Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,12,Mod(1,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(209.757688293\) |
Analytic rank: | \(1\) |
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: | \( x^{16} - x^{15} - 26640 x^{14} - 38138 x^{13} + 279954048 x^{12} + 940095168 x^{11} - 1473489774048 x^{10} - 6951601887328 x^{9} + \cdots + 45\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{12}\cdot 5\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(41.2629\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 37.2629 | 0.823402 | 0.411701 | − | 0.911319i | \(-0.364935\pi\) | ||||
0.411701 | + | 0.911319i | \(0.364935\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −659.475 | −0.322009 | ||||||||
\(5\) | 3035.84 | 0.434454 | 0.217227 | − | 0.976121i | \(-0.430299\pi\) | ||||
0.217227 | + | 0.976121i | \(0.430299\pi\) | |||||||
\(6\) | −9054.89 | −0.475391 | ||||||||
\(7\) | 16807.0 | 0.377964 | ||||||||
\(8\) | −100888. | −1.08854 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 113124. | 0.357731 | ||||||||
\(11\) | 349838. | 0.654949 | 0.327474 | − | 0.944860i | \(-0.393802\pi\) | ||||
0.327474 | + | 0.944860i | \(0.393802\pi\) | |||||||
\(12\) | 160252. | 0.185912 | ||||||||
\(13\) | −371293. | −0.277350 | ||||||||
\(14\) | 626278. | 0.311217 | ||||||||
\(15\) | −737710. | −0.250832 | ||||||||
\(16\) | −2.40879e6 | −0.574301 | ||||||||
\(17\) | 4.65704e6 | 0.795502 | 0.397751 | − | 0.917493i | \(-0.369791\pi\) | ||||
0.397751 | + | 0.917493i | \(0.369791\pi\) | |||||||
\(18\) | 2.20034e6 | 0.274467 | ||||||||
\(19\) | −4.50229e6 | −0.417146 | −0.208573 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208573 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(20\) | −2.00206e6 | −0.139898 | ||||||||
\(21\) | −4.08410e6 | −0.218218 | ||||||||
\(22\) | 1.30360e7 | 0.539286 | ||||||||
\(23\) | −3.89018e7 | −1.26028 | −0.630140 | − | 0.776481i | \(-0.717003\pi\) | ||||
−0.630140 | + | 0.776481i | \(0.717003\pi\) | |||||||
\(24\) | 2.45159e7 | 0.628472 | ||||||||
\(25\) | −3.96118e7 | −0.811249 | ||||||||
\(26\) | −1.38355e7 | −0.228371 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −1.10838e7 | −0.121708 | ||||||||
\(29\) | 7.68779e7 | 0.696005 | 0.348002 | − | 0.937494i | \(-0.386860\pi\) | ||||
0.348002 | + | 0.937494i | \(0.386860\pi\) | |||||||
\(30\) | −2.74892e7 | −0.206536 | ||||||||
\(31\) | −5.73477e7 | −0.359771 | −0.179886 | − | 0.983688i | \(-0.557573\pi\) | ||||
−0.179886 | + | 0.983688i | \(0.557573\pi\) | |||||||
\(32\) | 1.16861e8 | 0.615665 | ||||||||
\(33\) | −8.50107e7 | −0.378135 | ||||||||
\(34\) | 1.73535e8 | 0.655018 | ||||||||
\(35\) | 5.10234e7 | 0.164208 | ||||||||
\(36\) | −3.89413e7 | −0.107336 | ||||||||
\(37\) | 2.31992e8 | 0.550002 | 0.275001 | − | 0.961444i | \(-0.411322\pi\) | ||||
0.275001 | + | 0.961444i | \(0.411322\pi\) | |||||||
\(38\) | −1.67768e8 | −0.343479 | ||||||||
\(39\) | 9.02242e7 | 0.160128 | ||||||||
\(40\) | −3.06281e8 | −0.472923 | ||||||||
\(41\) | 4.48764e7 | 0.0604932 | 0.0302466 | − | 0.999542i | \(-0.490371\pi\) | ||||
0.0302466 | + | 0.999542i | \(0.490371\pi\) | |||||||
\(42\) | −1.52186e8 | −0.179681 | ||||||||
\(43\) | 6.56941e8 | 0.681475 | 0.340737 | − | 0.940158i | \(-0.389323\pi\) | ||||
0.340737 | + | 0.940158i | \(0.389323\pi\) | |||||||
\(44\) | −2.30710e8 | −0.210900 | ||||||||
\(45\) | 1.79263e8 | 0.144818 | ||||||||
\(46\) | −1.44960e9 | −1.03772 | ||||||||
\(47\) | 2.23582e9 | 1.42200 | 0.710998 | − | 0.703194i | \(-0.248244\pi\) | ||||
0.710998 | + | 0.703194i | \(0.248244\pi\) | |||||||
\(48\) | 5.85336e8 | 0.331573 | ||||||||
\(49\) | 2.82475e8 | 0.142857 | ||||||||
\(50\) | −1.47605e9 | −0.667984 | ||||||||
\(51\) | −1.13166e9 | −0.459283 | ||||||||
\(52\) | 2.44858e8 | 0.0893093 | ||||||||
\(53\) | 4.17552e9 | 1.37149 | 0.685746 | − | 0.727841i | \(-0.259476\pi\) | ||||
0.685746 | + | 0.727841i | \(0.259476\pi\) | |||||||
\(54\) | −5.34682e8 | −0.158464 | ||||||||
\(55\) | 1.06205e9 | 0.284545 | ||||||||
\(56\) | −1.69563e9 | −0.411431 | ||||||||
\(57\) | 1.09406e9 | 0.240839 | ||||||||
\(58\) | 2.86469e9 | 0.573092 | ||||||||
\(59\) | 5.16620e9 | 0.940773 | 0.470387 | − | 0.882460i | \(-0.344114\pi\) | ||||
0.470387 | + | 0.882460i | \(0.344114\pi\) | |||||||
\(60\) | 4.86501e8 | 0.0807704 | ||||||||
\(61\) | −9.97103e9 | −1.51156 | −0.755781 | − | 0.654824i | \(-0.772743\pi\) | ||||
−0.755781 | + | 0.654824i | \(0.772743\pi\) | |||||||
\(62\) | −2.13694e9 | −0.296236 | ||||||||
\(63\) | 9.92437e8 | 0.125988 | ||||||||
\(64\) | 9.28778e9 | 1.08124 | ||||||||
\(65\) | −1.12719e9 | −0.120496 | ||||||||
\(66\) | −3.16775e9 | −0.311357 | ||||||||
\(67\) | −3.36147e9 | −0.304171 | −0.152086 | − | 0.988367i | \(-0.548599\pi\) | ||||
−0.152086 | + | 0.988367i | \(0.548599\pi\) | |||||||
\(68\) | −3.07120e9 | −0.256159 | ||||||||
\(69\) | 9.45315e9 | 0.727623 | ||||||||
\(70\) | 1.90128e9 | 0.135209 | ||||||||
\(71\) | −1.55923e10 | −1.02563 | −0.512813 | − | 0.858500i | \(-0.671397\pi\) | ||||
−0.512813 | + | 0.858500i | \(0.671397\pi\) | |||||||
\(72\) | −5.95736e9 | −0.362848 | ||||||||
\(73\) | −1.68502e10 | −0.951327 | −0.475663 | − | 0.879627i | \(-0.657792\pi\) | ||||
−0.475663 | + | 0.879627i | \(0.657792\pi\) | |||||||
\(74\) | 8.64471e9 | 0.452873 | ||||||||
\(75\) | 9.62566e9 | 0.468375 | ||||||||
\(76\) | 2.96915e9 | 0.134325 | ||||||||
\(77\) | 5.87973e9 | 0.247547 | ||||||||
\(78\) | 3.36202e9 | 0.131850 | ||||||||
\(79\) | −3.64367e10 | −1.33226 | −0.666132 | − | 0.745834i | \(-0.732051\pi\) | ||||
−0.666132 | + | 0.745834i | \(0.732051\pi\) | |||||||
\(80\) | −7.31271e9 | −0.249507 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 1.67222e9 | 0.0498102 | ||||||||
\(83\) | 2.09943e10 | 0.585020 | 0.292510 | − | 0.956262i | \(-0.405509\pi\) | ||||
0.292510 | + | 0.956262i | \(0.405509\pi\) | |||||||
\(84\) | 2.69336e9 | 0.0702682 | ||||||||
\(85\) | 1.41380e10 | 0.345609 | ||||||||
\(86\) | 2.44795e10 | 0.561128 | ||||||||
\(87\) | −1.86813e10 | −0.401839 | ||||||||
\(88\) | −3.52946e10 | −0.712941 | ||||||||
\(89\) | −3.68249e10 | −0.699032 | −0.349516 | − | 0.936930i | \(-0.613654\pi\) | ||||
−0.349516 | + | 0.936930i | \(0.613654\pi\) | |||||||
\(90\) | 6.67988e9 | 0.119244 | ||||||||
\(91\) | −6.24032e9 | −0.104828 | ||||||||
\(92\) | 2.56548e10 | 0.405822 | ||||||||
\(93\) | 1.39355e10 | 0.207714 | ||||||||
\(94\) | 8.33131e10 | 1.17087 | ||||||||
\(95\) | −1.36682e10 | −0.181231 | ||||||||
\(96\) | −2.83972e10 | −0.355454 | ||||||||
\(97\) | 1.38985e11 | 1.64332 | 0.821660 | − | 0.569978i | \(-0.193048\pi\) | ||||
0.821660 | + | 0.569978i | \(0.193048\pi\) | |||||||
\(98\) | 1.05259e10 | 0.117629 | ||||||||
\(99\) | 2.06576e10 | 0.218316 | ||||||||
\(100\) | 2.61230e10 | 0.261230 | ||||||||
\(101\) | −1.83966e11 | −1.74168 | −0.870842 | − | 0.491564i | \(-0.836426\pi\) | ||||
−0.870842 | + | 0.491564i | \(0.836426\pi\) | |||||||
\(102\) | −4.21690e10 | −0.378175 | ||||||||
\(103\) | −1.80056e10 | −0.153040 | −0.0765198 | − | 0.997068i | \(-0.524381\pi\) | ||||
−0.0765198 | + | 0.997068i | \(0.524381\pi\) | |||||||
\(104\) | 3.74592e10 | 0.301908 | ||||||||
\(105\) | −1.23987e10 | −0.0948057 | ||||||||
\(106\) | 1.55592e11 | 1.12929 | ||||||||
\(107\) | 1.92018e11 | 1.32352 | 0.661759 | − | 0.749716i | \(-0.269810\pi\) | ||||
0.661759 | + | 0.749716i | \(0.269810\pi\) | |||||||
\(108\) | 9.46275e9 | 0.0619707 | ||||||||
\(109\) | 1.61795e11 | 1.00721 | 0.503605 | − | 0.863934i | \(-0.332007\pi\) | ||||
0.503605 | + | 0.863934i | \(0.332007\pi\) | |||||||
\(110\) | 3.95752e10 | 0.234295 | ||||||||
\(111\) | −5.63742e10 | −0.317544 | ||||||||
\(112\) | −4.04846e10 | −0.217065 | ||||||||
\(113\) | −3.27978e11 | −1.67461 | −0.837303 | − | 0.546739i | \(-0.815869\pi\) | ||||
−0.837303 | + | 0.546739i | \(0.815869\pi\) | |||||||
\(114\) | 4.07677e10 | 0.198308 | ||||||||
\(115\) | −1.18100e11 | −0.547534 | ||||||||
\(116\) | −5.06990e10 | −0.224120 | ||||||||
\(117\) | −2.19245e10 | −0.0924500 | ||||||||
\(118\) | 1.92508e11 | 0.774635 | ||||||||
\(119\) | 7.82709e10 | 0.300671 | ||||||||
\(120\) | 7.44264e10 | 0.273042 | ||||||||
\(121\) | −1.62925e11 | −0.571042 | ||||||||
\(122\) | −3.71550e11 | −1.24462 | ||||||||
\(123\) | −1.09050e10 | −0.0349258 | ||||||||
\(124\) | 3.78194e10 | 0.115850 | ||||||||
\(125\) | −2.68490e11 | −0.786905 | ||||||||
\(126\) | 3.69811e10 | 0.103739 | ||||||||
\(127\) | 4.72055e11 | 1.26786 | 0.633932 | − | 0.773389i | \(-0.281440\pi\) | ||||
0.633932 | + | 0.773389i | \(0.281440\pi\) | |||||||
\(128\) | 1.06759e11 | 0.274630 | ||||||||
\(129\) | −1.59637e11 | −0.393450 | ||||||||
\(130\) | −4.20023e10 | −0.0992166 | ||||||||
\(131\) | −3.40224e11 | −0.770499 | −0.385250 | − | 0.922812i | \(-0.625885\pi\) | ||||
−0.385250 | + | 0.922812i | \(0.625885\pi\) | |||||||
\(132\) | 5.60624e10 | 0.121763 | ||||||||
\(133\) | −7.56699e10 | −0.157666 | ||||||||
\(134\) | −1.25258e11 | −0.250455 | ||||||||
\(135\) | −4.35610e10 | −0.0836108 | ||||||||
\(136\) | −4.69842e11 | −0.865939 | ||||||||
\(137\) | 3.24673e11 | 0.574755 | 0.287378 | − | 0.957817i | \(-0.407217\pi\) | ||||
0.287378 | + | 0.957817i | \(0.407217\pi\) | |||||||
\(138\) | 3.52252e11 | 0.599126 | ||||||||
\(139\) | −9.62198e11 | −1.57284 | −0.786418 | − | 0.617695i | \(-0.788067\pi\) | ||||
−0.786418 | + | 0.617695i | \(0.788067\pi\) | |||||||
\(140\) | −3.36487e10 | −0.0528766 | ||||||||
\(141\) | −5.43304e11 | −0.820989 | ||||||||
\(142\) | −5.81014e11 | −0.844503 | ||||||||
\(143\) | −1.29892e11 | −0.181650 | ||||||||
\(144\) | −1.42237e11 | −0.191434 | ||||||||
\(145\) | 2.33389e11 | 0.302382 | ||||||||
\(146\) | −6.27888e11 | −0.783324 | ||||||||
\(147\) | −6.86415e10 | −0.0824786 | ||||||||
\(148\) | −1.52993e11 | −0.177106 | ||||||||
\(149\) | 1.15790e12 | 1.29165 | 0.645825 | − | 0.763485i | \(-0.276513\pi\) | ||||
0.645825 | + | 0.763485i | \(0.276513\pi\) | |||||||
\(150\) | 3.58680e11 | 0.385661 | ||||||||
\(151\) | −1.82109e12 | −1.88781 | −0.943903 | − | 0.330223i | \(-0.892876\pi\) | ||||
−0.943903 | + | 0.330223i | \(0.892876\pi\) | |||||||
\(152\) | 4.54228e11 | 0.454082 | ||||||||
\(153\) | 2.74994e11 | 0.265167 | ||||||||
\(154\) | 2.19096e11 | 0.203831 | ||||||||
\(155\) | −1.74098e11 | −0.156304 | ||||||||
\(156\) | −5.95006e10 | −0.0515628 | ||||||||
\(157\) | 8.12422e11 | 0.679725 | 0.339863 | − | 0.940475i | \(-0.389619\pi\) | ||||
0.339863 | + | 0.940475i | \(0.389619\pi\) | |||||||
\(158\) | −1.35774e12 | −1.09699 | ||||||||
\(159\) | −1.01465e12 | −0.791832 | ||||||||
\(160\) | 3.54771e11 | 0.267478 | ||||||||
\(161\) | −6.53823e11 | −0.476341 | ||||||||
\(162\) | 1.29928e11 | 0.0914891 | ||||||||
\(163\) | −2.19880e12 | −1.49677 | −0.748384 | − | 0.663266i | \(-0.769170\pi\) | ||||
−0.748384 | + | 0.663266i | \(0.769170\pi\) | |||||||
\(164\) | −2.95949e10 | −0.0194794 | ||||||||
\(165\) | −2.58079e11 | −0.164282 | ||||||||
\(166\) | 7.82307e11 | 0.481707 | ||||||||
\(167\) | 1.76362e12 | 1.05067 | 0.525334 | − | 0.850896i | \(-0.323940\pi\) | ||||
0.525334 | + | 0.850896i | \(0.323940\pi\) | |||||||
\(168\) | 4.12038e11 | 0.237540 | ||||||||
\(169\) | 1.37858e11 | 0.0769231 | ||||||||
\(170\) | 5.26825e11 | 0.284575 | ||||||||
\(171\) | −2.65855e11 | −0.139049 | ||||||||
\(172\) | −4.33236e11 | −0.219441 | ||||||||
\(173\) | −4.54586e11 | −0.223029 | −0.111515 | − | 0.993763i | \(-0.535570\pi\) | ||||
−0.111515 | + | 0.993763i | \(0.535570\pi\) | |||||||
\(174\) | −6.96120e11 | −0.330875 | ||||||||
\(175\) | −6.65755e11 | −0.306623 | ||||||||
\(176\) | −8.42687e11 | −0.376138 | ||||||||
\(177\) | −1.25539e12 | −0.543156 | ||||||||
\(178\) | −1.37220e12 | −0.575584 | ||||||||
\(179\) | −4.18301e12 | −1.70136 | −0.850681 | − | 0.525682i | \(-0.823810\pi\) | ||||
−0.850681 | + | 0.525682i | \(0.823810\pi\) | |||||||
\(180\) | −1.18220e11 | −0.0466328 | ||||||||
\(181\) | −4.41868e12 | −1.69068 | −0.845338 | − | 0.534232i | \(-0.820601\pi\) | ||||
−0.845338 | + | 0.534232i | \(0.820601\pi\) | |||||||
\(182\) | −2.32533e11 | −0.0863160 | ||||||||
\(183\) | 2.42296e12 | 0.872701 | ||||||||
\(184\) | 3.92475e12 | 1.37187 | ||||||||
\(185\) | 7.04292e11 | 0.238951 | ||||||||
\(186\) | 5.19277e11 | 0.171032 | ||||||||
\(187\) | 1.62921e12 | 0.521013 | ||||||||
\(188\) | −1.47447e12 | −0.457896 | ||||||||
\(189\) | −2.41162e11 | −0.0727393 | ||||||||
\(190\) | −5.09318e11 | −0.149226 | ||||||||
\(191\) | −2.38573e12 | −0.679107 | −0.339554 | − | 0.940587i | \(-0.610276\pi\) | ||||
−0.339554 | + | 0.940587i | \(0.610276\pi\) | |||||||
\(192\) | −2.25693e12 | −0.624254 | ||||||||
\(193\) | −1.64628e12 | −0.442527 | −0.221263 | − | 0.975214i | \(-0.571018\pi\) | ||||
−0.221263 | + | 0.975214i | \(0.571018\pi\) | |||||||
\(194\) | 5.17897e12 | 1.35311 | ||||||||
\(195\) | 2.73906e11 | 0.0695684 | ||||||||
\(196\) | −1.86285e11 | −0.0460013 | ||||||||
\(197\) | −4.20144e12 | −1.00887 | −0.504434 | − | 0.863450i | \(-0.668299\pi\) | ||||
−0.504434 | + | 0.863450i | \(0.668299\pi\) | |||||||
\(198\) | 7.69762e11 | 0.179762 | ||||||||
\(199\) | −6.43492e12 | −1.46168 | −0.730839 | − | 0.682550i | \(-0.760871\pi\) | ||||
−0.730839 | + | 0.682550i | \(0.760871\pi\) | |||||||
\(200\) | 3.99637e12 | 0.883081 | ||||||||
\(201\) | 8.16838e11 | 0.175613 | ||||||||
\(202\) | −6.85510e12 | −1.43411 | ||||||||
\(203\) | 1.29209e12 | 0.263065 | ||||||||
\(204\) | 7.46302e11 | 0.147893 | ||||||||
\(205\) | 1.36238e11 | 0.0262815 | ||||||||
\(206\) | −6.70943e11 | −0.126013 | ||||||||
\(207\) | −2.29712e12 | −0.420093 | ||||||||
\(208\) | 8.94367e11 | 0.159282 | ||||||||
\(209\) | −1.57507e12 | −0.273209 | ||||||||
\(210\) | −4.62011e11 | −0.0780632 | ||||||||
\(211\) | −4.83623e12 | −0.796074 | −0.398037 | − | 0.917369i | \(-0.630308\pi\) | ||||
−0.398037 | + | 0.917369i | \(0.630308\pi\) | |||||||
\(212\) | −2.75365e12 | −0.441633 | ||||||||
\(213\) | 3.78893e12 | 0.592146 | ||||||||
\(214\) | 7.15513e12 | 1.08979 | ||||||||
\(215\) | 1.99437e12 | 0.296070 | ||||||||
\(216\) | 1.44764e12 | 0.209491 | ||||||||
\(217\) | −9.63842e11 | −0.135981 | ||||||||
\(218\) | 6.02896e12 | 0.829339 | ||||||||
\(219\) | 4.09460e12 | 0.549249 | ||||||||
\(220\) | −7.00398e11 | −0.0916263 | ||||||||
\(221\) | −1.72913e12 | −0.220632 | ||||||||
\(222\) | −2.10067e12 | −0.261466 | ||||||||
\(223\) | −6.49076e12 | −0.788167 | −0.394084 | − | 0.919075i | \(-0.628938\pi\) | ||||
−0.394084 | + | 0.919075i | \(0.628938\pi\) | |||||||
\(224\) | 1.96408e12 | 0.232699 | ||||||||
\(225\) | −2.33904e12 | −0.270416 | ||||||||
\(226\) | −1.22214e13 | −1.37887 | ||||||||
\(227\) | −1.02175e13 | −1.12513 | −0.562563 | − | 0.826754i | \(-0.690185\pi\) | ||||
−0.562563 | + | 0.826754i | \(0.690185\pi\) | |||||||
\(228\) | −7.21502e11 | −0.0775525 | ||||||||
\(229\) | −1.74772e13 | −1.83390 | −0.916952 | − | 0.398997i | \(-0.869358\pi\) | ||||
−0.916952 | + | 0.398997i | \(0.869358\pi\) | |||||||
\(230\) | −4.40075e12 | −0.450841 | ||||||||
\(231\) | −1.42877e12 | −0.142922 | ||||||||
\(232\) | −7.75609e12 | −0.757633 | ||||||||
\(233\) | 1.96809e13 | 1.87753 | 0.938766 | − | 0.344556i | \(-0.111970\pi\) | ||||
0.938766 | + | 0.344556i | \(0.111970\pi\) | |||||||
\(234\) | −8.16970e11 | −0.0761235 | ||||||||
\(235\) | 6.78759e12 | 0.617792 | ||||||||
\(236\) | −3.40698e12 | −0.302938 | ||||||||
\(237\) | 8.85412e12 | 0.769183 | ||||||||
\(238\) | 2.91660e12 | 0.247573 | ||||||||
\(239\) | −2.64938e12 | −0.219764 | −0.109882 | − | 0.993945i | \(-0.535047\pi\) | ||||
−0.109882 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(240\) | 1.77699e12 | 0.144053 | ||||||||
\(241\) | 1.73879e13 | 1.37769 | 0.688846 | − | 0.724907i | \(-0.258117\pi\) | ||||
0.688846 | + | 0.724907i | \(0.258117\pi\) | |||||||
\(242\) | −6.07106e12 | −0.470197 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 6.57565e12 | 0.486737 | ||||||||
\(245\) | 8.57550e11 | 0.0620649 | ||||||||
\(246\) | −4.06351e11 | −0.0287579 | ||||||||
\(247\) | 1.67167e12 | 0.115696 | ||||||||
\(248\) | 5.78571e12 | 0.391627 | ||||||||
\(249\) | −5.10160e12 | −0.337762 | ||||||||
\(250\) | −1.00047e13 | −0.647939 | ||||||||
\(251\) | −4.59100e11 | −0.0290872 | −0.0145436 | − | 0.999894i | \(-0.504630\pi\) | ||||
−0.0145436 | + | 0.999894i | \(0.504630\pi\) | |||||||
\(252\) | −6.54487e11 | −0.0405694 | ||||||||
\(253\) | −1.36093e13 | −0.825419 | ||||||||
\(254\) | 1.75902e13 | 1.04396 | ||||||||
\(255\) | −3.43555e12 | −0.199538 | ||||||||
\(256\) | −1.50432e13 | −0.855109 | ||||||||
\(257\) | 2.55683e13 | 1.42255 | 0.711277 | − | 0.702911i | \(-0.248117\pi\) | ||||
0.711277 | + | 0.702911i | \(0.248117\pi\) | |||||||
\(258\) | −5.94853e12 | −0.323967 | ||||||||
\(259\) | 3.89910e12 | 0.207881 | ||||||||
\(260\) | 7.43352e11 | 0.0388008 | ||||||||
\(261\) | 4.53956e12 | 0.232002 | ||||||||
\(262\) | −1.26777e13 | −0.634431 | ||||||||
\(263\) | 9.19464e11 | 0.0450586 | 0.0225293 | − | 0.999746i | \(-0.492828\pi\) | ||||
0.0225293 | + | 0.999746i | \(0.492828\pi\) | |||||||
\(264\) | 8.57659e12 | 0.411617 | ||||||||
\(265\) | 1.26762e13 | 0.595851 | ||||||||
\(266\) | −2.81968e12 | −0.129823 | ||||||||
\(267\) | 8.94846e12 | 0.403586 | ||||||||
\(268\) | 2.21681e12 | 0.0979460 | ||||||||
\(269\) | 4.54900e12 | 0.196915 | 0.0984575 | − | 0.995141i | \(-0.468609\pi\) | ||||
0.0984575 | + | 0.995141i | \(0.468609\pi\) | |||||||
\(270\) | −1.62321e12 | −0.0688453 | ||||||||
\(271\) | 4.01167e13 | 1.66723 | 0.833613 | − | 0.552349i | \(-0.186268\pi\) | ||||
0.833613 | + | 0.552349i | \(0.186268\pi\) | |||||||
\(272\) | −1.12178e13 | −0.456857 | ||||||||
\(273\) | 1.51640e12 | 0.0605228 | ||||||||
\(274\) | 1.20983e13 | 0.473255 | ||||||||
\(275\) | −1.38577e13 | −0.531327 | ||||||||
\(276\) | −6.23412e12 | −0.234301 | ||||||||
\(277\) | −2.94514e13 | −1.08509 | −0.542547 | − | 0.840025i | \(-0.682540\pi\) | ||||
−0.542547 | + | 0.840025i | \(0.682540\pi\) | |||||||
\(278\) | −3.58543e13 | −1.29508 | ||||||||
\(279\) | −3.38632e12 | −0.119924 | ||||||||
\(280\) | −5.14767e12 | −0.178748 | ||||||||
\(281\) | 2.64894e13 | 0.901959 | 0.450980 | − | 0.892534i | \(-0.351075\pi\) | ||||
0.450980 | + | 0.892534i | \(0.351075\pi\) | |||||||
\(282\) | −2.02451e13 | −0.676004 | ||||||||
\(283\) | −4.45950e12 | −0.146036 | −0.0730182 | − | 0.997331i | \(-0.523263\pi\) | ||||
−0.0730182 | + | 0.997331i | \(0.523263\pi\) | |||||||
\(284\) | 1.02827e13 | 0.330261 | ||||||||
\(285\) | 3.32138e12 | 0.104634 | ||||||||
\(286\) | −4.84017e12 | −0.149571 | ||||||||
\(287\) | 7.54237e11 | 0.0228643 | ||||||||
\(288\) | 6.90052e12 | 0.205222 | ||||||||
\(289\) | −1.25839e13 | −0.367177 | ||||||||
\(290\) | 8.69676e12 | 0.248982 | ||||||||
\(291\) | −3.37733e13 | −0.948771 | ||||||||
\(292\) | 1.11123e13 | 0.306336 | ||||||||
\(293\) | −5.48510e13 | −1.48393 | −0.741963 | − | 0.670440i | \(-0.766105\pi\) | ||||
−0.741963 | + | 0.670440i | \(0.766105\pi\) | |||||||
\(294\) | −2.55778e12 | −0.0679130 | ||||||||
\(295\) | 1.56838e13 | 0.408723 | ||||||||
\(296\) | −2.34053e13 | −0.598702 | ||||||||
\(297\) | −5.01979e12 | −0.126045 | ||||||||
\(298\) | 4.31466e13 | 1.06355 | ||||||||
\(299\) | 1.44440e13 | 0.349539 | ||||||||
\(300\) | −6.34789e12 | −0.150821 | ||||||||
\(301\) | 1.10412e13 | 0.257573 | ||||||||
\(302\) | −6.78590e13 | −1.55442 | ||||||||
\(303\) | 4.47037e13 | 1.00556 | ||||||||
\(304\) | 1.08451e13 | 0.239567 | ||||||||
\(305\) | −3.02705e13 | −0.656705 | ||||||||
\(306\) | 1.02471e13 | 0.218339 | ||||||||
\(307\) | −8.62310e13 | −1.80469 | −0.902344 | − | 0.431017i | \(-0.858155\pi\) | ||||
−0.902344 | + | 0.431017i | \(0.858155\pi\) | |||||||
\(308\) | −3.87754e12 | −0.0797126 | ||||||||
\(309\) | 4.37537e12 | 0.0883575 | ||||||||
\(310\) | −6.48742e12 | −0.128701 | ||||||||
\(311\) | −6.54436e13 | −1.27551 | −0.637756 | − | 0.770238i | \(-0.720137\pi\) | ||||
−0.637756 | + | 0.770238i | \(0.720137\pi\) | |||||||
\(312\) | −9.10258e12 | −0.174307 | ||||||||
\(313\) | −6.19679e13 | −1.16593 | −0.582965 | − | 0.812497i | \(-0.698108\pi\) | ||||
−0.582965 | + | 0.812497i | \(0.698108\pi\) | |||||||
\(314\) | 3.02732e13 | 0.559687 | ||||||||
\(315\) | 3.01288e12 | 0.0547361 | ||||||||
\(316\) | 2.40291e13 | 0.429001 | ||||||||
\(317\) | 7.69685e13 | 1.35048 | 0.675238 | − | 0.737600i | \(-0.264041\pi\) | ||||
0.675238 | + | 0.737600i | \(0.264041\pi\) | |||||||
\(318\) | −3.78089e13 | −0.651996 | ||||||||
\(319\) | 2.68948e13 | 0.455848 | ||||||||
\(320\) | 2.81962e13 | 0.469750 | ||||||||
\(321\) | −4.66603e13 | −0.764134 | ||||||||
\(322\) | −2.43634e13 | −0.392220 | ||||||||
\(323\) | −2.09673e13 | −0.331840 | ||||||||
\(324\) | −2.29945e12 | −0.0357788 | ||||||||
\(325\) | 1.47076e13 | 0.225000 | ||||||||
\(326\) | −8.19338e13 | −1.23244 | ||||||||
\(327\) | −3.93162e13 | −0.581513 | ||||||||
\(328\) | −4.52751e12 | −0.0658496 | ||||||||
\(329\) | 3.75774e13 | 0.537464 | ||||||||
\(330\) | −9.61678e12 | −0.135270 | ||||||||
\(331\) | −8.49103e13 | −1.17464 | −0.587322 | − | 0.809353i | \(-0.699818\pi\) | ||||
−0.587322 | + | 0.809353i | \(0.699818\pi\) | |||||||
\(332\) | −1.38452e13 | −0.188382 | ||||||||
\(333\) | 1.36989e13 | 0.183334 | ||||||||
\(334\) | 6.57178e13 | 0.865122 | ||||||||
\(335\) | −1.02049e13 | −0.132149 | ||||||||
\(336\) | 9.83775e12 | 0.125323 | ||||||||
\(337\) | −3.43643e13 | −0.430668 | −0.215334 | − | 0.976540i | \(-0.569084\pi\) | ||||
−0.215334 | + | 0.976540i | \(0.569084\pi\) | |||||||
\(338\) | 5.13701e12 | 0.0633386 | ||||||||
\(339\) | 7.96986e13 | 0.966834 | ||||||||
\(340\) | −9.32369e12 | −0.111289 | ||||||||
\(341\) | −2.00624e13 | −0.235632 | ||||||||
\(342\) | −9.90655e12 | −0.114493 | ||||||||
\(343\) | 4.74756e12 | 0.0539949 | ||||||||
\(344\) | −6.62777e13 | −0.741816 | ||||||||
\(345\) | 2.86983e13 | 0.316119 | ||||||||
\(346\) | −1.69392e13 | −0.183643 | ||||||||
\(347\) | 1.50594e14 | 1.60693 | 0.803463 | − | 0.595354i | \(-0.202988\pi\) | ||||
0.803463 | + | 0.595354i | \(0.202988\pi\) | |||||||
\(348\) | 1.23199e13 | 0.129396 | ||||||||
\(349\) | 7.44243e13 | 0.769440 | 0.384720 | − | 0.923033i | \(-0.374298\pi\) | ||||
0.384720 | + | 0.923033i | \(0.374298\pi\) | |||||||
\(350\) | −2.48080e13 | −0.252474 | ||||||||
\(351\) | 5.32765e12 | 0.0533761 | ||||||||
\(352\) | 4.08824e13 | 0.403229 | ||||||||
\(353\) | −6.82587e13 | −0.662822 | −0.331411 | − | 0.943486i | \(-0.607525\pi\) | ||||
−0.331411 | + | 0.943486i | \(0.607525\pi\) | |||||||
\(354\) | −4.67794e13 | −0.447236 | ||||||||
\(355\) | −4.73358e13 | −0.445588 | ||||||||
\(356\) | 2.42851e13 | 0.225095 | ||||||||
\(357\) | −1.90198e13 | −0.173593 | ||||||||
\(358\) | −1.55871e14 | −1.40091 | ||||||||
\(359\) | −1.31323e14 | −1.16231 | −0.581153 | − | 0.813794i | \(-0.697398\pi\) | ||||
−0.581153 | + | 0.813794i | \(0.697398\pi\) | |||||||
\(360\) | −1.80856e13 | −0.157641 | ||||||||
\(361\) | −9.62197e13 | −0.825989 | ||||||||
\(362\) | −1.64653e14 | −1.39211 | ||||||||
\(363\) | 3.95908e13 | 0.329691 | ||||||||
\(364\) | 4.11534e12 | 0.0337558 | ||||||||
\(365\) | −5.11546e13 | −0.413308 | ||||||||
\(366\) | 9.02866e13 | 0.718584 | ||||||||
\(367\) | 5.27754e13 | 0.413779 | 0.206890 | − | 0.978364i | \(-0.433666\pi\) | ||||
0.206890 | + | 0.978364i | \(0.433666\pi\) | |||||||
\(368\) | 9.37064e13 | 0.723780 | ||||||||
\(369\) | 2.64991e12 | 0.0201644 | ||||||||
\(370\) | 2.62440e13 | 0.196753 | ||||||||
\(371\) | 7.01780e13 | 0.518376 | ||||||||
\(372\) | −9.19010e12 | −0.0668858 | ||||||||
\(373\) | 2.63210e13 | 0.188757 | 0.0943787 | − | 0.995536i | \(-0.469914\pi\) | ||||
0.0943787 | + | 0.995536i | \(0.469914\pi\) | |||||||
\(374\) | 6.07091e13 | 0.429003 | ||||||||
\(375\) | 6.52430e13 | 0.454320 | ||||||||
\(376\) | −2.25568e14 | −1.54791 | ||||||||
\(377\) | −2.85442e13 | −0.193037 | ||||||||
\(378\) | −8.98640e12 | −0.0598937 | ||||||||
\(379\) | −2.17845e13 | −0.143097 | −0.0715486 | − | 0.997437i | \(-0.522794\pi\) | ||||
−0.0715486 | + | 0.997437i | \(0.522794\pi\) | |||||||
\(380\) | 9.01386e12 | 0.0583581 | ||||||||
\(381\) | −1.14709e14 | −0.732001 | ||||||||
\(382\) | −8.88994e13 | −0.559178 | ||||||||
\(383\) | 2.25785e14 | 1.39991 | 0.699956 | − | 0.714185i | \(-0.253203\pi\) | ||||
0.699956 | + | 0.714185i | \(0.253203\pi\) | |||||||
\(384\) | −2.59424e13 | −0.158558 | ||||||||
\(385\) | 1.78499e13 | 0.107548 | ||||||||
\(386\) | −6.13454e13 | −0.364378 | ||||||||
\(387\) | 3.87917e13 | 0.227158 | ||||||||
\(388\) | −9.16569e13 | −0.529164 | ||||||||
\(389\) | −4.75630e13 | −0.270737 | −0.135368 | − | 0.990795i | \(-0.543222\pi\) | ||||
−0.135368 | + | 0.990795i | \(0.543222\pi\) | |||||||
\(390\) | 1.02066e13 | 0.0572827 | ||||||||
\(391\) | −1.81168e14 | −1.00255 | ||||||||
\(392\) | −2.84985e13 | −0.155506 | ||||||||
\(393\) | 8.26743e13 | 0.444848 | ||||||||
\(394\) | −1.56558e14 | −0.830704 | ||||||||
\(395\) | −1.10616e14 | −0.578808 | ||||||||
\(396\) | −1.36232e13 | −0.0702999 | ||||||||
\(397\) | 1.45288e14 | 0.739404 | 0.369702 | − | 0.929150i | \(-0.379460\pi\) | ||||
0.369702 | + | 0.929150i | \(0.379460\pi\) | |||||||
\(398\) | −2.39784e14 | −1.20355 | ||||||||
\(399\) | 1.83878e13 | 0.0910288 | ||||||||
\(400\) | 9.54165e13 | 0.465901 | ||||||||
\(401\) | 6.42242e12 | 0.0309318 | 0.0154659 | − | 0.999880i | \(-0.495077\pi\) | ||||
0.0154659 | + | 0.999880i | \(0.495077\pi\) | |||||||
\(402\) | 3.04378e13 | 0.144600 | ||||||||
\(403\) | 2.12928e13 | 0.0997826 | ||||||||
\(404\) | 1.21321e14 | 0.560838 | ||||||||
\(405\) | 1.05853e13 | 0.0482727 | ||||||||
\(406\) | 4.81469e13 | 0.216608 | ||||||||
\(407\) | 8.11598e13 | 0.360223 | ||||||||
\(408\) | 1.14172e14 | 0.499950 | ||||||||
\(409\) | −2.25782e14 | −0.975463 | −0.487731 | − | 0.872994i | \(-0.662175\pi\) | ||||
−0.487731 | + | 0.872994i | \(0.662175\pi\) | |||||||
\(410\) | 5.07661e12 | 0.0216403 | ||||||||
\(411\) | −7.88955e13 | −0.331835 | ||||||||
\(412\) | 1.18743e13 | 0.0492802 | ||||||||
\(413\) | 8.68283e13 | 0.355579 | ||||||||
\(414\) | −8.55972e13 | −0.345906 | ||||||||
\(415\) | 6.37353e13 | 0.254165 | ||||||||
\(416\) | −4.33896e13 | −0.170755 | ||||||||
\(417\) | 2.33814e14 | 0.908077 | ||||||||
\(418\) | −5.86917e13 | −0.224961 | ||||||||
\(419\) | −2.18264e14 | −0.825666 | −0.412833 | − | 0.910807i | \(-0.635461\pi\) | ||||
−0.412833 | + | 0.910807i | \(0.635461\pi\) | |||||||
\(420\) | 8.17663e12 | 0.0305283 | ||||||||
\(421\) | −3.00322e14 | −1.10671 | −0.553357 | − | 0.832944i | \(-0.686653\pi\) | ||||
−0.553357 | + | 0.832944i | \(0.686653\pi\) | |||||||
\(422\) | −1.80212e14 | −0.655489 | ||||||||
\(423\) | 1.32023e14 | 0.473998 | ||||||||
\(424\) | −4.21262e14 | −1.49293 | ||||||||
\(425\) | −1.84474e14 | −0.645350 | ||||||||
\(426\) | 1.41187e14 | 0.487574 | ||||||||
\(427\) | −1.67583e14 | −0.571317 | ||||||||
\(428\) | −1.26631e14 | −0.426185 | ||||||||
\(429\) | 3.15639e13 | 0.104876 | ||||||||
\(430\) | 7.43160e13 | 0.243784 | ||||||||
\(431\) | 5.60779e14 | 1.81621 | 0.908106 | − | 0.418740i | \(-0.137528\pi\) | ||||
0.908106 | + | 0.418740i | \(0.137528\pi\) | |||||||
\(432\) | 3.45635e13 | 0.110524 | ||||||||
\(433\) | 3.66243e14 | 1.15634 | 0.578170 | − | 0.815917i | \(-0.303767\pi\) | ||||
0.578170 | + | 0.815917i | \(0.303767\pi\) | |||||||
\(434\) | −3.59156e13 | −0.111967 | ||||||||
\(435\) | −5.67135e13 | −0.174581 | ||||||||
\(436\) | −1.06700e14 | −0.324331 | ||||||||
\(437\) | 1.75147e14 | 0.525721 | ||||||||
\(438\) | 1.52577e14 | 0.452253 | ||||||||
\(439\) | −3.40906e14 | −0.997882 | −0.498941 | − | 0.866636i | \(-0.666278\pi\) | ||||
−0.498941 | + | 0.866636i | \(0.666278\pi\) | |||||||
\(440\) | −1.07149e14 | −0.309740 | ||||||||
\(441\) | 1.66799e13 | 0.0476190 | ||||||||
\(442\) | −6.44323e13 | −0.181669 | ||||||||
\(443\) | −3.75147e13 | −0.104468 | −0.0522338 | − | 0.998635i | \(-0.516634\pi\) | ||||
−0.0522338 | + | 0.998635i | \(0.516634\pi\) | |||||||
\(444\) | 3.71774e13 | 0.102252 | ||||||||
\(445\) | −1.11795e14 | −0.303698 | ||||||||
\(446\) | −2.41864e14 | −0.648979 | ||||||||
\(447\) | −2.81369e14 | −0.745735 | ||||||||
\(448\) | 1.56100e14 | 0.408670 | ||||||||
\(449\) | −6.49981e14 | −1.68092 | −0.840458 | − | 0.541877i | \(-0.817714\pi\) | ||||
−0.840458 | + | 0.541877i | \(0.817714\pi\) | |||||||
\(450\) | −8.71593e13 | −0.222661 | ||||||||
\(451\) | 1.56995e13 | 0.0396200 | ||||||||
\(452\) | 2.16293e14 | 0.539239 | ||||||||
\(453\) | 4.42524e14 | 1.08993 | ||||||||
\(454\) | −3.80733e14 | −0.926431 | ||||||||
\(455\) | −1.89446e13 | −0.0455432 | ||||||||
\(456\) | −1.10378e14 | −0.262165 | ||||||||
\(457\) | −6.61580e14 | −1.55254 | −0.776270 | − | 0.630400i | \(-0.782891\pi\) | ||||
−0.776270 | + | 0.630400i | \(0.782891\pi\) | |||||||
\(458\) | −6.51251e14 | −1.51004 | ||||||||
\(459\) | −6.68235e13 | −0.153094 | ||||||||
\(460\) | 7.78839e13 | 0.176311 | ||||||||
\(461\) | 1.19329e14 | 0.266926 | 0.133463 | − | 0.991054i | \(-0.457390\pi\) | ||||
0.133463 | + | 0.991054i | \(0.457390\pi\) | |||||||
\(462\) | −5.32403e13 | −0.117682 | ||||||||
\(463\) | −1.81496e14 | −0.396435 | −0.198217 | − | 0.980158i | \(-0.563515\pi\) | ||||
−0.198217 | + | 0.980158i | \(0.563515\pi\) | |||||||
\(464\) | −1.85183e14 | −0.399716 | ||||||||
\(465\) | 4.23059e13 | 0.0902423 | ||||||||
\(466\) | 7.33368e14 | 1.54596 | ||||||||
\(467\) | −6.47256e14 | −1.34845 | −0.674223 | − | 0.738528i | \(-0.735521\pi\) | ||||
−0.674223 | + | 0.738528i | \(0.735521\pi\) | |||||||
\(468\) | 1.44586e13 | 0.0297698 | ||||||||
\(469\) | −5.64963e13 | −0.114966 | ||||||||
\(470\) | 2.52925e14 | 0.508691 | ||||||||
\(471\) | −1.97418e14 | −0.392440 | ||||||||
\(472\) | −5.21210e14 | −1.02407 | ||||||||
\(473\) | 2.29823e14 | 0.446331 | ||||||||
\(474\) | 3.29930e14 | 0.633346 | ||||||||
\(475\) | 1.78344e14 | 0.338410 | ||||||||
\(476\) | −5.16177e13 | −0.0968190 | ||||||||
\(477\) | 2.46560e14 | 0.457164 | ||||||||
\(478\) | −9.87237e13 | −0.180954 | ||||||||
\(479\) | 8.54467e14 | 1.54828 | 0.774141 | − | 0.633014i | \(-0.218182\pi\) | ||||
0.774141 | + | 0.633014i | \(0.218182\pi\) | |||||||
\(480\) | −8.62094e13 | −0.154429 | ||||||||
\(481\) | −8.61372e13 | −0.152543 | ||||||||
\(482\) | 6.47922e14 | 1.13439 | ||||||||
\(483\) | 1.58879e14 | 0.275016 | ||||||||
\(484\) | 1.07445e14 | 0.183881 | ||||||||
\(485\) | 4.21935e14 | 0.713948 | ||||||||
\(486\) | −3.15724e13 | −0.0528213 | ||||||||
\(487\) | 6.82021e14 | 1.12821 | 0.564103 | − | 0.825705i | \(-0.309222\pi\) | ||||
0.564103 | + | 0.825705i | \(0.309222\pi\) | |||||||
\(488\) | 1.00596e15 | 1.64540 | ||||||||
\(489\) | 5.34309e14 | 0.864159 | ||||||||
\(490\) | 3.19548e13 | 0.0511044 | ||||||||
\(491\) | 1.03914e15 | 1.64334 | 0.821668 | − | 0.569967i | \(-0.193044\pi\) | ||||
0.821668 | + | 0.569967i | \(0.193044\pi\) | |||||||
\(492\) | 7.19155e12 | 0.0112464 | ||||||||
\(493\) | 3.58023e14 | 0.553673 | ||||||||
\(494\) | 6.22912e13 | 0.0952639 | ||||||||
\(495\) | 6.27132e13 | 0.0948485 | ||||||||
\(496\) | 1.38139e14 | 0.206617 | ||||||||
\(497\) | −2.62060e14 | −0.387650 | ||||||||
\(498\) | −1.90101e14 | −0.278114 | ||||||||
\(499\) | 1.34100e15 | 1.94033 | 0.970164 | − | 0.242448i | \(-0.0779505\pi\) | ||||
0.970164 | + | 0.242448i | \(0.0779505\pi\) | |||||||
\(500\) | 1.77062e14 | 0.253391 | ||||||||
\(501\) | −4.28561e14 | −0.606603 | ||||||||
\(502\) | −1.71074e13 | −0.0239504 | ||||||||
\(503\) | 5.26904e14 | 0.729638 | 0.364819 | − | 0.931078i | \(-0.381131\pi\) | ||||
0.364819 | + | 0.931078i | \(0.381131\pi\) | |||||||
\(504\) | −1.00125e14 | −0.137144 | ||||||||
\(505\) | −5.58491e14 | −0.756682 | ||||||||
\(506\) | −5.07124e14 | −0.679652 | ||||||||
\(507\) | −3.34996e13 | −0.0444116 | ||||||||
\(508\) | −3.11309e14 | −0.408264 | ||||||||
\(509\) | 7.55877e14 | 0.980625 | 0.490313 | − | 0.871547i | \(-0.336883\pi\) | ||||
0.490313 | + | 0.871547i | \(0.336883\pi\) | |||||||
\(510\) | −1.28018e14 | −0.164300 | ||||||||
\(511\) | −2.83202e14 | −0.359568 | ||||||||
\(512\) | −7.79197e14 | −0.978729 | ||||||||
\(513\) | 6.46029e13 | 0.0802798 | ||||||||
\(514\) | 9.52748e14 | 1.17133 | ||||||||
\(515\) | −5.46623e13 | −0.0664888 | ||||||||
\(516\) | 1.05276e14 | 0.126694 | ||||||||
\(517\) | 7.82174e14 | 0.931334 | ||||||||
\(518\) | 1.45292e14 | 0.171170 | ||||||||
\(519\) | 1.10464e14 | 0.128766 | ||||||||
\(520\) | 1.13720e14 | 0.131165 | ||||||||
\(521\) | 1.55318e15 | 1.77261 | 0.886306 | − | 0.463101i | \(-0.153263\pi\) | ||||
0.886306 | + | 0.463101i | \(0.153263\pi\) | |||||||
\(522\) | 1.69157e14 | 0.191031 | ||||||||
\(523\) | 6.01398e14 | 0.672051 | 0.336026 | − | 0.941853i | \(-0.390917\pi\) | ||||
0.336026 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(524\) | 2.24369e14 | 0.248108 | ||||||||
\(525\) | 1.61779e14 | 0.177029 | ||||||||
\(526\) | 3.42619e13 | 0.0371014 | ||||||||
\(527\) | −2.67070e14 | −0.286199 | ||||||||
\(528\) | 2.04773e14 | 0.217163 | ||||||||
\(529\) | 5.60544e14 | 0.588306 | ||||||||
\(530\) | 4.72353e14 | 0.490625 | ||||||||
\(531\) | 3.05059e14 | 0.313591 | ||||||||
\(532\) | 4.99024e13 | 0.0507701 | ||||||||
\(533\) | −1.66623e13 | −0.0167778 | ||||||||
\(534\) | 3.33446e14 | 0.332314 | ||||||||
\(535\) | 5.82935e14 | 0.575009 | ||||||||
\(536\) | 3.39134e14 | 0.331104 | ||||||||
\(537\) | 1.01647e15 | 0.982282 | ||||||||
\(538\) | 1.69509e14 | 0.162140 | ||||||||
\(539\) | 9.88206e13 | 0.0935641 | ||||||||
\(540\) | 2.87274e13 | 0.0269235 | ||||||||
\(541\) | −1.89035e15 | −1.75371 | −0.876854 | − | 0.480757i | \(-0.840362\pi\) | ||||
−0.876854 | + | 0.480757i | \(0.840362\pi\) | |||||||
\(542\) | 1.49487e15 | 1.37280 | ||||||||
\(543\) | 1.07374e15 | 0.976112 | ||||||||
\(544\) | 5.44226e14 | 0.489762 | ||||||||
\(545\) | 4.91185e14 | 0.437587 | ||||||||
\(546\) | 5.65054e13 | 0.0498345 | ||||||||
\(547\) | 1.41581e15 | 1.23616 | 0.618079 | − | 0.786116i | \(-0.287911\pi\) | ||||
0.618079 | + | 0.786116i | \(0.287911\pi\) | |||||||
\(548\) | −2.14114e14 | −0.185077 | ||||||||
\(549\) | −5.88780e14 | −0.503854 | ||||||||
\(550\) | −5.16379e14 | −0.437495 | ||||||||
\(551\) | −3.46126e14 | −0.290336 | ||||||||
\(552\) | −9.53713e14 | −0.792050 | ||||||||
\(553\) | −6.12392e14 | −0.503548 | ||||||||
\(554\) | −1.09745e15 | −0.893468 | ||||||||
\(555\) | −1.71143e14 | −0.137958 | ||||||||
\(556\) | 6.34546e14 | 0.506468 | ||||||||
\(557\) | −6.60429e14 | −0.521943 | −0.260971 | − | 0.965347i | \(-0.584043\pi\) | ||||
−0.260971 | + | 0.965347i | \(0.584043\pi\) | |||||||
\(558\) | −1.26184e14 | −0.0987454 | ||||||||
\(559\) | −2.43918e14 | −0.189007 | ||||||||
\(560\) | −1.22905e14 | −0.0943050 | ||||||||
\(561\) | −3.95898e14 | −0.300807 | ||||||||
\(562\) | 9.87071e14 | 0.742675 | ||||||||
\(563\) | −2.54912e15 | −1.89931 | −0.949653 | − | 0.313305i | \(-0.898564\pi\) | ||||
−0.949653 | + | 0.313305i | \(0.898564\pi\) | |||||||
\(564\) | 3.58295e14 | 0.264366 | ||||||||
\(565\) | −9.95688e14 | −0.727540 | ||||||||
\(566\) | −1.66174e14 | −0.120247 | ||||||||
\(567\) | 5.86024e13 | 0.0419961 | ||||||||
\(568\) | 1.57308e15 | 1.11644 | ||||||||
\(569\) | −5.20210e14 | −0.365646 | −0.182823 | − | 0.983146i | \(-0.558524\pi\) | ||||
−0.182823 | + | 0.983146i | \(0.558524\pi\) | |||||||
\(570\) | 1.23764e14 | 0.0861556 | ||||||||
\(571\) | 5.35292e14 | 0.369056 | 0.184528 | − | 0.982827i | \(-0.440924\pi\) | ||||
0.184528 | + | 0.982827i | \(0.440924\pi\) | |||||||
\(572\) | 8.56608e13 | 0.0584930 | ||||||||
\(573\) | 5.79733e14 | 0.392083 | ||||||||
\(574\) | 2.81051e13 | 0.0188265 | ||||||||
\(575\) | 1.54097e15 | 1.02240 | ||||||||
\(576\) | 5.48434e14 | 0.360413 | ||||||||
\(577\) | −2.67229e14 | −0.173947 | −0.0869735 | − | 0.996211i | \(-0.527720\pi\) | ||||
−0.0869735 | + | 0.996211i | \(0.527720\pi\) | |||||||
\(578\) | −4.68911e14 | −0.302334 | ||||||||
\(579\) | 4.00047e14 | 0.255493 | ||||||||
\(580\) | −1.53914e14 | −0.0973700 | ||||||||
\(581\) | 3.52850e14 | 0.221117 | ||||||||
\(582\) | −1.25849e15 | −0.781220 | ||||||||
\(583\) | 1.46076e15 | 0.898258 | ||||||||
\(584\) | 1.69999e15 | 1.03556 | ||||||||
\(585\) | −6.65593e13 | −0.0401653 | ||||||||
\(586\) | −2.04391e15 | −1.22187 | ||||||||
\(587\) | −1.19351e15 | −0.706831 | −0.353415 | − | 0.935466i | \(-0.614980\pi\) | ||||
−0.353415 | + | 0.935466i | \(0.614980\pi\) | |||||||
\(588\) | 4.52674e13 | 0.0265589 | ||||||||
\(589\) | 2.58196e14 | 0.150077 | ||||||||
\(590\) | 5.84423e14 | 0.336543 | ||||||||
\(591\) | 1.02095e15 | 0.582470 | ||||||||
\(592\) | −5.58821e14 | −0.315867 | ||||||||
\(593\) | 2.08117e15 | 1.16549 | 0.582743 | − | 0.812657i | \(-0.301980\pi\) | ||||
0.582743 | + | 0.812657i | \(0.301980\pi\) | |||||||
\(594\) | −1.87052e14 | −0.103786 | ||||||||
\(595\) | 2.37618e14 | 0.130628 | ||||||||
\(596\) | −7.63604e14 | −0.415924 | ||||||||
\(597\) | 1.56369e15 | 0.843900 | ||||||||
\(598\) | 5.38225e14 | 0.287811 | ||||||||
\(599\) | −5.53856e13 | −0.0293460 | −0.0146730 | − | 0.999892i | \(-0.504671\pi\) | ||||
−0.0146730 | + | 0.999892i | \(0.504671\pi\) | |||||||
\(600\) | −9.71118e14 | −0.509847 | ||||||||
\(601\) | −1.82715e14 | −0.0950527 | −0.0475263 | − | 0.998870i | \(-0.515134\pi\) | ||||
−0.0475263 | + | 0.998870i | \(0.515134\pi\) | |||||||
\(602\) | 4.11428e14 | 0.212086 | ||||||||
\(603\) | −1.98492e14 | −0.101390 | ||||||||
\(604\) | 1.20096e15 | 0.607891 | ||||||||
\(605\) | −4.94615e14 | −0.248092 | ||||||||
\(606\) | 1.66579e15 | 0.827981 | ||||||||
\(607\) | −7.64019e14 | −0.376328 | −0.188164 | − | 0.982138i | \(-0.560254\pi\) | ||||
−0.188164 | + | 0.982138i | \(0.560254\pi\) | |||||||
\(608\) | −5.26141e14 | −0.256822 | ||||||||
\(609\) | −3.13977e14 | −0.151881 | ||||||||
\(610\) | −1.12797e15 | −0.540732 | ||||||||
\(611\) | −8.30143e14 | −0.394391 | ||||||||
\(612\) | −1.81351e14 | −0.0853863 | ||||||||
\(613\) | −3.22110e15 | −1.50304 | −0.751522 | − | 0.659708i | \(-0.770680\pi\) | ||||
−0.751522 | + | 0.659708i | \(0.770680\pi\) | |||||||
\(614\) | −3.21322e15 | −1.48598 | ||||||||
\(615\) | −3.31057e13 | −0.0151737 | ||||||||
\(616\) | −5.93197e14 | −0.269466 | ||||||||
\(617\) | −1.29898e14 | −0.0584835 | −0.0292417 | − | 0.999572i | \(-0.509309\pi\) | ||||
−0.0292417 | + | 0.999572i | \(0.509309\pi\) | |||||||
\(618\) | 1.63039e14 | 0.0727537 | ||||||||
\(619\) | 1.59258e15 | 0.704373 | 0.352186 | − | 0.935930i | \(-0.385438\pi\) | ||||
0.352186 | + | 0.935930i | \(0.385438\pi\) | |||||||
\(620\) | 1.14814e14 | 0.0503314 | ||||||||
\(621\) | 5.58199e14 | 0.242541 | ||||||||
\(622\) | −2.43862e15 | −1.05026 | ||||||||
\(623\) | −6.18917e14 | −0.264209 | ||||||||
\(624\) | −2.17331e14 | −0.0919617 | ||||||||
\(625\) | 1.11908e15 | 0.469375 | ||||||||
\(626\) | −2.30910e15 | −0.960029 | ||||||||
\(627\) | 3.82742e14 | 0.157738 | ||||||||
\(628\) | −5.35772e14 | −0.218878 | ||||||||
\(629\) | 1.08040e15 | 0.437528 | ||||||||
\(630\) | 1.12269e14 | 0.0450698 | ||||||||
\(631\) | 2.13905e15 | 0.851255 | 0.425627 | − | 0.904898i | \(-0.360053\pi\) | ||||
0.425627 | + | 0.904898i | \(0.360053\pi\) | |||||||
\(632\) | 3.67604e15 | 1.45023 | ||||||||
\(633\) | 1.17520e15 | 0.459614 | ||||||||
\(634\) | 2.86807e15 | 1.11198 | ||||||||
\(635\) | 1.43309e15 | 0.550829 | ||||||||
\(636\) | 6.69138e14 | 0.254977 | ||||||||
\(637\) | −1.04881e14 | −0.0396214 | ||||||||
\(638\) | 1.00218e15 | 0.375346 | ||||||||
\(639\) | −9.20710e14 | −0.341875 | ||||||||
\(640\) | 3.24103e14 | 0.119314 | ||||||||
\(641\) | 4.33157e15 | 1.58098 | 0.790490 | − | 0.612475i | \(-0.209826\pi\) | ||||
0.790490 | + | 0.612475i | \(0.209826\pi\) | |||||||
\(642\) | −1.73870e15 | −0.629189 | ||||||||
\(643\) | −1.76449e15 | −0.633082 | −0.316541 | − | 0.948579i | \(-0.602521\pi\) | ||||
−0.316541 | + | 0.948579i | \(0.602521\pi\) | |||||||
\(644\) | 4.31180e14 | 0.153386 | ||||||||
\(645\) | −4.84632e14 | −0.170936 | ||||||||
\(646\) | −7.81304e14 | −0.273238 | ||||||||
\(647\) | 1.41745e15 | 0.491511 | 0.245756 | − | 0.969332i | \(-0.420964\pi\) | ||||
0.245756 | + | 0.969332i | \(0.420964\pi\) | |||||||
\(648\) | −3.51776e14 | −0.120949 | ||||||||
\(649\) | 1.80733e15 | 0.616158 | ||||||||
\(650\) | 5.48047e14 | 0.185265 | ||||||||
\(651\) | 2.34214e14 | 0.0785085 | ||||||||
\(652\) | 1.45006e15 | 0.481973 | ||||||||
\(653\) | −3.09019e15 | −1.01850 | −0.509252 | − | 0.860618i | \(-0.670078\pi\) | ||||
−0.509252 | + | 0.860618i | \(0.670078\pi\) | |||||||
\(654\) | −1.46504e15 | −0.478819 | ||||||||
\(655\) | −1.03287e15 | −0.334747 | ||||||||
\(656\) | −1.08098e14 | −0.0347413 | ||||||||
\(657\) | −9.94988e14 | −0.317109 | ||||||||
\(658\) | 1.40024e15 | 0.442549 | ||||||||
\(659\) | −1.36283e15 | −0.427141 | −0.213570 | − | 0.976928i | \(-0.568509\pi\) | ||||
−0.213570 | + | 0.976928i | \(0.568509\pi\) | |||||||
\(660\) | 1.70197e14 | 0.0529005 | ||||||||
\(661\) | 6.24406e15 | 1.92468 | 0.962341 | − | 0.271845i | \(-0.0876340\pi\) | ||||
0.962341 | + | 0.271845i | \(0.0876340\pi\) | |||||||
\(662\) | −3.16400e15 | −0.967204 | ||||||||
\(663\) | 4.20178e14 | 0.127382 | ||||||||
\(664\) | −2.11808e15 | −0.636821 | ||||||||
\(665\) | −2.29722e14 | −0.0684989 | ||||||||
\(666\) | 5.10462e14 | 0.150958 | ||||||||
\(667\) | −2.99069e15 | −0.877161 | ||||||||
\(668\) | −1.16307e15 | −0.338325 | ||||||||
\(669\) | 1.57725e15 | 0.455049 | ||||||||
\(670\) | −3.80265e14 | −0.108811 | ||||||||
\(671\) | −3.48825e15 | −0.989996 | ||||||||
\(672\) | −4.77272e14 | −0.134349 | ||||||||
\(673\) | 2.71811e15 | 0.758900 | 0.379450 | − | 0.925212i | \(-0.376113\pi\) | ||||
0.379450 | + | 0.925212i | \(0.376113\pi\) | |||||||
\(674\) | −1.28051e15 | −0.354613 | ||||||||
\(675\) | 5.68386e14 | 0.156125 | ||||||||
\(676\) | −9.09142e13 | −0.0247699 | ||||||||
\(677\) | −2.84608e15 | −0.769148 | −0.384574 | − | 0.923094i | \(-0.625652\pi\) | ||||
−0.384574 | + | 0.923094i | \(0.625652\pi\) | |||||||
\(678\) | 2.96980e15 | 0.796093 | ||||||||
\(679\) | 2.33591e15 | 0.621117 | ||||||||
\(680\) | −1.42637e15 | −0.376211 | ||||||||
\(681\) | 2.48285e15 | 0.649592 | ||||||||
\(682\) | −7.47583e14 | −0.194020 | ||||||||
\(683\) | −1.43943e15 | −0.370577 | −0.185288 | − | 0.982684i | \(-0.559322\pi\) | ||||
−0.185288 | + | 0.982684i | \(0.559322\pi\) | |||||||
\(684\) | 1.75325e14 | 0.0447750 | ||||||||
\(685\) | 9.85656e14 | 0.249705 | ||||||||
\(686\) | 1.76908e14 | 0.0444595 | ||||||||
\(687\) | 4.24696e15 | 1.05881 | ||||||||
\(688\) | −1.58243e15 | −0.391372 | ||||||||
\(689\) | −1.55034e15 | −0.380384 | ||||||||
\(690\) | 1.06938e15 | 0.260293 | ||||||||
\(691\) | −6.64085e14 | −0.160359 | −0.0801797 | − | 0.996780i | \(-0.525549\pi\) | ||||
−0.0801797 | + | 0.996780i | \(0.525549\pi\) | |||||||
\(692\) | 2.99788e14 | 0.0718176 | ||||||||
\(693\) | 3.47192e14 | 0.0825158 | ||||||||
\(694\) | 5.61158e15 | 1.32315 | ||||||||
\(695\) | −2.92108e15 | −0.683325 | ||||||||
\(696\) | 1.88473e15 | 0.437419 | ||||||||
\(697\) | 2.08991e14 | 0.0481224 | ||||||||
\(698\) | 2.77327e15 | 0.633558 | ||||||||
\(699\) | −4.78246e15 | −1.08399 | ||||||||
\(700\) | 4.39049e14 | 0.0987356 | ||||||||
\(701\) | −5.62068e15 | −1.25412 | −0.627061 | − | 0.778970i | \(-0.715742\pi\) | ||||
−0.627061 | + | 0.778970i | \(0.715742\pi\) | |||||||
\(702\) | 1.98524e14 | 0.0439499 | ||||||||
\(703\) | −1.04450e15 | −0.229431 | ||||||||
\(704\) | 3.24922e15 | 0.708157 | ||||||||
\(705\) | −1.64938e15 | −0.356682 | ||||||||
\(706\) | −2.54352e15 | −0.545769 | ||||||||
\(707\) | −3.09191e15 | −0.658294 | ||||||||
\(708\) | 8.27896e14 | 0.174901 | ||||||||
\(709\) | −2.48632e15 | −0.521199 | −0.260599 | − | 0.965447i | \(-0.583920\pi\) | ||||
−0.260599 | + | 0.965447i | \(0.583920\pi\) | |||||||
\(710\) | −1.76387e15 | −0.366898 | ||||||||
\(711\) | −2.15155e15 | −0.444088 | ||||||||
\(712\) | 3.71521e15 | 0.760928 | ||||||||
\(713\) | 2.23093e15 | 0.453412 | ||||||||
\(714\) | −7.08734e14 | −0.142937 | ||||||||
\(715\) | −3.94333e14 | −0.0789187 | ||||||||
\(716\) | 2.75859e15 | 0.547855 | ||||||||
\(717\) | 6.43800e14 | 0.126881 | ||||||||
\(718\) | −4.89347e15 | −0.957045 | ||||||||
\(719\) | −7.41628e14 | −0.143939 | −0.0719693 | − | 0.997407i | \(-0.522928\pi\) | ||||
−0.0719693 | + | 0.997407i | \(0.522928\pi\) | |||||||
\(720\) | −4.31808e14 | −0.0831692 | ||||||||
\(721\) | −3.02621e14 | −0.0578436 | ||||||||
\(722\) | −3.58543e15 | −0.680121 | ||||||||
\(723\) | −4.22525e15 | −0.795411 | ||||||||
\(724\) | 2.91401e15 | 0.544413 | ||||||||
\(725\) | −3.04527e15 | −0.564634 | ||||||||
\(726\) | 1.47527e15 | 0.271468 | ||||||||
\(727\) | 3.94395e15 | 0.720264 | 0.360132 | − | 0.932901i | \(-0.382732\pi\) | ||||
0.360132 | + | 0.932901i | \(0.382732\pi\) | |||||||
\(728\) | 6.29576e14 | 0.114111 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −1.90617e15 | −0.340319 | ||||||||
\(731\) | 3.05940e15 | 0.542114 | ||||||||
\(732\) | −1.59788e15 | −0.281018 | ||||||||
\(733\) | 5.50036e15 | 0.960107 | 0.480053 | − | 0.877239i | \(-0.340617\pi\) | ||||
0.480053 | + | 0.877239i | \(0.340617\pi\) | |||||||
\(734\) | 1.96657e15 | 0.340706 | ||||||||
\(735\) | −2.08385e14 | −0.0358332 | ||||||||
\(736\) | −4.54610e15 | −0.775910 | ||||||||
\(737\) | −1.17597e15 | −0.199217 | ||||||||
\(738\) | 9.87432e13 | 0.0166034 | ||||||||
\(739\) | −4.77070e15 | −0.796229 | −0.398114 | − | 0.917336i | \(-0.630335\pi\) | ||||
−0.398114 | + | 0.917336i | \(0.630335\pi\) | |||||||
\(740\) | −4.64463e14 | −0.0769444 | ||||||||
\(741\) | −4.06215e14 | −0.0667968 | ||||||||
\(742\) | 2.61504e15 | 0.426831 | ||||||||
\(743\) | −1.04075e16 | −1.68619 | −0.843096 | − | 0.537763i | \(-0.819270\pi\) | ||||
−0.843096 | + | 0.537763i | \(0.819270\pi\) | |||||||
\(744\) | −1.40593e15 | −0.226106 | ||||||||
\(745\) | 3.51519e15 | 0.561163 | ||||||||
\(746\) | 9.80798e14 | 0.155423 | ||||||||
\(747\) | 1.23969e15 | 0.195007 | ||||||||
\(748\) | −1.07442e15 | −0.167771 | ||||||||
\(749\) | 3.22724e15 | 0.500243 | ||||||||
\(750\) | 2.43114e15 | 0.374088 | ||||||||
\(751\) | −4.26891e15 | −0.652074 | −0.326037 | − | 0.945357i | \(-0.605713\pi\) | ||||
−0.326037 | + | 0.945357i | \(0.605713\pi\) | |||||||
\(752\) | −5.38562e15 | −0.816653 | ||||||||
\(753\) | 1.11561e14 | 0.0167935 | ||||||||
\(754\) | −1.06364e15 | −0.158947 | ||||||||
\(755\) | −5.52853e15 | −0.820166 | ||||||||
\(756\) | 1.59040e14 | 0.0234227 | ||||||||
\(757\) | −1.13376e16 | −1.65765 | −0.828825 | − | 0.559508i | \(-0.810990\pi\) | ||||
−0.828825 | + | 0.559508i | \(0.810990\pi\) | |||||||
\(758\) | −8.11752e14 | −0.117826 | ||||||||
\(759\) | 3.30707e15 | 0.476556 | ||||||||
\(760\) | 1.37897e15 | 0.197278 | ||||||||
\(761\) | −2.83667e15 | −0.402896 | −0.201448 | − | 0.979499i | \(-0.564565\pi\) | ||||
−0.201448 | + | 0.979499i | \(0.564565\pi\) | |||||||
\(762\) | −4.27441e15 | −0.602731 | ||||||||
\(763\) | 2.71929e15 | 0.380690 | ||||||||
\(764\) | 1.57333e15 | 0.218679 | ||||||||
\(765\) | 8.34837e14 | 0.115203 | ||||||||
\(766\) | 8.41339e15 | 1.15269 | ||||||||
\(767\) | −1.91817e15 | −0.260924 | ||||||||
\(768\) | 3.65551e15 | 0.493697 | ||||||||
\(769\) | −6.87447e15 | −0.921816 | −0.460908 | − | 0.887448i | \(-0.652476\pi\) | ||||
−0.460908 | + | 0.887448i | \(0.652476\pi\) | |||||||
\(770\) | 6.65141e14 | 0.0885553 | ||||||||
\(771\) | −6.21309e15 | −0.821312 | ||||||||
\(772\) | 1.08568e15 | 0.142498 | ||||||||
\(773\) | 3.05904e15 | 0.398656 | 0.199328 | − | 0.979933i | \(-0.436124\pi\) | ||||
0.199328 | + | 0.979933i | \(0.436124\pi\) | |||||||
\(774\) | 1.44549e15 | 0.187043 | ||||||||
\(775\) | 2.27164e15 | 0.291864 | ||||||||
\(776\) | −1.40219e16 | −1.78883 | ||||||||
\(777\) | −9.47480e14 | −0.120020 | ||||||||
\(778\) | −1.77234e15 | −0.222925 | ||||||||
\(779\) | −2.02046e14 | −0.0252345 | ||||||||
\(780\) | −1.80635e14 | −0.0224017 | ||||||||
\(781\) | −5.45478e15 | −0.671733 | ||||||||
\(782\) | −6.75083e15 | −0.825506 | ||||||||
\(783\) | −1.10311e15 | −0.133946 | ||||||||
\(784\) | −6.80424e14 | −0.0820430 | ||||||||
\(785\) | 2.46638e15 | 0.295310 | ||||||||
\(786\) | 3.08069e15 | 0.366289 | ||||||||
\(787\) | 1.15821e16 | 1.36749 | 0.683745 | − | 0.729721i | \(-0.260350\pi\) | ||||
0.683745 | + | 0.729721i | \(0.260350\pi\) | |||||||
\(788\) | 2.77075e15 | 0.324865 | ||||||||
\(789\) | −2.23430e14 | −0.0260146 | ||||||||
\(790\) | −4.12188e15 | −0.476591 | ||||||||
\(791\) | −5.51232e15 | −0.632942 | ||||||||
\(792\) | −2.08411e15 | −0.237647 | ||||||||
\(793\) | 3.70218e15 | 0.419232 | ||||||||
\(794\) | 5.41385e15 | 0.608827 | ||||||||
\(795\) | −3.08032e15 | −0.344015 | ||||||||
\(796\) | 4.24367e15 | 0.470674 | ||||||||
\(797\) | −1.48374e16 | −1.63431 | −0.817157 | − | 0.576415i | \(-0.804451\pi\) | ||||
−0.817157 | + | 0.576415i | \(0.804451\pi\) | |||||||
\(798\) | 6.85183e14 | 0.0749532 | ||||||||
\(799\) | 1.04123e16 | 1.13120 | ||||||||
\(800\) | −4.62907e15 | −0.499458 | ||||||||
\(801\) | −2.17448e15 | −0.233011 | ||||||||
\(802\) | 2.39318e14 | 0.0254693 | ||||||||
\(803\) | −5.89485e15 | −0.623070 | ||||||||
\(804\) | −5.38684e14 | −0.0565492 | ||||||||
\(805\) | −1.98490e15 | −0.206949 | ||||||||
\(806\) | 7.93431e14 | 0.0821612 | ||||||||
\(807\) | −1.10541e15 | −0.113689 | ||||||||
\(808\) | 1.85600e16 | 1.89590 | ||||||||
\(809\) | −6.62670e15 | −0.672327 | −0.336163 | − | 0.941804i | \(-0.609129\pi\) | ||||
−0.336163 | + | 0.941804i | \(0.609129\pi\) | |||||||
\(810\) | 3.94440e14 | 0.0397478 | ||||||||
\(811\) | 6.81374e15 | 0.681979 | 0.340990 | − | 0.940067i | \(-0.389238\pi\) | ||||
0.340990 | + | 0.940067i | \(0.389238\pi\) | |||||||
\(812\) | −8.52099e14 | −0.0847094 | ||||||||
\(813\) | −9.74837e15 | −0.962574 | ||||||||
\(814\) | 3.02425e15 | 0.296608 | ||||||||
\(815\) | −6.67522e15 | −0.650277 | ||||||||
\(816\) | 2.72594e15 | 0.263767 | ||||||||
\(817\) | −2.95774e15 | −0.284275 | ||||||||
\(818\) | −8.41329e15 | −0.803198 | ||||||||
\(819\) | −3.68485e14 | −0.0349428 | ||||||||
\(820\) | −8.98453e13 | −0.00846290 | ||||||||
\(821\) | 1.09253e16 | 1.02222 | 0.511110 | − | 0.859515i | \(-0.329234\pi\) | ||||
0.511110 | + | 0.859515i | \(0.329234\pi\) | |||||||
\(822\) | −2.93988e15 | −0.273234 | ||||||||
\(823\) | −1.18483e16 | −1.09384 | −0.546922 | − | 0.837183i | \(-0.684201\pi\) | ||||
−0.546922 | + | 0.837183i | \(0.684201\pi\) | |||||||
\(824\) | 1.81656e15 | 0.166591 | ||||||||
\(825\) | 3.36742e15 | 0.306762 | ||||||||
\(826\) | 3.23548e15 | 0.292784 | ||||||||
\(827\) | −8.89785e15 | −0.799843 | −0.399922 | − | 0.916549i | \(-0.630963\pi\) | ||||
−0.399922 | + | 0.916549i | \(0.630963\pi\) | |||||||
\(828\) | 1.51489e15 | 0.135274 | ||||||||
\(829\) | −5.95278e15 | −0.528043 | −0.264022 | − | 0.964517i | \(-0.585049\pi\) | ||||
−0.264022 | + | 0.964517i | \(0.585049\pi\) | |||||||
\(830\) | 2.37496e15 | 0.209280 | ||||||||
\(831\) | 7.15669e15 | 0.626479 | ||||||||
\(832\) | −3.44849e15 | −0.299882 | ||||||||
\(833\) | 1.31550e15 | 0.113643 | ||||||||
\(834\) | 8.71260e15 | 0.747712 | ||||||||
\(835\) | 5.35409e15 | 0.456467 | ||||||||
\(836\) | 1.03872e15 | 0.0879760 | ||||||||
\(837\) | 8.22876e14 | 0.0692380 | ||||||||
\(838\) | −8.13314e15 | −0.679855 | ||||||||
\(839\) | 2.17822e16 | 1.80888 | 0.904442 | − | 0.426596i | \(-0.140287\pi\) | ||||
0.904442 | + | 0.426596i | \(0.140287\pi\) | |||||||
\(840\) | 1.25088e15 | 0.103200 | ||||||||
\(841\) | −6.29030e15 | −0.515577 | ||||||||
\(842\) | −1.11909e16 | −0.911270 | ||||||||
\(843\) | −6.43692e15 | −0.520747 | ||||||||
\(844\) | 3.18937e15 | 0.256343 | ||||||||
\(845\) | 4.18517e14 | 0.0334196 | ||||||||
\(846\) | 4.91955e15 | 0.390291 | ||||||||
\(847\) | −2.73828e15 | −0.215834 | ||||||||
\(848\) | −1.00580e16 | −0.787649 | ||||||||
\(849\) | 1.08366e15 | 0.0843141 | ||||||||
\(850\) | −6.87403e15 | −0.531383 | ||||||||
\(851\) | −9.02493e15 | −0.693157 | ||||||||
\(852\) | −2.49870e15 | −0.190676 | ||||||||
\(853\) | 2.15102e16 | 1.63089 | 0.815446 | − | 0.578834i | \(-0.196492\pi\) | ||||
0.815446 | + | 0.578834i | \(0.196492\pi\) | |||||||
\(854\) | −6.24464e15 | −0.470423 | ||||||||
\(855\) | −8.07095e14 | −0.0604103 | ||||||||
\(856\) | −1.93723e16 | −1.44071 | ||||||||
\(857\) | 1.11459e16 | 0.823607 | 0.411803 | − | 0.911273i | \(-0.364899\pi\) | ||||
0.411803 | + | 0.911273i | \(0.364899\pi\) | |||||||
\(858\) | 1.17616e15 | 0.0863549 | ||||||||
\(859\) | 9.59422e15 | 0.699918 | 0.349959 | − | 0.936765i | \(-0.386196\pi\) | ||||
0.349959 | + | 0.936765i | \(0.386196\pi\) | |||||||
\(860\) | −1.31524e15 | −0.0953372 | ||||||||
\(861\) | −1.83280e14 | −0.0132007 | ||||||||
\(862\) | 2.08963e16 | 1.49547 | ||||||||
\(863\) | −1.35396e16 | −0.962826 | −0.481413 | − | 0.876494i | \(-0.659876\pi\) | ||||
−0.481413 | + | 0.876494i | \(0.659876\pi\) | |||||||
\(864\) | −1.67683e15 | −0.118485 | ||||||||
\(865\) | −1.38005e15 | −0.0968961 | ||||||||
\(866\) | 1.36473e16 | 0.952132 | ||||||||
\(867\) | 3.05788e15 | 0.211990 | ||||||||
\(868\) | 6.35630e14 | 0.0437871 | ||||||||
\(869\) | −1.27469e16 | −0.872564 | ||||||||
\(870\) | −2.11331e15 | −0.143750 | ||||||||
\(871\) | 1.24809e15 | 0.0843619 | ||||||||
\(872\) | −1.63233e16 | −1.09639 | ||||||||
\(873\) | 8.20690e15 | 0.547773 | ||||||||
\(874\) | 6.52650e15 | 0.432880 | ||||||||
\(875\) | −4.51251e15 | −0.297422 | ||||||||
\(876\) | −2.70029e15 | −0.176863 | ||||||||
\(877\) | 1.04172e16 | 0.678034 | 0.339017 | − | 0.940780i | \(-0.389906\pi\) | ||||
0.339017 | + | 0.940780i | \(0.389906\pi\) | |||||||
\(878\) | −1.27031e16 | −0.821658 | ||||||||
\(879\) | 1.33288e16 | 0.856746 | ||||||||
\(880\) | −2.55827e15 | −0.163415 | ||||||||
\(881\) | −1.25439e16 | −0.796278 | −0.398139 | − | 0.917325i | \(-0.630344\pi\) | ||||
−0.398139 | + | 0.917325i | \(0.630344\pi\) | |||||||
\(882\) | 6.21541e14 | 0.0392096 | ||||||||
\(883\) | −3.98189e15 | −0.249635 | −0.124817 | − | 0.992180i | \(-0.539834\pi\) | ||||
−0.124817 | + | 0.992180i | \(0.539834\pi\) | |||||||
\(884\) | 1.14032e15 | 0.0710457 | ||||||||
\(885\) | −3.81116e15 | −0.235976 | ||||||||
\(886\) | −1.39791e15 | −0.0860188 | ||||||||
\(887\) | −3.03520e16 | −1.85612 | −0.928061 | − | 0.372427i | \(-0.878526\pi\) | ||||
−0.928061 | + | 0.372427i | \(0.878526\pi\) | |||||||
\(888\) | 5.68750e15 | 0.345661 | ||||||||
\(889\) | 7.93383e15 | 0.479207 | ||||||||
\(890\) | −4.16580e15 | −0.250065 | ||||||||
\(891\) | 1.21981e15 | 0.0727721 | ||||||||
\(892\) | 4.28049e15 | 0.253797 | ||||||||
\(893\) | −1.00663e16 | −0.593180 | ||||||||
\(894\) | −1.04846e16 | −0.614039 | ||||||||
\(895\) | −1.26990e16 | −0.739165 | ||||||||
\(896\) | 1.79429e15 | 0.103801 | ||||||||
\(897\) | −3.50989e15 | −0.201806 | ||||||||
\(898\) | −2.42202e16 | −1.38407 | ||||||||
\(899\) | −4.40876e15 | −0.250402 | ||||||||
\(900\) | 1.54254e15 | 0.0870766 | ||||||||
\(901\) | 1.94456e16 | 1.09102 | ||||||||
\(902\) | 5.85008e14 | 0.0326231 | ||||||||
\(903\) | −2.68301e15 | −0.148710 | ||||||||
\(904\) | 3.30891e16 | 1.82288 | ||||||||
\(905\) | −1.34144e16 | −0.734522 | ||||||||
\(906\) | 1.64897e16 | 0.897447 | ||||||||
\(907\) | −2.77273e16 | −1.49992 | −0.749959 | − | 0.661484i | \(-0.769927\pi\) | ||||
−0.749959 | + | 0.661484i | \(0.769927\pi\) | |||||||
\(908\) | 6.73817e15 | 0.362301 | ||||||||
\(909\) | −1.08630e16 | −0.580561 | ||||||||
\(910\) | −7.05932e14 | −0.0375004 | ||||||||
\(911\) | −1.34276e16 | −0.709002 | −0.354501 | − | 0.935056i | \(-0.615349\pi\) | ||||
−0.354501 | + | 0.935056i | \(0.615349\pi\) | |||||||
\(912\) | −2.63535e15 | −0.138314 | ||||||||
\(913\) | 7.34459e15 | 0.383158 | ||||||||
\(914\) | −2.46524e16 | −1.27836 | ||||||||
\(915\) | 7.35573e15 | 0.379149 | ||||||||
\(916\) | 1.15258e16 | 0.590534 | ||||||||
\(917\) | −5.71814e15 | −0.291221 | ||||||||
\(918\) | −2.49004e15 | −0.126058 | ||||||||
\(919\) | 1.05159e16 | 0.529187 | 0.264594 | − | 0.964360i | \(-0.414762\pi\) | ||||
0.264594 | + | 0.964360i | \(0.414762\pi\) | |||||||
\(920\) | 1.19149e16 | 0.596016 | ||||||||
\(921\) | 2.09541e16 | 1.04194 | ||||||||
\(922\) | 4.44655e15 | 0.219788 | ||||||||
\(923\) | 5.78931e15 | 0.284458 | ||||||||
\(924\) | 9.42241e14 | 0.0460221 | ||||||||
\(925\) | −9.18963e15 | −0.446189 | ||||||||
\(926\) | −6.76307e15 | −0.326425 | ||||||||
\(927\) | −1.06322e15 | −0.0510132 | ||||||||
\(928\) | 8.98401e15 | 0.428506 | ||||||||
\(929\) | 1.11643e15 | 0.0529354 | 0.0264677 | − | 0.999650i | \(-0.491574\pi\) | ||||
0.0264677 | + | 0.999650i | \(0.491574\pi\) | |||||||
\(930\) | 1.57644e15 | 0.0743056 | ||||||||
\(931\) | −1.27178e15 | −0.0595923 | ||||||||
\(932\) | −1.29791e16 | −0.604583 | ||||||||
\(933\) | 1.59028e16 | 0.736418 | ||||||||
\(934\) | −2.41186e16 | −1.11031 | ||||||||
\(935\) | 4.94603e15 | 0.226356 | ||||||||
\(936\) | 2.21193e15 | 0.100636 | ||||||||
\(937\) | 3.32493e16 | 1.50389 | 0.751943 | − | 0.659229i | \(-0.229117\pi\) | ||||
0.751943 | + | 0.659229i | \(0.229117\pi\) | |||||||
\(938\) | −2.10522e15 | −0.0946632 | ||||||||
\(939\) | 1.50582e16 | 0.673150 | ||||||||
\(940\) | −4.47625e15 | −0.198935 | ||||||||
\(941\) | −5.82322e15 | −0.257289 | −0.128644 | − | 0.991691i | \(-0.541063\pi\) | ||||
−0.128644 | + | 0.991691i | \(0.541063\pi\) | |||||||
\(942\) | −7.35639e15 | −0.323136 | ||||||||
\(943\) | −1.74577e15 | −0.0762384 | ||||||||
\(944\) | −1.24443e16 | −0.540287 | ||||||||
\(945\) | −7.32130e14 | −0.0316019 | ||||||||
\(946\) | 8.56388e15 | 0.367510 | ||||||||
\(947\) | 2.20671e16 | 0.941499 | 0.470750 | − | 0.882267i | \(-0.343984\pi\) | ||||
0.470750 | + | 0.882267i | \(0.343984\pi\) | |||||||
\(948\) | −5.83907e15 | −0.247684 | ||||||||
\(949\) | 6.25637e15 | 0.263851 | ||||||||
\(950\) | 6.64560e15 | 0.278647 | ||||||||
\(951\) | −1.87033e16 | −0.779698 | ||||||||
\(952\) | −7.89663e15 | −0.327294 | ||||||||
\(953\) | 1.18910e16 | 0.490011 | 0.245005 | − | 0.969522i | \(-0.421210\pi\) | ||||
0.245005 | + | 0.969522i | \(0.421210\pi\) | |||||||
\(954\) | 9.18756e15 | 0.376430 | ||||||||
\(955\) | −7.24271e15 | −0.295041 | ||||||||
\(956\) | 1.74720e15 | 0.0707660 | ||||||||
\(957\) | −6.53544e15 | −0.263184 | ||||||||
\(958\) | 3.18399e16 | 1.27486 | ||||||||
\(959\) | 5.45678e15 | 0.217237 | ||||||||
\(960\) | −6.85169e15 | −0.271210 | ||||||||
\(961\) | −2.21197e16 | −0.870565 | ||||||||
\(962\) | −3.20972e15 | −0.125604 | ||||||||
\(963\) | 1.13384e16 | 0.441173 | ||||||||
\(964\) | −1.14669e16 | −0.443630 | ||||||||
\(965\) | −4.99786e15 | −0.192258 | ||||||||
\(966\) | 5.92030e15 | 0.226448 | ||||||||
\(967\) | −4.59256e16 | −1.74666 | −0.873332 | − | 0.487126i | \(-0.838045\pi\) | ||||
−0.873332 | + | 0.487126i | \(0.838045\pi\) | |||||||
\(968\) | 1.64372e16 | 0.621605 | ||||||||
\(969\) | 5.09506e15 | 0.191588 | ||||||||
\(970\) | 1.57225e16 | 0.587866 | ||||||||
\(971\) | 3.49556e16 | 1.29960 | 0.649802 | − | 0.760103i | \(-0.274852\pi\) | ||||
0.649802 | + | 0.760103i | \(0.274852\pi\) | |||||||
\(972\) | 5.58766e14 | 0.0206569 | ||||||||
\(973\) | −1.61717e16 | −0.594476 | ||||||||
\(974\) | 2.54141e16 | 0.928966 | ||||||||
\(975\) | −3.57394e15 | −0.129904 | ||||||||
\(976\) | 2.40181e16 | 0.868091 | ||||||||
\(977\) | 2.00159e16 | 0.719376 | 0.359688 | − | 0.933073i | \(-0.382883\pi\) | ||||
0.359688 | + | 0.933073i | \(0.382883\pi\) | |||||||
\(978\) | 1.99099e16 | 0.711550 | ||||||||
\(979\) | −1.28828e16 | −0.457830 | ||||||||
\(980\) | −5.65533e14 | −0.0199855 | ||||||||
\(981\) | 9.55385e15 | 0.335737 | ||||||||
\(982\) | 3.87214e16 | 1.35313 | ||||||||
\(983\) | 2.88215e14 | 0.0100155 | 0.00500774 | − | 0.999987i | \(-0.498406\pi\) | ||||
0.00500774 | + | 0.999987i | \(0.498406\pi\) | |||||||
\(984\) | 1.10018e15 | 0.0380183 | ||||||||
\(985\) | −1.27549e16 | −0.438307 | ||||||||
\(986\) | 1.33410e16 | 0.455895 | ||||||||
\(987\) | −9.13131e15 | −0.310305 | ||||||||
\(988\) | −1.10242e15 | −0.0372550 | ||||||||
\(989\) | −2.55562e16 | −0.858849 | ||||||||
\(990\) | 2.33688e15 | 0.0780984 | ||||||||
\(991\) | −2.39038e16 | −0.794440 | −0.397220 | − | 0.917723i | \(-0.630025\pi\) | ||||
−0.397220 | + | 0.917723i | \(0.630025\pi\) | |||||||
\(992\) | −6.70170e15 | −0.221498 | ||||||||
\(993\) | 2.06332e16 | 0.678181 | ||||||||
\(994\) | −9.76511e15 | −0.319192 | ||||||||
\(995\) | −1.95354e16 | −0.635032 | ||||||||
\(996\) | 3.36438e15 | 0.108762 | ||||||||
\(997\) | 7.30428e15 | 0.234830 | 0.117415 | − | 0.993083i | \(-0.462539\pi\) | ||||
0.117415 | + | 0.993083i | \(0.462539\pi\) | |||||||
\(998\) | 4.99695e16 | 1.59767 | ||||||||
\(999\) | −3.32884e15 | −0.105848 |
(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 | 273.12.a.c.1.12 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.12.a.c.1.12 | ✓ | 16 | 1.1 | even | 1 | trivial |