Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,6,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.a (trivial) |
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: | yes |
Analytic conductor: | \(157.657294876\) |
Analytic rank: | \(0\) |
Dimension: | \(218\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.4420 | −1.84591 | −0.922954 | − | 0.384910i | \(-0.874232\pi\) | ||||
−0.922954 | + | 0.384910i | \(0.874232\pi\) | |||||||
\(3\) | 0.0889574 | 0.00570662 | 0.00285331 | − | 0.999996i | \(-0.499092\pi\) | ||||
0.00285331 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(4\) | 77.0361 | 2.40738 | ||||||||
\(5\) | −100.525 | −1.79825 | −0.899123 | − | 0.437696i | \(-0.855794\pi\) | ||||
−0.899123 | + | 0.437696i | \(0.855794\pi\) | |||||||
\(6\) | −0.928896 | −0.0105339 | ||||||||
\(7\) | 31.6163 | 0.243875 | 0.121937 | − | 0.992538i | \(-0.461089\pi\) | ||||
0.121937 | + | 0.992538i | \(0.461089\pi\) | |||||||
\(8\) | −470.268 | −2.59789 | ||||||||
\(9\) | −242.992 | −0.999967 | ||||||||
\(10\) | 1049.69 | 3.31940 | ||||||||
\(11\) | −159.766 | −0.398111 | −0.199055 | − | 0.979988i | \(-0.563787\pi\) | ||||
−0.199055 | + | 0.979988i | \(0.563787\pi\) | |||||||
\(12\) | 6.85293 | 0.0137380 | ||||||||
\(13\) | −98.8165 | −0.162170 | −0.0810851 | − | 0.996707i | \(-0.525839\pi\) | ||||
−0.0810851 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(14\) | −330.139 | −0.450170 | ||||||||
\(15\) | −8.94244 | −0.0102619 | ||||||||
\(16\) | 2445.40 | 2.38809 | ||||||||
\(17\) | 2018.30 | 1.69380 | 0.846901 | − | 0.531751i | \(-0.178466\pi\) | ||||
0.846901 | + | 0.531751i | \(0.178466\pi\) | |||||||
\(18\) | 2537.33 | 1.84585 | ||||||||
\(19\) | 697.965 | 0.443557 | 0.221779 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221779 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(20\) | −7744.05 | −4.32905 | ||||||||
\(21\) | 2.81251 | 0.00139170 | ||||||||
\(22\) | 1668.29 | 0.734876 | ||||||||
\(23\) | −85.8780 | −0.0338503 | −0.0169251 | − | 0.999857i | \(-0.505388\pi\) | ||||
−0.0169251 | + | 0.999857i | \(0.505388\pi\) | |||||||
\(24\) | −41.8338 | −0.0148252 | ||||||||
\(25\) | 6980.27 | 2.23369 | ||||||||
\(26\) | 1031.84 | 0.299351 | ||||||||
\(27\) | −43.2326 | −0.0114131 | ||||||||
\(28\) | 2435.60 | 0.587098 | ||||||||
\(29\) | −2639.98 | −0.582915 | −0.291457 | − | 0.956584i | \(-0.594140\pi\) | ||||
−0.291457 | + | 0.956584i | \(0.594140\pi\) | |||||||
\(30\) | 93.3772 | 0.0189425 | ||||||||
\(31\) | 5111.75 | 0.955356 | 0.477678 | − | 0.878535i | \(-0.341479\pi\) | ||||
0.477678 | + | 0.878535i | \(0.341479\pi\) | |||||||
\(32\) | −10486.4 | −1.81030 | ||||||||
\(33\) | −14.2124 | −0.00227187 | ||||||||
\(34\) | −21075.1 | −3.12660 | ||||||||
\(35\) | −3178.23 | −0.438546 | ||||||||
\(36\) | −18719.2 | −2.40730 | ||||||||
\(37\) | −6797.95 | −0.816345 | −0.408172 | − | 0.912905i | \(-0.633834\pi\) | ||||
−0.408172 | + | 0.912905i | \(0.633834\pi\) | |||||||
\(38\) | −7288.18 | −0.818766 | ||||||||
\(39\) | −8.79045 | −0.000925443 0 | ||||||||
\(40\) | 47273.7 | 4.67164 | ||||||||
\(41\) | 11125.9 | 1.03365 | 0.516826 | − | 0.856091i | \(-0.327114\pi\) | ||||
0.516826 | + | 0.856091i | \(0.327114\pi\) | |||||||
\(42\) | −29.3683 | −0.00256895 | ||||||||
\(43\) | 4402.13 | 0.363071 | 0.181536 | − | 0.983384i | \(-0.441893\pi\) | ||||
0.181536 | + | 0.983384i | \(0.441893\pi\) | |||||||
\(44\) | −12307.8 | −0.958403 | ||||||||
\(45\) | 24426.8 | 1.79819 | ||||||||
\(46\) | 896.741 | 0.0624845 | ||||||||
\(47\) | −23451.8 | −1.54858 | −0.774288 | − | 0.632834i | \(-0.781892\pi\) | ||||
−0.774288 | + | 0.632834i | \(0.781892\pi\) | |||||||
\(48\) | 217.536 | 0.0136279 | ||||||||
\(49\) | −15807.4 | −0.940525 | ||||||||
\(50\) | −72888.2 | −4.12318 | ||||||||
\(51\) | 179.542 | 0.00966588 | ||||||||
\(52\) | −7612.43 | −0.390405 | ||||||||
\(53\) | −26681.2 | −1.30471 | −0.652357 | − | 0.757912i | \(-0.726220\pi\) | ||||
−0.652357 | + | 0.757912i | \(0.726220\pi\) | |||||||
\(54\) | 451.436 | 0.0210674 | ||||||||
\(55\) | 16060.5 | 0.715901 | ||||||||
\(56\) | −14868.2 | −0.633559 | ||||||||
\(57\) | 62.0892 | 0.00253121 | ||||||||
\(58\) | 27566.7 | 1.07601 | ||||||||
\(59\) | −12245.4 | −0.457978 | −0.228989 | − | 0.973429i | \(-0.573542\pi\) | ||||
−0.228989 | + | 0.973429i | \(0.573542\pi\) | |||||||
\(60\) | −688.890 | −0.0247043 | ||||||||
\(61\) | 24761.1 | 0.852010 | 0.426005 | − | 0.904721i | \(-0.359921\pi\) | ||||
0.426005 | + | 0.904721i | \(0.359921\pi\) | |||||||
\(62\) | −53377.1 | −1.76350 | ||||||||
\(63\) | −7682.52 | −0.243867 | ||||||||
\(64\) | 31246.2 | 0.953559 | ||||||||
\(65\) | 9933.52 | 0.291622 | ||||||||
\(66\) | 148.406 | 0.00419366 | ||||||||
\(67\) | 13373.6 | 0.363967 | 0.181983 | − | 0.983302i | \(-0.441748\pi\) | ||||
0.181983 | + | 0.983302i | \(0.441748\pi\) | |||||||
\(68\) | 155482. | 4.07762 | ||||||||
\(69\) | −7.63948 | −0.000193171 0 | ||||||||
\(70\) | 33187.2 | 0.809517 | ||||||||
\(71\) | −60264.0 | −1.41877 | −0.709385 | − | 0.704822i | \(-0.751027\pi\) | ||||
−0.709385 | + | 0.704822i | \(0.751027\pi\) | |||||||
\(72\) | 114271. | 2.59780 | ||||||||
\(73\) | −44967.0 | −0.987612 | −0.493806 | − | 0.869572i | \(-0.664395\pi\) | ||||
−0.493806 | + | 0.869572i | \(0.664395\pi\) | |||||||
\(74\) | 70984.4 | 1.50690 | ||||||||
\(75\) | 620.947 | 0.0127468 | ||||||||
\(76\) | 53768.5 | 1.06781 | ||||||||
\(77\) | −5051.23 | −0.0970891 | ||||||||
\(78\) | 91.7902 | 0.00170828 | ||||||||
\(79\) | −681.501 | −0.0122857 | −0.00614284 | − | 0.999981i | \(-0.501955\pi\) | ||||
−0.00614284 | + | 0.999981i | \(0.501955\pi\) | |||||||
\(80\) | −245824. | −4.29436 | ||||||||
\(81\) | 59043.2 | 0.999902 | ||||||||
\(82\) | −116177. | −1.90803 | ||||||||
\(83\) | 25226.1 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(84\) | 216.664 | 0.00335034 | ||||||||
\(85\) | −202889. | −3.04587 | ||||||||
\(86\) | −45967.2 | −0.670196 | ||||||||
\(87\) | −234.845 | −0.00332647 | ||||||||
\(88\) | 75133.1 | 1.03425 | ||||||||
\(89\) | −1264.98 | −0.0169281 | −0.00846406 | − | 0.999964i | \(-0.502694\pi\) | ||||
−0.00846406 | + | 0.999964i | \(0.502694\pi\) | |||||||
\(90\) | −255065. | −3.31929 | ||||||||
\(91\) | −3124.22 | −0.0395492 | ||||||||
\(92\) | −6615.70 | −0.0814904 | ||||||||
\(93\) | 454.728 | 0.00545185 | ||||||||
\(94\) | 244885. | 2.85853 | ||||||||
\(95\) | −70163.0 | −0.797625 | ||||||||
\(96\) | −932.840 | −0.0103307 | ||||||||
\(97\) | 116731. | 1.25967 | 0.629833 | − | 0.776731i | \(-0.283123\pi\) | ||||
0.629833 | + | 0.776731i | \(0.283123\pi\) | |||||||
\(98\) | 165061. | 1.73612 | ||||||||
\(99\) | 38822.0 | 0.398098 | ||||||||
\(100\) | 537733. | 5.37733 | ||||||||
\(101\) | 73619.7 | 0.718110 | 0.359055 | − | 0.933316i | \(-0.383099\pi\) | ||||
0.359055 | + | 0.933316i | \(0.383099\pi\) | |||||||
\(102\) | −1874.79 | −0.0178423 | ||||||||
\(103\) | 104162. | 0.967421 | 0.483711 | − | 0.875228i | \(-0.339289\pi\) | ||||
0.483711 | + | 0.875228i | \(0.339289\pi\) | |||||||
\(104\) | 46470.2 | 0.421300 | ||||||||
\(105\) | −282.727 | −0.00250262 | ||||||||
\(106\) | 278606. | 2.40838 | ||||||||
\(107\) | −168312. | −1.42120 | −0.710600 | − | 0.703596i | \(-0.751577\pi\) | ||||
−0.710600 | + | 0.703596i | \(0.751577\pi\) | |||||||
\(108\) | −3330.47 | −0.0274755 | ||||||||
\(109\) | 134927. | 1.08776 | 0.543880 | − | 0.839163i | \(-0.316955\pi\) | ||||
0.543880 | + | 0.839163i | \(0.316955\pi\) | |||||||
\(110\) | −167705. | −1.32149 | ||||||||
\(111\) | −604.728 | −0.00465857 | ||||||||
\(112\) | 77314.6 | 0.582394 | ||||||||
\(113\) | −144432. | −1.06406 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(114\) | −648.337 | −0.00467239 | ||||||||
\(115\) | 8632.88 | 0.0608711 | ||||||||
\(116\) | −203373. | −1.40330 | ||||||||
\(117\) | 24011.6 | 0.162165 | ||||||||
\(118\) | 127867. | 0.845385 | ||||||||
\(119\) | 63811.1 | 0.413075 | ||||||||
\(120\) | 4205.34 | 0.0266593 | ||||||||
\(121\) | −135526. | −0.841508 | ||||||||
\(122\) | −258556. | −1.57273 | ||||||||
\(123\) | 989.728 | 0.00589865 | ||||||||
\(124\) | 393789. | 2.29990 | ||||||||
\(125\) | −387551. | −2.21847 | ||||||||
\(126\) | 80221.2 | 0.450155 | ||||||||
\(127\) | −254256. | −1.39882 | −0.699411 | − | 0.714720i | \(-0.746554\pi\) | ||||
−0.699411 | + | 0.714720i | \(0.746554\pi\) | |||||||
\(128\) | 9289.65 | 0.0501158 | ||||||||
\(129\) | 391.602 | 0.00207191 | ||||||||
\(130\) | −103726. | −0.538307 | ||||||||
\(131\) | −265140. | −1.34989 | −0.674943 | − | 0.737870i | \(-0.735832\pi\) | ||||
−0.674943 | + | 0.737870i | \(0.735832\pi\) | |||||||
\(132\) | −1094.87 | −0.00546924 | ||||||||
\(133\) | 22067.1 | 0.108172 | ||||||||
\(134\) | −139648. | −0.671849 | ||||||||
\(135\) | 4345.95 | 0.0205235 | ||||||||
\(136\) | −949140. | −4.40031 | ||||||||
\(137\) | 401274. | 1.82658 | 0.913291 | − | 0.407307i | \(-0.133532\pi\) | ||||
0.913291 | + | 0.407307i | \(0.133532\pi\) | |||||||
\(138\) | 79.7717 | 0.000356575 0 | ||||||||
\(139\) | −419606. | −1.84206 | −0.921031 | − | 0.389489i | \(-0.872651\pi\) | ||||
−0.921031 | + | 0.389489i | \(0.872651\pi\) | |||||||
\(140\) | −244839. | −1.05575 | ||||||||
\(141\) | −2086.21 | −0.00883713 | ||||||||
\(142\) | 629278. | 2.61892 | ||||||||
\(143\) | 15787.6 | 0.0645617 | ||||||||
\(144\) | −594213. | −2.38801 | ||||||||
\(145\) | 265384. | 1.04822 | ||||||||
\(146\) | 469547. | 1.82304 | ||||||||
\(147\) | −1406.19 | −0.00536722 | ||||||||
\(148\) | −523687. | −1.96525 | ||||||||
\(149\) | −62487.5 | −0.230583 | −0.115292 | − | 0.993332i | \(-0.536780\pi\) | ||||
−0.115292 | + | 0.993332i | \(0.536780\pi\) | |||||||
\(150\) | −6483.95 | −0.0235294 | ||||||||
\(151\) | −31897.9 | −0.113847 | −0.0569233 | − | 0.998379i | \(-0.518129\pi\) | ||||
−0.0569233 | + | 0.998379i | \(0.518129\pi\) | |||||||
\(152\) | −328231. | −1.15231 | ||||||||
\(153\) | −490430. | −1.69375 | ||||||||
\(154\) | 52745.1 | 0.179218 | ||||||||
\(155\) | −513859. | −1.71797 | ||||||||
\(156\) | −677.182 | −0.00222789 | ||||||||
\(157\) | −187586. | −0.607366 | −0.303683 | − | 0.952773i | \(-0.598216\pi\) | ||||
−0.303683 | + | 0.952773i | \(0.598216\pi\) | |||||||
\(158\) | 7116.26 | 0.0226782 | ||||||||
\(159\) | −2373.49 | −0.00744551 | ||||||||
\(160\) | 1.05414e6 | 3.25536 | ||||||||
\(161\) | −2715.15 | −0.00825522 | ||||||||
\(162\) | −616531. | −1.84573 | ||||||||
\(163\) | 180119. | 0.530995 | 0.265497 | − | 0.964112i | \(-0.414464\pi\) | ||||
0.265497 | + | 0.964112i | \(0.414464\pi\) | |||||||
\(164\) | 857092. | 2.48839 | ||||||||
\(165\) | 1428.70 | 0.00408537 | ||||||||
\(166\) | −263412. | −0.741933 | ||||||||
\(167\) | −490978. | −1.36229 | −0.681146 | − | 0.732147i | \(-0.738518\pi\) | ||||
−0.681146 | + | 0.732147i | \(0.738518\pi\) | |||||||
\(168\) | −1322.63 | −0.00361548 | ||||||||
\(169\) | −361528. | −0.973701 | ||||||||
\(170\) | 2.11858e6 | 5.62240 | ||||||||
\(171\) | −169600. | −0.443543 | ||||||||
\(172\) | 339123. | 0.874049 | ||||||||
\(173\) | 194845. | 0.494965 | 0.247482 | − | 0.968892i | \(-0.420397\pi\) | ||||
0.247482 | + | 0.968892i | \(0.420397\pi\) | |||||||
\(174\) | 2452.26 | 0.00614036 | ||||||||
\(175\) | 220691. | 0.544740 | ||||||||
\(176\) | −390693. | −0.950723 | ||||||||
\(177\) | −1089.32 | −0.00261350 | ||||||||
\(178\) | 13209.0 | 0.0312477 | ||||||||
\(179\) | −52037.2 | −0.121390 | −0.0606948 | − | 0.998156i | \(-0.519332\pi\) | ||||
−0.0606948 | + | 0.998156i | \(0.519332\pi\) | |||||||
\(180\) | 1.88174e6 | 4.32891 | ||||||||
\(181\) | −237165. | −0.538088 | −0.269044 | − | 0.963128i | \(-0.586708\pi\) | ||||
−0.269044 | + | 0.963128i | \(0.586708\pi\) | |||||||
\(182\) | 32623.2 | 0.0730042 | ||||||||
\(183\) | 2202.68 | 0.00486210 | ||||||||
\(184\) | 40385.7 | 0.0879392 | ||||||||
\(185\) | 683364. | 1.46799 | ||||||||
\(186\) | −4748.28 | −0.0100636 | ||||||||
\(187\) | −322456. | −0.674321 | ||||||||
\(188\) | −1.80664e6 | −3.72800 | ||||||||
\(189\) | −1366.86 | −0.00278335 | ||||||||
\(190\) | 732644. | 1.47234 | ||||||||
\(191\) | −583998. | −1.15832 | −0.579159 | − | 0.815214i | \(-0.696619\pi\) | ||||
−0.579159 | + | 0.815214i | \(0.696619\pi\) | |||||||
\(192\) | 2779.58 | 0.00544160 | ||||||||
\(193\) | 924290. | 1.78614 | 0.893069 | − | 0.449920i | \(-0.148548\pi\) | ||||
0.893069 | + | 0.449920i | \(0.148548\pi\) | |||||||
\(194\) | −1.21890e6 | −2.32523 | ||||||||
\(195\) | 883.660 | 0.00166417 | ||||||||
\(196\) | −1.21774e6 | −2.26420 | ||||||||
\(197\) | −951391. | −1.74660 | −0.873300 | − | 0.487184i | \(-0.838024\pi\) | ||||
−0.873300 | + | 0.487184i | \(0.838024\pi\) | |||||||
\(198\) | −405381. | −0.734852 | ||||||||
\(199\) | 646034. | 1.15644 | 0.578219 | − | 0.815881i | \(-0.303748\pi\) | ||||
0.578219 | + | 0.815881i | \(0.303748\pi\) | |||||||
\(200\) | −3.28260e6 | −5.80287 | ||||||||
\(201\) | 1189.68 | 0.00207702 | ||||||||
\(202\) | −768740. | −1.32556 | ||||||||
\(203\) | −83466.4 | −0.142158 | ||||||||
\(204\) | 13831.2 | 0.0232694 | ||||||||
\(205\) | −1.11843e6 | −1.85876 | ||||||||
\(206\) | −1.08766e6 | −1.78577 | ||||||||
\(207\) | 20867.7 | 0.0338492 | ||||||||
\(208\) | −241646. | −0.387276 | ||||||||
\(209\) | −111511. | −0.176585 | ||||||||
\(210\) | 2952.25 | 0.00461960 | ||||||||
\(211\) | 247955. | 0.383413 | 0.191706 | − | 0.981452i | \(-0.438598\pi\) | ||||
0.191706 | + | 0.981452i | \(0.438598\pi\) | |||||||
\(212\) | −2.05541e6 | −3.14094 | ||||||||
\(213\) | −5360.92 | −0.00809638 | ||||||||
\(214\) | 1.75752e6 | 2.62341 | ||||||||
\(215\) | −442524. | −0.652891 | ||||||||
\(216\) | 20330.9 | 0.0296498 | ||||||||
\(217\) | 161615. | 0.232987 | ||||||||
\(218\) | −1.40891e6 | −2.00790 | ||||||||
\(219\) | −4000.14 | −0.00563593 | ||||||||
\(220\) | 1.23724e6 | 1.72344 | ||||||||
\(221\) | −199441. | −0.274684 | ||||||||
\(222\) | 6314.59 | 0.00859929 | ||||||||
\(223\) | −1.12586e6 | −1.51608 | −0.758039 | − | 0.652210i | \(-0.773842\pi\) | ||||
−0.758039 | + | 0.652210i | \(0.773842\pi\) | |||||||
\(224\) | −331541. | −0.441486 | ||||||||
\(225\) | −1.69615e6 | −2.23361 | ||||||||
\(226\) | 1.50816e6 | 1.96416 | ||||||||
\(227\) | 139771. | 0.180033 | 0.0900165 | − | 0.995940i | \(-0.471308\pi\) | ||||
0.0900165 | + | 0.995940i | \(0.471308\pi\) | |||||||
\(228\) | 4783.10 | 0.00609358 | ||||||||
\(229\) | 7027.20 | 0.00885510 | 0.00442755 | − | 0.999990i | \(-0.498591\pi\) | ||||
0.00442755 | + | 0.999990i | \(0.498591\pi\) | |||||||
\(230\) | −90144.8 | −0.112362 | ||||||||
\(231\) | −449.344 | −0.000554051 0 | ||||||||
\(232\) | 1.24150e6 | 1.51435 | ||||||||
\(233\) | −221897. | −0.267770 | −0.133885 | − | 0.990997i | \(-0.542745\pi\) | ||||
−0.133885 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(234\) | −250730. | −0.299341 | ||||||||
\(235\) | 2.35750e6 | 2.78472 | ||||||||
\(236\) | −943340. | −1.10252 | ||||||||
\(237\) | −60.6246 | −7.01096e−5 0 | ||||||||
\(238\) | −666318. | −0.762499 | ||||||||
\(239\) | 1.59854e6 | 1.81021 | 0.905105 | − | 0.425188i | \(-0.139792\pi\) | ||||
0.905105 | + | 0.425188i | \(0.139792\pi\) | |||||||
\(240\) | −21867.8 | −0.0245063 | ||||||||
\(241\) | −401743. | −0.445559 | −0.222780 | − | 0.974869i | \(-0.571513\pi\) | ||||
−0.222780 | + | 0.974869i | \(0.571513\pi\) | |||||||
\(242\) | 1.41516e6 | 1.55335 | ||||||||
\(243\) | 15757.8 | 0.0171191 | ||||||||
\(244\) | 1.90750e6 | 2.05111 | ||||||||
\(245\) | 1.58904e6 | 1.69130 | ||||||||
\(246\) | −10334.8 | −0.0108884 | ||||||||
\(247\) | −68970.5 | −0.0719318 | ||||||||
\(248\) | −2.40389e6 | −2.48191 | ||||||||
\(249\) | 2244.05 | 0.00229368 | ||||||||
\(250\) | 4.04682e6 | 4.09510 | ||||||||
\(251\) | −719741. | −0.721094 | −0.360547 | − | 0.932741i | \(-0.617410\pi\) | ||||
−0.360547 | + | 0.932741i | \(0.617410\pi\) | |||||||
\(252\) | −591831. | −0.587079 | ||||||||
\(253\) | 13720.4 | 0.0134762 | ||||||||
\(254\) | 2.65495e6 | 2.58210 | ||||||||
\(255\) | −18048.5 | −0.0173816 | ||||||||
\(256\) | −1.09688e6 | −1.04607 | ||||||||
\(257\) | −432916. | −0.408856 | −0.204428 | − | 0.978882i | \(-0.565533\pi\) | ||||
−0.204428 | + | 0.978882i | \(0.565533\pi\) | |||||||
\(258\) | −4089.12 | −0.00382455 | ||||||||
\(259\) | −214926. | −0.199086 | ||||||||
\(260\) | 765239. | 0.702043 | ||||||||
\(261\) | 641493. | 0.582896 | ||||||||
\(262\) | 2.76860e6 | 2.49176 | ||||||||
\(263\) | −1.38264e6 | −1.23259 | −0.616296 | − | 0.787514i | \(-0.711368\pi\) | ||||
−0.616296 | + | 0.787514i | \(0.711368\pi\) | |||||||
\(264\) | 6683.64 | 0.00590205 | ||||||||
\(265\) | 2.68213e6 | 2.34620 | ||||||||
\(266\) | −230426. | −0.199676 | ||||||||
\(267\) | −112.529 | −9.66023e−5 0 | ||||||||
\(268\) | 1.03025e6 | 0.876205 | ||||||||
\(269\) | 2.00653e6 | 1.69069 | 0.845347 | − | 0.534217i | \(-0.179394\pi\) | ||||
0.845347 | + | 0.534217i | \(0.179394\pi\) | |||||||
\(270\) | −45380.6 | −0.0378844 | ||||||||
\(271\) | 418116. | 0.345839 | 0.172919 | − | 0.984936i | \(-0.444680\pi\) | ||||
0.172919 | + | 0.984936i | \(0.444680\pi\) | |||||||
\(272\) | 4.93554e6 | 4.04494 | ||||||||
\(273\) | −277.922 | −0.000225692 0 | ||||||||
\(274\) | −4.19011e6 | −3.37170 | ||||||||
\(275\) | −1.11521e6 | −0.889255 | ||||||||
\(276\) | −588.515 | −0.000465034 0 | ||||||||
\(277\) | −3749.78 | −0.00293634 | −0.00146817 | − | 0.999999i | \(-0.500467\pi\) | ||||
−0.00146817 | + | 0.999999i | \(0.500467\pi\) | |||||||
\(278\) | 4.38153e6 | 3.40028 | ||||||||
\(279\) | −1.24211e6 | −0.955325 | ||||||||
\(280\) | 1.49462e6 | 1.13929 | ||||||||
\(281\) | 557740. | 0.421372 | 0.210686 | − | 0.977554i | \(-0.432430\pi\) | ||||
0.210686 | + | 0.977554i | \(0.432430\pi\) | |||||||
\(282\) | 21784.3 | 0.0163125 | ||||||||
\(283\) | 483364. | 0.358763 | 0.179382 | − | 0.983780i | \(-0.442590\pi\) | ||||
0.179382 | + | 0.983780i | \(0.442590\pi\) | |||||||
\(284\) | −4.64250e6 | −3.41551 | ||||||||
\(285\) | −6241.51 | −0.00455174 | ||||||||
\(286\) | −164854. | −0.119175 | ||||||||
\(287\) | 351759. | 0.252081 | ||||||||
\(288\) | 2.54811e6 | 1.81024 | ||||||||
\(289\) | 2.65366e6 | 1.86896 | ||||||||
\(290\) | −2.77114e6 | −1.93493 | ||||||||
\(291\) | 10384.0 | 0.00718843 | ||||||||
\(292\) | −3.46408e6 | −2.37755 | ||||||||
\(293\) | −156481. | −0.106486 | −0.0532429 | − | 0.998582i | \(-0.516956\pi\) | ||||
−0.0532429 | + | 0.998582i | \(0.516956\pi\) | |||||||
\(294\) | 14683.4 | 0.00990739 | ||||||||
\(295\) | 1.23097e6 | 0.823556 | ||||||||
\(296\) | 3.19686e6 | 2.12077 | ||||||||
\(297\) | 6907.12 | 0.00454366 | ||||||||
\(298\) | 652496. | 0.425635 | ||||||||
\(299\) | 8486.16 | 0.00548950 | ||||||||
\(300\) | 47835.3 | 0.0306864 | ||||||||
\(301\) | 139179. | 0.0885438 | ||||||||
\(302\) | 333079. | 0.210150 | ||||||||
\(303\) | 6549.02 | 0.00409798 | ||||||||
\(304\) | 1.70680e6 | 1.05925 | ||||||||
\(305\) | −2.48911e6 | −1.53212 | ||||||||
\(306\) | 5.12109e6 | 3.12650 | ||||||||
\(307\) | 2.92997e6 | 1.77426 | 0.887130 | − | 0.461520i | \(-0.152696\pi\) | ||||
0.887130 | + | 0.461520i | \(0.152696\pi\) | |||||||
\(308\) | −389127. | −0.233730 | ||||||||
\(309\) | 9265.97 | 0.00552071 | ||||||||
\(310\) | 5.36573e6 | 3.17121 | ||||||||
\(311\) | 2.78448e6 | 1.63246 | 0.816231 | − | 0.577725i | \(-0.196060\pi\) | ||||
0.816231 | + | 0.577725i | \(0.196060\pi\) | |||||||
\(312\) | 4133.87 | 0.00240420 | ||||||||
\(313\) | 1.58517e6 | 0.914568 | 0.457284 | − | 0.889321i | \(-0.348822\pi\) | ||||
0.457284 | + | 0.889321i | \(0.348822\pi\) | |||||||
\(314\) | 1.95877e6 | 1.12114 | ||||||||
\(315\) | 772286. | 0.438532 | ||||||||
\(316\) | −52500.2 | −0.0295762 | ||||||||
\(317\) | −1.04444e6 | −0.583759 | −0.291879 | − | 0.956455i | \(-0.594281\pi\) | ||||
−0.291879 | + | 0.956455i | \(0.594281\pi\) | |||||||
\(318\) | 24784.1 | 0.0137437 | ||||||||
\(319\) | 421780. | 0.232065 | ||||||||
\(320\) | −3.14103e6 | −1.71473 | ||||||||
\(321\) | −14972.6 | −0.00811025 | ||||||||
\(322\) | 28351.7 | 0.0152384 | ||||||||
\(323\) | 1.40870e6 | 0.751298 | ||||||||
\(324\) | 4.54846e6 | 2.40714 | ||||||||
\(325\) | −689766. | −0.362237 | ||||||||
\(326\) | −1.88081e6 | −0.980168 | ||||||||
\(327\) | 12002.8 | 0.00620743 | ||||||||
\(328\) | −5.23214e6 | −2.68531 | ||||||||
\(329\) | −741462. | −0.377658 | ||||||||
\(330\) | −14918.6 | −0.00754123 | ||||||||
\(331\) | −365932. | −0.183582 | −0.0917912 | − | 0.995778i | \(-0.529259\pi\) | ||||
−0.0917912 | + | 0.995778i | \(0.529259\pi\) | |||||||
\(332\) | 1.94332e6 | 0.967606 | ||||||||
\(333\) | 1.65185e6 | 0.816318 | ||||||||
\(334\) | 5.12680e6 | 2.51467 | ||||||||
\(335\) | −1.34438e6 | −0.654501 | ||||||||
\(336\) | 6877.71 | 0.00332350 | ||||||||
\(337\) | −1.92618e6 | −0.923892 | −0.461946 | − | 0.886908i | \(-0.652849\pi\) | ||||
−0.461946 | + | 0.886908i | \(0.652849\pi\) | |||||||
\(338\) | 3.77509e6 | 1.79736 | ||||||||
\(339\) | −12848.3 | −0.00607221 | ||||||||
\(340\) | −1.56298e7 | −7.33256 | ||||||||
\(341\) | −816686. | −0.380338 | ||||||||
\(342\) | 1.77097e6 | 0.818740 | ||||||||
\(343\) | −1.03115e6 | −0.473245 | ||||||||
\(344\) | −2.07018e6 | −0.943218 | ||||||||
\(345\) | 767.959 | 0.000347368 0 | ||||||||
\(346\) | −2.03458e6 | −0.913660 | ||||||||
\(347\) | −175556. | −0.0782696 | −0.0391348 | − | 0.999234i | \(-0.512460\pi\) | ||||
−0.0391348 | + | 0.999234i | \(0.512460\pi\) | |||||||
\(348\) | −18091.6 | −0.00800807 | ||||||||
\(349\) | 2.21755e6 | 0.974562 | 0.487281 | − | 0.873245i | \(-0.337989\pi\) | ||||
0.487281 | + | 0.873245i | \(0.337989\pi\) | |||||||
\(350\) | −2.30446e6 | −1.00554 | ||||||||
\(351\) | 4272.09 | 0.00185086 | ||||||||
\(352\) | 1.67537e6 | 0.720700 | ||||||||
\(353\) | 4.28620e6 | 1.83078 | 0.915388 | − | 0.402573i | \(-0.131884\pi\) | ||||
0.915388 | + | 0.402573i | \(0.131884\pi\) | |||||||
\(354\) | 11374.7 | 0.00482429 | ||||||||
\(355\) | 6.05803e6 | 2.55130 | ||||||||
\(356\) | −97449.0 | −0.0407523 | ||||||||
\(357\) | 5676.47 | 0.00235726 | ||||||||
\(358\) | 543374. | 0.224074 | ||||||||
\(359\) | −4.30538e6 | −1.76310 | −0.881548 | − | 0.472095i | \(-0.843498\pi\) | ||||
−0.881548 | + | 0.472095i | \(0.843498\pi\) | |||||||
\(360\) | −1.14871e7 | −4.67149 | ||||||||
\(361\) | −1.98894e6 | −0.803257 | ||||||||
\(362\) | 2.47648e6 | 0.993262 | ||||||||
\(363\) | −12056.0 | −0.00480216 | ||||||||
\(364\) | −240677. | −0.0952098 | ||||||||
\(365\) | 4.52030e6 | 1.77597 | ||||||||
\(366\) | −23000.5 | −0.00897499 | ||||||||
\(367\) | −40326.4 | −0.0156287 | −0.00781437 | − | 0.999969i | \(-0.502487\pi\) | ||||
−0.00781437 | + | 0.999969i | \(0.502487\pi\) | |||||||
\(368\) | −210006. | −0.0808374 | ||||||||
\(369\) | −2.70350e6 | −1.03362 | ||||||||
\(370\) | −7.13571e6 | −2.70977 | ||||||||
\(371\) | −843562. | −0.318187 | ||||||||
\(372\) | 35030.4 | 0.0131247 | ||||||||
\(373\) | 996746. | 0.370947 | 0.185474 | − | 0.982649i | \(-0.440618\pi\) | ||||
0.185474 | + | 0.982649i | \(0.440618\pi\) | |||||||
\(374\) | 3.36710e6 | 1.24473 | ||||||||
\(375\) | −34475.5 | −0.0126600 | ||||||||
\(376\) | 1.10287e7 | 4.02303 | ||||||||
\(377\) | 260873. | 0.0945314 | ||||||||
\(378\) | 14272.8 | 0.00513782 | ||||||||
\(379\) | −71793.7 | −0.0256737 | −0.0128368 | − | 0.999918i | \(-0.504086\pi\) | ||||
−0.0128368 | + | 0.999918i | \(0.504086\pi\) | |||||||
\(380\) | −5.40508e6 | −1.92018 | ||||||||
\(381\) | −22618.0 | −0.00798255 | ||||||||
\(382\) | 6.09813e6 | 2.13815 | ||||||||
\(383\) | 2.07445e6 | 0.722614 | 0.361307 | − | 0.932447i | \(-0.382331\pi\) | ||||
0.361307 | + | 0.932447i | \(0.382331\pi\) | |||||||
\(384\) | 826.383 | 0.000285992 0 | ||||||||
\(385\) | 507775. | 0.174590 | ||||||||
\(386\) | −9.65146e6 | −3.29705 | ||||||||
\(387\) | −1.06968e6 | −0.363059 | ||||||||
\(388\) | 8.99246e6 | 3.03249 | ||||||||
\(389\) | −3.92235e6 | −1.31423 | −0.657117 | − | 0.753789i | \(-0.728224\pi\) | ||||
−0.657117 | + | 0.753789i | \(0.728224\pi\) | |||||||
\(390\) | −9227.21 | −0.00307191 | ||||||||
\(391\) | −173327. | −0.0573356 | ||||||||
\(392\) | 7.43372e6 | 2.44338 | ||||||||
\(393\) | −23586.2 | −0.00770328 | ||||||||
\(394\) | 9.93445e6 | 3.22406 | ||||||||
\(395\) | 68507.9 | 0.0220927 | ||||||||
\(396\) | 2.99069e6 | 0.958371 | ||||||||
\(397\) | −3.37991e6 | −1.07629 | −0.538144 | − | 0.842853i | \(-0.680874\pi\) | ||||
−0.538144 | + | 0.842853i | \(0.680874\pi\) | |||||||
\(398\) | −6.74591e6 | −2.13468 | ||||||||
\(399\) | 1963.03 | 0.000617299 0 | ||||||||
\(400\) | 1.70696e7 | 5.33424 | ||||||||
\(401\) | −783083. | −0.243191 | −0.121595 | − | 0.992580i | \(-0.538801\pi\) | ||||
−0.121595 | + | 0.992580i | \(0.538801\pi\) | |||||||
\(402\) | −12422.7 | −0.00383399 | ||||||||
\(403\) | −505125. | −0.154930 | ||||||||
\(404\) | 5.67137e6 | 1.72876 | ||||||||
\(405\) | −5.93532e6 | −1.79807 | ||||||||
\(406\) | 871559. | 0.262411 | ||||||||
\(407\) | 1.08608e6 | 0.324996 | ||||||||
\(408\) | −84433.0 | −0.0251109 | ||||||||
\(409\) | −260533. | −0.0770113 | −0.0385056 | − | 0.999258i | \(-0.512260\pi\) | ||||
−0.0385056 | + | 0.999258i | \(0.512260\pi\) | |||||||
\(410\) | 1.16787e7 | 3.43110 | ||||||||
\(411\) | 35696.3 | 0.0104236 | ||||||||
\(412\) | 8.02422e6 | 2.32895 | ||||||||
\(413\) | −387156. | −0.111689 | ||||||||
\(414\) | −217901. | −0.0624825 | ||||||||
\(415\) | −2.53585e6 | −0.722776 | ||||||||
\(416\) | 1.03623e6 | 0.293576 | ||||||||
\(417\) | −37327.0 | −0.0105119 | ||||||||
\(418\) | 1.16441e6 | 0.325960 | ||||||||
\(419\) | 1.92332e6 | 0.535202 | 0.267601 | − | 0.963530i | \(-0.413769\pi\) | ||||
0.267601 | + | 0.963530i | \(0.413769\pi\) | |||||||
\(420\) | −21780.2 | −0.00602474 | ||||||||
\(421\) | −1.94410e6 | −0.534580 | −0.267290 | − | 0.963616i | \(-0.586128\pi\) | ||||
−0.267290 | + | 0.963616i | \(0.586128\pi\) | |||||||
\(422\) | −2.58915e6 | −0.707744 | ||||||||
\(423\) | 5.69861e6 | 1.54853 | ||||||||
\(424\) | 1.25473e7 | 3.38950 | ||||||||
\(425\) | 1.40883e7 | 3.78342 | ||||||||
\(426\) | 55978.9 | 0.0149452 | ||||||||
\(427\) | 782855. | 0.207784 | ||||||||
\(428\) | −1.29661e7 | −3.42136 | ||||||||
\(429\) | 1404.42 | 0.000368429 0 | ||||||||
\(430\) | 4.62085e6 | 1.20518 | ||||||||
\(431\) | −2.11453e6 | −0.548303 | −0.274152 | − | 0.961686i | \(-0.588397\pi\) | ||||
−0.274152 | + | 0.961686i | \(0.588397\pi\) | |||||||
\(432\) | −105721. | −0.0272553 | ||||||||
\(433\) | 4.91778e6 | 1.26052 | 0.630260 | − | 0.776384i | \(-0.282948\pi\) | ||||
0.630260 | + | 0.776384i | \(0.282948\pi\) | |||||||
\(434\) | −1.68759e6 | −0.430073 | ||||||||
\(435\) | 23607.8 | 0.00598181 | ||||||||
\(436\) | 1.03943e7 | 2.61865 | ||||||||
\(437\) | −59939.8 | −0.0150145 | ||||||||
\(438\) | 41769.6 | 0.0104034 | ||||||||
\(439\) | 1.10707e6 | 0.274167 | 0.137084 | − | 0.990559i | \(-0.456227\pi\) | ||||
0.137084 | + | 0.990559i | \(0.456227\pi\) | |||||||
\(440\) | −7.55275e6 | −1.85983 | ||||||||
\(441\) | 3.84107e6 | 0.940495 | ||||||||
\(442\) | 2.08257e6 | 0.507041 | ||||||||
\(443\) | 244752. | 0.0592538 | 0.0296269 | − | 0.999561i | \(-0.490568\pi\) | ||||
0.0296269 | + | 0.999561i | \(0.490568\pi\) | |||||||
\(444\) | −46585.8 | −0.0112149 | ||||||||
\(445\) | 127162. | 0.0304409 | ||||||||
\(446\) | 1.17562e7 | 2.79854 | ||||||||
\(447\) | −5558.72 | −0.00131585 | ||||||||
\(448\) | 987892. | 0.232549 | ||||||||
\(449\) | 6.29578e6 | 1.47378 | 0.736891 | − | 0.676011i | \(-0.236293\pi\) | ||||
0.736891 | + | 0.676011i | \(0.236293\pi\) | |||||||
\(450\) | 1.77113e7 | 4.12305 | ||||||||
\(451\) | −1.77754e6 | −0.411508 | ||||||||
\(452\) | −1.11265e7 | −2.56160 | ||||||||
\(453\) | −2837.56 | −0.000649679 0 | ||||||||
\(454\) | −1.45949e6 | −0.332324 | ||||||||
\(455\) | 314062. | 0.0711191 | ||||||||
\(456\) | −29198.5 | −0.00657581 | ||||||||
\(457\) | −3.86683e6 | −0.866094 | −0.433047 | − | 0.901371i | \(-0.642562\pi\) | ||||
−0.433047 | + | 0.901371i | \(0.642562\pi\) | |||||||
\(458\) | −73378.3 | −0.0163457 | ||||||||
\(459\) | −87256.1 | −0.0193314 | ||||||||
\(460\) | 665043. | 0.146540 | ||||||||
\(461\) | −643858. | −0.141103 | −0.0705517 | − | 0.997508i | \(-0.522476\pi\) | ||||
−0.0705517 | + | 0.997508i | \(0.522476\pi\) | |||||||
\(462\) | 4692.07 | 0.00102273 | ||||||||
\(463\) | 2.77132e6 | 0.600806 | 0.300403 | − | 0.953812i | \(-0.402879\pi\) | ||||
0.300403 | + | 0.953812i | \(0.402879\pi\) | |||||||
\(464\) | −6.45580e6 | −1.39205 | ||||||||
\(465\) | −45711.5 | −0.00980377 | ||||||||
\(466\) | 2.31706e6 | 0.494280 | ||||||||
\(467\) | 1.91983e6 | 0.407353 | 0.203676 | − | 0.979038i | \(-0.434711\pi\) | ||||
0.203676 | + | 0.979038i | \(0.434711\pi\) | |||||||
\(468\) | 1.84976e6 | 0.390392 | ||||||||
\(469\) | 422825. | 0.0887622 | ||||||||
\(470\) | −2.46171e7 | −5.14034 | ||||||||
\(471\) | −16687.1 | −0.00346600 | ||||||||
\(472\) | 5.75864e6 | 1.18977 | ||||||||
\(473\) | −703313. | −0.144543 | ||||||||
\(474\) | 633.044 | 0.000129416 0 | ||||||||
\(475\) | 4.87199e6 | 0.990769 | ||||||||
\(476\) | 4.91576e6 | 0.994428 | ||||||||
\(477\) | 6.48332e6 | 1.30467 | ||||||||
\(478\) | −1.66920e7 | −3.34148 | ||||||||
\(479\) | 3.58877e6 | 0.714673 | 0.357336 | − | 0.933976i | \(-0.383685\pi\) | ||||
0.357336 | + | 0.933976i | \(0.383685\pi\) | |||||||
\(480\) | 93773.7 | 0.0185771 | ||||||||
\(481\) | 671749. | 0.132387 | ||||||||
\(482\) | 4.19501e6 | 0.822462 | ||||||||
\(483\) | −241.532 | −4.71094e−5 0 | ||||||||
\(484\) | −1.04404e7 | −2.02583 | ||||||||
\(485\) | −1.17343e7 | −2.26519 | ||||||||
\(486\) | −164544. | −0.0316003 | ||||||||
\(487\) | −1.13660e6 | −0.217163 | −0.108582 | − | 0.994088i | \(-0.534631\pi\) | ||||
−0.108582 | + | 0.994088i | \(0.534631\pi\) | |||||||
\(488\) | −1.16443e7 | −2.21343 | ||||||||
\(489\) | 16022.9 | 0.00303018 | ||||||||
\(490\) | −1.65928e7 | −3.12198 | ||||||||
\(491\) | 1.08305e6 | 0.202742 | 0.101371 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101371 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(492\) | 76244.7 | 0.0142003 | ||||||||
\(493\) | −5.32825e6 | −0.987342 | ||||||||
\(494\) | 720192. | 0.132779 | ||||||||
\(495\) | −3.90258e6 | −0.715878 | ||||||||
\(496\) | 1.25003e7 | 2.28147 | ||||||||
\(497\) | −1.90533e6 | −0.346002 | ||||||||
\(498\) | −23432.4 | −0.00423393 | ||||||||
\(499\) | 3.16842e6 | 0.569627 | 0.284814 | − | 0.958583i | \(-0.408068\pi\) | ||||
0.284814 | + | 0.958583i | \(0.408068\pi\) | |||||||
\(500\) | −2.98554e7 | −5.34070 | ||||||||
\(501\) | −43676.1 | −0.00777409 | ||||||||
\(502\) | 7.51556e6 | 1.33107 | ||||||||
\(503\) | −1.22467e6 | −0.215824 | −0.107912 | − | 0.994160i | \(-0.534416\pi\) | ||||
−0.107912 | + | 0.994160i | \(0.534416\pi\) | |||||||
\(504\) | 3.61284e6 | 0.633538 | ||||||||
\(505\) | −7.40062e6 | −1.29134 | ||||||||
\(506\) | −143269. | −0.0248758 | ||||||||
\(507\) | −32160.6 | −0.00555654 | ||||||||
\(508\) | −1.95869e7 | −3.36749 | ||||||||
\(509\) | −4.33780e6 | −0.742122 | −0.371061 | − | 0.928609i | \(-0.621006\pi\) | ||||
−0.371061 | + | 0.928609i | \(0.621006\pi\) | |||||||
\(510\) | 188463. | 0.0320849 | ||||||||
\(511\) | −1.42169e6 | −0.240854 | ||||||||
\(512\) | 1.11564e7 | 1.88083 | ||||||||
\(513\) | −30174.8 | −0.00506234 | ||||||||
\(514\) | 4.52052e6 | 0.754711 | ||||||||
\(515\) | −1.04709e7 | −1.73966 | ||||||||
\(516\) | 30167.5 | 0.00498786 | ||||||||
\(517\) | 3.74682e6 | 0.616505 | ||||||||
\(518\) | 2.24427e6 | 0.367494 | ||||||||
\(519\) | 17332.9 | 0.00282458 | ||||||||
\(520\) | −4.67142e6 | −0.757601 | ||||||||
\(521\) | −8.15290e6 | −1.31588 | −0.657942 | − | 0.753068i | \(-0.728573\pi\) | ||||
−0.657942 | + | 0.753068i | \(0.728573\pi\) | |||||||
\(522\) | −6.69850e6 | −1.07597 | ||||||||
\(523\) | 9.26451e6 | 1.48105 | 0.740523 | − | 0.672032i | \(-0.234578\pi\) | ||||
0.740523 | + | 0.672032i | \(0.234578\pi\) | |||||||
\(524\) | −2.04253e7 | −3.24968 | ||||||||
\(525\) | 19632.1 | 0.00310862 | ||||||||
\(526\) | 1.44376e7 | 2.27525 | ||||||||
\(527\) | 1.03170e7 | 1.61818 | ||||||||
\(528\) | −34755.0 | −0.00542541 | ||||||||
\(529\) | −6.42897e6 | −0.998854 | ||||||||
\(530\) | −2.80069e7 | −4.33087 | ||||||||
\(531\) | 2.97554e6 | 0.457963 | ||||||||
\(532\) | 1.69996e6 | 0.260412 | ||||||||
\(533\) | −1.09942e6 | −0.167627 | ||||||||
\(534\) | 1175.03 | 0.000178319 0 | ||||||||
\(535\) | 1.69195e7 | 2.55567 | ||||||||
\(536\) | −6.28918e6 | −0.945544 | ||||||||
\(537\) | −4629.09 | −0.000692724 0 | ||||||||
\(538\) | −2.09523e7 | −3.12087 | ||||||||
\(539\) | 2.52549e6 | 0.374433 | ||||||||
\(540\) | 334795. | 0.0494077 | ||||||||
\(541\) | −7.81513e6 | −1.14800 | −0.574002 | − | 0.818854i | \(-0.694610\pi\) | ||||
−0.574002 | + | 0.818854i | \(0.694610\pi\) | |||||||
\(542\) | −4.36598e6 | −0.638387 | ||||||||
\(543\) | −21097.6 | −0.00307067 | ||||||||
\(544\) | −2.11646e7 | −3.06629 | ||||||||
\(545\) | −1.35635e7 | −1.95606 | ||||||||
\(546\) | 2902.07 | 0.000416607 0 | ||||||||
\(547\) | −2.68525e6 | −0.383721 | −0.191861 | − | 0.981422i | \(-0.561452\pi\) | ||||
−0.191861 | + | 0.981422i | \(0.561452\pi\) | |||||||
\(548\) | 3.09125e7 | 4.39727 | ||||||||
\(549\) | −6.01674e6 | −0.851983 | ||||||||
\(550\) | 1.16451e7 | 1.64148 | ||||||||
\(551\) | −1.84261e6 | −0.258556 | ||||||||
\(552\) | 3592.60 | 0.000501836 0 | ||||||||
\(553\) | −21546.6 | −0.00299616 | ||||||||
\(554\) | 39155.3 | 0.00542022 | ||||||||
\(555\) | 60790.2 | 0.00837725 | ||||||||
\(556\) | −3.23248e7 | −4.43454 | ||||||||
\(557\) | 2.78292e6 | 0.380070 | 0.190035 | − | 0.981777i | \(-0.439140\pi\) | ||||
0.190035 | + | 0.981777i | \(0.439140\pi\) | |||||||
\(558\) | 1.29702e7 | 1.76344 | ||||||||
\(559\) | −435003. | −0.0588793 | ||||||||
\(560\) | −7.77205e6 | −1.04729 | ||||||||
\(561\) | −28684.8 | −0.00384809 | ||||||||
\(562\) | −5.82394e6 | −0.777815 | ||||||||
\(563\) | −5.91196e6 | −0.786069 | −0.393034 | − | 0.919524i | \(-0.628575\pi\) | ||||
−0.393034 | + | 0.919524i | \(0.628575\pi\) | |||||||
\(564\) | −160714. | −0.0212743 | ||||||||
\(565\) | 1.45190e7 | 1.91345 | ||||||||
\(566\) | −5.04730e6 | −0.662244 | ||||||||
\(567\) | 1.86673e6 | 0.243851 | ||||||||
\(568\) | 2.83402e7 | 3.68580 | ||||||||
\(569\) | −448359. | −0.0580557 | −0.0290279 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290279 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(570\) | 65174.1 | 0.00840210 | ||||||||
\(571\) | 621363. | 0.0797545 | 0.0398772 | − | 0.999205i | \(-0.487303\pi\) | ||||
0.0398772 | + | 0.999205i | \(0.487303\pi\) | |||||||
\(572\) | 1.21621e6 | 0.155424 | ||||||||
\(573\) | −51950.9 | −0.00661008 | ||||||||
\(574\) | −3.67308e6 | −0.465319 | ||||||||
\(575\) | −599452. | −0.0756109 | ||||||||
\(576\) | −7.59259e6 | −0.953528 | ||||||||
\(577\) | 498167. | 0.0622925 | 0.0311463 | − | 0.999515i | \(-0.490084\pi\) | ||||
0.0311463 | + | 0.999515i | \(0.490084\pi\) | |||||||
\(578\) | −2.77096e7 | −3.44994 | ||||||||
\(579\) | 82222.4 | 0.0101928 | ||||||||
\(580\) | 2.04441e7 | 2.52347 | ||||||||
\(581\) | 797557. | 0.0980215 | ||||||||
\(582\) | −108431. | −0.0132692 | ||||||||
\(583\) | 4.26276e6 | 0.519421 | ||||||||
\(584\) | 2.11465e7 | 2.56571 | ||||||||
\(585\) | −2.41377e6 | −0.291612 | ||||||||
\(586\) | 1.63398e6 | 0.196563 | ||||||||
\(587\) | −6.21374e6 | −0.744317 | −0.372158 | − | 0.928169i | \(-0.621382\pi\) | ||||
−0.372158 | + | 0.928169i | \(0.621382\pi\) | |||||||
\(588\) | −108327. | −0.0129209 | ||||||||
\(589\) | 3.56782e6 | 0.423755 | ||||||||
\(590\) | −1.28539e7 | −1.52021 | ||||||||
\(591\) | −84633.2 | −0.00996718 | ||||||||
\(592\) | −1.66237e7 | −1.94950 | ||||||||
\(593\) | 9.00459e6 | 1.05154 | 0.525772 | − | 0.850626i | \(-0.323777\pi\) | ||||
0.525772 | + | 0.850626i | \(0.323777\pi\) | |||||||
\(594\) | −72124.4 | −0.00838718 | ||||||||
\(595\) | −6.41461e6 | −0.742811 | ||||||||
\(596\) | −4.81379e6 | −0.555100 | ||||||||
\(597\) | 57469.5 | 0.00659935 | ||||||||
\(598\) | −88612.7 | −0.0101331 | ||||||||
\(599\) | −1.01975e7 | −1.16125 | −0.580626 | − | 0.814170i | \(-0.697192\pi\) | ||||
−0.580626 | + | 0.814170i | \(0.697192\pi\) | |||||||
\(600\) | −292011. | −0.0331148 | ||||||||
\(601\) | −4.69600e6 | −0.530325 | −0.265162 | − | 0.964204i | \(-0.585426\pi\) | ||||
−0.265162 | + | 0.964204i | \(0.585426\pi\) | |||||||
\(602\) | −1.45331e6 | −0.163444 | ||||||||
\(603\) | −3.24968e6 | −0.363955 | ||||||||
\(604\) | −2.45729e6 | −0.274072 | ||||||||
\(605\) | 1.36237e7 | 1.51324 | ||||||||
\(606\) | −68385.1 | −0.00756449 | ||||||||
\(607\) | −2.60515e6 | −0.286986 | −0.143493 | − | 0.989651i | \(-0.545833\pi\) | ||||
−0.143493 | + | 0.989651i | \(0.545833\pi\) | |||||||
\(608\) | −7.31912e6 | −0.802971 | ||||||||
\(609\) | −7424.95 | −0.000811242 0 | ||||||||
\(610\) | 2.59913e7 | 2.82816 | ||||||||
\(611\) | 2.31743e6 | 0.251133 | ||||||||
\(612\) | −3.77808e7 | −4.07749 | ||||||||
\(613\) | −5.37292e6 | −0.577510 | −0.288755 | − | 0.957403i | \(-0.593241\pi\) | ||||
−0.288755 | + | 0.957403i | \(0.593241\pi\) | |||||||
\(614\) | −3.05948e7 | −3.27512 | ||||||||
\(615\) | −99492.3 | −0.0106072 | ||||||||
\(616\) | 2.37543e6 | 0.252227 | ||||||||
\(617\) | 1.49370e7 | 1.57961 | 0.789805 | − | 0.613358i | \(-0.210182\pi\) | ||||
0.789805 | + | 0.613358i | \(0.210182\pi\) | |||||||
\(618\) | −96755.5 | −0.0101907 | ||||||||
\(619\) | 1.32292e6 | 0.138773 | 0.0693866 | − | 0.997590i | \(-0.477896\pi\) | ||||
0.0693866 | + | 0.997590i | \(0.477896\pi\) | |||||||
\(620\) | −3.95856e7 | −4.13579 | ||||||||
\(621\) | 3712.73 | 0.000386335 0 | ||||||||
\(622\) | −2.90756e7 | −3.01338 | ||||||||
\(623\) | −39994.0 | −0.00412834 | ||||||||
\(624\) | −21496.2 | −0.00221004 | ||||||||
\(625\) | 1.71452e7 | 1.75567 | ||||||||
\(626\) | −1.65524e7 | −1.68821 | ||||||||
\(627\) | −9919.77 | −0.00100770 | ||||||||
\(628\) | −1.44508e7 | −1.46216 | ||||||||
\(629\) | −1.37203e7 | −1.38273 | ||||||||
\(630\) | −8.06423e6 | −0.809490 | ||||||||
\(631\) | 1.10949e7 | 1.10931 | 0.554653 | − | 0.832082i | \(-0.312851\pi\) | ||||
0.554653 | + | 0.832082i | \(0.312851\pi\) | |||||||
\(632\) | 320488. | 0.0319168 | ||||||||
\(633\) | 22057.4 | 0.00218799 | ||||||||
\(634\) | 1.09060e7 | 1.07757 | ||||||||
\(635\) | 2.55591e7 | 2.51543 | ||||||||
\(636\) | −182844. | −0.0179241 | ||||||||
\(637\) | 1.56203e6 | 0.152525 | ||||||||
\(638\) | −4.40424e6 | −0.428370 | ||||||||
\(639\) | 1.46437e7 | 1.41872 | ||||||||
\(640\) | −933842. | −0.0901205 | ||||||||
\(641\) | −5.36946e6 | −0.516162 | −0.258081 | − | 0.966123i | \(-0.583090\pi\) | ||||
−0.258081 | + | 0.966123i | \(0.583090\pi\) | |||||||
\(642\) | 156344. | 0.0149708 | ||||||||
\(643\) | 1.43277e7 | 1.36663 | 0.683314 | − | 0.730124i | \(-0.260538\pi\) | ||||
0.683314 | + | 0.730124i | \(0.260538\pi\) | |||||||
\(644\) | −209164. | −0.0198734 | ||||||||
\(645\) | −39365.8 | −0.00372580 | ||||||||
\(646\) | −1.47097e7 | −1.38683 | ||||||||
\(647\) | 1.91039e7 | 1.79417 | 0.897083 | − | 0.441863i | \(-0.145682\pi\) | ||||
0.897083 | + | 0.441863i | \(0.145682\pi\) | |||||||
\(648\) | −2.77661e7 | −2.59763 | ||||||||
\(649\) | 1.95641e6 | 0.182326 | ||||||||
\(650\) | 7.20256e6 | 0.668657 | ||||||||
\(651\) | 14376.8 | 0.00132957 | ||||||||
\(652\) | 1.38756e7 | 1.27830 | ||||||||
\(653\) | −1.10569e7 | −1.01473 | −0.507367 | − | 0.861730i | \(-0.669381\pi\) | ||||
−0.507367 | + | 0.861730i | \(0.669381\pi\) | |||||||
\(654\) | −125333. | −0.0114583 | ||||||||
\(655\) | 2.66532e7 | 2.42743 | ||||||||
\(656\) | 2.72072e7 | 2.46845 | ||||||||
\(657\) | 1.09266e7 | 0.987580 | ||||||||
\(658\) | 7.74237e6 | 0.697123 | ||||||||
\(659\) | −1.56580e7 | −1.40451 | −0.702253 | − | 0.711928i | \(-0.747822\pi\) | ||||
−0.702253 | + | 0.711928i | \(0.747822\pi\) | |||||||
\(660\) | 110062. | 0.00983503 | ||||||||
\(661\) | −4.90242e6 | −0.436422 | −0.218211 | − | 0.975902i | \(-0.570022\pi\) | ||||
−0.218211 | + | 0.975902i | \(0.570022\pi\) | |||||||
\(662\) | 3.82108e6 | 0.338876 | ||||||||
\(663\) | −17741.7 | −0.00156752 | ||||||||
\(664\) | −1.18630e7 | −1.04418 | ||||||||
\(665\) | −2.21830e6 | −0.194521 | ||||||||
\(666\) | −1.72486e7 | −1.50685 | ||||||||
\(667\) | 226716. | 0.0197318 | ||||||||
\(668\) | −3.78230e7 | −3.27955 | ||||||||
\(669\) | −100153. | −0.00865167 | ||||||||
\(670\) | 1.40381e7 | 1.20815 | ||||||||
\(671\) | −3.95599e6 | −0.339195 | ||||||||
\(672\) | −29493.0 | −0.00251939 | ||||||||
\(673\) | −3.58886e6 | −0.305435 | −0.152717 | − | 0.988270i | \(-0.548802\pi\) | ||||
−0.152717 | + | 0.988270i | \(0.548802\pi\) | |||||||
\(674\) | 2.01132e7 | 1.70542 | ||||||||
\(675\) | −301775. | −0.0254932 | ||||||||
\(676\) | −2.78507e7 | −2.34406 | ||||||||
\(677\) | 2.29248e6 | 0.192235 | 0.0961176 | − | 0.995370i | \(-0.469358\pi\) | ||||
0.0961176 | + | 0.995370i | \(0.469358\pi\) | |||||||
\(678\) | 134162. | 0.0112087 | ||||||||
\(679\) | 3.69060e6 | 0.307201 | ||||||||
\(680\) | 9.54123e7 | 7.91283 | ||||||||
\(681\) | 12433.7 | 0.00102738 | ||||||||
\(682\) | 8.52786e6 | 0.702068 | ||||||||
\(683\) | 4.74085e6 | 0.388870 | 0.194435 | − | 0.980915i | \(-0.437713\pi\) | ||||
0.194435 | + | 0.980915i | \(0.437713\pi\) | |||||||
\(684\) | −1.30653e7 | −1.06778 | ||||||||
\(685\) | −4.03380e7 | −3.28464 | ||||||||
\(686\) | 1.07673e7 | 0.873567 | ||||||||
\(687\) | 625.121 | 5.05327e−5 0 | ||||||||
\(688\) | 1.07650e7 | 0.867045 | ||||||||
\(689\) | 2.63654e6 | 0.211586 | ||||||||
\(690\) | −8019.05 | −0.000641210 0 | ||||||||
\(691\) | 1.78575e7 | 1.42274 | 0.711368 | − | 0.702819i | \(-0.248076\pi\) | ||||
0.711368 | + | 0.702819i | \(0.248076\pi\) | |||||||
\(692\) | 1.50101e7 | 1.19157 | ||||||||
\(693\) | 1.22741e6 | 0.0970860 | ||||||||
\(694\) | 1.83317e6 | 0.144478 | ||||||||
\(695\) | 4.21808e7 | 3.31248 | ||||||||
\(696\) | 110440. | 0.00864180 | ||||||||
\(697\) | 2.24553e7 | 1.75080 | ||||||||
\(698\) | −2.31557e7 | −1.79895 | ||||||||
\(699\) | −19739.4 | −0.00152806 | ||||||||
\(700\) | 1.70011e7 | 1.31139 | ||||||||
\(701\) | 2.21731e7 | 1.70425 | 0.852123 | − | 0.523342i | \(-0.175315\pi\) | ||||
0.852123 | + | 0.523342i | \(0.175315\pi\) | |||||||
\(702\) | −44609.3 | −0.00341651 | ||||||||
\(703\) | −4.74473e6 | −0.362096 | ||||||||
\(704\) | −4.99210e6 | −0.379622 | ||||||||
\(705\) | 209717. | 0.0158913 | ||||||||
\(706\) | −4.47566e7 | −3.37944 | ||||||||
\(707\) | 2.32759e6 | 0.175129 | ||||||||
\(708\) | −83917.1 | −0.00629169 | ||||||||
\(709\) | −2.21990e7 | −1.65851 | −0.829256 | − | 0.558869i | \(-0.811235\pi\) | ||||
−0.829256 | + | 0.558869i | \(0.811235\pi\) | |||||||
\(710\) | −6.32582e7 | −4.70946 | ||||||||
\(711\) | 165599. | 0.0122853 | ||||||||
\(712\) | 594879. | 0.0439773 | ||||||||
\(713\) | −438987. | −0.0323391 | ||||||||
\(714\) | −59273.9 | −0.00435129 | ||||||||
\(715\) | −1.58704e6 | −0.116098 | ||||||||
\(716\) | −4.00874e6 | −0.292230 | ||||||||
\(717\) | 142202. | 0.0103302 | ||||||||
\(718\) | 4.49570e7 | 3.25451 | ||||||||
\(719\) | 1.65127e6 | 0.119123 | 0.0595617 | − | 0.998225i | \(-0.481030\pi\) | ||||
0.0595617 | + | 0.998225i | \(0.481030\pi\) | |||||||
\(720\) | 5.97332e7 | 4.29422 | ||||||||
\(721\) | 3.29322e6 | 0.235930 | ||||||||
\(722\) | 2.07686e7 | 1.48274 | ||||||||
\(723\) | −35738.0 | −0.00254264 | ||||||||
\(724\) | −1.82702e7 | −1.29538 | ||||||||
\(725\) | −1.84278e7 | −1.30205 | ||||||||
\(726\) | 125889. | 0.00886435 | ||||||||
\(727\) | 2.79297e6 | 0.195988 | 0.0979942 | − | 0.995187i | \(-0.468757\pi\) | ||||
0.0979942 | + | 0.995187i | \(0.468757\pi\) | |||||||
\(728\) | 1.46922e6 | 0.102744 | ||||||||
\(729\) | −1.43461e7 | −0.999805 | ||||||||
\(730\) | −4.72012e7 | −3.27828 | ||||||||
\(731\) | 8.88480e6 | 0.614970 | ||||||||
\(732\) | 169686. | 0.0117049 | ||||||||
\(733\) | −1.07026e7 | −0.735751 | −0.367875 | − | 0.929875i | \(-0.619915\pi\) | ||||
−0.367875 | + | 0.929875i | \(0.619915\pi\) | |||||||
\(734\) | 421089. | 0.0288492 | ||||||||
\(735\) | 141357. | 0.00965158 | ||||||||
\(736\) | 900548. | 0.0612791 | ||||||||
\(737\) | −2.13665e6 | −0.144899 | ||||||||
\(738\) | 2.82300e7 | 1.90796 | ||||||||
\(739\) | 1.14888e7 | 0.773863 | 0.386932 | − | 0.922108i | \(-0.373535\pi\) | ||||
0.386932 | + | 0.922108i | \(0.373535\pi\) | |||||||
\(740\) | 5.26436e7 | 3.53400 | ||||||||
\(741\) | −6135.43 | −0.000410487 0 | ||||||||
\(742\) | 8.80850e6 | 0.587344 | ||||||||
\(743\) | 1.74855e7 | 1.16200 | 0.580999 | − | 0.813904i | \(-0.302662\pi\) | ||||
0.580999 | + | 0.813904i | \(0.302662\pi\) | |||||||
\(744\) | −213844. | −0.0141633 | ||||||||
\(745\) | 6.28155e6 | 0.414645 | ||||||||
\(746\) | −1.04081e7 | −0.684735 | ||||||||
\(747\) | −6.12974e6 | −0.401921 | ||||||||
\(748\) | −2.48407e7 | −1.62334 | ||||||||
\(749\) | −5.32141e6 | −0.346595 | ||||||||
\(750\) | 359995. | 0.0233692 | ||||||||
\(751\) | −315794. | −0.0204317 | −0.0102158 | − | 0.999948i | \(-0.503252\pi\) | ||||
−0.0102158 | + | 0.999948i | \(0.503252\pi\) | |||||||
\(752\) | −5.73491e7 | −3.69813 | ||||||||
\(753\) | −64026.3 | −0.00411501 | ||||||||
\(754\) | −2.72405e6 | −0.174496 | ||||||||
\(755\) | 3.20654e6 | 0.204724 | ||||||||
\(756\) | −105297. | −0.00670058 | ||||||||
\(757\) | −9.36700e6 | −0.594101 | −0.297051 | − | 0.954862i | \(-0.596003\pi\) | ||||
−0.297051 | + | 0.954862i | \(0.596003\pi\) | |||||||
\(758\) | 749672. | 0.0473913 | ||||||||
\(759\) | 1220.53 | 7.69033e−5 0 | ||||||||
\(760\) | 3.29954e7 | 2.07214 | ||||||||
\(761\) | 1.44409e7 | 0.903926 | 0.451963 | − | 0.892037i | \(-0.350724\pi\) | ||||
0.451963 | + | 0.892037i | \(0.350724\pi\) | |||||||
\(762\) | 236178. | 0.0147350 | ||||||||
\(763\) | 4.26590e6 | 0.265277 | ||||||||
\(764\) | −4.49889e7 | −2.78851 | ||||||||
\(765\) | 4.93005e7 | 3.04577 | ||||||||
\(766\) | −2.16615e7 | −1.33388 | ||||||||
\(767\) | 1.21005e6 | 0.0742703 | ||||||||
\(768\) | −97575.8 | −0.00596951 | ||||||||
\(769\) | 2.40377e7 | 1.46581 | 0.732903 | − | 0.680334i | \(-0.238165\pi\) | ||||
0.732903 | + | 0.680334i | \(0.238165\pi\) | |||||||
\(770\) | −5.30220e6 | −0.322277 | ||||||||
\(771\) | −38511.0 | −0.00233319 | ||||||||
\(772\) | 7.12036e7 | 4.29991 | ||||||||
\(773\) | 2.30732e7 | 1.38886 | 0.694430 | − | 0.719560i | \(-0.255657\pi\) | ||||
0.694430 | + | 0.719560i | \(0.255657\pi\) | |||||||
\(774\) | 1.11697e7 | 0.670174 | ||||||||
\(775\) | 3.56814e7 | 2.13397 | ||||||||
\(776\) | −5.48947e7 | −3.27247 | ||||||||
\(777\) | −19119.3 | −0.00113611 | ||||||||
\(778\) | 4.09573e7 | 2.42595 | ||||||||
\(779\) | 7.76547e6 | 0.458484 | ||||||||
\(780\) | 68073.7 | 0.00400629 | ||||||||
\(781\) | 9.62816e6 | 0.564827 | ||||||||
\(782\) | 1.80989e6 | 0.105836 | ||||||||
\(783\) | 114133. | 0.00665284 | ||||||||
\(784\) | −3.86554e7 | −2.24605 | ||||||||
\(785\) | 1.88570e7 | 1.09219 | ||||||||
\(786\) | 246287. | 0.0142195 | ||||||||
\(787\) | 1.28552e7 | 0.739847 | 0.369923 | − | 0.929062i | \(-0.379384\pi\) | ||||
0.369923 | + | 0.929062i | \(0.379384\pi\) | |||||||
\(788\) | −7.32914e7 | −4.20472 | ||||||||
\(789\) | −122996. | −0.00703394 | ||||||||
\(790\) | −715362. | −0.0407810 | ||||||||
\(791\) | −4.56642e6 | −0.259498 | ||||||||
\(792\) | −1.82567e7 | −1.03421 | ||||||||
\(793\) | −2.44680e6 | −0.138171 | ||||||||
\(794\) | 3.52931e7 | 1.98673 | ||||||||
\(795\) | 238595. | 0.0133889 | ||||||||
\(796\) | 4.97679e7 | 2.78398 | ||||||||
\(797\) | 3.15312e7 | 1.75831 | 0.879153 | − | 0.476540i | \(-0.158109\pi\) | ||||
0.879153 | + | 0.476540i | \(0.158109\pi\) | |||||||
\(798\) | −20498.1 | −0.00113948 | ||||||||
\(799\) | −4.73328e7 | −2.62298 | ||||||||
\(800\) | −7.31977e7 | −4.04364 | ||||||||
\(801\) | 307380. | 0.0169276 | ||||||||
\(802\) | 8.17698e6 | 0.448908 | ||||||||
\(803\) | 7.18422e6 | 0.393179 | ||||||||
\(804\) | 91648.3 | 0.00500017 | ||||||||
\(805\) | 272940. | 0.0148449 | ||||||||
\(806\) | 5.27453e6 | 0.285987 | ||||||||
\(807\) | 178496. | 0.00964815 | ||||||||
\(808\) | −3.46210e7 | −1.86557 | ||||||||
\(809\) | 2.88320e7 | 1.54883 | 0.774416 | − | 0.632677i | \(-0.218044\pi\) | ||||
0.774416 | + | 0.632677i | \(0.218044\pi\) | |||||||
\(810\) | 6.19768e7 | 3.31907 | ||||||||
\(811\) | −1.99774e7 | −1.06656 | −0.533281 | − | 0.845938i | \(-0.679041\pi\) | ||||
−0.533281 | + | 0.845938i | \(0.679041\pi\) | |||||||
\(812\) | −6.42992e6 | −0.342228 | ||||||||
\(813\) | 37194.5 | 0.00197357 | ||||||||
\(814\) | −1.13409e7 | −0.599912 | ||||||||
\(815\) | −1.81064e7 | −0.954859 | ||||||||
\(816\) | 439053. | 0.0230829 | ||||||||
\(817\) | 3.07253e6 | 0.161043 | ||||||||
\(818\) | 2.72049e6 | 0.142156 | ||||||||
\(819\) | 759160. | 0.0395479 | ||||||||
\(820\) | −8.61592e7 | −4.47473 | ||||||||
\(821\) | −1.23656e7 | −0.640259 | −0.320130 | − | 0.947374i | \(-0.603727\pi\) | ||||
−0.320130 | + | 0.947374i | \(0.603727\pi\) | |||||||
\(822\) | −372741. | −0.0192410 | ||||||||
\(823\) | 3.86496e6 | 0.198905 | 0.0994524 | − | 0.995042i | \(-0.468291\pi\) | ||||
0.0994524 | + | 0.995042i | \(0.468291\pi\) | |||||||
\(824\) | −4.89840e7 | −2.51325 | ||||||||
\(825\) | −99206.5 | −0.00507464 | ||||||||
\(826\) | 4.04270e6 | 0.206168 | ||||||||
\(827\) | 2.97722e7 | 1.51372 | 0.756862 | − | 0.653574i | \(-0.226731\pi\) | ||||
0.756862 | + | 0.653574i | \(0.226731\pi\) | |||||||
\(828\) | 1.60756e6 | 0.0814877 | ||||||||
\(829\) | −2.29386e7 | −1.15926 | −0.579630 | − | 0.814880i | \(-0.696803\pi\) | ||||
−0.579630 | + | 0.814880i | \(0.696803\pi\) | |||||||
\(830\) | 2.64795e7 | 1.33418 | ||||||||
\(831\) | −333.571 | −1.67566e−5 0 | ||||||||
\(832\) | −3.08764e6 | −0.154639 | ||||||||
\(833\) | −3.19040e7 | −1.59306 | ||||||||
\(834\) | 389770. | 0.0194041 | ||||||||
\(835\) | 4.93555e7 | 2.44974 | ||||||||
\(836\) | −8.59040e6 | −0.425107 | ||||||||
\(837\) | −220994. | −0.0109035 | ||||||||
\(838\) | −2.00834e7 | −0.987933 | ||||||||
\(839\) | 2.32540e7 | 1.14049 | 0.570246 | − | 0.821474i | \(-0.306848\pi\) | ||||
0.570246 | + | 0.821474i | \(0.306848\pi\) | |||||||
\(840\) | 132958. | 0.00650152 | ||||||||
\(841\) | −1.35417e7 | −0.660210 | ||||||||
\(842\) | 2.03003e7 | 0.986786 | ||||||||
\(843\) | 49615.1 | 0.00240461 | ||||||||
\(844\) | 1.91015e7 | 0.923019 | ||||||||
\(845\) | 3.63426e7 | 1.75095 | ||||||||
\(846\) | −5.95051e7 | −2.85844 | ||||||||
\(847\) | −4.28483e6 | −0.205222 | ||||||||
\(848\) | −6.52462e7 | −3.11577 | ||||||||
\(849\) | 42998.8 | 0.00204733 | ||||||||
\(850\) | −1.47110e8 | −6.98385 | ||||||||
\(851\) | 583794. | 0.0276335 | ||||||||
\(852\) | −412984. | −0.0194910 | ||||||||
\(853\) | −2.88545e7 | −1.35782 | −0.678909 | − | 0.734222i | \(-0.737547\pi\) | ||||
−0.678909 | + | 0.734222i | \(0.737547\pi\) | |||||||
\(854\) | −8.17459e6 | −0.383550 | ||||||||
\(855\) | 1.70490e7 | 0.797599 | ||||||||
\(856\) | 7.91517e7 | 3.69212 | ||||||||
\(857\) | 3.82033e7 | 1.77684 | 0.888420 | − | 0.459031i | \(-0.151803\pi\) | ||||
0.888420 | + | 0.459031i | \(0.151803\pi\) | |||||||
\(858\) | −14665.0 | −0.000680086 0 | ||||||||
\(859\) | −2.75321e7 | −1.27308 | −0.636542 | − | 0.771242i | \(-0.719636\pi\) | ||||
−0.636542 | + | 0.771242i | \(0.719636\pi\) | |||||||
\(860\) | −3.40903e7 | −1.57175 | ||||||||
\(861\) | 31291.6 | 0.00143853 | ||||||||
\(862\) | 2.20800e7 | 1.01212 | ||||||||
\(863\) | 3.05194e7 | 1.39492 | 0.697460 | − | 0.716624i | \(-0.254313\pi\) | ||||
0.697460 | + | 0.716624i | \(0.254313\pi\) | |||||||
\(864\) | 453353. | 0.0206610 | ||||||||
\(865\) | −1.95868e7 | −0.890068 | ||||||||
\(866\) | −5.13517e7 | −2.32680 | ||||||||
\(867\) | 236063. | 0.0106655 | ||||||||
\(868\) | 1.24502e7 | 0.560888 | ||||||||
\(869\) | 108881. | 0.00489106 | ||||||||
\(870\) | −246514. | −0.0110419 | ||||||||
\(871\) | −1.32153e6 | −0.0590245 | ||||||||
\(872\) | −6.34519e7 | −2.82588 | ||||||||
\(873\) | −2.83646e7 | −1.25962 | ||||||||
\(874\) | 625894. | 0.0277155 | ||||||||
\(875\) | −1.22530e7 | −0.541029 | ||||||||
\(876\) | −308155. | −0.0135678 | ||||||||
\(877\) | −8.70280e6 | −0.382085 | −0.191042 | − | 0.981582i | \(-0.561187\pi\) | ||||
−0.191042 | + | 0.981582i | \(0.561187\pi\) | |||||||
\(878\) | −1.15601e7 | −0.506087 | ||||||||
\(879\) | −13920.1 | −0.000607673 0 | ||||||||
\(880\) | 3.92744e7 | 1.70963 | ||||||||
\(881\) | 2.81193e7 | 1.22057 | 0.610287 | − | 0.792180i | \(-0.291054\pi\) | ||||
0.610287 | + | 0.792180i | \(0.291054\pi\) | |||||||
\(882\) | −4.01086e7 | −1.73607 | ||||||||
\(883\) | 3.78696e7 | 1.63452 | 0.817258 | − | 0.576272i | \(-0.195493\pi\) | ||||
0.817258 | + | 0.576272i | \(0.195493\pi\) | |||||||
\(884\) | −1.53641e7 | −0.661268 | ||||||||
\(885\) | 109504. | 0.00469972 | ||||||||
\(886\) | −2.55570e6 | −0.109377 | ||||||||
\(887\) | −4.01123e7 | −1.71186 | −0.855931 | − | 0.517090i | \(-0.827015\pi\) | ||||
−0.855931 | + | 0.517090i | \(0.827015\pi\) | |||||||
\(888\) | 284384. | 0.0121024 | ||||||||
\(889\) | −8.03866e6 | −0.341137 | ||||||||
\(890\) | −1.32783e6 | −0.0561911 | ||||||||
\(891\) | −9.43313e6 | −0.398072 | ||||||||
\(892\) | −8.67316e7 | −3.64977 | ||||||||
\(893\) | −1.63686e7 | −0.686882 | ||||||||
\(894\) | 58044.4 | 0.00242894 | ||||||||
\(895\) | 5.23104e6 | 0.218288 | ||||||||
\(896\) | 293705. | 0.0122220 | ||||||||
\(897\) | 754.906 | 3.13265e−5 0 | ||||||||
\(898\) | −6.57407e7 | −2.72047 | ||||||||
\(899\) | −1.34949e7 | −0.556891 | ||||||||
\(900\) | −1.30665e8 | −5.37715 | ||||||||
\(901\) | −5.38505e7 | −2.20993 | ||||||||
\(902\) | 1.85611e7 | 0.759605 | ||||||||
\(903\) | 12381.0 | 0.000505286 0 | ||||||||
\(904\) | 6.79218e7 | 2.76432 | ||||||||
\(905\) | 2.38410e7 | 0.967615 | ||||||||
\(906\) | 29629.9 | 0.00119925 | ||||||||
\(907\) | −2.61559e7 | −1.05573 | −0.527863 | − | 0.849330i | \(-0.677007\pi\) | ||||
−0.527863 | + | 0.849330i | \(0.677007\pi\) | |||||||
\(908\) | 1.07674e7 | 0.433407 | ||||||||
\(909\) | −1.78890e7 | −0.718086 | ||||||||
\(910\) | −3.27944e6 | −0.131279 | ||||||||
\(911\) | 8.13328e6 | 0.324690 | 0.162345 | − | 0.986734i | \(-0.448094\pi\) | ||||
0.162345 | + | 0.986734i | \(0.448094\pi\) | |||||||
\(912\) | 151833. | 0.00604475 | ||||||||
\(913\) | −4.03028e6 | −0.160014 | ||||||||
\(914\) | 4.03776e7 | 1.59873 | ||||||||
\(915\) | −221424. | −0.00874325 | ||||||||
\(916\) | 541348. | 0.0213176 | ||||||||
\(917\) | −8.38276e6 | −0.329203 | ||||||||
\(918\) | 911132. | 0.0356841 | ||||||||
\(919\) | 1.94329e7 | 0.759010 | 0.379505 | − | 0.925190i | \(-0.376094\pi\) | ||||
0.379505 | + | 0.925190i | \(0.376094\pi\) | |||||||
\(920\) | −4.05977e6 | −0.158136 | ||||||||
\(921\) | 260642. | 0.0101250 | ||||||||
\(922\) | 6.72319e6 | 0.260464 | ||||||||
\(923\) | 5.95507e6 | 0.230082 | ||||||||
\(924\) | −34615.7 | −0.00133381 | ||||||||
\(925\) | −4.74515e7 | −1.82346 | ||||||||
\(926\) | −2.89382e7 | −1.10903 | ||||||||
\(927\) | −2.53105e7 | −0.967390 | ||||||||
\(928\) | 2.76838e7 | 1.05525 | ||||||||
\(929\) | 2.81125e6 | 0.106871 | 0.0534355 | − | 0.998571i | \(-0.482983\pi\) | ||||
0.0534355 | + | 0.998571i | \(0.482983\pi\) | |||||||
\(930\) | 477321. | 0.0180969 | ||||||||
\(931\) | −1.10330e7 | −0.417177 | ||||||||
\(932\) | −1.70941e7 | −0.644624 | ||||||||
\(933\) | 247700. | 0.00931584 | ||||||||
\(934\) | −2.00469e7 | −0.751936 | ||||||||
\(935\) | 3.24149e7 | 1.21259 | ||||||||
\(936\) | −1.12919e7 | −0.421286 | ||||||||
\(937\) | 3.29554e7 | 1.22625 | 0.613123 | − | 0.789988i | \(-0.289913\pi\) | ||||
0.613123 | + | 0.789988i | \(0.289913\pi\) | |||||||
\(938\) | −4.41515e6 | −0.163847 | ||||||||
\(939\) | 141013. | 0.00521909 | ||||||||
\(940\) | 1.81612e8 | 6.70387 | ||||||||
\(941\) | 1.20204e7 | 0.442531 | 0.221265 | − | 0.975214i | \(-0.428981\pi\) | ||||
0.221265 | + | 0.975214i | \(0.428981\pi\) | |||||||
\(942\) | 174247. | 0.00639792 | ||||||||
\(943\) | −955466. | −0.0349894 | ||||||||
\(944\) | −2.99450e7 | −1.09369 | ||||||||
\(945\) | 137403. | 0.00500515 | ||||||||
\(946\) | 7.34402e6 | 0.266812 | ||||||||
\(947\) | 3.05242e7 | 1.10604 | 0.553019 | − | 0.833169i | \(-0.313476\pi\) | ||||
0.553019 | + | 0.833169i | \(0.313476\pi\) | |||||||
\(948\) | −4670.28 | −0.000168780 0 | ||||||||
\(949\) | 4.44348e6 | 0.160161 | ||||||||
\(950\) | −5.08735e7 | −1.82887 | ||||||||
\(951\) | −92910.3 | −0.00333129 | ||||||||
\(952\) | −3.00083e7 | −1.07312 | ||||||||
\(953\) | −5.11762e7 | −1.82531 | −0.912654 | − | 0.408733i | \(-0.865971\pi\) | ||||
−0.912654 | + | 0.408733i | \(0.865971\pi\) | |||||||
\(954\) | −6.76990e7 | −2.40831 | ||||||||
\(955\) | 5.87064e7 | 2.08294 | ||||||||
\(956\) | 1.23145e8 | 4.35786 | ||||||||
\(957\) | 37520.4 | 0.00132430 | ||||||||
\(958\) | −3.74741e7 | −1.31922 | ||||||||
\(959\) | 1.26868e7 | 0.445457 | ||||||||
\(960\) | −279418. | −0.00978533 | ||||||||
\(961\) | −2.49917e6 | −0.0872946 | ||||||||
\(962\) | −7.01443e6 | −0.244374 | ||||||||
\(963\) | 4.08985e7 | 1.42115 | ||||||||
\(964\) | −3.09487e7 | −1.07263 | ||||||||
\(965\) | −9.29142e7 | −3.21191 | ||||||||
\(966\) | 2522.09 | 8.69596e−5 0 | ||||||||
\(967\) | −4.38794e6 | −0.150902 | −0.0754509 | − | 0.997150i | \(-0.524040\pi\) | ||||
−0.0754509 | + | 0.997150i | \(0.524040\pi\) | |||||||
\(968\) | 6.37334e7 | 2.18614 | ||||||||
\(969\) | 125314. | 0.00428737 | ||||||||
\(970\) | 1.22530e8 | 4.18133 | ||||||||
\(971\) | −1.15532e7 | −0.393236 | −0.196618 | − | 0.980480i | \(-0.562996\pi\) | ||||
−0.196618 | + | 0.980480i | \(0.562996\pi\) | |||||||
\(972\) | 1.21392e6 | 0.0412122 | ||||||||
\(973\) | −1.32664e7 | −0.449232 | ||||||||
\(974\) | 1.18684e7 | 0.400863 | ||||||||
\(975\) | −61359.8 | −0.00206715 | ||||||||
\(976\) | 6.05507e7 | 2.03467 | ||||||||
\(977\) | 2.24021e7 | 0.750850 | 0.375425 | − | 0.926853i | \(-0.377497\pi\) | ||||
0.375425 | + | 0.926853i | \(0.377497\pi\) | |||||||
\(978\) | −167312. | −0.00559344 | ||||||||
\(979\) | 202101. | 0.00673926 | ||||||||
\(980\) | 1.22413e8 | 4.07158 | ||||||||
\(981\) | −3.27862e7 | −1.08772 | ||||||||
\(982\) | −1.13092e7 | −0.374243 | ||||||||
\(983\) | 966289. | 0.0318950 | ||||||||
\(984\) | −465437. | −0.0153240 | ||||||||
\(985\) | 9.56385e7 | 3.14081 | ||||||||
\(986\) | 5.56378e7 | 1.82254 | ||||||||
\(987\) | −65958.5 | −0.00215515 | ||||||||
\(988\) | −5.31321e6 | −0.173167 | ||||||||
\(989\) | −378046. | −0.0122901 | ||||||||
\(990\) | 4.07509e7 | 1.32144 | ||||||||
\(991\) | −3.76398e7 | −1.21748 | −0.608741 | − | 0.793369i | \(-0.708325\pi\) | ||||
−0.608741 | + | 0.793369i | \(0.708325\pi\) | |||||||
\(992\) | −5.36037e7 | −1.72948 | ||||||||
\(993\) | −32552.4 | −0.00104763 | ||||||||
\(994\) | 1.98955e7 | 0.638688 | ||||||||
\(995\) | −6.49425e7 | −2.07956 | ||||||||
\(996\) | 172872. | 0.00552176 | ||||||||
\(997\) | −2.78546e7 | −0.887480 | −0.443740 | − | 0.896156i | \(-0.646349\pi\) | ||||
−0.443740 | + | 0.896156i | \(0.646349\pi\) | |||||||
\(998\) | −3.30847e7 | −1.05148 | ||||||||
\(999\) | 293893. | 0.00931698 |
(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 | 983.6.a.b.1.11 | ✓ | 218 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.6.a.b.1.11 | ✓ | 218 | 1.1 | even | 1 | trivial |