Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,5,Mod(2,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([9]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.2");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.f (of order \(14\), degree \(6\), 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: | \(4.44490841261\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Relative dimension: | \(13\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 2.6 | ||
Character | \(\chi\) | \(=\) | 43.2 |
Dual form | 43.5.f.a.22.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{9}{14}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.495110 | − | 1.02811i | −0.123778 | − | 0.257027i | 0.829868 | − | 0.557961i | \(-0.188416\pi\) |
−0.953645 | + | 0.300934i | \(0.902702\pi\) | |||||||
\(3\) | 6.66668 | − | 13.8435i | 0.740743 | − | 1.53817i | −0.0989417 | − | 0.995093i | \(-0.531546\pi\) |
0.839684 | − | 0.543075i | \(-0.182740\pi\) | |||||||
\(4\) | 9.16397 | − | 11.4913i | 0.572748 | − | 0.718203i | ||||
\(5\) | −12.7517 | − | 2.91049i | −0.510067 | − | 0.116420i | −0.0402612 | − | 0.999189i | \(-0.512819\pi\) |
−0.469806 | + | 0.882770i | \(0.655676\pi\) | |||||||
\(6\) | −17.5333 | −0.487037 | ||||||||
\(7\) | 56.8875i | 1.16097i | 0.814271 | + | 0.580485i | \(0.197137\pi\) | ||||
−0.814271 | + | 0.580485i | \(0.802863\pi\) | |||||||
\(8\) | −34.1514 | − | 7.79484i | −0.533616 | − | 0.121794i | ||||
\(9\) | −96.6955 | − | 121.252i | −1.19377 | − | 1.49694i | ||||
\(10\) | 3.32119 | + | 14.5511i | 0.0332119 | + | 0.145511i | ||||
\(11\) | 117.846 | + | 147.774i | 0.973932 | + | 1.22127i | 0.975212 | + | 0.221273i | \(0.0710211\pi\) |
−0.00128019 | + | 0.999999i | \(0.500407\pi\) | |||||||
\(12\) | −97.9860 | − | 203.470i | −0.680458 | − | 1.41299i | ||||
\(13\) | 54.4721 | − | 238.658i | 0.322320 | − | 1.41218i | −0.511093 | − | 0.859526i | \(-0.670759\pi\) |
0.833413 | − | 0.552651i | \(-0.186384\pi\) | |||||||
\(14\) | 58.4865 | − | 28.1656i | 0.298400 | − | 0.143702i | ||||
\(15\) | −125.303 | + | 157.125i | −0.556901 | + | 0.698332i | ||||
\(16\) | −43.4345 | − | 190.299i | −0.169666 | − | 0.743356i | ||||
\(17\) | −7.56301 | − | 33.1357i | −0.0261696 | − | 0.114656i | 0.960156 | − | 0.279464i | \(-0.0901568\pi\) |
−0.986326 | + | 0.164808i | \(0.947300\pi\) | |||||||
\(18\) | −76.7854 | + | 159.446i | −0.236992 | + | 0.492119i | ||||
\(19\) | 174.096 | + | 138.837i | 0.482259 | + | 0.384589i | 0.834225 | − | 0.551424i | \(-0.185915\pi\) |
−0.351966 | + | 0.936013i | \(0.614487\pi\) | |||||||
\(20\) | −150.301 | + | 119.861i | −0.375753 | + | 0.299653i | ||||
\(21\) | 787.523 | + | 379.251i | 1.78577 | + | 0.859980i | ||||
\(22\) | 93.5807 | − | 194.322i | 0.193349 | − | 0.401492i | ||||
\(23\) | 318.858 | + | 399.835i | 0.602756 | + | 0.755833i | 0.985805 | − | 0.167896i | \(-0.0536972\pi\) |
−0.383048 | + | 0.923728i | \(0.625126\pi\) | |||||||
\(24\) | −335.585 | + | 420.810i | −0.582613 | + | 0.730573i | ||||
\(25\) | −408.971 | − | 196.950i | −0.654354 | − | 0.315120i | ||||
\(26\) | −272.335 | + | 62.1588i | −0.402863 | + | 0.0919509i | ||||
\(27\) | −1109.82 | + | 253.310i | −1.52239 | + | 0.347476i | ||||
\(28\) | 653.709 | + | 521.316i | 0.833813 | + | 0.664943i | ||||
\(29\) | −75.2411 | − | 156.240i | −0.0894662 | − | 0.185778i | 0.851435 | − | 0.524461i | \(-0.175733\pi\) |
−0.940901 | + | 0.338682i | \(0.890019\pi\) | |||||||
\(30\) | 223.580 | + | 51.0306i | 0.248422 | + | 0.0567007i | ||||
\(31\) | 1312.63 | − | 632.129i | 1.36590 | − | 0.657783i | 0.399956 | − | 0.916534i | \(-0.369025\pi\) |
0.965944 | + | 0.258751i | \(0.0833111\pi\) | |||||||
\(32\) | −612.340 | + | 488.325i | −0.597988 | + | 0.476880i | ||||
\(33\) | 2831.35 | − | 646.237i | 2.59995 | − | 0.593423i | ||||
\(34\) | −30.3225 | + | 24.1814i | −0.0262305 | + | 0.0209182i | ||||
\(35\) | 165.571 | − | 725.412i | 0.135160 | − | 0.592173i | ||||
\(36\) | −2279.45 | −1.75884 | ||||||||
\(37\) | 2035.36i | 1.48675i | 0.668877 | + | 0.743373i | \(0.266775\pi\) | ||||
−0.668877 | + | 0.743373i | \(0.733225\pi\) | |||||||
\(38\) | 56.5424 | − | 247.728i | 0.0391568 | − | 0.171557i | ||||
\(39\) | −2940.71 | − | 2345.14i | −1.93341 | − | 1.54184i | ||||
\(40\) | 412.802 | + | 198.795i | 0.258001 | + | 0.124247i | ||||
\(41\) | −885.872 | + | 426.614i | −0.526991 | + | 0.253786i | −0.678409 | − | 0.734684i | \(-0.737330\pi\) |
0.151418 | + | 0.988470i | \(0.451616\pi\) | |||||||
\(42\) | − | 997.429i | − | 0.565436i | ||||||
\(43\) | −63.1291 | − | 1847.92i | −0.0341423 | − | 0.999417i | ||||
\(44\) | 2778.04 | 1.43494 | ||||||||
\(45\) | 880.127 | + | 1827.60i | 0.434630 | + | 0.902519i | ||||
\(46\) | 253.204 | − | 525.783i | 0.119661 | − | 0.248480i | ||||
\(47\) | −256.907 | + | 322.151i | −0.116300 | + | 0.145836i | −0.836574 | − | 0.547854i | \(-0.815445\pi\) |
0.720274 | + | 0.693690i | \(0.244016\pi\) | |||||||
\(48\) | −2923.97 | − | 667.377i | −1.26908 | − | 0.289660i | ||||
\(49\) | −835.193 | −0.347852 | ||||||||
\(50\) | 517.978i | 0.207191i | ||||||||
\(51\) | −509.135 | − | 116.207i | −0.195746 | − | 0.0446777i | ||||
\(52\) | −2243.30 | − | 2813.01i | −0.829622 | − | 1.04031i | ||||
\(53\) | 506.658 | + | 2219.81i | 0.180369 | + | 0.790250i | 0.981454 | + | 0.191699i | \(0.0613997\pi\) |
−0.801084 | + | 0.598551i | \(0.795743\pi\) | |||||||
\(54\) | 809.914 | + | 1015.60i | 0.277748 | + | 0.348285i | ||||
\(55\) | −1072.64 | − | 2227.35i | −0.354591 | − | 0.736316i | ||||
\(56\) | 443.430 | − | 1942.79i | 0.141400 | − | 0.619513i | ||||
\(57\) | 3082.63 | − | 1484.51i | 0.948792 | − | 0.456914i | ||||
\(58\) | −123.378 | + | 154.712i | −0.0366761 | + | 0.0459904i | ||||
\(59\) | 1300.81 | + | 5699.21i | 0.373688 | + | 1.63723i | 0.716326 | + | 0.697766i | \(0.245822\pi\) |
−0.342639 | + | 0.939467i | \(0.611321\pi\) | |||||||
\(60\) | 657.289 | + | 2879.77i | 0.182580 | + | 0.799937i | ||||
\(61\) | 475.087 | − | 986.529i | 0.127677 | − | 0.265125i | −0.827325 | − | 0.561724i | \(-0.810138\pi\) |
0.955002 | + | 0.296599i | \(0.0958526\pi\) | |||||||
\(62\) | −1299.79 | − | 1036.55i | −0.338135 | − | 0.269654i | ||||
\(63\) | 6897.74 | − | 5500.77i | 1.73790 | − | 1.38593i | ||||
\(64\) | −2008.58 | − | 967.281i | −0.490376 | − | 0.236152i | ||||
\(65\) | −1389.22 | + | 2884.75i | −0.328810 | + | 0.682781i | ||||
\(66\) | −2066.23 | − | 2590.97i | −0.474341 | − | 0.594805i | ||||
\(67\) | −3578.65 | + | 4487.48i | −0.797204 | + | 0.999662i | 0.202588 | + | 0.979264i | \(0.435065\pi\) |
−0.999792 | + | 0.0203982i | \(0.993507\pi\) | |||||||
\(68\) | −450.078 | − | 216.746i | −0.0973352 | − | 0.0468741i | ||||
\(69\) | 7660.85 | − | 1748.54i | 1.60908 | − | 0.367263i | ||||
\(70\) | −827.776 | + | 188.935i | −0.168934 | + | 0.0385581i | ||||
\(71\) | −587.312 | − | 468.366i | −0.116507 | − | 0.0929113i | 0.563503 | − | 0.826114i | \(-0.309453\pi\) |
−0.680010 | + | 0.733203i | \(0.738025\pi\) | |||||||
\(72\) | 2357.15 | + | 4894.67i | 0.454697 | + | 0.944187i | ||||
\(73\) | 469.645 | + | 107.193i | 0.0881301 | + | 0.0201151i | 0.266359 | − | 0.963874i | \(-0.414179\pi\) |
−0.178228 | + | 0.983989i | \(0.557037\pi\) | |||||||
\(74\) | 2092.56 | − | 1007.73i | 0.382134 | − | 0.184026i | ||||
\(75\) | −5452.96 | + | 4348.59i | −0.969415 | + | 0.773083i | ||||
\(76\) | 3190.81 | − | 728.282i | 0.552426 | − | 0.126088i | ||||
\(77\) | −8406.49 | + | 6703.96i | −1.41786 | + | 1.13071i | ||||
\(78\) | −955.078 | + | 4184.47i | −0.156982 | + | 0.687783i | ||||
\(79\) | 3176.92 | 0.509041 | 0.254520 | − | 0.967067i | \(-0.418082\pi\) | ||||
0.254520 | + | 0.967067i | \(0.418082\pi\) | |||||||
\(80\) | 2553.05i | 0.398914i | ||||||||
\(81\) | −1096.81 | + | 4805.46i | −0.167172 | + | 0.732428i | ||||
\(82\) | 877.209 | + | 699.550i | 0.130459 | + | 0.104038i | ||||
\(83\) | −7134.64 | − | 3435.86i | −1.03566 | − | 0.498746i | −0.162767 | − | 0.986664i | \(-0.552042\pi\) |
−0.872889 | + | 0.487919i | \(0.837756\pi\) | |||||||
\(84\) | 11574.9 | − | 5574.18i | 1.64044 | − | 0.789992i | ||||
\(85\) | 444.548i | 0.0615291i | ||||||||
\(86\) | −1868.60 | + | 979.828i | −0.252651 | + | 0.132481i | ||||
\(87\) | −2664.51 | −0.352030 | ||||||||
\(88\) | −2872.73 | − | 5965.28i | −0.370962 | − | 0.770310i | ||||
\(89\) | −5712.31 | + | 11861.7i | −0.721160 | + | 1.49750i | 0.140535 | + | 0.990076i | \(0.455118\pi\) |
−0.861694 | + | 0.507428i | \(0.830596\pi\) | |||||||
\(90\) | 1443.21 | − | 1809.73i | 0.178174 | − | 0.223423i | ||||
\(91\) | 13576.7 | + | 3098.78i | 1.63950 | + | 0.374204i | ||||
\(92\) | 7516.61 | 0.888069 | ||||||||
\(93\) | − | 22385.6i | − | 2.58823i | ||||||
\(94\) | 458.403 | + | 104.628i | 0.0518790 | + | 0.0118411i | ||||
\(95\) | −1815.93 | − | 2277.10i | −0.201211 | − | 0.252311i | ||||
\(96\) | 2677.85 | + | 11732.4i | 0.290566 | + | 1.27305i | ||||
\(97\) | −7688.43 | − | 9640.99i | −0.817136 | − | 1.02466i | −0.999144 | − | 0.0413593i | \(-0.986831\pi\) |
0.182008 | − | 0.983297i | \(-0.441740\pi\) | |||||||
\(98\) | 413.512 | + | 858.667i | 0.0430563 | + | 0.0894073i | ||||
\(99\) | 6522.77 | − | 28578.1i | 0.665521 | − | 2.91584i | ||||
\(100\) | −6011.00 | + | 2894.75i | −0.601100 | + | 0.289475i | ||||
\(101\) | 3609.28 | − | 4525.89i | 0.353816 | − | 0.443671i | −0.572792 | − | 0.819701i | \(-0.694140\pi\) |
0.926608 | + | 0.376030i | \(0.122711\pi\) | |||||||
\(102\) | 132.605 | + | 580.980i | 0.0127456 | + | 0.0558420i | ||||
\(103\) | 200.488 | + | 878.395i | 0.0188979 | + | 0.0827972i | 0.983498 | − | 0.180922i | \(-0.0579080\pi\) |
−0.964600 | + | 0.263719i | \(0.915051\pi\) | |||||||
\(104\) | −3720.60 | + | 7725.91i | −0.343991 | + | 0.714304i | ||||
\(105\) | −8938.44 | − | 7128.17i | −0.810743 | − | 0.646546i | ||||
\(106\) | 2031.35 | − | 1619.95i | 0.180790 | − | 0.144175i | ||||
\(107\) | −19033.7 | − | 9166.14i | −1.66248 | − | 0.800606i | −0.998607 | − | 0.0527564i | \(-0.983199\pi\) |
−0.663868 | − | 0.747850i | \(-0.731086\pi\) | |||||||
\(108\) | −7259.54 | + | 15074.6i | −0.622388 | + | 1.29240i | ||||
\(109\) | −2215.89 | − | 2778.63i | −0.186507 | − | 0.233872i | 0.679784 | − | 0.733413i | \(-0.262074\pi\) |
−0.866290 | + | 0.499541i | \(0.833502\pi\) | |||||||
\(110\) | −1758.88 | + | 2205.57i | −0.145362 | + | 0.182279i | ||||
\(111\) | 28176.5 | + | 13569.1i | 2.28687 | + | 1.10130i | ||||
\(112\) | 10825.6 | − | 2470.88i | 0.863014 | − | 0.196977i | ||||
\(113\) | −5905.80 | + | 1347.96i | −0.462511 | + | 0.105565i | −0.447426 | − | 0.894321i | \(-0.647659\pi\) |
−0.0150853 | + | 0.999886i | \(0.504802\pi\) | |||||||
\(114\) | −3052.48 | − | 2434.27i | −0.234878 | − | 0.187309i | ||||
\(115\) | −2902.26 | − | 6026.61i | −0.219453 | − | 0.455698i | ||||
\(116\) | −2484.90 | − | 567.161i | −0.184668 | − | 0.0421493i | ||||
\(117\) | −34205.0 | + | 16472.3i | −2.49872 | + | 1.20332i | ||||
\(118\) | 5215.35 | − | 4159.10i | 0.374558 | − | 0.298700i | ||||
\(119\) | 1885.01 | − | 430.241i | 0.133113 | − | 0.0303821i | ||||
\(120\) | 5504.03 | − | 4389.32i | 0.382225 | − | 0.304814i | ||||
\(121\) | −4691.57 | + | 20555.1i | −0.320441 | + | 1.40394i | ||||
\(122\) | −1249.48 | −0.0839477 | ||||||||
\(123\) | 15107.7i | 0.998591i | ||||||||
\(124\) | 4764.94 | − | 20876.6i | 0.309895 | − | 1.35774i | ||||
\(125\) | 11033.1 | + | 8798.63i | 0.706121 | + | 0.563112i | ||||
\(126\) | −9070.52 | − | 4368.13i | −0.571335 | − | 0.275141i | ||||
\(127\) | 15475.5 | − | 7452.59i | 0.959481 | − | 0.462062i | 0.112480 | − | 0.993654i | \(-0.464120\pi\) |
0.847000 | + | 0.531592i | \(0.178406\pi\) | |||||||
\(128\) | 15075.3i | 0.920126i | ||||||||
\(129\) | −26002.6 | − | 11445.6i | −1.56256 | − | 0.687794i | ||||
\(130\) | 3653.65 | 0.216192 | ||||||||
\(131\) | 5991.97 | + | 12442.5i | 0.349162 | + | 0.725043i | 0.999398 | − | 0.0346896i | \(-0.0110443\pi\) |
−0.650236 | + | 0.759732i | \(0.725330\pi\) | |||||||
\(132\) | 18520.3 | − | 38457.9i | 1.06292 | − | 2.20718i | ||||
\(133\) | −7898.07 | + | 9903.87i | −0.446496 | + | 0.559889i | ||||
\(134\) | 6385.44 | + | 1457.43i | 0.355616 | + | 0.0811670i | ||||
\(135\) | 14889.4 | 0.816975 | ||||||||
\(136\) | 1190.58i | 0.0643698i | ||||||||
\(137\) | 20387.4 | + | 4653.28i | 1.08623 | + | 0.247924i | 0.727907 | − | 0.685676i | \(-0.240493\pi\) |
0.358318 | + | 0.933600i | \(0.383350\pi\) | |||||||
\(138\) | −5590.65 | − | 7010.45i | −0.293565 | − | 0.368119i | ||||
\(139\) | 197.492 | + | 865.270i | 0.0102216 | + | 0.0447839i | 0.979782 | − | 0.200070i | \(-0.0641170\pi\) |
−0.969560 | + | 0.244854i | \(0.921260\pi\) | |||||||
\(140\) | −6818.61 | − | 8550.26i | −0.347888 | − | 0.436238i | ||||
\(141\) | 2746.99 | + | 5704.18i | 0.138171 | + | 0.286916i | ||||
\(142\) | −190.746 | + | 835.712i | −0.00945972 | + | 0.0414458i | ||||
\(143\) | 41686.7 | − | 20075.3i | 2.03857 | − | 0.981723i | ||||
\(144\) | −18874.3 | + | 23667.6i | −0.910218 | + | 1.14138i | ||||
\(145\) | 504.716 | + | 2211.31i | 0.0240055 | + | 0.105175i | ||||
\(146\) | −122.320 | − | 535.918i | −0.00573840 | − | 0.0251416i | ||||
\(147\) | −5567.97 | + | 11562.0i | −0.257669 | + | 0.535055i | ||||
\(148\) | 23388.8 | + | 18651.9i | 1.06779 | + | 0.851531i | ||||
\(149\) | 11529.4 | − | 9194.36i | 0.519318 | − | 0.414142i | −0.328441 | − | 0.944525i | \(-0.606523\pi\) |
0.847758 | + | 0.530383i | \(0.177952\pi\) | |||||||
\(150\) | 7170.63 | + | 3453.19i | 0.318695 | + | 0.153475i | ||||
\(151\) | −10639.8 | + | 22093.9i | −0.466639 | + | 0.968986i | 0.526293 | + | 0.850303i | \(0.323581\pi\) |
−0.992932 | + | 0.118683i | \(0.962133\pi\) | |||||||
\(152\) | −4863.41 | − | 6098.52i | −0.210501 | − | 0.263959i | ||||
\(153\) | −3286.47 | + | 4121.10i | −0.140393 | + | 0.176048i | ||||
\(154\) | 11054.5 | + | 5323.58i | 0.466121 | + | 0.224472i | ||||
\(155\) | −18578.0 | + | 4240.32i | −0.773280 | + | 0.176496i | ||||
\(156\) | −53897.2 | + | 12301.7i | −2.21471 | + | 0.505494i | ||||
\(157\) | 6996.97 | + | 5579.90i | 0.283864 | + | 0.226374i | 0.755062 | − | 0.655653i | \(-0.227607\pi\) |
−0.471198 | + | 0.882028i | \(0.656178\pi\) | |||||||
\(158\) | −1572.93 | − | 3266.22i | −0.0630078 | − | 0.130837i | ||||
\(159\) | 34107.7 | + | 7784.87i | 1.34914 | + | 0.307934i | ||||
\(160\) | 9229.63 | − | 4444.76i | 0.360532 | − | 0.173623i | ||||
\(161\) | −22745.7 | + | 18139.1i | −0.877499 | + | 0.699782i | ||||
\(162\) | 5483.57 | − | 1251.59i | 0.208946 | − | 0.0476905i | ||||
\(163\) | −27957.1 | + | 22295.1i | −1.05225 | + | 0.839138i | −0.987319 | − | 0.158752i | \(-0.949253\pi\) |
−0.0649278 | + | 0.997890i | \(0.520682\pi\) | |||||||
\(164\) | −3215.78 | + | 14089.3i | −0.119564 | + | 0.523842i | ||||
\(165\) | −37985.3 | −1.39524 | ||||||||
\(166\) | 9036.30i | 0.327925i | ||||||||
\(167\) | 8037.08 | − | 35212.7i | 0.288181 | − | 1.26260i | −0.598838 | − | 0.800870i | \(-0.704371\pi\) |
0.887019 | − | 0.461733i | \(-0.152772\pi\) | |||||||
\(168\) | −23938.9 | − | 19090.6i | −0.848174 | − | 0.676396i | ||||
\(169\) | −28257.8 | − | 13608.2i | −0.989384 | − | 0.476462i | ||||
\(170\) | 457.043 | − | 220.100i | 0.0158146 | − | 0.00761592i | ||||
\(171\) | − | 34534.4i | − | 1.18103i | ||||||
\(172\) | −21813.5 | − | 16208.9i | −0.737339 | − | 0.547893i | ||||
\(173\) | 26418.4 | 0.882702 | 0.441351 | − | 0.897335i | \(-0.354499\pi\) | ||||
0.441351 | + | 0.897335i | \(0.354499\pi\) | |||||||
\(174\) | 1319.23 | + | 2739.40i | 0.0435734 | + | 0.0904811i | ||||
\(175\) | 11204.0 | − | 23265.4i | 0.365845 | − | 0.759685i | ||||
\(176\) | 23002.7 | − | 28844.4i | 0.742596 | − | 0.931186i | ||||
\(177\) | 87569.1 | + | 19987.1i | 2.79515 | + | 0.637974i | ||||
\(178\) | 15023.3 | 0.474162 | ||||||||
\(179\) | 22298.0i | 0.695921i | 0.937509 | + | 0.347961i | \(0.113126\pi\) | ||||
−0.937509 | + | 0.347961i | \(0.886874\pi\) | |||||||
\(180\) | 29066.9 | + | 6634.33i | 0.897126 | + | 0.204763i | ||||
\(181\) | −17325.5 | − | 21725.5i | −0.528845 | − | 0.663150i | 0.443616 | − | 0.896217i | \(-0.353695\pi\) |
−0.972461 | + | 0.233067i | \(0.925124\pi\) | |||||||
\(182\) | −3536.06 | − | 15492.5i | −0.106752 | − | 0.467712i | ||||
\(183\) | −10489.8 | − | 13153.8i | −0.313230 | − | 0.392778i | ||||
\(184\) | −7772.81 | − | 16140.4i | −0.229584 | − | 0.476737i | ||||
\(185\) | 5923.88 | − | 25954.2i | 0.173086 | − | 0.758341i | ||||
\(186\) | −23014.8 | + | 11083.3i | −0.665244 | + | 0.320365i | ||||
\(187\) | 4005.32 | − | 5022.52i | 0.114539 | − | 0.143628i | ||||
\(188\) | 1347.63 | + | 5904.37i | 0.0381291 | + | 0.167054i | ||||
\(189\) | −14410.2 | − | 63135.1i | −0.403409 | − | 1.76745i | ||||
\(190\) | −1442.02 | + | 2994.39i | −0.0399452 | + | 0.0829470i | ||||
\(191\) | −31033.7 | − | 24748.5i | −0.850680 | − | 0.678395i | 0.0978089 | − | 0.995205i | \(-0.468817\pi\) |
−0.948489 | + | 0.316811i | \(0.897388\pi\) | |||||||
\(192\) | −26781.1 | + | 21357.2i | −0.726484 | + | 0.579352i | ||||
\(193\) | −25793.9 | − | 12421.7i | −0.692473 | − | 0.333477i | 0.0543298 | − | 0.998523i | \(-0.482698\pi\) |
−0.746803 | + | 0.665046i | \(0.768412\pi\) | |||||||
\(194\) | −6105.35 | + | 12677.9i | −0.162221 | + | 0.336855i | ||||
\(195\) | 30673.6 | + | 38463.4i | 0.806668 | + | 1.01153i | ||||
\(196\) | −7653.68 | + | 9597.41i | −0.199232 | + | 0.249828i | ||||
\(197\) | −56049.6 | − | 26992.1i | −1.44424 | − | 0.695510i | −0.462657 | − | 0.886537i | \(-0.653104\pi\) |
−0.981585 | + | 0.191027i | \(0.938818\pi\) | |||||||
\(198\) | −32610.9 | + | 7443.21i | −0.831825 | + | 0.189859i | ||||
\(199\) | 51355.3 | − | 11721.5i | 1.29682 | − | 0.295990i | 0.482237 | − | 0.876041i | \(-0.339824\pi\) |
0.814581 | + | 0.580051i | \(0.196967\pi\) | |||||||
\(200\) | 12431.8 | + | 9913.99i | 0.310794 | + | 0.247850i | ||||
\(201\) | 38264.8 | + | 79457.7i | 0.947125 | + | 1.96673i | ||||
\(202\) | −6440.09 | − | 1469.91i | −0.157830 | − | 0.0360236i | ||||
\(203\) | 8888.09 | − | 4280.28i | 0.215683 | − | 0.103868i | ||||
\(204\) | −6001.05 | + | 4785.68i | −0.144201 | + | 0.114996i | ||||
\(205\) | 12538.0 | − | 2861.72i | 0.298347 | − | 0.0680957i | ||||
\(206\) | 803.820 | − | 641.025i | 0.0189419 | − | 0.0151057i | ||||
\(207\) | 17648.8 | − | 77324.5i | 0.411884 | − | 1.80458i | ||||
\(208\) | −47782.3 | −1.10444 | ||||||||
\(209\) | 42088.1i | 0.963533i | ||||||||
\(210\) | −2903.01 | + | 12718.9i | −0.0658278 | + | 0.288410i | ||||
\(211\) | 20195.7 | + | 16105.5i | 0.453622 | + | 0.361751i | 0.823488 | − | 0.567334i | \(-0.192025\pi\) |
−0.369866 | + | 0.929085i | \(0.620596\pi\) | |||||||
\(212\) | 30151.4 | + | 14520.2i | 0.670867 | + | 0.323072i | ||||
\(213\) | −10399.3 | + | 5008.02i | −0.229215 | + | 0.110384i | ||||
\(214\) | 24106.9i | 0.526398i | ||||||||
\(215\) | −4573.35 | + | 23747.9i | −0.0989368 | + | 0.513745i | ||||
\(216\) | 39876.6 | 0.854693 | ||||||||
\(217\) | 35960.3 | + | 74672.3i | 0.763666 | + | 1.58577i | ||||
\(218\) | −1759.62 | + | 3653.89i | −0.0370260 | + | 0.0768853i | ||||
\(219\) | 4614.91 | − | 5786.92i | 0.0962222 | − | 0.120659i | ||||
\(220\) | −35424.7 | − | 8085.46i | −0.731915 | − | 0.167055i | ||||
\(221\) | −8320.07 | −0.170350 | ||||||||
\(222\) | − | 35686.6i | − | 0.724101i | ||||||
\(223\) | −61992.9 | − | 14149.5i | −1.24661 | − | 0.284531i | −0.452205 | − | 0.891914i | \(-0.649362\pi\) |
−0.794409 | + | 0.607383i | \(0.792219\pi\) | |||||||
\(224\) | −27779.6 | − | 34834.5i | −0.553643 | − | 0.694247i | ||||
\(225\) | 15665.0 | + | 68632.9i | 0.309432 | + | 1.35571i | ||||
\(226\) | 4309.87 | + | 5404.41i | 0.0843815 | + | 0.105811i | ||||
\(227\) | −39846.9 | − | 82743.0i | −0.773291 | − | 1.60576i | −0.795463 | − | 0.606002i | \(-0.792772\pi\) |
0.0221720 | − | 0.999754i | \(-0.492942\pi\) | |||||||
\(228\) | 11190.2 | − | 49027.3i | 0.215262 | − | 0.943122i | ||||
\(229\) | −22480.0 | + | 10825.8i | −0.428671 | + | 0.206437i | −0.635763 | − | 0.771884i | \(-0.719314\pi\) |
0.207092 | + | 0.978322i | \(0.433600\pi\) | |||||||
\(230\) | −4759.06 | + | 5967.67i | −0.0899633 | + | 0.112810i | ||||
\(231\) | 36762.8 | + | 161069.i | 0.688946 | + | 3.01847i | ||||
\(232\) | 1351.73 | + | 5922.30i | 0.0251138 | + | 0.110031i | ||||
\(233\) | 21629.5 | − | 44914.2i | 0.398415 | − | 0.827317i | −0.601187 | − | 0.799108i | \(-0.705305\pi\) |
0.999602 | − | 0.0282085i | \(-0.00898023\pi\) | |||||||
\(234\) | 33870.5 | + | 27010.8i | 0.618571 | + | 0.493294i | ||||
\(235\) | 4213.62 | − | 3360.25i | 0.0762991 | − | 0.0608465i | ||||
\(236\) | 77411.6 | + | 37279.5i | 1.38989 | + | 0.669338i | ||||
\(237\) | 21179.5 | − | 43979.8i | 0.377068 | − | 0.782990i | ||||
\(238\) | −1375.62 | − | 1724.97i | −0.0242854 | − | 0.0304529i | ||||
\(239\) | 44061.3 | − | 55251.2i | 0.771368 | − | 0.967265i | −0.228612 | − | 0.973518i | \(-0.573419\pi\) |
0.999980 | + | 0.00625234i | \(0.00199020\pi\) | |||||||
\(240\) | 35343.2 | + | 17020.4i | 0.613597 | + | 0.295493i | ||||
\(241\) | 38199.9 | − | 8718.88i | 0.657700 | − | 0.150116i | 0.119370 | − | 0.992850i | \(-0.461912\pi\) |
0.538330 | + | 0.842734i | \(0.319055\pi\) | |||||||
\(242\) | 23455.7 | − | 5353.61i | 0.400514 | − | 0.0914147i | ||||
\(243\) | −12878.4 | − | 10270.2i | −0.218097 | − | 0.173927i | ||||
\(244\) | −6982.77 | − | 14499.9i | −0.117286 | − | 0.243548i | ||||
\(245\) | 10650.1 | + | 2430.82i | 0.177428 | + | 0.0404968i | ||||
\(246\) | 15532.3 | − | 7479.96i | 0.256664 | − | 0.123603i | ||||
\(247\) | 42617.8 | − | 33986.6i | 0.698549 | − | 0.557075i | ||||
\(248\) | −49755.6 | + | 11356.4i | −0.808981 | + | 0.184645i | ||||
\(249\) | −95128.7 | + | 75862.6i | −1.53431 | + | 1.22357i | ||||
\(250\) | 3583.31 | − | 15699.5i | 0.0573330 | − | 0.251192i | ||||
\(251\) | −55273.8 | −0.877347 | −0.438674 | − | 0.898646i | \(-0.644552\pi\) | ||||
−0.438674 | + | 0.898646i | \(0.644552\pi\) | |||||||
\(252\) | − | 129673.i | − | 2.04196i | ||||||
\(253\) | −21509.2 | + | 94237.8i | −0.336033 | + | 1.47226i | ||||
\(254\) | −15324.1 | − | 12220.6i | −0.237524 | − | 0.189419i | ||||
\(255\) | 6154.10 | + | 2963.66i | 0.0946421 | + | 0.0455772i | ||||
\(256\) | −16638.2 | + | 8012.54i | −0.253879 | + | 0.122262i | ||||
\(257\) | − | 32766.5i | − | 0.496094i | −0.968748 | − | 0.248047i | \(-0.920211\pi\) | ||
0.968748 | − | 0.248047i | \(-0.0797887\pi\) | |||||||
\(258\) | 1106.86 | + | 32400.3i | 0.0166286 | + | 0.486753i | ||||
\(259\) | −115786. | −1.72607 | ||||||||
\(260\) | 20418.6 | + | 42399.6i | 0.302050 | + | 0.627214i | ||||
\(261\) | −11668.9 | + | 24230.8i | −0.171297 | + | 0.355703i | ||||
\(262\) | 9825.49 | − | 12320.8i | 0.143137 | − | 0.179488i | ||||
\(263\) | −23381.9 | − | 5336.77i | −0.338040 | − | 0.0771554i | 0.0501313 | − | 0.998743i | \(-0.484036\pi\) |
−0.388171 | + | 0.921587i | \(0.626893\pi\) | |||||||
\(264\) | −101732. | −1.45965 | ||||||||
\(265\) | − | 29781.0i | − | 0.424079i | ||||||
\(266\) | 14092.7 | + | 3216.56i | 0.199173 | + | 0.0454598i | ||||
\(267\) | 126126. | + | 158157.i | 1.76922 | + | 2.21853i | ||||
\(268\) | 18772.2 | + | 82246.3i | 0.261364 | + | 1.14511i | ||||
\(269\) | 57867.1 | + | 72563.0i | 0.799700 | + | 1.00279i | 0.999735 | + | 0.0230035i | \(0.00732289\pi\) |
−0.200035 | + | 0.979789i | \(0.564106\pi\) | |||||||
\(270\) | −7371.88 | − | 15307.9i | −0.101123 | − | 0.209984i | ||||
\(271\) | −14981.1 | + | 65636.3i | −0.203988 | + | 0.893728i | 0.764492 | + | 0.644634i | \(0.222990\pi\) |
−0.968479 | + | 0.249094i | \(0.919867\pi\) | |||||||
\(272\) | −5977.20 | + | 2878.47i | −0.0807904 | + | 0.0389066i | ||||
\(273\) | 133409. | − | 167290.i | 1.79003 | − | 2.24463i | ||||
\(274\) | −5309.92 | − | 23264.3i | −0.0707272 | − | 0.309876i | ||||
\(275\) | −19091.4 | − | 83645.0i | −0.252449 | − | 1.10605i | ||||
\(276\) | 50110.9 | − | 104056.i | 0.657830 | − | 1.36600i | ||||
\(277\) | 10093.0 | + | 8048.93i | 0.131541 | + | 0.104901i | 0.687050 | − | 0.726610i | \(-0.258905\pi\) |
−0.555509 | + | 0.831510i | \(0.687477\pi\) | |||||||
\(278\) | 791.810 | − | 631.447i | 0.0102455 | − | 0.00817048i | ||||
\(279\) | −203572. | − | 98035.3i | −2.61523 | − | 1.25943i | ||||
\(280\) | −11308.9 | + | 23483.3i | −0.144247 | + | 0.299531i | ||||
\(281\) | −16056.0 | − | 20133.5i | −0.203340 | − | 0.254981i | 0.669697 | − | 0.742635i | \(-0.266424\pi\) |
−0.873037 | + | 0.487654i | \(0.837853\pi\) | |||||||
\(282\) | 4504.44 | − | 5648.39i | 0.0566425 | − | 0.0710275i | ||||
\(283\) | 33665.3 | + | 16212.3i | 0.420348 | + | 0.202429i | 0.632087 | − | 0.774897i | \(-0.282198\pi\) |
−0.211739 | + | 0.977326i | \(0.567913\pi\) | |||||||
\(284\) | −10764.2 | + | 2456.86i | −0.133458 | + | 0.0304610i | ||||
\(285\) | −43629.3 | + | 9958.11i | −0.537142 | + | 0.122599i | ||||
\(286\) | −41279.0 | − | 32918.9i | −0.504658 | − | 0.402451i | ||||
\(287\) | −24269.0 | − | 50395.1i | −0.294638 | − | 0.611821i | ||||
\(288\) | 118421. | + | 27028.8i | 1.42772 | + | 0.325868i | ||||
\(289\) | 74209.0 | − | 35737.2i | 0.888508 | − | 0.427883i | ||||
\(290\) | 2023.57 | − | 1613.74i | 0.0240615 | − | 0.0191884i | ||||
\(291\) | −184722. | + | 42161.5i | −2.18138 | + | 0.497886i | ||||
\(292\) | 5535.60 | − | 4414.50i | 0.0649231 | − | 0.0517744i | ||||
\(293\) | 141.537 | − | 620.116i | 0.00164868 | − | 0.00722334i | −0.974097 | − | 0.226131i | \(-0.927392\pi\) |
0.975746 | + | 0.218908i | \(0.0702494\pi\) | |||||||
\(294\) | 14643.7 | 0.169417 | ||||||||
\(295\) | − | 76460.5i | − | 0.878603i | ||||||
\(296\) | 15865.3 | − | 69510.3i | 0.181077 | − | 0.793352i | ||||
\(297\) | −168221. | − | 134151.i | −1.90707 | − | 1.52084i | ||||
\(298\) | −15161.1 | − | 7301.20i | −0.170725 | − | 0.0822170i | ||||
\(299\) | 112793. | − | 54318.1i | 1.26165 | − | 0.607579i | ||||
\(300\) | 102512.i | 1.13902i | ||||||||
\(301\) | 105124. | − | 3591.26i | 1.16029 | − | 0.0396382i | ||||
\(302\) | 27982.7 | 0.306815 | ||||||||
\(303\) | −38592.3 | − | 80137.7i | −0.420354 | − | 0.872874i | ||||
\(304\) | 18858.7 | − | 39160.5i | 0.204063 | − | 0.423742i | ||||
\(305\) | −8929.44 | + | 11197.2i | −0.0959897 | + | 0.120367i | ||||
\(306\) | 5864.10 | + | 1338.44i | 0.0626265 | + | 0.0142941i | ||||
\(307\) | 61943.9 | 0.657237 | 0.328619 | − | 0.944463i | \(-0.393417\pi\) | ||||
0.328619 | + | 0.944463i | \(0.393417\pi\) | |||||||
\(308\) | 158036.i | 1.66592i | ||||||||
\(309\) | 13496.7 | + | 3080.53i | 0.141354 | + | 0.0322632i | ||||
\(310\) | 13557.7 | + | 17000.8i | 0.141079 | + | 0.176907i | ||||
\(311\) | 10419.5 | + | 45650.7i | 0.107727 | + | 0.471983i | 0.999798 | + | 0.0200880i | \(0.00639464\pi\) |
−0.892071 | + | 0.451895i | \(0.850748\pi\) | |||||||
\(312\) | 82149.6 | + | 103012.i | 0.843911 | + | 1.05823i | ||||
\(313\) | 30952.8 | + | 64274.2i | 0.315945 | + | 0.656067i | 0.997102 | − | 0.0760704i | \(-0.0242374\pi\) |
−0.681157 | + | 0.732137i | \(0.738523\pi\) | |||||||
\(314\) | 2272.46 | − | 9956.30i | 0.0230482 | − | 0.100981i | ||||
\(315\) | −103968. | + | 50068.2i | −1.04780 | + | 0.504593i | ||||
\(316\) | 29113.2 | − | 36506.8i | 0.291552 | − | 0.365595i | ||||
\(317\) | −39137.3 | − | 171472.i | −0.389468 | − | 1.70637i | −0.666494 | − | 0.745510i | \(-0.732206\pi\) |
0.277026 | − | 0.960862i | \(-0.410651\pi\) | |||||||
\(318\) | −8883.41 | − | 38920.8i | −0.0878467 | − | 0.384881i | ||||
\(319\) | 14221.3 | − | 29530.8i | 0.139752 | − | 0.290198i | ||||
\(320\) | 22797.5 | + | 18180.4i | 0.222632 | + | 0.177543i | ||||
\(321\) | −253783. | + | 202385.i | −2.46293 | + | 1.96412i | ||||
\(322\) | 29910.5 | + | 14404.1i | 0.288477 | + | 0.138923i | ||||
\(323\) | 3283.76 | − | 6818.80i | 0.0314751 | − | 0.0653586i | ||||
\(324\) | 45169.6 | + | 56640.8i | 0.430285 | + | 0.539560i | ||||
\(325\) | −69281.2 | + | 86875.9i | −0.655917 | + | 0.822494i | ||||
\(326\) | 36763.6 | + | 17704.4i | 0.345925 | + | 0.166589i | ||||
\(327\) | −53238.6 | + | 12151.4i | −0.497888 | + | 0.113640i | ||||
\(328\) | 33579.2 | − | 7664.23i | 0.312121 | − | 0.0712395i | ||||
\(329\) | −18326.4 | − | 14614.8i | −0.169311 | − | 0.135021i | ||||
\(330\) | 18806.9 | + | 39053.0i | 0.172699 | + | 0.358613i | ||||
\(331\) | −20957.6 | − | 4783.44i | −0.191287 | − | 0.0436601i | 0.125804 | − | 0.992055i | \(-0.459849\pi\) |
−0.317091 | + | 0.948395i | \(0.602706\pi\) | |||||||
\(332\) | −104864. | + | 50499.8i | −0.951371 | + | 0.458156i | ||||
\(333\) | 246792. | − | 196810.i | 2.22557 | − | 1.77484i | ||||
\(334\) | −40181.7 | + | 9171.21i | −0.360193 | + | 0.0822117i | ||||
\(335\) | 58694.6 | − | 46807.4i | 0.523008 | − | 0.417085i | ||||
\(336\) | 37965.5 | − | 166338.i | 0.336287 | − | 1.47337i | ||||
\(337\) | −35182.6 | −0.309790 | −0.154895 | − | 0.987931i | \(-0.549504\pi\) | ||||
−0.154895 | + | 0.987931i | \(0.549504\pi\) | |||||||
\(338\) | 35789.6i | 0.313273i | ||||||||
\(339\) | −20711.6 | + | 90743.5i | −0.180225 | + | 0.789616i | ||||
\(340\) | 5108.41 | + | 4073.82i | 0.0441904 | + | 0.0352407i | ||||
\(341\) | 248100. | + | 119479.i | 2.13363 | + | 1.02750i | ||||
\(342\) | −35505.0 | + | 17098.3i | −0.303555 | + | 0.146184i | ||||
\(343\) | 89074.9i | 0.757124i | ||||||||
\(344\) | −12248.3 | + | 63601.3i | −0.103505 | + | 0.537463i | ||||
\(345\) | −102778. | −0.863498 | ||||||||
\(346\) | −13080.0 | − | 27160.9i | −0.109259 | − | 0.226878i | ||||
\(347\) | −13809.1 | + | 28674.9i | −0.114685 | + | 0.238146i | −0.950408 | − | 0.311005i | \(-0.899334\pi\) |
0.835723 | + | 0.549151i | \(0.185049\pi\) | |||||||
\(348\) | −24417.5 | + | 30618.6i | −0.201624 | + | 0.252829i | ||||
\(349\) | 30927.2 | + | 7058.94i | 0.253916 | + | 0.0579547i | 0.347584 | − | 0.937649i | \(-0.387002\pi\) |
−0.0936680 | + | 0.995603i | \(0.529859\pi\) | |||||||
\(350\) | −29466.5 | −0.240543 | ||||||||
\(351\) | 278666.i | 2.26188i | ||||||||
\(352\) | −144323. | − | 32940.9i | −1.16480 | − | 0.265858i | ||||
\(353\) | −48610.0 | − | 60955.0i | −0.390100 | − | 0.489170i | 0.547539 | − | 0.836780i | \(-0.315565\pi\) |
−0.937639 | + | 0.347610i | \(0.886993\pi\) | |||||||
\(354\) | −22807.5 | − | 99926.2i | −0.182000 | − | 0.797394i | ||||
\(355\) | 6126.05 | + | 7681.82i | 0.0486098 | + | 0.0609547i | ||||
\(356\) | 83958.7 | + | 174342.i | 0.662469 | + | 1.37563i | ||||
\(357\) | 6610.71 | − | 28963.4i | 0.0518695 | − | 0.227255i | ||||
\(358\) | 22924.7 | − | 11040.0i | 0.178870 | − | 0.0861394i | ||||
\(359\) | 45405.6 | − | 56936.9i | 0.352307 | − | 0.441779i | −0.573826 | − | 0.818978i | \(-0.694541\pi\) |
0.926132 | + | 0.377199i | \(0.123113\pi\) | |||||||
\(360\) | −15811.7 | − | 69275.7i | −0.122004 | − | 0.534535i | ||||
\(361\) | −17965.5 | − | 78711.9i | −0.137856 | − | 0.603985i | ||||
\(362\) | −13758.1 | + | 28568.9i | −0.104988 | + | 0.218010i | ||||
\(363\) | 253278. | + | 201982.i | 1.92214 | + | 1.53285i | ||||
\(364\) | 160025. | − | 127616.i | 1.20777 | − | 0.963166i | ||||
\(365\) | −5676.78 | − | 2733.79i | −0.0426105 | − | 0.0205201i | ||||
\(366\) | −8329.87 | + | 17297.2i | −0.0621836 | + | 0.129126i | ||||
\(367\) | 112796. | + | 141441.i | 0.837453 | + | 1.05013i | 0.998007 | + | 0.0631059i | \(0.0201006\pi\) |
−0.160554 | + | 0.987027i | \(0.551328\pi\) | |||||||
\(368\) | 62238.9 | − | 78045.1i | 0.459585 | − | 0.576302i | ||||
\(369\) | 137388. | + | 66162.4i | 1.00901 | + | 0.485913i | ||||
\(370\) | −29616.7 | + | 6759.81i | −0.216338 | + | 0.0493777i | ||||
\(371\) | −126280. | + | 28822.5i | −0.917457 | + | 0.209404i | ||||
\(372\) | −257239. | − | 205141.i | −1.85888 | − | 1.48240i | ||||
\(373\) | −74044.4 | − | 153755.i | −0.532200 | − | 1.10512i | −0.977732 | − | 0.209858i | \(-0.932700\pi\) |
0.445532 | − | 0.895266i | \(-0.353015\pi\) | |||||||
\(374\) | −7146.76 | − | 1631.20i | −0.0510935 | − | 0.0116618i | ||||
\(375\) | 195358. | − | 94079.6i | 1.38921 | − | 0.669011i | ||||
\(376\) | 11284.9 | − | 8999.38i | 0.0798217 | − | 0.0636556i | ||||
\(377\) | −41386.4 | + | 9446.17i | −0.291189 | + | 0.0664619i | ||||
\(378\) | −57775.0 | + | 46074.0i | −0.404349 | + | 0.322458i | ||||
\(379\) | 21230.2 | − | 93015.5i | 0.147800 | − | 0.647555i | −0.845694 | − | 0.533669i | \(-0.820813\pi\) |
0.993494 | − | 0.113886i | \(-0.0363299\pi\) | |||||||
\(380\) | −42807.9 | −0.296454 | ||||||||
\(381\) | − | 263919.i | − | 1.81811i | ||||||
\(382\) | −10079.0 | + | 44159.1i | −0.0690704 | + | 0.302617i | ||||
\(383\) | −116913. | − | 93235.2i | −0.797014 | − | 0.635598i | 0.137910 | − | 0.990445i | \(-0.455962\pi\) |
−0.934924 | + | 0.354847i | \(0.884533\pi\) | |||||||
\(384\) | 208696. | + | 100503.i | 1.41531 | + | 0.681576i | ||||
\(385\) | 126709. | − | 61019.7i | 0.854840 | − | 0.411669i | ||||
\(386\) | 32669.0i | 0.219261i | ||||||||
\(387\) | −217960. | + | 186340.i | −1.45531 | + | 1.24418i | ||||
\(388\) | −181244. | −1.20392 | ||||||||
\(389\) | 73556.8 | + | 152742.i | 0.486098 | + | 1.00939i | 0.989391 | + | 0.145277i | \(0.0464073\pi\) |
−0.503293 | + | 0.864116i | \(0.667878\pi\) | |||||||
\(390\) | 24357.7 | − | 50579.3i | 0.160143 | − | 0.332540i | ||||
\(391\) | 10837.3 | − | 13589.5i | 0.0708872 | − | 0.0888897i | ||||
\(392\) | 28523.0 | + | 6510.20i | 0.185620 | + | 0.0423664i | ||||
\(393\) | 212194. | 1.37388 | ||||||||
\(394\) | 70989.0i | 0.457297i | ||||||||
\(395\) | −40511.1 | − | 9246.40i | −0.259645 | − | 0.0592623i | ||||
\(396\) | −268624. | − | 336844.i | −1.71299 | − | 2.14802i | ||||
\(397\) | −2008.83 | − | 8801.25i | −0.0127456 | − | 0.0558423i | 0.968155 | − | 0.250351i | \(-0.0805460\pi\) |
−0.980901 | + | 0.194509i | \(0.937689\pi\) | |||||||
\(398\) | −37477.5 | − | 46995.3i | −0.236594 | − | 0.296680i | ||||
\(399\) | 84450.4 | + | 175363.i | 0.530464 | + | 1.10152i | ||||
\(400\) | −19716.0 | + | 86381.3i | −0.123225 | + | 0.539883i | ||||
\(401\) | −107557. | + | 51796.8i | −0.668884 | + | 0.322118i | −0.737326 | − | 0.675537i | \(-0.763912\pi\) |
0.0684414 | + | 0.997655i | \(0.478197\pi\) | |||||||
\(402\) | 62745.7 | − | 78680.6i | 0.388268 | − | 0.486873i | ||||
\(403\) | −79360.9 | − | 347703.i | −0.488649 | − | 2.14091i | ||||
\(404\) | −18932.8 | − | 82950.2i | −0.115999 | − | 0.508223i | ||||
\(405\) | 27972.5 | − | 58085.4i | 0.170538 | − | 0.354125i | ||||
\(406\) | −8801.17 | − | 7018.70i | −0.0533935 | − | 0.0425799i | ||||
\(407\) | −300773. | + | 239858.i | −1.81572 | + | 1.44799i | ||||
\(408\) | 16481.9 | + | 7937.25i | 0.0990116 | + | 0.0476815i | ||||
\(409\) | −63883.3 | + | 132655.i | −0.381892 | + | 0.793007i | 0.618084 | + | 0.786112i | \(0.287909\pi\) |
−0.999976 | + | 0.00689485i | \(0.997805\pi\) | |||||||
\(410\) | −9149.85 | − | 11473.6i | −0.0544310 | − | 0.0682543i | ||||
\(411\) | 200334. | − | 251211.i | 1.18596 | − | 1.48715i | ||||
\(412\) | 11931.1 | + | 5745.73i | 0.0702890 | + | 0.0338494i | ||||
\(413\) | −324214. | + | 73999.7i | −1.90078 | + | 0.433840i | ||||
\(414\) | −88236.0 | + | 20139.3i | −0.514808 | + | 0.117502i | ||||
\(415\) | 80978.6 | + | 64578.3i | 0.470191 | + | 0.374965i | ||||
\(416\) | 83187.1 | + | 172740.i | 0.480695 | + | 0.998173i | ||||
\(417\) | 13295.0 | + | 3034.50i | 0.0764568 | + | 0.0174508i | ||||
\(418\) | 43271.0 | − | 20838.2i | 0.247654 | − | 0.119264i | ||||
\(419\) | 75694.5 | − | 60364.3i | 0.431158 | − | 0.343837i | −0.383740 | − | 0.923441i | \(-0.625364\pi\) |
0.814898 | + | 0.579604i | \(0.196793\pi\) | |||||||
\(420\) | −163823. | + | 37391.6i | −0.928703 | + | 0.211970i | ||||
\(421\) | −216534. | + | 172680.i | −1.22169 | + | 0.974266i | −1.00000 | 0.000850673i | \(-0.999729\pi\) | |
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(422\) | 6559.11 | − | 28737.3i | 0.0368316 | − | 0.161370i | ||||
\(423\) | 63903.3 | 0.357143 | ||||||||
\(424\) | − | 79759.1i | − | 0.443658i | ||||||
\(425\) | −3433.03 | + | 15041.1i | −0.0190064 | + | 0.0832724i | ||||
\(426\) | 10297.6 | + | 8212.02i | 0.0567433 | + | 0.0452513i | ||||
\(427\) | 56121.2 | + | 27026.6i | 0.307802 | + | 0.148230i | ||||
\(428\) | −279754. | + | 134723.i | −1.52718 | + | 0.735450i | ||||
\(429\) | − | 710926.i | − | 3.86287i | ||||||
\(430\) | 26679.6 | − | 7055.91i | 0.144292 | − | 0.0381607i | ||||
\(431\) | 298979. | 1.60948 | 0.804742 | − | 0.593625i | \(-0.202304\pi\) | ||||
0.804742 | + | 0.593625i | \(0.202304\pi\) | |||||||
\(432\) | 96409.3 | + | 200196.i | 0.516596 | + | 1.07272i | ||||
\(433\) | −28980.8 | + | 60179.2i | −0.154573 | + | 0.320974i | −0.963847 | − | 0.266458i | \(-0.914147\pi\) |
0.809273 | + | 0.587432i | \(0.199861\pi\) | |||||||
\(434\) | 58966.8 | − | 73942.0i | 0.313060 | − | 0.392565i | ||||
\(435\) | 33977.0 | + | 7755.04i | 0.179559 | + | 0.0409832i | ||||
\(436\) | −52236.3 | −0.274789 | ||||||||
\(437\) | 113879.i | 0.596321i | ||||||||
\(438\) | −8234.46 | − | 1879.46i | −0.0429227 | − | 0.00979682i | ||||
\(439\) | 175445. | + | 220001.i | 0.910357 | + | 1.14155i | 0.989478 | + | 0.144687i | \(0.0462174\pi\) |
−0.0791205 | + | 0.996865i | \(0.525211\pi\) | |||||||
\(440\) | 19270.2 | + | 84428.4i | 0.0995363 | + | 0.436097i | ||||
\(441\) | 80759.4 | + | 101269.i | 0.415256 | + | 0.520714i | ||||
\(442\) | 4119.35 | + | 8553.92i | 0.0210855 | + | 0.0437845i | ||||
\(443\) | 8893.34 | − | 38964.3i | 0.0453166 | − | 0.198545i | −0.947202 | − | 0.320637i | \(-0.896103\pi\) |
0.992519 | + | 0.122092i | \(0.0389602\pi\) | |||||||
\(444\) | 414134. | − | 199436.i | 2.10075 | − | 1.01167i | ||||
\(445\) | 107365. | − | 134631.i | 0.542179 | − | 0.679870i | ||||
\(446\) | 16146.1 | + | 70740.8i | 0.0811706 | + | 0.355632i | ||||
\(447\) | −50419.6 | − | 220903.i | −0.252339 | − | 1.10557i | ||||
\(448\) | 55026.2 | − | 114263.i | 0.274166 | − | 0.569312i | ||||
\(449\) | −255841. | − | 204026.i | −1.26905 | − | 1.01203i | −0.998787 | − | 0.0492439i | \(-0.984319\pi\) |
−0.270260 | − | 0.962787i | \(-0.587110\pi\) | |||||||
\(450\) | 62806.0 | − | 50086.1i | 0.310153 | − | 0.247339i | ||||
\(451\) | −167439. | − | 80634.2i | −0.823195 | − | 0.396430i | ||||
\(452\) | −38630.8 | + | 80217.7i | −0.189085 | + | 0.392639i | ||||
\(453\) | 234924. | + | 294585.i | 1.14480 | + | 1.43554i | ||||
\(454\) | −65340.0 | + | 81933.8i | −0.317006 | + | 0.397513i | ||||
\(455\) | −164106. | − | 79029.4i | −0.792688 | − | 0.381739i | ||||
\(456\) | −116848. | + | 26669.7i | −0.561941 | + | 0.128259i | ||||
\(457\) | 193301. | − | 44119.6i | 0.925552 | − | 0.211251i | 0.266922 | − | 0.963718i | \(-0.413993\pi\) |
0.658630 | + | 0.752467i | \(0.271136\pi\) | |||||||
\(458\) | 22260.1 | + | 17751.8i | 0.106120 | + | 0.0846277i | ||||
\(459\) | 16787.2 | + | 34859.0i | 0.0796807 | + | 0.165459i | ||||
\(460\) | −95849.5 | − | 21877.0i | −0.452975 | − | 0.103389i | ||||
\(461\) | 33869.0 | − | 16310.5i | 0.159368 | − | 0.0767475i | −0.352500 | − | 0.935812i | \(-0.614668\pi\) |
0.511867 | + | 0.859064i | \(0.328954\pi\) | |||||||
\(462\) | 147394. | − | 117543.i | 0.690551 | − | 0.550696i | ||||
\(463\) | 77250.4 | − | 17631.9i | 0.360362 | − | 0.0822502i | −0.0385068 | − | 0.999258i | \(-0.512260\pi\) |
0.398869 | + | 0.917008i | \(0.369403\pi\) | |||||||
\(464\) | −26464.2 | + | 21104.5i | −0.122920 | + | 0.0980255i | ||||
\(465\) | −65153.1 | + | 285454.i | −0.301321 | + | 1.32017i | ||||
\(466\) | −56885.6 | −0.261957 | ||||||||
\(467\) | 308210.i | 1.41323i | 0.707599 | + | 0.706614i | \(0.249778\pi\) | ||||
−0.707599 | + | 0.706614i | \(0.750222\pi\) | |||||||
\(468\) | −124167. | + | 544010.i | −0.566909 | + | 2.48379i | ||||
\(469\) | −255282. | − | 203581.i | −1.16058 | − | 0.925530i | ||||
\(470\) | −5540.89 | − | 2668.35i | −0.0250833 | − | 0.0120795i | ||||
\(471\) | 123892. | − | 59663.2i | 0.558472 | − | 0.268946i | ||||
\(472\) | − | 204776.i | − | 0.919167i | ||||||
\(473\) | 265635. | − | 227099.i | 1.18731 | − | 1.01506i | ||||
\(474\) | −55702.1 | −0.247922 | ||||||||
\(475\) | −43856.2 | − | 91068.3i | −0.194376 | − | 0.403627i | ||||
\(476\) | 12330.1 | − | 25603.8i | 0.0544195 | − | 0.113003i | ||||
\(477\) | 220166. | − | 276079.i | 0.967639 | − | 1.21338i | ||||
\(478\) | −78619.3 | − | 17944.3i | −0.344091 | − | 0.0785365i | ||||
\(479\) | −329421. | −1.43575 | −0.717877 | − | 0.696170i | \(-0.754886\pi\) | ||||
−0.717877 | + | 0.696170i | \(0.754886\pi\) | |||||||
\(480\) | − | 157402.i | − | 0.683170i | ||||||
\(481\) | 485754. | + | 110870.i | 2.09955 | + | 0.479208i | ||||
\(482\) | −27877.1 | − | 34956.8i | −0.119992 | − | 0.150466i | ||||
\(483\) | 99470.1 | + | 435807.i | 0.426382 | + | 1.86810i | ||||
\(484\) | 193211. | + | 242279.i | 0.824785 | + | 1.03425i | ||||
\(485\) | 69980.5 | + | 145316.i | 0.297504 | + | 0.617774i | ||||
\(486\) | −4182.62 | + | 18325.3i | −0.0177083 | + | 0.0775850i | ||||
\(487\) | −266723. | + | 128447.i | −1.12461 | + | 0.541585i | −0.901315 | − | 0.433165i | \(-0.857397\pi\) |
−0.223298 | + | 0.974750i | \(0.571682\pi\) | |||||||
\(488\) | −23914.8 | + | 29988.2i | −0.100421 | + | 0.125924i | ||||
\(489\) | 122261. | + | 535659.i | 0.511292 | + | 2.24012i | ||||
\(490\) | −2773.84 | − | 12153.0i | −0.0115528 | − | 0.0506163i | ||||
\(491\) | −17005.3 | + | 35311.8i | −0.0705376 | + | 0.146473i | −0.933256 | − | 0.359211i | \(-0.883046\pi\) |
0.862719 | + | 0.505684i | \(0.168760\pi\) | |||||||
\(492\) | 173606. | + | 138446.i | 0.717191 | + | 0.571941i | ||||
\(493\) | −4608.06 | + | 3674.81i | −0.0189594 | + | 0.0151196i | ||||
\(494\) | −56042.3 | − | 26988.6i | −0.229648 | − | 0.110593i | ||||
\(495\) | −166353. | + | 345435.i | −0.678921 | + | 1.40979i | ||||
\(496\) | −177307. | − | 222336.i | −0.720714 | − | 0.903746i | ||||
\(497\) | 26644.2 | − | 33410.8i | 0.107867 | − | 0.135261i | ||||
\(498\) | 125094. | + | 60242.1i | 0.504403 | + | 0.242908i | ||||
\(499\) | −73826.4 | + | 16850.4i | −0.296490 | + | 0.0676720i | −0.368179 | − | 0.929755i | \(-0.620018\pi\) |
0.0716882 | + | 0.997427i | \(0.477161\pi\) | |||||||
\(500\) | 202215. | − | 46154.2i | 0.808858 | − | 0.184617i | ||||
\(501\) | −433887. | − | 346014.i | −1.72863 | − | 1.37853i | ||||
\(502\) | 27366.6 | + | 56827.3i | 0.108596 | + | 0.225502i | ||||
\(503\) | −45091.7 | − | 10291.9i | −0.178222 | − | 0.0406779i | 0.132479 | − | 0.991186i | \(-0.457706\pi\) |
−0.310700 | + | 0.950508i | \(0.600564\pi\) | |||||||
\(504\) | −278446. | + | 134092.i | −1.09617 | + | 0.527889i | ||||
\(505\) | −59196.9 | + | 47207.9i | −0.232122 | + | 0.185111i | ||||
\(506\) | 107536. | − | 24544.4i | 0.420003 | − | 0.0958630i | ||||
\(507\) | −376772. | + | 300465.i | −1.46576 | + | 1.16890i | ||||
\(508\) | 56177.1 | − | 246128.i | 0.217687 | − | 0.953747i | ||||
\(509\) | 156279. | 0.603206 | 0.301603 | − | 0.953434i | \(-0.402478\pi\) | ||||
0.301603 | + | 0.953434i | \(0.402478\pi\) | |||||||
\(510\) | − | 7794.41i | − | 0.0299670i | ||||||
\(511\) | −6097.97 | + | 26717.0i | −0.0233531 | + | 0.102316i | ||||
\(512\) | 205058. | + | 163528.i | 0.782232 | + | 0.623809i | ||||
\(513\) | −228384. | − | 109984.i | −0.867823 | − | 0.417921i | ||||
\(514\) | −33687.4 | + | 16223.0i | −0.127509 | + | 0.0614052i | ||||
\(515\) | − | 11784.5i | − | 0.0444322i | ||||||
\(516\) | −369811. | + | 193915.i | −1.38893 | + | 0.728304i | ||||
\(517\) | −77881.0 | −0.291374 | ||||||||
\(518\) | 57327.0 | + | 119041.i | 0.213649 | + | 0.443646i | ||||
\(519\) | 176123. | − | 365723.i | 0.653855 | − | 1.35774i | ||||
\(520\) | 69930.1 | − | 87689.6i | 0.258617 | − | 0.324296i | ||||
\(521\) | 205308. | + | 46860.3i | 0.756365 | + | 0.172635i | 0.583279 | − | 0.812272i | \(-0.301769\pi\) |
0.173085 | + | 0.984907i | \(0.444626\pi\) | |||||||
\(522\) | 30689.3 | 0.112628 | ||||||||
\(523\) | − | 442638.i | − | 1.61825i | −0.587638 | − | 0.809124i | \(-0.699942\pi\) | ||
0.587638 | − | 0.809124i | \(-0.300058\pi\) | |||||||
\(524\) | 197890. | + | 45167.0i | 0.720710 | + | 0.164497i | ||||
\(525\) | −247381. | − | 310206.i | −0.897526 | − | 1.12546i | ||||
\(526\) | 6089.85 | + | 26681.4i | 0.0220108 | + | 0.0964354i | ||||
\(527\) | −30873.5 | − | 38714.1i | −0.111164 | − | 0.139395i | ||||
\(528\) | −245957. | − | 510734.i | −0.882248 | − | 1.83201i | ||||
\(529\) | 4072.61 | − | 17843.3i | 0.0145533 | − | 0.0637622i | ||||
\(530\) | −30618.0 | + | 14744.9i | −0.109000 | + | 0.0524915i | ||||
\(531\) | 565260. | − | 708813.i | 2.00474 | − | 2.51387i | ||||
\(532\) | 41430.2 | + | 181517.i | 0.146384 | + | 0.641350i | ||||
\(533\) | 53559.4 | + | 234659.i | 0.188530 | + | 0.826005i | ||||
\(534\) | 100156. | − | 207976.i | 0.351232 | − | 0.729340i | ||||
\(535\) | 216034. | + | 172281.i | 0.754768 | + | 0.601908i | ||||
\(536\) | 157195. | − | 125359.i | 0.547154 | − | 0.436341i | ||||
\(537\) | 308683. | + | 148654.i | 1.07044 | + | 0.515498i | ||||
\(538\) | 45952.0 | − | 95420.2i | 0.158759 | − | 0.329667i | ||||
\(539\) | −98423.9 | − | 123420.i | −0.338784 | − | 0.424822i | ||||
\(540\) | 136446. | − | 171097.i | 0.467921 | − | 0.586754i | ||||
\(541\) | 71091.5 | + | 34235.8i | 0.242897 | + | 0.116973i | 0.551372 | − | 0.834259i | \(-0.314104\pi\) |
−0.308475 | + | 0.951232i | \(0.599819\pi\) | |||||||
\(542\) | 74898.4 | − | 17095.1i | 0.254961 | − | 0.0581932i | ||||
\(543\) | −416260. | + | 95008.7i | −1.41177 | + | 0.322228i | ||||
\(544\) | 20812.1 | + | 16597.1i | 0.0703264 | + | 0.0560834i | ||||
\(545\) | 20169.1 | + | 41881.5i | 0.0679037 | + | 0.141003i | ||||
\(546\) | −238044. | − | 54332.1i | −0.798496 | − | 0.182251i | ||||
\(547\) | 177676. | − | 85564.1i | 0.593818 | − | 0.285968i | −0.112738 | − | 0.993625i | \(-0.535962\pi\) |
0.706556 | + | 0.707657i | \(0.250248\pi\) | |||||||
\(548\) | 240301. | − | 191634.i | 0.800193 | − | 0.638133i | ||||
\(549\) | −165558. | + | 37787.5i | −0.549294 | + | 0.125373i | ||||
\(550\) | −76543.6 | + | 61041.5i | −0.253037 | + | 0.201790i | ||||
\(551\) | 8592.65 | − | 37646.9i | 0.0283024 | − | 0.124001i | ||||
\(552\) | −275259. | −0.903364 | ||||||||
\(553\) | 180727.i | 0.590981i | ||||||||
\(554\) | 3277.99 | − | 14361.8i | 0.0106804 | − | 0.0467940i | ||||
\(555\) | −319805. | − | 255036.i | −1.03824 | − | 0.827971i | ||||
\(556\) | 11752.9 | + | 5659.88i | 0.0380184 | + | 0.0183087i | ||||
\(557\) | 222408. | − | 107106.i | 0.716869 | − | 0.345226i | −0.0396359 | − | 0.999214i | \(-0.512620\pi\) |
0.756505 | + | 0.653988i | \(0.226906\pi\) | |||||||
\(558\) | 257832.i | 0.828074i | ||||||||
\(559\) | −444460. | − | 85593.9i | −1.42236 | − | 0.273917i | ||||
\(560\) | −145237. | −0.463127 | ||||||||
\(561\) | −42827.0 | − | 88931.3i | −0.136079 | − | 0.282572i | ||||
\(562\) | −12750.0 | + | 26475.6i | −0.0403679 | + | 0.0838248i | ||||
\(563\) | −642.352 | + | 805.484i | −0.00202655 | + | 0.00254121i | −0.782844 | − | 0.622218i | \(-0.786232\pi\) |
0.780817 | + | 0.624760i | \(0.214803\pi\) | |||||||
\(564\) | 90721.4 | + | 20706.6i | 0.285201 | + | 0.0650954i | ||||
\(565\) | 79232.2 | 0.248202 | ||||||||
\(566\) | − | 42638.4i | − | 0.133097i | ||||||
\(567\) | −273371. | − | 62395.1i | −0.850327 | − | 0.194082i | ||||
\(568\) | 16406.7 | + | 20573.4i | 0.0508540 | + | 0.0637689i | ||||
\(569\) | 129203. | + | 566074.i | 0.399068 | + | 1.74843i | 0.631080 | + | 0.775717i | \(0.282612\pi\) |
−0.232013 | + | 0.972713i | \(0.574531\pi\) | |||||||
\(570\) | 31839.3 | + | 39925.2i | 0.0979973 | + | 0.122885i | ||||
\(571\) | −45418.3 | − | 94312.1i | −0.139303 | − | 0.289265i | 0.819633 | − | 0.572889i | \(-0.194177\pi\) |
−0.958935 | + | 0.283624i | \(0.908463\pi\) | |||||||
\(572\) | 151326. | − | 663002.i | 0.462510 | − | 2.02639i | ||||
\(573\) | −549498. | + | 264624.i | −1.67362 | + | 0.805973i | ||||
\(574\) | −39795.7 | + | 49902.2i | −0.120785 | + | 0.151459i | ||||
\(575\) | −51656.1 | − | 226320.i | −0.156238 | − | 0.684522i | ||||
\(576\) | 76935.5 | + | 337076.i | 0.231890 | + | 1.01598i | ||||
\(577\) | −205709. | + | 427160.i | −0.617878 | + | 1.28304i | 0.323674 | + | 0.946169i | \(0.395082\pi\) |
−0.941552 | + | 0.336868i | \(0.890632\pi\) | |||||||
\(578\) | −73483.3 | − | 58601.0i | −0.219955 | − | 0.175408i | ||||
\(579\) | −343920. | + | 274267.i | −1.02589 | + | 0.818119i | ||||
\(580\) | 30035.9 | + | 14464.5i | 0.0892862 | + | 0.0429980i | ||||
\(581\) | 195458. | − | 405872.i | 0.579029 | − | 1.20237i | ||||
\(582\) | 134804. | + | 169039.i | 0.397976 | + | 0.499046i | ||||
\(583\) | −268323. | + | 336466.i | −0.789443 | + | 0.989930i | ||||
\(584\) | −15203.5 | − | 7321.62i | −0.0445778 | − | 0.0214675i | ||||
\(585\) | 484114. | − | 110496.i | 1.41461 | − | 0.322875i | ||||
\(586\) | −707.622 | + | 161.510i | −0.00206066 | + | 0.000470332i | ||||
\(587\) | 209105. | + | 166756.i | 0.606861 | + | 0.483955i | 0.878049 | − | 0.478571i | \(-0.158845\pi\) |
−0.271188 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(588\) | 81837.2 | + | 169937.i | 0.236699 | + | 0.491510i | ||||
\(589\) | 316286. | + | 72190.2i | 0.911694 | + | 0.208088i | ||||
\(590\) | −78609.5 | + | 37856.3i | −0.225825 | + | 0.108751i | ||||
\(591\) | −747330. | + | 595975.i | −2.13962 | + | 1.70629i | ||||
\(592\) | 387326. | − | 88404.7i | 1.10518 | − | 0.252251i | ||||
\(593\) | −150358. | + | 119907.i | −0.427580 | + | 0.340984i | −0.813517 | − | 0.581541i | \(-0.802450\pi\) |
0.385936 | + | 0.922525i | \(0.373878\pi\) | |||||||
\(594\) | −54634.3 | + | 239368.i | −0.154843 | + | 0.678413i | ||||
\(595\) | −25289.2 | −0.0714335 | ||||||||
\(596\) | − | 216744.i | − | 0.610175i | ||||||
\(597\) | 180103. | − | 789081.i | 0.505326 | − | 2.21398i | ||||
\(598\) | −111690. | − | 89069.5i | −0.312328 | − | 0.249073i | ||||
\(599\) | −451404. | − | 217385.i | −1.25809 | − | 0.605865i | −0.318422 | − | 0.947949i | \(-0.603153\pi\) |
−0.939669 | + | 0.342084i | \(0.888867\pi\) | |||||||
\(600\) | 220123. | − | 106006.i | 0.611453 | − | 0.294460i | ||||
\(601\) | 171866.i | 0.475819i | 0.971287 | + | 0.237909i | \(0.0764621\pi\) | ||||
−0.971287 | + | 0.237909i | \(0.923538\pi\) | |||||||
\(602\) | −55740.0 | − | 106300.i | −0.153806 | − | 0.293320i | ||||
\(603\) | 890157. | 2.44812 | ||||||||
\(604\) | 156383. | + | 324732.i | 0.428662 | + | 0.890127i | ||||
\(605\) | 119651. | − | 248458.i | 0.326893 | − | 0.678800i | ||||
\(606\) | −63282.7 | + | 79354.0i | −0.172322 | + | 0.216084i | ||||
\(607\) | 474591. | + | 108322.i | 1.28808 | + | 0.293995i | 0.811093 | − | 0.584917i | \(-0.198873\pi\) |
0.476984 | + | 0.878912i | \(0.341730\pi\) | |||||||
\(608\) | −174403. | −0.471788 | ||||||||
\(609\) | − | 151578.i | − | 0.408696i | ||||||
\(610\) | 15932.9 | + | 3636.59i | 0.0428190 | + | 0.00977315i | ||||
\(611\) | 62889.7 | + | 78861.2i | 0.168460 | + | 0.211242i | ||||
\(612\) | 17239.5 | + | 75531.3i | 0.0460280 | + | 0.201662i | ||||
\(613\) | −105723. | − | 132572.i | −0.281350 | − | 0.352802i | 0.620996 | − | 0.783814i | \(-0.286728\pi\) |
−0.902346 | + | 0.431011i | \(0.858157\pi\) | |||||||
\(614\) | −30669.1 | − | 63685.0i | −0.0813512 | − | 0.168927i | ||||
\(615\) | 43970.7 | − | 192648.i | 0.116255 | − | 0.509349i | ||||
\(616\) | 339350. | − | 163422.i | 0.894307 | − | 0.430676i | ||||
\(617\) | −74768.4 | + | 93756.6i | −0.196403 | + | 0.246281i | −0.870275 | − | 0.492567i | \(-0.836059\pi\) |
0.673872 | + | 0.738848i | \(0.264630\pi\) | |||||||
\(618\) | −3515.23 | − | 15401.2i | −0.00920399 | − | 0.0403253i | ||||
\(619\) | −63202.1 | − | 276907.i | −0.164949 | − | 0.722690i | −0.987966 | − | 0.154673i | \(-0.950568\pi\) |
0.823017 | − | 0.568017i | \(-0.192289\pi\) | |||||||
\(620\) | −121522. | + | 252343.i | −0.316134 | + | 0.656460i | ||||
\(621\) | −455158. | − | 362977.i | −1.18026 | − | 0.941230i | ||||
\(622\) | 41775.0 | − | 33314.4i | 0.107978 | − | 0.0861096i | ||||
\(623\) | −674784. | − | 324959.i | −1.73856 | − | 0.837245i | ||||
\(624\) | −318550. | + | 661475.i | −0.818103 | + | 1.69881i | ||||
\(625\) | 61802.8 | + | 77498.2i | 0.158215 | + | 0.198395i | ||||
\(626\) | 50755.7 | − | 63645.6i | 0.129520 | − | 0.162413i | ||||
\(627\) | 582647. | + | 280588.i | 1.48208 | + | 0.713730i | ||||
\(628\) | 128240. | − | 29270.0i | 0.325165 | − | 0.0742169i | ||||
\(629\) | 67442.9 | − | 15393.4i | 0.170465 | − | 0.0389075i | ||||
\(630\) | 102951. | + | 82100.7i | 0.259388 | + | 0.206855i | ||||
\(631\) | −31478.6 | − | 65365.9i | −0.0790599 | − | 0.164170i | 0.857692 | − | 0.514164i | \(-0.171898\pi\) |
−0.936752 | + | 0.349994i | \(0.886183\pi\) | |||||||
\(632\) | −108496. | − | 24763.6i | −0.271632 | − | 0.0619983i | ||||
\(633\) | 357595. | − | 172209.i | 0.892451 | − | 0.429782i | ||||
\(634\) | −156914. | + | 125135.i | −0.390376 | + | 0.311314i | ||||
\(635\) | −219029. | + | 49991.9i | −0.543193 | + | 0.123980i | ||||
\(636\) | 402020. | − | 320600.i | 0.993879 | − | 0.792592i | ||||
\(637\) | −45494.7 | + | 199325.i | −0.112120 | + | 0.491229i | ||||
\(638\) | −37402.0 | −0.0918868 | ||||||||
\(639\) | 116502.i | 0.285319i | ||||||||
\(640\) | 43876.6 | − | 192236.i | 0.107121 | − | 0.469326i | ||||
\(641\) | 50504.8 | + | 40276.2i | 0.122918 | + | 0.0980241i | 0.683020 | − | 0.730400i | \(-0.260666\pi\) |
−0.560101 | + | 0.828424i | \(0.689238\pi\) | |||||||
\(642\) | 333724. | + | 160713.i | 0.809688 | + | 0.389925i | ||||
\(643\) | 172994. | − | 83309.3i | 0.418416 | − | 0.201498i | −0.212817 | − | 0.977092i | \(-0.568264\pi\) |
0.631232 | + | 0.775594i | \(0.282549\pi\) | |||||||
\(644\) | 427602.i | 1.03102i | ||||||||
\(645\) | 298265. | + | 221631.i | 0.716939 | + | 0.532734i | ||||
\(646\) | −8636.28 | −0.0206948 | ||||||||
\(647\) | −149887. | − | 311244.i | −0.358060 | − | 0.743520i | 0.641664 | − | 0.766986i | \(-0.278244\pi\) |
−0.999725 | + | 0.0234658i | \(0.992530\pi\) | |||||||
\(648\) | 74915.6 | − | 155564.i | 0.178411 | − | 0.370475i | ||||
\(649\) | −688900. | + | 863853.i | −1.63556 | + | 2.05093i | ||||
\(650\) | 123619. | + | 28215.3i | 0.292591 | + | 0.0667819i | ||||
\(651\) | 1.27346e6 | 3.00486 | ||||||||
\(652\) | 525574.i | 1.23634i | ||||||||
\(653\) | −238658. | − | 54472.1i | −0.559692 | − | 0.127746i | −0.0666894 | − | 0.997774i | \(-0.521244\pi\) |
−0.493003 | + | 0.870028i | \(0.664101\pi\) | |||||||
\(654\) | 38851.9 | + | 48718.7i | 0.0908357 | + | 0.113904i | ||||
\(655\) | −40194.1 | − | 176102.i | −0.0936871 | − | 0.410470i | ||||
\(656\) | 119662. | + | 150051.i | 0.278066 | + | 0.348683i | ||||
\(657\) | −32415.1 | − | 67310.7i | −0.0750960 | − | 0.155938i | ||||
\(658\) | −5952.00 | + | 26077.4i | −0.0137471 | + | 0.0602300i | ||||
\(659\) | 514617. | − | 247826.i | 1.18499 | − | 0.570659i | 0.265626 | − | 0.964076i | \(-0.414421\pi\) |
0.919360 | + | 0.393417i | \(0.128707\pi\) | |||||||
\(660\) | −348096. | + | 436499.i | −0.799119 | + | 1.00206i | ||||
\(661\) | 26060.2 | + | 114177.i | 0.0596450 | + | 0.261322i | 0.995955 | − | 0.0898525i | \(-0.0286396\pi\) |
−0.936310 | + | 0.351174i | \(0.885782\pi\) | |||||||
\(662\) | 5458.45 | + | 23915.0i | 0.0124553 | + | 0.0545701i | ||||
\(663\) | −55467.3 | + | 115179.i | −0.126186 | + | 0.262027i | ||||
\(664\) | 216876. | + | 172953.i | 0.491899 | + | 0.392276i | ||||
\(665\) | 129539. | − | 103304.i | 0.292925 | − | 0.233600i | ||||
\(666\) | −324530. | − | 156286.i | −0.731656 | − | 0.352347i | ||||
\(667\) | 38478.9 | − | 79902.3i | 0.0864911 | − | 0.179601i | ||||
\(668\) | −330987. | − | 415044.i | −0.741751 | − | 0.930126i | ||||
\(669\) | −609165. | + | 763869.i | −1.36108 | + | 1.70674i | ||||
\(670\) | −77183.2 | − | 37169.5i | −0.171939 | − | 0.0828012i | ||||
\(671\) | 201770. | − | 46052.7i | 0.448138 | − | 0.102285i | ||||
\(672\) | −667430. | + | 152337.i | −1.47798 | + | 0.337338i | ||||
\(673\) | −569913. | − | 454490.i | −1.25828 | − | 1.00345i | −0.999294 | − | 0.0375665i | \(-0.988039\pi\) |
−0.258989 | − | 0.965880i | \(-0.583389\pi\) | |||||||
\(674\) | 17419.2 | + | 36171.4i | 0.0383451 | + | 0.0796243i | ||||
\(675\) | 503775. | + | 114983.i | 1.10568 | + | 0.252364i | ||||
\(676\) | −415329. | + | 200012.i | −0.908865 | + | 0.437686i | ||||
\(677\) | −385340. | + | 307298.i | −0.840749 | + | 0.670475i | −0.946070 | − | 0.323963i | \(-0.894985\pi\) |
0.105320 | + | 0.994438i | \(0.466413\pi\) | |||||||
\(678\) | 103549. | − | 23634.3i | 0.225260 | − | 0.0514142i | ||||
\(679\) | 548452. | − | 437376.i | 1.18960 | − | 0.948671i | ||||
\(680\) | 3465.18 | − | 15182.0i | 0.00749390 | − | 0.0328329i | ||||
\(681\) | −1.41110e6 | −3.04273 | ||||||||
\(682\) | − | 314228.i | − | 0.675580i | ||||||
\(683\) | −79597.7 | + | 348740.i | −0.170631 | + | 0.747585i | 0.815108 | + | 0.579309i | \(0.196677\pi\) |
−0.985740 | + | 0.168277i | \(0.946180\pi\) | |||||||
\(684\) | −396843. | − | 316472.i | −0.848216 | − | 0.676430i | ||||
\(685\) | −246430. | − | 118674.i | −0.525185 | − | 0.252916i | ||||
\(686\) | 91578.5 | − | 44101.9i | 0.194601 | − | 0.0937150i | ||||
\(687\) | 383374.i | 0.812285i | ||||||||
\(688\) | −348916. | + | 92277.0i | −0.737130 | + | 0.194947i | ||||
\(689\) | 557375. | 1.17411 | ||||||||
\(690\) | 50886.4 | + | 105667.i | 0.106882 | + | 0.221942i | ||||
\(691\) | 34238.3 | − | 71096.5i | 0.0717060 | − | 0.148899i | −0.862035 | − | 0.506849i | \(-0.830810\pi\) |
0.933741 | + | 0.357950i | \(0.116524\pi\) | |||||||
\(692\) | 242097. | − | 303580.i | 0.505566 | − | 0.633960i | ||||
\(693\) | 1.62574e6 | + | 371064.i | 3.38520 | + | 0.772650i | ||||
\(694\) | 36317.9 | 0.0754052 | ||||||||
\(695\) | − | 11608.5i | − | 0.0240328i | ||||||
\(696\) | 90997.0 | + | 20769.5i | 0.187849 | + | 0.0428753i | ||||
\(697\) | 20836.0 | + | 26127.5i | 0.0428893 | + | 0.0537814i | ||||
\(698\) | −8055.04 | − | 35291.5i | −0.0165332 | − | 0.0724367i | ||||
\(699\) | −477573. | − | 598857.i | −0.977429 | − | 1.22566i | ||||
\(700\) | −164675. | − | 341951.i | −0.336071 | − | 0.697859i | ||||
\(701\) | 154827. | − | 678342.i | 0.315073 | − | 1.38042i | −0.531007 | − | 0.847367i | \(-0.678186\pi\) |
0.846080 | − | 0.533056i | \(-0.178957\pi\) | |||||||
\(702\) | 286499. | − | 137971.i | 0.581365 | − | 0.279970i | ||||
\(703\) | −282582. | + | 354347.i | −0.571786 | + | 0.716997i | ||||
\(704\) | −93763.7 | − | 410805.i | −0.189186 | − | 0.828878i | ||||
\(705\) | −18426.8 | − | 80732.9i | −0.0370741 | − | 0.162432i | ||||
\(706\) | −38600.9 | + | 80155.6i | −0.0774441 | + | 0.160814i | ||||
\(707\) | 257467. | + | 205323.i | 0.515089 | + | 0.410770i | ||||
\(708\) | 1.03216e6 | − | 823118.i | 2.05911 | − | 1.64208i | ||||
\(709\) | −97775.0 | − | 47086.0i | −0.194507 | − | 0.0936697i | 0.334095 | − | 0.942539i | \(-0.391569\pi\) |
−0.528602 | + | 0.848870i | \(0.677284\pi\) | |||||||
\(710\) | 4864.66 | − | 10101.6i | 0.00965019 | − | 0.0200388i | ||||
\(711\) | −307194. | − | 385209.i | −0.607678 | − | 0.762004i | ||||
\(712\) | 287544. | − | 360568.i | 0.567210 | − | 0.711259i | ||||
\(713\) | 671290. | + | 323276.i | 1.32048 | + | 0.635909i | ||||
\(714\) | −33050.5 | + | 7543.56i | −0.0648309 | + | 0.0147972i | ||||
\(715\) | −590005. | + | 134665.i | −1.15410 | + | 0.263416i | ||||
\(716\) | 256232. | + | 204338.i | 0.499813 | + | 0.398587i | ||||
\(717\) | −471127. | − | 978305.i | −0.916431 | − | 1.90299i | ||||
\(718\) | −81018.0 | − | 18491.8i | −0.157157 | − | 0.0358700i | ||||
\(719\) | −206375. | + | 99385.2i | −0.399209 | + | 0.192249i | −0.622706 | − | 0.782456i | \(-0.713967\pi\) |
0.223497 | + | 0.974705i | \(0.428253\pi\) | |||||||
\(720\) | 309563. | − | 246868.i | 0.597151 | − | 0.476212i | ||||
\(721\) | −49969.8 | + | 11405.3i | −0.0961251 | + | 0.0219399i | ||||
\(722\) | −72029.3 | + | 57441.5i | −0.138177 | + | 0.110192i | ||||
\(723\) | 133967. | − | 586947.i | 0.256283 | − | 1.12285i | ||||
\(724\) | −408423. | −0.779171 | ||||||||
\(725\) | 78716.2i | 0.149757i | ||||||||
\(726\) | 82259.0 | − | 360400.i | 0.156067 | − | 0.683773i | ||||
\(727\) | 632880. | + | 504705.i | 1.19744 | + | 0.954925i | 0.999679 | − | 0.0253262i | \(-0.00806244\pi\) |
0.197758 | + | 0.980251i | \(0.436634\pi\) | |||||||
\(728\) | −439508. | − | 211656.i | −0.829285 | − | 0.399363i | ||||
\(729\) | −587746. | + | 283044.i | −1.10595 | + | 0.532596i | ||||
\(730\) | 7189.87i | 0.0134920i | ||||||||
\(731\) | −60754.7 | + | 16067.7i | −0.113696 | + | 0.0300689i | ||||
\(732\) | −247281. | −0.461497 | ||||||||
\(733\) | 404049. | + | 839015.i | 0.752013 | + | 1.56157i | 0.825582 | + | 0.564282i | \(0.190847\pi\) |
−0.0735690 | + | 0.997290i | \(0.523439\pi\) | |||||||
\(734\) | 89570.5 | − | 185995.i | 0.166254 | − | 0.345231i | ||||
\(735\) | 104652. | − | 131229.i | 0.193719 | − | 0.242916i | ||||
\(736\) | −390499. | − | 89128.9i | −0.720883 | − | 0.164537i | ||||
\(737\) | −1.08486e6 | −1.99728 | ||||||||
\(738\) | − | 174007.i | − | 0.319487i | ||||||
\(739\) | 420928. | + | 96074.2i | 0.770760 | + | 0.175921i | 0.589778 | − | 0.807565i | \(-0.299215\pi\) |
0.180982 | + | 0.983486i | \(0.442072\pi\) | |||||||
\(740\) | −243960. | − | 305916.i | −0.445508 | − | 0.558649i | ||||
\(741\) | −186374. | − | 816558.i | −0.339429 | − | 1.48714i | ||||
\(742\) | 92155.0 | + | 115559.i | 0.167383 | + | 0.209891i | ||||
\(743\) | 23074.3 | + | 47914.3i | 0.0417976 | + | 0.0867935i | 0.920822 | − | 0.389983i | \(-0.127519\pi\) |
−0.879024 | + | 0.476777i | \(0.841805\pi\) | |||||||
\(744\) | −174492. | + | 764501.i | −0.315232 | + | 1.38112i | ||||
\(745\) | −173779. | + | 83687.5i | −0.313101 | + | 0.150782i | ||||
\(746\) | −121416. | + | 152251.i | −0.218172 | + | 0.273579i | ||||
\(747\) | 273281. | + | 1.19732e6i | 0.489743 | + | 2.14571i | ||||
\(748\) | −21010.3 | − | 92052.3i | −0.0375517 | − | 0.164525i | ||||
\(749\) | 521439. | − | 1.08278e6i | 0.929480 | − | 1.93008i | ||||
\(750\) | −193448. | − | 154269.i | −0.343907 | − | 0.274257i | ||||
\(751\) | 632528. | − | 504424.i | 1.12150 | − | 0.894368i | 0.126279 | − | 0.991995i | \(-0.459697\pi\) |
0.995223 | + | 0.0976270i | \(0.0311252\pi\) | |||||||
\(752\) | 72463.7 | + | 34896.7i | 0.128140 | + | 0.0617090i | ||||
\(753\) | −368493. | + | 765183.i | −0.649889 | + | 1.34951i | ||||
\(754\) | 30202.5 | + | 37872.7i | 0.0531251 | + | 0.0666168i | ||||
\(755\) | 199980. | − | 250767.i | 0.350826 | − | 0.439922i | ||||
\(756\) | −857556. | − | 412977.i | −1.50044 | − | 0.722574i | ||||
\(757\) | −550142. | + | 125566.i | −0.960027 | + | 0.219120i | −0.673694 | − | 0.739010i | \(-0.735293\pi\) |
−0.286333 | + | 0.958130i | \(0.592436\pi\) | |||||||
\(758\) | −106141. | + | 24226.0i | −0.184733 | + | 0.0421642i | ||||
\(759\) | 1.16119e6 | + | 926016.i | 2.01567 | + | 1.60744i | ||||
\(760\) | 44266.9 | + | 91921.2i | 0.0766394 | + | 0.159143i | ||||
\(761\) | 31454.2 | + | 7179.22i | 0.0543137 | + | 0.0123968i | 0.249591 | − | 0.968351i | \(-0.419704\pi\) |
−0.195278 | + | 0.980748i | \(0.562561\pi\) | |||||||
\(762\) | −271337. | + | 130669.i | −0.467303 | + | 0.225041i | ||||
\(763\) | 158070. | − | 126056.i | 0.271518 | − | 0.216529i | ||||
\(764\) | −568783. | + | 129821.i | −0.974450 | + | 0.222412i | ||||
\(765\) | 53902.4 | − | 42985.8i | 0.0921055 | − | 0.0734517i | ||||
\(766\) | −37970.8 | + | 166361.i | −0.0647131 | + | 0.283527i | ||||
\(767\) | 1.43102e6 | 2.43251 | ||||||||
\(768\) | 283748.i | 0.481073i | ||||||||
\(769\) | 105464. | − | 462067.i | 0.178341 | − | 0.781361i | −0.804056 | − | 0.594554i | \(-0.797329\pi\) |
0.982397 | − | 0.186808i | \(-0.0598141\pi\) | |||||||
\(770\) | −125470. | − | 100059.i | −0.211620 | − | 0.168761i | ||||
\(771\) | −453603. | − | 218444.i | −0.763075 | − | 0.367478i | ||||
\(772\) | −379116. | + | 182572.i | −0.636117 | + | 0.306338i | ||||
\(773\) | 341880.i | 0.572157i | 0.958206 | + | 0.286078i | \(0.0923518\pi\) | ||||
−0.958206 | + | 0.286078i | \(0.907648\pi\) | |||||||
\(774\) | 299492. | + | 131828.i | 0.499923 | + | 0.220052i | ||||
\(775\) | −661326. | −1.10106 | ||||||||
\(776\) | 187421. | + | 389184.i | 0.311240 | + | 0.646296i | ||||
\(777\) | −771911. | + | 1.60289e6i | −1.27857 | + | 2.65498i | ||||
\(778\) | 120617. | − | 151249.i | 0.199273 | − | 0.249880i | ||||
\(779\) | −213456. | − | 48719.9i | −0.351750 | − | 0.0802845i | ||||
\(780\) | 723084. | 1.18850 | ||||||||
\(781\) | − | 141984.i | − | 0.232776i | ||||||
\(782\) | −19337.2 | − | 4413.58i | −0.0316213 | − | 0.00721734i | ||||
\(783\) | 123081. | + | 154339.i | 0.200756 | + | 0.251740i | ||||
\(784\) | 36276.2 | + | 158936.i | 0.0590187 | + | 0.258578i | ||||
\(785\) | −72982.9 | − | 91517.7i | −0.118436 | − | 0.148513i | ||||
\(786\) | −105059. | − | 218158.i | −0.170055 | − | 0.353123i | ||||
\(787\) | 176656. | − | 773983.i | 0.285220 | − | 1.24963i | −0.605782 | − | 0.795631i | \(-0.707139\pi\) |
0.891002 | − | 0.454000i | \(-0.150003\pi\) | |||||||
\(788\) | −823809. | + | 396725.i | −1.32670 | + | 0.638907i | ||||
\(789\) | −229759. | + | 288109.i | −0.369079 | + | 0.462810i | ||||
\(790\) | 10551.2 | + | 46227.7i | 0.0169062 | + | 0.0740710i | ||||
\(791\) | −76682.2 | − | 335967.i | −0.122558 | − | 0.536962i | ||||
\(792\) | −445524. | + | 925140.i | −0.710266 | + | 1.47488i | ||||
\(793\) | −209564. | − | 167122.i | −0.333250 | − | 0.265758i | ||||
\(794\) | −8054.03 | + | 6422.87i | −0.0127753 | + | 0.0101880i | ||||
\(795\) | −412273. | − | 198540.i | −0.652305 | − | 0.314134i | ||||
\(796\) | 335923. | − | 697552.i | 0.530169 | − | 1.10091i | ||||
\(797\) | 143017. | + | 179338.i | 0.225150 | + | 0.282329i | 0.881557 | − | 0.472078i | \(-0.156496\pi\) |
−0.656407 | + | 0.754407i | \(0.727925\pi\) | |||||||
\(798\) | 138480. | − | 173648.i | 0.217460 | − | 0.272687i | ||||
\(799\) | 12617.7 | + | 6076.36i | 0.0197645 | + | 0.00951810i | ||||
\(800\) | 346605. | − | 79110.3i | 0.541570 | − | 0.123610i | ||||
\(801\) | 1.99061e6 | − | 454345.i | 3.10257 | − | 0.708142i | ||||
\(802\) | 106505. | + | 84935.2i | 0.165586 | + | 0.132050i | ||||
\(803\) | 39505.3 | + | 82033.6i | 0.0612667 | + | 0.127222i | ||||
\(804\) | 1.26373e6 | + | 288437.i | 1.95497 | + | 0.446210i | ||||
\(805\) | 342839. | − | 165103.i | 0.529052 | − | 0.254778i | ||||
\(806\) | −318183. | + | 253743.i | −0.489787 | + | 0.390592i | ||||
\(807\) | 1.39031e6 | − | 317329.i | 2.13483 | − | 0.487262i | ||||
\(808\) | −158541. | + | 126432.i | −0.242839 | + | 0.193657i | ||||
\(809\) | −133692. | + | 585742.i | −0.204272 | + | 0.894972i | 0.764028 | + | 0.645183i | \(0.223219\pi\) |
−0.968300 | + | 0.249790i | \(0.919638\pi\) | |||||||
\(810\) | −73567.5 | −0.112128 | ||||||||
\(811\) | 1.26190e6i | 1.91859i | 0.282400 | + | 0.959297i | \(0.408869\pi\) | ||||
−0.282400 | + | 0.959297i | \(0.591131\pi\) | |||||||
\(812\) | 32264.4 | − | 141360.i | 0.0489341 | − | 0.214394i | ||||
\(813\) | 808763. | + | 644967.i | 1.22360 | + | 0.975790i | ||||
\(814\) | 395515. | + | 190470.i | 0.596918 | + | 0.287460i | ||||
\(815\) | 421390. | − | 202931.i | 0.634409 | − | 0.305515i | ||||
\(816\) | 101935.i | 0.153089i | ||||||||
\(817\) | 245569. | − | 330480.i | 0.367899 | − | 0.495109i | ||||
\(818\) | 168013. | 0.251093 | ||||||||
\(819\) | −937067. | − | 1.94584e6i | −1.39702 | − | 2.90094i | ||||
\(820\) | 82013.2 | − | 170302.i | 0.121971 | − | 0.253275i | ||||
\(821\) | −27330.5 | + | 34271.3i | −0.0405472 | + | 0.0508445i | −0.801692 | − | 0.597738i | \(-0.796066\pi\) |
0.761144 | + | 0.648582i | \(0.224638\pi\) | |||||||
\(822\) | −357459. | − | 81587.6i | −0.529032 | − | 0.120748i | ||||
\(823\) | −162705. | −0.240216 | −0.120108 | − | 0.992761i | \(-0.538324\pi\) | ||||
−0.120108 | + | 0.992761i | \(0.538324\pi\) | |||||||
\(824\) | − | 31561.2i | − | 0.0464836i | ||||||
\(825\) | −1.28522e6 | − | 293342.i | −1.88829 | − | 0.430990i | ||||
\(826\) | 236601. | + | 296688.i | 0.346782 | + | 0.434851i | ||||
\(827\) | 275858. | + | 1.20861e6i | 0.403344 | + | 1.76716i | 0.613700 | + | 0.789539i | \(0.289680\pi\) |
−0.210356 | + | 0.977625i | \(0.567462\pi\) | |||||||
\(828\) | −726823. | − | 911407.i | −1.06015 | − | 1.32939i | ||||
\(829\) | −276961. | − | 575115.i | −0.403004 | − | 0.836847i | −0.999416 | − | 0.0341681i | \(-0.989122\pi\) |
0.596412 | − | 0.802678i | \(-0.296592\pi\) | |||||||
\(830\) | 26300.0 | − | 115228.i | 0.0381769 | − | 0.167264i | ||||
\(831\) | 178712. | − | 86063.4i | 0.258793 | − | 0.124628i | ||||
\(832\) | −340261. | + | 426673.i | −0.491547 | + | 0.616381i | ||||
\(833\) | 6316.57 | + | 27674.7i | 0.00910314 | + | 0.0398835i | ||||
\(834\) | −3462.70 | − | 15171.1i | −0.00497832 | − | 0.0218115i | ||||
\(835\) | −204973. | + | 425630.i | −0.293983 | + | 0.610463i | ||||
\(836\) | 483645. | + | 385694.i | 0.692013 | + | 0.551862i | ||||
\(837\) | −1.29666e6 | + | 1.03405e6i | −1.85087 | + | 1.47602i | ||||
\(838\) | −99538.0 | − | 47935.0i | −0.141743 | − | 0.0682597i | ||||
\(839\) | 307723. | − | 638993.i | 0.437155 | − | 0.907762i | −0.559714 | − | 0.828686i | \(-0.689089\pi\) |
0.996869 | − | 0.0790756i | \(-0.0251969\pi\) | |||||||
\(840\) | 249698. | + | 313111.i | 0.353880 | + | 0.443751i | ||||
\(841\) | 422233. | − | 529463.i | 0.596980 | − | 0.748590i | ||||
\(842\) | 284741. | + | 137124.i | 0.401630 | + | 0.193415i | ||||
\(843\) | −385759. | + | 88047.0i | −0.542826 | + | 0.123897i | ||||
\(844\) | 370145. | − | 84483.3i | 0.519622 | − | 0.118600i | ||||
\(845\) | 320728. | + | 255772.i | 0.449183 | + | 0.358212i | ||||
\(846\) | −31639.2 | − | 65699.4i | −0.0442063 | − | 0.0917954i | ||||
\(847\) | −1.16933e6 | − | 266892.i | −1.62994 | − | 0.372022i | ||||
\(848\) | 400422. | − | 192833.i | 0.556834 | − | 0.268157i | ||||
\(849\) | 448872. | − | 357963.i | 0.622740 | − | 0.496618i | ||||
\(850\) | 17163.6 | − | 3917.47i | 0.0237558 | − | 0.00542210i | ||||
\(851\) | −813807. | + | 648990.i | −1.12373 | + | 0.896146i | ||||
\(852\) | −37750.0 | + | 165394.i | −0.0520042 | + | 0.227845i | ||||
\(853\) | 464727. | 0.638705 | 0.319352 | − | 0.947636i | \(-0.396535\pi\) | ||||
0.319352 | + | 0.947636i | \(0.396535\pi\) | |||||||
\(854\) | − | 71079.7i | − | 0.0974608i | ||||||
\(855\) | −100512. | + | 440371.i | −0.137494 | + | 0.602402i | ||||
\(856\) | 578579. | + | 461401.i | 0.789615 | + | 0.629697i | ||||
\(857\) | −653636. | − | 314774.i | −0.889968 | − | 0.428586i | −0.0677125 | − | 0.997705i | \(-0.521570\pi\) |
−0.822255 | + | 0.569119i | \(0.807284\pi\) | |||||||
\(858\) | −730908. | + | 351987.i | −0.992860 | + | 0.478136i | ||||
\(859\) | − | 1.45027e6i | − | 1.96545i | −0.185073 | − | 0.982725i | \(-0.559252\pi\) | ||
0.185073 | − | 0.982725i | \(-0.440748\pi\) | |||||||
\(860\) | 230982. | + | 270178.i | 0.312307 | + | 0.365303i | ||||
\(861\) | −859439. | −1.15933 | ||||||||
\(862\) | −148028. | − | 307382.i | −0.199218 | − | 0.413680i | ||||
\(863\) | 348155. | − | 722952.i | 0.467468 | − | 0.970707i | −0.525329 | − | 0.850899i | \(-0.676058\pi\) |
0.992797 | − | 0.119808i | \(-0.0382278\pi\) | |||||||
\(864\) | 555892. | − | 697066.i | 0.744668 | − | 0.933784i | ||||
\(865\) | −336879. | − | 76890.4i | −0.450238 | − | 0.102764i | ||||
\(866\) | 76219.3 | 0.101632 | ||||||||
\(867\) | − | 1.26556e6i | − | 1.68362i | ||||||
\(868\) | 1.18762e6 | + | 271066.i | 1.57629 | + | 0.359779i | ||||
\(869\) | 374387. | + | 469466.i | 0.495771 | + | 0.621677i | ||||
\(870\) | −8849.37 | − | 38771.6i | −0.0116916 | − | 0.0512242i | ||||
\(871\) | 876037. | + | 1.09852e6i | 1.15474 | + | 1.44800i | ||||
\(872\) | 54016.7 | + | 112167.i | 0.0710387 | + | 0.147513i | ||||
\(873\) | −425555. | + | 1.86448e6i | −0.558377 | + | 2.44641i | ||||
\(874\) | 117080. | − | 56382.5i | 0.153270 | − | 0.0738111i | ||||
\(875\) | −500532. | + | 627648.i | −0.653757 | + | 0.819785i | ||||
\(876\) | −24208.0 | − | 106062.i | −0.0315465 | − | 0.138214i | ||||
\(877\) | −91224.6 | − | 399681.i | −0.118608 | − | 0.519654i | −0.998971 | − | 0.0453542i | \(-0.985558\pi\) |
0.880363 | − | 0.474300i | \(-0.157299\pi\) | |||||||
\(878\) | 139320. | − | 289301.i | 0.180727 | − | 0.375284i | ||||
\(879\) | −7641.00 | − | 6093.49i | −0.00988946 | − | 0.00788658i | ||||
\(880\) | −377274. | + | 300866.i | −0.487182 | + | 0.388515i | ||||
\(881\) | 598573. | + | 288257.i | 0.771196 | + | 0.371389i | 0.777737 | − | 0.628590i | \(-0.216368\pi\) |
−0.00654043 | + | 0.999979i | \(0.502082\pi\) | |||||||
\(882\) | 64130.6 | − | 133169.i | 0.0824381 | − | 0.171185i | ||||
\(883\) | −239651. | − | 300513.i | −0.307368 | − | 0.385427i | 0.604024 | − | 0.796966i | \(-0.293563\pi\) |
−0.911392 | + | 0.411539i | \(0.864992\pi\) | |||||||
\(884\) | −76244.8 | + | 95608.0i | −0.0975677 | + | 0.122346i | ||||
\(885\) | −1.05848e6 | − | 509738.i | −1.35144 | − | 0.650819i | ||||
\(886\) | −44462.6 | + | 10148.3i | −0.0566406 | + | 0.0129278i | ||||
\(887\) | 431550. | − | 98498.5i | 0.548509 | − | 0.125194i | 0.0607196 | − | 0.998155i | \(-0.480660\pi\) |
0.487790 | + | 0.872961i | \(0.337803\pi\) | |||||||
\(888\) | −856498. | − | 683035.i | −1.08618 | − | 0.866197i | ||||
\(889\) | 423960. | + | 880361.i | 0.536440 | + | 1.11393i | ||||
\(890\) | −191573. | − | 43725.2i | −0.241854 | − | 0.0552017i | ||||
\(891\) | −839376. | + | 404222.i | −1.05731 | + | 0.509172i | ||||
\(892\) | −730696. | + | 582710.i | −0.918347 | + | 0.732357i | ||||
\(893\) | −89452.8 | + | 20417.0i | −0.112174 | + | 0.0256029i | ||||
\(894\) | −202148. | + | 161208.i | −0.252927 | + | 0.201703i | ||||
\(895\) | 64898.1 | − | 284337.i | 0.0810188 | − | 0.354967i | ||||
\(896\) | −857599. | −1.06824 | ||||||||
\(897\) | − | 1.92357e6i | − | 2.39069i | ||||||
\(898\) | −83091.5 | + | 364048.i | −0.103040 | + | 0.451446i | ||||
\(899\) | −197527. | − | 157523.i | −0.244404 | − | 0.194905i | ||||
\(900\) | 932231. | + | 448939.i | 1.15090 | + | 0.554245i | ||||
\(901\) | 69723.2 | − | 33576.9i | 0.0858870 | − | 0.0413610i | ||||
\(902\) | 212068.i | 0.260652i | ||||||||
\(903\) | 651111. | − | 1.47922e6i | 0.798509 | − | 1.81409i | ||||
\(904\) | 212199. | 0.259661 | ||||||||
\(905\) | 157697. | + | 327462.i | 0.192543 | + | 0.399819i | ||||
\(906\) | 186552. | − | 387379.i | 0.227271 | − | 0.471932i | ||||
\(907\) | 266420. | − | 334080.i | 0.323856 | − | 0.406103i | −0.593075 | − | 0.805147i | \(-0.702086\pi\) |
0.916932 | + | 0.399044i | \(0.130658\pi\) | |||||||
\(908\) | −1.31598e6 | − | 300363.i | −1.59616 | − | 0.364313i | ||||
\(909\) | −897775. | −1.08653 | ||||||||
\(910\) | 207847.i | 0.250993i | ||||||||
\(911\) | −443226. | − | 101163.i | −0.534058 | − | 0.121895i | −0.0530174 | − | 0.998594i | \(-0.516884\pi\) |
−0.481041 | + | 0.876698i | \(0.659741\pi\) | |||||||
\(912\) | −416394. | − | 522142.i | −0.500628 | − | 0.627767i | ||||
\(913\) | −333056. | − | 1.45921e6i | −0.399554 | − | 1.75056i | ||||
\(914\) | −141065. | − | 176890.i | −0.168860 | − | 0.211743i | ||||
\(915\) | 95478.4 | + | 198263.i | 0.114041 | + | 0.236810i | ||||
\(916\) | −81603.9 | + | 357530.i | −0.0972568 | + | 0.426110i | ||||
\(917\) | −707821. | + | 340869.i | −0.841753 | + | 0.405367i | ||||
\(918\) | 27527.2 | − | 34518.1i | 0.0326646 | − | 0.0409601i | ||||
\(919\) | 63261.7 | + | 277167.i | 0.0749048 | + | 0.328179i | 0.998472 | − | 0.0552568i | \(-0.0175978\pi\) |
−0.923567 | + | 0.383436i | \(0.874741\pi\) | |||||||
\(920\) | 52139.9 | + | 228440.i | 0.0616020 | + | 0.269896i | ||||
\(921\) | 412961. | − | 857522.i | 0.486843 | − | 1.01094i | ||||
\(922\) | −33537.8 | − | 26745.5i | −0.0394523 | − | 0.0314622i | ||||
\(923\) | −143771. | + | 114654.i | −0.168760 | + | 0.134581i | ||||
\(924\) | 2.18777e6 | + | 1.05358e6i | 2.56247 | + | 1.23402i | ||||
\(925\) | 400864. | − | 832402.i | 0.468504 | − | 0.972858i | ||||
\(926\) | −56374.9 | − | 70691.9i | −0.0657452 | − | 0.0824418i | ||||
\(927\) | 87121.2 | − | 109246.i | 0.101383 | − | 0.127130i | ||||
\(928\) | 122369. | + | 58929.7i | 0.142094 | + | 0.0684287i | ||||
\(929\) | 373829. | − | 85324.1i | 0.433154 | − | 0.0988645i | −0.000384025 | − | 1.00000i | \(-0.500122\pi\) |
0.433538 | + | 0.901135i | \(0.357265\pi\) | |||||||
\(930\) | 325735. | − | 74347.0i | 0.376616 | − | 0.0859602i | ||||
\(931\) | −145403. | − | 115955.i | −0.167755 | − | 0.133780i | ||||
\(932\) | −317908. | − | 660143.i | −0.365990 | − | 0.759987i | ||||
\(933\) | 701429. | + | 160097.i | 0.805787 | + | 0.183916i | ||||
\(934\) | 316872. | − | 152598.i | 0.363237 | − | 0.174926i | ||||
\(935\) | −65692.6 | + | 52388.1i | −0.0751438 | + | 0.0599252i | ||||
\(936\) | 1.29655e6 | − | 295929.i | 1.47992 | − | 0.337781i | ||||
\(937\) | 515138. | − | 410809.i | 0.586739 | − | 0.467909i | −0.284562 | − | 0.958658i | \(-0.591848\pi\) |
0.871301 | + | 0.490749i | \(0.163277\pi\) | |||||||
\(938\) | −82909.9 | + | 363252.i | −0.0942325 | + | 0.412859i | ||||
\(939\) | 1.09613e6 | 1.24317 | ||||||||
\(940\) | − | 79212.9i | − | 0.0896479i | ||||||
\(941\) | −203162. | + | 890113.i | −0.229437 | + | 1.00523i | 0.720663 | + | 0.693286i | \(0.243838\pi\) |
−0.950100 | + | 0.311945i | \(0.899019\pi\) | |||||||
\(942\) | −122680. | − | 97834.3i | −0.138253 | − | 0.110253i | ||||
\(943\) | −453043. | − | 218174.i | −0.509467 | − | 0.245346i | ||||
\(944\) | 1.02805e6 | − | 495085.i | 1.15364 | − | 0.555566i | ||||
\(945\) | 847020.i | 0.948484i | ||||||||
\(946\) | −365000. | − | 160662.i | −0.407860 | − | 0.179528i | ||||
\(947\) | −725516. | −0.808997 | −0.404499 | − | 0.914539i | \(-0.632554\pi\) | ||||
−0.404499 | + | 0.914539i | \(0.632554\pi\) | |||||||
\(948\) | −311294. | − | 646409.i | −0.346381 | − | 0.719268i | ||||
\(949\) | 51165.1 | − | 106246.i | 0.0568122 | − | 0.117972i | ||||
\(950\) | −71914.3 | + | 90177.7i | −0.0796834 | + | 0.0999198i | ||||
\(951\) | −2.63469e6 | − | 601350.i | −2.91318 | − | 0.664915i | ||||
\(952\) | −67729.4 | −0.0747314 | ||||||||
\(953\) | 741988.i | 0.816980i | 0.912763 | + | 0.408490i | \(0.133944\pi\) | ||||
−0.912763 | + | 0.408490i | \(0.866056\pi\) | |||||||
\(954\) | −392845. | − | 89664.4i | −0.431643 | − | 0.0985197i | ||||
\(955\) | 323701. | + | 405908.i | 0.354926 | + | 0.445063i | ||||
\(956\) | −231128. | − | 1.01264e6i | −0.252893 | − | 1.10800i | ||||
\(957\) | −314002. | − | 393746.i | −0.342853 | − | 0.429924i | ||||
\(958\) | 163099. | + | 338680.i | 0.177714 | + | 0.369027i | ||||
\(959\) | −264714. | + | 1.15979e6i | −0.287832 | + | 1.26108i | ||||
\(960\) | 403664. | − | 194394.i | 0.438004 | − | 0.210932i | ||||
\(961\) | 747604. | − | 937466.i | 0.809515 | − | 1.01510i | ||||
\(962\) | −126515. | − | 554300.i | −0.136708 | − | 0.598955i | ||||
\(963\) | 729056. | + | 3.19420e6i | 0.786155 | + | 3.44437i | ||||
\(964\) | 249872. | − | 518864.i | 0.268883 | − | 0.558341i | ||||
\(965\) | 292763. | + | 233470.i | 0.314385 | + | 0.250713i | ||||
\(966\) | 398807. | − | 318038.i | 0.427375 | − | 0.340820i | ||||
\(967\) | 446319. | + | 214936.i | 0.477301 | + | 0.229856i | 0.657036 | − | 0.753859i | \(-0.271810\pi\) |
−0.179735 | + | 0.983715i | \(0.557524\pi\) | |||||||
\(968\) | 320448. | − | 665417.i | 0.341985 | − | 0.710139i | ||||
\(969\) | −72504.3 | − | 90917.6i | −0.0772176 | − | 0.0968278i | ||||
\(970\) | 114752. | − | 143895.i | 0.121960 | − | 0.152933i | ||||
\(971\) | −313328. | − | 150891.i | −0.332323 | − | 0.160038i | 0.260280 | − | 0.965533i | \(-0.416185\pi\) |
−0.592603 | + | 0.805495i | \(0.701900\pi\) | |||||||
\(972\) | −236035. | + | 53873.4i | −0.249830 | + | 0.0570220i | ||||
\(973\) | −49223.1 | + | 11234.9i | −0.0519928 | + | 0.0118670i | ||||
\(974\) | 264115. | + | 210625.i | 0.278404 | + | 0.222019i | ||||
\(975\) | 740791. | + | 1.53827e6i | 0.779268 | + | 1.61817i | ||||
\(976\) | −208371. | − | 47559.3i | −0.218744 | − | 0.0499270i | ||||
\(977\) | 171495. | − | 82587.6i | 0.179665 | − | 0.0865219i | −0.341889 | − | 0.939740i | \(-0.611067\pi\) |
0.521554 | + | 0.853218i | \(0.325353\pi\) | |||||||
\(978\) | 490182. | − | 390907.i | 0.512483 | − | 0.408692i | ||||
\(979\) | −2.42602e6 | + | 553724.i | −2.53122 | + | 0.577734i | ||||
\(980\) | 125530. | − | 100107.i | 0.130706 | − | 0.104235i | ||||
\(981\) | −122649. | + | 537362.i | −0.127446 | + | 0.558379i | ||||
\(982\) | 44723.8 | 0.0463784 | ||||||||
\(983\) | 1.58916e6i | 1.64460i | 0.569051 | + | 0.822302i | \(0.307311\pi\) | ||||
−0.569051 | + | 0.822302i | \(0.692689\pi\) | |||||||
\(984\) | 117762. | − | 515949.i | 0.121623 | − | 0.532864i | ||||
\(985\) | 636166. | + | 507326.i | 0.655689 | + | 0.522895i | ||||
\(986\) | 6059.59 | + | 2918.15i | 0.00623289 | + | 0.00300160i | ||||
\(987\) | −324497. | + | 156269.i | −0.333101 | + | 0.160413i | ||||
\(988\) | − | 801184.i | − | 0.820764i | ||||||
\(989\) | 718735. | − | 614466.i | 0.734812 | − | 0.628211i | ||||
\(990\) | 437507. | 0.446390 | ||||||||
\(991\) | −109074. | − | 226495.i | −0.111064 | − | 0.230628i | 0.838027 | − | 0.545629i | \(-0.183709\pi\) |
−0.949091 | + | 0.315001i | \(0.897995\pi\) | |||||||
\(992\) | −495092. | + | 1.02807e6i | −0.503109 | + | 1.04472i | ||||
\(993\) | −205938. | + | 258238.i | −0.208851 | + | 0.261891i | ||||
\(994\) | −47541.6 | − | 10851.1i | −0.0481173 | − | 0.0109825i | ||||
\(995\) | −688982. | −0.695923 | ||||||||
\(996\) | 1.78835e6i | 1.80274i | ||||||||
\(997\) | −300388. | − | 68561.7i | −0.302199 | − | 0.0689749i | 0.0687328 | − | 0.997635i | \(-0.478104\pi\) |
−0.370932 | + | 0.928660i | \(0.620962\pi\) | |||||||
\(998\) | 53876.2 | + | 67558.6i | 0.0540924 | + | 0.0678297i | ||||
\(999\) | −515576. | − | 2.25889e6i | −0.516609 | − | 2.26341i |
(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 | 43.5.f.a.2.6 | ✓ | 78 | |
43.22 | odd | 14 | inner | 43.5.f.a.22.6 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.f.a.2.6 | ✓ | 78 | 1.1 | even | 1 | trivial | |
43.5.f.a.22.6 | yes | 78 | 43.22 | odd | 14 | inner |