Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + 45662797046 x^{5} + 1825619566875 x^{4} + \cdots + 245077910606835 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-31.5756\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −30.5756 | −1.35126 | −0.675631 | − | 0.737240i | \(-0.736129\pi\) | ||||
−0.675631 | + | 0.737240i | \(0.736129\pi\) | |||||||
\(3\) | 194.921 | 1.38935 | 0.694676 | − | 0.719322i | \(-0.255548\pi\) | ||||
0.694676 | + | 0.719322i | \(0.255548\pi\) | |||||||
\(4\) | 422.865 | 0.825909 | ||||||||
\(5\) | −941.135 | −0.673421 | −0.336711 | − | 0.941608i | \(-0.609314\pi\) | ||||
−0.336711 | + | 0.941608i | \(0.609314\pi\) | |||||||
\(6\) | −5959.81 | −1.87738 | ||||||||
\(7\) | 4513.44 | 0.710504 | 0.355252 | − | 0.934771i | \(-0.384395\pi\) | ||||
0.355252 | + | 0.934771i | \(0.384395\pi\) | |||||||
\(8\) | 2725.35 | 0.235243 | ||||||||
\(9\) | 18311.1 | 0.930301 | ||||||||
\(10\) | 28775.7 | 0.909968 | ||||||||
\(11\) | −41597.1 | −0.856635 | −0.428317 | − | 0.903628i | \(-0.640894\pi\) | ||||
−0.428317 | + | 0.903628i | \(0.640894\pi\) | |||||||
\(12\) | 82425.2 | 1.14748 | ||||||||
\(13\) | 101290. | 0.983602 | 0.491801 | − | 0.870708i | \(-0.336339\pi\) | ||||
0.491801 | + | 0.870708i | \(0.336339\pi\) | |||||||
\(14\) | −138001. | −0.960077 | ||||||||
\(15\) | −183447. | −0.935620 | ||||||||
\(16\) | −299836. | −1.14378 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −559873. | −1.25708 | ||||||||
\(19\) | 878675. | 1.54681 | 0.773405 | − | 0.633912i | \(-0.218552\pi\) | ||||
0.773405 | + | 0.633912i | \(0.218552\pi\) | |||||||
\(20\) | −397973. | −0.556184 | ||||||||
\(21\) | 879763. | 0.987140 | ||||||||
\(22\) | 1.27185e6 | 1.15754 | ||||||||
\(23\) | 1.58058e6 | 1.17772 | 0.588860 | − | 0.808235i | \(-0.299577\pi\) | ||||
0.588860 | + | 0.808235i | \(0.299577\pi\) | |||||||
\(24\) | 531227. | 0.326836 | ||||||||
\(25\) | −1.06739e6 | −0.546504 | ||||||||
\(26\) | −3.09699e6 | −1.32910 | ||||||||
\(27\) | −267410. | −0.0968367 | ||||||||
\(28\) | 1.90858e6 | 0.586811 | ||||||||
\(29\) | −1.94618e6 | −0.510966 | −0.255483 | − | 0.966814i | \(-0.582234\pi\) | ||||
−0.255483 | + | 0.966814i | \(0.582234\pi\) | |||||||
\(30\) | 5.60899e6 | 1.26427 | ||||||||
\(31\) | 4.44805e6 | 0.865051 | 0.432525 | − | 0.901622i | \(-0.357623\pi\) | ||||
0.432525 | + | 0.901622i | \(0.357623\pi\) | |||||||
\(32\) | 7.77228e6 | 1.31031 | ||||||||
\(33\) | −8.10814e6 | −1.19017 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.24775e6 | −0.478468 | ||||||||
\(36\) | 7.74313e6 | 0.768344 | ||||||||
\(37\) | −9.92035e6 | −0.870200 | −0.435100 | − | 0.900382i | \(-0.643287\pi\) | ||||
−0.435100 | + | 0.900382i | \(0.643287\pi\) | |||||||
\(38\) | −2.68660e7 | −2.09015 | ||||||||
\(39\) | 1.97434e7 | 1.36657 | ||||||||
\(40\) | −2.56492e6 | −0.158418 | ||||||||
\(41\) | 3.03121e7 | 1.67528 | 0.837642 | − | 0.546220i | \(-0.183934\pi\) | ||||
0.837642 | + | 0.546220i | \(0.183934\pi\) | |||||||
\(42\) | −2.68993e7 | −1.33389 | ||||||||
\(43\) | −4.15989e7 | −1.85555 | −0.927777 | − | 0.373135i | \(-0.878283\pi\) | ||||
−0.927777 | + | 0.373135i | \(0.878283\pi\) | |||||||
\(44\) | −1.75900e7 | −0.707502 | ||||||||
\(45\) | −1.72332e7 | −0.626484 | ||||||||
\(46\) | −4.83272e7 | −1.59141 | ||||||||
\(47\) | 2.96697e7 | 0.886897 | 0.443449 | − | 0.896300i | \(-0.353755\pi\) | ||||
0.443449 | + | 0.896300i | \(0.353755\pi\) | |||||||
\(48\) | −5.84443e7 | −1.58912 | ||||||||
\(49\) | −1.99825e7 | −0.495184 | ||||||||
\(50\) | 3.26361e7 | 0.738470 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.28318e7 | 0.812366 | ||||||||
\(53\) | −1.85086e7 | −0.322204 | −0.161102 | − | 0.986938i | \(-0.551505\pi\) | ||||
−0.161102 | + | 0.986938i | \(0.551505\pi\) | |||||||
\(54\) | 8.17620e6 | 0.130852 | ||||||||
\(55\) | 3.91485e7 | 0.576876 | ||||||||
\(56\) | 1.23007e7 | 0.167141 | ||||||||
\(57\) | 1.71272e8 | 2.14907 | ||||||||
\(58\) | 5.95055e7 | 0.690448 | ||||||||
\(59\) | 3.51354e7 | 0.377495 | 0.188747 | − | 0.982026i | \(-0.439557\pi\) | ||||
0.188747 | + | 0.982026i | \(0.439557\pi\) | |||||||
\(60\) | −7.75732e7 | −0.772736 | ||||||||
\(61\) | 1.88656e8 | 1.74456 | 0.872279 | − | 0.489009i | \(-0.162641\pi\) | ||||
0.872279 | + | 0.489009i | \(0.162641\pi\) | |||||||
\(62\) | −1.36002e8 | −1.16891 | ||||||||
\(63\) | 8.26461e7 | 0.660982 | ||||||||
\(64\) | −8.41258e7 | −0.626786 | ||||||||
\(65\) | −9.53271e7 | −0.662379 | ||||||||
\(66\) | 2.47911e8 | 1.60823 | ||||||||
\(67\) | 2.08556e8 | 1.26440 | 0.632201 | − | 0.774804i | \(-0.282152\pi\) | ||||
0.632201 | + | 0.774804i | \(0.282152\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.08088e8 | 1.63627 | ||||||||
\(70\) | 1.29878e8 | 0.646536 | ||||||||
\(71\) | −4.89810e7 | −0.228752 | −0.114376 | − | 0.993438i | \(-0.536487\pi\) | ||||
−0.114376 | + | 0.993438i | \(0.536487\pi\) | |||||||
\(72\) | 4.99041e7 | 0.218847 | ||||||||
\(73\) | −1.30289e8 | −0.536978 | −0.268489 | − | 0.963283i | \(-0.586524\pi\) | ||||
−0.268489 | + | 0.963283i | \(0.586524\pi\) | |||||||
\(74\) | 3.03320e8 | 1.17587 | ||||||||
\(75\) | −2.08057e8 | −0.759287 | ||||||||
\(76\) | 3.71561e8 | 1.27752 | ||||||||
\(77\) | −1.87746e8 | −0.608642 | ||||||||
\(78\) | −6.03667e8 | −1.84659 | ||||||||
\(79\) | −2.59845e8 | −0.750571 | −0.375286 | − | 0.926909i | \(-0.622455\pi\) | ||||
−0.375286 | + | 0.926909i | \(0.622455\pi\) | |||||||
\(80\) | 2.82186e8 | 0.770248 | ||||||||
\(81\) | −4.12541e8 | −1.06484 | ||||||||
\(82\) | −9.26809e8 | −2.26375 | ||||||||
\(83\) | 4.12715e8 | 0.954550 | 0.477275 | − | 0.878754i | \(-0.341625\pi\) | ||||
0.477275 | + | 0.878754i | \(0.341625\pi\) | |||||||
\(84\) | 3.72021e8 | 0.815288 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.27191e9 | 2.50734 | ||||||||
\(87\) | −3.79351e8 | −0.709912 | ||||||||
\(88\) | −1.13366e8 | −0.201517 | ||||||||
\(89\) | 1.05219e9 | 1.77763 | 0.888815 | − | 0.458267i | \(-0.151530\pi\) | ||||
0.888815 | + | 0.458267i | \(0.151530\pi\) | |||||||
\(90\) | 5.26916e8 | 0.846544 | ||||||||
\(91\) | 4.57164e8 | 0.698853 | ||||||||
\(92\) | 6.68373e8 | 0.972689 | ||||||||
\(93\) | 8.67017e8 | 1.20186 | ||||||||
\(94\) | −9.07169e8 | −1.19843 | ||||||||
\(95\) | −8.26952e8 | −1.04166 | ||||||||
\(96\) | 1.51498e9 | 1.82048 | ||||||||
\(97\) | −1.29676e9 | −1.48726 | −0.743628 | − | 0.668594i | \(-0.766896\pi\) | ||||
−0.743628 | + | 0.668594i | \(0.766896\pi\) | |||||||
\(98\) | 6.10975e8 | 0.669124 | ||||||||
\(99\) | −7.61689e8 | −0.796928 | ||||||||
\(100\) | −4.51362e8 | −0.451362 | ||||||||
\(101\) | 5.40379e8 | 0.516717 | 0.258358 | − | 0.966049i | \(-0.416818\pi\) | ||||
0.258358 | + | 0.966049i | \(0.416818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.13430e9 | −1.86848 | −0.934238 | − | 0.356649i | \(-0.883919\pi\) | ||||
−0.934238 | + | 0.356649i | \(0.883919\pi\) | |||||||
\(104\) | 2.76049e8 | 0.231386 | ||||||||
\(105\) | −8.27976e8 | −0.664761 | ||||||||
\(106\) | 5.65910e8 | 0.435382 | ||||||||
\(107\) | 5.12879e6 | 0.00378258 | 0.00189129 | − | 0.999998i | \(-0.499398\pi\) | ||||
0.00189129 | + | 0.999998i | \(0.499398\pi\) | |||||||
\(108\) | −1.13078e8 | −0.0799783 | ||||||||
\(109\) | −4.25009e8 | −0.288389 | −0.144195 | − | 0.989549i | \(-0.546059\pi\) | ||||
−0.144195 | + | 0.989549i | \(0.546059\pi\) | |||||||
\(110\) | −1.19699e9 | −0.779511 | ||||||||
\(111\) | −1.93368e9 | −1.20902 | ||||||||
\(112\) | −1.35329e9 | −0.812663 | ||||||||
\(113\) | −7.28636e8 | −0.420395 | −0.210197 | − | 0.977659i | \(-0.567411\pi\) | ||||
−0.210197 | + | 0.977659i | \(0.567411\pi\) | |||||||
\(114\) | −5.23674e9 | −2.90395 | ||||||||
\(115\) | −1.48754e9 | −0.793101 | ||||||||
\(116\) | −8.22971e8 | −0.422011 | ||||||||
\(117\) | 1.85472e9 | 0.915046 | ||||||||
\(118\) | −1.07429e9 | −0.510095 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.99956e8 | −0.220098 | ||||||||
\(121\) | −6.27630e8 | −0.266177 | ||||||||
\(122\) | −5.76825e9 | −2.35735 | ||||||||
\(123\) | 5.90845e9 | 2.32756 | ||||||||
\(124\) | 1.88092e9 | 0.714453 | ||||||||
\(125\) | 2.84271e9 | 1.04145 | ||||||||
\(126\) | −2.52695e9 | −0.893160 | ||||||||
\(127\) | −2.52131e9 | −0.860022 | −0.430011 | − | 0.902824i | \(-0.641490\pi\) | ||||
−0.430011 | + | 0.902824i | \(0.641490\pi\) | |||||||
\(128\) | −1.40721e9 | −0.463356 | ||||||||
\(129\) | −8.10849e9 | −2.57802 | ||||||||
\(130\) | 2.91468e9 | 0.895047 | ||||||||
\(131\) | 5.51873e9 | 1.63726 | 0.818631 | − | 0.574320i | \(-0.194733\pi\) | ||||
0.818631 | + | 0.574320i | \(0.194733\pi\) | |||||||
\(132\) | −3.42865e9 | −0.982970 | ||||||||
\(133\) | 3.96585e9 | 1.09902 | ||||||||
\(134\) | −6.37671e9 | −1.70854 | ||||||||
\(135\) | 2.51668e8 | 0.0652119 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.40891e8 | 0.228190 | 0.114095 | − | 0.993470i | \(-0.463603\pi\) | ||||
0.114095 | + | 0.993470i | \(0.463603\pi\) | |||||||
\(138\) | −9.41998e9 | −2.21103 | ||||||||
\(139\) | −8.97314e8 | −0.203881 | −0.101941 | − | 0.994790i | \(-0.532505\pi\) | ||||
−0.101941 | + | 0.994790i | \(0.532505\pi\) | |||||||
\(140\) | −1.79623e9 | −0.395171 | ||||||||
\(141\) | 5.78325e9 | 1.23221 | ||||||||
\(142\) | 1.49762e9 | 0.309104 | ||||||||
\(143\) | −4.21335e9 | −0.842588 | ||||||||
\(144\) | −5.49033e9 | −1.06406 | ||||||||
\(145\) | 1.83162e9 | 0.344095 | ||||||||
\(146\) | 3.98367e9 | 0.725598 | ||||||||
\(147\) | −3.89500e9 | −0.687986 | ||||||||
\(148\) | −4.19497e9 | −0.718706 | ||||||||
\(149\) | −1.30561e9 | −0.217009 | −0.108504 | − | 0.994096i | \(-0.534606\pi\) | ||||
−0.108504 | + | 0.994096i | \(0.534606\pi\) | |||||||
\(150\) | 6.36145e9 | 1.02599 | ||||||||
\(151\) | −6.19193e9 | −0.969236 | −0.484618 | − | 0.874726i | \(-0.661041\pi\) | ||||
−0.484618 | + | 0.874726i | \(0.661041\pi\) | |||||||
\(152\) | 2.39469e9 | 0.363876 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.74044e9 | 0.822435 | ||||||||
\(155\) | −4.18621e9 | −0.582544 | ||||||||
\(156\) | 8.34881e9 | 1.12866 | ||||||||
\(157\) | 1.28176e10 | 1.68367 | 0.841834 | − | 0.539736i | \(-0.181476\pi\) | ||||
0.841834 | + | 0.539736i | \(0.181476\pi\) | |||||||
\(158\) | 7.94490e9 | 1.01422 | ||||||||
\(159\) | −3.60770e9 | −0.447655 | ||||||||
\(160\) | −7.31476e9 | −0.882389 | ||||||||
\(161\) | 7.13386e9 | 0.836774 | ||||||||
\(162\) | 1.26137e10 | 1.43888 | ||||||||
\(163\) | 9.23048e9 | 1.02419 | 0.512095 | − | 0.858929i | \(-0.328870\pi\) | ||||
0.512095 | + | 0.858929i | \(0.328870\pi\) | |||||||
\(164\) | 1.28179e10 | 1.38363 | ||||||||
\(165\) | 7.63085e9 | 0.801485 | ||||||||
\(166\) | −1.26190e10 | −1.28985 | ||||||||
\(167\) | −2.26110e9 | −0.224955 | −0.112477 | − | 0.993654i | \(-0.535879\pi\) | ||||
−0.112477 | + | 0.993654i | \(0.535879\pi\) | |||||||
\(168\) | 2.39766e9 | 0.232218 | ||||||||
\(169\) | −3.44926e8 | −0.0325264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.60895e10 | 1.43900 | ||||||||
\(172\) | −1.75907e10 | −1.53252 | ||||||||
\(173\) | 6.75290e8 | 0.0573169 | 0.0286585 | − | 0.999589i | \(-0.490876\pi\) | ||||
0.0286585 | + | 0.999589i | \(0.490876\pi\) | |||||||
\(174\) | 1.15989e10 | 0.959276 | ||||||||
\(175\) | −4.81760e9 | −0.388293 | ||||||||
\(176\) | 1.24723e10 | 0.979805 | ||||||||
\(177\) | 6.84862e9 | 0.524474 | ||||||||
\(178\) | −3.21715e10 | −2.40204 | ||||||||
\(179\) | 1.70190e10 | 1.23907 | 0.619533 | − | 0.784971i | \(-0.287322\pi\) | ||||
0.619533 | + | 0.784971i | \(0.287322\pi\) | |||||||
\(180\) | −7.28733e9 | −0.517419 | ||||||||
\(181\) | −9.47430e9 | −0.656136 | −0.328068 | − | 0.944654i | \(-0.606397\pi\) | ||||
−0.328068 | + | 0.944654i | \(0.606397\pi\) | |||||||
\(182\) | −1.39781e10 | −0.944334 | ||||||||
\(183\) | 3.67729e10 | 2.42381 | ||||||||
\(184\) | 4.30763e9 | 0.277050 | ||||||||
\(185\) | 9.33639e9 | 0.586011 | ||||||||
\(186\) | −2.65095e10 | −1.62403 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.25463e10 | 0.732496 | ||||||||
\(189\) | −1.20694e9 | −0.0688028 | ||||||||
\(190\) | 2.52845e10 | 1.40755 | ||||||||
\(191\) | −5.23707e8 | −0.0284733 | −0.0142367 | − | 0.999899i | \(-0.504532\pi\) | ||||
−0.0142367 | + | 0.999899i | \(0.504532\pi\) | |||||||
\(192\) | −1.63979e10 | −0.870827 | ||||||||
\(193\) | 1.35576e10 | 0.703355 | 0.351678 | − | 0.936121i | \(-0.385611\pi\) | ||||
0.351678 | + | 0.936121i | \(0.385611\pi\) | |||||||
\(194\) | 3.96491e10 | 2.00967 | ||||||||
\(195\) | −1.85812e10 | −0.920278 | ||||||||
\(196\) | −8.44989e9 | −0.408977 | ||||||||
\(197\) | −2.22167e10 | −1.05095 | −0.525474 | − | 0.850810i | \(-0.676112\pi\) | ||||
−0.525474 | + | 0.850810i | \(0.676112\pi\) | |||||||
\(198\) | 2.32891e10 | 1.07686 | ||||||||
\(199\) | 1.58102e10 | 0.714659 | 0.357329 | − | 0.933978i | \(-0.383687\pi\) | ||||
0.357329 | + | 0.933978i | \(0.383687\pi\) | |||||||
\(200\) | −2.90901e9 | −0.128561 | ||||||||
\(201\) | 4.06518e10 | 1.75670 | ||||||||
\(202\) | −1.65224e10 | −0.698220 | ||||||||
\(203\) | −8.78396e9 | −0.363043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.85278e10 | −1.12817 | ||||||||
\(206\) | 6.52574e10 | 2.52480 | ||||||||
\(207\) | 2.89422e10 | 1.09563 | ||||||||
\(208\) | −3.03703e10 | −1.12503 | ||||||||
\(209\) | −3.65503e10 | −1.32505 | ||||||||
\(210\) | 2.53158e10 | 0.898267 | ||||||||
\(211\) | 4.76983e10 | 1.65666 | 0.828328 | − | 0.560244i | \(-0.189293\pi\) | ||||
0.828328 | + | 0.560244i | \(0.189293\pi\) | |||||||
\(212\) | −7.82663e9 | −0.266111 | ||||||||
\(213\) | −9.54742e9 | −0.317818 | ||||||||
\(214\) | −1.56816e8 | −0.00511125 | ||||||||
\(215\) | 3.91502e10 | 1.24957 | ||||||||
\(216\) | −7.28784e8 | −0.0227802 | ||||||||
\(217\) | 2.00760e10 | 0.614622 | ||||||||
\(218\) | 1.29949e10 | 0.389690 | ||||||||
\(219\) | −2.53961e10 | −0.746052 | ||||||||
\(220\) | 1.65545e10 | 0.476447 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.91234e10 | 1.63370 | ||||||||
\(223\) | 4.45882e10 | 1.20739 | 0.603696 | − | 0.797215i | \(-0.293694\pi\) | ||||
0.603696 | + | 0.797215i | \(0.293694\pi\) | |||||||
\(224\) | 3.50797e10 | 0.930979 | ||||||||
\(225\) | −1.95451e10 | −0.508413 | ||||||||
\(226\) | 2.22784e10 | 0.568064 | ||||||||
\(227\) | 6.65541e10 | 1.66364 | 0.831818 | − | 0.555048i | \(-0.187300\pi\) | ||||
0.831818 | + | 0.555048i | \(0.187300\pi\) | |||||||
\(228\) | 7.24250e10 | 1.77493 | ||||||||
\(229\) | 3.55296e10 | 0.853749 | 0.426875 | − | 0.904311i | \(-0.359615\pi\) | ||||
0.426875 | + | 0.904311i | \(0.359615\pi\) | |||||||
\(230\) | 4.54824e10 | 1.07169 | ||||||||
\(231\) | −3.65956e10 | −0.845619 | ||||||||
\(232\) | −5.30401e9 | −0.120201 | ||||||||
\(233\) | −4.02652e10 | −0.895010 | −0.447505 | − | 0.894281i | \(-0.647687\pi\) | ||||
−0.447505 | + | 0.894281i | \(0.647687\pi\) | |||||||
\(234\) | −5.67092e10 | −1.23647 | ||||||||
\(235\) | −2.79232e10 | −0.597256 | ||||||||
\(236\) | 1.48575e10 | 0.311776 | ||||||||
\(237\) | −5.06491e10 | −1.04281 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.30898e10 | 0.259503 | 0.129752 | − | 0.991547i | \(-0.458582\pi\) | ||||
0.129752 | + | 0.991547i | \(0.458582\pi\) | |||||||
\(240\) | 5.50039e10 | 1.07015 | ||||||||
\(241\) | 3.29841e10 | 0.629836 | 0.314918 | − | 0.949119i | \(-0.398023\pi\) | ||||
0.314918 | + | 0.949119i | \(0.398023\pi\) | |||||||
\(242\) | 1.91902e10 | 0.359674 | ||||||||
\(243\) | −7.51494e10 | −1.38260 | ||||||||
\(244\) | 7.97759e10 | 1.44085 | ||||||||
\(245\) | 1.88062e10 | 0.333468 | ||||||||
\(246\) | −1.80654e11 | −3.14514 | ||||||||
\(247\) | 8.90006e10 | 1.52145 | ||||||||
\(248\) | 1.21225e10 | 0.203497 | ||||||||
\(249\) | 8.04467e10 | 1.32621 | ||||||||
\(250\) | −8.69175e10 | −1.40727 | ||||||||
\(251\) | −5.32797e10 | −0.847285 | −0.423643 | − | 0.905829i | \(-0.639249\pi\) | ||||
−0.423643 | + | 0.905829i | \(0.639249\pi\) | |||||||
\(252\) | 3.49482e10 | 0.545911 | ||||||||
\(253\) | −6.57476e10 | −1.00888 | ||||||||
\(254\) | 7.70905e10 | 1.16212 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.60987e10 | 1.25290 | ||||||||
\(257\) | 3.34024e10 | 0.477615 | 0.238808 | − | 0.971067i | \(-0.423243\pi\) | ||||
0.238808 | + | 0.971067i | \(0.423243\pi\) | |||||||
\(258\) | 2.47922e11 | 3.48358 | ||||||||
\(259\) | −4.47749e10 | −0.618281 | ||||||||
\(260\) | −4.03105e10 | −0.547064 | ||||||||
\(261\) | −3.56367e10 | −0.475352 | ||||||||
\(262\) | −1.68738e11 | −2.21237 | ||||||||
\(263\) | 2.58102e10 | 0.332653 | 0.166326 | − | 0.986071i | \(-0.446810\pi\) | ||||
0.166326 | + | 0.986071i | \(0.446810\pi\) | |||||||
\(264\) | −2.20975e10 | −0.279979 | ||||||||
\(265\) | 1.74190e10 | 0.216979 | ||||||||
\(266\) | −1.21258e11 | −1.48506 | ||||||||
\(267\) | 2.05095e11 | 2.46975 | ||||||||
\(268\) | 8.81909e10 | 1.04428 | ||||||||
\(269\) | −3.02035e10 | −0.351700 | −0.175850 | − | 0.984417i | \(-0.556267\pi\) | ||||
−0.175850 | + | 0.984417i | \(0.556267\pi\) | |||||||
\(270\) | −7.69490e9 | −0.0881183 | ||||||||
\(271\) | −7.25899e10 | −0.817550 | −0.408775 | − | 0.912635i | \(-0.634044\pi\) | ||||
−0.408775 | + | 0.912635i | \(0.634044\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.91108e10 | 0.970954 | ||||||||
\(274\) | −2.87683e10 | −0.308345 | ||||||||
\(275\) | 4.44003e10 | 0.468154 | ||||||||
\(276\) | 1.30280e11 | 1.35141 | ||||||||
\(277\) | 8.69284e9 | 0.0887161 | 0.0443581 | − | 0.999016i | \(-0.485876\pi\) | ||||
0.0443581 | + | 0.999016i | \(0.485876\pi\) | |||||||
\(278\) | 2.74359e10 | 0.275497 | ||||||||
\(279\) | 8.14487e10 | 0.804758 | ||||||||
\(280\) | −1.15766e10 | −0.112556 | ||||||||
\(281\) | 1.30456e10 | 0.124820 | 0.0624100 | − | 0.998051i | \(-0.480121\pi\) | ||||
0.0624100 | + | 0.998051i | \(0.480121\pi\) | |||||||
\(282\) | −1.76826e11 | −1.66504 | ||||||||
\(283\) | 1.25572e11 | 1.16374 | 0.581869 | − | 0.813282i | \(-0.302321\pi\) | ||||
0.581869 | + | 0.813282i | \(0.302321\pi\) | |||||||
\(284\) | −2.07124e10 | −0.188929 | ||||||||
\(285\) | −1.61190e11 | −1.44723 | ||||||||
\(286\) | 1.28826e11 | 1.13856 | ||||||||
\(287\) | 1.36812e11 | 1.19030 | ||||||||
\(288\) | 1.42319e11 | 1.21898 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −5.60027e10 | −0.464963 | ||||||||
\(291\) | −2.52765e11 | −2.06632 | ||||||||
\(292\) | −5.50949e10 | −0.443495 | ||||||||
\(293\) | 2.09036e11 | 1.65698 | 0.828488 | − | 0.560006i | \(-0.189201\pi\) | ||||
0.828488 | + | 0.560006i | \(0.189201\pi\) | |||||||
\(294\) | 1.19092e11 | 0.929649 | ||||||||
\(295\) | −3.30672e10 | −0.254213 | ||||||||
\(296\) | −2.70364e10 | −0.204709 | ||||||||
\(297\) | 1.11235e10 | 0.0829537 | ||||||||
\(298\) | 3.99199e10 | 0.293235 | ||||||||
\(299\) | 1.60096e11 | 1.15841 | ||||||||
\(300\) | −8.79799e10 | −0.627101 | ||||||||
\(301\) | −1.87754e11 | −1.31838 | ||||||||
\(302\) | 1.89322e11 | 1.30969 | ||||||||
\(303\) | 1.05331e11 | 0.717902 | ||||||||
\(304\) | −2.63458e11 | −1.76922 | ||||||||
\(305\) | −1.77550e11 | −1.17482 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.44198e11 | 0.926484 | 0.463242 | − | 0.886232i | \(-0.346686\pi\) | ||||
0.463242 | + | 0.886232i | \(0.346686\pi\) | |||||||
\(308\) | −7.93912e10 | −0.502683 | ||||||||
\(309\) | −4.16019e11 | −2.59597 | ||||||||
\(310\) | 1.27996e11 | 0.787169 | ||||||||
\(311\) | 3.05482e11 | 1.85167 | 0.925836 | − | 0.377925i | \(-0.123362\pi\) | ||||
0.925836 | + | 0.377925i | \(0.123362\pi\) | |||||||
\(312\) | 5.38077e10 | 0.321476 | ||||||||
\(313\) | 1.97546e11 | 1.16337 | 0.581685 | − | 0.813414i | \(-0.302394\pi\) | ||||
0.581685 | + | 0.813414i | \(0.302394\pi\) | |||||||
\(314\) | −3.91904e11 | −2.27508 | ||||||||
\(315\) | −7.77811e10 | −0.445120 | ||||||||
\(316\) | −1.09879e11 | −0.619903 | ||||||||
\(317\) | 2.53026e11 | 1.40734 | 0.703670 | − | 0.710527i | \(-0.251543\pi\) | ||||
0.703670 | + | 0.710527i | \(0.251543\pi\) | |||||||
\(318\) | 1.10308e11 | 0.604899 | ||||||||
\(319\) | 8.09554e10 | 0.437711 | ||||||||
\(320\) | 7.91737e10 | 0.422091 | ||||||||
\(321\) | 9.99708e8 | 0.00525534 | ||||||||
\(322\) | −2.18122e11 | −1.13070 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.74449e11 | −0.879462 | ||||||||
\(325\) | −1.08115e11 | −0.537542 | ||||||||
\(326\) | −2.82227e11 | −1.38395 | ||||||||
\(327\) | −8.28432e10 | −0.400675 | ||||||||
\(328\) | 8.26109e10 | 0.394099 | ||||||||
\(329\) | 1.33913e11 | 0.630144 | ||||||||
\(330\) | −2.33318e11 | −1.08302 | ||||||||
\(331\) | 4.14467e11 | 1.89786 | 0.948930 | − | 0.315486i | \(-0.102167\pi\) | ||||
0.948930 | + | 0.315486i | \(0.102167\pi\) | |||||||
\(332\) | 1.74523e11 | 0.788371 | ||||||||
\(333\) | −1.81653e11 | −0.809548 | ||||||||
\(334\) | 6.91343e10 | 0.303973 | ||||||||
\(335\) | −1.96279e11 | −0.851475 | ||||||||
\(336\) | −2.63785e11 | −1.12907 | ||||||||
\(337\) | −1.55413e11 | −0.656375 | −0.328187 | − | 0.944613i | \(-0.606438\pi\) | ||||
−0.328187 | + | 0.944613i | \(0.606438\pi\) | |||||||
\(338\) | 1.05463e10 | 0.0439517 | ||||||||
\(339\) | −1.42026e11 | −0.584077 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.85026e11 | −0.741033 | ||||||||
\(342\) | −4.91946e11 | −1.94447 | ||||||||
\(343\) | −2.72323e11 | −1.06233 | ||||||||
\(344\) | −1.13371e11 | −0.436506 | ||||||||
\(345\) | −2.89953e11 | −1.10190 | ||||||||
\(346\) | −2.06474e10 | −0.0774501 | ||||||||
\(347\) | −1.69024e11 | −0.625844 | −0.312922 | − | 0.949779i | \(-0.601308\pi\) | ||||
−0.312922 | + | 0.949779i | \(0.601308\pi\) | |||||||
\(348\) | −1.60414e11 | −0.586322 | ||||||||
\(349\) | −2.15573e11 | −0.777823 | −0.388911 | − | 0.921275i | \(-0.627149\pi\) | ||||
−0.388911 | + | 0.921275i | \(0.627149\pi\) | |||||||
\(350\) | 1.47301e11 | 0.524686 | ||||||||
\(351\) | −2.70858e10 | −0.0952488 | ||||||||
\(352\) | −3.23304e11 | −1.12246 | ||||||||
\(353\) | 3.02994e11 | 1.03860 | 0.519299 | − | 0.854593i | \(-0.326193\pi\) | ||||
0.519299 | + | 0.854593i | \(0.326193\pi\) | |||||||
\(354\) | −2.09401e11 | −0.708701 | ||||||||
\(355\) | 4.60978e10 | 0.154047 | ||||||||
\(356\) | 4.44937e11 | 1.46816 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.20364e11 | −1.67430 | ||||||||
\(359\) | −2.90075e11 | −0.921692 | −0.460846 | − | 0.887480i | \(-0.652454\pi\) | ||||
−0.460846 | + | 0.887480i | \(0.652454\pi\) | |||||||
\(360\) | −4.69665e10 | −0.147376 | ||||||||
\(361\) | 4.49383e11 | 1.39262 | ||||||||
\(362\) | 2.89682e11 | 0.886611 | ||||||||
\(363\) | −1.22338e11 | −0.369813 | ||||||||
\(364\) | 1.93319e11 | 0.577189 | ||||||||
\(365\) | 1.22620e11 | 0.361612 | ||||||||
\(366\) | −1.12435e12 | −3.27520 | ||||||||
\(367\) | −1.41373e11 | −0.406789 | −0.203394 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203394 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(368\) | −4.73915e11 | −1.34706 | ||||||||
\(369\) | 5.55048e11 | 1.55852 | ||||||||
\(370\) | −2.85465e11 | −0.791855 | ||||||||
\(371\) | −8.35372e10 | −0.228927 | ||||||||
\(372\) | 3.66631e11 | 0.992627 | ||||||||
\(373\) | 1.79070e11 | 0.478998 | 0.239499 | − | 0.970897i | \(-0.423017\pi\) | ||||
0.239499 | + | 0.970897i | \(0.423017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.54104e11 | 1.44694 | ||||||||
\(376\) | 8.08603e10 | 0.208636 | ||||||||
\(377\) | −1.97128e11 | −0.502587 | ||||||||
\(378\) | 3.69028e10 | 0.0929707 | ||||||||
\(379\) | 2.66182e11 | 0.662677 | 0.331338 | − | 0.943512i | \(-0.392500\pi\) | ||||
0.331338 | + | 0.943512i | \(0.392500\pi\) | |||||||
\(380\) | −3.49689e11 | −0.860312 | ||||||||
\(381\) | −4.91456e11 | −1.19487 | ||||||||
\(382\) | 1.60126e10 | 0.0384749 | ||||||||
\(383\) | 6.18970e11 | 1.46986 | 0.734928 | − | 0.678145i | \(-0.237216\pi\) | ||||
0.734928 | + | 0.678145i | \(0.237216\pi\) | |||||||
\(384\) | −2.74295e11 | −0.643765 | ||||||||
\(385\) | 1.76694e11 | 0.409873 | ||||||||
\(386\) | −4.14531e11 | −0.950417 | ||||||||
\(387\) | −7.61722e11 | −1.72622 | ||||||||
\(388\) | −5.48353e11 | −1.22834 | ||||||||
\(389\) | −1.72722e11 | −0.382450 | −0.191225 | − | 0.981546i | \(-0.561246\pi\) | ||||
−0.191225 | + | 0.981546i | \(0.561246\pi\) | |||||||
\(390\) | 5.68132e11 | 1.24354 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.44592e10 | −0.116489 | ||||||||
\(393\) | 1.07572e12 | 2.27473 | ||||||||
\(394\) | 6.79288e11 | 1.42011 | ||||||||
\(395\) | 2.44549e11 | 0.505451 | ||||||||
\(396\) | −3.22092e11 | −0.658190 | ||||||||
\(397\) | −5.98018e9 | −0.0120825 | −0.00604125 | − | 0.999982i | \(-0.501923\pi\) | ||||
−0.00604125 | + | 0.999982i | \(0.501923\pi\) | |||||||
\(398\) | −4.83406e11 | −0.965691 | ||||||||
\(399\) | 7.73026e11 | 1.52692 | ||||||||
\(400\) | 3.20042e11 | 0.625082 | ||||||||
\(401\) | 2.91381e9 | 0.00562745 | 0.00281372 | − | 0.999996i | \(-0.499104\pi\) | ||||
0.00281372 | + | 0.999996i | \(0.499104\pi\) | |||||||
\(402\) | −1.24295e12 | −2.37376 | ||||||||
\(403\) | 4.50541e11 | 0.850866 | ||||||||
\(404\) | 2.28508e11 | 0.426761 | ||||||||
\(405\) | 3.88257e11 | 0.717087 | ||||||||
\(406\) | 2.68575e11 | 0.490566 | ||||||||
\(407\) | 4.12658e11 | 0.745444 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.39771e11 | 0.777091 | 0.388546 | − | 0.921430i | \(-0.372978\pi\) | ||||
0.388546 | + | 0.921430i | \(0.372978\pi\) | |||||||
\(410\) | 8.72252e11 | 1.52446 | ||||||||
\(411\) | 1.83399e11 | 0.317037 | ||||||||
\(412\) | −9.02521e11 | −1.54319 | ||||||||
\(413\) | 1.58582e11 | 0.268212 | ||||||||
\(414\) | −8.84925e11 | −1.48049 | ||||||||
\(415\) | −3.88420e11 | −0.642814 | ||||||||
\(416\) | 7.87251e11 | 1.28882 | ||||||||
\(417\) | −1.74905e11 | −0.283263 | ||||||||
\(418\) | 1.11755e12 | 1.79049 | ||||||||
\(419\) | 8.88321e11 | 1.40801 | 0.704006 | − | 0.710194i | \(-0.251393\pi\) | ||||
0.704006 | + | 0.710194i | \(0.251393\pi\) | |||||||
\(420\) | −3.50122e11 | −0.549032 | ||||||||
\(421\) | 3.91195e11 | 0.606910 | 0.303455 | − | 0.952846i | \(-0.401860\pi\) | ||||
0.303455 | + | 0.952846i | \(0.401860\pi\) | |||||||
\(422\) | −1.45840e12 | −2.23858 | ||||||||
\(423\) | 5.43286e11 | 0.825081 | ||||||||
\(424\) | −5.04422e10 | −0.0757963 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.91918e11 | 0.429455 | ||||||||
\(427\) | 8.51485e11 | 1.23951 | ||||||||
\(428\) | 2.16879e9 | 0.00312406 | ||||||||
\(429\) | −8.21269e11 | −1.17065 | ||||||||
\(430\) | −1.19704e12 | −1.68850 | ||||||||
\(431\) | 7.81278e11 | 1.09058 | 0.545291 | − | 0.838247i | \(-0.316419\pi\) | ||||
0.545291 | + | 0.838247i | \(0.316419\pi\) | |||||||
\(432\) | 8.01790e10 | 0.110760 | ||||||||
\(433\) | 9.03790e11 | 1.23558 | 0.617791 | − | 0.786342i | \(-0.288028\pi\) | ||||
0.617791 | + | 0.786342i | \(0.288028\pi\) | |||||||
\(434\) | −6.13835e11 | −0.830515 | ||||||||
\(435\) | 3.57020e11 | 0.478070 | ||||||||
\(436\) | −1.79722e11 | −0.238183 | ||||||||
\(437\) | 1.38882e12 | 1.82171 | ||||||||
\(438\) | 7.76501e11 | 1.00811 | ||||||||
\(439\) | −5.14908e11 | −0.661667 | −0.330834 | − | 0.943689i | \(-0.607330\pi\) | ||||
−0.330834 | + | 0.943689i | \(0.607330\pi\) | |||||||
\(440\) | 1.06693e11 | 0.135706 | ||||||||
\(441\) | −3.65901e11 | −0.460670 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.59851e12 | −1.97196 | −0.985981 | − | 0.166856i | \(-0.946638\pi\) | ||||
−0.985981 | + | 0.166856i | \(0.946638\pi\) | |||||||
\(444\) | −8.17687e11 | −0.998536 | ||||||||
\(445\) | −9.90257e11 | −1.19709 | ||||||||
\(446\) | −1.36331e12 | −1.63150 | ||||||||
\(447\) | −2.54491e11 | −0.301501 | ||||||||
\(448\) | −3.79697e11 | −0.445334 | ||||||||
\(449\) | 8.81603e11 | 1.02368 | 0.511840 | − | 0.859081i | \(-0.328964\pi\) | ||||
0.511840 | + | 0.859081i | \(0.328964\pi\) | |||||||
\(450\) | 5.97603e11 | 0.686999 | ||||||||
\(451\) | −1.26089e12 | −1.43511 | ||||||||
\(452\) | −3.08115e11 | −0.347208 | ||||||||
\(453\) | −1.20694e12 | −1.34661 | ||||||||
\(454\) | −2.03493e12 | −2.24801 | ||||||||
\(455\) | −4.30253e11 | −0.470623 | ||||||||
\(456\) | 4.66776e11 | 0.505553 | ||||||||
\(457\) | −4.45550e11 | −0.477830 | −0.238915 | − | 0.971041i | \(-0.576792\pi\) | ||||
−0.238915 | + | 0.971041i | \(0.576792\pi\) | |||||||
\(458\) | −1.08634e12 | −1.15364 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.29029e11 | −0.655029 | ||||||||
\(461\) | 1.05555e12 | 1.08849 | 0.544247 | − | 0.838925i | \(-0.316815\pi\) | ||||
0.544247 | + | 0.838925i | \(0.316815\pi\) | |||||||
\(462\) | 1.11893e12 | 1.14265 | ||||||||
\(463\) | −6.82069e11 | −0.689785 | −0.344892 | − | 0.938642i | \(-0.612085\pi\) | ||||
−0.344892 | + | 0.938642i | \(0.612085\pi\) | |||||||
\(464\) | 5.83534e11 | 0.584434 | ||||||||
\(465\) | −8.15980e11 | −0.809359 | ||||||||
\(466\) | 1.23113e12 | 1.20939 | ||||||||
\(467\) | −1.14817e12 | −1.11707 | −0.558533 | − | 0.829482i | \(-0.688636\pi\) | ||||
−0.558533 | + | 0.829482i | \(0.688636\pi\) | |||||||
\(468\) | 7.84298e11 | 0.755745 | ||||||||
\(469\) | 9.41303e11 | 0.898363 | ||||||||
\(470\) | 8.53768e11 | 0.807049 | ||||||||
\(471\) | 2.49841e12 | 2.33921 | ||||||||
\(472\) | 9.57562e10 | 0.0888031 | ||||||||
\(473\) | 1.73039e12 | 1.58953 | ||||||||
\(474\) | 1.54863e12 | 1.40911 | ||||||||
\(475\) | −9.37889e11 | −0.845338 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.38912e11 | −0.299747 | ||||||||
\(478\) | −4.00228e11 | −0.350657 | ||||||||
\(479\) | −1.39726e11 | −0.121274 | −0.0606369 | − | 0.998160i | \(-0.519313\pi\) | ||||
−0.0606369 | + | 0.998160i | \(0.519313\pi\) | |||||||
\(480\) | −1.42580e12 | −1.22595 | ||||||||
\(481\) | −1.00483e12 | −0.855931 | ||||||||
\(482\) | −1.00851e12 | −0.851074 | ||||||||
\(483\) | 1.39054e12 | 1.16257 | ||||||||
\(484\) | −2.65403e11 | −0.219837 | ||||||||
\(485\) | 1.22042e12 | 1.00155 | ||||||||
\(486\) | 2.29774e12 | 1.86826 | ||||||||
\(487\) | −6.54778e11 | −0.527489 | −0.263745 | − | 0.964593i | \(-0.584958\pi\) | ||||
−0.263745 | + | 0.964593i | \(0.584958\pi\) | |||||||
\(488\) | 5.14152e11 | 0.410395 | ||||||||
\(489\) | 1.79921e12 | 1.42296 | ||||||||
\(490\) | −5.75010e11 | −0.450602 | ||||||||
\(491\) | −1.33697e11 | −0.103814 | −0.0519069 | − | 0.998652i | \(-0.516530\pi\) | ||||
−0.0519069 | + | 0.998652i | \(0.516530\pi\) | |||||||
\(492\) | 2.49848e12 | 1.92235 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.72124e12 | −2.05587 | ||||||||
\(495\) | 7.16852e11 | 0.536668 | ||||||||
\(496\) | −1.33368e12 | −0.989431 | ||||||||
\(497\) | −2.21073e11 | −0.162529 | ||||||||
\(498\) | −2.45970e12 | −1.79205 | ||||||||
\(499\) | −7.51123e11 | −0.542323 | −0.271162 | − | 0.962534i | \(-0.587408\pi\) | ||||
−0.271162 | + | 0.962534i | \(0.587408\pi\) | |||||||
\(500\) | 1.20208e12 | 0.860141 | ||||||||
\(501\) | −4.40735e11 | −0.312541 | ||||||||
\(502\) | 1.62906e12 | 1.14490 | ||||||||
\(503\) | 3.90993e10 | 0.0272341 | 0.0136170 | − | 0.999907i | \(-0.495665\pi\) | ||||
0.0136170 | + | 0.999907i | \(0.495665\pi\) | |||||||
\(504\) | 2.25239e11 | 0.155491 | ||||||||
\(505\) | −5.08570e11 | −0.347968 | ||||||||
\(506\) | 2.01027e12 | 1.36326 | ||||||||
\(507\) | −6.72332e10 | −0.0451906 | ||||||||
\(508\) | −1.06617e12 | −0.710300 | ||||||||
\(509\) | −1.04082e12 | −0.687296 | −0.343648 | − | 0.939098i | \(-0.611663\pi\) | ||||
−0.343648 | + | 0.939098i | \(0.611663\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.88054e11 | −0.381525 | ||||||||
\(512\) | −1.91202e12 | −1.22964 | ||||||||
\(513\) | −2.34966e11 | −0.149788 | ||||||||
\(514\) | −1.02130e12 | −0.645383 | ||||||||
\(515\) | 2.00866e12 | 1.25827 | ||||||||
\(516\) | −3.42880e12 | −2.12921 | ||||||||
\(517\) | −1.23417e12 | −0.759747 | ||||||||
\(518\) | 1.36902e12 | 0.835459 | ||||||||
\(519\) | 1.31628e11 | 0.0796334 | ||||||||
\(520\) | −2.59799e11 | −0.155820 | ||||||||
\(521\) | −2.49791e12 | −1.48528 | −0.742638 | − | 0.669693i | \(-0.766426\pi\) | ||||
−0.742638 | + | 0.669693i | \(0.766426\pi\) | |||||||
\(522\) | 1.08961e12 | 0.642325 | ||||||||
\(523\) | 2.04811e11 | 0.119700 | 0.0598501 | − | 0.998207i | \(-0.480938\pi\) | ||||
0.0598501 | + | 0.998207i | \(0.480938\pi\) | |||||||
\(524\) | 2.33368e12 | 1.35223 | ||||||||
\(525\) | −9.39050e11 | −0.539476 | ||||||||
\(526\) | −7.89162e11 | −0.449501 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.43111e12 | 1.36129 | ||||||||
\(529\) | 6.97088e11 | 0.387023 | ||||||||
\(530\) | −5.32597e11 | −0.293196 | ||||||||
\(531\) | 6.43369e11 | 0.351184 | ||||||||
\(532\) | 1.67702e12 | 0.907686 | ||||||||
\(533\) | 3.07030e12 | 1.64781 | ||||||||
\(534\) | −6.27088e12 | −3.33728 | ||||||||
\(535\) | −4.82688e9 | −0.00254727 | ||||||||
\(536\) | 5.68386e11 | 0.297442 | ||||||||
\(537\) | 3.31735e12 | 1.72150 | ||||||||
\(538\) | 9.23489e11 | 0.475238 | ||||||||
\(539\) | 8.31213e11 | 0.424192 | ||||||||
\(540\) | 1.06422e11 | 0.0538591 | ||||||||
\(541\) | 2.24094e12 | 1.12471 | 0.562357 | − | 0.826894i | \(-0.309895\pi\) | ||||
0.562357 | + | 0.826894i | \(0.309895\pi\) | |||||||
\(542\) | 2.21948e12 | 1.10472 | ||||||||
\(543\) | −1.84674e12 | −0.911604 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.99991e11 | 0.194208 | ||||||||
\(546\) | −2.72461e12 | −1.31201 | ||||||||
\(547\) | 1.94999e12 | 0.931300 | 0.465650 | − | 0.884969i | \(-0.345821\pi\) | ||||
0.465650 | + | 0.884969i | \(0.345821\pi\) | |||||||
\(548\) | 3.97870e11 | 0.188464 | ||||||||
\(549\) | 3.45449e12 | 1.62296 | ||||||||
\(550\) | −1.35756e12 | −0.632599 | ||||||||
\(551\) | −1.71006e12 | −0.790367 | ||||||||
\(552\) | 8.39647e11 | 0.384921 | ||||||||
\(553\) | −1.17279e12 | −0.533284 | ||||||||
\(554\) | −2.65788e11 | −0.119879 | ||||||||
\(555\) | 1.81986e12 | 0.814177 | ||||||||
\(556\) | −3.79443e11 | −0.168387 | ||||||||
\(557\) | −3.69055e12 | −1.62459 | −0.812293 | − | 0.583250i | \(-0.801781\pi\) | ||||
−0.812293 | + | 0.583250i | \(0.801781\pi\) | |||||||
\(558\) | −2.49034e12 | −1.08744 | ||||||||
\(559\) | −4.21353e12 | −1.82513 | ||||||||
\(560\) | 1.27363e12 | 0.547264 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.98876e11 | −0.168665 | ||||||||
\(563\) | −7.69327e11 | −0.322718 | −0.161359 | − | 0.986896i | \(-0.551588\pi\) | ||||
−0.161359 | + | 0.986896i | \(0.551588\pi\) | |||||||
\(564\) | 2.44553e12 | 1.01770 | ||||||||
\(565\) | 6.85744e11 | 0.283103 | ||||||||
\(566\) | −3.83945e12 | −1.57252 | ||||||||
\(567\) | −1.86198e12 | −0.756574 | ||||||||
\(568\) | −1.33490e11 | −0.0538124 | ||||||||
\(569\) | 4.75620e11 | 0.190219 | 0.0951097 | − | 0.995467i | \(-0.469680\pi\) | ||||
0.0951097 | + | 0.995467i | \(0.469680\pi\) | |||||||
\(570\) | 4.92848e12 | 1.95558 | ||||||||
\(571\) | −3.53469e12 | −1.39152 | −0.695759 | − | 0.718276i | \(-0.744932\pi\) | ||||
−0.695759 | + | 0.718276i | \(0.744932\pi\) | |||||||
\(572\) | −1.78168e12 | −0.695901 | ||||||||
\(573\) | −1.02081e11 | −0.0395595 | ||||||||
\(574\) | −4.18310e12 | −1.60840 | ||||||||
\(575\) | −1.68710e12 | −0.643628 | ||||||||
\(576\) | −1.54044e12 | −0.583099 | ||||||||
\(577\) | −6.21322e11 | −0.233360 | −0.116680 | − | 0.993170i | \(-0.537225\pi\) | ||||
−0.116680 | + | 0.993170i | \(0.537225\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.64266e12 | 0.977209 | ||||||||
\(580\) | 7.74527e11 | 0.284191 | ||||||||
\(581\) | 1.86276e12 | 0.678211 | ||||||||
\(582\) | 7.72842e12 | 2.79214 | ||||||||
\(583\) | 7.69902e11 | 0.276011 | ||||||||
\(584\) | −3.55084e11 | −0.126320 | ||||||||
\(585\) | −1.74555e12 | −0.616212 | ||||||||
\(586\) | −6.39139e12 | −2.23901 | ||||||||
\(587\) | −5.46826e12 | −1.90098 | −0.950490 | − | 0.310756i | \(-0.899418\pi\) | ||||
−0.950490 | + | 0.310756i | \(0.899418\pi\) | |||||||
\(588\) | −1.64706e12 | −0.568213 | ||||||||
\(589\) | 3.90839e12 | 1.33807 | ||||||||
\(590\) | 1.01105e12 | 0.343509 | ||||||||
\(591\) | −4.33049e12 | −1.46014 | ||||||||
\(592\) | 2.97448e12 | 0.995321 | ||||||||
\(593\) | 1.92966e12 | 0.640819 | 0.320410 | − | 0.947279i | \(-0.396179\pi\) | ||||
0.320410 | + | 0.947279i | \(0.396179\pi\) | |||||||
\(594\) | −3.40106e11 | −0.112092 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.52099e11 | −0.179229 | ||||||||
\(597\) | 3.08174e12 | 0.992913 | ||||||||
\(598\) | −4.89504e12 | −1.56531 | ||||||||
\(599\) | −4.29083e12 | −1.36182 | −0.680911 | − | 0.732366i | \(-0.738416\pi\) | ||||
−0.680911 | + | 0.732366i | \(0.738416\pi\) | |||||||
\(600\) | −5.67026e11 | −0.178617 | ||||||||
\(601\) | −1.72436e12 | −0.539128 | −0.269564 | − | 0.962982i | \(-0.586880\pi\) | ||||
−0.269564 | + | 0.962982i | \(0.586880\pi\) | |||||||
\(602\) | 5.74069e12 | 1.78147 | ||||||||
\(603\) | 3.81888e12 | 1.17627 | ||||||||
\(604\) | −2.61835e12 | −0.800500 | ||||||||
\(605\) | 5.90685e11 | 0.179249 | ||||||||
\(606\) | −3.22056e12 | −0.970073 | ||||||||
\(607\) | −3.54265e12 | −1.05920 | −0.529602 | − | 0.848246i | \(-0.677659\pi\) | ||||
−0.529602 | + | 0.848246i | \(0.677659\pi\) | |||||||
\(608\) | 6.82931e12 | 2.02680 | ||||||||
\(609\) | −1.71218e12 | −0.504395 | ||||||||
\(610\) | 5.42870e12 | 1.58749 | ||||||||
\(611\) | 3.00523e12 | 0.872354 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.75371e12 | −0.787674 | −0.393837 | − | 0.919180i | \(-0.628853\pi\) | ||||
−0.393837 | + | 0.919180i | \(0.628853\pi\) | |||||||
\(614\) | −4.40895e12 | −1.25192 | ||||||||
\(615\) | −5.56065e12 | −1.56743 | ||||||||
\(616\) | −5.11673e11 | −0.143179 | ||||||||
\(617\) | 6.84976e12 | 1.90280 | 0.951398 | − | 0.307963i | \(-0.0996474\pi\) | ||||
0.951398 | + | 0.307963i | \(0.0996474\pi\) | |||||||
\(618\) | 1.27200e13 | 3.50784 | ||||||||
\(619\) | −6.91984e11 | −0.189447 | −0.0947235 | − | 0.995504i | \(-0.530197\pi\) | ||||
−0.0947235 | + | 0.995504i | \(0.530197\pi\) | |||||||
\(620\) | −1.77020e12 | −0.481128 | ||||||||
\(621\) | −4.22663e11 | −0.114046 | ||||||||
\(622\) | −9.34029e12 | −2.50209 | ||||||||
\(623\) | 4.74902e12 | 1.26301 | ||||||||
\(624\) | −5.91979e12 | −1.56306 | ||||||||
\(625\) | −5.90629e11 | −0.154830 | ||||||||
\(626\) | −6.04007e12 | −1.57202 | ||||||||
\(627\) | −7.12442e12 | −1.84097 | ||||||||
\(628\) | 5.42010e12 | 1.39056 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.37820e12 | 0.601473 | ||||||||
\(631\) | 2.99016e12 | 0.750866 | 0.375433 | − | 0.926850i | \(-0.377494\pi\) | ||||
0.375433 | + | 0.926850i | \(0.377494\pi\) | |||||||
\(632\) | −7.08167e11 | −0.176567 | ||||||||
\(633\) | 9.29740e12 | 2.30168 | ||||||||
\(634\) | −7.73643e12 | −1.90169 | ||||||||
\(635\) | 2.37289e12 | 0.579157 | ||||||||
\(636\) | −1.52557e12 | −0.369722 | ||||||||
\(637\) | −2.02402e12 | −0.487065 | ||||||||
\(638\) | −2.47526e12 | −0.591462 | ||||||||
\(639\) | −8.96897e11 | −0.212808 | ||||||||
\(640\) | 1.32438e12 | 0.312034 | ||||||||
\(641\) | −3.46519e12 | −0.810711 | −0.405356 | − | 0.914159i | \(-0.632852\pi\) | ||||
−0.405356 | + | 0.914159i | \(0.632852\pi\) | |||||||
\(642\) | −3.05666e10 | −0.00710133 | ||||||||
\(643\) | 3.07922e10 | 0.00710381 | 0.00355190 | − | 0.999994i | \(-0.498869\pi\) | ||||
0.00355190 | + | 0.999994i | \(0.498869\pi\) | |||||||
\(644\) | 3.01666e12 | 0.691099 | ||||||||
\(645\) | 7.63118e12 | 1.73609 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.58031e11 | −0.192501 | −0.0962506 | − | 0.995357i | \(-0.530685\pi\) | ||||
−0.0962506 | + | 0.995357i | \(0.530685\pi\) | |||||||
\(648\) | −1.12432e12 | −0.250496 | ||||||||
\(649\) | −1.46153e12 | −0.323375 | ||||||||
\(650\) | 3.30569e12 | 0.726361 | ||||||||
\(651\) | 3.91323e12 | 0.853927 | ||||||||
\(652\) | 3.90325e12 | 0.845887 | ||||||||
\(653\) | 7.56711e12 | 1.62862 | 0.814312 | − | 0.580428i | \(-0.197115\pi\) | ||||
0.814312 | + | 0.580428i | \(0.197115\pi\) | |||||||
\(654\) | 2.53298e12 | 0.541416 | ||||||||
\(655\) | −5.19387e12 | −1.10257 | ||||||||
\(656\) | −9.08865e12 | −1.91616 | ||||||||
\(657\) | −2.38575e12 | −0.499551 | ||||||||
\(658\) | −4.09445e12 | −0.851489 | ||||||||
\(659\) | 1.21600e12 | 0.251159 | 0.125580 | − | 0.992084i | \(-0.459921\pi\) | ||||
0.125580 | + | 0.992084i | \(0.459921\pi\) | |||||||
\(660\) | 3.22682e12 | 0.661953 | ||||||||
\(661\) | −6.17442e11 | −0.125803 | −0.0629013 | − | 0.998020i | \(-0.520035\pi\) | ||||
−0.0629013 | + | 0.998020i | \(0.520035\pi\) | |||||||
\(662\) | −1.26726e13 | −2.56451 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.12479e12 | 0.224551 | ||||||||
\(665\) | −3.73240e12 | −0.740100 | ||||||||
\(666\) | 5.55413e12 | 1.09391 | ||||||||
\(667\) | −3.07610e12 | −0.601774 | ||||||||
\(668\) | −9.56139e11 | −0.185792 | ||||||||
\(669\) | 8.69117e12 | 1.67749 | ||||||||
\(670\) | 6.00134e12 | 1.15057 | ||||||||
\(671\) | −7.84752e12 | −1.49445 | ||||||||
\(672\) | 6.83776e12 | 1.29346 | ||||||||
\(673\) | −4.43202e12 | −0.832786 | −0.416393 | − | 0.909185i | \(-0.636706\pi\) | ||||
−0.416393 | + | 0.909185i | \(0.636706\pi\) | |||||||
\(674\) | 4.75183e12 | 0.886934 | ||||||||
\(675\) | 2.85430e11 | 0.0529216 | ||||||||
\(676\) | −1.45857e11 | −0.0268638 | ||||||||
\(677\) | −7.03236e12 | −1.28663 | −0.643313 | − | 0.765603i | \(-0.722441\pi\) | ||||
−0.643313 | + | 0.765603i | \(0.722441\pi\) | |||||||
\(678\) | 4.34253e12 | 0.789241 | ||||||||
\(679\) | −5.85283e12 | −1.05670 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.29728e13 | 2.31138 | ||||||||
\(682\) | 5.65727e12 | 1.00133 | ||||||||
\(683\) | 3.12019e12 | 0.548640 | 0.274320 | − | 0.961638i | \(-0.411547\pi\) | ||||
0.274320 | + | 0.961638i | \(0.411547\pi\) | |||||||
\(684\) | 6.80370e12 | 1.18848 | ||||||||
\(685\) | −8.85505e11 | −0.153668 | ||||||||
\(686\) | 8.32644e12 | 1.43549 | ||||||||
\(687\) | 6.92545e12 | 1.18616 | ||||||||
\(688\) | 1.24728e13 | 2.12235 | ||||||||
\(689\) | −1.87472e12 | −0.316921 | ||||||||
\(690\) | 8.86547e12 | 1.48895 | ||||||||
\(691\) | −7.61866e10 | −0.0127124 | −0.00635620 | − | 0.999980i | \(-0.502023\pi\) | ||||
−0.00635620 | + | 0.999980i | \(0.502023\pi\) | |||||||
\(692\) | 2.85557e11 | 0.0473385 | ||||||||
\(693\) | −3.43784e12 | −0.566221 | ||||||||
\(694\) | 5.16801e12 | 0.845679 | ||||||||
\(695\) | 8.44493e11 | 0.137298 | ||||||||
\(696\) | −1.03386e12 | −0.167002 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6.59128e12 | 1.05104 | ||||||||
\(699\) | −7.84852e12 | −1.24348 | ||||||||
\(700\) | −2.03720e12 | −0.320695 | ||||||||
\(701\) | −4.55938e12 | −0.713139 | −0.356570 | − | 0.934269i | \(-0.616054\pi\) | ||||
−0.356570 | + | 0.934269i | \(0.616054\pi\) | |||||||
\(702\) | 8.28163e11 | 0.128706 | ||||||||
\(703\) | −8.71677e12 | −1.34604 | ||||||||
\(704\) | 3.49939e12 | 0.536927 | ||||||||
\(705\) | −5.44282e12 | −0.829799 | ||||||||
\(706\) | −9.26420e12 | −1.40342 | ||||||||
\(707\) | 2.43897e12 | 0.367129 | ||||||||
\(708\) | 2.89605e12 | 0.433167 | ||||||||
\(709\) | 9.54492e12 | 1.41861 | 0.709307 | − | 0.704899i | \(-0.249008\pi\) | ||||
0.709307 | + | 0.704899i | \(0.249008\pi\) | |||||||
\(710\) | −1.40947e12 | −0.208157 | ||||||||
\(711\) | −4.75804e12 | −0.698257 | ||||||||
\(712\) | 2.86760e12 | 0.418175 | ||||||||
\(713\) | 7.03050e12 | 1.01879 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.96533e12 | 0.567417 | ||||||||
\(716\) | 7.19673e12 | 1.02336 | ||||||||
\(717\) | 2.55148e12 | 0.360541 | ||||||||
\(718\) | 8.86922e12 | 1.24545 | ||||||||
\(719\) | 1.65457e12 | 0.230890 | 0.115445 | − | 0.993314i | \(-0.463171\pi\) | ||||
0.115445 | + | 0.993314i | \(0.463171\pi\) | |||||||
\(720\) | 5.16714e12 | 0.716563 | ||||||||
\(721\) | −9.63303e12 | −1.32756 | ||||||||
\(722\) | −1.37401e13 | −1.88180 | ||||||||
\(723\) | 6.42928e12 | 0.875065 | ||||||||
\(724\) | −4.00635e12 | −0.541908 | ||||||||
\(725\) | 2.07733e12 | 0.279245 | ||||||||
\(726\) | 3.74056e12 | 0.499714 | ||||||||
\(727\) | −2.21622e12 | −0.294244 | −0.147122 | − | 0.989118i | \(-0.547001\pi\) | ||||
−0.147122 | + | 0.989118i | \(0.547001\pi\) | |||||||
\(728\) | 1.24593e12 | 0.164400 | ||||||||
\(729\) | −6.52814e12 | −0.856082 | ||||||||
\(730\) | −3.74918e12 | −0.488633 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.55500e13 | 2.00184 | ||||||||
\(733\) | 2.96185e11 | 0.0378961 | 0.0189481 | − | 0.999820i | \(-0.493968\pi\) | ||||
0.0189481 | + | 0.999820i | \(0.493968\pi\) | |||||||
\(734\) | 4.32255e12 | 0.549678 | ||||||||
\(735\) | 3.66572e12 | 0.463304 | ||||||||
\(736\) | 1.22847e13 | 1.54318 | ||||||||
\(737\) | −8.67530e12 | −1.08313 | ||||||||
\(738\) | −1.69709e13 | −2.10597 | ||||||||
\(739\) | −4.82363e12 | −0.594941 | −0.297470 | − | 0.954731i | \(-0.596143\pi\) | ||||
−0.297470 | + | 0.954731i | \(0.596143\pi\) | |||||||
\(740\) | 3.94803e12 | 0.483992 | ||||||||
\(741\) | 1.73481e13 | 2.11383 | ||||||||
\(742\) | 2.55420e12 | 0.309341 | ||||||||
\(743\) | 4.52977e12 | 0.545288 | 0.272644 | − | 0.962115i | \(-0.412102\pi\) | ||||
0.272644 | + | 0.962115i | \(0.412102\pi\) | |||||||
\(744\) | 2.36292e12 | 0.282729 | ||||||||
\(745\) | 1.22876e12 | 0.146138 | ||||||||
\(746\) | −5.47518e12 | −0.647252 | ||||||||
\(747\) | 7.55726e12 | 0.888018 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.31485e10 | 0.00268754 | ||||||||
\(750\) | −1.69420e13 | −1.95519 | ||||||||
\(751\) | 1.65211e13 | 1.89522 | 0.947610 | − | 0.319430i | \(-0.103491\pi\) | ||||
0.947610 | + | 0.319430i | \(0.103491\pi\) | |||||||
\(752\) | −8.89606e12 | −1.01442 | ||||||||
\(753\) | −1.03853e13 | −1.17718 | ||||||||
\(754\) | 6.02729e12 | 0.679127 | ||||||||
\(755\) | 5.82744e12 | 0.652704 | ||||||||
\(756\) | −5.10372e11 | −0.0568249 | ||||||||
\(757\) | 1.53269e13 | 1.69638 | 0.848192 | − | 0.529690i | \(-0.177692\pi\) | ||||
0.848192 | + | 0.529690i | \(0.177692\pi\) | |||||||
\(758\) | −8.13865e12 | −0.895450 | ||||||||
\(759\) | −1.28156e13 | −1.40168 | ||||||||
\(760\) | −2.25373e12 | −0.245042 | ||||||||
\(761\) | 2.48205e12 | 0.268274 | 0.134137 | − | 0.990963i | \(-0.457174\pi\) | ||||
0.134137 | + | 0.990963i | \(0.457174\pi\) | |||||||
\(762\) | 1.50265e13 | 1.61459 | ||||||||
\(763\) | −1.91825e12 | −0.204902 | ||||||||
\(764\) | −2.21457e11 | −0.0235164 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.89254e13 | −1.98616 | ||||||||
\(767\) | 3.55885e12 | 0.371305 | ||||||||
\(768\) | 1.67824e13 | 1.74072 | ||||||||
\(769\) | 1.57447e13 | 1.62356 | 0.811778 | − | 0.583967i | \(-0.198500\pi\) | ||||
0.811778 | + | 0.583967i | \(0.198500\pi\) | |||||||
\(770\) | −5.40253e12 | −0.553845 | ||||||||
\(771\) | 6.51082e12 | 0.663576 | ||||||||
\(772\) | 5.73304e12 | 0.580907 | ||||||||
\(773\) | −1.47271e11 | −0.0148357 | −0.00741786 | − | 0.999972i | \(-0.502361\pi\) | ||||
−0.00741786 | + | 0.999972i | \(0.502361\pi\) | |||||||
\(774\) | 2.32901e13 | 2.33258 | ||||||||
\(775\) | −4.74780e12 | −0.472754 | ||||||||
\(776\) | −3.53411e12 | −0.349866 | ||||||||
\(777\) | −8.72756e12 | −0.859010 | ||||||||
\(778\) | 5.28108e12 | 0.516790 | ||||||||
\(779\) | 2.66345e13 | 2.59135 | ||||||||
\(780\) | −7.85736e12 | −0.760065 | ||||||||
\(781\) | 2.03747e12 | 0.195957 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.20427e11 | 0.0494802 | ||||||||
\(784\) | 5.99147e12 | 0.566384 | ||||||||
\(785\) | −1.20630e13 | −1.13382 | ||||||||
\(786\) | −3.28906e13 | −3.07376 | ||||||||
\(787\) | −1.64023e13 | −1.52412 | −0.762059 | − | 0.647508i | \(-0.775811\pi\) | ||||
−0.762059 | + | 0.647508i | \(0.775811\pi\) | |||||||
\(788\) | −9.39466e12 | −0.867987 | ||||||||
\(789\) | 5.03095e12 | 0.462172 | ||||||||
\(790\) | −7.47722e12 | −0.682996 | ||||||||
\(791\) | −3.28865e12 | −0.298692 | ||||||||
\(792\) | −2.07587e12 | −0.187472 | ||||||||
\(793\) | 1.91088e13 | 1.71595 | ||||||||
\(794\) | 1.82847e11 | 0.0163266 | ||||||||
\(795\) | 3.39533e12 | 0.301461 | ||||||||
\(796\) | 6.68559e12 | 0.590243 | ||||||||
\(797\) | −3.29266e12 | −0.289058 | −0.144529 | − | 0.989501i | \(-0.546167\pi\) | ||||
−0.144529 | + | 0.989501i | \(0.546167\pi\) | |||||||
\(798\) | −2.36357e13 | −2.06327 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −8.29605e12 | −0.716088 | ||||||||
\(801\) | 1.92669e13 | 1.65373 | ||||||||
\(802\) | −8.90914e10 | −0.00760416 | ||||||||
\(803\) | 5.41966e12 | 0.459994 | ||||||||
\(804\) | 1.71902e13 | 1.45087 | ||||||||
\(805\) | −6.71393e12 | −0.563501 | ||||||||
\(806\) | −1.37755e13 | −1.14974 | ||||||||
\(807\) | −5.88729e12 | −0.488635 | ||||||||
\(808\) | 1.47272e12 | 0.121554 | ||||||||
\(809\) | 1.55916e13 | 1.27974 | 0.639870 | − | 0.768483i | \(-0.278988\pi\) | ||||
0.639870 | + | 0.768483i | \(0.278988\pi\) | |||||||
\(810\) | −1.18712e13 | −0.968972 | ||||||||
\(811\) | −1.51604e11 | −0.0123060 | −0.00615301 | − | 0.999981i | \(-0.501959\pi\) | ||||
−0.00615301 | + | 0.999981i | \(0.501959\pi\) | |||||||
\(812\) | −3.71443e12 | −0.299840 | ||||||||
\(813\) | −1.41493e13 | −1.13587 | ||||||||
\(814\) | −1.26172e13 | −1.00729 | ||||||||
\(815\) | −8.68713e12 | −0.689711 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.65519e13 | −2.87019 | ||||||||
\(818\) | −1.34463e13 | −1.05005 | ||||||||
\(819\) | 8.37119e12 | 0.650144 | ||||||||
\(820\) | −1.20634e13 | −0.931767 | ||||||||
\(821\) | 1.44623e13 | 1.11095 | 0.555475 | − | 0.831533i | \(-0.312536\pi\) | ||||
0.555475 | + | 0.831533i | \(0.312536\pi\) | |||||||
\(822\) | −5.60754e12 | −0.428399 | ||||||||
\(823\) | 2.42578e13 | 1.84311 | 0.921557 | − | 0.388243i | \(-0.126918\pi\) | ||||
0.921557 | + | 0.388243i | \(0.126918\pi\) | |||||||
\(824\) | −5.81670e12 | −0.439546 | ||||||||
\(825\) | 8.65455e12 | 0.650431 | ||||||||
\(826\) | −4.84872e12 | −0.362424 | ||||||||
\(827\) | −6.48867e12 | −0.482371 | −0.241185 | − | 0.970479i | \(-0.577536\pi\) | ||||
−0.241185 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(828\) | 1.22387e13 | 0.904893 | ||||||||
\(829\) | −1.83303e12 | −0.134795 | −0.0673977 | − | 0.997726i | \(-0.521470\pi\) | ||||
−0.0673977 | + | 0.997726i | \(0.521470\pi\) | |||||||
\(830\) | 1.18762e13 | 0.868610 | ||||||||
\(831\) | 1.69441e12 | 0.123258 | ||||||||
\(832\) | −8.52106e12 | −0.616508 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.34782e12 | 0.382763 | ||||||||
\(835\) | 2.12800e12 | 0.151489 | ||||||||
\(836\) | −1.54559e13 | −1.09437 | ||||||||
\(837\) | −1.18945e12 | −0.0837687 | ||||||||
\(838\) | −2.71609e13 | −1.90259 | ||||||||
\(839\) | −2.21690e13 | −1.54461 | −0.772303 | − | 0.635254i | \(-0.780895\pi\) | ||||
−0.772303 | + | 0.635254i | \(0.780895\pi\) | |||||||
\(840\) | −2.25652e12 | −0.156380 | ||||||||
\(841\) | −1.07195e13 | −0.738914 | ||||||||
\(842\) | −1.19610e13 | −0.820094 | ||||||||
\(843\) | 2.54285e12 | 0.173419 | ||||||||
\(844\) | 2.01700e13 | 1.36825 | ||||||||
\(845\) | 3.24622e11 | 0.0219040 | ||||||||
\(846\) | −1.66113e13 | −1.11490 | ||||||||
\(847\) | −2.83277e12 | −0.189119 | ||||||||
\(848\) | 5.54953e12 | 0.368532 | ||||||||
\(849\) | 2.44767e13 | 1.61684 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.56799e13 | −1.02485 | ||||||||
\(852\) | −4.03727e12 | −0.262488 | ||||||||
\(853\) | −1.03748e13 | −0.670979 | −0.335489 | − | 0.942044i | \(-0.608902\pi\) | ||||
−0.335489 | + | 0.942044i | \(0.608902\pi\) | |||||||
\(854\) | −2.60346e13 | −1.67491 | ||||||||
\(855\) | −1.51424e13 | −0.969053 | ||||||||
\(856\) | 1.39777e10 | 0.000889825 0 | ||||||||
\(857\) | 6.86176e12 | 0.434532 | 0.217266 | − | 0.976112i | \(-0.430286\pi\) | ||||
0.217266 | + | 0.976112i | \(0.430286\pi\) | |||||||
\(858\) | 2.51108e13 | 1.58186 | ||||||||
\(859\) | −1.74774e13 | −1.09524 | −0.547619 | − | 0.836728i | \(-0.684466\pi\) | ||||
−0.547619 | + | 0.836728i | \(0.684466\pi\) | |||||||
\(860\) | 1.65552e13 | 1.03203 | ||||||||
\(861\) | 2.66674e13 | 1.65374 | ||||||||
\(862\) | −2.38880e13 | −1.47366 | ||||||||
\(863\) | 2.44274e13 | 1.49910 | 0.749548 | − | 0.661950i | \(-0.230271\pi\) | ||||
0.749548 | + | 0.661950i | \(0.230271\pi\) | |||||||
\(864\) | −2.07838e12 | −0.126886 | ||||||||
\(865\) | −6.35539e11 | −0.0385984 | ||||||||
\(866\) | −2.76339e13 | −1.66960 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.48944e12 | 0.507622 | ||||||||
\(869\) | 1.08088e13 | 0.642965 | ||||||||
\(870\) | −1.09161e13 | −0.645997 | ||||||||
\(871\) | 2.11245e13 | 1.24367 | ||||||||
\(872\) | −1.15830e12 | −0.0678416 | ||||||||
\(873\) | −2.37450e13 | −1.38359 | ||||||||
\(874\) | −4.24639e13 | −2.46161 | ||||||||
\(875\) | 1.28304e13 | 0.739953 | ||||||||
\(876\) | −1.07391e13 | −0.616171 | ||||||||
\(877\) | −2.67317e13 | −1.52591 | −0.762953 | − | 0.646454i | \(-0.776251\pi\) | ||||
−0.762953 | + | 0.646454i | \(0.776251\pi\) | |||||||
\(878\) | 1.57436e13 | 0.894086 | ||||||||
\(879\) | 4.07454e13 | 2.30212 | ||||||||
\(880\) | −1.17381e13 | −0.659822 | ||||||||
\(881\) | 1.44360e13 | 0.807338 | 0.403669 | − | 0.914905i | \(-0.367735\pi\) | ||||
0.403669 | + | 0.914905i | \(0.367735\pi\) | |||||||
\(882\) | 1.11876e13 | 0.622486 | ||||||||
\(883\) | 4.32149e12 | 0.239227 | 0.119613 | − | 0.992821i | \(-0.461834\pi\) | ||||
0.119613 | + | 0.992821i | \(0.461834\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.44548e12 | −0.353192 | ||||||||
\(886\) | 4.88754e13 | 2.66464 | ||||||||
\(887\) | 1.12787e13 | 0.611792 | 0.305896 | − | 0.952065i | \(-0.401044\pi\) | ||||
0.305896 | + | 0.952065i | \(0.401044\pi\) | |||||||
\(888\) | −5.26995e12 | −0.284412 | ||||||||
\(889\) | −1.13798e13 | −0.611049 | ||||||||
\(890\) | 3.02777e13 | 1.61759 | ||||||||
\(891\) | 1.71605e13 | 0.912180 | ||||||||
\(892\) | 1.88548e13 | 0.997195 | ||||||||
\(893\) | 2.60701e13 | 1.37186 | ||||||||
\(894\) | 7.78122e12 | 0.407407 | ||||||||
\(895\) | −1.60171e13 | −0.834413 | ||||||||
\(896\) | −6.35137e12 | −0.329216 | ||||||||
\(897\) | 3.12061e13 | 1.60944 | ||||||||
\(898\) | −2.69555e13 | −1.38326 | ||||||||
\(899\) | −8.65669e12 | −0.442011 | ||||||||
\(900\) | −8.26494e12 | −0.419903 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.85526e13 | 1.93920 | ||||||||
\(903\) | −3.65972e13 | −1.83169 | ||||||||
\(904\) | −1.98578e12 | −0.0988950 | ||||||||
\(905\) | 8.91659e12 | 0.441856 | ||||||||
\(906\) | 3.69027e13 | 1.81962 | ||||||||
\(907\) | −5.70352e12 | −0.279840 | −0.139920 | − | 0.990163i | \(-0.544685\pi\) | ||||
−0.139920 | + | 0.990163i | \(0.544685\pi\) | |||||||
\(908\) | 2.81434e13 | 1.37401 | ||||||||
\(909\) | 9.89495e12 | 0.480702 | ||||||||
\(910\) | 1.31552e13 | 0.635934 | ||||||||
\(911\) | 3.37049e13 | 1.62129 | 0.810643 | − | 0.585540i | \(-0.199118\pi\) | ||||
0.810643 | + | 0.585540i | \(0.199118\pi\) | |||||||
\(912\) | −5.13535e13 | −2.45807 | ||||||||
\(913\) | −1.71677e13 | −0.817701 | ||||||||
\(914\) | 1.36229e13 | 0.645673 | ||||||||
\(915\) | −3.46082e13 | −1.63224 | ||||||||
\(916\) | 1.50242e13 | 0.705119 | ||||||||
\(917\) | 2.49084e13 | 1.16328 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.15276e13 | −0.995577 | −0.497789 | − | 0.867298i | \(-0.665854\pi\) | ||||
−0.497789 | + | 0.867298i | \(0.665854\pi\) | |||||||
\(920\) | −4.05406e12 | −0.186572 | ||||||||
\(921\) | 2.81073e13 | 1.28721 | ||||||||
\(922\) | −3.22742e13 | −1.47084 | ||||||||
\(923\) | −4.96127e12 | −0.225001 | ||||||||
\(924\) | −1.54750e13 | −0.698404 | ||||||||
\(925\) | 1.05889e13 | 0.475568 | ||||||||
\(926\) | 2.08546e13 | 0.932080 | ||||||||
\(927\) | −3.90814e13 | −1.73825 | ||||||||
\(928\) | −1.51262e13 | −0.669522 | ||||||||
\(929\) | −3.52619e13 | −1.55323 | −0.776613 | − | 0.629978i | \(-0.783064\pi\) | ||||
−0.776613 | + | 0.629978i | \(0.783064\pi\) | |||||||
\(930\) | 2.49490e13 | 1.09366 | ||||||||
\(931\) | −1.75581e13 | −0.765957 | ||||||||
\(932\) | −1.70267e13 | −0.739196 | ||||||||
\(933\) | 5.95448e13 | 2.57263 | ||||||||
\(934\) | 3.51059e13 | 1.50945 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.05477e12 | 0.215258 | ||||||||
\(937\) | −6.89322e12 | −0.292142 | −0.146071 | − | 0.989274i | \(-0.546663\pi\) | ||||
−0.146071 | + | 0.989274i | \(0.546663\pi\) | |||||||
\(938\) | −2.87809e13 | −1.21392 | ||||||||
\(939\) | 3.85058e13 | 1.61633 | ||||||||
\(940\) | −1.18078e13 | −0.493279 | ||||||||
\(941\) | 5.81040e12 | 0.241575 | 0.120788 | − | 0.992678i | \(-0.461458\pi\) | ||||
0.120788 | + | 0.992678i | \(0.461458\pi\) | |||||||
\(942\) | −7.63902e13 | −3.16088 | ||||||||
\(943\) | 4.79107e13 | 1.97301 | ||||||||
\(944\) | −1.05349e13 | −0.431773 | ||||||||
\(945\) | 1.13589e12 | 0.0463333 | ||||||||
\(946\) | −5.29077e13 | −2.14788 | ||||||||
\(947\) | −2.09948e13 | −0.848277 | −0.424139 | − | 0.905597i | \(-0.639423\pi\) | ||||
−0.424139 | + | 0.905597i | \(0.639423\pi\) | |||||||
\(948\) | −2.14178e13 | −0.861264 | ||||||||
\(949\) | −1.31970e13 | −0.528173 | ||||||||
\(950\) | 2.86765e13 | 1.14227 | ||||||||
\(951\) | 4.93201e13 | 1.95529 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.60372e13 | 1.80797 | 0.903984 | − | 0.427567i | \(-0.140629\pi\) | ||||
0.903984 | + | 0.427567i | \(0.140629\pi\) | |||||||
\(954\) | 1.03624e13 | 0.405036 | ||||||||
\(955\) | 4.92879e11 | 0.0191745 | ||||||||
\(956\) | 5.53522e12 | 0.214326 | ||||||||
\(957\) | 1.57799e13 | 0.608135 | ||||||||
\(958\) | 4.27220e12 | 0.163873 | ||||||||
\(959\) | 4.24666e12 | 0.162130 | ||||||||
\(960\) | 1.54326e13 | 0.586433 | ||||||||
\(961\) | −6.65451e12 | −0.251687 | ||||||||
\(962\) | 3.07232e13 | 1.15659 | ||||||||
\(963\) | 9.39138e10 | 0.00351894 | ||||||||
\(964\) | 1.39478e13 | 0.520187 | ||||||||
\(965\) | −1.27595e13 | −0.473655 | ||||||||
\(966\) | −4.25165e13 | −1.57094 | ||||||||
\(967\) | −3.36646e13 | −1.23809 | −0.619047 | − | 0.785354i | \(-0.712481\pi\) | ||||
−0.619047 | + | 0.785354i | \(0.712481\pi\) | |||||||
\(968\) | −1.71051e12 | −0.0626162 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.73151e13 | −1.35336 | ||||||||
\(971\) | −4.32838e13 | −1.56257 | −0.781284 | − | 0.624175i | \(-0.785435\pi\) | ||||
−0.781284 | + | 0.624175i | \(0.785435\pi\) | |||||||
\(972\) | −3.17781e13 | −1.14190 | ||||||||
\(973\) | −4.04997e12 | −0.144859 | ||||||||
\(974\) | 2.00202e13 | 0.712776 | ||||||||
\(975\) | −2.10740e13 | −0.746836 | ||||||||
\(976\) | −5.65657e13 | −1.99540 | ||||||||
\(977\) | −2.72015e13 | −0.955141 | −0.477570 | − | 0.878593i | \(-0.658482\pi\) | ||||
−0.477570 | + | 0.878593i | \(0.658482\pi\) | |||||||
\(978\) | −5.50120e13 | −1.92279 | ||||||||
\(979\) | −4.37682e13 | −1.52278 | ||||||||
\(980\) | 7.95249e12 | 0.275414 | ||||||||
\(981\) | −7.78240e12 | −0.268289 | ||||||||
\(982\) | 4.08787e12 | 0.140280 | ||||||||
\(983\) | −3.51517e13 | −1.20076 | −0.600379 | − | 0.799716i | \(-0.704984\pi\) | ||||
−0.600379 | + | 0.799716i | \(0.704984\pi\) | |||||||
\(984\) | 1.61026e13 | 0.547542 | ||||||||
\(985\) | 2.09089e13 | 0.707731 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.61023e13 | 0.875492 | ||||||||
\(988\) | 3.76353e13 | 1.25658 | ||||||||
\(989\) | −6.57505e13 | −2.18532 | ||||||||
\(990\) | −2.19182e13 | −0.725180 | ||||||||
\(991\) | 2.19268e13 | 0.722177 | 0.361088 | − | 0.932532i | \(-0.382405\pi\) | ||||
0.361088 | + | 0.932532i | \(0.382405\pi\) | |||||||
\(992\) | 3.45715e13 | 1.13348 | ||||||||
\(993\) | 8.07883e13 | 2.63680 | ||||||||
\(994\) | 6.75943e12 | 0.219620 | ||||||||
\(995\) | −1.48795e13 | −0.481266 | ||||||||
\(996\) | 3.40181e13 | 1.09532 | ||||||||
\(997\) | 5.52175e13 | 1.76990 | 0.884949 | − | 0.465688i | \(-0.154193\pi\) | ||||
0.884949 | + | 0.465688i | \(0.154193\pi\) | |||||||
\(998\) | 2.29660e13 | 0.732821 | ||||||||
\(999\) | 2.65280e12 | 0.0842673 |
(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 | 289.10.a.e.1.3 | yes | 12 | |
17.16 | even | 2 | 289.10.a.d.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.d.1.3 | ✓ | 12 | 17.16 | even | 2 | ||
289.10.a.e.1.3 | yes | 12 | 1.1 | even | 1 | trivial |