Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(244,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.244");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.b (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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + \cdots + 614656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{12}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 244.12 | ||
Root | \(2.67506i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.244 |
Dual form | 405.4.b.e.244.5 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67506i | 0.945778i | 0.881122 | + | 0.472889i | \(0.156789\pi\) | ||||
−0.881122 | + | 0.472889i | \(0.843211\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.844033 | 0.105504 | ||||||||
\(5\) | −10.9788 | + | 2.11350i | −0.981970 | + | 0.189037i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 15.4153i | − | 0.832349i | −0.909285 | − | 0.416175i | \(-0.863371\pi\) | ||
0.909285 | − | 0.416175i | \(-0.136629\pi\) | |||||||
\(8\) | 23.6584i | 1.04556i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.65374 | − | 29.3689i | −0.178787 | − | 0.928726i | ||||
\(11\) | 44.5598 | 1.22139 | 0.610694 | − | 0.791866i | \(-0.290890\pi\) | ||||
0.610694 | + | 0.791866i | \(0.290890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28.0233i | 0.597867i | 0.954274 | + | 0.298933i | \(0.0966309\pi\) | ||||
−0.954274 | + | 0.298933i | \(0.903369\pi\) | |||||||
\(14\) | 41.2370 | 0.787217 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −56.5353 | −0.883365 | ||||||||
\(17\) | 92.6615i | 1.32198i | 0.750394 | + | 0.660991i | \(0.229864\pi\) | ||||
−0.750394 | + | 0.660991i | \(0.770136\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −49.5811 | −0.598667 | −0.299334 | − | 0.954149i | \(-0.596764\pi\) | ||||
−0.299334 | + | 0.954149i | \(0.596764\pi\) | |||||||
\(20\) | −9.26644 | + | 1.78386i | −0.103602 | + | 0.0199442i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 119.200i | 1.15516i | ||||||||
\(23\) | 0.922809i | 0.00836604i | 0.999991 | + | 0.00418302i | \(0.00133150\pi\) | ||||
−0.999991 | + | 0.00418302i | \(0.998668\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 116.066 | − | 46.4071i | 0.928530 | − | 0.371257i | ||||
\(26\) | −74.9642 | −0.565449 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 13.0110i | − | 0.0878163i | ||||||
\(29\) | −189.849 | −1.21566 | −0.607830 | − | 0.794067i | \(-0.707960\pi\) | ||||
−0.607830 | + | 0.794067i | \(0.707960\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −299.180 | −1.73337 | −0.866683 | − | 0.498859i | \(-0.833752\pi\) | ||||
−0.866683 | + | 0.498859i | \(0.833752\pi\) | |||||||
\(32\) | 38.0312i | 0.210095i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −247.875 | −1.25030 | ||||||||
\(35\) | 32.5802 | + | 169.241i | 0.157345 | + | 0.817342i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 57.8330i | − | 0.256965i | −0.991712 | − | 0.128482i | \(-0.958989\pi\) | ||
0.991712 | − | 0.128482i | \(-0.0410105\pi\) | |||||||
\(38\) | − | 132.633i | − | 0.566206i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −50.0019 | − | 259.739i | −0.197650 | − | 1.02671i | ||||
\(41\) | −287.880 | −1.09657 | −0.548284 | − | 0.836292i | \(-0.684719\pi\) | ||||
−0.548284 | + | 0.836292i | \(0.684719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.591953i | − | 0.00209935i | −0.999999 | − | 0.00104967i | \(-0.999666\pi\) | ||
0.999999 | − | 0.00104967i | \(-0.000334122\pi\) | |||||||
\(44\) | 37.6099 | 0.128862 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.46857 | −0.00791242 | ||||||||
\(47\) | 598.302i | 1.85684i | 0.371536 | + | 0.928418i | \(0.378831\pi\) | ||||
−0.371536 | + | 0.928418i | \(0.621169\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 105.368 | 0.307195 | ||||||||
\(50\) | 124.142 | + | 310.485i | 0.351127 | + | 0.878183i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 23.6526i | 0.0630774i | ||||||||
\(53\) | − | 146.339i | − | 0.379267i | −0.981855 | − | 0.189634i | \(-0.939270\pi\) | ||
0.981855 | − | 0.189634i | \(-0.0607301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −489.211 | + | 94.1769i | −1.19937 | + | 0.230888i | ||||
\(56\) | 364.701 | 0.870272 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 507.859i | − | 1.14975i | ||||||
\(59\) | 193.066 | 0.426018 | 0.213009 | − | 0.977050i | \(-0.431674\pi\) | ||||
0.213009 | + | 0.977050i | \(0.431674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −566.153 | −1.18833 | −0.594167 | − | 0.804341i | \(-0.702518\pi\) | ||||
−0.594167 | + | 0.804341i | \(0.702518\pi\) | |||||||
\(62\) | − | 800.326i | − | 1.63938i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −554.019 | −1.08207 | ||||||||
\(65\) | −59.2272 | − | 307.661i | −0.113019 | − | 0.587087i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 355.163i | 0.647613i | 0.946123 | + | 0.323806i | \(0.104963\pi\) | ||||
−0.946123 | + | 0.323806i | \(0.895037\pi\) | |||||||
\(68\) | 78.2093i | 0.139475i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −452.731 | + | 87.1542i | −0.773024 | + | 0.148813i | ||||
\(71\) | −320.703 | −0.536062 | −0.268031 | − | 0.963410i | \(-0.586373\pi\) | ||||
−0.268031 | + | 0.963410i | \(0.586373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 636.782i | 1.02095i | 0.859891 | + | 0.510477i | \(0.170531\pi\) | ||||
−0.859891 | + | 0.510477i | \(0.829469\pi\) | |||||||
\(74\) | 154.707 | 0.243031 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −41.8481 | −0.0631619 | ||||||||
\(77\) | − | 686.903i | − | 1.01662i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 287.765 | 0.409824 | 0.204912 | − | 0.978780i | \(-0.434309\pi\) | ||||
0.204912 | + | 0.978780i | \(0.434309\pi\) | |||||||
\(80\) | 620.688 | − | 119.487i | 0.867438 | − | 0.166989i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 770.097i | − | 1.03711i | ||||||
\(83\) | − | 285.058i | − | 0.376978i | −0.982075 | − | 0.188489i | \(-0.939641\pi\) | ||
0.982075 | − | 0.188489i | \(-0.0603590\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −195.840 | − | 1017.31i | −0.249904 | − | 1.29815i | ||||
\(86\) | 1.58351 | 0.00198552 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1054.21i | 1.27704i | ||||||||
\(89\) | 331.615 | 0.394957 | 0.197478 | − | 0.980307i | \(-0.436725\pi\) | ||||
0.197478 | + | 0.980307i | \(0.436725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 431.988 | 0.497634 | ||||||||
\(92\) | 0.778881i | 0.000882652i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1600.50 | −1.75616 | ||||||||
\(95\) | 544.339 | − | 104.789i | 0.587873 | − | 0.113170i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1821.63i | − | 1.90679i | −0.301730 | − | 0.953393i | \(-0.597564\pi\) | ||
0.301730 | − | 0.953393i | \(-0.402436\pi\) | |||||||
\(98\) | 281.866i | 0.290538i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 97.9638 | − | 39.1692i | 0.0979638 | − | 0.0391692i | ||||
\(101\) | −1147.37 | −1.13037 | −0.565184 | − | 0.824965i | \(-0.691195\pi\) | ||||
−0.565184 | + | 0.824965i | \(0.691195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1582.54i | 1.51391i | 0.653467 | + | 0.756955i | \(0.273314\pi\) | ||||
−0.653467 | + | 0.756955i | \(0.726686\pi\) | |||||||
\(104\) | −662.986 | −0.625107 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 391.466 | 0.358703 | ||||||||
\(107\) | 385.387i | 0.348194i | 0.984728 | + | 0.174097i | \(0.0557007\pi\) | ||||
−0.984728 | + | 0.174097i | \(0.944299\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 203.502 | 0.178825 | 0.0894126 | − | 0.995995i | \(-0.471501\pi\) | ||||
0.0894126 | + | 0.995995i | \(0.471501\pi\) | |||||||
\(110\) | −251.929 | − | 1308.67i | −0.218368 | − | 1.13433i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 871.510i | 0.735268i | ||||||||
\(113\) | 66.0150i | 0.0549573i | 0.999622 | + | 0.0274786i | \(0.00874782\pi\) | ||||
−0.999622 | + | 0.0274786i | \(0.991252\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.95035 | − | 10.1313i | −0.00158149 | − | 0.00821520i | ||||
\(116\) | −160.239 | −0.128257 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 516.464i | 0.402918i | ||||||||
\(119\) | 1428.41 | 1.10035 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 654.573 | 0.491790 | ||||||||
\(122\) | − | 1514.49i | − | 1.12390i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −252.518 | −0.182877 | ||||||||
\(125\) | −1176.18 | + | 754.799i | −0.841607 | + | 0.540090i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1821.52i | − | 1.27270i | −0.771399 | − | 0.636352i | \(-0.780443\pi\) | ||
0.771399 | − | 0.636352i | \(-0.219557\pi\) | |||||||
\(128\) | − | 1177.79i | − | 0.813301i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 823.013 | − | 158.437i | 0.555254 | − | 0.106891i | ||||
\(131\) | 238.258 | 0.158906 | 0.0794530 | − | 0.996839i | \(-0.474683\pi\) | ||||
0.0794530 | + | 0.996839i | \(0.474683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 764.308i | 0.498300i | ||||||||
\(134\) | −950.083 | −0.612498 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2192.22 | −1.38221 | ||||||||
\(137\) | 2047.48i | 1.27685i | 0.769685 | + | 0.638424i | \(0.220413\pi\) | ||||
−0.769685 | + | 0.638424i | \(0.779587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2179.37 | 1.32987 | 0.664934 | − | 0.746902i | \(-0.268460\pi\) | ||||
0.664934 | + | 0.746902i | \(0.268460\pi\) | |||||||
\(140\) | 27.4988 | + | 142.845i | 0.0166005 | + | 0.0862330i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 857.901i | − | 0.506996i | ||||||
\(143\) | 1248.71i | 0.730228i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2084.31 | − | 401.246i | 1.19374 | − | 0.229805i | ||||
\(146\) | −1703.43 | −0.965596 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 48.8130i | − | 0.0271108i | ||||||
\(149\) | −155.948 | −0.0857435 | −0.0428717 | − | 0.999081i | \(-0.513651\pi\) | ||||
−0.0428717 | + | 0.999081i | \(0.513651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1614.14 | 0.869914 | 0.434957 | − | 0.900451i | \(-0.356764\pi\) | ||||
0.434957 | + | 0.900451i | \(0.356764\pi\) | |||||||
\(152\) | − | 1173.01i | − | 0.625943i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1837.51 | 0.961498 | ||||||||
\(155\) | 3284.63 | − | 632.316i | 1.70211 | − | 0.327670i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 988.508i | 0.502494i | 0.967923 | + | 0.251247i | \(0.0808406\pi\) | ||||
−0.967923 | + | 0.251247i | \(0.919159\pi\) | |||||||
\(158\) | 769.791i | 0.387603i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −80.3788 | − | 417.535i | −0.0397156 | − | 0.206307i | ||||
\(161\) | 14.2254 | 0.00696347 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2974.11i | 1.42914i | 0.699564 | + | 0.714570i | \(0.253378\pi\) | ||||
−0.699564 | + | 0.714570i | \(0.746622\pi\) | |||||||
\(164\) | −242.980 | −0.115692 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 762.548 | 0.356537 | ||||||||
\(167\) | 2438.96i | 1.13013i | 0.825045 | + | 0.565067i | \(0.191150\pi\) | ||||
−0.825045 | + | 0.565067i | \(0.808850\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1411.69 | 0.642555 | ||||||||
\(170\) | 2721.36 | − | 523.884i | 1.22776 | − | 0.236353i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 0.499628i | − | 0.000221490i | ||||||
\(173\) | 2653.59i | 1.16618i | 0.812409 | + | 0.583089i | \(0.198156\pi\) | ||||
−0.812409 | + | 0.583089i | \(0.801844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −715.381 | − | 1789.20i | −0.309016 | − | 0.772861i | ||||
\(176\) | −2519.20 | −1.07893 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 887.092i | 0.373541i | ||||||||
\(179\) | 2102.30 | 0.877841 | 0.438921 | − | 0.898526i | \(-0.355361\pi\) | ||||
0.438921 | + | 0.898526i | \(0.355361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1597.36 | 0.655973 | 0.327987 | − | 0.944682i | \(-0.393630\pi\) | ||||
0.327987 | + | 0.944682i | \(0.393630\pi\) | |||||||
\(182\) | 1155.60i | 0.470651i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −21.8321 | −0.00874721 | ||||||||
\(185\) | 122.230 | + | 634.935i | 0.0485758 | + | 0.252331i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4128.97i | 1.61465i | ||||||||
\(188\) | 504.987i | 0.195904i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 280.318 | + | 1456.14i | 0.107034 | + | 0.555997i | ||||
\(191\) | −3407.43 | −1.29085 | −0.645426 | − | 0.763823i | \(-0.723320\pi\) | ||||
−0.645426 | + | 0.763823i | \(0.723320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 819.130i | − | 0.305504i | −0.988265 | − | 0.152752i | \(-0.951186\pi\) | ||
0.988265 | − | 0.152752i | \(-0.0488135\pi\) | |||||||
\(194\) | 4872.97 | 1.80340 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 88.9340 | 0.0324103 | ||||||||
\(197\) | 359.979i | 0.130190i | 0.997879 | + | 0.0650950i | \(0.0207350\pi\) | ||||
−0.997879 | + | 0.0650950i | \(0.979265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1338.34 | 0.476745 | 0.238372 | − | 0.971174i | \(-0.423386\pi\) | ||||
0.238372 | + | 0.971174i | \(0.423386\pi\) | |||||||
\(200\) | 1097.92 | + | 2745.94i | 0.388172 | + | 0.970835i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3069.28i | − | 1.06908i | ||||||
\(203\) | 2926.59i | 1.01185i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3160.56 | − | 608.433i | 1.07680 | − | 0.207292i | ||||
\(206\) | −4233.41 | −1.43182 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1584.31i | − | 0.528135i | ||||||
\(209\) | −2209.32 | −0.731205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1068.23 | 0.348530 | 0.174265 | − | 0.984699i | \(-0.444245\pi\) | ||||
0.174265 | + | 0.984699i | \(0.444245\pi\) | |||||||
\(212\) | − | 123.515i | − | 0.0400143i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1030.94 | −0.329315 | ||||||||
\(215\) | 1.25109 | + | 6.49891i | 0.000396855 | + | 0.00206150i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4611.96i | 1.44277i | ||||||||
\(218\) | 544.381i | 0.169129i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −412.910 | + | 79.4885i | −0.126538 | + | 0.0243596i | ||||
\(221\) | −2596.68 | −0.790370 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1518.83i | 0.456091i | 0.973650 | + | 0.228046i | \(0.0732335\pi\) | ||||
−0.973650 | + | 0.228046i | \(0.926766\pi\) | |||||||
\(224\) | 586.263 | 0.174872 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −176.594 | −0.0519774 | ||||||||
\(227\) | − | 4235.12i | − | 1.23830i | −0.785271 | − | 0.619152i | \(-0.787476\pi\) | ||
0.785271 | − | 0.619152i | \(-0.212524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5536.52 | 1.59766 | 0.798829 | − | 0.601558i | \(-0.205453\pi\) | ||||
0.798829 | + | 0.601558i | \(0.205453\pi\) | |||||||
\(230\) | 27.1019 | − | 5.21732i | 0.00776976 | − | 0.00149574i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 4491.53i | − | 1.27105i | ||||||
\(233\) | − | 6337.30i | − | 1.78185i | −0.454154 | − | 0.890923i | \(-0.650059\pi\) | ||
0.454154 | − | 0.890923i | \(-0.349941\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1264.51 | − | 6568.61i | −0.351011 | − | 1.82336i | ||||
\(236\) | 162.954 | 0.0449466 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3821.08i | 1.04069i | ||||||||
\(239\) | −2542.87 | −0.688220 | −0.344110 | − | 0.938929i | \(-0.611819\pi\) | ||||
−0.344110 | + | 0.938929i | \(0.611819\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2051.42 | 0.548314 | 0.274157 | − | 0.961685i | \(-0.411601\pi\) | ||||
0.274157 | + | 0.961685i | \(0.411601\pi\) | |||||||
\(242\) | 1751.02i | 0.465124i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −477.852 | −0.125374 | ||||||||
\(245\) | −1156.81 | + | 222.695i | −0.301656 | + | 0.0580712i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1389.43i | − | 0.357923i | ||||||
\(248\) | − | 7078.11i | − | 1.81234i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2019.13 | − | 3146.36i | −0.510805 | − | 0.795974i | ||||
\(251\) | −2770.89 | −0.696801 | −0.348401 | − | 0.937346i | \(-0.613275\pi\) | ||||
−0.348401 | + | 0.937346i | \(0.613275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.1201i | 0.0102182i | ||||||||
\(254\) | 4872.67 | 1.20370 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1281.50 | −0.312865 | ||||||||
\(257\) | − | 426.755i | − | 0.103581i | −0.998658 | − | 0.0517904i | \(-0.983507\pi\) | ||
0.998658 | − | 0.0517904i | \(-0.0164928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −891.514 | −0.213884 | ||||||||
\(260\) | −49.9897 | − | 259.676i | −0.0119240 | − | 0.0619402i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 637.355i | 0.150290i | ||||||||
\(263\) | − | 3762.39i | − | 0.882125i | −0.897476 | − | 0.441063i | \(-0.854602\pi\) | ||
0.897476 | − | 0.441063i | \(-0.145398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 309.287 | + | 1606.62i | 0.0716956 | + | 0.372429i | ||||
\(266\) | −2044.57 | −0.471281 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 299.769i | 0.0683258i | ||||||||
\(269\) | 1980.25 | 0.448839 | 0.224420 | − | 0.974493i | \(-0.427951\pi\) | ||||
0.224420 | + | 0.974493i | \(0.427951\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5659.70 | 1.26864 | 0.634321 | − | 0.773070i | \(-0.281280\pi\) | ||||
0.634321 | + | 0.773070i | \(0.281280\pi\) | |||||||
\(272\) | − | 5238.65i | − | 1.16779i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5477.14 | −1.20761 | ||||||||
\(275\) | 5171.89 | − | 2067.89i | 1.13410 | − | 0.453449i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6169.57i | 1.33824i | 0.743153 | + | 0.669121i | \(0.233329\pi\) | ||||
−0.743153 | + | 0.669121i | \(0.766671\pi\) | |||||||
\(278\) | 5829.95i | 1.25776i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4003.97 | + | 770.795i | −0.854581 | + | 0.164514i | ||||
\(281\) | 3343.45 | 0.709800 | 0.354900 | − | 0.934904i | \(-0.384515\pi\) | ||||
0.354900 | + | 0.934904i | \(0.384515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5103.32i | 1.07195i | 0.844235 | + | 0.535973i | \(0.180055\pi\) | ||||
−0.844235 | + | 0.535973i | \(0.819945\pi\) | |||||||
\(284\) | −270.684 | −0.0565568 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3340.39 | −0.690633 | ||||||||
\(287\) | 4437.76i | 0.912727i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3673.14 | −0.747638 | ||||||||
\(290\) | 1073.36 | + | 5575.67i | 0.217344 | + | 1.12902i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 537.465i | 0.107715i | ||||||||
\(293\) | − | 4130.28i | − | 0.823527i | −0.911291 | − | 0.411764i | \(-0.864913\pi\) | ||
0.911291 | − | 0.411764i | \(-0.135087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2119.62 | + | 408.044i | −0.418337 | + | 0.0805331i | ||||
\(296\) | 1368.23 | 0.268672 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 417.172i | − | 0.0810943i | ||||||
\(299\) | −25.8602 | −0.00500178 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.12515 | −0.00174739 | ||||||||
\(302\) | 4317.93i | 0.822746i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2803.08 | 0.528841 | ||||||||
\(305\) | 6215.65 | − | 1196.56i | 1.16691 | − | 0.224639i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3382.52i | − | 0.628830i | −0.949286 | − | 0.314415i | \(-0.898192\pi\) | ||
0.949286 | − | 0.314415i | \(-0.101808\pi\) | |||||||
\(308\) | − | 579.769i | − | 0.107258i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1691.49 | + | 8786.59i | 0.309903 | + | 1.60982i | ||||
\(311\) | −6021.22 | −1.09785 | −0.548926 | − | 0.835871i | \(-0.684963\pi\) | ||||
−0.548926 | + | 0.835871i | \(0.684963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10192.9i | − | 1.84070i | −0.391096 | − | 0.920350i | \(-0.627904\pi\) | ||
0.391096 | − | 0.920350i | \(-0.372096\pi\) | |||||||
\(314\) | −2644.32 | −0.475247 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 242.884 | 0.0432382 | ||||||||
\(317\) | − | 5400.59i | − | 0.956869i | −0.878123 | − | 0.478435i | \(-0.841204\pi\) | ||
0.878123 | − | 0.478435i | \(-0.158796\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8459.65 | −1.48479 | ||||||||
\(320\) | 6082.44 | − | 1170.92i | 1.06256 | − | 0.204551i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 38.0538i | 0.00658589i | ||||||||
\(323\) | − | 4594.25i | − | 0.791428i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1300.48 | + | 3252.56i | 0.221962 | + | 0.555137i | ||||
\(326\) | −7955.92 | −1.35165 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6810.76i | − | 1.14653i | ||||||
\(329\) | 9223.02 | 1.54554 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2302.90 | −0.382413 | −0.191206 | − | 0.981550i | \(-0.561240\pi\) | ||||
−0.191206 | + | 0.981550i | \(0.561240\pi\) | |||||||
\(332\) | − | 240.598i | − | 0.0397727i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6524.37 | −1.06886 | ||||||||
\(335\) | −750.636 | − | 3899.25i | −0.122423 | − | 0.635936i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9566.33i | − | 1.54632i | −0.634209 | − | 0.773162i | \(-0.718674\pi\) | ||
0.634209 | − | 0.773162i | \(-0.281326\pi\) | |||||||
\(338\) | 3776.37i | 0.607714i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −165.295 | − | 858.641i | −0.0263659 | − | 0.136960i | ||||
\(341\) | −13331.4 | −2.11711 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6911.73i | − | 1.08804i | ||||||
\(344\) | 14.0046 | 0.00219500 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7098.52 | −1.10294 | ||||||||
\(347\) | 81.5218i | 0.0126119i | 0.999980 | + | 0.00630593i | \(0.00200725\pi\) | ||||
−0.999980 | + | 0.00630593i | \(0.997993\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −93.5719 | −0.0143518 | −0.00717591 | − | 0.999974i | \(-0.502284\pi\) | ||||
−0.00717591 | + | 0.999974i | \(0.502284\pi\) | |||||||
\(350\) | 4786.22 | − | 1913.69i | 0.730955 | − | 0.292260i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1694.66i | 0.256607i | ||||||||
\(353\) | 6675.41i | 1.00651i | 0.864139 | + | 0.503253i | \(0.167864\pi\) | ||||
−0.864139 | + | 0.503253i | \(0.832136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3520.92 | − | 677.805i | 0.526397 | − | 0.101336i | ||||
\(356\) | 279.894 | 0.0416696 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5623.80i | 0.830243i | ||||||||
\(359\) | 8334.50 | 1.22529 | 0.612644 | − | 0.790359i | \(-0.290106\pi\) | ||||
0.612644 | + | 0.790359i | \(0.290106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4400.72 | −0.641598 | ||||||||
\(362\) | 4273.05i | 0.620405i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 364.613 | 0.0525025 | ||||||||
\(365\) | −1345.84 | − | 6991.07i | −0.192998 | − | 1.00255i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 125.761i | − | 0.0178874i | −0.999960 | − | 0.00894369i | \(-0.997153\pi\) | ||
0.999960 | − | 0.00894369i | \(-0.00284690\pi\) | |||||||
\(368\) | − | 52.1713i | − | 0.00739026i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1698.49 | + | 326.973i | −0.238649 | + | 0.0459419i | ||||
\(371\) | −2255.86 | −0.315683 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1435.76i | − | 0.199305i | −0.995022 | − | 0.0996525i | \(-0.968227\pi\) | ||
0.995022 | − | 0.0996525i | \(-0.0317731\pi\) | |||||||
\(374\) | −11045.3 | −1.52710 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14154.8 | −1.94144 | ||||||||
\(377\) | − | 5320.21i | − | 0.726803i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2125.04 | 0.288010 | 0.144005 | − | 0.989577i | \(-0.454002\pi\) | ||||
0.144005 | + | 0.989577i | \(0.454002\pi\) | |||||||
\(380\) | 459.440 | − | 88.4458i | 0.0620231 | − | 0.0119399i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 9115.09i | − | 1.22086i | ||||||
\(383\) | 7060.76i | 0.942005i | 0.882132 | + | 0.471002i | \(0.156108\pi\) | ||||
−0.882132 | + | 0.471002i | \(0.843892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1451.77 | + | 7541.34i | 0.192179 | + | 0.998292i | ||||
\(386\) | 2191.22 | 0.288939 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1537.51i | − | 0.201174i | ||||||
\(389\) | 9819.12 | 1.27982 | 0.639909 | − | 0.768451i | \(-0.278972\pi\) | ||||
0.639909 | + | 0.768451i | \(0.278972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −85.5088 | −0.0110598 | ||||||||
\(392\) | 2492.83i | 0.321191i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −962.967 | −0.123131 | ||||||||
\(395\) | −3159.31 | + | 608.191i | −0.402435 | + | 0.0774720i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10995.5i | 1.39005i | 0.718987 | + | 0.695023i | \(0.244606\pi\) | ||||
−0.718987 | + | 0.695023i | \(0.755394\pi\) | |||||||
\(398\) | 3580.14i | 0.450895i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6561.85 | + | 2623.64i | −0.820231 | + | 0.327956i | ||||
\(401\) | −6531.81 | −0.813424 | −0.406712 | − | 0.913556i | \(-0.633325\pi\) | ||||
−0.406712 | + | 0.913556i | \(0.633325\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8384.02i | − | 1.03632i | ||||||
\(404\) | −968.415 | −0.119259 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7828.82 | −0.956989 | ||||||||
\(407\) | − | 2577.02i | − | 0.313854i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5005.34 | 0.605130 | 0.302565 | − | 0.953129i | \(-0.402157\pi\) | ||||
0.302565 | + | 0.953129i | \(0.402157\pi\) | |||||||
\(410\) | 1627.60 | + | 8454.71i | 0.196052 | + | 1.01841i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1335.72i | 0.159724i | ||||||||
\(413\) | − | 2976.17i | − | 0.354596i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 602.469 | + | 3129.58i | 0.0712627 | + | 0.370181i | ||||
\(416\) | −1065.76 | −0.125609 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 5910.07i | − | 0.691558i | ||||||
\(419\) | 73.4944 | 0.00856907 | 0.00428453 | − | 0.999991i | \(-0.498636\pi\) | ||||
0.00428453 | + | 0.999991i | \(0.498636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5030.81 | 0.582391 | 0.291195 | − | 0.956664i | \(-0.405947\pi\) | ||||
0.291195 | + | 0.956664i | \(0.405947\pi\) | |||||||
\(422\) | 2857.58i | 0.329632i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3462.13 | 0.396547 | ||||||||
\(425\) | 4300.15 | + | 10754.9i | 0.490796 | + | 1.22750i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8727.43i | 0.989110i | ||||||||
\(428\) | 325.280i | 0.0367360i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.3850 | + | 3.34675i | −0.00194972 | + | 0.000375336i | ||||
\(431\) | −1951.29 | −0.218075 | −0.109037 | − | 0.994038i | \(-0.534777\pi\) | ||||
−0.109037 | + | 0.994038i | \(0.534777\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3805.50i | 0.422357i | 0.977448 | + | 0.211178i | \(0.0677301\pi\) | ||||
−0.977448 | + | 0.211178i | \(0.932270\pi\) | |||||||
\(434\) | −12337.3 | −1.36454 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 171.762 | 0.0188668 | ||||||||
\(437\) | − | 45.7538i | − | 0.00500847i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11904.4 | −1.29422 | −0.647111 | − | 0.762395i | \(-0.724023\pi\) | ||||
−0.647111 | + | 0.762395i | \(0.724023\pi\) | |||||||
\(440\) | −2228.07 | − | 11573.9i | −0.241407 | − | 1.25401i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 6946.29i | − | 0.747514i | ||||||
\(443\) | 9068.45i | 0.972585i | 0.873796 | + | 0.486292i | \(0.161651\pi\) | ||||
−0.873796 | + | 0.486292i | \(0.838349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3640.72 | + | 700.868i | −0.387836 | + | 0.0746614i | ||||
\(446\) | −4062.97 | −0.431361 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8540.37i | 0.900658i | ||||||||
\(449\) | −7332.48 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12827.9 | −1.33934 | ||||||||
\(452\) | 55.7189i | 0.00579822i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11329.2 | 1.17116 | ||||||||
\(455\) | −4742.70 | + | 913.006i | −0.488662 | + | 0.0940712i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1170.43i | 0.119804i | 0.998204 | + | 0.0599019i | \(0.0190788\pi\) | ||||
−0.998204 | + | 0.0599019i | \(0.980921\pi\) | |||||||
\(458\) | 14810.5i | 1.51103i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.64616 | − | 8.55115i | −0.000166854 | − | 0.000866738i | ||||
\(461\) | −14747.8 | −1.48996 | −0.744981 | − | 0.667086i | \(-0.767541\pi\) | ||||
−0.744981 | + | 0.667086i | \(0.767541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2085.51i | − | 0.209334i | −0.994507 | − | 0.104667i | \(-0.966622\pi\) | ||
0.994507 | − | 0.104667i | \(-0.0333777\pi\) | |||||||
\(464\) | 10733.2 | 1.07387 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16952.7 | 1.68523 | ||||||||
\(467\) | 9943.76i | 0.985315i | 0.870223 | + | 0.492658i | \(0.163975\pi\) | ||||
−0.870223 | + | 0.492658i | \(0.836025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5474.95 | 0.539040 | ||||||||
\(470\) | 17571.5 | − | 3382.64i | 1.72449 | − | 0.331978i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4567.62i | 0.445428i | ||||||||
\(473\) | − | 26.3773i | − | 0.00256412i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5754.69 | + | 2300.92i | −0.555880 | + | 0.222260i | ||||
\(476\) | 1205.62 | 0.116092 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 6802.34i | − | 0.650903i | ||||||
\(479\) | 2664.20 | 0.254134 | 0.127067 | − | 0.991894i | \(-0.459444\pi\) | ||||
0.127067 | + | 0.991894i | \(0.459444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1620.67 | 0.153631 | ||||||||
\(482\) | 5487.68i | 0.518583i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 552.481 | 0.0518859 | ||||||||
\(485\) | 3850.01 | + | 19999.2i | 0.360453 | + | 1.87241i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 3071.50i | − | 0.285797i | −0.989737 | − | 0.142898i | \(-0.954358\pi\) | ||
0.989737 | − | 0.142898i | \(-0.0456422\pi\) | |||||||
\(488\) | − | 13394.2i | − | 1.24248i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −595.723 | − | 3094.54i | −0.0549225 | − | 0.285300i | ||||
\(491\) | 16089.6 | 1.47885 | 0.739423 | − | 0.673241i | \(-0.235098\pi\) | ||||
0.739423 | + | 0.673241i | \(0.235098\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 17591.7i | − | 1.60708i | ||||||
\(494\) | 3716.80 | 0.338516 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16914.3 | 1.53119 | ||||||||
\(497\) | 4943.74i | 0.446191i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12060.6 | −1.08197 | −0.540987 | − | 0.841031i | \(-0.681949\pi\) | ||||
−0.540987 | + | 0.841031i | \(0.681949\pi\) | |||||||
\(500\) | −992.737 | + | 637.075i | −0.0887931 | + | 0.0569817i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 7412.31i | − | 0.659019i | ||||||
\(503\) | − | 1324.90i | − | 0.117444i | −0.998274 | − | 0.0587222i | \(-0.981297\pi\) | ||
0.998274 | − | 0.0587222i | \(-0.0187026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12596.7 | − | 2424.95i | 1.10999 | − | 0.213681i | ||||
\(506\) | −109.999 | −0.00966413 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 1537.42i | − | 0.134276i | ||||||
\(509\) | 12121.1 | 1.05551 | 0.527757 | − | 0.849395i | \(-0.323033\pi\) | ||||
0.527757 | + | 0.849395i | \(0.323033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9816.20 | 0.849791 | ||||||||
\(512\) | − | 12850.4i | − | 1.10920i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1141.60 | 0.0979644 | ||||||||
\(515\) | −3344.70 | − | 17374.4i | −0.286185 | − | 1.48661i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26660.2i | 2.26792i | ||||||||
\(518\) | − | 2384.86i | − | 0.202287i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7278.76 | − | 1401.22i | 0.613836 | − | 0.118168i | ||||
\(521\) | 17997.6 | 1.51342 | 0.756708 | − | 0.653753i | \(-0.226807\pi\) | ||||
0.756708 | + | 0.653753i | \(0.226807\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6451.03i | − | 0.539357i | −0.962950 | − | 0.269679i | \(-0.913083\pi\) | ||
0.962950 | − | 0.269679i | \(-0.0869174\pi\) | |||||||
\(524\) | 201.098 | 0.0167653 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10064.6 | 0.834294 | ||||||||
\(527\) | − | 27722.5i | − | 2.29148i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12166.1 | 0.999930 | ||||||||
\(530\) | −4297.81 | + | 827.361i | −0.352235 | + | 0.0678081i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 645.101i | 0.0525727i | ||||||||
\(533\) | − | 8067.35i | − | 0.655602i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −814.515 | − | 4231.07i | −0.0658216 | − | 0.341916i | ||||
\(536\) | −8402.57 | −0.677119 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5297.29i | 0.424502i | ||||||||
\(539\) | 4695.17 | 0.375204 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −520.899 | −0.0413959 | −0.0206980 | − | 0.999786i | \(-0.506589\pi\) | ||||
−0.0206980 | + | 0.999786i | \(0.506589\pi\) | |||||||
\(542\) | 15140.1i | 1.19985i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3524.02 | −0.277741 | ||||||||
\(545\) | −2234.20 | + | 430.101i | −0.175601 | + | 0.0338046i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8098.33i | 0.633015i | 0.948590 | + | 0.316508i | \(0.102510\pi\) | ||||
−0.948590 | + | 0.316508i | \(0.897490\pi\) | |||||||
\(548\) | 1728.14i | 0.134713i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5531.74 | + | 13835.1i | 0.428862 | + | 1.07260i | ||||
\(551\) | 9412.94 | 0.727776 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4436.00i | − | 0.341117i | ||||||
\(554\) | −16504.0 | −1.26568 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1839.46 | 0.140307 | ||||||||
\(557\) | − | 6687.22i | − | 0.508701i | −0.967112 | − | 0.254351i | \(-0.918138\pi\) | ||
0.967112 | − | 0.254351i | \(-0.0818617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.5885 | 0.00125513 | ||||||||
\(560\) | −1841.93 | − | 9568.10i | −0.138993 | − | 0.722011i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8943.95i | 0.671313i | ||||||||
\(563\) | − | 2427.54i | − | 0.181720i | −0.995864 | − | 0.0908602i | \(-0.971038\pi\) | ||
0.995864 | − | 0.0908602i | \(-0.0289616\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −139.523 | − | 724.763i | −0.0103890 | − | 0.0539664i | ||||
\(566\) | −13651.7 | −1.01382 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 7587.30i | − | 0.560486i | ||||||
\(569\) | −2553.65 | −0.188145 | −0.0940727 | − | 0.995565i | \(-0.529989\pi\) | ||||
−0.0940727 | + | 0.995565i | \(0.529989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9036.15 | 0.662261 | 0.331130 | − | 0.943585i | \(-0.392570\pi\) | ||||
0.331130 | + | 0.943585i | \(0.392570\pi\) | |||||||
\(572\) | 1053.95i | 0.0770421i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11871.3 | −0.863237 | ||||||||
\(575\) | 42.8249 | + | 107.107i | 0.00310595 | + | 0.00776812i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5427.02i | 0.391560i | 0.980648 | + | 0.195780i | \(0.0627238\pi\) | ||||
−0.980648 | + | 0.195780i | \(0.937276\pi\) | |||||||
\(578\) | − | 9825.90i | − | 0.707099i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1759.23 | − | 338.665i | 0.125945 | − | 0.0242454i | ||||
\(581\) | −4394.26 | −0.313777 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 6520.82i | − | 0.463233i | ||||||
\(584\) | −15065.2 | −1.06747 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11048.8 | 0.778874 | ||||||||
\(587\) | 5339.38i | 0.375434i | 0.982223 | + | 0.187717i | \(0.0601088\pi\) | ||||
−0.982223 | + | 0.187717i | \(0.939891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14833.7 | 1.03771 | ||||||||
\(590\) | −1091.54 | − | 5670.13i | −0.0761664 | − | 0.395654i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3269.61i | 0.226993i | ||||||||
\(593\) | − | 4617.67i | − | 0.319772i | −0.987135 | − | 0.159886i | \(-0.948887\pi\) | ||
0.987135 | − | 0.159886i | \(-0.0511127\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15682.1 | + | 3018.93i | −1.08051 | + | 0.208007i | ||||
\(596\) | −131.626 | −0.00904629 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 69.1776i | − | 0.00473057i | ||||||
\(599\) | −10888.4 | −0.742716 | −0.371358 | − | 0.928490i | \(-0.621108\pi\) | ||||
−0.371358 | + | 0.928490i | \(0.621108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11273.2 | −0.765131 | −0.382566 | − | 0.923928i | \(-0.624959\pi\) | ||||
−0.382566 | + | 0.923928i | \(0.624959\pi\) | |||||||
\(602\) | − | 24.4104i | − | 0.00165264i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1362.39 | 0.0917795 | ||||||||
\(605\) | −7186.39 | + | 1383.44i | −0.482923 | + | 0.0929665i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10224.7i | 0.683702i | 0.939754 | + | 0.341851i | \(0.111054\pi\) | ||||
−0.939754 | + | 0.341851i | \(0.888946\pi\) | |||||||
\(608\) | − | 1885.63i | − | 0.125777i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3200.88 | + | 16627.3i | 0.212459 | + | 1.10364i | ||||
\(611\) | −16766.4 | −1.11014 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7119.74i | 0.469109i | 0.972103 | + | 0.234554i | \(0.0753631\pi\) | ||||
−0.972103 | + | 0.234554i | \(0.924637\pi\) | |||||||
\(614\) | 9048.46 | 0.594733 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16251.0 | 1.06294 | ||||||||
\(617\) | 5358.95i | 0.349665i | 0.984598 | + | 0.174832i | \(0.0559384\pi\) | ||||
−0.984598 | + | 0.174832i | \(0.944062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21597.2 | 1.40237 | 0.701183 | − | 0.712981i | \(-0.252656\pi\) | ||||
0.701183 | + | 0.712981i | \(0.252656\pi\) | |||||||
\(620\) | 2772.33 | − | 533.696i | 0.179580 | − | 0.0345706i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 16107.1i | − | 1.03832i | ||||||
\(623\) | − | 5111.96i | − | 0.328742i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11317.8 | − | 10772.6i | 0.724336 | − | 0.689447i | ||||
\(626\) | 27266.8 | 1.74089 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 834.333i | 0.0530152i | ||||||||
\(629\) | 5358.89 | 0.339703 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1384.23 | −0.0873305 | −0.0436652 | − | 0.999046i | \(-0.513903\pi\) | ||||
−0.0436652 | + | 0.999046i | \(0.513903\pi\) | |||||||
\(632\) | 6808.06i | 0.428497i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14446.9 | 0.904986 | ||||||||
\(635\) | 3849.77 | + | 19998.0i | 0.240588 | + | 1.24976i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2952.76i | 0.183662i | ||||||||
\(638\) | − | 22630.1i | − | 1.40429i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2489.25 | + | 12930.6i | 0.153744 | + | 0.798637i | ||||
\(641\) | −1623.14 | −0.100016 | −0.0500080 | − | 0.998749i | \(-0.515925\pi\) | ||||
−0.0500080 | + | 0.998749i | \(0.515925\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 28170.8i | − | 1.72776i | −0.503699 | − | 0.863879i | \(-0.668028\pi\) | ||
0.503699 | − | 0.863879i | \(-0.331972\pi\) | |||||||
\(644\) | 12.0067 | 0.000734675 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12289.9 | 0.748515 | ||||||||
\(647\) | − | 16695.3i | − | 1.01447i | −0.861808 | − | 0.507235i | \(-0.830668\pi\) | ||
0.861808 | − | 0.507235i | \(-0.169332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8602.97 | 0.520333 | ||||||||
\(650\) | −8700.81 | + | 3478.87i | −0.525037 | + | 0.209927i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2510.24i | 0.150780i | ||||||||
\(653\) | − | 4489.96i | − | 0.269075i | −0.990909 | − | 0.134537i | \(-0.957045\pi\) | ||
0.990909 | − | 0.134537i | \(-0.0429548\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2615.78 | + | 503.558i | −0.156041 | + | 0.0300391i | ||||
\(656\) | 16275.4 | 0.968669 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24672.2i | 1.46173i | ||||||||
\(659\) | 15300.9 | 0.904459 | 0.452229 | − | 0.891902i | \(-0.350629\pi\) | ||||
0.452229 | + | 0.891902i | \(0.350629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20634.9 | −1.21423 | −0.607113 | − | 0.794615i | \(-0.707673\pi\) | ||||
−0.607113 | + | 0.794615i | \(0.707673\pi\) | |||||||
\(662\) | − | 6160.39i | − | 0.361678i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6744.00 | 0.394154 | ||||||||
\(665\) | −1615.36 | − | 8391.15i | −0.0941971 | − | 0.489316i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 175.195i | − | 0.0101703i | ||||||
\(668\) | 2058.56i | 0.119234i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10430.7 | − | 2008.00i | 0.601454 | − | 0.115785i | ||||
\(671\) | −25227.6 | −1.45142 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17553.8i | 1.00542i | 0.864454 | + | 0.502712i | \(0.167664\pi\) | ||||
−0.864454 | + | 0.502712i | \(0.832336\pi\) | |||||||
\(674\) | 25590.5 | 1.46248 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1191.52 | 0.0677922 | ||||||||
\(677\) | 15182.6i | 0.861915i | 0.902372 | + | 0.430958i | \(0.141824\pi\) | ||||
−0.902372 | + | 0.430958i | \(0.858176\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28081.0 | −1.58711 | ||||||||
\(680\) | 24067.8 | − | 4633.25i | 1.35729 | − | 0.261289i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 35662.3i | − | 2.00232i | ||||||
\(683\) | − | 1735.90i | − | 0.0972510i | −0.998817 | − | 0.0486255i | \(-0.984516\pi\) | ||
0.998817 | − | 0.0486255i | \(-0.0154841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4327.34 | − | 22478.8i | −0.241371 | − | 1.25383i | ||||
\(686\) | 18489.3 | 1.02905 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 33.4663i | 0.00185449i | ||||||||
\(689\) | 4100.90 | 0.226751 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27648.0 | −1.52211 | −0.761055 | − | 0.648687i | \(-0.775318\pi\) | ||||
−0.761055 | + | 0.648687i | \(0.775318\pi\) | |||||||
\(692\) | 2239.72i | 0.123037i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −218.076 | −0.0119280 | ||||||||
\(695\) | −23926.8 | + | 4606.09i | −1.30589 | + | 0.251394i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 26675.4i | − | 1.44964i | ||||||
\(698\) | − | 250.311i | − | 0.0135736i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −603.805 | − | 1510.14i | −0.0326024 | − | 0.0815401i | ||||
\(701\) | 19116.9 | 1.03001 | 0.515005 | − | 0.857187i | \(-0.327790\pi\) | ||||
0.515005 | + | 0.857187i | \(0.327790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2867.42i | 0.153836i | ||||||||
\(704\) | −24686.9 | −1.32162 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17857.2 | −0.951931 | ||||||||
\(707\) | 17687.0i | 0.940861i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10045.3 | 0.532099 | 0.266050 | − | 0.963959i | \(-0.414281\pi\) | ||||
0.266050 | + | 0.963959i | \(0.414281\pi\) | |||||||
\(710\) | 1813.17 | + | 9418.68i | 0.0958410 | + | 0.497855i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7845.47i | 0.412952i | ||||||||
\(713\) | − | 276.086i | − | 0.0145014i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2639.15 | − | 13709.3i | −0.138040 | − | 0.717062i | ||||
\(716\) | 1774.41 | 0.0926159 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22295.3i | 1.15885i | ||||||||
\(719\) | −22559.7 | −1.17014 | −0.585072 | − | 0.810981i | \(-0.698934\pi\) | ||||
−0.585072 | + | 0.810981i | \(0.698934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24395.4 | 1.26010 | ||||||||
\(722\) | − | 11772.2i | − | 0.606809i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1348.23 | 0.0692079 | ||||||||
\(725\) | −22035.1 | + | 8810.37i | −1.12878 | + | 0.451323i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3668.07i | 0.187127i | 0.995613 | + | 0.0935635i | \(0.0298258\pi\) | ||||
−0.995613 | + | 0.0935635i | \(0.970174\pi\) | |||||||
\(728\) | 10220.1i | 0.520307i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18701.6 | − | 3600.20i | 0.948187 | − | 0.182533i | ||||
\(731\) | 54.8513 | 0.00277530 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31428.4i | 1.58368i | 0.610731 | + | 0.791838i | \(0.290876\pi\) | ||||
−0.610731 | + | 0.791838i | \(0.709124\pi\) | |||||||
\(734\) | 336.419 | 0.0169175 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.0955 | −0.00175766 | ||||||||
\(737\) | 15826.0i | 0.790987i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17467.0 | −0.869465 | −0.434732 | − | 0.900560i | \(-0.643157\pi\) | ||||
−0.434732 | + | 0.900560i | \(0.643157\pi\) | |||||||
\(740\) | 103.166 | + | 535.906i | 0.00512495 | + | 0.0266220i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 6034.57i | − | 0.298566i | ||||||
\(743\) | 24993.4i | 1.23408i | 0.786933 | + | 0.617038i | \(0.211668\pi\) | ||||
−0.786933 | + | 0.617038i | \(0.788332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1712.12 | − | 329.596i | 0.0841975 | − | 0.0162087i | ||||
\(746\) | 3840.74 | 0.188498 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3484.99i | 0.170353i | ||||||||
\(749\) | 5940.87 | 0.289819 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9348.04 | −0.454214 | −0.227107 | − | 0.973870i | \(-0.572927\pi\) | ||||
−0.227107 | + | 0.973870i | \(0.572927\pi\) | |||||||
\(752\) | − | 33825.2i | − | 1.64026i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14231.9 | 0.687395 | ||||||||
\(755\) | −17721.3 | + | 3411.48i | −0.854230 | + | 0.164446i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11708.4i | − | 0.562153i | −0.959685 | − | 0.281076i | \(-0.909309\pi\) | ||
0.959685 | − | 0.281076i | \(-0.0906915\pi\) | |||||||
\(758\) | 5684.61i | 0.272394i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2479.15 | + | 12878.2i | 0.118326 | + | 0.614658i | ||||
\(761\) | 19410.7 | 0.924621 | 0.462310 | − | 0.886718i | \(-0.347021\pi\) | ||||
0.462310 | + | 0.886718i | \(0.347021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3137.05i | − | 0.148845i | ||||||
\(764\) | −2875.98 | −0.136190 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18888.0 | −0.890927 | ||||||||
\(767\) | 5410.35i | 0.254702i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9857.66 | 0.462258 | 0.231129 | − | 0.972923i | \(-0.425758\pi\) | ||||
0.231129 | + | 0.972923i | \(0.425758\pi\) | |||||||
\(770\) | −20173.6 | + | 3883.57i | −0.944162 | + | 0.181759i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 691.373i | − | 0.0322319i | ||||||
\(773\) | 27574.5i | 1.28303i | 0.767108 | + | 0.641517i | \(0.221695\pi\) | ||||
−0.767108 | + | 0.641517i | \(0.778305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34724.7 | + | 13884.1i | −1.60948 | + | 0.643525i | ||||
\(776\) | 43096.7 | 1.99366 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26266.8i | 1.21042i | ||||||||
\(779\) | 14273.4 | 0.656479 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14290.4 | −0.654741 | ||||||||
\(782\) | − | 228.741i | − | 0.0104601i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5957.01 | −0.271365 | ||||||||
\(785\) | −2089.21 | − | 10852.6i | −0.0949899 | − | 0.493434i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11777.0i | 0.533425i | 0.963776 | + | 0.266712i | \(0.0859374\pi\) | ||||
−0.963776 | + | 0.266712i | \(0.914063\pi\) | |||||||
\(788\) | 303.834i | 0.0137356i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1626.95 | − | 8451.35i | −0.0732713 | − | 0.380614i | ||||
\(791\) | 1017.64 | 0.0457436 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15865.5i | − | 0.710466i | ||||||
\(794\) | −29413.7 | −1.31468 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1129.60 | 0.0502985 | ||||||||
\(797\) | 24659.8i | 1.09598i | 0.836485 | + | 0.547990i | \(0.184607\pi\) | ||||
−0.836485 | + | 0.547990i | \(0.815393\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55439.5 | −2.45471 | ||||||||
\(800\) | 1764.92 | + | 4414.14i | 0.0779991 | + | 0.195079i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 17473.0i | − | 0.769318i | ||||||
\(803\) | 28374.9i | 1.24698i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −156.177 | + | 30.0653i | −0.00683791 | + | 0.00131635i | ||||
\(806\) | 22427.8 | 0.980130 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 27144.8i | − | 1.18187i | ||||||
\(809\) | −19263.0 | −0.837144 | −0.418572 | − | 0.908184i | \(-0.637469\pi\) | ||||
−0.418572 | + | 0.908184i | \(0.637469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13597.4 | −0.588741 | −0.294370 | − | 0.955691i | \(-0.595110\pi\) | ||||
−0.294370 | + | 0.955691i | \(0.595110\pi\) | |||||||
\(812\) | 2470.14i | 0.106755i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6893.71 | 0.296836 | ||||||||
\(815\) | −6285.76 | − | 32652.0i | −0.270160 | − | 1.40337i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.3497i | 0.00125681i | ||||||||
\(818\) | 13389.6i | 0.572318i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2667.62 | − | 513.538i | 0.113607 | − | 0.0218701i | ||||
\(821\) | 28673.6 | 1.21890 | 0.609449 | − | 0.792825i | \(-0.291391\pi\) | ||||
0.609449 | + | 0.792825i | \(0.291391\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8437.62i | 0.357372i | 0.983906 | + | 0.178686i | \(0.0571846\pi\) | ||||
−0.983906 | + | 0.178686i | \(0.942815\pi\) | |||||||
\(824\) | −37440.4 | −1.58289 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7961.46 | 0.335369 | ||||||||
\(827\) | 11315.7i | 0.475799i | 0.971290 | + | 0.237900i | \(0.0764590\pi\) | ||||
−0.971290 | + | 0.237900i | \(0.923541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6773.57 | −0.283783 | −0.141891 | − | 0.989882i | \(-0.545318\pi\) | ||||
−0.141891 | + | 0.989882i | \(0.545318\pi\) | |||||||
\(830\) | −8371.83 | + | 1611.64i | −0.350109 | + | 0.0673987i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 15525.4i | − | 0.646932i | ||||||
\(833\) | 9763.54i | 0.406106i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5154.73 | − | 26776.7i | −0.213637 | − | 1.10976i | ||||
\(836\) | −1864.74 | −0.0771452 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 196.602i | 0.00810443i | ||||||||
\(839\) | −8913.89 | −0.366796 | −0.183398 | − | 0.983039i | \(-0.558710\pi\) | ||||
−0.183398 | + | 0.983039i | \(0.558710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11653.8 | 0.477831 | ||||||||
\(842\) | 13457.7i | 0.550812i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 901.621 | 0.0367714 | ||||||||
\(845\) | −15498.6 | + | 2983.61i | −0.630970 | + | 0.121467i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10090.4i | − | 0.409341i | ||||||
\(848\) | 8273.31i | 0.335031i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28770.0 | + | 11503.2i | −1.16094 | + | 0.464184i | ||||
\(851\) | 53.3688 | 0.00214978 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31669.2i | 1.27120i | 0.772018 | + | 0.635600i | \(0.219247\pi\) | ||||
−0.772018 | + | 0.635600i | \(0.780753\pi\) | |||||||
\(854\) | −23346.4 | −0.935478 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9117.63 | −0.364059 | ||||||||
\(857\) | − | 44054.8i | − | 1.75599i | −0.478670 | − | 0.877995i | \(-0.658881\pi\) | ||
0.478670 | − | 0.877995i | \(-0.341119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19069.4 | −0.757438 | −0.378719 | − | 0.925512i | \(-0.623635\pi\) | ||||
−0.378719 | + | 0.925512i | \(0.623635\pi\) | |||||||
\(860\) | 1.05596 | + | 5.48530i | 4.18698e−5 | + | 0.000217497i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 5219.82i | − | 0.206250i | ||||||
\(863\) | 6256.14i | 0.246769i | 0.992359 | + | 0.123384i | \(0.0393748\pi\) | ||||
−0.992359 | + | 0.123384i | \(0.960625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5608.35 | − | 29133.1i | −0.220451 | − | 1.14515i | ||||
\(866\) | −10179.9 | −0.399456 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3892.65i | 0.152218i | ||||||||
\(869\) | 12822.8 | 0.500555 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9952.84 | −0.387186 | ||||||||
\(872\) | 4814.52i | 0.186973i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 122.394 | 0.00473690 | ||||||||
\(875\) | 11635.5 | + | 18131.2i | 0.449543 | + | 0.700511i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6957.46i | 0.267887i | 0.990989 | + | 0.133943i | \(0.0427640\pi\) | ||||
−0.990989 | + | 0.133943i | \(0.957236\pi\) | |||||||
\(878\) | − | 31844.9i | − | 1.22405i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 27657.7 | − | 5324.33i | 1.05948 | − | 0.203958i | ||||
\(881\) | 10626.4 | 0.406371 | 0.203186 | − | 0.979140i | \(-0.434871\pi\) | ||||
0.203186 | + | 0.979140i | \(0.434871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31013.5i | 1.18198i | 0.806679 | + | 0.590990i | \(0.201263\pi\) | ||||
−0.806679 | + | 0.590990i | \(0.798737\pi\) | |||||||
\(884\) | −2191.69 | −0.0833873 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24258.7 | −0.919849 | ||||||||
\(887\) | − | 9397.37i | − | 0.355730i | −0.984055 | − | 0.177865i | \(-0.943081\pi\) | ||
0.984055 | − | 0.177865i | \(-0.0569191\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28079.3 | −1.05933 | ||||||||
\(890\) | −1874.87 | − | 9739.17i | −0.0706131 | − | 0.366806i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1281.94i | 0.0481195i | ||||||||
\(893\) | − | 29664.5i | − | 1.11163i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23080.7 | + | 4443.21i | −0.862014 | + | 0.165944i | ||||
\(896\) | −18155.9 | −0.676950 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 19614.8i | − | 0.728904i | ||||||
\(899\) | 56799.2 | 2.10718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13560.0 | 0.501385 | ||||||||
\(902\) | − | 34315.3i | − | 1.26671i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1561.81 | −0.0574612 | ||||||||
\(905\) | −17537.1 | + | 3376.03i | −0.644146 | + | 0.124003i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27560.5i | 1.00896i | 0.863422 | + | 0.504482i | \(0.168316\pi\) | ||||
−0.863422 | + | 0.504482i | \(0.831684\pi\) | |||||||
\(908\) | − | 3574.58i | − | 0.130646i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2442.35 | − | 12687.0i | −0.0889705 | − | 0.462165i | ||||
\(911\) | −35870.1 | −1.30453 | −0.652266 | − | 0.757990i | \(-0.726181\pi\) | ||||
−0.652266 | + | 0.757990i | \(0.726181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12702.1i | − | 0.460436i | ||||||
\(914\) | −3130.97 | −0.113308 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4673.01 | 0.168560 | ||||||||
\(917\) | − | 3672.82i | − | 0.132265i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3081.79 | −0.110619 | −0.0553095 | − | 0.998469i | \(-0.517615\pi\) | ||||
−0.0553095 | + | 0.998469i | \(0.517615\pi\) | |||||||
\(920\) | 239.690 | − | 46.1422i | 0.00858950 | − | 0.00165355i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 39451.2i | − | 1.40917i | ||||||
\(923\) | − | 8987.16i | − | 0.320494i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2683.86 | − | 6712.46i | −0.0953999 | − | 0.238599i | ||||
\(926\) | 5578.86 | 0.197984 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7220.20i | − | 0.255404i | ||||||
\(929\) | 4270.03 | 0.150802 | 0.0754011 | − | 0.997153i | \(-0.475976\pi\) | ||||
0.0754011 | + | 0.997153i | \(0.475976\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5224.25 | −0.183908 | ||||||||
\(932\) | − | 5348.89i | − | 0.187992i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26600.2 | −0.931890 | ||||||||
\(935\) | −8726.57 | − | 45331.0i | −0.305229 | − | 1.58554i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49225.3i | 1.71624i | 0.513446 | + | 0.858122i | \(0.328369\pi\) | ||||
−0.513446 | + | 0.858122i | \(0.671631\pi\) | |||||||
\(938\) | 14645.8i | 0.509812i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1067.29 | − | 5544.13i | −0.0370331 | − | 0.192372i | ||||
\(941\) | 34569.7 | 1.19760 | 0.598800 | − | 0.800899i | \(-0.295644\pi\) | ||||
0.598800 | + | 0.800899i | \(0.295644\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 265.658i | − | 0.00917393i | ||||||
\(944\) | −10915.1 | −0.376329 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 70.5610 | 0.00242509 | ||||||||
\(947\) | 27342.4i | 0.938234i | 0.883136 | + | 0.469117i | \(0.155428\pi\) | ||||
−0.883136 | + | 0.469117i | \(0.844572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17844.7 | −0.610395 | ||||||||
\(950\) | −6155.10 | − | 15394.2i | −0.210208 | − | 0.525739i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 33793.7i | 1.15048i | ||||||||
\(953\) | − | 45941.5i | − | 1.56158i | −0.624791 | − | 0.780792i | \(-0.714816\pi\) | ||
0.624791 | − | 0.780792i | \(-0.285184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37409.3 | − | 7201.59i | 1.26758 | − | 0.244019i | ||||
\(956\) | −2146.27 | −0.0726101 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7126.90i | 0.240355i | ||||||||
\(959\) | 31562.6 | 1.06278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59717.8 | 2.00456 | ||||||||
\(962\) | 4335.40i | 0.145300i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1731.47 | 0.0578494 | ||||||||
\(965\) | 1731.23 | + | 8993.03i | 0.0577515 | + | 0.299996i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47338.8i | − | 1.57426i | −0.616785 | − | 0.787132i | \(-0.711565\pi\) | ||
0.616785 | − | 0.787132i | \(-0.288435\pi\) | |||||||
\(968\) | 15486.1i | 0.514197i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −53499.2 | + | 10299.0i | −1.77088 | + | 0.340909i | ||||
\(971\) | 50168.3 | 1.65806 | 0.829031 | − | 0.559202i | \(-0.188893\pi\) | ||||
0.829031 | + | 0.559202i | \(0.188893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 33595.7i | − | 1.10691i | ||||||
\(974\) | 8216.46 | 0.270300 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32007.6 | 1.04973 | ||||||||
\(977\) | 47642.1i | 1.56009i | 0.625725 | + | 0.780044i | \(0.284803\pi\) | ||||
−0.625725 | + | 0.780044i | \(0.715197\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14776.7 | 0.482396 | ||||||||
\(980\) | −976.385 | + | 187.962i | −0.0318260 | + | 0.00612675i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 43040.7i | 1.39866i | ||||||||
\(983\) | 11158.1i | 0.362044i | 0.983479 | + | 0.181022i | \(0.0579405\pi\) | ||||
−0.983479 | + | 0.181022i | \(0.942060\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −760.814 | − | 3952.12i | −0.0246107 | − | 0.127843i | ||||
\(986\) | 47059.0 | 1.51994 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1172.72i | − | 0.0377624i | ||||||
\(989\) | 0.546260 | 1.75632e−5 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57670.7 | −1.84861 | −0.924304 | − | 0.381658i | \(-0.875353\pi\) | ||||
−0.924304 | + | 0.381658i | \(0.875353\pi\) | |||||||
\(992\) | − | 11378.2i | − | 0.364171i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13224.8 | −0.421998 | ||||||||
\(995\) | −14693.3 | + | 2828.57i | −0.468149 | + | 0.0901223i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 51730.8i | − | 1.64326i | −0.570021 | − | 0.821630i | \(-0.693065\pi\) | ||
0.570021 | − | 0.821630i | \(-0.306935\pi\) | |||||||
\(998\) | − | 32262.8i | − | 1.02331i | ||||||
\(999\) | 0 | 0 |
(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 | 405.4.b.e.244.12 | 16 | ||
3.2 | odd | 2 | 405.4.b.f.244.5 | 16 | |||
5.2 | odd | 4 | 2025.4.a.bk.1.5 | 16 | |||
5.3 | odd | 4 | 2025.4.a.bk.1.12 | 16 | |||
5.4 | even | 2 | inner | 405.4.b.e.244.5 | 16 | ||
9.2 | odd | 6 | 135.4.j.a.64.5 | 32 | |||
9.4 | even | 3 | 45.4.j.a.34.5 | yes | 32 | ||
9.5 | odd | 6 | 135.4.j.a.19.12 | 32 | |||
9.7 | even | 3 | 45.4.j.a.4.12 | yes | 32 | ||
15.2 | even | 4 | 2025.4.a.bl.1.12 | 16 | |||
15.8 | even | 4 | 2025.4.a.bl.1.5 | 16 | |||
15.14 | odd | 2 | 405.4.b.f.244.12 | 16 | |||
45.4 | even | 6 | 45.4.j.a.34.12 | yes | 32 | ||
45.7 | odd | 12 | 225.4.e.g.76.12 | 32 | |||
45.13 | odd | 12 | 225.4.e.g.151.5 | 32 | |||
45.14 | odd | 6 | 135.4.j.a.19.5 | 32 | |||
45.22 | odd | 12 | 225.4.e.g.151.12 | 32 | |||
45.29 | odd | 6 | 135.4.j.a.64.12 | 32 | |||
45.34 | even | 6 | 45.4.j.a.4.5 | ✓ | 32 | ||
45.43 | odd | 12 | 225.4.e.g.76.5 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.j.a.4.5 | ✓ | 32 | 45.34 | even | 6 | ||
45.4.j.a.4.12 | yes | 32 | 9.7 | even | 3 | ||
45.4.j.a.34.5 | yes | 32 | 9.4 | even | 3 | ||
45.4.j.a.34.12 | yes | 32 | 45.4 | even | 6 | ||
135.4.j.a.19.5 | 32 | 45.14 | odd | 6 | |||
135.4.j.a.19.12 | 32 | 9.5 | odd | 6 | |||
135.4.j.a.64.5 | 32 | 9.2 | odd | 6 | |||
135.4.j.a.64.12 | 32 | 45.29 | odd | 6 | |||
225.4.e.g.76.5 | 32 | 45.43 | odd | 12 | |||
225.4.e.g.76.12 | 32 | 45.7 | odd | 12 | |||
225.4.e.g.151.5 | 32 | 45.13 | odd | 12 | |||
225.4.e.g.151.12 | 32 | 45.22 | odd | 12 | |||
405.4.b.e.244.5 | 16 | 5.4 | even | 2 | inner | ||
405.4.b.e.244.12 | 16 | 1.1 | even | 1 | trivial | ||
405.4.b.f.244.5 | 16 | 3.2 | odd | 2 | |||
405.4.b.f.244.12 | 16 | 15.14 | odd | 2 | |||
2025.4.a.bk.1.5 | 16 | 5.2 | odd | 4 | |||
2025.4.a.bk.1.12 | 16 | 5.3 | odd | 4 | |||
2025.4.a.bl.1.5 | 16 | 15.8 | even | 4 | |||
2025.4.a.bl.1.12 | 16 | 15.2 | even | 4 |