6i | −0.770609 | + | 1.47131i | ||||
\(472\) | 8645.60 | + | 4991.54i | 0.843106 | + | 0.486768i | ||||
\(473\) | 12646.4 | + | 7301.40i | 1.22935 | + | 0.709765i | ||||
\(474\) | 65.6718 | − | 125.386i | 0.00636372 | − | 0.0121502i | ||||
\(475\) | 7428.79 | − | 4289.02i | 0.717592 | − | 0.414302i | ||||
\(476\) | 11942.9 | − | 3280.33i | 1.15000 | − | 0.315869i | ||||
\(477\) | −521.838 | − | 6329.80i | −0.0500908 | − | 0.607593i | ||||
\(478\) | 2670.82 | 0.255565 | ||||||||
\(479\) | −6951.30 | − | 12040.0i | −0.663075 | − | 1.14848i | −0.979803 | − | 0.199964i | \(-0.935917\pi\) |
0.316728 | − | 0.948516i | \(-0.397416\pi\) | |||||||
\(480\) | −1613.95 | − | 2547.45i | −0.153471 | − | 0.242239i | ||||
\(481\) | −3025.73 | − | 1746.90i | −0.286822 | − | 0.165597i | ||||
\(482\) | −4479.17 | + | 7758.15i | −0.423279 | + | 0.733141i | ||||
\(483\) | −4938.36 | + | 1577.46i | −0.465224 | + | 0.148607i | ||||
\(484\) | 1922.38 | + | 3329.65i | 0.180539 | + | 0.312702i | ||||
\(485\) | − | 234.111i | − | 0.0219184i | ||||||
\(486\) | 3222.04 | + | 3605.91i | 0.300730 | + | 0.336558i | ||||
\(487\) | −7608.36 | −0.707942 | −0.353971 | − | 0.935256i | \(-0.615169\pi\) | ||||
−0.353971 | + | 0.935256i | \(0.615169\pi\) | |||||||
\(488\) | 3404.93 | + | 5897.52i | 0.315849 | + | 0.547066i | ||||
\(489\) | −147.301 | − | 3579.52i | −0.0136220 | − | 0.331025i | ||||
\(490\) | −1396.79 | + | 17.4852i | −0.128776 | + | 0.00161205i | ||||
\(491\) | 14278.7 | + | 8243.83i | 1.31240 | + | 0.757717i | 0.982494 | − | 0.186296i | \(-0.0596482\pi\) |
0.329910 | + | 0.944012i | \(0.392982\pi\) | |||||||
\(492\) | 11917.5 | − | 7550.38i | 1.09204 | − | 0.691865i | ||||
\(493\) | −2764.26 | + | 1595.95i | −0.252528 | + | 0.145797i | ||||
\(494\) | − | 7225.69i | − | 0.658095i | ||||||
\(495\) | −311.276 | − | 3775.73i | −0.0282643 | − | 0.342841i | ||||
\(496\) | 3537.65i | 0.320253i | ||||||||
\(497\) | −12684.1 | + | 12843.9i | −1.14479 | + | 1.15921i | ||||
\(498\) | 1038.21 | − | 1982.25i | 0.0934207 | − | 0.178367i | ||||
\(499\) | 1546.08 | − | 2677.88i | 0.138701 | − | 0.240237i | −0.788304 | − | 0.615286i | \(-0.789041\pi\) |
0.927005 | + | 0.375049i | \(0.122374\pi\) | |||||||
\(500\) | −2436.91 | + | 4220.86i | −0.217964 | + | 0.377525i | ||||
\(501\) | −6295.35 | − | 3297.23i | −0.561389 | − | 0.294030i | ||||
\(502\) | 8021.49 | − | 4631.21i | 0.713181 | − | 0.411755i | ||||
\(503\) | −5624.21 | −0.498551 | −0.249275 | − | 0.968433i | \(-0.580192\pi\) | ||||
−0.249275 | + | 0.968433i | \(0.580192\pi\) | |||||||
\(504\) | 5887.75 | − | 7034.55i | 0.520359 | − | 0.621714i | ||||
\(505\) | 2822.56 | 0.248718 | ||||||||
\(506\) | 2619.52 | − | 1512.38i | 0.230142 | − | 0.132873i | ||||
\(507\) | 15552.9 | − | 9853.62i | 1.36239 | − | 0.863145i | ||||
\(508\) | 1807.58 | − | 3130.82i | 0.157871 | − | 0.273441i | ||||
\(509\) | −2174.06 | + | 3765.58i | −0.189319 | + | 0.327910i | −0.945023 | − | 0.327003i | \(-0.893961\pi\) |
0.755704 | + | 0.654913i | \(0.227295\pi\) | |||||||
\(510\) | 2219.62 | − | 91.3393i | 0.192718 | − | 0.00793053i | ||||
\(511\) | −7499.71 | + | 7594.18i | −0.649252 | + | 0.657430i | ||||
\(512\) | − | 9053.06i | − | 0.781431i | ||||||
\(513\) | 10401.4 | − | 1289.91i | 0.895191 | − | 0.111015i | ||||
\(514\) | 1290.54i | 0.110745i | ||||||||
\(515\) | −123.489 | + | 71.2961i | −0.0105661 | + | 0.00610035i | ||||
\(516\) | −451.859 | − | 10980.5i | −0.0385503 | − | 0.936803i | ||||
\(517\) | 12962.1 | + | 7483.66i | 1.10265 | + | 0.636617i | ||||
\(518\) | 1054.85 | + | 275.583i | 0.0894741 | + | 0.0233753i | ||||
\(519\) | −5385.76 | + | 3412.17i | −0.455508 | + | 0.288589i | ||||
\(520\) | 2217.04 | + | 3840.03i | 0.186969 | + | 0.323839i | ||||
\(521\) | −16584.8 | −1.39461 | −0.697305 | − | 0.716774i | \(-0.745618\pi\) | ||||
−0.697305 | + | 0.716774i | \(0.745618\pi\) | |||||||
\(522\) | −447.666 | + | 947.597i | −0.0375360 | + | 0.0794544i | ||||
\(523\) | − | 15080.9i | − | 1.26088i | −0.776237 | − | 0.630441i | \(-0.782874\pi\) | ||
0.776237 | − | 0.630441i | \(-0.217126\pi\) | |||||||
\(524\) | 3841.77 | + | 6654.14i | 0.320284 | + | 0.554747i | ||||
\(525\) | −10796.8 | − | 2351.12i | −0.897547 | − | 0.195450i | ||||
\(526\) | −2030.50 | + | 3516.93i | −0.168316 | + | 0.291532i | ||||
\(527\) | −11676.7 | − | 6741.54i | −0.965171 | − | 0.557242i | ||||
\(528\) | 2920.66 | − | 5576.37i | 0.240730 | − | 0.459622i | ||||
\(529\) | −4632.48 | − | 8023.69i | −0.380741 | − | 0.659463i | ||||
\(530\) | −958.003 | −0.0785151 | ||||||||
\(531\) | 6276.19 | − | 13285.1i | 0.512925 | − | 1.08573i | ||||
\(532\) | −2334.45 | − | 8499.14i | −0.190246 | − | 0.692640i | ||||
\(533\) | −27965.4 | + | 16145.8i | −2.27263 | + | 1.31211i | ||||
\(534\) | −3635.49 | − | 5738.26i | −0.294613 | − | 0.465016i | ||||
\(535\) | −1428.88 | − | 824.966i | −0.115469 | − | 0.0666662i | ||||
\(536\) | 1695.11 | + | 978.671i | 0.136600 | + | 0.0788660i | ||||
\(537\) | 8293.18 | − | 341.272i | 0.666438 | − | 0.0274245i | ||||
\(538\) | −1356.65 | + | 783.264i | −0.108717 | + | 0.0627675i | ||||
\(539\) | −7706.10 | − | 12969.7i | −0.615817 | − | 1.03645i | ||||
\(540\) | −2274.98 | + | 1718.64i | −0.181295 | + | 0.136960i | ||||
\(541\) | −17064.6 | −1.35613 | −0.678064 | − | 0.735003i | \(-0.737181\pi\) | ||||
−0.678064 | + | 0.735003i | \(0.737181\pi\) | |||||||
\(542\) | −4610.18 | − | 7985.06i | −0.365358 | − | 0.632819i | ||||
\(543\) | −2855.46 | + | 117.505i | −0.225671 | + | 0.00928658i | ||||
\(544\) | 16539.0 | + | 9548.80i | 1.30350 | + | 0.752576i | ||||
\(545\) | −63.2476 | + | 109.548i | −0.00497106 | + | 0.00861013i | ||||
\(546\) | −6262.47 | + | 6886.00i | −0.490859 | + | 0.539732i | ||||
\(547\) | 226.704 | + | 392.663i | 0.0177206 | + | 0.0306929i | 0.874750 | − | 0.484575i | \(-0.161026\pi\) |
−0.857029 | + | 0.515268i | \(0.827692\pi\) | |||||||
\(548\) | 3842.78i | 0.299554i | ||||||||
\(549\) | 8238.82 | − | 5707.57i | 0.640482 | − | 0.443704i | ||||
\(550\) | 6447.15 | 0.499831 | ||||||||
\(551\) | 1135.76 | + | 1967.19i | 0.0878127 | + | 0.152096i | ||||
\(552\) | −4548.96 | − | 2382.54i | −0.350755 | − | 0.183710i | ||||
\(553\) | −99.8910 | + | 382.355i | −0.00768137 | + | 0.0294021i | ||||
\(554\) | 2503.07 | + | 1445.15i | 0.191959 | + | 0.110827i | ||||
\(555\) | −677.161 | − | 354.667i | −0.0517908 | − | 0.0271257i | ||||
\(556\) | −1902.10 | + | 1098.18i | −0.145084 | + | 0.0837644i | ||||
\(557\) | − | 19320.2i | − | 1.46970i | −0.678229 | − | 0.734850i | \(-0.737252\pi\) | ||
0.678229 | − | 0.734850i | \(-0.262748\pi\) | |||||||
\(558\) | −4412.04 | + | 363.735i | −0.334725 | + | 0.0275952i | ||||
\(559\) | 25154.5i | 1.90326i | ||||||||
\(560\) | 1157.90 | + | 1143.50i | 0.0873755 | + | 0.0862886i | ||||
\(561\) | 12840.1 | + | 20266.8i | 0.966328 | + | 1.52525i | ||||
\(562\) | −633.710 | + | 1097.62i | −0.0475649 | + | 0.0823848i | ||||
\(563\) | 1038.78 | − | 1799.22i | 0.0777608 | − | 0.134686i | −0.824523 | − | 0.565829i | \(-0.808556\pi\) |
0.902283 | + | 0.431143i | \(0.141890\pi\) | |||||||
\(564\) | −463.138 | − | 11254.6i | −0.0345774 | − | 0.840257i | ||||
\(565\) | 2003.26 | − | 1156.58i | 0.149164 | − | 0.0861201i | ||||
\(566\) | −7276.09 | −0.540348 | ||||||||
\(567\) | −11030.4 | − | 7785.57i | −0.816988 | − | 0.576655i | ||||
\(568\) | −17880.5 | −1.32086 | ||||||||
\(569\) | 16935.0 | − | 9777.42i | 1.24772 | − | 0.720370i | 0.277064 | − | 0.960851i | \(-0.410639\pi\) |
0.970654 | + | 0.240481i | \(0.0773052\pi\) | |||||||
\(570\) | −65.0016 | − | 1579.59i | −0.00477652 | − | 0.116073i | ||||
\(571\) | −3001.96 | + | 5199.54i | −0.220014 | + | 0.381075i | −0.954812 | − | 0.297211i | \(-0.903944\pi\) |
0.734798 | + | 0.678286i | \(0.237277\pi\) | |||||||
\(572\) | −10614.2 | + | 18384.4i | −0.775879 | + | 1.34386i | ||||
\(573\) | −10447.7 | − | 16490.7i | −0.761711 | − | 1.20228i | ||||
\(574\) | 7080.59 | − | 7169.79i | 0.514875 | − | 0.521361i | ||||
\(575\) | 6185.56i | 0.448619i | ||||||||
\(576\) | 319.968 | − | 26.3787i | 0.0231459 | − | 0.00190818i | ||||
\(577\) | 18306.7i | 1.32083i | 0.750901 | + | 0.660415i | \(0.229619\pi\) | ||||
−0.750901 | + | 0.660415i | \(0.770381\pi\) | |||||||
\(578\) | −6751.83 | + | 3898.17i | −0.485881 | + | 0.280523i | ||||
\(579\) | 12073.0 | + | 6323.32i | 0.866559 | + | 0.453865i | ||||
\(580\) | −535.137 | − | 308.961i | −0.0383109 | − | 0.0221188i | ||||
\(581\) | −1579.19 | + | 6044.70i | −0.112764 | + | 0.431629i | ||||
\(582\) | 431.218 | + | 225.853i | 0.0307123 | + | 0.0160858i | ||||
\(583\) | −5173.17 | − | 8960.18i | −0.367497 | − | 0.636523i | ||||
\(584\) | −10572.2 | −0.749111 | ||||||||
\(585\) | 5364.52 | − | 3716.35i | 0.379137 | − | 0.262653i | ||||
\(586\) | − | 2835.42i | − | 0.199881i | ||||||
\(587\) | −10160.7 | − | 17598.8i | −0.714440 | − | 1.23745i | −0.963175 | − | 0.268875i | \(-0.913348\pi\) |
0.248735 | − | 0.968572i | \(-0.419985\pi\) | |||||||
\(588\) | −5141.46 | + | 10122.8i | −0.360596 | + | 0.709964i | ||||
\(589\) | −4797.62 | + | 8309.72i | −0.335624 | + | 0.581317i | ||||
\(590\) | −1919.32 | − | 1108.12i | −0.133927 | − | 0.0773230i | ||||
\(591\) | 23902.5 | − | 983.609i | 1.66365 | − | 0.0684607i | ||||
\(592\) | −635.069 | − | 1099.97i | −0.0440898 | − | 0.0763658i | ||||
\(593\) | 27525.8 | 1.90616 | 0.953078 | − | 0.302725i | \(-0.0978965\pi\) | ||||
0.953078 | + | 0.302725i | \(0.0978965\pi\) | |||||||
\(594\) | 7254.95 | + | 3069.19i | 0.501135 | + | 0.212004i | ||||
\(595\) | −5980.89 | + | 1642.76i | −0.412088 | + | 0.113188i | ||||
\(596\) | −1261.13 | + | 728.112i | −0.0866741 | + | 0.0500413i | ||||
\(597\) | −16328.1 | + | 671.915i | −1.11937 | + | 0.0460631i | ||||
\(598\) | 4512.34 | + | 2605.20i | 0.308567 | + | 0.178151i | ||||
\(599\) | −17841.0 | − | 10300.5i | −1.21697 | − | 0.702616i | −0.252699 | − | 0.967545i | \(-0.581318\pi\) |
−0.964268 | + | 0.264929i | \(0.914652\pi\) | |||||||
\(600\) | −5857.75 | − | 9245.86i | −0.398569 | − | 0.629101i | ||||
\(601\) | −13383.7 | + | 7727.08i | −0.908374 | + | 0.524450i | −0.879907 | − | 0.475145i | \(-0.842396\pi\) |
−0.0284661 | + | 0.999595i | \(0.509062\pi\) | |||||||
\(602\) | −2079.03 | − | 7569.23i | −0.140756 | − | 0.512456i | ||||
\(603\) | 1230.55 | − | 2604.76i | 0.0831040 | − | 0.175910i | ||||
\(604\) | 21625.3 | 1.45682 | ||||||||
\(605\) | −962.710 | − | 1667.46i | −0.0646938 | − | 0.112053i | ||||
\(606\) | −2723.00 | + | 5198.99i | −0.182532 | + | 0.348506i | ||||
\(607\) | −21073.4 | − | 12166.7i | −1.40913 | − | 0.813562i | −0.413827 | − | 0.910356i | \(-0.635808\pi\) |
−0.995305 | + | 0.0967932i | \(0.969141\pi\) | |||||||
\(608\) | 6795.40 | − | 11770.0i | 0.453273 | − | 0.785091i | ||||
\(609\) | 622.589 | − | 2859.06i | 0.0414262 | − | 0.190238i | ||||
\(610\) | −755.894 | − | 1309.25i | −0.0501725 | − | 0.0869014i | ||||
\(611\) | 25782.4i | 1.70711i | ||||||||
\(612\) | 7712.66 | − | 16325.8i | 0.509421 | − | 1.07832i | ||||
\(613\) | 16221.1 | 1.06879 | 0.534393 | − | 0.845236i | \(-0.320540\pi\) | ||||
0.534393 | + | 0.845236i | \(0.320540\pi\) | |||||||
\(614\) | −1919.30 | − | 3324.32i | −0.126151 | − | 0.218499i | ||||
\(615\) | −5968.19 | + | 3781.17i | −0.391318 | + | 0.247921i | ||||
\(616\) | 3777.26 | − | 14458.3i | 0.247062 | − | 0.945683i | ||||
\(617\) | 17506.0 | + | 10107.1i | 1.14224 | + | 0.659475i | 0.946986 | − | 0.321276i | \(-0.104112\pi\) |
0.195259 | + | 0.980752i | \(0.437445\pi\) | |||||||
\(618\) | −12.1905 | − | 296.239i | −0.000793487 | − | 0.0192824i | ||||
\(619\) | −14613.8 | + | 8437.29i | −0.948915 | + | 0.547857i | −0.892744 | − | 0.450565i | \(-0.851223\pi\) |
−0.0561715 | + | 0.998421i | \(0.517889\pi\) | |||||||
\(620\) | − | 2610.21i | − | 0.169078i | ||||||
\(621\) | −2944.66 | + | 6960.59i | −0.190282 | + | 0.449789i | ||||
\(622\) | − | 3240.71i | − | 0.208908i | ||||||
\(623\) | 13494.6 | + | 13326.7i | 0.867817 | + | 0.857021i | ||||
\(624\) | 10834.3 | − | 445.843i | 0.695065 | − | 0.0286026i | ||||
\(625\) | −5956.03 | + | 10316.1i | −0.381186 | + | 0.660233i | ||||
\(626\) | −3623.84 | + | 6276.67i | −0.231370 | + | 0.400745i | ||||
\(627\) | 14422.9 | − | 9137.66i | 0.918650 | − | 0.582014i | ||||
\(628\) | 18025.4 | − | 10407.0i | 1.14537 | − | 0.661280i | ||||
\(629\) | 4840.89 | 0.306866 | ||||||||
\(630\) | −1307.08 | + | 1561.67i | −0.0826591 | + | 0.0987592i | ||||
\(631\) | 30726.8 | 1.93853 | 0.969266 | − | 0.246014i | \(-0.0791209\pi\) | ||||
0.969266 | + | 0.246014i | \(0.0791209\pi\) | |||||||
\(632\) | −339.004 | + | 195.724i | −0.0213368 | + | 0.0123188i | ||||
\(633\) | −3147.80 | − | 1648.68i | −0.197652 | − | 0.103521i | ||||
\(634\) | −4910.60 | + | 8505.41i | −0.307610 | + | 0.532797i | ||||
\(635\) | −905.222 | + | 1567.89i | −0.0565711 | + | 0.0979840i | ||||
\(636\) | −3612.68 | + | 6897.65i | −0.225239 | + | 0.430047i | ||||
\(637\) | 12711.0 | − | 22666.6i | 0.790622 | − | 1.40986i | ||||
\(638\) | 1707.24i | 0.105941i | ||||||||
\(639\) | 2162.23 | + | 26227.4i | 0.133860 | + | 1.62370i | ||||
\(640\) | 4594.51i | 0.283772i | ||||||||
\(641\) | 13756.1 | − | 7942.11i | 0.847636 | − | 0.489383i | −0.0122166 | − | 0.999925i | \(-0.503889\pi\) |
0.859852 | + | 0.510543i | \(0.170555\pi\) | |||||||
\(642\) | 2898.02 | − | 1836.05i | 0.178155 | − | 0.112871i | ||||
\(643\) | 1909.66 | + | 1102.54i | 0.117122 | + | 0.0676206i | 0.557417 | − | 0.830233i | \(-0.311793\pi\) |
−0.440294 | + | 0.897853i | \(0.645126\pi\) | |||||||
\(644\) | 6149.26 | + | 1606.51i | 0.376265 | + | 0.0983002i | ||||
\(645\) | 226.287 | + | 5498.95i | 0.0138140 | + | 0.335692i | ||||
\(646\) | 5005.82 | + | 8670.34i | 0.304878 | + | 0.528065i | ||||
\(647\) | −3584.90 | −0.217831 | −0.108916 | − | 0.994051i | \(-0.534738\pi\) | ||||
−0.108916 | + | 0.994051i | \(0.534738\pi\) | |||||||
\(648\) | −2190.18 | − | 13192.9i | −0.132775 | − | 0.799796i | ||||
\(649\) | − | 23935.1i | − | 1.44767i | ||||||
\(650\) | 5552.86 | + | 9617.83i | 0.335078 | + | 0.580373i | ||||
\(651\) | 11774.1 | − | 3760.99i | 0.708851 | − | 0.226428i | ||||
\(652\) | −2196.05 | + | 3803.66i | −0.131908 | + | 0.228471i | ||||
\(653\) | −394.355 | − | 227.681i | −0.0236329 | − | 0.0136445i | 0.488137 | − | 0.872767i | \(-0.337677\pi\) |
−0.511770 | + | 0.859123i | \(0.671010\pi\) | |||||||
\(654\) | −140.764 | − | 222.182i | −0.00841639 | − | 0.0132844i | ||||
\(655\) | −1923.93 | − | 3332.34i | −0.114770 | − | 0.198787i | ||||
\(656\) | −11739.3 | −0.698692 | ||||||||
\(657\) | 1278.46 | + | 15507.5i | 0.0759169 | + | 0.920858i | ||||
\(658\) | −2130.93 | − | 7758.17i | −0.126250 | − | 0.459643i | ||||
\(659\) | 8929.73 | − | 5155.58i | 0.527850 | − | 0.304754i | −0.212291 | − | 0.977207i | \(-0.568092\pi\) |
0.740140 | + | 0.672452i | \(0.234759\pi\) | |||||||
\(660\) | −2154.96 | + | 4114.45i | −0.127094 | + | 0.242659i | ||||
\(661\) | 7083.52 | + | 4089.67i | 0.416818 | + | 0.240650i | 0.693715 | − | 0.720250i | \(-0.255973\pi\) |
−0.276897 | + | 0.960900i | \(0.589306\pi\) | |||||||
\(662\) | −1884.36 | − | 1087.94i | −0.110631 | − | 0.0638730i | ||||
\(663\) | −19174.9 | + | 36610.4i | −1.12322 | + | 2.14454i | ||||
\(664\) | −5359.36 | + | 3094.23i | −0.313228 | + | 0.180842i | ||||
\(665\) | 1169.07 | + | 4256.30i | 0.0681724 | + | 0.248199i | ||||
\(666\) | 1306.55 | − | 905.133i | 0.0760177 | − | 0.0526625i | ||||
\(667\) | −1637.97 | −0.0950862 | ||||||||
\(668\) | 4356.21 | + | 7545.18i | 0.252316 | + | 0.437023i | ||||
\(669\) | −6519.33 | − | 10290.1i | −0.376759 | − | 0.594676i | ||||
\(670\) | −376.313 | − | 217.265i | −0.0216989 | − | 0.0125279i | ||||
\(671\) | 8163.57 | − | 14139.7i | 0.469674 | − | 0.813499i | ||||
\(672\) | −16676.9 | + | 5327.11i | −0.957330 | + | 0.305800i | ||||
\(673\) | 11433.9 | + | 19804.0i | 0.654893 | + | 1.13431i | 0.981921 | + | 0.189293i | \(0.0606195\pi\) |
−0.327028 | + | 0.945015i | \(0.606047\pi\) | |||||||
\(674\) | 9626.65i | 0.550155i | ||||||||
\(675\) | −12853.6 | + | 9710.30i | −0.732942 | + | 0.553703i | ||||
\(676\) | −22572.1 | −1.28426 | ||||||||
\(677\) | 2461.68 | + | 4263.75i | 0.139749 | + | 0.242052i | 0.927401 | − | 0.374067i | \(-0.122037\pi\) |
−0.787653 | + | 0.616120i | \(0.788704\pi\) | |||||||
\(678\) | 197.758 | + | 4805.67i | 0.0112018 | + | 0.272214i | ||||
\(679\) | −1314.96 | − | 343.537i | −0.0743205 | − | 0.0194164i | ||||
\(680\) | −5320.60 | − | 3071.85i | −0.300053 | − | 0.173235i | ||||
\(681\) | 13485.5 | − | 8543.78i | 0.758833 | − | 0.480761i | ||||
\(682\) | −6245.48 | + | 3605.83i | −0.350663 | + | 0.202455i | ||||
\(683\) | 15195.6i | 0.851310i | 0.904885 | + | 0.425655i | \(0.139956\pi\) | ||||
−0.904885 | + | 0.425655i | \(0.860044\pi\) | |||||||
\(684\) | −11618.2 | − | 5488.71i | −0.649464 | − | 0.306822i | ||||
\(685\) | − | 1924.43i | − | 0.107341i | ||||||
\(686\) | −1951.45 | + | 7871.17i | −0.108610 | + | 0.438080i | ||||
\(687\) | 3378.89 | − | 6451.28i | 0.187646 | − | 0.358270i | ||||
\(688\) | −4572.32 | + | 7919.50i | −0.253370 | + | 0.438849i | ||||
\(689\) | 8911.18 | − | 15434.6i | 0.492727 | − | 0.853428i | ||||
\(690\) | 1009.87 | + | 528.923i | 0.0557173 | + | 0.0291823i | ||||
\(691\) | −4745.60 | + | 2739.88i | −0.261261 | + | 0.150839i | −0.624910 | − | 0.780697i | \(-0.714864\pi\) |
0.363649 | + | 0.931536i | \(0.381531\pi\) | |||||||
\(692\) | 7816.39 | 0.429385 | ||||||||
\(693\) | −21664.4 | − | 3792.15i | −1.18754 | − | 0.207867i | ||||
\(694\) | 2393.50 | 0.130916 | ||||||||
\(695\) | 952.554 | − | 549.957i | 0.0519891 | − | 0.0300159i | ||||
\(696\) | 2448.35 | − | 1551.16i | 0.133340 | − | 0.0844780i | ||||
\(697\) | 22371.0 | − | 38747.7i | 1.21573 | − | 2.10570i | ||||
\(698\) | −1106.65 | + | 1916.77i | −0.0600104 | + | 0.103941i | ||||
\(699\) | 27005.4 | − | 1111.30i | 1.46128 | − | 0.0601332i | ||||
\(700\) | 9638.78 | + | 9518.87i | 0.520445 | + | 0.513971i | ||||
\(701\) | − | 5356.09i | − | 0.288583i | −0.989535 | − | 0.144292i | \(-0.953910\pi\) | ||
0.989535 | − | 0.144292i | \(-0.0460903\pi\) | |||||||
\(702\) | 1670.01 | + | 13466.4i | 0.0897868 | + | 0.724011i | ||||
\(703\) | − | 3445.02i | − | 0.184824i | ||||||
\(704\) | 452.933 | − | 261.501i | 0.0242479 | − | 0.0139996i | ||||
\(705\) | 231.936 | + | 5636.22i | 0.0123904 | + | 0.301096i | ||||
\(706\) | −10345.3 | − | 5972.88i | −0.551489 | − | 0.318402i | ||||
\(707\) | 4141.86 | − | 15853.9i | 0.220326 | − | 0.843347i | ||||
\(708\) | −15216.4 | + | 9640.38i | −0.807720 | + | 0.511734i | ||||
\(709\) | −6540.71 | − | 11328.8i | −0.346462 | − | 0.600090i | 0.639156 | − | 0.769077i | \(-0.279284\pi\) |
−0.985618 | + | 0.168987i | \(0.945950\pi\) | |||||||
\(710\) | 3969.47 | 0.209819 | ||||||||
\(711\) | 328.085 | + | 473.587i | 0.0173054 | + | 0.0249802i | ||||
\(712\) | 18786.4i | 0.988836i | ||||||||
\(713\) | −3459.53 | − | 5992.08i | −0.181712 | − | 0.314734i | ||||
\(714\) | 2744.05 | − | 12601.3i | 0.143828 | − | 0.660490i | ||||
\(715\) | 5315.52 | − | 9206.75i | 0.278027 | − | 0.481556i | ||||
\(716\) | −8812.49 | − | 5087.89i | −0.459970 | − | 0.265564i | ||||
\(717\) | −5043.88 | + | 9630.21i | −0.262715 | + | 0.501599i | ||||
\(718\) | −7377.61 | − | 12778.4i | −0.383468 | − | 0.664186i | ||||
\(719\) | 11546.9 | 0.598925 | 0.299463 | − | 0.954108i | \(-0.403193\pi\) | ||||
0.299463 | + | 0.954108i | \(0.403193\pi\) | |||||||
\(720\) | 2364.46 | − | 194.929i | 0.122386 | − | 0.0100897i | ||||
\(721\) | 219.250 | + | 798.235i | 0.0113250 | + | 0.0412314i | ||||
\(722\) | −1412.78 | + | 815.671i | −0.0728232 | + | 0.0420445i | ||||
\(723\) | −19514.7 | − | 30802.0i | −1.00382 | − | 1.58442i | ||||
\(724\) | 3034.26 | + | 1751.83i | 0.155756 | + | 0.0899259i | ||||
\(725\) | −3023.52 | − | 1745.63i | −0.154884 | − | 0.0894221i | ||||
\(726\) | 4000.12 | − | 164.608i | 0.204488 | − | 0.00841487i | ||||
\(727\) | −8018.50 | + | 4629.49i | −0.409064 | + | 0.236173i | −0.690388 | − | 0.723440i | \(-0.742560\pi\) |
0.281323 | + | 0.959613i | \(0.409227\pi\) | |||||||
\(728\) | 24822.1 | − | 6817.86i | 1.26369 | − | 0.347097i | ||||
\(729\) | −19086.8 | + | 4807.96i | −0.969707 | + | 0.244270i | ||||
\(730\) | 2347.02 | 0.118996 | ||||||||
\(731\) | −17426.5 | − | 30183.7i | −0.881729 | − | 1.52720i | ||||
\(732\) | −12277.1 | + | 505.215i | −0.619912 | + | 0.0255100i | ||||
\(733\) | −30748.8 | − | 17752.8i | −1.54943 | − | 0.894564i | −0.998185 | − | 0.0602216i | \(-0.980819\pi\) |
−0.551246 | − | 0.834343i | \(-0.685847\pi\) | |||||||
\(734\) | 5274.55 | − | 9135.79i | 0.265242 | − | 0.459412i | ||||
\(735\) | 2574.80 | − | 5069.43i | 0.129215 | − | 0.254407i | ||||
\(736\) | 4900.12 | + | 8487.25i | 0.245409 | + | 0.425060i | ||||
\(737\) | − | 4692.87i | − | 0.234551i | ||||||
\(738\) | −1207.01 | − | 14640.8i | −0.0602042 | − | 0.730266i | ||||
\(739\) | −17773.8 | −0.884734 | −0.442367 | − | 0.896834i | \(-0.645861\pi\) | ||||
−0.442367 | + | 0.896834i | \(0.645861\pi\) | |||||||
\(740\) | 468.577 | + | 811.599i | 0.0232773 | + | 0.0403175i | ||||
\(741\) | 26053.8 | + | 13645.8i | 1.29165 | + | 0.676507i | ||||
\(742\) | −1405.78 | + | 5380.94i | −0.0695525 | + | 0.266227i | ||||
\(743\) | 9171.95 | + | 5295.43i | 0.452875 | + | 0.261468i | 0.709044 | − | 0.705164i | \(-0.249127\pi\) |
−0.256168 | + | 0.966632i | \(0.582460\pi\) | |||||||
\(744\) | 10845.6 | + | 5680.47i | 0.534437 | + | 0.279914i | ||||
\(745\) | 631.562 | − | 364.633i | 0.0310586 | − | 0.0179317i | ||||
\(746\) | 11722.3i | 0.575316i | ||||||||
\(747\) | 5186.75 | + | 7487.02i | 0.254047 | + | 0.366714i | ||||
\(748\) | − | 29413.3i | − | 1.43778i | ||||||
\(749\) | −6730.45 | + | 6815.24i | −0.328338 | + | 0.332474i | ||||
\(750\) | 2716.10 | + | 4287.08i | 0.132237 | + | 0.208723i | ||||
\(751\) | −2521.66 | + | 4367.64i | −0.122525 | + | 0.212220i | −0.920763 | − | 0.390123i | \(-0.872433\pi\) |
0.798238 | + | 0.602343i | \(0.205766\pi\) | |||||||
\(752\) | −4686.46 | + | 8117.19i | −0.227257 | + | 0.393621i | ||||
\(753\) | 1550.13 | + | 37669.3i | 0.0750197 | + | 1.82304i | ||||
\(754\) | −2546.85 | + | 1470.43i | −0.123012 | + | 0.0710210i | ||||
\(755\) | −10829.8 | −0.522035 | ||||||||
\(756\) | 6314.99 | + | 15300.1i | 0.303801 | + | 0.736059i | ||||
\(757\) | −36576.1 | −1.75612 | −0.878060 | − | 0.478551i | \(-0.841162\pi\) | ||||
−0.878060 | + | 0.478551i | \(0.841162\pi\) | |||||||
\(758\) | 10278.4 | − | 5934.25i | 0.492518 | − | 0.284356i | ||||
\(759\) | 506.215 | + | 12301.4i | 0.0242087 | + | 0.588292i | ||||
\(760\) | −2186.08 | + | 3786.40i | −0.104339 | + | 0.180720i | ||||
\(761\) | 9686.08 | − | 16776.8i | 0.461393 | − | 0.799157i | −0.537637 | − | 0.843176i | \(-0.680683\pi\) |
0.999031 | + | 0.0440195i | \(0.0140164\pi\) | |||||||
\(762\) | −2014.67 | − | 3179.95i | −0.0957792 | − | 0.151178i | ||||
\(763\) | 522.503 | + | 516.003i | 0.0247915 | + | 0.0244831i | ||||
\(764\) | 23933.0i | 1.13333i | ||||||||
\(765\) | −3862.44 | + | 8175.81i | −0.182545 | + | 0.386401i | ||||
\(766\) | 9382.26i | 0.442552i | ||||||||
\(767\) | 35706.4 | − | 20615.1i | 1.68094 | − | 0.970492i | ||||
\(768\) | −8900.68 | − | 4661.78i | −0.418198 | − | 0.219033i | ||||
\(769\) | −983.118 | − | 567.603i | −0.0461016 | − | 0.0266168i | 0.476772 | − | 0.879027i | \(-0.341807\pi\) |
−0.522874 | + | 0.852410i | \(0.675140\pi\) | |||||||
\(770\) | −838.549 | + | 3209.73i | −0.0392457 | + | 0.150222i | ||||
\(771\) | −4653.30 | − | 2437.19i | −0.217360 | − | 0.113844i | ||||
\(772\) | −8354.20 | − | 14469.9i | −0.389474 | − | 0.674589i | ||||
\(773\) | 4858.97 | 0.226087 | 0.113043 | − | 0.993590i | \(-0.463940\pi\) | ||||
0.113043 | + | 0.993590i | \(0.463940\pi\) | |||||||
\(774\) | −10347.0 | − | 4888.18i | −0.480513 | − | 0.227005i | ||||
\(775\) | − | 14747.6i | − | 0.683550i | ||||||
\(776\) | −673.118 | − | 1165.87i | −0.0311385 | − | 0.0539335i | ||||
\(777\) | −2985.78 | + | 3283.06i | −0.137856 | + | 0.151582i | ||||
\(778\) | 3340.01 | − | 5785.06i | 0.153914 | − | 0.266587i | ||||
\(779\) | −27574.8 | − | 15920.3i | −1.26825 | − | 0.732227i | ||||
\(780\) | −7993.97 | + | 328.959i | −0.366961 | + | 0.0151008i | ||||
\(781\) | 21434.9 | + | 37126.4i | 0.982077 | + | 1.70101i | ||||
\(782\) | −7219.33 | −0.330131 | ||||||||
\(783\) | −2571.34 | − | 3403.71i | −0.117359 | − | 0.155349i | ||||
\(784\) | 8121.95 | − | 4825.76i | 0.369987 | − | 0.219832i | ||||
\(785\) | −9026.99 | + | 5211.74i | −0.410429 | + | 0.236962i | ||||
\(786\) | 7994.03 | − | 328.962i | 0.362771 | − | 0.0149283i | ||||
\(787\) | −6311.59 | − | 3644.00i | −0.285875 | − | 0.165050i | 0.350205 | − | 0.936673i | \(-0.386112\pi\) |
−0.636080 | + | 0.771623i | \(0.719445\pi\) | |||||||
\(788\) | −25399.2 | − | 14664.2i | −1.14824 | − | 0.662934i | ||||
\(789\) | −8846.43 | − | 13963.2i | −0.399165 | − | 0.630042i | ||||
\(790\) | 75.2586 | − | 43.4506i | 0.00338934 | − | 0.00195684i | ||||
\(791\) | −3556.73 | − | 12949.2i | −0.159877 | − | 0.582073i | ||||
\(792\) | −12406.1 | − | 17908.1i | −0.556608 | − | 0.803457i | ||||
\(793\) | 28124.8 | 1.25945 | ||||||||
\(794\) | 6411.74 | + | 11105.5i | 0.286580 | + | 0.496370i | ||||
\(795\) | 1809.20 | − | 3454.29i | 0.0807117 | − | 0.154102i | ||||
\(796\) | 17350.5 | + | 10017.3i | 0.772579 | + | 0.446049i | ||||
\(797\) | −4956.07 | + | 8584.16i | −0.220267 | + | 0.381514i | −0.954889 | − | 0.296963i | \(-0.904026\pi\) |
0.734622 | + | 0.678477i | \(0.237360\pi\) | |||||||
\(798\) | −8967.68 | − | 1952.80i | −0.397810 | − | 0.0866272i | ||||
\(799\) | −17861.5 | − | 30937.1i | −0.790859 | − | 1.36981i | ||||
\(800\) | 20888.7i | 0.923160i | ||||||||
\(801\) | 27556.2 | − | 2271.78i | 1.21554 | − | 0.100211i | ||||
\(802\) | 9552.05 | 0.420567 | ||||||||
\(803\) | 12673.8 | + | 21951.7i | 0.556972 | + | 0.964704i | ||||
\(804\) | −2983.41 | + | 1890.15i | −0.130867 | + | 0.0829110i | ||||
\(805\) | −3079.50 | − | 804.526i | −0.134830 | − | 0.0352246i | ||||
\(806\) | −10758.3 | − | 6211.33i | −0.470157 | − | 0.271445i | ||||
\(807\) | −262.169 | − | 6370.91i | −0.0114359 | − | 0.277902i | ||||
\(808\) | 14056.4 | − | 8115.45i | 0.612007 | − | 0.353342i | ||||
\(809\) | 39890.5i | 1.73359i | 0.498664 | + | 0.866795i | \(0.333824\pi\) | ||||
−0.498664 | + | 0.866795i | \(0.666176\pi\) | |||||||
\(810\) | 486.218 | + | 2928.83i | 0.0210913 | + | 0.127047i | ||||
\(811\) | 17543.5i | 0.759601i | 0.925069 | + | 0.379800i | \(0.124007\pi\) | ||||
−0.925069 | + | 0.379800i | \(0.875993\pi\) | |||||||
\(812\) | −2520.65 | + | 2552.40i | −0.108938 | + | 0.110310i | ||||
\(813\) | 37498.2 | − | 1543.09i | 1.61761 | − | 0.0665663i | ||||
\(814\) | 1294.62 | − | 2242.34i | 0.0557448 | − | 0.0965529i | ||||
\(815\) | 1099.76 | − | 1904.84i | 0.0472675 | − | 0.0818697i | ||||
\(816\) | −12691.6 | + | 8040.81i | −0.544479 | + | 0.344957i | ||||
\(817\) | −21480.2 | + | 12401.6i | −0.919824 | + | 0.531061i | ||||
\(818\) | 14561.4 | 0.622407 | ||||||||
\(819\) | −13002.2 | − | 35585.0i | −0.554741 | − | 1.51824i | ||||
\(820\) | 8661.67 | 0.368876 | ||||||||
\(821\) | −869.844 | + | 502.205i | −0.0369766 | + | 0.0213484i | −0.518374 | − | 0.855154i | \(-0.673463\pi\) |
0.481398 | + | 0.876502i | \(0.340129\pi\) | |||||||
\(822\) | 3544.69 | + | 1856.55i | 0.150408 | + | 0.0787769i | ||||
\(823\) | 404.664 | − | 700.898i | 0.0171394 | − | 0.0296862i | −0.857329 | − | 0.514770i | \(-0.827877\pi\) |
0.874468 | + | 0.485083i | \(0.161211\pi\) | |||||||
\(824\) | −409.982 | + | 710.110i | −0.0173330 | + | 0.0300217i | ||||
\(825\) | −12175.5 | + | 23246.6i | −0.513815 | + | 0.981020i | ||||
\(826\) | −9040.55 | + | 9154.43i | −0.380825 | + | 0.385622i | ||||
\(827\) | − | 27558.4i | − | 1.15877i | −0.815056 | − | 0.579383i | \(-0.803294\pi\) | ||
0.815056 | − | 0.579383i | \(-0.196706\pi\) | |||||||
\(828\) | 7616.53 | − | 5276.47i | 0.319677 | − | 0.221461i | ||||
\(829\) | − | 11232.4i | − | 0.470588i | −0.971924 | − | 0.235294i | \(-0.924395\pi\) | ||
0.971924 | − | 0.235294i | \(-0.0756053\pi\) | |||||||
\(830\) | 1189.78 | − | 686.917i | 0.0497563 | − | 0.0287268i | ||||
\(831\) | −9937.87 | + | 6296.17i | −0.414851 | + | 0.262830i | ||||
\(832\) | 780.212 | + | 450.456i | 0.0325108 | + | 0.0187701i | ||||
\(833\) | 450.709 | + | 36004.3i | 0.0187469 | + | 1.49757i | ||||
\(834\) | 94.0341 | + | 2285.10i | 0.00390424 | + | 0.0948761i | ||||
\(835\) | −2181.55 | − | 3778.56i | −0.0904141 | − | 0.156602i | ||||
\(836\) | −20932.0 | −0.865967 | ||||||||
\(837\) | 7020.67 | − | 16595.5i | 0.289928 | − | 0.685333i | ||||
\(838\) | − | 7729.16i | − | 0.318615i | ||||||
\(839\) | 10338.7 | + | 17907.2i | 0.425425 | + | 0.736859i | 0.996460 | − | 0.0840675i | \(-0.0267911\pi\) |
−0.571035 | + | 0.820926i | \(0.693458\pi\) | |||||||
\(840\) | 5364.97 | − | 1713.73i | 0.220368 | − | 0.0703921i | ||||
\(841\) | −11732.2 | + | 20320.8i | −0.481047 | + | 0.833197i | ||||
\(842\) | 7594.31 | + | 4384.58i | 0.310828 | + | 0.179457i | ||||
\(843\) | −2760.93 | − | 4357.85i | −0.112801 | − | 0.178045i | ||||
\(844\) | 2178.19 | + | 3772.73i | 0.0888345 | + | 0.153866i | ||||
\(845\) | 11303.9 | 0.460197 | ||||||||
\(846\) | −10605.3 | − | 5010.20i | −0.430991 | − | 0.203610i | ||||
\(847\) | −10778.6 | + | 2960.53i | −0.437256 | + | 0.120100i | ||||
\(848\) | 5611.10 | − | 3239.57i | 0.227224 | − | 0.131188i | ||||
\(849\) | 13741.0 | − | 26235.5i | 0.555465 | − | 1.06054i | ||||
\(850\) | −13326.1 | − | 7693.83i | −0.537743 | − | 0.310466i | ||||
\(851\) | 2151.36 | + | 1242.09i | 0.0866601 | + | 0.0500332i | ||||
\(852\) | 14969.1 | − | 28580.3i | 0.601917 | − | 1.14923i | ||||
\(853\) | 12678.1 | − | 7319.71i | 0.508899 | − | 0.293813i | −0.223482 | − | 0.974708i | \(-0.571742\pi\) |
0.732381 | + | 0.680895i | \(0.238409\pi\) | |||||||
\(854\) | −8463.02 | + | 2324.53i | −0.339109 | + | 0.0931425i | ||||
\(855\) | 5818.31 | + | 2748.70i | 0.232727 | + | 0.109946i | ||||
\(856\) | −9487.79 | −0.378839 | ||||||||
\(857\) | 5363.52 | + | 9289.90i | 0.213786 | + | 0.370288i | 0.952896 | − | 0.303296i | \(-0.0980872\pi\) |
−0.739110 | + | 0.673584i | \(0.764754\pi\) | |||||||
\(858\) | 11830.2 | + | 18672.8i | 0.470720 | + | 0.742984i | ||||
\(859\) | 37326.6 | + | 21550.5i | 1.48262 | + | 0.855988i | 0.999805 | − | 0.0197364i | \(-0.00628272\pi\) |
0.482810 | + | 0.875725i | \(0.339616\pi\) | |||||||
\(860\) | 3373.63 | − | 5843.29i | 0.133767 | − | 0.231691i | ||||
\(861\) | 12480.4 | + | 39070.9i | 0.493997 | + | 1.54649i | ||||
\(862\) | −4954.21 | − | 8580.94i | −0.195755 | − | 0.339058i | ||||
\(863\) | − | 2755.10i | − | 0.108673i | −0.998523 | − | 0.0543363i | \(-0.982696\pi\) | ||
0.998523 | − | 0.0543363i | \(-0.0173043\pi\) | |||||||
\(864\) | −9944.16 | + | 23506.0i | −0.391559 | + | 0.925568i | ||||
\(865\) | −3914.38 | −0.153865 | ||||||||
\(866\) | 4771.06 | + | 8263.71i | 0.187214 | + | 0.324264i | ||||
\(867\) | −1304.77 | − | 31706.9i | −0.0511099 | − | 1.24201i | ||||
\(868\) | −14661.1 | − | 3830.25i | −0.573307 | − | 0.149778i | ||||
\(869\) | 812.785 | + | 469.262i | 0.0317283 | + | 0.0183183i | ||||
\(870\) | −543.534 | + | 344.358i | −0.0211811 | + | 0.0134193i | ||||
\(871\) | 7000.80 | − | 4041.92i | 0.272346 | − | 0.157239i | ||||
\(872\) | 727.400i | 0.0282487i | ||||||||
\(873\) | −1628.72 | + | 1128.32i | −0.0631431 | + | 0.0437434i | ||||
\(874\) | 5137.63i | 0.198836i | ||||||||
\(875\) | −10081.9 | − | 9956.47i | −0.389520 | − | 0.384674i | ||||
\(876\) | 8850.76 | − | 16898.6i | 0.341369 | − | 0.651772i | ||||
\(877\) | 14479.0 | − | 25078.4i | 0.557494 | − | 0.965609i | −0.440210 | − | 0.897895i | \(-0.645096\pi\) |
0.997705 | − | 0.0677140i | \(-0.0215705\pi\) | |||||||
\(878\) | −592.617 | + | 1026.44i | −0.0227789 | + | 0.0394541i | ||||
\(879\) | 10223.7 | + | 5354.74i | 0.392307 | + | 0.205473i | ||||
\(880\) | 3347.02 | − | 1932.40i | 0.128214 | − | 0.0740242i | ||||
\(881\) | −41511.7 | −1.58747 | −0.793737 | − | 0.608261i | \(-0.791867\pi\) | ||||
−0.793737 | + | 0.608261i | \(0.791867\pi\) | |||||||
\(882\) | 6853.61 | + | 9633.24i | 0.261647 | + | 0.367764i | ||||
\(883\) | 34478.4 | 1.31403 | 0.657016 | − | 0.753877i | \(-0.271818\pi\) | ||||
0.657016 | + | 0.753877i | \(0.271818\pi\) | |||||||
\(884\) | 43878.7 | − | 25333.4i | 1.66946 | − | 0.963862i | ||||
\(885\) | 7620.23 | − | 4827.82i | 0.289436 | − | 0.183373i | ||||
\(886\) | −3537.08 | + | 6126.40i | −0.134120 | + | 0.232303i | ||||
\(887\) | 19033.5 | − | 32967.0i | 0.720499 | − | 1.24794i | −0.240302 | − | 0.970698i | \(-0.577246\pi\) |
0.960800 | − | 0.277242i | \(-0.0894203\pi\) | |||||||
\(888\) | −4392.01 | + | 180.735i | −0.165975 | + | 0.00683004i | ||||
\(889\) | 7478.25 | + | 7385.22i | 0.282129 | + | 0.278619i | ||||
\(890\) | − | 4170.58i | − | 0.157077i | ||||||
\(891\) | −24767.7 | + | 20363.1i | −0.931256 | + | 0.765644i | ||||
\(892\) | 14934.1i | 0.560572i | ||||||||
\(893\) | −22016.4 | + | 12711.2i | −0.825028 | + | 0.476330i | ||||
\(894\) | 62.3465 | + | 1515.07i | 0.00233241 | + | 0.0566795i | ||||
\(895\) | 4413.22 | + | 2547.98i | 0.164824 | + | 0.0951614i | ||||
\(896\) | 25806.6 | + | 6742.04i | 0.962208 | + | 0.251379i | ||||
\(897\) | −17915.2 | + | 11350.2i | −0.666858 | + | 0.422490i | ||||
\(898\) | 8354.13 | + | 14469.8i | 0.310446 | + | 0.537709i | ||||
\(899\) | 3905.26 | 0.144881 | ||||||||
\(900\) | 19682.6 | − | 1622.66i | 0.728984 | − | 0.0600985i | ||||
\(901\) | 24694.0i | 0.913070i | ||||||||
\(902\) | −11965.5 | − | 20724.9i | −0.441695 | − | 0.765037i | ||||
\(903\) | 31218.8 | + | 6798.20i | 1.15049 | + | 0.250532i | ||||
\(904\) | 6650.84 | − | 11519.6i | 0.244694 | − | 0.423823i | ||||
\(905\) | −1519.53 | − | 877.303i | −0.0558133 | − | 0.0322238i | ||||
\(906\) | 10447.8 | − | 19947.8i | 0.383117 | − | 0.731481i | ||||
\(907\) | 13062.6 | + | 22625.2i | 0.478212 | + | 0.828287i | 0.999688 | − | 0.0249790i | \(-0.00795188\pi\) |
−0.521476 | + | 0.853266i | \(0.674619\pi\) | |||||||
\(908\) | −19571.6 | −0.715314 | ||||||||
\(909\) | −13603.7 | − | 19636.7i | −0.496375 | − | 0.716512i | ||||
\(910\) | −5510.50 | + | 1513.56i | −0.200738 | + | 0.0551364i | ||||
\(911\) | 13990.6 | − | 8077.47i | 0.508813 | − | 0.293763i | −0.223532 | − | 0.974696i | \(-0.571759\pi\) |
0.732346 | + | 0.680933i | \(0.238426\pi\) | |||||||
\(912\) | 5722.24 | + | 9031.97i | 0.207766 | + | 0.327937i | ||||
\(913\) | 12849.4 | + | 7418.63i | 0.465777 | + | 0.268917i | ||||
\(914\) | −12760.9 | − | 7367.52i | −0.461809 | − | 0.266626i | ||||
\(915\) | 6148.29 | − | 253.008i | 0.222138 | − | 0.00914118i | ||||
\(916\) | −7732.06 | + | 4464.11i | −0.278902 | + | 0.161024i | ||||
\(917\) | −21540.4 | + | 5916.47i | −0.775710 | + | 0.213063i | ||||
\(918\) | −11333.1 | − | 15001.8i | −0.407461 | − | 0.539360i | ||||
\(919\) | −26587.5 | −0.954344 | −0.477172 | − | 0.878810i | \(-0.658338\pi\) | ||||
−0.477172 | + | 0.878810i | \(0.658338\pi\) | |||||||
\(920\) | −1576.37 | − | 2730.35i | −0.0564906 | − | 0.0978446i | ||||
\(921\) | 15611.2 | − | 642.414i | 0.558529 | − | 0.0229840i | ||||
\(922\) | 10076.7 | + | 5817.79i | 0.359933 | + | 0.207808i | ||||
\(923\) | −36923.4 | + | 63953.1i | −1.31674 | + | 2.28065i | ||||
\(924\) | 19947.9 | + | 18141.7i | 0.710216 | + | 0.645906i | ||||
\(925\) | 2647.45 | + | 4585.52i | 0.0941057 | + | 0.162996i | ||||
\(926\) | − | 4066.01i | − | 0.144295i | ||||||
\(927\) | 1091.18 | + | 515.497i | 0.0386612 | + | 0.0182644i | ||||
\(928\) | −5531.45 | −0.195667 | ||||||||
\(929\) | −14089.6 | − | 24403.9i | −0.497594 | − | 0.861857i | 0.502403 | − | 0.864634i | \(-0.332450\pi\) |
−0.999996 | + | 0.00277655i | \(0.999116\pi\) | |||||||
\(930\) | −2407.73 | − | 1261.06i | −0.0848952 | − | 0.0444644i | ||||
\(931\) | 25622.4 | − | 320.747i | 0.901978 | − | 0.0112911i | ||||
\(932\) | −28696.4 | − | 16567.9i | −1.00857 | − | 0.582296i | ||||
\(933\) | 11685.1 | + | 6120.13i | 0.410024 | + | 0.214753i | ||||
\(934\) | −1100.19 | + | 635.195i | −0.0385432 | + | 0.0222529i | ||||
\(935\) | 14730.0i | 0.515210i | ||||||||
\(936\) | 16030.0 | − | 33931.5i | 0.559784 | − | 1.18492i | ||||
\(937\) | 10247.7i | 0.357288i | 0.983914 | + | 0.178644i | \(0.0571711\pi\) | ||||
−0.983914 | + | 0.178644i | \(0.942829\pi\) | |||||||
\(938\) | −1772.54 | + | 1794.87i | −0.0617011 | + | 0.0624783i | ||||
\(939\) | −15788.2 | − | 24920.1i | −0.548700 | − | 0.866067i | ||||
\(940\) | 3457.84 | − | 5989.15i | 0.119981 | − | 0.207813i | ||||
\(941\) | −7953.42 | + | 13775.7i | −0.275530 | + | 0.477232i | −0.970269 | − | 0.242030i | \(-0.922187\pi\) |
0.694739 | + | 0.719262i | \(0.255520\pi\) | |||||||
\(942\) | −891.126 | − | 21655.1i | −0.0308221 | − | 0.749002i | ||||
\(943\) | 19884.0 | − | 11480.0i | 0.686652 | − | 0.396439i | ||||
\(944\) | 14988.8 | 0.516784 | ||||||||
\(945\) | −3162.49 | − | 7662.18i | −0.108863 | − | 0.263757i | ||||
\(946\) | −18641.8 | −0.640694 | ||||||||
\(947\) | −28572.1 | + | 16496.1i | −0.980432 | + | 0.566053i | −0.902401 | − | 0.430898i | \(-0.858197\pi\) |
−0.0780317 | + | 0.996951i | \(0.524864\pi\) | |||||||
\(948\) | −29.0410 | − | 705.719i | −0.000994945 | − | 0.0241779i | ||||
\(949\) | −21831.6 | + | 37813.5i | −0.746769 | + | 1.29344i | ||||
\(950\) | −5475.31 | + | 9483.51i | −0.186992 | + | 0.323880i | ||||
\(951\) | −21394.4 | − | 33768.8i | −0.729505 | − | 1.15145i | ||||
\(952\) | −25061.6 | + | 25377.3i | −0.853204 | + | 0.863952i | ||||
\(953\) | − | 37129.3i | − | 1.26205i | −0.775761 | − | 0.631027i | \(-0.782634\pi\) | ||
0.775761 | − | 0.631027i | \(-0.217366\pi\) | |||||||
\(954\) | 4617.20 | + | 6664.88i | 0.156695 | + | 0.226188i | ||||
\(955\) | − | 11985.5i | − | 0.406116i | ||||||
\(956\) | 11542.1 | − | 6663.84i | 0.390479 | − | 0.225443i | ||||
\(957\) | −6155.82 | − | 3224.15i | −0.207930 | − | 0.108905i | ||||
\(958\) | 15370.1 | + | 8873.96i | 0.518358 | + | 0.299274i | ||||
\(959\) | −10809.2 | − | 2823.93i | −0.363971 | − | 0.0950881i | ||||
\(960\) | 174.613 | + | 91.4543i | 0.00587041 | + | 0.00307466i | ||||
\(961\) | −6647.27 | − | 11513.4i | −0.223130 | − | 0.386473i | ||||
\(962\) | 4460.16 | 0.149482 | ||||||||
\(963\) | 1147.32 | + | 13916.8i | 0.0383925 | + | 0.465694i | ||||
\(964\) | 44703.1i | 1.49356i | ||||||||
\(965\) | 4183.71 | + | 7246.41i | 0.139563 | + | 0.241731i | ||||
\(966\) | 4452.76 | − | 4896.10i | 0.148308 | − | 0.163074i | ||||
\(967\) | −31.4682 | + | 54.5045i | −0.00104648 | + | 0.00181256i | −0.866548 | − | 0.499093i | \(-0.833666\pi\) |
0.865502 | + | 0.500906i | \(0.167000\pi\) | |||||||
\(968\) | −9588.60 | − | 5535.98i | −0.318377 | − | 0.183815i | ||||
\(969\) | −40716.3 | + | 1675.52i | −1.34984 | + | 0.0555473i | ||||
\(970\) | 149.432 | + | 258.823i | 0.00494636 | + | 0.00856734i | ||||
\(971\) | −26793.4 | −0.885521 | −0.442761 | − | 0.896640i | \(-0.646001\pi\) | ||||
−0.442761 | + | 0.896640i | \(0.646001\pi\) | |||||||
\(972\) | 22921.2 | + | 7543.99i | 0.756376 | + | 0.248944i | ||||
\(973\) | −1691.23 | − | 6157.35i | −0.0557229 | − | 0.202873i | ||||
\(974\) | 8411.49 | − | 4856.38i | 0.276716 | − | 0.159762i | ||||
\(975\) | −45165.8 | + | 1858.62i | −1.48355 | + | 0.0610496i | ||||
\(976\) | 8854.66 | + | 5112.24i | 0.290400 | + | 0.167663i | ||||
\(977\) | 22941.3 | + | 13245.2i | 0.751235 | + | 0.433726i | 0.826140 | − | 0.563465i | \(-0.190532\pi\) |
−0.0749048 | + | 0.997191i | \(0.523865\pi\) | |||||||
\(978\) | 2447.64 | + | 3863.35i | 0.0800274 | + | 0.126315i | ||||
\(979\) | 39007.3 | − | 22520.9i | 1.27342 | − | 0.735211i | ||||
\(980\) | −5992.67 | + | 3560.62i | −0.195336 | + | 0.116061i | ||||
\(981\) | 1066.96 | − | 87.9618i | 0.0347252 | − | 0.00286280i | ||||
\(982\) | −21048.0 | −0.683979 | ||||||||
\(983\) | 11945.2 | + | 20689.7i | 0.387582 | + | 0.671313i | 0.992124 | − | 0.125261i | \(-0.0399769\pi\) |
−0.604541 | + | 0.796574i | \(0.706644\pi\) | |||||||
\(984\) | −18850.0 | + | 35990.0i | −0.610686 | + | 1.16598i | ||||
\(985\) | 12719.7 | + | 7343.73i | 0.411456 | + | 0.237554i | ||||
\(986\) | 2037.37 | − | 3528.83i | 0.0658043 | − | 0.113976i | ||||
\(987\) | 31998.1 | + | 6967.90i | 1.03192 | + | 0.224712i | ||||
\(988\) | −18028.5 | − | 31226.3i | −0.580529 | − | 1.00551i | ||||
\(989\) | − | 17885.4i | − | 0.575048i | ||||||
\(990\) | 2754.16 | + | 3975.60i | 0.0884171 | + | 0.127629i | ||||
\(991\) | 377.774 | 0.0121094 | 0.00605468 | − | 0.999982i | \(-0.498073\pi\) | ||||
0.00605468 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(992\) | −11682.9 | − | 20235.3i | −0.373923 | − | 0.647654i | ||||
\(993\) | 7481.44 | − | 4739.89i | 0.239090 | − | 0.151476i | ||||
\(994\) | 5824.84 | − | 22295.9i | 0.185868 | − | 0.711451i | ||||
\(995\) | −8689.00 | − | 5016.59i | −0.276844 | − | 0.159836i | ||||
\(996\) | −459.114 | − | 11156.8i | −0.0146060 | − | 0.354937i | ||||
\(997\) | −854.102 | + | 493.116i | −0.0271311 | + | 0.0156641i | −0.513504 | − | 0.858087i | \(-0.671653\pi\) |
0.486373 | + | 0.873751i | \(0.338320\pi\) | |||||||
\(998\) | 3947.40i | 0.125203i | ||||||||
\(999\) | 796.215 | + | 6420.41i | 0.0252163 | + | 0.203336i |
(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 | 63.4.o.a.41.9 | yes | 44 | |
3.2 | odd | 2 | 189.4.o.a.125.13 | 44 | |||
7.6 | odd | 2 | inner | 63.4.o.a.41.10 | yes | 44 | |
9.2 | odd | 6 | inner | 63.4.o.a.20.10 | yes | 44 | |
9.4 | even | 3 | 567.4.c.c.566.25 | 44 | |||
9.5 | odd | 6 | 567.4.c.c.566.20 | 44 | |||
9.7 | even | 3 | 189.4.o.a.62.14 | 44 | |||
21.20 | even | 2 | 189.4.o.a.125.14 | 44 | |||
63.13 | odd | 6 | 567.4.c.c.566.19 | 44 | |||
63.20 | even | 6 | inner | 63.4.o.a.20.9 | ✓ | 44 | |
63.34 | odd | 6 | 189.4.o.a.62.13 | 44 | |||
63.41 | even | 6 | 567.4.c.c.566.26 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.o.a.20.9 | ✓ | 44 | 63.20 | even | 6 | inner | |
63.4.o.a.20.10 | yes | 44 | 9.2 | odd | 6 | inner | |
63.4.o.a.41.9 | yes | 44 | 1.1 | even | 1 | trivial | |
63.4.o.a.41.10 | yes | 44 | 7.6 | odd | 2 | inner | |
189.4.o.a.62.13 | 44 | 63.34 | odd | 6 | |||
189.4.o.a.62.14 | 44 | 9.7 | even | 3 | |||
189.4.o.a.125.13 | 44 | 3.2 | odd | 2 | |||
189.4.o.a.125.14 | 44 | 21.20 | even | 2 | |||
567.4.c.c.566.19 | 44 | 63.13 | odd | 6 | |||
567.4.c.c.566.20 | 44 | 9.5 | odd | 6 | |||
567.4.c.c.566.25 | 44 | 9.4 | even | 3 | |||
567.4.c.c.566.26 | 44 | 63.41 | even | 6 |