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 | 22.3 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.4 |
$q$-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 | \(-0.653343\pi\) | ||
0.463324 | − | 0.886189i | \(-0.346657\pi\) | |||||||
\(6\) | −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 | \(-0.966747\pi\) | ||
0.994548 | − | 0.104277i | \(-0.0332529\pi\) | |||||||
\(12\) | 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 | \(-0.933059\pi\) | ||
0.977968 | − | 0.208754i | \(-0.0669409\pi\) | |||||||
\(18\) | −11.5072 | −0.639288 | ||||||||
\(19\) | − | 22.0994i | − | 1.16313i | −0.813502 | − | 0.581563i | \(-0.802442\pi\) | ||
0.813502 | − | 0.581563i | \(-0.197558\pi\) | |||||||
\(20\) | − | 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 | \(0.148180\pi\) | ||||
−0.893588 | + | 0.448888i | \(0.851820\pi\) | |||||||
\(38\) | 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 | \(-0.705852\pi\) | ||
0.602559 | − | 0.798074i | \(-0.294148\pi\) | |||||||
\(44\) | − | 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 | \(0.0181438\pi\) | ||||
−0.998376 | + | 0.0569696i | \(0.981856\pi\) | |||||||
\(54\) | −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 | \(-0.920746\pi\) | ||
0.969163 | − | 0.246420i | \(-0.0792541\pi\) | |||||||
\(62\) | −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 | \(0.414595\pi\) | ||||
−0.265100 | + | 0.964221i | \(0.585405\pi\) | |||||||
\(68\) | − | 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 | \(-0.834678\pi\) | ||
0.868130 | − | 0.496338i | \(-0.165322\pi\) | |||||||
\(80\) | − | 495.498i | − | 6.19373i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 25.9630 | 0.316623 | ||||||||
\(83\) | − | 71.3251i | − | 0.859339i | −0.902986 | − | 0.429669i | \(-0.858630\pi\) | ||
0.902986 | − | 0.429669i | \(-0.141370\pi\) | |||||||
\(84\) | 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 | \(-0.679350\pi\) | ||
0.534101 | − | 0.845421i | \(-0.320650\pi\) | |||||||
\(90\) | 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 | \(-0.676669\pi\) | ||
0.526961 | − | 0.849889i | \(-0.323331\pi\) | |||||||
\(98\) | 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 | \(-0.973047\pi\) | ||
0.996417 | − | 0.0845730i | \(-0.0269526\pi\) | |||||||
\(104\) | −387.690 | −3.72779 | ||||||||
\(105\) | 40.6103 | 0.386765 | ||||||||
\(106\) | − | 23.1631i | − | 0.218520i | ||||||
\(107\) | 174.982i | 1.63535i | 0.575681 | + | 0.817674i | \(0.304737\pi\) | ||||
−0.575681 | + | 0.817674i | \(0.695263\pi\) | |||||||
\(108\) | 55.6655 | 0.515421 | ||||||||
\(109\) | − | 126.918i | − | 1.16439i | −0.813051 | − | 0.582193i | \(-0.802195\pi\) | ||
0.813051 | − | 0.582193i | \(-0.197805\pi\) | |||||||
\(110\) | 77.9805 | 0.708913 | ||||||||
\(111\) | 57.5347i | 0.518331i | ||||||||
\(112\) | 147.933i | 1.32083i | ||||||||
\(113\) | − | 28.0406i | − | 0.248147i | −0.992273 | − | 0.124073i | \(-0.960404\pi\) | ||
0.992273 | − | 0.124073i | \(-0.0395958\pi\) | |||||||
\(114\) | 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 | \(0.421692\pi\) | ||||
−0.243537 | + | 0.969892i | \(0.578308\pi\) | |||||||
\(138\) | −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 | \(-0.891663\pi\) | ||
0.942638 | − | 0.333817i | \(-0.108337\pi\) | |||||||
\(150\) | 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 | \(0.164269\pi\) | ||||
−0.869767 | + | 0.493462i | \(0.835731\pi\) | |||||||
\(158\) | 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 | \(-0.999878\pi\) | |||
1.00000 | 0.000382939i | \(-0.000121893\pi\) | ||||||||
\(182\) | − | 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 | \(0.125880\pi\) | ||||
−0.922818 | + | 0.385237i | \(0.874120\pi\) | |||||||
\(192\) | 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 | \(-0.945575\pi\) | ||
0.985418 | − | 0.170151i | \(-0.0544254\pi\) | |||||||
\(200\) | 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 | \(-0.912758\pi\) | ||
0.962675 | − | 0.270662i | \(-0.0872424\pi\) | |||||||
\(228\) | − | 410.058i | − | 1.79850i | ||||||
\(229\) | − | 46.7869i | − | 0.204309i | −0.994769 | − | 0.102155i | \(-0.967426\pi\) | ||
0.994769 | − | 0.102155i | \(-0.0325737\pi\) | |||||||
\(230\) | −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 | \(-0.903016\pi\) | ||
0.953942 | − | 0.299992i | \(-0.0969840\pi\) | |||||||
\(242\) | −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 | \(-0.893479\pi\) | ||
0.944527 | − | 0.328433i | \(-0.106521\pi\) | |||||||
\(252\) | 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 | \(-0.977306\pi\) | ||
0.997460 | − | 0.0712344i | \(-0.0226938\pi\) | |||||||
\(264\) | 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 | \(0.156759\pi\) | ||||
−0.881166 | + | 0.472807i | \(0.843241\pi\) | |||||||
\(282\) | 378.062 | 1.34064 | ||||||||
\(283\) | 463.763i | 1.63874i | 0.573266 | + | 0.819370i | \(0.305676\pi\) | ||||
−0.573266 | + | 0.819370i | \(0.694324\pi\) | |||||||
\(284\) | 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 | \(0.170730\pi\) | ||||
−0.859572 | + | 0.511014i | \(0.829270\pi\) | |||||||
\(294\) | 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 | \(0.195472\pi\) | ||||
−0.817297 | + | 0.576217i | \(0.804528\pi\) | |||||||
\(314\) | − | 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 | \(0.138046\pi\) | ||||
−0.907424 | + | 0.420217i | \(0.861954\pi\) | |||||||
\(338\) | −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 | \(0.0635175\pi\) | ||||
−0.980157 | + | 0.198224i | \(0.936483\pi\) | |||||||
\(360\) | 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 | \(-0.984396\pi\) | ||
0.998799 | − | 0.0490027i | \(-0.0156043\pi\) | |||||||
\(368\) | 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 | \(-0.808270\pi\) | ||
0.824013 | − | 0.566571i | \(-0.191730\pi\) | |||||||
\(374\) | 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 | \(0.248517\pi\) | ||||
−0.710394 | + | 0.703805i | \(0.751483\pi\) | |||||||
\(380\) | −2098.02 | −5.52112 | ||||||||
\(381\) | 236.198 | 0.619943 | ||||||||
\(382\) | − | 564.469i | − | 1.47767i | ||||||
\(383\) | 447.089i | 1.16734i | 0.811993 | + | 0.583668i | \(0.198383\pi\) | ||||
−0.811993 | + | 0.583668i | \(0.801617\pi\) | |||||||
\(384\) | −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 | \(-0.835524\pi\) | ||
0.869446 | − | 0.494027i | \(-0.164476\pi\) | |||||||
\(390\) | 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 | \(0.0206714\pi\) | ||||
−0.997892 | + | 0.0648955i | \(0.979329\pi\) | |||||||
\(402\) | − | 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 | \(0.328064\pi\) | ||||
−0.514266 | + | 0.857631i | \(0.671936\pi\) | |||||||
\(420\) | 435.051 | 1.03584 | ||||||||
\(421\) | 320.503i | 0.761290i | 0.924721 | + | 0.380645i | \(0.124298\pi\) | ||||
−0.924721 | + | 0.380645i | \(0.875702\pi\) | |||||||
\(422\) | −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 | \(0.162258\pi\) | ||||
−0.872867 | + | 0.487959i | \(0.837742\pi\) | |||||||
\(432\) | 290.534 | 0.672533 | ||||||||
\(433\) | − | 317.443i | − | 0.733125i | −0.930393 | − | 0.366562i | \(-0.880535\pi\) | ||
0.930393 | − | 0.366562i | \(-0.119465\pi\) | |||||||
\(434\) | − | 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 | \(-0.919609\pi\) | ||
0.968277 | − | 0.249878i | \(-0.0803905\pi\) | |||||||
\(458\) | 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 | \(0.320271\pi\) | ||||
−0.535107 | + | 0.844784i | \(0.679729\pi\) | |||||||
\(468\) | 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 | \(-0.847548\pi\) | ||
0.887483 | − | 0.460840i | \(-0.152452\pi\) | |||||||
\(480\) | 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 | \(-0.804739\pi\) | ||
0.817677 | − | 0.575677i | \(-0.195261\pi\) | |||||||
\(504\) | − | 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 | \(-0.860719\pi\) | ||
0.905787 | − | 0.423733i | \(-0.139281\pi\) | |||||||
\(522\) | −452.747 | −0.867331 | ||||||||
\(523\) | 62.9887i | 0.120437i | 0.998185 | + | 0.0602187i | \(0.0191798\pi\) | ||||
−0.998185 | + | 0.0602187i | \(0.980820\pi\) | |||||||
\(524\) | −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 | \(-0.939367\pi\) | ||
0.981912 | − | 0.189335i | \(-0.0606333\pi\) | |||||||
\(558\) | −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 | \(0.161969\pi\) | ||||
−0.873309 | + | 0.487166i | \(0.838031\pi\) | |||||||
\(564\) | −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 | \(0.166809\pi\) | ||||
−0.865802 | + | 0.500386i | \(0.833191\pi\) | |||||||
\(570\) | 1301.11 | 2.28266 | ||||||||
\(571\) | 124.187i | 0.217490i | 0.994070 | + | 0.108745i | \(0.0346832\pi\) | ||||
−0.994070 | + | 0.108745i | \(0.965317\pi\) | |||||||
\(572\) | − | 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 | \(0.0568843\pi\) | ||||
−0.984074 | + | 0.177758i | \(0.943116\pi\) | |||||||
\(614\) | −2155.85 | −3.51116 | ||||||||
\(615\) | 103.895i | 0.168935i | ||||||||
\(616\) | −156.284 | −0.253708 | ||||||||
\(617\) | − | 907.090i | − | 1.47016i | −0.677979 | − | 0.735081i | \(-0.737144\pi\) | ||
0.677979 | − | 0.735081i | \(-0.262856\pi\) | |||||||
\(618\) | 115.746i | 0.187292i | ||||||||
\(619\) | 974.089i | 1.57365i | 0.617177 | + | 0.786824i | \(0.288276\pi\) | ||||
−0.617177 | + | 0.786824i | \(0.711724\pi\) | |||||||
\(620\) | − | 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 | \(-0.944747\pi\) | ||
0.984972 | − | 0.172713i | \(-0.0552533\pi\) | |||||||
\(632\) | 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 | \(-0.793023\pi\) | ||
0.795940 | − | 0.605375i | \(-0.206977\pi\) | |||||||
\(642\) | − | 1162.53i | − | 1.81079i | ||||||
\(643\) | − | 405.054i | − | 0.629945i | −0.949101 | − | 0.314972i | \(-0.898005\pi\) | ||
0.949101 | − | 0.314972i | \(-0.101995\pi\) | |||||||
\(644\) | −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 | \(-0.749968\pi\) | ||
0.707036 | − | 0.707178i | \(-0.250032\pi\) | |||||||
\(660\) | −377.227 | −0.571556 | ||||||||
\(661\) | 573.064i | 0.866965i | 0.901162 | + | 0.433483i | \(0.142715\pi\) | ||||
−0.901162 | + | 0.433483i | \(0.857285\pi\) | |||||||
\(662\) | −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 | \(-0.895261\pi\) | ||
0.946350 | − | 0.323143i | \(-0.104739\pi\) | |||||||
\(678\) | 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 | \(0.223750\pi\) | ||||
−0.762951 | + | 0.646456i | \(0.776250\pi\) | |||||||
\(702\) | −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 | \(-0.634627\pi\) | ||
0.410447 | − | 0.911885i | \(-0.365373\pi\) | |||||||
\(710\) | 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 | \(-0.751846\pi\) | ||
0.711195 | − | 0.702995i | \(-0.248154\pi\) | |||||||
\(728\) | − | 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 | \(0.214146\pi\) | ||||
−0.782105 | + | 0.623146i | \(0.785854\pi\) | |||||||
\(734\) | 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 | \(0.0745009\pi\) | ||||
−0.972735 | + | 0.231920i | \(0.925499\pi\) | |||||||
\(744\) | −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 | \(0.128083\pi\) | ||||
−0.920130 | + | 0.391614i | \(0.871917\pi\) | |||||||
\(752\) | −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 | \(-0.998737\pi\) | ||
0.999992 | − | 0.00396709i | \(-0.00126277\pi\) | |||||||
\(758\) | − | 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 | \(-0.937573\pi\) | ||
0.980830 | − | 0.194866i | \(-0.0624272\pi\) | |||||||
\(770\) | 206.317i | 0.267944i | ||||||||
\(771\) | 121.372 | 0.157422 | ||||||||
\(772\) | 1113.72 | 1.44264 | ||||||||
\(773\) | 374.493i | 0.484468i | 0.970218 | + | 0.242234i | \(0.0778801\pi\) | ||||
−0.970218 | + | 0.242234i | \(0.922120\pi\) | |||||||
\(774\) | 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 | \(0.0126377\pi\) | ||||
−0.999212 | + | 0.0396922i | \(0.987362\pi\) | |||||||
\(788\) | −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 | \(-0.737462\pi\) | ||
0.678714 | − | 0.734403i | \(-0.262538\pi\) | |||||||
\(798\) | −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 | \(0.158402\pi\) | ||||
−0.878714 | + | 0.477348i | \(0.841598\pi\) | |||||||
\(828\) | 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 | \(0.0312210\pi\) | ||||
−0.995194 | + | 0.0979266i | \(0.968779\pi\) | |||||||
\(840\) | −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 | \(-0.946011\pi\) | ||
0.985650 | − | 0.168800i | \(-0.0539893\pi\) | |||||||
\(882\) | 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 | \(0.198451\pi\) | ||||
−0.811867 | + | 0.583842i | \(0.801549\pi\) | |||||||
\(908\) | − | 1316.40i | − | 1.44978i | ||||||
\(909\) | −13.3897 | −0.0147302 | ||||||||
\(910\) | −1354.11 | −1.48803 | ||||||||
\(911\) | − | 867.979i | − | 0.952776i | −0.879235 | − | 0.476388i | \(-0.841946\pi\) | ||
0.879235 | − | 0.476388i | \(-0.158054\pi\) | |||||||
\(912\) | − | 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 | \(0.172638\pi\) | ||||
−0.856494 | + | 0.516156i | \(0.827362\pi\) | |||||||
\(920\) | −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 | \(0.236070\pi\) | ||||
−0.737364 | + | 0.675495i | \(0.763930\pi\) | |||||||
\(938\) | 1311.23 | 1.39790 | ||||||||
\(939\) | 624.772i | 0.665358i | ||||||||
\(940\) | 5402.37i | 5.74721i | ||||||||
\(941\) | 388.953i | 0.413340i | 0.978411 | + | 0.206670i | \(0.0662627\pi\) | ||||
−0.978411 | + | 0.206670i | \(0.933737\pi\) | |||||||
\(942\) | − | 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 | \(0.0565556\pi\) | ||||
−0.984257 | + | 0.176741i | \(0.943444\pi\) | |||||||
\(954\) | − | 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 | \(-0.841270\pi\) | ||
0.878222 | − | 0.478253i | \(-0.158730\pi\) | |||||||
\(972\) | 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 | \(-0.881256\pi\) | ||
0.931222 | − | 0.364453i | \(-0.118744\pi\) | |||||||
\(978\) | 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 | \(-0.698106\pi\) | ||
0.582961 | − | 0.812500i | \(-0.301894\pi\) | |||||||
\(984\) | 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.22.3 | ✓ | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.4 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.3 | ✓ | 48 | 1.1 | even | 1 | trivial | |
483.3.f.a.22.4 | yes | 48 | 23.22 | odd | 2 | inner |