Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.4 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.3 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.83573 | −1.91787 | −0.958933 | − | 0.283634i | \(-0.908460\pi\) | ||||
−0.958933 | + | 0.283634i | \(0.908460\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 10.7128 | 2.67821 | ||||||||
\(5\) | 8.86189i | 1.77238i | 0.463324 | + | 0.886189i | \(0.346657\pi\) | ||||
−0.463324 | + | 0.886189i | \(0.653343\pi\) | |||||||
\(6\) | −6.64368 | −1.10728 | ||||||||
\(7\) | − | 2.64575i | − | 0.377964i | ||||||
\(8\) | −25.7486 | −3.21857 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 33.9918i | − | 3.39918i | ||||||
\(11\) | 2.29410i | 0.208554i | 0.994548 | + | 0.104277i | \(0.0332529\pi\) | ||||
−0.994548 | + | 0.104277i | \(0.966747\pi\) | |||||||
\(12\) | 18.5552 | 1.54626 | ||||||||
\(13\) | 15.0567 | 1.15821 | 0.579105 | − | 0.815253i | \(-0.303402\pi\) | ||||
0.579105 | + | 0.815253i | \(0.303402\pi\) | |||||||
\(14\) | 10.1484i | 0.724885i | ||||||||
\(15\) | 15.3492i | 1.02328i | ||||||||
\(16\) | 55.9134 | 3.49459 | ||||||||
\(17\) | 7.09765i | 0.417509i | 0.977968 | + | 0.208754i | \(0.0669409\pi\) | ||||
−0.977968 | + | 0.208754i | \(0.933059\pi\) | |||||||
\(18\) | −11.5072 | −0.639288 | ||||||||
\(19\) | 22.0994i | 1.16313i | 0.813502 | + | 0.581563i | \(0.197558\pi\) | ||||
−0.813502 | + | 0.581563i | \(0.802442\pi\) | |||||||
\(20\) | 94.9359i | 4.74680i | ||||||||
\(21\) | − | 4.58258i | − | 0.218218i | ||||||
\(22\) | − | 8.79953i | − | 0.399979i | ||||||
\(23\) | 22.1641 | − | 6.14418i | 0.963658 | − | 0.267138i | ||||
\(24\) | −44.5979 | −1.85825 | ||||||||
\(25\) | −53.5331 | −2.14132 | ||||||||
\(26\) | −57.7536 | −2.22129 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 28.3435i | − | 1.01227i | ||||||
\(29\) | 39.3447 | 1.35671 | 0.678356 | − | 0.734733i | \(-0.262693\pi\) | ||||
0.678356 | + | 0.734733i | \(0.262693\pi\) | |||||||
\(30\) | − | 58.8756i | − | 1.96252i | ||||||
\(31\) | 6.20172 | 0.200055 | 0.100028 | − | 0.994985i | \(-0.468107\pi\) | ||||
0.100028 | + | 0.994985i | \(0.468107\pi\) | |||||||
\(32\) | −111.474 | −3.48357 | ||||||||
\(33\) | 3.97349i | 0.120409i | ||||||||
\(34\) | − | 27.2247i | − | 0.800725i | ||||||
\(35\) | 23.4464 | 0.669896 | ||||||||
\(36\) | 32.1385 | 0.892736 | ||||||||
\(37\) | − | 33.2177i | − | 0.897776i | −0.893588 | − | 0.448888i | \(-0.851820\pi\) | ||
0.893588 | − | 0.448888i | \(-0.148180\pi\) | |||||||
\(38\) | − | 84.7673i | − | 2.23072i | ||||||
\(39\) | 26.0790 | 0.668693 | ||||||||
\(40\) | − | 228.181i | − | 5.70453i | ||||||
\(41\) | −6.76874 | −0.165091 | −0.0825456 | − | 0.996587i | \(-0.526305\pi\) | ||||
−0.0825456 | + | 0.996587i | \(0.526305\pi\) | |||||||
\(42\) | 17.5775i | 0.418513i | ||||||||
\(43\) | 68.6344i | 1.59615i | 0.602559 | + | 0.798074i | \(0.294148\pi\) | ||||
−0.602559 | + | 0.798074i | \(0.705852\pi\) | |||||||
\(44\) | 24.5762i | 0.558551i | ||||||||
\(45\) | 26.5857i | 0.590793i | ||||||||
\(46\) | −85.0157 | + | 23.5674i | −1.84817 | + | 0.512336i | ||||
\(47\) | −56.9055 | −1.21076 | −0.605378 | − | 0.795938i | \(-0.706978\pi\) | ||||
−0.605378 | + | 0.795938i | \(0.706978\pi\) | |||||||
\(48\) | 96.8448 | 2.01760 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 205.339 | 4.10677 | ||||||||
\(51\) | 12.2935i | 0.241049i | ||||||||
\(52\) | 161.300 | 3.10193 | ||||||||
\(53\) | − | 6.03878i | − | 0.113939i | −0.998376 | − | 0.0569696i | \(-0.981856\pi\) | ||
0.998376 | − | 0.0569696i | \(-0.0181438\pi\) | |||||||
\(54\) | −19.9310 | −0.369093 | ||||||||
\(55\) | −20.3300 | −0.369637 | ||||||||
\(56\) | 68.1244i | 1.21651i | ||||||||
\(57\) | 38.2772i | 0.671531i | ||||||||
\(58\) | −150.916 | −2.60199 | ||||||||
\(59\) | −103.615 | −1.75618 | −0.878092 | − | 0.478492i | \(-0.841183\pi\) | ||||
−0.878092 | + | 0.478492i | \(0.841183\pi\) | |||||||
\(60\) | 164.434i | 2.74056i | ||||||||
\(61\) | 30.0632i | 0.492839i | 0.969163 | + | 0.246420i | \(0.0792541\pi\) | ||||
−0.969163 | + | 0.246420i | \(0.920746\pi\) | |||||||
\(62\) | −23.7881 | −0.383679 | ||||||||
\(63\) | − | 7.93725i | − | 0.125988i | ||||||
\(64\) | 203.932 | 3.18643 | ||||||||
\(65\) | 133.431i | 2.05279i | ||||||||
\(66\) | − | 15.2412i | − | 0.230928i | ||||||
\(67\) | − | 129.206i | − | 1.92844i | −0.265100 | − | 0.964221i | \(-0.585405\pi\) | ||
0.265100 | − | 0.964221i | \(-0.414595\pi\) | |||||||
\(68\) | 76.0359i | 1.11817i | ||||||||
\(69\) | 38.3894 | − | 10.6420i | 0.556368 | − | 0.154232i | ||||
\(70\) | −89.9339 | −1.28477 | ||||||||
\(71\) | 25.8589 | 0.364210 | 0.182105 | − | 0.983279i | \(-0.441709\pi\) | ||||
0.182105 | + | 0.983279i | \(0.441709\pi\) | |||||||
\(72\) | −77.2458 | −1.07286 | ||||||||
\(73\) | 0.973133 | 0.0133306 | 0.00666529 | − | 0.999978i | \(-0.497878\pi\) | ||||
0.00666529 | + | 0.999978i | \(0.497878\pi\) | |||||||
\(74\) | 127.414i | 1.72181i | ||||||||
\(75\) | −92.7221 | −1.23629 | ||||||||
\(76\) | 236.747i | 3.11509i | ||||||||
\(77\) | 6.06961 | 0.0788260 | ||||||||
\(78\) | −100.032 | −1.28246 | ||||||||
\(79\) | 78.4213i | 0.992675i | 0.868130 | + | 0.496338i | \(0.165322\pi\) | ||||
−0.868130 | + | 0.496338i | \(0.834678\pi\) | |||||||
\(80\) | 495.498i | 6.19373i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 25.9630 | 0.316623 | ||||||||
\(83\) | 71.3251i | 0.859339i | 0.902986 | + | 0.429669i | \(0.141370\pi\) | ||||
−0.902986 | + | 0.429669i | \(0.858630\pi\) | |||||||
\(84\) | − | 49.0923i | − | 0.584433i | ||||||
\(85\) | −62.8986 | −0.739983 | ||||||||
\(86\) | − | 263.263i | − | 3.06120i | ||||||
\(87\) | 68.1470 | 0.783298 | ||||||||
\(88\) | − | 59.0697i | − | 0.671247i | ||||||
\(89\) | 150.485i | 1.69084i | 0.534101 | + | 0.845421i | \(0.320650\pi\) | ||||
−0.534101 | + | 0.845421i | \(0.679350\pi\) | |||||||
\(90\) | − | 101.975i | − | 1.13306i | ||||||
\(91\) | − | 39.8364i | − | 0.437762i | ||||||
\(92\) | 237.441 | − | 65.8216i | 2.58088 | − | 0.715452i | ||||
\(93\) | 10.7417 | 0.115502 | ||||||||
\(94\) | 218.274 | 2.32206 | ||||||||
\(95\) | −195.842 | −2.06150 | ||||||||
\(96\) | −193.079 | −2.01124 | ||||||||
\(97\) | 164.879i | 1.69978i | 0.526961 | + | 0.849889i | \(0.323331\pi\) | ||||
−0.526961 | + | 0.849889i | \(0.676669\pi\) | |||||||
\(98\) | 26.8501 | 0.273981 | ||||||||
\(99\) | 6.88229i | 0.0695180i | ||||||||
\(100\) | −573.491 | −5.73491 | ||||||||
\(101\) | −4.46324 | −0.0441905 | −0.0220953 | − | 0.999756i | \(-0.507034\pi\) | ||||
−0.0220953 | + | 0.999756i | \(0.507034\pi\) | |||||||
\(102\) | − | 47.1545i | − | 0.462299i | ||||||
\(103\) | 17.4220i | 0.169146i | 0.996417 | + | 0.0845730i | \(0.0269526\pi\) | ||||
−0.996417 | + | 0.0845730i | \(0.973047\pi\) | |||||||
\(104\) | −387.690 | −3.72779 | ||||||||
\(105\) | 40.6103 | 0.386765 | ||||||||
\(106\) | 23.1631i | 0.218520i | ||||||||
\(107\) | − | 174.982i | − | 1.63535i | −0.575681 | − | 0.817674i | \(-0.695263\pi\) | ||
0.575681 | − | 0.817674i | \(-0.304737\pi\) | |||||||
\(108\) | 55.6655 | 0.515421 | ||||||||
\(109\) | 126.918i | 1.16439i | 0.813051 | + | 0.582193i | \(0.197805\pi\) | ||||
−0.813051 | + | 0.582193i | \(0.802195\pi\) | |||||||
\(110\) | 77.9805 | 0.708913 | ||||||||
\(111\) | − | 57.5347i | − | 0.518331i | ||||||
\(112\) | − | 147.933i | − | 1.32083i | ||||||
\(113\) | 28.0406i | 0.248147i | 0.992273 | + | 0.124073i | \(0.0395958\pi\) | ||||
−0.992273 | + | 0.124073i | \(0.960404\pi\) | |||||||
\(114\) | − | 146.821i | − | 1.28791i | ||||||
\(115\) | 54.4491 | + | 196.416i | 0.473470 | + | 1.70797i | ||||
\(116\) | 421.493 | 3.63356 | ||||||||
\(117\) | 45.1702 | 0.386070 | ||||||||
\(118\) | 397.439 | 3.36812 | ||||||||
\(119\) | 18.7786 | 0.157803 | ||||||||
\(120\) | − | 395.222i | − | 3.29351i | ||||||
\(121\) | 115.737 | 0.956505 | ||||||||
\(122\) | − | 115.314i | − | 0.945199i | ||||||
\(123\) | −11.7238 | −0.0953154 | ||||||||
\(124\) | 66.4379 | 0.535790 | ||||||||
\(125\) | − | 252.857i | − | 2.02286i | ||||||
\(126\) | 30.4452i | 0.241628i | ||||||||
\(127\) | 136.369 | 1.07377 | 0.536886 | − | 0.843655i | \(-0.319600\pi\) | ||||
0.536886 | + | 0.843655i | \(0.319600\pi\) | |||||||
\(128\) | −336.330 | −2.62758 | ||||||||
\(129\) | 118.878i | 0.921536i | ||||||||
\(130\) | − | 511.806i | − | 3.93697i | ||||||
\(131\) | −109.648 | −0.837005 | −0.418502 | − | 0.908216i | \(-0.637445\pi\) | ||||
−0.418502 | + | 0.908216i | \(0.637445\pi\) | |||||||
\(132\) | 42.5673i | 0.322480i | ||||||||
\(133\) | 58.4695 | 0.439620 | ||||||||
\(134\) | 495.598i | 3.69849i | ||||||||
\(135\) | 46.0477i | 0.341094i | ||||||||
\(136\) | − | 182.754i | − | 1.34378i | ||||||
\(137\) | − | 265.750i | − | 1.93978i | −0.243537 | − | 0.969892i | \(-0.578308\pi\) | ||
0.243537 | − | 0.969892i | \(-0.421692\pi\) | |||||||
\(138\) | −147.251 | + | 40.8200i | −1.06704 | + | 0.295797i | ||||
\(139\) | −202.123 | −1.45412 | −0.727061 | − | 0.686573i | \(-0.759114\pi\) | ||||
−0.727061 | + | 0.686573i | \(0.759114\pi\) | |||||||
\(140\) | 251.177 | 1.79412 | ||||||||
\(141\) | −98.5632 | −0.699030 | ||||||||
\(142\) | −99.1878 | −0.698505 | ||||||||
\(143\) | 34.5416i | 0.241549i | ||||||||
\(144\) | 167.740 | 1.16486 | ||||||||
\(145\) | 348.668i | 2.40461i | ||||||||
\(146\) | −3.73267 | −0.0255663 | ||||||||
\(147\) | −12.1244 | −0.0824786 | ||||||||
\(148\) | − | 355.856i | − | 2.40443i | ||||||
\(149\) | 99.4774i | 0.667634i | 0.942638 | + | 0.333817i | \(0.108337\pi\) | ||||
−0.942638 | + | 0.333817i | \(0.891663\pi\) | |||||||
\(150\) | 355.657 | 2.37105 | ||||||||
\(151\) | −40.4629 | −0.267966 | −0.133983 | − | 0.990984i | \(-0.542777\pi\) | ||||
−0.133983 | + | 0.990984i | \(0.542777\pi\) | |||||||
\(152\) | − | 569.028i | − | 3.74361i | ||||||
\(153\) | 21.2929i | 0.139170i | ||||||||
\(154\) | −23.2814 | −0.151178 | ||||||||
\(155\) | 54.9589i | 0.354574i | ||||||||
\(156\) | 279.380 | 1.79090 | ||||||||
\(157\) | − | 154.947i | − | 0.986925i | −0.869767 | − | 0.493462i | \(-0.835731\pi\) | ||
0.869767 | − | 0.493462i | \(-0.164269\pi\) | |||||||
\(158\) | − | 300.803i | − | 1.90382i | ||||||
\(159\) | − | 10.4595i | − | 0.0657829i | ||||||
\(160\) | − | 987.872i | − | 6.17420i | ||||||
\(161\) | −16.2560 | − | 58.6408i | −0.100969 | − | 0.364229i | ||||
\(162\) | −34.5216 | −0.213096 | ||||||||
\(163\) | −157.550 | −0.966562 | −0.483281 | − | 0.875465i | \(-0.660555\pi\) | ||||
−0.483281 | + | 0.875465i | \(0.660555\pi\) | |||||||
\(164\) | −72.5123 | −0.442148 | ||||||||
\(165\) | −35.2126 | −0.213410 | ||||||||
\(166\) | − | 273.584i | − | 1.64810i | ||||||
\(167\) | −57.3615 | −0.343482 | −0.171741 | − | 0.985142i | \(-0.554939\pi\) | ||||
−0.171741 | + | 0.985142i | \(0.554939\pi\) | |||||||
\(168\) | 117.995i | 0.702351i | ||||||||
\(169\) | 57.7051 | 0.341450 | ||||||||
\(170\) | 241.262 | 1.41919 | ||||||||
\(171\) | 66.2981i | 0.387708i | ||||||||
\(172\) | 735.268i | 4.27481i | ||||||||
\(173\) | 268.463 | 1.55181 | 0.775903 | − | 0.630852i | \(-0.217294\pi\) | ||||
0.775903 | + | 0.630852i | \(0.217294\pi\) | |||||||
\(174\) | −261.393 | −1.50226 | ||||||||
\(175\) | 141.635i | 0.809344i | ||||||||
\(176\) | 128.271i | 0.728810i | ||||||||
\(177\) | −179.466 | −1.01393 | ||||||||
\(178\) | − | 577.219i | − | 3.24281i | ||||||
\(179\) | −90.7832 | −0.507169 | −0.253584 | − | 0.967313i | \(-0.581610\pi\) | ||||
−0.253584 | + | 0.967313i | \(0.581610\pi\) | |||||||
\(180\) | 284.808i | 1.58227i | ||||||||
\(181\) | 0.138624i | 0.000765878i | 1.00000 | 0.000382939i | \(0.000121893\pi\) | |||||
−1.00000 | 0.000382939i | \(0.999878\pi\) | ||||||||
\(182\) | 152.802i | 0.839569i | ||||||||
\(183\) | 52.0710i | 0.284541i | ||||||||
\(184\) | −570.695 | + | 158.204i | −3.10161 | + | 0.859805i | ||||
\(185\) | 294.372 | 1.59120 | ||||||||
\(186\) | −41.2022 | −0.221517 | ||||||||
\(187\) | −16.2827 | −0.0870731 | ||||||||
\(188\) | −609.619 | −3.24265 | ||||||||
\(189\) | − | 13.7477i | − | 0.0727393i | ||||||
\(190\) | 751.198 | 3.95367 | ||||||||
\(191\) | − | 147.161i | − | 0.770475i | −0.922818 | − | 0.385237i | \(-0.874120\pi\) | ||
0.922818 | − | 0.385237i | \(-0.125880\pi\) | |||||||
\(192\) | 353.220 | 1.83969 | ||||||||
\(193\) | 103.961 | 0.538659 | 0.269329 | − | 0.963048i | \(-0.413198\pi\) | ||||
0.269329 | + | 0.963048i | \(0.413198\pi\) | |||||||
\(194\) | − | 632.430i | − | 3.25995i | ||||||
\(195\) | 231.109i | 1.18518i | ||||||||
\(196\) | −74.9898 | −0.382601 | ||||||||
\(197\) | −104.624 | −0.531089 | −0.265544 | − | 0.964099i | \(-0.585552\pi\) | ||||
−0.265544 | + | 0.964099i | \(0.585552\pi\) | |||||||
\(198\) | − | 26.3986i | − | 0.133326i | ||||||
\(199\) | 67.7199i | 0.340301i | 0.985418 | + | 0.170151i | \(0.0544254\pi\) | ||||
−0.985418 | + | 0.170151i | \(0.945575\pi\) | |||||||
\(200\) | 1378.40 | 6.89201 | ||||||||
\(201\) | − | 223.791i | − | 1.11339i | ||||||
\(202\) | 17.1198 | 0.0847514 | ||||||||
\(203\) | − | 104.096i | − | 0.512789i | ||||||
\(204\) | 131.698i | 0.645578i | ||||||||
\(205\) | − | 59.9838i | − | 0.292604i | ||||||
\(206\) | − | 66.8262i | − | 0.324399i | ||||||
\(207\) | 66.4924 | − | 18.4326i | 0.321219 | − | 0.0890462i | ||||
\(208\) | 841.872 | 4.04746 | ||||||||
\(209\) | −50.6981 | −0.242575 | ||||||||
\(210\) | −155.770 | −0.741762 | ||||||||
\(211\) | 205.955 | 0.976089 | 0.488045 | − | 0.872819i | \(-0.337710\pi\) | ||||
0.488045 | + | 0.872819i | \(0.337710\pi\) | |||||||
\(212\) | − | 64.6924i | − | 0.305153i | ||||||
\(213\) | 44.7889 | 0.210277 | ||||||||
\(214\) | 671.185i | 3.13638i | ||||||||
\(215\) | −608.230 | −2.82898 | ||||||||
\(216\) | −133.794 | −0.619415 | ||||||||
\(217\) | − | 16.4082i | − | 0.0756138i | ||||||
\(218\) | − | 486.823i | − | 2.23313i | ||||||
\(219\) | 1.68552 | 0.00769642 | ||||||||
\(220\) | −217.792 | −0.989964 | ||||||||
\(221\) | 106.867i | 0.483562i | ||||||||
\(222\) | 220.688i | 0.994089i | ||||||||
\(223\) | −222.235 | −0.996569 | −0.498285 | − | 0.867013i | \(-0.666037\pi\) | ||||
−0.498285 | + | 0.867013i | \(0.666037\pi\) | |||||||
\(224\) | 294.933i | 1.31667i | ||||||||
\(225\) | −160.599 | −0.713775 | ||||||||
\(226\) | − | 107.556i | − | 0.475912i | ||||||
\(227\) | 122.880i | 0.541323i | 0.962675 | + | 0.270662i | \(0.0872424\pi\) | ||||
−0.962675 | + | 0.270662i | \(0.912758\pi\) | |||||||
\(228\) | 410.058i | 1.79850i | ||||||||
\(229\) | 46.7869i | 0.204309i | 0.994769 | + | 0.102155i | \(0.0325737\pi\) | ||||
−0.994769 | + | 0.102155i | \(0.967426\pi\) | |||||||
\(230\) | −208.852 | − | 753.399i | −0.908052 | − | 3.27565i | ||||
\(231\) | 10.5129 | 0.0455102 | ||||||||
\(232\) | −1013.07 | −4.36668 | ||||||||
\(233\) | 370.382 | 1.58962 | 0.794812 | − | 0.606856i | \(-0.207569\pi\) | ||||
0.794812 | + | 0.606856i | \(0.207569\pi\) | |||||||
\(234\) | −173.261 | −0.740430 | ||||||||
\(235\) | − | 504.290i | − | 2.14592i | ||||||
\(236\) | −1110.01 | −4.70342 | ||||||||
\(237\) | 135.830i | 0.573121i | ||||||||
\(238\) | −72.0297 | −0.302646 | ||||||||
\(239\) | 244.361 | 1.02243 | 0.511216 | − | 0.859452i | \(-0.329195\pi\) | ||||
0.511216 | + | 0.859452i | \(0.329195\pi\) | |||||||
\(240\) | 858.228i | 3.57595i | ||||||||
\(241\) | 144.596i | 0.599984i | 0.953942 | + | 0.299992i | \(0.0969840\pi\) | ||||
−0.953942 | + | 0.299992i | \(0.903016\pi\) | |||||||
\(242\) | −443.936 | −1.83445 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 322.062i | 1.31993i | ||||||||
\(245\) | − | 62.0332i | − | 0.253197i | ||||||
\(246\) | 44.9693 | 0.182802 | ||||||||
\(247\) | 332.744i | 1.34714i | ||||||||
\(248\) | −159.685 | −0.643893 | ||||||||
\(249\) | 123.539i | 0.496140i | ||||||||
\(250\) | 969.892i | 3.87957i | ||||||||
\(251\) | 164.873i | 0.656866i | 0.944527 | + | 0.328433i | \(0.106521\pi\) | ||||
−0.944527 | + | 0.328433i | \(0.893479\pi\) | |||||||
\(252\) | − | 85.0304i | − | 0.337422i | ||||||
\(253\) | 14.0953 | + | 50.8466i | 0.0557128 | + | 0.200975i | ||||
\(254\) | −523.075 | −2.05935 | ||||||||
\(255\) | −108.943 | −0.427229 | ||||||||
\(256\) | 474.344 | 1.85291 | ||||||||
\(257\) | 70.0744 | 0.272663 | 0.136332 | − | 0.990663i | \(-0.456469\pi\) | ||||
0.136332 | + | 0.990663i | \(0.456469\pi\) | |||||||
\(258\) | − | 455.985i | − | 1.76738i | ||||||
\(259\) | −87.8858 | −0.339327 | ||||||||
\(260\) | 1429.42i | 5.49779i | ||||||||
\(261\) | 118.034 | 0.452238 | ||||||||
\(262\) | 420.579 | 1.60526 | ||||||||
\(263\) | 37.4693i | 0.142469i | 0.997460 | + | 0.0712344i | \(0.0226938\pi\) | ||||
−0.997460 | + | 0.0712344i | \(0.977306\pi\) | |||||||
\(264\) | − | 102.312i | − | 0.387545i | ||||||
\(265\) | 53.5150 | 0.201943 | ||||||||
\(266\) | −224.273 | −0.843132 | ||||||||
\(267\) | 260.647i | 0.976208i | ||||||||
\(268\) | − | 1384.16i | − | 5.16477i | ||||||
\(269\) | −231.229 | −0.859586 | −0.429793 | − | 0.902927i | \(-0.641414\pi\) | ||||
−0.429793 | + | 0.902927i | \(0.641414\pi\) | |||||||
\(270\) | − | 176.627i | − | 0.654173i | ||||||
\(271\) | 48.6653 | 0.179577 | 0.0897884 | − | 0.995961i | \(-0.471381\pi\) | ||||
0.0897884 | + | 0.995961i | \(0.471381\pi\) | |||||||
\(272\) | 396.853i | 1.45902i | ||||||||
\(273\) | − | 68.9986i | − | 0.252742i | ||||||
\(274\) | 1019.35i | 3.72024i | ||||||||
\(275\) | − | 122.810i | − | 0.446582i | ||||||
\(276\) | 411.259 | − | 114.006i | 1.49007 | − | 0.413066i | ||||
\(277\) | −12.4790 | −0.0450504 | −0.0225252 | − | 0.999746i | \(-0.507171\pi\) | ||||
−0.0225252 | + | 0.999746i | \(0.507171\pi\) | |||||||
\(278\) | 775.289 | 2.78881 | ||||||||
\(279\) | 18.6051 | 0.0666851 | ||||||||
\(280\) | −603.711 | −2.15611 | ||||||||
\(281\) | − | 265.717i | − | 0.945613i | −0.881166 | − | 0.472807i | \(-0.843241\pi\) | ||
0.881166 | − | 0.472807i | \(-0.156759\pi\) | |||||||
\(282\) | 378.062 | 1.34064 | ||||||||
\(283\) | − | 463.763i | − | 1.63874i | −0.573266 | − | 0.819370i | \(-0.694324\pi\) | ||
0.573266 | − | 0.819370i | \(-0.305676\pi\) | |||||||
\(284\) | 277.022 | 0.975429 | ||||||||
\(285\) | −339.209 | −1.19021 | ||||||||
\(286\) | − | 132.492i | − | 0.463259i | ||||||
\(287\) | 17.9084i | 0.0623986i | ||||||||
\(288\) | −334.423 | −1.16119 | ||||||||
\(289\) | 238.623 | 0.825687 | ||||||||
\(290\) | − | 1337.40i | − | 4.61171i | ||||||
\(291\) | 285.578i | 0.981368i | ||||||||
\(292\) | 10.4250 | 0.0357021 | ||||||||
\(293\) | − | 299.454i | − | 1.02203i | −0.859572 | − | 0.511014i | \(-0.829270\pi\) | ||
0.859572 | − | 0.511014i | \(-0.170730\pi\) | |||||||
\(294\) | 46.5058 | 0.158183 | ||||||||
\(295\) | − | 918.223i | − | 3.11262i | ||||||
\(296\) | 855.309i | 2.88956i | ||||||||
\(297\) | 11.9205i | 0.0401363i | ||||||||
\(298\) | − | 381.569i | − | 1.28043i | ||||||
\(299\) | 333.719 | − | 92.5113i | 1.11612 | − | 0.309402i | ||||
\(300\) | −993.315 | −3.31105 | ||||||||
\(301\) | 181.589 | 0.603287 | ||||||||
\(302\) | 155.205 | 0.513923 | ||||||||
\(303\) | −7.73056 | −0.0255134 | ||||||||
\(304\) | 1235.65i | 4.06464i | ||||||||
\(305\) | −266.417 | −0.873497 | ||||||||
\(306\) | − | 81.6740i | − | 0.266908i | ||||||
\(307\) | 562.045 | 1.83077 | 0.915383 | − | 0.402583i | \(-0.131888\pi\) | ||||
0.915383 | + | 0.402583i | \(0.131888\pi\) | |||||||
\(308\) | 65.0226 | 0.211112 | ||||||||
\(309\) | 30.1759i | 0.0976565i | ||||||||
\(310\) | − | 210.808i | − | 0.680025i | ||||||
\(311\) | 153.549 | 0.493726 | 0.246863 | − | 0.969050i | \(-0.420600\pi\) | ||||
0.246863 | + | 0.969050i | \(0.420600\pi\) | |||||||
\(312\) | −671.498 | −2.15224 | ||||||||
\(313\) | − | 360.712i | − | 1.15243i | −0.817297 | − | 0.576217i | \(-0.804528\pi\) | ||
0.817297 | − | 0.576217i | \(-0.195472\pi\) | |||||||
\(314\) | 594.336i | 1.89279i | ||||||||
\(315\) | 70.3391 | 0.223299 | ||||||||
\(316\) | 840.114i | 2.65859i | ||||||||
\(317\) | 168.048 | 0.530119 | 0.265059 | − | 0.964232i | \(-0.414608\pi\) | ||||
0.265059 | + | 0.964232i | \(0.414608\pi\) | |||||||
\(318\) | 40.1197i | 0.126163i | ||||||||
\(319\) | 90.2604i | 0.282948i | ||||||||
\(320\) | 1807.22i | 5.64756i | ||||||||
\(321\) | − | 303.078i | − | 0.944169i | ||||||
\(322\) | 62.3536 | + | 224.930i | 0.193645 | + | 0.698541i | ||||
\(323\) | −156.854 | −0.485615 | ||||||||
\(324\) | 96.4155 | 0.297579 | ||||||||
\(325\) | −806.033 | −2.48010 | ||||||||
\(326\) | 604.318 | 1.85374 | ||||||||
\(327\) | 219.828i | 0.672258i | ||||||||
\(328\) | 174.285 | 0.531358 | ||||||||
\(329\) | 150.558i | 0.457622i | ||||||||
\(330\) | 135.066 | 0.409291 | ||||||||
\(331\) | 546.021 | 1.64961 | 0.824805 | − | 0.565417i | \(-0.191285\pi\) | ||||
0.824805 | + | 0.565417i | \(0.191285\pi\) | |||||||
\(332\) | 764.094i | 2.30149i | ||||||||
\(333\) | − | 99.6531i | − | 0.299259i | ||||||
\(334\) | 220.023 | 0.658752 | ||||||||
\(335\) | 1145.01 | 3.41793 | ||||||||
\(336\) | − | 256.227i | − | 0.762581i | ||||||
\(337\) | − | 283.226i | − | 0.840434i | −0.907424 | − | 0.420217i | \(-0.861954\pi\) | ||
0.907424 | − | 0.420217i | \(-0.138046\pi\) | |||||||
\(338\) | −221.341 | −0.654855 | ||||||||
\(339\) | 48.5677i | 0.143268i | ||||||||
\(340\) | −673.821 | −1.98183 | ||||||||
\(341\) | 14.2273i | 0.0417224i | ||||||||
\(342\) | − | 254.302i | − | 0.743572i | ||||||
\(343\) | 18.5203i | 0.0539949i | ||||||||
\(344\) | − | 1767.24i | − | 5.13732i | ||||||
\(345\) | 94.3086 | + | 340.203i | 0.273358 | + | 0.986095i | ||||
\(346\) | −1029.75 | −2.97616 | ||||||||
\(347\) | 123.133 | 0.354850 | 0.177425 | − | 0.984134i | \(-0.443223\pi\) | ||||
0.177425 | + | 0.984134i | \(0.443223\pi\) | |||||||
\(348\) | 730.047 | 2.09784 | ||||||||
\(349\) | −330.667 | −0.947470 | −0.473735 | − | 0.880667i | \(-0.657095\pi\) | ||||
−0.473735 | + | 0.880667i | \(0.657095\pi\) | |||||||
\(350\) | − | 543.275i | − | 1.55221i | ||||||
\(351\) | 78.2371 | 0.222898 | ||||||||
\(352\) | − | 255.733i | − | 0.726513i | ||||||
\(353\) | −2.49981 | −0.00708161 | −0.00354080 | − | 0.999994i | \(-0.501127\pi\) | ||||
−0.00354080 | + | 0.999994i | \(0.501127\pi\) | |||||||
\(354\) | 688.384 | 1.94459 | ||||||||
\(355\) | 229.159i | 0.645518i | ||||||||
\(356\) | 1612.12i | 4.52842i | ||||||||
\(357\) | 32.5255 | 0.0911078 | ||||||||
\(358\) | 348.220 | 0.972681 | ||||||||
\(359\) | − | 142.325i | − | 0.396449i | −0.980157 | − | 0.198224i | \(-0.936483\pi\) | ||
0.980157 | − | 0.198224i | \(-0.0635175\pi\) | |||||||
\(360\) | − | 684.544i | − | 1.90151i | ||||||
\(361\) | −127.383 | −0.352860 | ||||||||
\(362\) | − | 0.531724i | − | 0.00146885i | ||||||
\(363\) | 200.463 | 0.552239 | ||||||||
\(364\) | − | 426.760i | − | 1.17242i | ||||||
\(365\) | 8.62379i | 0.0236268i | ||||||||
\(366\) | − | 199.730i | − | 0.545711i | ||||||
\(367\) | 35.9679i | 0.0980053i | 0.998799 | + | 0.0490027i | \(0.0156043\pi\) | ||||
−0.998799 | + | 0.0490027i | \(0.984396\pi\) | |||||||
\(368\) | 1239.27 | − | 343.542i | 3.36759 | − | 0.933538i | ||||
\(369\) | −20.3062 | −0.0550304 | ||||||||
\(370\) | −1129.13 | −3.05170 | ||||||||
\(371\) | −15.9771 | −0.0430650 | ||||||||
\(372\) | 115.074 | 0.309338 | ||||||||
\(373\) | 422.662i | 1.13314i | 0.824013 | + | 0.566571i | \(0.191730\pi\) | ||||
−0.824013 | + | 0.566571i | \(0.808270\pi\) | |||||||
\(374\) | 62.4559 | 0.166995 | ||||||||
\(375\) | − | 437.962i | − | 1.16790i | ||||||
\(376\) | 1465.24 | 3.89691 | ||||||||
\(377\) | 592.402 | 1.57136 | ||||||||
\(378\) | 52.7326i | 0.139504i | ||||||||
\(379\) | − | 533.484i | − | 1.40761i | −0.710394 | − | 0.703805i | \(-0.751483\pi\) | ||
0.710394 | − | 0.703805i | \(-0.248517\pi\) | |||||||
\(380\) | −2098.02 | −5.52112 | ||||||||
\(381\) | 236.198 | 0.619943 | ||||||||
\(382\) | 564.469i | 1.47767i | ||||||||
\(383\) | − | 447.089i | − | 1.16734i | −0.811993 | − | 0.583668i | \(-0.801617\pi\) | ||
0.811993 | − | 0.583668i | \(-0.198383\pi\) | |||||||
\(384\) | −582.540 | −1.51703 | ||||||||
\(385\) | 53.7882i | 0.139710i | ||||||||
\(386\) | −398.767 | −1.03308 | ||||||||
\(387\) | 205.903i | 0.532049i | ||||||||
\(388\) | 1766.32i | 4.55236i | ||||||||
\(389\) | 384.353i | 0.988055i | 0.869446 | + | 0.494027i | \(0.164476\pi\) | ||||
−0.869446 | + | 0.494027i | \(0.835524\pi\) | |||||||
\(390\) | − | 886.473i | − | 2.27301i | ||||||
\(391\) | 43.6092 | + | 157.313i | 0.111533 | + | 0.402335i | ||||
\(392\) | 180.240 | 0.459796 | ||||||||
\(393\) | −189.915 | −0.483245 | ||||||||
\(394\) | 401.311 | 1.01856 | ||||||||
\(395\) | −694.961 | −1.75940 | ||||||||
\(396\) | 73.7287i | 0.186184i | ||||||||
\(397\) | −427.857 | −1.07772 | −0.538862 | − | 0.842394i | \(-0.681146\pi\) | ||||
−0.538862 | + | 0.842394i | \(0.681146\pi\) | |||||||
\(398\) | − | 259.755i | − | 0.652652i | ||||||
\(399\) | 101.272 | 0.253815 | ||||||||
\(400\) | −2993.22 | −7.48304 | ||||||||
\(401\) | − | 52.0462i | − | 0.129791i | −0.997892 | − | 0.0648955i | \(-0.979329\pi\) | ||
0.997892 | − | 0.0648955i | \(-0.0206714\pi\) | |||||||
\(402\) | 858.401i | 2.13533i | ||||||||
\(403\) | 93.3775 | 0.231706 | ||||||||
\(404\) | −47.8139 | −0.118351 | ||||||||
\(405\) | 79.7570i | 0.196931i | ||||||||
\(406\) | 399.285i | 0.983461i | ||||||||
\(407\) | 76.2046 | 0.187235 | ||||||||
\(408\) | − | 316.540i | − | 0.775833i | ||||||
\(409\) | 409.460 | 1.00112 | 0.500562 | − | 0.865701i | \(-0.333127\pi\) | ||||
0.500562 | + | 0.865701i | \(0.333127\pi\) | |||||||
\(410\) | 230.082i | 0.561175i | ||||||||
\(411\) | − | 460.293i | − | 1.11993i | ||||||
\(412\) | 186.639i | 0.453008i | ||||||||
\(413\) | 274.139i | 0.663775i | ||||||||
\(414\) | −255.047 | + | 70.7023i | −0.616055 | + | 0.170779i | ||||
\(415\) | −632.076 | −1.52307 | ||||||||
\(416\) | −1678.44 | −4.03470 | ||||||||
\(417\) | −350.087 | −0.839537 | ||||||||
\(418\) | 194.464 | 0.465225 | ||||||||
\(419\) | − | 718.694i | − | 1.71526i | −0.514266 | − | 0.857631i | \(-0.671936\pi\) | ||
0.514266 | − | 0.857631i | \(-0.328064\pi\) | |||||||
\(420\) | 435.051 | 1.03584 | ||||||||
\(421\) | − | 320.503i | − | 0.761290i | −0.924721 | − | 0.380645i | \(-0.875702\pi\) | ||
0.924721 | − | 0.380645i | \(-0.124298\pi\) | |||||||
\(422\) | −789.987 | −1.87201 | ||||||||
\(423\) | −170.716 | −0.403585 | ||||||||
\(424\) | 155.490i | 0.366722i | ||||||||
\(425\) | − | 379.959i | − | 0.894021i | ||||||
\(426\) | −171.798 | −0.403282 | ||||||||
\(427\) | 79.5397 | 0.186276 | ||||||||
\(428\) | − | 1874.56i | − | 4.37980i | ||||||
\(429\) | 59.8277i | 0.139459i | ||||||||
\(430\) | 2333.01 | 5.42560 | ||||||||
\(431\) | − | 420.620i | − | 0.975918i | −0.872867 | − | 0.487959i | \(-0.837742\pi\) | ||
0.872867 | − | 0.487959i | \(-0.162258\pi\) | |||||||
\(432\) | 290.534 | 0.672533 | ||||||||
\(433\) | 317.443i | 0.733125i | 0.930393 | + | 0.366562i | \(0.119465\pi\) | ||||
−0.930393 | + | 0.366562i | \(0.880535\pi\) | |||||||
\(434\) | 62.9374i | 0.145017i | ||||||||
\(435\) | 603.911i | 1.38830i | ||||||||
\(436\) | 1359.65i | 3.11847i | ||||||||
\(437\) | 135.783 | + | 489.814i | 0.310716 | + | 1.12086i | ||||
\(438\) | −6.46518 | −0.0147607 | ||||||||
\(439\) | 151.755 | 0.345684 | 0.172842 | − | 0.984950i | \(-0.444705\pi\) | ||||
0.172842 | + | 0.984950i | \(0.444705\pi\) | |||||||
\(440\) | 523.470 | 1.18970 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | − | 409.914i | − | 0.927408i | ||||||
\(443\) | −170.396 | −0.384641 | −0.192320 | − | 0.981332i | \(-0.561601\pi\) | ||||
−0.192320 | + | 0.981332i | \(0.561601\pi\) | |||||||
\(444\) | − | 616.360i | − | 1.38820i | ||||||
\(445\) | −1333.58 | −2.99681 | ||||||||
\(446\) | 852.433 | 1.91129 | ||||||||
\(447\) | 172.300i | 0.385458i | ||||||||
\(448\) | − | 539.552i | − | 1.20436i | ||||||
\(449\) | 632.355 | 1.40836 | 0.704181 | − | 0.710020i | \(-0.251314\pi\) | ||||
0.704181 | + | 0.710020i | \(0.251314\pi\) | |||||||
\(450\) | 616.016 | 1.36892 | ||||||||
\(451\) | − | 15.5281i | − | 0.0344304i | ||||||
\(452\) | 300.394i | 0.664588i | ||||||||
\(453\) | −70.0838 | −0.154710 | ||||||||
\(454\) | − | 471.336i | − | 1.03818i | ||||||
\(455\) | 353.025 | 0.775880 | ||||||||
\(456\) | − | 985.586i | − | 2.16137i | ||||||
\(457\) | 228.388i | 0.499756i | 0.968277 | + | 0.249878i | \(0.0803905\pi\) | ||||
−0.968277 | + | 0.249878i | \(0.919609\pi\) | |||||||
\(458\) | − | 179.462i | − | 0.391838i | ||||||
\(459\) | 36.8804i | 0.0803496i | ||||||||
\(460\) | 583.304 | + | 2104.17i | 1.26805 | + | 4.57429i | ||||
\(461\) | 577.925 | 1.25363 | 0.626817 | − | 0.779167i | \(-0.284357\pi\) | ||||
0.626817 | + | 0.779167i | \(0.284357\pi\) | |||||||
\(462\) | −40.3245 | −0.0872825 | ||||||||
\(463\) | −175.547 | −0.379151 | −0.189576 | − | 0.981866i | \(-0.560711\pi\) | ||||
−0.189576 | + | 0.981866i | \(0.560711\pi\) | |||||||
\(464\) | 2199.89 | 4.74115 | ||||||||
\(465\) | 95.1916i | 0.204713i | ||||||||
\(466\) | −1420.69 | −3.04868 | ||||||||
\(467\) | − | 789.029i | − | 1.68957i | −0.535107 | − | 0.844784i | \(-0.679729\pi\) | ||
0.535107 | − | 0.844784i | \(-0.320271\pi\) | |||||||
\(468\) | 483.900 | 1.03398 | ||||||||
\(469\) | −341.846 | −0.728883 | ||||||||
\(470\) | 1934.32i | 4.11558i | ||||||||
\(471\) | − | 268.376i | − | 0.569801i | ||||||
\(472\) | 2667.94 | 5.65241 | ||||||||
\(473\) | −157.454 | −0.332883 | ||||||||
\(474\) | − | 521.006i | − | 1.09917i | ||||||
\(475\) | − | 1183.05i | − | 2.49063i | ||||||
\(476\) | 201.172 | 0.422630 | ||||||||
\(477\) | − | 18.1163i | − | 0.0379798i | ||||||
\(478\) | −937.303 | −1.96089 | ||||||||
\(479\) | 441.484i | 0.921680i | 0.887483 | + | 0.460840i | \(0.152452\pi\) | ||||
−0.887483 | + | 0.460840i | \(0.847548\pi\) | |||||||
\(480\) | − | 1711.05i | − | 3.56468i | ||||||
\(481\) | − | 500.150i | − | 1.03981i | ||||||
\(482\) | − | 554.632i | − | 1.15069i | ||||||
\(483\) | −28.1562 | − | 101.569i | −0.0582944 | − | 0.210287i | ||||
\(484\) | 1239.87 | 2.56172 | ||||||||
\(485\) | −1461.14 | −3.01265 | ||||||||
\(486\) | −59.7931 | −0.123031 | ||||||||
\(487\) | −516.547 | −1.06067 | −0.530335 | − | 0.847788i | \(-0.677934\pi\) | ||||
−0.530335 | + | 0.847788i | \(0.677934\pi\) | |||||||
\(488\) | − | 774.085i | − | 1.58624i | ||||||
\(489\) | −272.884 | −0.558045 | ||||||||
\(490\) | 237.943i | 0.485597i | ||||||||
\(491\) | −23.6429 | −0.0481525 | −0.0240763 | − | 0.999710i | \(-0.507664\pi\) | ||||
−0.0240763 | + | 0.999710i | \(0.507664\pi\) | |||||||
\(492\) | −125.595 | −0.255274 | ||||||||
\(493\) | 279.254i | 0.566439i | ||||||||
\(494\) | − | 1276.32i | − | 2.58364i | ||||||
\(495\) | −60.9901 | −0.123212 | ||||||||
\(496\) | 346.759 | 0.699111 | ||||||||
\(497\) | − | 68.4162i | − | 0.137658i | ||||||
\(498\) | − | 473.861i | − | 0.951529i | ||||||
\(499\) | 88.3199 | 0.176994 | 0.0884969 | − | 0.996076i | \(-0.471794\pi\) | ||||
0.0884969 | + | 0.996076i | \(0.471794\pi\) | |||||||
\(500\) | − | 2708.82i | − | 5.41763i | ||||||
\(501\) | −99.3530 | −0.198309 | ||||||||
\(502\) | − | 632.410i | − | 1.25978i | ||||||
\(503\) | 579.131i | 1.15135i | 0.817677 | + | 0.575677i | \(0.195261\pi\) | ||||
−0.817677 | + | 0.575677i | \(0.804739\pi\) | |||||||
\(504\) | 204.373i | 0.405502i | ||||||||
\(505\) | − | 39.5528i | − | 0.0783223i | ||||||
\(506\) | −54.0659 | − | 195.034i | −0.106850 | − | 0.385443i | ||||
\(507\) | 99.9481 | 0.197136 | ||||||||
\(508\) | 1460.90 | 2.87578 | ||||||||
\(509\) | −345.867 | −0.679502 | −0.339751 | − | 0.940515i | \(-0.610343\pi\) | ||||
−0.339751 | + | 0.940515i | \(0.610343\pi\) | |||||||
\(510\) | 417.878 | 0.819368 | ||||||||
\(511\) | − | 2.57467i | − | 0.00503849i | ||||||
\(512\) | −474.136 | −0.926047 | ||||||||
\(513\) | 114.832i | 0.223844i | ||||||||
\(514\) | −268.787 | −0.522931 | ||||||||
\(515\) | −154.392 | −0.299791 | ||||||||
\(516\) | 1273.52i | 2.46807i | ||||||||
\(517\) | − | 130.547i | − | 0.252508i | ||||||
\(518\) | 337.106 | 0.650784 | ||||||||
\(519\) | 464.991 | 0.895936 | ||||||||
\(520\) | − | 3435.66i | − | 6.60704i | ||||||
\(521\) | 441.530i | 0.847466i | 0.905787 | + | 0.423733i | \(0.139281\pi\) | ||||
−0.905787 | + | 0.423733i | \(0.860719\pi\) | |||||||
\(522\) | −452.747 | −0.867331 | ||||||||
\(523\) | − | 62.9887i | − | 0.120437i | −0.998185 | − | 0.0602187i | \(-0.980820\pi\) | ||
0.998185 | − | 0.0602187i | \(-0.0191798\pi\) | |||||||
\(524\) | −1174.64 | −2.24167 | ||||||||
\(525\) | 245.319i | 0.467275i | ||||||||
\(526\) | − | 143.722i | − | 0.273236i | ||||||
\(527\) | 44.0176i | 0.0835248i | ||||||||
\(528\) | 222.171i | 0.420779i | ||||||||
\(529\) | 453.498 | − | 272.361i | 0.857274 | − | 0.514860i | ||||
\(530\) | −205.269 | −0.387300 | ||||||||
\(531\) | −310.844 | −0.585395 | ||||||||
\(532\) | 626.373 | 1.17739 | ||||||||
\(533\) | −101.915 | −0.191210 | ||||||||
\(534\) | − | 999.773i | − | 1.87223i | ||||||
\(535\) | 1550.67 | 2.89846 | ||||||||
\(536\) | 3326.86i | 6.20684i | ||||||||
\(537\) | −157.241 | −0.292814 | ||||||||
\(538\) | 886.931 | 1.64857 | ||||||||
\(539\) | − | 16.0587i | − | 0.0297934i | ||||||
\(540\) | 493.301i | 0.913521i | ||||||||
\(541\) | −618.050 | −1.14242 | −0.571211 | − | 0.820803i | \(-0.693526\pi\) | ||||
−0.571211 | + | 0.820803i | \(0.693526\pi\) | |||||||
\(542\) | −186.667 | −0.344404 | ||||||||
\(543\) | 0.240104i | 0.000442180i | ||||||||
\(544\) | − | 791.205i | − | 1.45442i | ||||||
\(545\) | −1124.73 | −2.06373 | ||||||||
\(546\) | 264.660i | 0.484725i | ||||||||
\(547\) | −315.255 | −0.576334 | −0.288167 | − | 0.957580i | \(-0.593046\pi\) | ||||
−0.288167 | + | 0.957580i | \(0.593046\pi\) | |||||||
\(548\) | − | 2846.94i | − | 5.19514i | ||||||
\(549\) | 90.1896i | 0.164280i | ||||||||
\(550\) | 471.066i | 0.856484i | ||||||||
\(551\) | 869.493i | 1.57803i | ||||||||
\(552\) | −988.474 | + | 274.018i | −1.79071 | + | 0.496409i | ||||
\(553\) | 207.483 | 0.375196 | ||||||||
\(554\) | 47.8659 | 0.0864006 | ||||||||
\(555\) | 509.867 | 0.918679 | ||||||||
\(556\) | −2165.31 | −3.89444 | ||||||||
\(557\) | 210.920i | 0.378671i | 0.981912 | + | 0.189335i | \(0.0606333\pi\) | ||||
−0.981912 | + | 0.189335i | \(0.939367\pi\) | |||||||
\(558\) | −71.3643 | −0.127893 | ||||||||
\(559\) | 1033.41i | 1.84867i | ||||||||
\(560\) | 1310.96 | 2.34101 | ||||||||
\(561\) | −28.2024 | −0.0502717 | ||||||||
\(562\) | 1019.22i | 1.81356i | ||||||||
\(563\) | − | 548.549i | − | 0.974332i | −0.873309 | − | 0.487166i | \(-0.838031\pi\) | ||
0.873309 | − | 0.487166i | \(-0.161969\pi\) | |||||||
\(564\) | −1055.89 | −1.87215 | ||||||||
\(565\) | −248.493 | −0.439810 | ||||||||
\(566\) | 1778.87i | 3.14288i | ||||||||
\(567\) | − | 23.8118i | − | 0.0419961i | ||||||
\(568\) | −665.830 | −1.17224 | ||||||||
\(569\) | − | 569.440i | − | 1.00077i | −0.865802 | − | 0.500386i | \(-0.833191\pi\) | ||
0.865802 | − | 0.500386i | \(-0.166809\pi\) | |||||||
\(570\) | 1301.11 | 2.28266 | ||||||||
\(571\) | − | 124.187i | − | 0.217490i | −0.994070 | − | 0.108745i | \(-0.965317\pi\) | ||
0.994070 | − | 0.108745i | \(-0.0346832\pi\) | |||||||
\(572\) | 370.038i | 0.646919i | ||||||||
\(573\) | − | 254.890i | − | 0.444834i | ||||||
\(574\) | − | 68.6918i | − | 0.119672i | ||||||
\(575\) | −1186.52 | + | 328.917i | −2.06350 | + | 0.572030i | ||||
\(576\) | 611.795 | 1.06214 | ||||||||
\(577\) | 880.984 | 1.52684 | 0.763418 | − | 0.645905i | \(-0.223520\pi\) | ||||
0.763418 | + | 0.645905i | \(0.223520\pi\) | |||||||
\(578\) | −915.295 | −1.58356 | ||||||||
\(579\) | 180.066 | 0.310995 | ||||||||
\(580\) | 3735.22i | 6.44004i | ||||||||
\(581\) | 188.709 | 0.324800 | ||||||||
\(582\) | − | 1095.40i | − | 1.88213i | ||||||
\(583\) | 13.8535 | 0.0237625 | ||||||||
\(584\) | −25.0568 | −0.0429055 | ||||||||
\(585\) | 400.293i | 0.684262i | ||||||||
\(586\) | 1148.63i | 1.96011i | ||||||||
\(587\) | 740.530 | 1.26155 | 0.630775 | − | 0.775965i | \(-0.282737\pi\) | ||||
0.630775 | + | 0.775965i | \(0.282737\pi\) | |||||||
\(588\) | −129.886 | −0.220895 | ||||||||
\(589\) | 137.054i | 0.232689i | ||||||||
\(590\) | 3522.06i | 5.96959i | ||||||||
\(591\) | −181.215 | −0.306624 | ||||||||
\(592\) | − | 1857.31i | − | 3.13735i | ||||||
\(593\) | 602.557 | 1.01612 | 0.508059 | − | 0.861323i | \(-0.330363\pi\) | ||||
0.508059 | + | 0.861323i | \(0.330363\pi\) | |||||||
\(594\) | − | 45.7237i | − | 0.0769759i | ||||||
\(595\) | 166.414i | 0.279687i | ||||||||
\(596\) | 1065.68i | 1.78806i | ||||||||
\(597\) | 117.294i | 0.196473i | ||||||||
\(598\) | −1280.06 | + | 354.848i | −2.14056 | + | 0.593392i | ||||
\(599\) | 643.607 | 1.07447 | 0.537235 | − | 0.843433i | \(-0.319469\pi\) | ||||
0.537235 | + | 0.843433i | \(0.319469\pi\) | |||||||
\(600\) | 2387.46 | 3.97911 | ||||||||
\(601\) | 177.729 | 0.295723 | 0.147861 | − | 0.989008i | \(-0.452761\pi\) | ||||
0.147861 | + | 0.989008i | \(0.452761\pi\) | |||||||
\(602\) | −696.528 | −1.15702 | ||||||||
\(603\) | − | 387.617i | − | 0.642814i | ||||||
\(604\) | −433.472 | −0.717669 | ||||||||
\(605\) | 1025.65i | 1.69529i | ||||||||
\(606\) | 29.6523 | 0.0489313 | ||||||||
\(607\) | −388.983 | −0.640829 | −0.320414 | − | 0.947277i | \(-0.603822\pi\) | ||||
−0.320414 | + | 0.947277i | \(0.603822\pi\) | |||||||
\(608\) | − | 2463.51i | − | 4.05183i | ||||||
\(609\) | − | 180.300i | − | 0.296059i | ||||||
\(610\) | 1021.90 | 1.67525 | ||||||||
\(611\) | −856.810 | −1.40231 | ||||||||
\(612\) | 228.108i | 0.372725i | ||||||||
\(613\) | − | 217.931i | − | 0.355515i | −0.984074 | − | 0.177758i | \(-0.943116\pi\) | ||
0.984074 | − | 0.177758i | \(-0.0568843\pi\) | |||||||
\(614\) | −2155.85 | −3.51116 | ||||||||
\(615\) | − | 103.895i | − | 0.168935i | ||||||
\(616\) | −156.284 | −0.253708 | ||||||||
\(617\) | 907.090i | 1.47016i | 0.677979 | + | 0.735081i | \(0.262856\pi\) | ||||
−0.677979 | + | 0.735081i | \(0.737144\pi\) | |||||||
\(618\) | − | 115.746i | − | 0.187292i | ||||||
\(619\) | − | 974.089i | − | 1.57365i | −0.617177 | − | 0.786824i | \(-0.711724\pi\) | ||
0.617177 | − | 0.786824i | \(-0.288276\pi\) | |||||||
\(620\) | 588.765i | 0.949622i | ||||||||
\(621\) | 115.168 | − | 31.9261i | 0.185456 | − | 0.0514108i | ||||
\(622\) | −588.971 | −0.946899 | ||||||||
\(623\) | 398.146 | 0.639078 | ||||||||
\(624\) | 1458.17 | 2.33680 | ||||||||
\(625\) | 902.466 | 1.44394 | ||||||||
\(626\) | 1383.59i | 2.21021i | ||||||||
\(627\) | −87.8117 | −0.140050 | ||||||||
\(628\) | − | 1659.92i | − | 2.64319i | ||||||
\(629\) | 235.767 | 0.374829 | ||||||||
\(630\) | −269.802 | −0.428257 | ||||||||
\(631\) | 217.964i | 0.345426i | 0.984972 | + | 0.172713i | \(0.0552533\pi\) | ||||
−0.984972 | + | 0.172713i | \(0.944747\pi\) | |||||||
\(632\) | − | 2019.24i | − | 3.19500i | ||||||
\(633\) | 356.724 | 0.563545 | ||||||||
\(634\) | −644.585 | −1.01670 | ||||||||
\(635\) | 1208.49i | 1.90313i | ||||||||
\(636\) | − | 112.051i | − | 0.176180i | ||||||
\(637\) | −105.397 | −0.165459 | ||||||||
\(638\) | − | 346.215i | − | 0.542656i | ||||||
\(639\) | 77.5767 | 0.121403 | ||||||||
\(640\) | − | 2980.52i | − | 4.65706i | ||||||
\(641\) | 776.091i | 1.21075i | 0.795940 | + | 0.605375i | \(0.206977\pi\) | ||||
−0.795940 | + | 0.605375i | \(0.793023\pi\) | |||||||
\(642\) | 1162.53i | 1.81079i | ||||||||
\(643\) | 405.054i | 0.629945i | 0.949101 | + | 0.314972i | \(0.101995\pi\) | ||||
−0.949101 | + | 0.314972i | \(0.898005\pi\) | |||||||
\(644\) | −174.148 | − | 628.209i | −0.270415 | − | 0.975479i | ||||
\(645\) | −1053.49 | −1.63331 | ||||||||
\(646\) | 601.648 | 0.931344 | ||||||||
\(647\) | 65.6081 | 0.101404 | 0.0507018 | − | 0.998714i | \(-0.483854\pi\) | ||||
0.0507018 | + | 0.998714i | \(0.483854\pi\) | |||||||
\(648\) | −231.737 | −0.357619 | ||||||||
\(649\) | − | 237.702i | − | 0.366259i | ||||||
\(650\) | 3091.73 | 4.75650 | ||||||||
\(651\) | − | 28.4198i | − | 0.0436557i | ||||||
\(652\) | −1687.80 | −2.58865 | ||||||||
\(653\) | 1053.55 | 1.61340 | 0.806701 | − | 0.590960i | \(-0.201251\pi\) | ||||
0.806701 | + | 0.590960i | \(0.201251\pi\) | |||||||
\(654\) | − | 843.203i | − | 1.28930i | ||||||
\(655\) | − | 971.685i | − | 1.48349i | ||||||
\(656\) | −378.463 | −0.576925 | ||||||||
\(657\) | 2.91940 | 0.00444353 | ||||||||
\(658\) | − | 577.499i | − | 0.877658i | ||||||
\(659\) | 932.060i | 1.41436i | 0.707036 | + | 0.707178i | \(0.250032\pi\) | ||||
−0.707036 | + | 0.707178i | \(0.749968\pi\) | |||||||
\(660\) | −377.227 | −0.571556 | ||||||||
\(661\) | − | 573.064i | − | 0.866965i | −0.901162 | − | 0.433483i | \(-0.857285\pi\) | ||
0.901162 | − | 0.433483i | \(-0.142715\pi\) | |||||||
\(662\) | −2094.39 | −3.16373 | ||||||||
\(663\) | 185.100i | 0.279185i | ||||||||
\(664\) | − | 1836.52i | − | 2.76585i | ||||||
\(665\) | 518.150i | 0.779173i | ||||||||
\(666\) | 382.242i | 0.573938i | ||||||||
\(667\) | 872.041 | − | 241.741i | 1.30741 | − | 0.362430i | ||||
\(668\) | −614.504 | −0.919915 | ||||||||
\(669\) | −384.922 | −0.575370 | ||||||||
\(670\) | −4391.93 | −6.55513 | ||||||||
\(671\) | −68.9678 | −0.102784 | ||||||||
\(672\) | 510.839i | 0.760177i | ||||||||
\(673\) | −754.416 | −1.12098 | −0.560488 | − | 0.828163i | \(-0.689386\pi\) | ||||
−0.560488 | + | 0.828163i | \(0.689386\pi\) | |||||||
\(674\) | 1086.38i | 1.61184i | ||||||||
\(675\) | −278.166 | −0.412098 | ||||||||
\(676\) | 618.184 | 0.914474 | ||||||||
\(677\) | 437.536i | 0.646286i | 0.946350 | + | 0.323143i | \(0.104739\pi\) | ||||
−0.946350 | + | 0.323143i | \(0.895261\pi\) | |||||||
\(678\) | − | 186.293i | − | 0.274768i | ||||||
\(679\) | 436.228 | 0.642456 | ||||||||
\(680\) | 1619.55 | 2.38169 | ||||||||
\(681\) | 212.835i | 0.312533i | ||||||||
\(682\) | − | 54.5722i | − | 0.0800179i | ||||||
\(683\) | −89.0019 | −0.130310 | −0.0651551 | − | 0.997875i | \(-0.520754\pi\) | ||||
−0.0651551 | + | 0.997875i | \(0.520754\pi\) | |||||||
\(684\) | 710.241i | 1.03836i | ||||||||
\(685\) | 2355.05 | 3.43803 | ||||||||
\(686\) | − | 71.0387i | − | 0.103555i | ||||||
\(687\) | 81.0372i | 0.117958i | ||||||||
\(688\) | 3837.58i | 5.57788i | ||||||||
\(689\) | − | 90.9243i | − | 0.131966i | ||||||
\(690\) | −361.742 | − | 1304.93i | −0.524264 | − | 1.89120i | ||||
\(691\) | 1196.81 | 1.73199 | 0.865995 | − | 0.500053i | \(-0.166686\pi\) | ||||
0.865995 | + | 0.500053i | \(0.166686\pi\) | |||||||
\(692\) | 2875.99 | 4.15606 | ||||||||
\(693\) | 18.2088 | 0.0262753 | ||||||||
\(694\) | −472.305 | −0.680554 | ||||||||
\(695\) | − | 1791.19i | − | 2.57725i | ||||||
\(696\) | −1754.69 | −2.52110 | ||||||||
\(697\) | − | 48.0421i | − | 0.0689269i | ||||||
\(698\) | 1268.35 | 1.81712 | ||||||||
\(699\) | 641.521 | 0.917770 | ||||||||
\(700\) | 1517.31i | 2.16759i | ||||||||
\(701\) | − | 906.332i | − | 1.29291i | −0.762951 | − | 0.646456i | \(-0.776250\pi\) | ||
0.762951 | − | 0.646456i | \(-0.223750\pi\) | |||||||
\(702\) | −300.096 | −0.427488 | ||||||||
\(703\) | 734.091 | 1.04423 | ||||||||
\(704\) | 467.839i | 0.664543i | ||||||||
\(705\) | − | 873.456i | − | 1.23894i | ||||||
\(706\) | 9.58859 | 0.0135816 | ||||||||
\(707\) | 11.8086i | 0.0167024i | ||||||||
\(708\) | −1922.59 | −2.71552 | ||||||||
\(709\) | 1293.05i | 1.82377i | 0.410447 | + | 0.911885i | \(0.365373\pi\) | ||||
−0.410447 | + | 0.911885i | \(0.634627\pi\) | |||||||
\(710\) | − | 878.991i | − | 1.23802i | ||||||
\(711\) | 235.264i | 0.330892i | ||||||||
\(712\) | − | 3874.77i | − | 5.44210i | ||||||
\(713\) | 137.456 | − | 38.1045i | 0.192785 | − | 0.0534425i | ||||
\(714\) | −124.759 | −0.174733 | ||||||||
\(715\) | −306.104 | −0.428117 | ||||||||
\(716\) | −972.545 | −1.35830 | ||||||||
\(717\) | 423.246 | 0.590301 | ||||||||
\(718\) | 545.921i | 0.760336i | ||||||||
\(719\) | −149.666 | −0.208159 | −0.104079 | − | 0.994569i | \(-0.533190\pi\) | ||||
−0.104079 | + | 0.994569i | \(0.533190\pi\) | |||||||
\(720\) | 1486.49i | 2.06458i | ||||||||
\(721\) | 46.0944 | 0.0639312 | ||||||||
\(722\) | 488.605 | 0.676739 | ||||||||
\(723\) | 250.448i | 0.346401i | ||||||||
\(724\) | 1.48505i | 0.00205118i | ||||||||
\(725\) | −2106.24 | −2.90516 | ||||||||
\(726\) | −768.920 | −1.05912 | ||||||||
\(727\) | 1022.15i | 1.40599i | 0.711195 | + | 0.702995i | \(0.248154\pi\) | ||||
−0.711195 | + | 0.702995i | \(0.751846\pi\) | |||||||
\(728\) | 1025.73i | 1.40897i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 33.0785i | − | 0.0453131i | ||||||
\(731\) | −487.142 | −0.666405 | ||||||||
\(732\) | 557.827i | 0.762059i | ||||||||
\(733\) | − | 913.532i | − | 1.24629i | −0.782105 | − | 0.623146i | \(-0.785854\pi\) | ||
0.782105 | − | 0.623146i | \(-0.214146\pi\) | |||||||
\(734\) | − | 137.963i | − | 0.187961i | ||||||
\(735\) | − | 107.445i | − | 0.146183i | ||||||
\(736\) | −2470.73 | + | 684.918i | −3.35697 | + | 0.930596i | ||||
\(737\) | 296.410 | 0.402185 | ||||||||
\(738\) | 77.8891 | 0.105541 | ||||||||
\(739\) | 127.300 | 0.172260 | 0.0861300 | − | 0.996284i | \(-0.472550\pi\) | ||||
0.0861300 | + | 0.996284i | \(0.472550\pi\) | |||||||
\(740\) | 3153.55 | 4.26156 | ||||||||
\(741\) | 576.330i | 0.777773i | ||||||||
\(742\) | 61.2839 | 0.0825929 | ||||||||
\(743\) | − | 344.634i | − | 0.463841i | −0.972735 | − | 0.231920i | \(-0.925499\pi\) | ||
0.972735 | − | 0.231920i | \(-0.0745009\pi\) | |||||||
\(744\) | −276.583 | −0.371752 | ||||||||
\(745\) | −881.558 | −1.18330 | ||||||||
\(746\) | − | 1621.22i | − | 2.17321i | ||||||
\(747\) | 213.975i | 0.286446i | ||||||||
\(748\) | −174.433 | −0.233200 | ||||||||
\(749\) | −462.960 | −0.618104 | ||||||||
\(750\) | 1679.90i | 2.23987i | ||||||||
\(751\) | − | 588.204i | − | 0.783228i | −0.920130 | − | 0.391614i | \(-0.871917\pi\) | ||
0.920130 | − | 0.391614i | \(-0.128083\pi\) | |||||||
\(752\) | −3181.78 | −4.23109 | ||||||||
\(753\) | 285.569i | 0.379242i | ||||||||
\(754\) | −2272.29 | −3.01365 | ||||||||
\(755\) | − | 358.578i | − | 0.474938i | ||||||
\(756\) | − | 147.277i | − | 0.194811i | ||||||
\(757\) | 6.00617i | 0.00793417i | 0.999992 | + | 0.00396709i | \(0.00126277\pi\) | ||||
−0.999992 | + | 0.00396709i | \(0.998737\pi\) | |||||||
\(758\) | 2046.30i | 2.69960i | ||||||||
\(759\) | 24.4139 | + | 88.0690i | 0.0321658 | + | 0.116033i | ||||
\(760\) | 5042.66 | 6.63508 | ||||||||
\(761\) | 659.193 | 0.866219 | 0.433109 | − | 0.901341i | \(-0.357416\pi\) | ||||
0.433109 | + | 0.901341i | \(0.357416\pi\) | |||||||
\(762\) | −905.993 | −1.18897 | ||||||||
\(763\) | 335.794 | 0.440096 | ||||||||
\(764\) | − | 1576.51i | − | 2.06349i | ||||||
\(765\) | −188.696 | −0.246661 | ||||||||
\(766\) | 1714.91i | 2.23879i | ||||||||
\(767\) | −1560.10 | −2.03403 | ||||||||
\(768\) | 821.588 | 1.06978 | ||||||||
\(769\) | 299.704i | 0.389732i | 0.980830 | + | 0.194866i | \(0.0624272\pi\) | ||||
−0.980830 | + | 0.194866i | \(0.937573\pi\) | |||||||
\(770\) | − | 206.317i | − | 0.267944i | ||||||
\(771\) | 121.372 | 0.157422 | ||||||||
\(772\) | 1113.72 | 1.44264 | ||||||||
\(773\) | − | 374.493i | − | 0.484468i | −0.970218 | − | 0.242234i | \(-0.922120\pi\) | ||
0.970218 | − | 0.242234i | \(-0.0778801\pi\) | |||||||
\(774\) | − | 789.789i | − | 1.02040i | ||||||
\(775\) | −331.997 | −0.428383 | ||||||||
\(776\) | − | 4245.39i | − | 5.47087i | ||||||
\(777\) | −152.223 | −0.195911 | ||||||||
\(778\) | − | 1474.28i | − | 1.89496i | ||||||
\(779\) | − | 149.585i | − | 0.192022i | ||||||
\(780\) | 2475.84i | 3.17415i | ||||||||
\(781\) | 59.3228i | 0.0759575i | ||||||||
\(782\) | −167.273 | − | 603.411i | −0.213904 | − | 0.771625i | ||||
\(783\) | 204.441 | 0.261099 | ||||||||
\(784\) | −391.394 | −0.499227 | ||||||||
\(785\) | 1373.13 | 1.74920 | ||||||||
\(786\) | 728.464 | 0.926799 | ||||||||
\(787\) | − | 62.4755i | − | 0.0793843i | −0.999212 | − | 0.0396922i | \(-0.987362\pi\) | ||
0.999212 | − | 0.0396922i | \(-0.0126377\pi\) | |||||||
\(788\) | −1120.82 | −1.42237 | ||||||||
\(789\) | 64.8987i | 0.0822544i | ||||||||
\(790\) | 2665.68 | 3.37428 | ||||||||
\(791\) | 74.1884 | 0.0937906 | ||||||||
\(792\) | − | 177.209i | − | 0.223749i | ||||||
\(793\) | 452.653i | 0.570811i | ||||||||
\(794\) | 1641.14 | 2.06693 | ||||||||
\(795\) | 92.6907 | 0.116592 | ||||||||
\(796\) | 725.472i | 0.911397i | ||||||||
\(797\) | 1170.64i | 1.46881i | 0.678714 | + | 0.734403i | \(0.262538\pi\) | ||||
−0.678714 | + | 0.734403i | \(0.737462\pi\) | |||||||
\(798\) | −388.452 | −0.486782 | ||||||||
\(799\) | − | 403.895i | − | 0.505501i | ||||||
\(800\) | 5967.56 | 7.45945 | ||||||||
\(801\) | 451.455i | 0.563614i | ||||||||
\(802\) | 199.635i | 0.248922i | ||||||||
\(803\) | 2.23246i | 0.00278015i | ||||||||
\(804\) | − | 2397.43i | − | 2.98188i | ||||||
\(805\) | 519.668 | − | 144.059i | 0.645551 | − | 0.178955i | ||||
\(806\) | −358.171 | −0.444381 | ||||||||
\(807\) | −400.500 | −0.496282 | ||||||||
\(808\) | 114.922 | 0.142230 | ||||||||
\(809\) | −694.362 | −0.858297 | −0.429148 | − | 0.903234i | \(-0.641186\pi\) | ||||
−0.429148 | + | 0.903234i | \(0.641186\pi\) | |||||||
\(810\) | − | 305.926i | − | 0.377687i | ||||||
\(811\) | 236.981 | 0.292208 | 0.146104 | − | 0.989269i | \(-0.453327\pi\) | ||||
0.146104 | + | 0.989269i | \(0.453327\pi\) | |||||||
\(812\) | − | 1115.16i | − | 1.37336i | ||||||
\(813\) | 84.2908 | 0.103679 | ||||||||
\(814\) | −292.300 | −0.359091 | ||||||||
\(815\) | − | 1396.19i | − | 1.71311i | ||||||
\(816\) | 687.370i | 0.842365i | ||||||||
\(817\) | −1516.78 | −1.85652 | ||||||||
\(818\) | −1570.58 | −1.92002 | ||||||||
\(819\) | − | 119.509i | − | 0.145921i | ||||||
\(820\) | − | 642.596i | − | 0.783654i | ||||||
\(821\) | −824.059 | −1.00373 | −0.501863 | − | 0.864947i | \(-0.667352\pi\) | ||||
−0.501863 | + | 0.864947i | \(0.667352\pi\) | |||||||
\(822\) | 1765.56i | 2.14788i | ||||||||
\(823\) | 1023.22 | 1.24328 | 0.621639 | − | 0.783304i | \(-0.286467\pi\) | ||||
0.621639 | + | 0.783304i | \(0.286467\pi\) | |||||||
\(824\) | − | 448.593i | − | 0.544409i | ||||||
\(825\) | − | 212.713i | − | 0.257834i | ||||||
\(826\) | − | 1051.52i | − | 1.27303i | ||||||
\(827\) | − | 789.533i | − | 0.954696i | −0.878714 | − | 0.477348i | \(-0.841598\pi\) | ||
0.878714 | − | 0.477348i | \(-0.158402\pi\) | |||||||
\(828\) | 712.322 | − | 197.465i | 0.860292 | − | 0.238484i | ||||
\(829\) | −270.227 | −0.325968 | −0.162984 | − | 0.986629i | \(-0.552112\pi\) | ||||
−0.162984 | + | 0.986629i | \(0.552112\pi\) | |||||||
\(830\) | 2424.47 | 2.92105 | ||||||||
\(831\) | −21.6142 | −0.0260099 | ||||||||
\(832\) | 3070.54 | 3.69056 | ||||||||
\(833\) | − | 49.6835i | − | 0.0596441i | ||||||
\(834\) | 1342.84 | 1.61012 | ||||||||
\(835\) | − | 508.331i | − | 0.608780i | ||||||
\(836\) | −543.120 | −0.649665 | ||||||||
\(837\) | 32.2251 | 0.0385007 | ||||||||
\(838\) | 2756.72i | 3.28964i | ||||||||
\(839\) | − | 164.321i | − | 0.195853i | −0.995194 | − | 0.0979266i | \(-0.968779\pi\) | ||
0.995194 | − | 0.0979266i | \(-0.0312210\pi\) | |||||||
\(840\) | −1045.66 | −1.24483 | ||||||||
\(841\) | 707.003 | 0.840669 | ||||||||
\(842\) | 1229.36i | 1.46005i | ||||||||
\(843\) | − | 460.236i | − | 0.545950i | ||||||
\(844\) | 2206.36 | 2.61417 | ||||||||
\(845\) | 511.376i | 0.605179i | ||||||||
\(846\) | 654.822 | 0.774022 | ||||||||
\(847\) | − | 306.212i | − | 0.361525i | ||||||
\(848\) | − | 337.649i | − | 0.398171i | ||||||
\(849\) | − | 803.261i | − | 0.946127i | ||||||
\(850\) | 1457.42i | 1.71461i | ||||||||
\(851\) | −204.096 | − | 736.242i | −0.239830 | − | 0.865149i | ||||
\(852\) | 479.816 | 0.563164 | ||||||||
\(853\) | −1240.03 | −1.45373 | −0.726863 | − | 0.686782i | \(-0.759023\pi\) | ||||
−0.726863 | + | 0.686782i | \(0.759023\pi\) | |||||||
\(854\) | −305.093 | −0.357252 | ||||||||
\(855\) | −587.527 | −0.687166 | ||||||||
\(856\) | 4505.55i | 5.26349i | ||||||||
\(857\) | −723.177 | −0.843847 | −0.421924 | − | 0.906631i | \(-0.638645\pi\) | ||||
−0.421924 | + | 0.906631i | \(0.638645\pi\) | |||||||
\(858\) | − | 229.483i | − | 0.267463i | ||||||
\(859\) | −825.639 | −0.961163 | −0.480582 | − | 0.876950i | \(-0.659574\pi\) | ||||
−0.480582 | + | 0.876950i | \(0.659574\pi\) | |||||||
\(860\) | −6515.87 | −7.57659 | ||||||||
\(861\) | 31.0182i | 0.0360258i | ||||||||
\(862\) | 1613.39i | 1.87168i | ||||||||
\(863\) | 1375.42 | 1.59377 | 0.796885 | − | 0.604131i | \(-0.206480\pi\) | ||||
0.796885 | + | 0.604131i | \(0.206480\pi\) | |||||||
\(864\) | −579.237 | −0.670413 | ||||||||
\(865\) | 2379.09i | 2.75039i | ||||||||
\(866\) | − | 1217.63i | − | 1.40603i | ||||||
\(867\) | 413.308 | 0.476710 | ||||||||
\(868\) | − | 175.778i | − | 0.202509i | ||||||
\(869\) | −179.906 | −0.207027 | ||||||||
\(870\) | − | 2316.44i | − | 2.66257i | ||||||
\(871\) | − | 1945.41i | − | 2.23354i | ||||||
\(872\) | − | 3267.96i | − | 3.74766i | ||||||
\(873\) | 494.636i | 0.566593i | ||||||||
\(874\) | −520.826 | − | 1878.79i | −0.595910 | − | 2.14965i | ||||
\(875\) | −668.997 | −0.764568 | ||||||||
\(876\) | 18.0566 | 0.0206126 | ||||||||
\(877\) | 755.845 | 0.861853 | 0.430927 | − | 0.902387i | \(-0.358187\pi\) | ||||
0.430927 | + | 0.902387i | \(0.358187\pi\) | |||||||
\(878\) | −582.093 | −0.662976 | ||||||||
\(879\) | − | 518.670i | − | 0.590068i | ||||||
\(880\) | −1136.72 | −1.29173 | ||||||||
\(881\) | 297.426i | 0.337601i | 0.985650 | + | 0.168800i | \(0.0539893\pi\) | ||||
−0.985650 | + | 0.168800i | \(0.946011\pi\) | |||||||
\(882\) | 80.5503 | 0.0913269 | ||||||||
\(883\) | −1449.28 | −1.64131 | −0.820656 | − | 0.571422i | \(-0.806392\pi\) | ||||
−0.820656 | + | 0.571422i | \(0.806392\pi\) | |||||||
\(884\) | 1144.85i | 1.29508i | ||||||||
\(885\) | − | 1590.41i | − | 1.79707i | ||||||
\(886\) | 653.592 | 0.737689 | ||||||||
\(887\) | −473.042 | −0.533306 | −0.266653 | − | 0.963793i | \(-0.585918\pi\) | ||||
−0.266653 | + | 0.963793i | \(0.585918\pi\) | |||||||
\(888\) | 1481.44i | 1.66829i | ||||||||
\(889\) | − | 360.799i | − | 0.405848i | ||||||
\(890\) | 5115.25 | 5.74748 | ||||||||
\(891\) | 20.6469i | 0.0231727i | ||||||||
\(892\) | −2380.77 | −2.66902 | ||||||||
\(893\) | − | 1257.58i | − | 1.40826i | ||||||
\(894\) | − | 660.896i | − | 0.739257i | ||||||
\(895\) | − | 804.511i | − | 0.898895i | ||||||
\(896\) | 889.845i | 0.993131i | ||||||||
\(897\) | 578.019 | − | 160.234i | 0.644391 | − | 0.178634i | ||||
\(898\) | −2425.54 | −2.70105 | ||||||||
\(899\) | 244.004 | 0.271418 | ||||||||
\(900\) | −1720.47 | −1.91164 | ||||||||
\(901\) | 42.8611 | 0.0475706 | ||||||||
\(902\) | 59.5617i | 0.0660329i | ||||||||
\(903\) | 314.522 | 0.348308 | ||||||||
\(904\) | − | 722.006i | − | 0.798679i | ||||||
\(905\) | −1.22847 | −0.00135743 | ||||||||
\(906\) | 268.823 | 0.296714 | ||||||||
\(907\) | − | 1059.09i | − | 1.16768i | −0.811867 | − | 0.583842i | \(-0.801549\pi\) | ||
0.811867 | − | 0.583842i | \(-0.198451\pi\) | |||||||
\(908\) | 1316.40i | 1.44978i | ||||||||
\(909\) | −13.3897 | −0.0147302 | ||||||||
\(910\) | −1354.11 | −1.48803 | ||||||||
\(911\) | 867.979i | 0.952776i | 0.879235 | + | 0.476388i | \(0.158054\pi\) | ||||
−0.879235 | + | 0.476388i | \(0.841946\pi\) | |||||||
\(912\) | 2140.21i | 2.34672i | ||||||||
\(913\) | −163.627 | −0.179219 | ||||||||
\(914\) | − | 876.037i | − | 0.958465i | ||||||
\(915\) | −461.447 | −0.504314 | ||||||||
\(916\) | 501.220i | 0.547183i | ||||||||
\(917\) | 290.100i | 0.316358i | ||||||||
\(918\) | − | 141.463i | − | 0.154100i | ||||||
\(919\) | − | 948.695i | − | 1.03231i | −0.856494 | − | 0.516156i | \(-0.827362\pi\) | ||
0.856494 | − | 0.516156i | \(-0.172638\pi\) | |||||||
\(920\) | −1401.99 | − | 5057.44i | −1.52390 | − | 5.49722i | ||||
\(921\) | 973.491 | 1.05699 | ||||||||
\(922\) | −2216.76 | −2.40430 | ||||||||
\(923\) | 389.350 | 0.421831 | ||||||||
\(924\) | 112.623 | 0.121886 | ||||||||
\(925\) | 1778.25i | 1.92243i | ||||||||
\(926\) | 673.351 | 0.727161 | ||||||||
\(927\) | 52.2661i | 0.0563820i | ||||||||
\(928\) | −4385.92 | −4.72620 | ||||||||
\(929\) | 1409.26 | 1.51696 | 0.758481 | − | 0.651696i | \(-0.225942\pi\) | ||||
0.758481 | + | 0.651696i | \(0.225942\pi\) | |||||||
\(930\) | − | 365.129i | − | 0.392612i | ||||||
\(931\) | − | 154.696i | − | 0.166161i | ||||||
\(932\) | 3967.84 | 4.25734 | ||||||||
\(933\) | 265.954 | 0.285053 | ||||||||
\(934\) | 3026.50i | 3.24037i | ||||||||
\(935\) | − | 144.295i | − | 0.154326i | ||||||
\(936\) | −1163.07 | −1.24260 | ||||||||
\(937\) | − | 1265.88i | − | 1.35099i | −0.737364 | − | 0.675495i | \(-0.763930\pi\) | ||
0.737364 | − | 0.675495i | \(-0.236070\pi\) | |||||||
\(938\) | 1311.23 | 1.39790 | ||||||||
\(939\) | − | 624.772i | − | 0.665358i | ||||||
\(940\) | − | 5402.37i | − | 5.74721i | ||||||
\(941\) | − | 388.953i | − | 0.413340i | −0.978411 | − | 0.206670i | \(-0.933737\pi\) | ||
0.978411 | − | 0.206670i | \(-0.0662627\pi\) | |||||||
\(942\) | 1029.42i | 1.09280i | ||||||||
\(943\) | −150.023 | + | 41.5884i | −0.159091 | + | 0.0441022i | ||||
\(944\) | −5793.45 | −6.13713 | ||||||||
\(945\) | 121.831 | 0.128922 | ||||||||
\(946\) | 603.950 | 0.638425 | ||||||||
\(947\) | −1096.67 | −1.15805 | −0.579026 | − | 0.815309i | \(-0.696567\pi\) | ||||
−0.579026 | + | 0.815309i | \(0.696567\pi\) | |||||||
\(948\) | 1455.12i | 1.53494i | ||||||||
\(949\) | 14.6522 | 0.0154396 | ||||||||
\(950\) | 4537.85i | 4.77669i | ||||||||
\(951\) | 291.067 | 0.306064 | ||||||||
\(952\) | −483.523 | −0.507902 | ||||||||
\(953\) | − | 336.869i | − | 0.353483i | −0.984257 | − | 0.176741i | \(-0.943444\pi\) | ||
0.984257 | − | 0.176741i | \(-0.0565556\pi\) | |||||||
\(954\) | 69.4894i | 0.0728401i | ||||||||
\(955\) | 1304.12 | 1.36557 | ||||||||
\(956\) | 2617.80 | 2.73828 | ||||||||
\(957\) | 156.336i | 0.163360i | ||||||||
\(958\) | − | 1693.42i | − | 1.76766i | ||||||
\(959\) | −703.109 | −0.733169 | ||||||||
\(960\) | 3130.20i | 3.26062i | ||||||||
\(961\) | −922.539 | −0.959978 | ||||||||
\(962\) | 1918.44i | 1.99422i | ||||||||
\(963\) | − | 524.947i | − | 0.545116i | ||||||
\(964\) | 1549.03i | 1.60688i | ||||||||
\(965\) | 921.292i | 0.954707i | ||||||||
\(966\) | 108.000 | + | 389.591i | 0.111801 | + | 0.403303i | ||||
\(967\) | −320.761 | −0.331707 | −0.165854 | − | 0.986150i | \(-0.553038\pi\) | ||||
−0.165854 | + | 0.986150i | \(0.553038\pi\) | |||||||
\(968\) | −2980.07 | −3.07858 | ||||||||
\(969\) | −271.678 | −0.280370 | ||||||||
\(970\) | 5604.52 | 5.77786 | ||||||||
\(971\) | 928.767i | 0.956505i | 0.878222 | + | 0.478253i | \(0.158730\pi\) | ||||
−0.878222 | + | 0.478253i | \(0.841270\pi\) | |||||||
\(972\) | 166.996 | 0.171807 | ||||||||
\(973\) | 534.767i | 0.549606i | ||||||||
\(974\) | 1981.33 | 2.03422 | ||||||||
\(975\) | −1396.09 | −1.43189 | ||||||||
\(976\) | 1680.93i | 1.72227i | ||||||||
\(977\) | 712.142i | 0.728907i | 0.931222 | + | 0.364453i | \(0.118744\pi\) | ||||
−0.931222 | + | 0.364453i | \(0.881256\pi\) | |||||||
\(978\) | 1046.71 | 1.07026 | ||||||||
\(979\) | −345.227 | −0.352632 | ||||||||
\(980\) | − | 664.551i | − | 0.678114i | ||||||
\(981\) | 380.754i | 0.388129i | ||||||||
\(982\) | 90.6877 | 0.0923500 | ||||||||
\(983\) | 1597.38i | 1.62500i | 0.582961 | + | 0.812500i | \(0.301894\pi\) | ||||
−0.582961 | + | 0.812500i | \(0.698106\pi\) | |||||||
\(984\) | 301.871 | 0.306780 | ||||||||
\(985\) | − | 927.171i | − | 0.941290i | ||||||
\(986\) | − | 1071.14i | − | 1.08635i | ||||||
\(987\) | 260.774i | 0.264208i | ||||||||
\(988\) | 3564.63i | 3.60793i | ||||||||
\(989\) | 421.702 | + | 1521.22i | 0.426393 | + | 1.53814i | ||||
\(990\) | 233.941 | 0.236304 | ||||||||
\(991\) | −1771.78 | −1.78788 | −0.893938 | − | 0.448191i | \(-0.852068\pi\) | ||||
−0.893938 | + | 0.448191i | \(0.852068\pi\) | |||||||
\(992\) | −691.331 | −0.696907 | ||||||||
\(993\) | 945.736 | 0.952403 | ||||||||
\(994\) | 262.426i | 0.264010i | ||||||||
\(995\) | −600.126 | −0.603142 | ||||||||
\(996\) | 1323.45i | 1.32876i | ||||||||
\(997\) | 124.674 | 0.125049 | 0.0625244 | − | 0.998043i | \(-0.480085\pi\) | ||||
0.0625244 | + | 0.998043i | \(0.480085\pi\) | |||||||
\(998\) | −338.771 | −0.339450 | ||||||||
\(999\) | − | 172.604i | − | 0.172777i |
(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 | 483.3.f.a.22.4 | yes | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.3 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.3 | ✓ | 48 | 23.22 | odd | 2 | inner | |
483.3.f.a.22.4 | yes | 48 | 1.1 | even | 1 | trivial |