Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,8,Mod(1,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.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: | \(93.7155076452\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 60) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 300.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1028.00 | −1.13279 | −0.566396 | − | 0.824133i | \(-0.691663\pi\) | ||||
−0.566396 | + | 0.824133i | \(0.691663\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3096.00 | 0.701337 | 0.350668 | − | 0.936500i | \(-0.385954\pi\) | ||||
0.350668 | + | 0.936500i | \(0.385954\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13030.0 | 1.64491 | 0.822456 | − | 0.568829i | \(-0.192603\pi\) | ||||
0.822456 | + | 0.568829i | \(0.192603\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1878.00 | −0.0927095 | −0.0463548 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463548 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31180.0 | −1.04289 | −0.521445 | − | 0.853285i | \(-0.674607\pi\) | ||||
−0.521445 | + | 0.853285i | \(0.674607\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −27756.0 | −0.654017 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33288.0 | 0.570480 | 0.285240 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285240 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −213054. | −1.62217 | −0.811086 | − | 0.584927i | \(-0.801123\pi\) | ||||
−0.811086 | + | 0.584927i | \(0.801123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −172696. | −1.04116 | −0.520579 | − | 0.853814i | \(-0.674284\pi\) | ||||
−0.520579 | + | 0.853814i | \(0.674284\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 83592.0 | 0.404917 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27434.0 | −0.0890396 | −0.0445198 | − | 0.999009i | \(-0.514176\pi\) | ||||
−0.0445198 | + | 0.999009i | \(0.514176\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 351810. | 0.949690 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 532650. | 1.20698 | 0.603488 | − | 0.797372i | \(-0.293777\pi\) | ||||
0.603488 | + | 0.797372i | \(0.293777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 911908. | 1.74909 | 0.874544 | − | 0.484947i | \(-0.161161\pi\) | ||||
0.874544 | + | 0.484947i | \(0.161161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 732648. | 1.02933 | 0.514663 | − | 0.857393i | \(-0.327917\pi\) | ||||
0.514663 | + | 0.857393i | \(0.327917\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 233241. | 0.283217 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −50706.0 | −0.0535259 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −409074. | −0.377430 | −0.188715 | − | 0.982032i | \(-0.560432\pi\) | ||||
−0.188715 | + | 0.982032i | \(0.560432\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −841860. | −0.602113 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50814e6 | 0.956001 | 0.478001 | − | 0.878359i | \(-0.341362\pi\) | ||||
0.478001 | + | 0.878359i | \(0.341362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −302578. | −0.170680 | −0.0853401 | − | 0.996352i | \(-0.527198\pi\) | ||||
−0.0853401 | + | 0.996352i | \(0.527198\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −749412. | −0.377597 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.25433e6 | −0.509508 | −0.254754 | − | 0.967006i | \(-0.581994\pi\) | ||||
−0.254754 | + | 0.967006i | \(0.581994\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 898776. | 0.329367 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.78128e6 | 1.58540 | 0.792702 | − | 0.609609i | \(-0.208674\pi\) | ||||
0.792702 | + | 0.609609i | \(0.208674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 502414. | 0.151158 | 0.0755791 | − | 0.997140i | \(-0.475919\pi\) | ||||
0.0755791 | + | 0.997140i | \(0.475919\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.18269e6 | −0.794468 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.99137e6 | −0.454419 | −0.227210 | − | 0.973846i | \(-0.572960\pi\) | ||||
−0.227210 | + | 0.973846i | \(0.572960\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.09927e6 | 1.55479 | 0.777396 | − | 0.629011i | \(-0.216540\pi\) | ||||
0.777396 | + | 0.629011i | \(0.216540\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.75246e6 | −0.936561 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.48797e6 | 1.12590 | 0.562949 | − | 0.826492i | \(-0.309667\pi\) | ||||
0.562949 | + | 0.826492i | \(0.309667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.33948e7 | −1.86334 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.66279e6 | −0.601112 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.71726e7 | 1.91044 | 0.955222 | − | 0.295890i | \(-0.0956162\pi\) | ||||
0.955222 | + | 0.295890i | \(0.0956162\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.25698e6 | 0.233779 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.74434e6 | −0.941083 | −0.470541 | − | 0.882378i | \(-0.655941\pi\) | ||||
−0.470541 | + | 0.882378i | \(0.655941\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.69855e7 | 1.53161 | 0.765803 | − | 0.643076i | \(-0.222342\pi\) | ||||
0.765803 | + | 0.643076i | \(0.222342\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.20386e7 | 0.950017 | 0.475008 | − | 0.879981i | \(-0.342445\pi\) | ||||
0.475008 | + | 0.879981i | \(0.342445\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.18251e7 | 0.874605 | 0.437303 | − | 0.899314i | \(-0.355934\pi\) | ||||
0.437303 | + | 0.899314i | \(0.355934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −740718. | −0.0514070 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.73862e7 | −1.13352 | −0.566761 | − | 0.823882i | \(-0.691804\pi\) | ||||
−0.566761 | + | 0.823882i | \(0.691804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.49887e6 | 0.548304 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.93058e6 | 0.105021 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.90196e6 | −0.508127 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.43816e7 | 0.696848 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.43900e7 | 0.623371 | 0.311686 | − | 0.950185i | \(-0.399106\pi\) | ||||
0.311686 | + | 0.950185i | \(0.399106\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.46215e7 | 1.00984 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.80590e7 | −0.701849 | −0.350924 | − | 0.936404i | \(-0.614133\pi\) | ||||
−0.350924 | + | 0.936404i | \(0.614133\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.20530e7 | 1.18138 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.51304e7 | −1.49950 | −0.749751 | − | 0.661720i | \(-0.769827\pi\) | ||||
−0.749751 | + | 0.661720i | \(0.769827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.34776e7 | 0.425658 | 0.212829 | − | 0.977089i | \(-0.431732\pi\) | ||||
0.212829 | + | 0.977089i | \(0.431732\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.97815e7 | 0.594282 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.03409e7 | 1.15364 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.29751e6 | 0.163515 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.31740e7 | 1.81219 | 0.906097 | − | 0.423069i | \(-0.139047\pi\) | ||||
0.906097 | + | 0.423069i | \(0.139047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.51556e6 | −0.0830951 | −0.0415475 | − | 0.999137i | \(-0.513229\pi\) | ||||
−0.0415475 | + | 0.999137i | \(0.513229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.36906e6 | −0.0309032 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.84023e7 | −0.998198 | −0.499099 | − | 0.866545i | \(-0.666336\pi\) | ||||
−0.499099 | + | 0.866545i | \(0.666336\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.10450e7 | −0.217909 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.42201e7 | −0.646235 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.46558e6 | −0.135023 | −0.0675114 | − | 0.997719i | \(-0.521506\pi\) | ||||
−0.0675114 | + | 0.997719i | \(0.521506\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.12908e7 | −0.187594 | −0.0937968 | − | 0.995591i | \(-0.529900\pi\) | ||||
−0.0937968 | + | 0.995591i | \(0.529900\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.07032e8 | 1.70574 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.27302e7 | −0.347630 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.89209e7 | 1.45254 | 0.726268 | − | 0.687412i | \(-0.241253\pi\) | ||||
0.726268 | + | 0.687412i | \(0.241253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.07197e7 | 0.551948 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.70144e7 | 1.00366 | 0.501830 | − | 0.864966i | \(-0.332660\pi\) | ||||
0.501830 | + | 0.864966i | \(0.332660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.06546e8 | 1.33555 | 0.667775 | − | 0.744363i | \(-0.267247\pi\) | ||||
0.667775 | + | 0.744363i | \(0.267247\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.16961e6 | −0.0985422 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.81429e6 | −0.0650206 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.02341e7 | −0.218006 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.98531e7 | −0.310008 | −0.155004 | − | 0.987914i | \(-0.549539\pi\) | ||||
−0.155004 | + | 0.987914i | \(0.549539\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.96359e7 | 0.797367 | 0.398683 | − | 0.917089i | \(-0.369467\pi\) | ||||
0.398683 | + | 0.917089i | \(0.369467\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.82207e7 | 0.822127 | 0.411063 | − | 0.911607i | \(-0.365157\pi\) | ||||
0.411063 | + | 0.911607i | \(0.365157\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.13663e8 | 1.02243 | 0.511215 | − | 0.859453i | \(-0.329196\pi\) | ||||
0.511215 | + | 0.859453i | \(0.329196\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.38670e7 | −0.294164 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.19020e8 | 1.83758 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.42670e7 | 0.190160 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.65333e7 | −0.731417 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.54455e7 | −0.552898 | −0.276449 | − | 0.961029i | \(-0.589158\pi\) | ||||
−0.276449 | + | 0.961029i | \(0.589158\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.29095e8 | 0.915333 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.77531e8 | 1.17941 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.35652e7 | 0.0872712 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.44703e7 | −0.152499 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.69318e8 | −1.02244 | −0.511218 | − | 0.859451i | \(-0.670805\pi\) | ||||
−0.511218 | + | 0.859451i | \(0.670805\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.32506e7 | −0.0751873 | −0.0375936 | − | 0.999293i | \(-0.511969\pi\) | ||||
−0.0375936 | + | 0.999293i | \(0.511969\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.44714e8 | 0.796315 | 0.398158 | − | 0.917317i | \(-0.369650\pi\) | ||||
0.398158 | + | 0.917317i | \(0.369650\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.59326e7 | −0.458686 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.13205e8 | −1.10421 | −0.552104 | − | 0.833775i | \(-0.686175\pi\) | ||||
−0.552104 | + | 0.833775i | \(0.686175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.37669e7 | −0.262359 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.36644e8 | −1.59507 | −0.797533 | − | 0.603275i | \(-0.793862\pi\) | ||||
−0.797533 | + | 0.603275i | \(0.793862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.40329e8 | −1.10598 | −0.552989 | − | 0.833188i | \(-0.686513\pi\) | ||||
−0.552989 | + | 0.833188i | \(0.686513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.06275e8 | −1.71546 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.18680e8 | 0.897660 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.75235e7 | 0.349355 | 0.174677 | − | 0.984626i | \(-0.444112\pi\) | ||||
0.174677 | + | 0.984626i | \(0.444112\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.03060e8 | 0.400098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.05874e8 | −0.389068 | −0.194534 | − | 0.980896i | \(-0.562319\pi\) | ||||
−0.194534 | + | 0.980896i | \(0.562319\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.82022e7 | 0.100863 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.55316e8 | −0.540724 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.81542e7 | −0.0954330 | −0.0477165 | − | 0.998861i | \(-0.515194\pi\) | ||||
−0.0477165 | + | 0.998861i | \(0.515194\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.02175e8 | 0.650038 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.80408e8 | −1.19156 | −0.595781 | − | 0.803147i | \(-0.703157\pi\) | ||||
−0.595781 | + | 0.803147i | \(0.703157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.13368e8 | 1.87210 | 0.936049 | − | 0.351870i | \(-0.114454\pi\) | ||||
0.936049 | + | 0.351870i | \(0.114454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.61661e8 | −1.07580 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.86407e8 | 0.809662 | 0.404831 | − | 0.914391i | \(-0.367330\pi\) | ||||
0.404831 | + | 0.914391i | \(0.367330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.25895e8 | −0.347052 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.38705e8 | 1.17951 | 0.589753 | − | 0.807584i | \(-0.299225\pi\) | ||||
0.589753 | + | 0.807584i | \(0.299225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.85747e8 | −1.27397 | −0.636983 | − | 0.770878i | \(-0.719818\pi\) | ||||
−0.636983 | + | 0.770878i | \(0.719818\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.47564e8 | −1.36725 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.06812e8 | −0.991405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.63659e8 | 1.10300 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.76441e8 | −0.874300 | −0.437150 | − | 0.899389i | \(-0.644012\pi\) | ||||
−0.437150 | + | 0.899389i | \(0.644012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.09386e7 | 0.134972 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.33743e8 | 0.938389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.37441e8 | −1.98135 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.63097e8 | −0.543334 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.22474e8 | 1.62232 | 0.811162 | − | 0.584821i | \(-0.198835\pi\) | ||||
0.811162 | + | 0.584821i | \(0.198835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.58607e8 | 0.884273 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.61865e8 | −0.870671 | −0.435335 | − | 0.900268i | \(-0.643370\pi\) | ||||
−0.435335 | + | 0.900268i | \(0.643370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.99153e8 | −0.551427 | −0.275714 | − | 0.961240i | \(-0.588914\pi\) | ||||
−0.275714 | + | 0.961240i | \(0.588914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.25971e8 | −1.10369 | −0.551844 | − | 0.833947i | \(-0.686076\pi\) | ||||
−0.551844 | + | 0.833947i | \(0.686076\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.59615e8 | −1.13769 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.25041e8 | 0.548492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.85560e7 | 0.0966858 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.19278e8 | 0.504954 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.53162e8 | −1.16601 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.12189e9 | 1.70041 | 0.850203 | − | 0.526455i | \(-0.176479\pi\) | ||||
0.850203 | + | 0.526455i | \(0.176479\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.99994e7 | −0.0296799 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.06060e8 | 0.293285 | 0.146642 | − | 0.989190i | \(-0.453153\pi\) | ||||
0.146642 | + | 0.989190i | \(0.453153\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.69428e8 | −0.654440 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.34667e8 | −0.730202 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.06830e8 | 0.811966 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.20291e8 | −0.668487 | −0.334244 | − | 0.942487i | \(-0.608481\pi\) | ||||
−0.334244 | + | 0.942487i | \(0.608481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.25363e9 | −1.57863 | −0.789313 | − | 0.613992i | \(-0.789563\pi\) | ||||
−0.789313 | + | 0.613992i | \(0.789563\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.56469e8 | 0.316563 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.54823e8 | 0.429339 | 0.214670 | − | 0.976687i | \(-0.431132\pi\) | ||||
0.214670 | + | 0.976687i | \(0.431132\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.21258e7 | 0.0606336 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.64905e9 | −1.88106 | −0.940530 | − | 0.339712i | \(-0.889670\pi\) | ||||
−0.940530 | + | 0.339712i | \(0.889670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.83207e7 | 0.0876196 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.67353e8 | −0.293367 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.96700e8 | 0.418920 | 0.209460 | − | 0.977817i | \(-0.432829\pi\) | ||||
0.209460 | + | 0.977817i | \(0.432829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.88302e8 | 0.402325 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.20528e8 | 0.427549 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.20145e8 | 0.219648 | 0.109824 | − | 0.993951i | \(-0.464971\pi\) | ||||
0.109824 | + | 0.993951i | \(0.464971\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.77609e9 | −2.66833 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.05423e8 | 0.571245 | 0.285622 | − | 0.958342i | \(-0.407800\pi\) | ||||
0.285622 | + | 0.958342i | \(0.407800\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.88529e8 | 0.359904 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.18802e6 | 0.00108051 | 0.000540256 | − | 1.00000i | \(-0.499828\pi\) | ||||
0.000540256 | 1.00000i | \(0.499828\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.64781e8 | 0.583029 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.16065e9 | −1.86106 | −0.930529 | − | 0.366217i | \(-0.880653\pi\) | ||||
−0.930529 | + | 0.366217i | \(0.880653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.25149e7 | −0.0528889 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.87592e8 | −0.405212 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.30762e9 | 1.04885 | 0.524427 | − | 0.851455i | \(-0.324280\pi\) | ||||
0.524427 | + | 0.851455i | \(0.324280\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.65432e8 | 0.682068 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.23318e9 | 0.955041 | 0.477521 | − | 0.878621i | \(-0.341536\pi\) | ||||
0.477521 | + | 0.878621i | \(0.341536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.25023e9 | −1.71261 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.49357e7 | −0.0624467 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.74339e9 | 1.98269 | 0.991346 | − | 0.131274i | \(-0.0419067\pi\) | ||||
0.991346 | + | 0.131274i | \(0.0419067\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.21852e9 | −0.865738 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.55036e9 | −1.08295 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.63895e8 | 0.245754 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.57548e9 | −1.04632 | −0.523158 | − | 0.852236i | \(-0.675246\pi\) | ||||
−0.523158 | + | 0.852236i | \(0.675246\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.15396e8 | −0.336631 | −0.168315 | − | 0.985733i | \(-0.553833\pi\) | ||||
−0.168315 | + | 0.985733i | \(0.553833\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.34100e8 | 0.343109 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.11050e8 | 0.193345 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.08920e9 | 0.666053 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.20461e8 | 0.553777 | 0.276888 | − | 0.960902i | \(-0.410697\pi\) | ||||
0.276888 | + | 0.960902i | \(0.410697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.01254e8 | −0.533507 | −0.266753 | − | 0.963765i | \(-0.585951\pi\) | ||||
−0.266753 | + | 0.963765i | \(0.585951\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.03792e9 | −0.594948 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.57869e8 | 0.427531 | 0.213766 | − | 0.976885i | \(-0.431427\pi\) | ||||
0.213766 | + | 0.976885i | \(0.431427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.70033e8 | 0.0944055 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.21270e9 | 1.20923 | 0.604615 | − | 0.796518i | \(-0.293327\pi\) | ||||
0.604615 | + | 0.796518i | \(0.293327\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.97570e9 | 1.04627 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.65506e9 | 1.38424 | 0.692121 | − | 0.721781i | \(-0.256676\pi\) | ||||
0.692121 | + | 0.721781i | \(0.256676\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.64908e9 | 0.846496 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.49201e7 | −0.0479750 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.38812e9 | −1.66055 | −0.830275 | − | 0.557354i | \(-0.811817\pi\) | ||||
−0.830275 | + | 0.557354i | \(0.811817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.69647e7 | −0.0178420 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.55176e9 | −1.21307 | −0.606536 | − | 0.795056i | \(-0.707442\pi\) | ||||
−0.606536 | + | 0.795056i | \(0.707442\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.40849e8 | −0.440541 | −0.220271 | − | 0.975439i | \(-0.570694\pi\) | ||||
−0.220271 | + | 0.975439i | \(0.570694\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.81198e9 | 1.27762 | 0.638811 | − | 0.769364i | \(-0.279427\pi\) | ||||
0.638811 | + | 0.769364i | \(0.279427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28945e9 | 0.577166 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.30686e9 | −0.576310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.82327e9 | 1.22670 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.98215e8 | −0.125810 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.41140e9 | −1.83401 | −0.917006 | − | 0.398873i | \(-0.869401\pi\) | ||||
−0.917006 | + | 0.398873i | \(0.869401\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.57465e8 | −0.146462 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.23942e8 | −0.373104 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.58482e9 | 0.621768 | 0.310884 | − | 0.950448i | \(-0.399375\pi\) | ||||
0.310884 | + | 0.950448i | \(0.399375\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.01571e8 | −0.0779554 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.25266e9 | −0.858836 | −0.429418 | − | 0.903106i | \(-0.641281\pi\) | ||||
−0.429418 | + | 0.903106i | \(0.641281\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00115e8 | 0.150391 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.91516e9 | −1.79593 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.21377e9 | 1.15788 | 0.578939 | − | 0.815371i | \(-0.303467\pi\) | ||||
0.578939 | + | 0.815371i | \(0.303467\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.04852e8 | −0.108307 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.46673e9 | 0.513879 | 0.256940 | − | 0.966427i | \(-0.417286\pi\) | ||||
0.256940 | + | 0.966427i | \(0.417286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.88987e9 | 0.984807 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.22223e8 | −0.209138 | −0.104569 | − | 0.994518i | \(-0.533346\pi\) | ||||
−0.104569 | + | 0.994518i | \(0.533346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.16482e8 | −0.171231 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.13716e8 | −0.200704 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.26828e9 | 0.721904 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.67086e9 | 0.838622 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.80030e9 | −1.17730 | −0.588648 | − | 0.808390i | \(-0.700339\pi\) | ||||
−0.588648 | + | 0.808390i | \(0.700339\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.04889e9 | 0.931936 | 0.465968 | − | 0.884802i | \(-0.345706\pi\) | ||||
0.465968 | + | 0.884802i | \(0.345706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.24323e8 | 0.0965252 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.29673e9 | −0.674553 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.09943e9 | 0.318667 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.94043e9 | 1.98537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.07939e9 | 0.579463 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.22114e8 | 0.198630 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.90621e9 | −1.33216 | −0.666079 | − | 0.745882i | \(-0.732028\pi\) | ||||
−0.666079 | + | 0.745882i | \(0.732028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.87673e9 | 0.771081 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.24362e9 | 1.10862 | 0.554308 | − | 0.832312i | \(-0.312983\pi\) | ||||
0.554308 | + | 0.832312i | \(0.312983\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.20579e8 | −0.0568934 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.64302e9 | 1.69175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.04713e9 | 0.514762 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.83397e9 | −1.67564 | −0.837818 | − | 0.545949i | \(-0.816169\pi\) | ||||
−0.837818 | + | 0.545949i | \(0.816169\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.18822e10 | 2.87709 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.56986e8 | −0.0375397 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.19575e9 | 1.22707 | 0.613534 | − | 0.789668i | \(-0.289747\pi\) | ||||
0.613534 | + | 0.789668i | \(0.289747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.46321e8 | −0.125866 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.99097e9 | 1.13577 | 0.567887 | − | 0.823107i | \(-0.307761\pi\) | ||||
0.567887 | + | 0.823107i | \(0.307761\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.63624e9 | 1.26696 | 0.633480 | − | 0.773759i | \(-0.281626\pi\) | ||||
0.633480 | + | 0.773759i | \(0.281626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.06034e8 | −0.178983 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.34583e8 | −0.0508372 | −0.0254186 | − | 0.999677i | \(-0.508092\pi\) | ||||
−0.0254186 | + | 0.999677i | \(0.508092\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.15017e9 | 0.460360 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.32605e9 | −1.76126 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.26649e9 | −0.264705 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.81690e9 | −1.39108 | −0.695542 | − | 0.718485i | \(-0.744836\pi\) | ||||
−0.695542 | + | 0.718485i | \(0.744836\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.38466e9 | 1.08581 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.38196e9 | 0.474655 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.44761e9 | −1.46665 | −0.733323 | − | 0.679880i | \(-0.762032\pi\) | ||||
−0.733323 | + | 0.679880i | \(0.762032\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.06890e9 | 0.590300 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.83339e9 | −0.918878 | −0.459439 | − | 0.888209i | \(-0.651950\pi\) | ||||
−0.459439 | + | 0.888209i | \(0.651950\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.34645e9 | 0.628816 | 0.314408 | − | 0.949288i | \(-0.398194\pi\) | ||||
0.314408 | + | 0.949288i | \(0.398194\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.14408e8 | −0.169836 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.46327e9 | 1.53595 | 0.767976 | − | 0.640479i | \(-0.221264\pi\) | ||||
0.767976 | + | 0.640479i | \(0.221264\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.91353e9 | 1.06093 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.54640e9 | 1.69315 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.10381e9 | 1.07026 | 0.535130 | − | 0.844769i | \(-0.320262\pi\) | ||||
0.535130 | + | 0.844769i | \(0.320262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.77521e9 | −0.304265 | −0.152133 | − | 0.988360i | \(-0.548614\pi\) | ||||
−0.152133 | + | 0.988360i | \(0.548614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.84220e9 | −1.49845 | −0.749226 | − | 0.662314i | \(-0.769574\pi\) | ||||
−0.749226 | + | 0.662314i | \(0.769574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.55208e8 | 0.109789 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.69763e9 | −1.27541 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.60640e9 | −0.422284 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.15211e7 | 0.00825482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.56994e9 | −0.882567 | −0.441284 | − | 0.897368i | \(-0.645477\pi\) | ||||
−0.441284 | + | 0.897368i | \(0.645477\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.03703e9 | −0.319216 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.03913e9 | 0.465866 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.48555e9 | 0.528468 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.17103e10 | −1.75616 | −0.878079 | − | 0.478516i | \(-0.841175\pi\) | ||||
−0.878079 | + | 0.478516i | \(0.841175\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.05369e9 | 0.898011 | 0.449005 | − | 0.893529i | \(-0.351778\pi\) | ||||
0.449005 | + | 0.893529i | \(0.351778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.16775e10 | −1.69506 | −0.847529 | − | 0.530749i | \(-0.821911\pi\) | ||||
−0.847529 | + | 0.530749i | \(0.821911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.66919e9 | 0.670479 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.79335e9 | 0.680935 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.81248e9 | 1.23852 | 0.619259 | − | 0.785187i | \(-0.287433\pi\) | ||||
0.619259 | + | 0.785187i | \(0.287433\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.66260e8 | 0.0503861 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.83941e9 | 0.250368 | 0.125184 | − | 0.992134i | \(-0.460048\pi\) | ||||
0.125184 | + | 0.992134i | \(0.460048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.81427e9 | −0.783050 | −0.391525 | − | 0.920167i | \(-0.628052\pi\) | ||||
−0.391525 | + | 0.920167i | \(0.628052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.60699e8 | −0.0880453 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.09214e9 | −0.925416 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.57159e9 | −0.590304 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.36781e8 | −0.119704 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.53129e9 | −1.07885 | −0.539426 | − | 0.842033i | \(-0.681359\pi\) | ||||
−0.539426 | + | 0.842033i | \(0.681359\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.03399e10 | 1.28073 | 0.640364 | − | 0.768071i | \(-0.278783\pi\) | ||||
0.640364 | + | 0.768071i | \(0.278783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.76534e10 | −2.16413 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.57766e8 | −0.0434094 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.04112e9 | 0.845609 | 0.422804 | − | 0.906221i | \(-0.361046\pi\) | ||||
0.422804 | + | 0.906221i | \(0.361046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.90727e9 | 0.459753 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.33023e9 | −0.620839 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.87229e9 | 0.561772 | 0.280886 | − | 0.959741i | \(-0.409372\pi\) | ||||
0.280886 | + | 0.959741i | \(0.409372\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.32018e9 | −0.264823 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.00032e9 | −0.111898 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.75653e9 | −0.637515 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.44547e10 | 1.58488 | 0.792439 | − | 0.609951i | \(-0.208811\pi\) | ||||
0.792439 | + | 0.609951i | \(0.208811\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.55392e8 | 0.0928585 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.00172e10 | 1.06605 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.76442e9 | −0.502052 | −0.251026 | − | 0.967980i | \(-0.580768\pi\) | ||||
−0.251026 | + | 0.967980i | \(0.580768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.45171e9 | −0.151473 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.74870e9 | −0.593959 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.08940e9 | −0.920912 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.59296e9 | 0.360497 | 0.180248 | − | 0.983621i | \(-0.442310\pi\) | ||||
0.180248 | + | 0.983621i | \(0.442310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.74610e10 | −1.73499 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.48889e9 | −0.638537 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.34517e10 | 1.29840 | 0.649198 | − | 0.760620i | \(-0.275105\pi\) | ||||
0.649198 | + | 0.760620i | \(0.275105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.71256e9 | −0.162157 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.21392e10 | −1.13848 | −0.569242 | − | 0.822170i | \(-0.692763\pi\) | ||||
−0.569242 | + | 0.822170i | \(0.692763\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.88341e9 | −0.357336 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.59124e9 | −0.327333 | −0.163666 | − | 0.986516i | \(-0.552332\pi\) | ||||
−0.163666 | + | 0.986516i | \(0.552332\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.09694e10 | −0.990423 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.30847e10 | −1.17031 | −0.585156 | − | 0.810921i | \(-0.698967\pi\) | ||||
−0.585156 | + | 0.810921i | \(0.698967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.90437e9 | 0.518264 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.23756e10 | −1.07617 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.09743e9 | 0.697602 | 0.348801 | − | 0.937197i | \(-0.386589\pi\) | ||||
0.348801 | + | 0.937197i | \(0.386589\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.36313e9 | 0.201700 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.65837e10 | −1.38946 | −0.694729 | − | 0.719271i | \(-0.744476\pi\) | ||||
−0.694729 | + | 0.719271i | \(0.744476\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.78261e9 | 0.230997 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.34197e9 | −0.192635 | −0.0963175 | − | 0.995351i | \(-0.530706\pi\) | ||||
−0.0963175 | + | 0.995351i | \(0.530706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.21562e10 | −0.990746 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.96510e10 | 1.57254 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.38432e9 | 0.109773 | 0.0548863 | − | 0.998493i | \(-0.482520\pi\) | ||||
0.0548863 | + | 0.998493i | \(0.482520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.85861e9 | −0.224628 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.23896e10 | −0.964785 | −0.482392 | − | 0.875955i | \(-0.660232\pi\) | ||||
−0.482392 | + | 0.875955i | \(0.660232\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.61458e8 | 0.0582334 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.66080e10 | −1.25874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.48028e10 | 1.11190 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.19354e9 | −0.312187 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.44776e9 | −0.252130 | −0.126065 | − | 0.992022i | \(-0.540235\pi\) | ||||
−0.126065 | + | 0.992022i | \(0.540235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.60164e8 | −0.0550983 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.78730e10 | 1.28404 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.94259e9 | −0.280754 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.58177e9 | 0.110673 | 0.0553364 | − | 0.998468i | \(-0.482377\pi\) | ||||
0.0553364 | + | 0.998468i | \(0.482377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.37591e9 | −0.0954283 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.45873e9 | 0.375299 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.55547e9 | 0.106013 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.02710e10 | −0.687948 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.06280e9 | 0.402581 | 0.201291 | − | 0.979532i | \(-0.435486\pi\) | ||||
0.201291 | + | 0.979532i | \(0.435486\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.09241e10 | 0.719140 | 0.359570 | − | 0.933118i | \(-0.382923\pi\) | ||||
0.359570 | + | 0.933118i | \(0.382923\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.65609e10 | 1.08086 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.84333e10 | −1.82411 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.76484e9 | −0.621114 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.10830e9 | 0.574429 | 0.287215 | − | 0.957866i | \(-0.407271\pi\) | ||||
0.287215 | + | 0.957866i | \(0.407271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.13411e9 | 0.133449 | 0.0667247 | − | 0.997771i | \(-0.478745\pi\) | ||||
0.0667247 | + | 0.997771i | \(0.478745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.74657e10 | −1.07379 | −0.536893 | − | 0.843651i | \(-0.680402\pi\) | ||||
−0.536893 | + | 0.843651i | \(0.680402\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.16797e10 | 1.32164 | 0.660818 | − | 0.750546i | \(-0.270210\pi\) | ||||
0.660818 | + | 0.750546i | \(0.270210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.73298e9 | 0.467459 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.38027e8 | −0.0262569 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.39918e9 | −0.200371 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.51956e10 | −0.888285 | −0.444142 | − | 0.895956i | \(-0.646492\pi\) | ||||
−0.444142 | + | 0.895956i | \(0.646492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.81421e10 | 1.63144 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.18450e10 | 0.680988 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.01792e10 | 0.575602 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.31152e10 | −0.735524 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.13223e8 | −0.0507953 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.88790e10 | −1.04150 | −0.520749 | − | 0.853710i | \(-0.674347\pi\) | ||||
−0.520749 | + | 0.853710i | \(0.674347\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.49105e9 | 0.135192 | 0.0675958 | − | 0.997713i | \(-0.478467\pi\) | ||||
0.0675958 | + | 0.997713i | \(0.478467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.61520e10 | −0.869460 | −0.434730 | − | 0.900561i | \(-0.643156\pi\) | ||||
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.47842e10 | −0.789383 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.91876e10 | −1.01621 | −0.508104 | − | 0.861296i | \(-0.669654\pi\) | ||||
−0.508104 | + | 0.861296i | \(0.669654\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.09839e10 | −0.572388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.16528e9 | −0.318701 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.63439e10 | −0.838095 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.25188e10 | 0.636815 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.04959e10 | −1.02605 | −0.513026 | − | 0.858373i | \(-0.671476\pi\) | ||||
−0.513026 | + | 0.858373i | \(0.671476\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.01639e10 | −0.504777 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.07168e10 | −1.02072 | −0.510360 | − | 0.859961i | \(-0.670488\pi\) | ||||
−0.510360 | + | 0.859961i | \(0.670488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.28980e9 | 0.258569 | 0.129285 | − | 0.991608i | \(-0.458732\pi\) | ||||
0.129285 | + | 0.991608i | \(0.458732\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.67479e10 | 1.28694 | 0.643468 | − | 0.765473i | \(-0.277495\pi\) | ||||
0.643468 | + | 0.765473i | \(0.277495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.47929e10 | −0.706150 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.64534e9 | 0.0779263 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.28440e10 | −1.07347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.17111e10 | 0.541779 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.67936e10 | 1.68894 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.68241e8 | 0.0349913 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.53109e10 | −1.14393 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.16032e8 | −0.0140639 | −0.00703194 | − | 0.999975i | \(-0.502238\pi\) | ||||
−0.00703194 | + | 0.999975i | \(0.502238\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.10363e9 | −0.313694 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.82747e10 | −0.800822 | −0.400411 | − | 0.916336i | \(-0.631133\pi\) | ||||
−0.400411 | + | 0.916336i | \(0.631133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.50753e10 | 1.09043 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.85646e10 | 0.795048 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.07018e10 | −1.72985 | −0.864927 | − | 0.501897i | \(-0.832636\pi\) | ||||
−0.864927 | + | 0.501897i | \(0.832636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.22068e10 | 0.936650 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.23001e10 | 2.60785 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.23824e10 | 0.510535 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.93743e10 | 1.61123 | 0.805616 | − | 0.592438i | \(-0.201835\pi\) | ||||
0.805616 | + | 0.592438i | \(0.201835\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.27245e9 | −0.295364 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.24704e10 | −0.502682 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.40969e10 | 0.956912 | 0.478456 | − | 0.878112i | \(-0.341197\pi\) | ||||
0.478456 | + | 0.878112i | \(0.341197\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.07713e9 | −0.318367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.57229e10 | −0.615131 | −0.307566 | − | 0.951527i | \(-0.599514\pi\) | ||||
−0.307566 | + | 0.951527i | \(0.599514\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.77309e10 | 0.688555 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.11795e10 | 0.427758 | 0.213879 | − | 0.976860i | \(-0.431390\pi\) | ||||
0.213879 | + | 0.976860i | \(0.431390\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.54645e9 | 0.248642 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.69012e10 | −0.637215 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.02371e9 | −0.262870 | −0.131435 | − | 0.991325i | \(-0.541959\pi\) | ||||
−0.131435 | + | 0.991325i | \(0.541959\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.78096e10 | −0.656845 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.63940e10 | 1.69862 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.31129e9 | 0.0840085 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.77611e9 | 0.316672 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.09820e9 | −0.288002 | −0.144001 | − | 0.989578i | \(-0.545997\pi\) | ||||
−0.144001 | + | 0.989578i | \(0.545997\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.58101e9 | 0.0558216 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.51850e10 | 1.23336 | 0.616681 | − | 0.787213i | \(-0.288477\pi\) | ||||
0.616681 | + | 0.787213i | \(0.288477\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.38550e10 | −0.482182 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.58518e10 | 1.22993 | 0.614964 | − | 0.788555i | \(-0.289170\pi\) | ||||
0.614964 | + | 0.788555i | \(0.289170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.31828e10 | 0.789634 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.62050e9 | 0.291535 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.86814e10 | 0.627295 | 0.313648 | − | 0.949539i | \(-0.398449\pi\) | ||||
0.313648 | + | 0.949539i | \(0.398449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.03354e10 | −0.673197 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.03556e10 | 0.997819 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.86496e9 | −0.224068 | −0.112034 | − | 0.993704i | \(-0.535737\pi\) | ||||
−0.112034 | + | 0.993704i | \(0.535737\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.02910e10 | 0.981730 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.82086e9 | −0.154060 | −0.0770302 | − | 0.997029i | \(-0.524544\pi\) | ||||
−0.0770302 | + | 0.997029i | \(0.524544\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.39983e8 | −0.0171357 |
(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 | 300.8.a.e.1.1 | 1 | ||
5.2 | odd | 4 | 300.8.d.d.49.1 | 2 | |||
5.3 | odd | 4 | 300.8.d.d.49.2 | 2 | |||
5.4 | even | 2 | 60.8.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 180.8.a.e.1.1 | 1 | |||
20.19 | odd | 2 | 240.8.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.8.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
180.8.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
240.8.a.i.1.1 | 1 | 20.19 | odd | 2 | |||
300.8.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
300.8.d.d.49.1 | 2 | 5.2 | odd | 4 | |||
300.8.d.d.49.2 | 2 | 5.3 | odd | 4 |