Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −43.6565 | −0.964681 | −0.482341 | − | 0.875984i | \(-0.660213\pi\) | ||||
−0.482341 | + | 0.875984i | \(0.660213\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −142.110 | −0.0693898 | ||||||||
\(5\) | 7124.43 | 1.01957 | 0.509783 | − | 0.860303i | \(-0.329726\pi\) | ||||
0.509783 | + | 0.860303i | \(0.329726\pi\) | |||||||
\(6\) | 10608.5 | 0.556959 | ||||||||
\(7\) | 50312.1 | 1.13145 | 0.565723 | − | 0.824596i | \(-0.308597\pi\) | ||||
0.565723 | + | 0.824596i | \(0.308597\pi\) | |||||||
\(8\) | 95612.5 | 1.03162 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −311028. | −0.983556 | ||||||||
\(11\) | 365340. | 0.683971 | 0.341985 | − | 0.939705i | \(-0.388901\pi\) | ||||
0.341985 | + | 0.939705i | \(0.388901\pi\) | |||||||
\(12\) | 34532.8 | 0.0400622 | ||||||||
\(13\) | 675470. | 0.504565 | 0.252283 | − | 0.967654i | \(-0.418819\pi\) | ||||
0.252283 | + | 0.967654i | \(0.418819\pi\) | |||||||
\(14\) | −2.19645e6 | −1.09148 | ||||||||
\(15\) | −1.73124e6 | −0.588647 | ||||||||
\(16\) | −3.88307e6 | −0.925795 | ||||||||
\(17\) | 5.75558e6 | 0.983151 | 0.491575 | − | 0.870835i | \(-0.336421\pi\) | ||||
0.491575 | + | 0.870835i | \(0.336421\pi\) | |||||||
\(18\) | −2.57787e6 | −0.321560 | ||||||||
\(19\) | 6.02412e6 | 0.558148 | 0.279074 | − | 0.960270i | \(-0.409973\pi\) | ||||
0.279074 | + | 0.960270i | \(0.409973\pi\) | |||||||
\(20\) | −1.01246e6 | −0.0707474 | ||||||||
\(21\) | −1.22259e7 | −0.653240 | ||||||||
\(22\) | −1.59495e7 | −0.659814 | ||||||||
\(23\) | −3.76836e7 | −1.22081 | −0.610406 | − | 0.792089i | \(-0.708994\pi\) | ||||
−0.610406 | + | 0.792089i | \(0.708994\pi\) | |||||||
\(24\) | −2.32338e7 | −0.595606 | ||||||||
\(25\) | 1.92941e6 | 0.0395142 | ||||||||
\(26\) | −2.94886e7 | −0.486745 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −7.14987e6 | −0.0785108 | ||||||||
\(29\) | −1.23657e8 | −1.11951 | −0.559755 | − | 0.828658i | \(-0.689105\pi\) | ||||
−0.559755 | + | 0.828658i | \(0.689105\pi\) | |||||||
\(30\) | 7.55797e7 | 0.567856 | ||||||||
\(31\) | −3.05132e8 | −1.91425 | −0.957125 | − | 0.289674i | \(-0.906453\pi\) | ||||
−0.957125 | + | 0.289674i | \(0.906453\pi\) | |||||||
\(32\) | −2.62934e7 | −0.138523 | ||||||||
\(33\) | −8.87776e7 | −0.394891 | ||||||||
\(34\) | −2.51269e8 | −0.948427 | ||||||||
\(35\) | 3.58445e8 | 1.15358 | ||||||||
\(36\) | −8.39147e6 | −0.0231299 | ||||||||
\(37\) | 4.58803e8 | 1.08772 | 0.543860 | − | 0.839176i | \(-0.316962\pi\) | ||||
0.543860 | + | 0.839176i | \(0.316962\pi\) | |||||||
\(38\) | −2.62992e8 | −0.538435 | ||||||||
\(39\) | −1.64139e8 | −0.291311 | ||||||||
\(40\) | 6.81185e8 | 1.05180 | ||||||||
\(41\) | −1.12154e9 | −1.51184 | −0.755919 | − | 0.654665i | \(-0.772810\pi\) | ||||
−0.755919 | + | 0.654665i | \(0.772810\pi\) | |||||||
\(42\) | 5.33738e8 | 0.630169 | ||||||||
\(43\) | −1.10767e9 | −1.14904 | −0.574519 | − | 0.818491i | \(-0.694811\pi\) | ||||
−0.574519 | + | 0.818491i | \(0.694811\pi\) | |||||||
\(44\) | −5.19186e7 | −0.0474606 | ||||||||
\(45\) | 4.20691e8 | 0.339855 | ||||||||
\(46\) | 1.64513e9 | 1.17769 | ||||||||
\(47\) | 1.34464e9 | 0.855200 | 0.427600 | − | 0.903968i | \(-0.359359\pi\) | ||||
0.427600 | + | 0.903968i | \(0.359359\pi\) | |||||||
\(48\) | 9.43585e8 | 0.534508 | ||||||||
\(49\) | 5.53985e8 | 0.280169 | ||||||||
\(50\) | −8.42311e7 | −0.0381186 | ||||||||
\(51\) | −1.39861e9 | −0.567622 | ||||||||
\(52\) | −9.59912e7 | −0.0350117 | ||||||||
\(53\) | −5.46355e9 | −1.79456 | −0.897279 | − | 0.441463i | \(-0.854460\pi\) | ||||
−0.897279 | + | 0.441463i | \(0.854460\pi\) | |||||||
\(54\) | 6.26423e8 | 0.185653 | ||||||||
\(55\) | 2.60284e9 | 0.697353 | ||||||||
\(56\) | 4.81047e9 | 1.16722 | ||||||||
\(57\) | −1.46386e9 | −0.322247 | ||||||||
\(58\) | 5.39841e9 | 1.07997 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 2.46027e8 | 0.0408461 | ||||||||
\(61\) | 2.87070e8 | 0.0435184 | 0.0217592 | − | 0.999763i | \(-0.493073\pi\) | ||||
0.0217592 | + | 0.999763i | \(0.493073\pi\) | |||||||
\(62\) | 1.33210e10 | 1.84664 | ||||||||
\(63\) | 2.97088e9 | 0.377148 | ||||||||
\(64\) | 9.10040e9 | 1.05943 | ||||||||
\(65\) | 4.81234e9 | 0.514438 | ||||||||
\(66\) | 3.87572e9 | 0.380944 | ||||||||
\(67\) | 6.29348e9 | 0.569481 | 0.284740 | − | 0.958605i | \(-0.408093\pi\) | ||||
0.284740 | + | 0.958605i | \(0.408093\pi\) | |||||||
\(68\) | −8.17927e8 | −0.0682206 | ||||||||
\(69\) | 9.15711e9 | 0.704836 | ||||||||
\(70\) | −1.56485e10 | −1.11284 | ||||||||
\(71\) | −1.39937e10 | −0.920474 | −0.460237 | − | 0.887796i | \(-0.652235\pi\) | ||||
−0.460237 | + | 0.887796i | \(0.652235\pi\) | |||||||
\(72\) | 5.64583e9 | 0.343873 | ||||||||
\(73\) | −2.18805e10 | −1.23533 | −0.617663 | − | 0.786443i | \(-0.711920\pi\) | ||||
−0.617663 | + | 0.786443i | \(0.711920\pi\) | |||||||
\(74\) | −2.00297e10 | −1.04930 | ||||||||
\(75\) | −4.68846e8 | −0.0228136 | ||||||||
\(76\) | −8.56090e8 | −0.0387297 | ||||||||
\(77\) | 1.83810e10 | 0.773876 | ||||||||
\(78\) | 7.16574e9 | 0.281022 | ||||||||
\(79\) | −1.00071e9 | −0.0365896 | −0.0182948 | − | 0.999833i | \(-0.505824\pi\) | ||||
−0.0182948 | + | 0.999833i | \(0.505824\pi\) | |||||||
\(80\) | −2.76646e10 | −0.943909 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 4.89627e10 | 1.45844 | ||||||||
\(83\) | −8.58714e9 | −0.239287 | −0.119643 | − | 0.992817i | \(-0.538175\pi\) | ||||
−0.119643 | + | 0.992817i | \(0.538175\pi\) | |||||||
\(84\) | 1.73742e9 | 0.0453282 | ||||||||
\(85\) | 4.10052e10 | 1.00239 | ||||||||
\(86\) | 4.83571e10 | 1.10846 | ||||||||
\(87\) | 3.00485e10 | 0.646350 | ||||||||
\(88\) | 3.49311e10 | 0.705598 | ||||||||
\(89\) | −9.54335e10 | −1.81157 | −0.905787 | − | 0.423734i | \(-0.860719\pi\) | ||||
−0.905787 | + | 0.423734i | \(0.860719\pi\) | |||||||
\(90\) | −1.83659e10 | −0.327852 | ||||||||
\(91\) | 3.39843e10 | 0.570888 | ||||||||
\(92\) | 5.35522e9 | 0.0847119 | ||||||||
\(93\) | 7.41471e10 | 1.10519 | ||||||||
\(94\) | −5.87023e10 | −0.824996 | ||||||||
\(95\) | 4.29185e10 | 0.569068 | ||||||||
\(96\) | 6.38929e9 | 0.0799763 | ||||||||
\(97\) | 7.20283e10 | 0.851645 | 0.425823 | − | 0.904807i | \(-0.359985\pi\) | ||||
0.425823 | + | 0.904807i | \(0.359985\pi\) | |||||||
\(98\) | −2.41851e10 | −0.270274 | ||||||||
\(99\) | 2.15730e10 | 0.227990 | ||||||||
\(100\) | −2.74188e8 | −0.00274188 | ||||||||
\(101\) | 1.68819e11 | 1.59828 | 0.799141 | − | 0.601144i | \(-0.205288\pi\) | ||||
0.799141 | + | 0.601144i | \(0.205288\pi\) | |||||||
\(102\) | 6.10583e10 | 0.547575 | ||||||||
\(103\) | −1.88225e11 | −1.59982 | −0.799912 | − | 0.600117i | \(-0.795121\pi\) | ||||
−0.799912 | + | 0.600117i | \(0.795121\pi\) | |||||||
\(104\) | 6.45834e10 | 0.520520 | ||||||||
\(105\) | −8.71022e10 | −0.666021 | ||||||||
\(106\) | 2.38519e11 | 1.73118 | ||||||||
\(107\) | −1.29332e11 | −0.891447 | −0.445723 | − | 0.895171i | \(-0.647053\pi\) | ||||
−0.445723 | + | 0.895171i | \(0.647053\pi\) | |||||||
\(108\) | 2.03913e9 | 0.0133541 | ||||||||
\(109\) | −2.33095e11 | −1.45107 | −0.725535 | − | 0.688186i | \(-0.758407\pi\) | ||||
−0.725535 | + | 0.688186i | \(0.758407\pi\) | |||||||
\(110\) | −1.13631e11 | −0.672724 | ||||||||
\(111\) | −1.11489e11 | −0.627995 | ||||||||
\(112\) | −1.95365e11 | −1.04749 | ||||||||
\(113\) | 1.34951e11 | 0.689041 | 0.344520 | − | 0.938779i | \(-0.388042\pi\) | ||||
0.344520 | + | 0.938779i | \(0.388042\pi\) | |||||||
\(114\) | 6.39071e10 | 0.310865 | ||||||||
\(115\) | −2.68474e11 | −1.24470 | ||||||||
\(116\) | 1.75729e10 | 0.0776826 | ||||||||
\(117\) | 3.98858e10 | 0.168188 | ||||||||
\(118\) | −3.12111e10 | −0.125591 | ||||||||
\(119\) | 2.89576e11 | 1.11238 | ||||||||
\(120\) | −1.65528e11 | −0.607260 | ||||||||
\(121\) | −1.51838e11 | −0.532184 | ||||||||
\(122\) | −1.25325e10 | −0.0419814 | ||||||||
\(123\) | 2.72535e11 | 0.872860 | ||||||||
\(124\) | 4.33624e10 | 0.132829 | ||||||||
\(125\) | −3.34127e11 | −0.979278 | ||||||||
\(126\) | −1.29698e11 | −0.363828 | ||||||||
\(127\) | 3.29222e11 | 0.884236 | 0.442118 | − | 0.896957i | \(-0.354227\pi\) | ||||
0.442118 | + | 0.896957i | \(0.354227\pi\) | |||||||
\(128\) | −3.43443e11 | −0.883485 | ||||||||
\(129\) | 2.69164e11 | 0.663398 | ||||||||
\(130\) | −2.10090e11 | −0.496268 | ||||||||
\(131\) | −7.93659e11 | −1.79739 | −0.898694 | − | 0.438577i | \(-0.855483\pi\) | ||||
−0.898694 | + | 0.438577i | \(0.855483\pi\) | |||||||
\(132\) | 1.26162e10 | 0.0274014 | ||||||||
\(133\) | 3.03087e11 | 0.631514 | ||||||||
\(134\) | −2.74751e11 | −0.549368 | ||||||||
\(135\) | −1.02228e11 | −0.196216 | ||||||||
\(136\) | 5.50306e11 | 1.01424 | ||||||||
\(137\) | 1.10881e12 | 1.96289 | 0.981443 | − | 0.191755i | \(-0.0614181\pi\) | ||||
0.981443 | + | 0.191755i | \(0.0614181\pi\) | |||||||
\(138\) | −3.99767e11 | −0.679942 | ||||||||
\(139\) | 9.06147e10 | 0.148121 | 0.0740606 | − | 0.997254i | \(-0.476404\pi\) | ||||
0.0740606 | + | 0.997254i | \(0.476404\pi\) | |||||||
\(140\) | −5.09388e10 | −0.0800469 | ||||||||
\(141\) | −3.26747e11 | −0.493750 | ||||||||
\(142\) | 6.10915e11 | 0.887964 | ||||||||
\(143\) | 2.46776e11 | 0.345108 | ||||||||
\(144\) | −2.29291e11 | −0.308598 | ||||||||
\(145\) | −8.80983e11 | −1.14141 | ||||||||
\(146\) | 9.55226e11 | 1.19170 | ||||||||
\(147\) | −1.34618e11 | −0.161756 | ||||||||
\(148\) | −6.52006e10 | −0.0754766 | ||||||||
\(149\) | −1.10067e12 | −1.22781 | −0.613905 | − | 0.789380i | \(-0.710402\pi\) | ||||
−0.613905 | + | 0.789380i | \(0.710402\pi\) | |||||||
\(150\) | 2.04682e10 | 0.0220078 | ||||||||
\(151\) | −3.52927e11 | −0.365857 | −0.182928 | − | 0.983126i | \(-0.558558\pi\) | ||||
−0.182928 | + | 0.983126i | \(0.558558\pi\) | |||||||
\(152\) | 5.75982e11 | 0.575797 | ||||||||
\(153\) | 3.39861e11 | 0.327717 | ||||||||
\(154\) | −8.02452e11 | −0.746543 | ||||||||
\(155\) | −2.17389e12 | −1.95170 | ||||||||
\(156\) | 2.33259e10 | 0.0202140 | ||||||||
\(157\) | 1.37272e12 | 1.14851 | 0.574254 | − | 0.818677i | \(-0.305292\pi\) | ||||
0.574254 | + | 0.818677i | \(0.305292\pi\) | |||||||
\(158\) | 4.36873e10 | 0.0352973 | ||||||||
\(159\) | 1.32764e12 | 1.03609 | ||||||||
\(160\) | −1.87325e11 | −0.141233 | ||||||||
\(161\) | −1.89594e12 | −1.38128 | ||||||||
\(162\) | −1.52221e11 | −0.107187 | ||||||||
\(163\) | −4.44642e11 | −0.302677 | −0.151338 | − | 0.988482i | \(-0.548358\pi\) | ||||
−0.151338 | + | 0.988482i | \(0.548358\pi\) | |||||||
\(164\) | 1.59383e11 | 0.104906 | ||||||||
\(165\) | −6.32490e11 | −0.402617 | ||||||||
\(166\) | 3.74884e11 | 0.230836 | ||||||||
\(167\) | −8.71475e11 | −0.519176 | −0.259588 | − | 0.965719i | \(-0.583587\pi\) | ||||
−0.259588 | + | 0.965719i | \(0.583587\pi\) | |||||||
\(168\) | −1.16894e12 | −0.673896 | ||||||||
\(169\) | −1.33590e12 | −0.745414 | ||||||||
\(170\) | −1.79015e12 | −0.966984 | ||||||||
\(171\) | 3.55719e11 | 0.186049 | ||||||||
\(172\) | 1.57412e11 | 0.0797315 | ||||||||
\(173\) | −6.43858e11 | −0.315891 | −0.157945 | − | 0.987448i | \(-0.550487\pi\) | ||||
−0.157945 | + | 0.987448i | \(0.550487\pi\) | |||||||
\(174\) | −1.31181e12 | −0.623522 | ||||||||
\(175\) | 9.70725e10 | 0.0447082 | ||||||||
\(176\) | −1.41864e12 | −0.633217 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | 4.16629e12 | 1.74759 | ||||||||
\(179\) | −4.41573e12 | −1.79602 | −0.898009 | − | 0.439978i | \(-0.854986\pi\) | ||||
−0.898009 | + | 0.439978i | \(0.854986\pi\) | |||||||
\(180\) | −5.97845e10 | −0.0235825 | ||||||||
\(181\) | −3.14280e12 | −1.20250 | −0.601250 | − | 0.799061i | \(-0.705330\pi\) | ||||
−0.601250 | + | 0.799061i | \(0.705330\pi\) | |||||||
\(182\) | −1.48364e12 | −0.550725 | ||||||||
\(183\) | −6.97580e10 | −0.0251254 | ||||||||
\(184\) | −3.60302e12 | −1.25941 | ||||||||
\(185\) | 3.26871e12 | 1.10900 | ||||||||
\(186\) | −3.23700e12 | −1.06616 | ||||||||
\(187\) | 2.10274e12 | 0.672446 | ||||||||
\(188\) | −1.91087e11 | −0.0593422 | ||||||||
\(189\) | −7.21924e11 | −0.217747 | ||||||||
\(190\) | −1.87367e12 | −0.548970 | ||||||||
\(191\) | 6.11106e12 | 1.73953 | 0.869767 | − | 0.493462i | \(-0.164269\pi\) | ||||
0.869767 | + | 0.493462i | \(0.164269\pi\) | |||||||
\(192\) | −2.21140e12 | −0.611660 | ||||||||
\(193\) | 1.44042e11 | 0.0387191 | 0.0193595 | − | 0.999813i | \(-0.493837\pi\) | ||||
0.0193595 | + | 0.999813i | \(0.493837\pi\) | |||||||
\(194\) | −3.14450e12 | −0.821566 | ||||||||
\(195\) | −1.16940e12 | −0.297011 | ||||||||
\(196\) | −7.87270e10 | −0.0194409 | ||||||||
\(197\) | 5.66244e12 | 1.35969 | 0.679844 | − | 0.733357i | \(-0.262047\pi\) | ||||
0.679844 | + | 0.733357i | \(0.262047\pi\) | |||||||
\(198\) | −9.41800e11 | −0.219938 | ||||||||
\(199\) | −5.90518e12 | −1.34135 | −0.670673 | − | 0.741753i | \(-0.733995\pi\) | ||||
−0.670673 | + | 0.741753i | \(0.733995\pi\) | |||||||
\(200\) | 1.84475e11 | 0.0407637 | ||||||||
\(201\) | −1.52931e12 | −0.328790 | ||||||||
\(202\) | −7.37004e12 | −1.54183 | ||||||||
\(203\) | −6.22143e12 | −1.26667 | ||||||||
\(204\) | 1.98756e11 | 0.0393872 | ||||||||
\(205\) | −7.99037e12 | −1.54142 | ||||||||
\(206\) | 8.21724e12 | 1.54332 | ||||||||
\(207\) | −2.22518e12 | −0.406937 | ||||||||
\(208\) | −2.62289e12 | −0.467124 | ||||||||
\(209\) | 2.20085e12 | 0.381757 | ||||||||
\(210\) | 3.80258e12 | 0.642499 | ||||||||
\(211\) | −4.07921e12 | −0.671464 | −0.335732 | − | 0.941958i | \(-0.608984\pi\) | ||||
−0.335732 | + | 0.941958i | \(0.608984\pi\) | |||||||
\(212\) | 7.76427e11 | 0.124524 | ||||||||
\(213\) | 3.40047e12 | 0.531436 | ||||||||
\(214\) | 5.64618e12 | 0.859962 | ||||||||
\(215\) | −7.89153e12 | −1.17152 | ||||||||
\(216\) | −1.37194e12 | −0.198535 | ||||||||
\(217\) | −1.53519e13 | −2.16587 | ||||||||
\(218\) | 1.01761e13 | 1.39982 | ||||||||
\(219\) | 5.31696e12 | 0.713216 | ||||||||
\(220\) | −3.69890e11 | −0.0483892 | ||||||||
\(221\) | 3.88772e12 | 0.496064 | ||||||||
\(222\) | 4.86723e12 | 0.605815 | ||||||||
\(223\) | −4.49033e12 | −0.545258 | −0.272629 | − | 0.962119i | \(-0.587893\pi\) | ||||
−0.272629 | + | 0.962119i | \(0.587893\pi\) | |||||||
\(224\) | −1.32288e12 | −0.156731 | ||||||||
\(225\) | 1.13929e11 | 0.0131714 | ||||||||
\(226\) | −5.89149e12 | −0.664705 | ||||||||
\(227\) | −1.31337e13 | −1.44625 | −0.723126 | − | 0.690716i | \(-0.757295\pi\) | ||||
−0.723126 | + | 0.690716i | \(0.757295\pi\) | |||||||
\(228\) | 2.08030e11 | 0.0223606 | ||||||||
\(229\) | 4.35598e12 | 0.457078 | 0.228539 | − | 0.973535i | \(-0.426605\pi\) | ||||
0.228539 | + | 0.973535i | \(0.426605\pi\) | |||||||
\(230\) | 1.17206e13 | 1.20074 | ||||||||
\(231\) | −4.46659e12 | −0.446797 | ||||||||
\(232\) | −1.18231e13 | −1.15491 | ||||||||
\(233\) | 6.64973e12 | 0.634376 | 0.317188 | − | 0.948363i | \(-0.397261\pi\) | ||||
0.317188 | + | 0.948363i | \(0.397261\pi\) | |||||||
\(234\) | −1.74127e12 | −0.162248 | ||||||||
\(235\) | 9.57979e12 | 0.871933 | ||||||||
\(236\) | −1.01598e11 | −0.00903378 | ||||||||
\(237\) | 2.43172e11 | 0.0211250 | ||||||||
\(238\) | −1.26419e13 | −1.07309 | ||||||||
\(239\) | 7.80698e11 | 0.0647582 | 0.0323791 | − | 0.999476i | \(-0.489692\pi\) | ||||
0.0323791 | + | 0.999476i | \(0.489692\pi\) | |||||||
\(240\) | 6.72251e12 | 0.544966 | ||||||||
\(241\) | −4.00251e12 | −0.317131 | −0.158566 | − | 0.987348i | \(-0.550687\pi\) | ||||
−0.158566 | + | 0.987348i | \(0.550687\pi\) | |||||||
\(242\) | 6.62873e12 | 0.513388 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −4.07956e10 | −0.00301974 | ||||||||
\(245\) | 3.94683e12 | 0.285651 | ||||||||
\(246\) | −1.18979e13 | −0.842032 | ||||||||
\(247\) | 4.06911e12 | 0.281622 | ||||||||
\(248\) | −2.91745e13 | −1.97478 | ||||||||
\(249\) | 2.08667e12 | 0.138152 | ||||||||
\(250\) | 1.45868e13 | 0.944692 | ||||||||
\(251\) | 9.31420e12 | 0.590120 | 0.295060 | − | 0.955479i | \(-0.404660\pi\) | ||||
0.295060 | + | 0.955479i | \(0.404660\pi\) | |||||||
\(252\) | −4.22193e11 | −0.0261703 | ||||||||
\(253\) | −1.37673e13 | −0.835000 | ||||||||
\(254\) | −1.43727e13 | −0.853006 | ||||||||
\(255\) | −9.96428e12 | −0.578728 | ||||||||
\(256\) | −3.64411e12 | −0.207144 | ||||||||
\(257\) | 2.27295e13 | 1.26462 | 0.632308 | − | 0.774717i | \(-0.282108\pi\) | ||||
0.632308 | + | 0.774717i | \(0.282108\pi\) | |||||||
\(258\) | −1.17508e13 | −0.639967 | ||||||||
\(259\) | 2.30834e13 | 1.23070 | ||||||||
\(260\) | −6.83883e11 | −0.0356967 | ||||||||
\(261\) | −7.30180e12 | −0.373170 | ||||||||
\(262\) | 3.46484e13 | 1.73391 | ||||||||
\(263\) | 3.42919e13 | 1.68049 | 0.840244 | − | 0.542208i | \(-0.182412\pi\) | ||||
0.840244 | + | 0.542208i | \(0.182412\pi\) | |||||||
\(264\) | −8.48825e12 | −0.407377 | ||||||||
\(265\) | −3.89247e13 | −1.82967 | ||||||||
\(266\) | −1.32317e13 | −0.609209 | ||||||||
\(267\) | 2.31904e13 | 1.04591 | ||||||||
\(268\) | −8.94368e11 | −0.0395162 | ||||||||
\(269\) | 3.52108e13 | 1.52419 | 0.762094 | − | 0.647467i | \(-0.224172\pi\) | ||||
0.762094 | + | 0.647467i | \(0.224172\pi\) | |||||||
\(270\) | 4.46291e12 | 0.189285 | ||||||||
\(271\) | 1.33516e13 | 0.554885 | 0.277442 | − | 0.960742i | \(-0.410513\pi\) | ||||
0.277442 | + | 0.960742i | \(0.410513\pi\) | |||||||
\(272\) | −2.23493e13 | −0.910196 | ||||||||
\(273\) | −8.25819e12 | −0.329602 | ||||||||
\(274\) | −4.84069e13 | −1.89356 | ||||||||
\(275\) | 7.04889e11 | 0.0270266 | ||||||||
\(276\) | −1.30132e12 | −0.0489084 | ||||||||
\(277\) | −3.73820e12 | −0.137728 | −0.0688642 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688642 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(278\) | −3.95592e12 | −0.142890 | ||||||||
\(279\) | −1.80178e13 | −0.638084 | ||||||||
\(280\) | 3.42719e13 | 1.19006 | ||||||||
\(281\) | 3.84494e13 | 1.30920 | 0.654598 | − | 0.755978i | \(-0.272838\pi\) | ||||
0.654598 | + | 0.755978i | \(0.272838\pi\) | |||||||
\(282\) | 1.42646e13 | 0.476311 | ||||||||
\(283\) | 4.47772e13 | 1.46633 | 0.733165 | − | 0.680051i | \(-0.238042\pi\) | ||||
0.733165 | + | 0.680051i | \(0.238042\pi\) | |||||||
\(284\) | 1.98865e12 | 0.0638715 | ||||||||
\(285\) | −1.04292e13 | −0.328552 | ||||||||
\(286\) | −1.07734e13 | −0.332919 | ||||||||
\(287\) | −5.64273e13 | −1.71056 | ||||||||
\(288\) | −1.55260e12 | −0.0461743 | ||||||||
\(289\) | −1.14518e12 | −0.0334145 | ||||||||
\(290\) | 3.84606e13 | 1.10110 | ||||||||
\(291\) | −1.75029e13 | −0.491698 | ||||||||
\(292\) | 3.10944e12 | 0.0857190 | ||||||||
\(293\) | 2.23241e13 | 0.603951 | 0.301976 | − | 0.953316i | \(-0.402354\pi\) | ||||
0.301976 | + | 0.953316i | \(0.402354\pi\) | |||||||
\(294\) | 5.87697e12 | 0.156043 | ||||||||
\(295\) | 5.09343e12 | 0.132736 | ||||||||
\(296\) | 4.38673e13 | 1.12211 | ||||||||
\(297\) | −5.24223e12 | −0.131630 | ||||||||
\(298\) | 4.80512e13 | 1.18445 | ||||||||
\(299\) | −2.54541e13 | −0.615980 | ||||||||
\(300\) | 6.66278e10 | 0.00158303 | ||||||||
\(301\) | −5.57293e13 | −1.30007 | ||||||||
\(302\) | 1.54075e13 | 0.352935 | ||||||||
\(303\) | −4.10230e13 | −0.922768 | ||||||||
\(304\) | −2.33921e13 | −0.516730 | ||||||||
\(305\) | 2.04521e12 | 0.0443699 | ||||||||
\(306\) | −1.48372e13 | −0.316142 | ||||||||
\(307\) | −4.79932e13 | −1.00443 | −0.502213 | − | 0.864744i | \(-0.667481\pi\) | ||||
−0.502213 | + | 0.864744i | \(0.667481\pi\) | |||||||
\(308\) | −2.61213e12 | −0.0536991 | ||||||||
\(309\) | 4.57386e13 | 0.923659 | ||||||||
\(310\) | 9.49046e13 | 1.88277 | ||||||||
\(311\) | 7.55495e13 | 1.47248 | 0.736240 | − | 0.676720i | \(-0.236599\pi\) | ||||
0.736240 | + | 0.676720i | \(0.236599\pi\) | |||||||
\(312\) | −1.56938e13 | −0.300522 | ||||||||
\(313\) | −4.55788e13 | −0.857568 | −0.428784 | − | 0.903407i | \(-0.641058\pi\) | ||||
−0.428784 | + | 0.903407i | \(0.641058\pi\) | |||||||
\(314\) | −5.99281e13 | −1.10794 | ||||||||
\(315\) | 2.11658e13 | 0.384528 | ||||||||
\(316\) | 1.42211e11 | 0.00253894 | ||||||||
\(317\) | −1.03923e13 | −0.182341 | −0.0911705 | − | 0.995835i | \(-0.529061\pi\) | ||||
−0.0911705 | + | 0.995835i | \(0.529061\pi\) | |||||||
\(318\) | −5.79602e13 | −0.999496 | ||||||||
\(319\) | −4.51767e13 | −0.765712 | ||||||||
\(320\) | 6.48352e13 | 1.08015 | ||||||||
\(321\) | 3.14277e13 | 0.514677 | ||||||||
\(322\) | 8.27701e13 | 1.33250 | ||||||||
\(323\) | 3.46723e13 | 0.548743 | ||||||||
\(324\) | −4.95508e11 | −0.00770998 | ||||||||
\(325\) | 1.30326e12 | 0.0199375 | ||||||||
\(326\) | 1.94115e13 | 0.291986 | ||||||||
\(327\) | 5.66422e13 | 0.837775 | ||||||||
\(328\) | −1.07234e14 | −1.55964 | ||||||||
\(329\) | 6.76517e13 | 0.967612 | ||||||||
\(330\) | 2.76123e13 | 0.388397 | ||||||||
\(331\) | −1.01393e13 | −0.140266 | −0.0701331 | − | 0.997538i | \(-0.522342\pi\) | ||||
−0.0701331 | + | 0.997538i | \(0.522342\pi\) | |||||||
\(332\) | 1.22032e12 | 0.0166041 | ||||||||
\(333\) | 2.70919e13 | 0.362573 | ||||||||
\(334\) | 3.80456e13 | 0.500839 | ||||||||
\(335\) | 4.48374e13 | 0.580623 | ||||||||
\(336\) | 4.74738e13 | 0.604767 | ||||||||
\(337\) | 7.30955e13 | 0.916065 | 0.458033 | − | 0.888935i | \(-0.348554\pi\) | ||||
0.458033 | + | 0.888935i | \(0.348554\pi\) | |||||||
\(338\) | 5.83208e13 | 0.719087 | ||||||||
\(339\) | −3.27931e13 | −0.397818 | ||||||||
\(340\) | −5.82727e12 | −0.0695554 | ||||||||
\(341\) | −1.11477e14 | −1.30929 | ||||||||
\(342\) | −1.55294e13 | −0.179478 | ||||||||
\(343\) | −7.16114e13 | −0.814450 | ||||||||
\(344\) | −1.05907e14 | −1.18537 | ||||||||
\(345\) | 6.52392e13 | 0.718627 | ||||||||
\(346\) | 2.81086e13 | 0.304734 | ||||||||
\(347\) | 1.43624e14 | 1.53255 | 0.766275 | − | 0.642513i | \(-0.222108\pi\) | ||||
0.766275 | + | 0.642513i | \(0.222108\pi\) | |||||||
\(348\) | −4.27021e12 | −0.0448501 | ||||||||
\(349\) | 7.75416e13 | 0.801669 | 0.400834 | − | 0.916150i | \(-0.368720\pi\) | ||||
0.400834 | + | 0.916150i | \(0.368720\pi\) | |||||||
\(350\) | −4.23785e12 | −0.0431292 | ||||||||
\(351\) | −9.69225e12 | −0.0971037 | ||||||||
\(352\) | −9.60603e12 | −0.0947456 | ||||||||
\(353\) | −6.17172e13 | −0.599301 | −0.299651 | − | 0.954049i | \(-0.596870\pi\) | ||||
−0.299651 | + | 0.954049i | \(0.596870\pi\) | |||||||
\(354\) | 7.58429e12 | 0.0725099 | ||||||||
\(355\) | −9.96971e13 | −0.938483 | ||||||||
\(356\) | 1.35621e13 | 0.125705 | ||||||||
\(357\) | −7.03669e13 | −0.642234 | ||||||||
\(358\) | 1.92775e14 | 1.73258 | ||||||||
\(359\) | 7.25911e13 | 0.642486 | 0.321243 | − | 0.946997i | \(-0.395899\pi\) | ||||
0.321243 | + | 0.946997i | \(0.395899\pi\) | |||||||
\(360\) | 4.02233e13 | 0.350602 | ||||||||
\(361\) | −8.02002e13 | −0.688471 | ||||||||
\(362\) | 1.37204e14 | 1.16003 | ||||||||
\(363\) | 3.68967e13 | 0.307257 | ||||||||
\(364\) | −4.82952e12 | −0.0396138 | ||||||||
\(365\) | −1.55886e14 | −1.25950 | ||||||||
\(366\) | 3.04539e12 | 0.0242380 | ||||||||
\(367\) | 2.32677e14 | 1.82427 | 0.912137 | − | 0.409886i | \(-0.134432\pi\) | ||||
0.912137 | + | 0.409886i | \(0.134432\pi\) | |||||||
\(368\) | 1.46328e14 | 1.13022 | ||||||||
\(369\) | −6.62261e13 | −0.503946 | ||||||||
\(370\) | −1.42701e14 | −1.06983 | ||||||||
\(371\) | −2.74883e14 | −2.03045 | ||||||||
\(372\) | −1.05371e13 | −0.0766891 | ||||||||
\(373\) | −1.34371e14 | −0.963622 | −0.481811 | − | 0.876275i | \(-0.660021\pi\) | ||||
−0.481811 | + | 0.876275i | \(0.660021\pi\) | |||||||
\(374\) | −9.17985e13 | −0.648696 | ||||||||
\(375\) | 8.11928e13 | 0.565387 | ||||||||
\(376\) | 1.28564e14 | 0.882242 | ||||||||
\(377\) | −8.35263e13 | −0.564866 | ||||||||
\(378\) | 3.15167e13 | 0.210056 | ||||||||
\(379\) | −2.47448e13 | −0.162543 | −0.0812714 | − | 0.996692i | \(-0.525898\pi\) | ||||
−0.0812714 | + | 0.996692i | \(0.525898\pi\) | |||||||
\(380\) | −6.09915e12 | −0.0394875 | ||||||||
\(381\) | −8.00010e13 | −0.510514 | ||||||||
\(382\) | −2.66787e14 | −1.67810 | ||||||||
\(383\) | 1.39855e14 | 0.867134 | 0.433567 | − | 0.901121i | \(-0.357255\pi\) | ||||
0.433567 | + | 0.901121i | \(0.357255\pi\) | |||||||
\(384\) | 8.34566e13 | 0.510081 | ||||||||
\(385\) | 1.30954e14 | 0.789017 | ||||||||
\(386\) | −6.28838e12 | −0.0373516 | ||||||||
\(387\) | −6.54069e13 | −0.383013 | ||||||||
\(388\) | −1.02360e13 | −0.0590955 | ||||||||
\(389\) | −1.11895e14 | −0.636924 | −0.318462 | − | 0.947936i | \(-0.603166\pi\) | ||||
−0.318462 | + | 0.947936i | \(0.603166\pi\) | |||||||
\(390\) | 5.10518e13 | 0.286521 | ||||||||
\(391\) | −2.16891e14 | −1.20024 | ||||||||
\(392\) | 5.29679e13 | 0.289028 | ||||||||
\(393\) | 1.92859e14 | 1.03772 | ||||||||
\(394\) | −2.47202e14 | −1.31167 | ||||||||
\(395\) | −7.12946e12 | −0.0373055 | ||||||||
\(396\) | −3.06574e12 | −0.0158202 | ||||||||
\(397\) | −1.57558e14 | −0.801847 | −0.400924 | − | 0.916111i | \(-0.631311\pi\) | ||||
−0.400924 | + | 0.916111i | \(0.631311\pi\) | |||||||
\(398\) | 2.57799e14 | 1.29397 | ||||||||
\(399\) | −7.36500e13 | −0.364605 | ||||||||
\(400\) | −7.49201e12 | −0.0365821 | ||||||||
\(401\) | −1.29783e14 | −0.625063 | −0.312531 | − | 0.949907i | \(-0.601177\pi\) | ||||
−0.312531 | + | 0.949907i | \(0.601177\pi\) | |||||||
\(402\) | 6.67645e13 | 0.317178 | ||||||||
\(403\) | −2.06108e14 | −0.965865 | ||||||||
\(404\) | −2.39909e13 | −0.110904 | ||||||||
\(405\) | 2.48414e13 | 0.113285 | ||||||||
\(406\) | 2.71606e14 | 1.22193 | ||||||||
\(407\) | 1.67619e14 | 0.743968 | ||||||||
\(408\) | −1.33724e14 | −0.585571 | ||||||||
\(409\) | 2.02205e14 | 0.873604 | 0.436802 | − | 0.899558i | \(-0.356111\pi\) | ||||
0.436802 | + | 0.899558i | \(0.356111\pi\) | |||||||
\(410\) | 3.48831e14 | 1.48698 | ||||||||
\(411\) | −2.69441e14 | −1.13327 | ||||||||
\(412\) | 2.67487e13 | 0.111011 | ||||||||
\(413\) | 3.59694e13 | 0.147302 | ||||||||
\(414\) | 9.71434e13 | 0.392565 | ||||||||
\(415\) | −6.11785e13 | −0.243969 | ||||||||
\(416\) | −1.77604e13 | −0.0698939 | ||||||||
\(417\) | −2.20194e13 | −0.0855178 | ||||||||
\(418\) | −9.60816e13 | −0.368274 | ||||||||
\(419\) | 3.51636e14 | 1.33020 | 0.665099 | − | 0.746755i | \(-0.268389\pi\) | ||||
0.665099 | + | 0.746755i | \(0.268389\pi\) | |||||||
\(420\) | 1.23781e13 | 0.0462151 | ||||||||
\(421\) | −2.61825e14 | −0.964849 | −0.482425 | − | 0.875937i | \(-0.660244\pi\) | ||||
−0.482425 | + | 0.875937i | \(0.660244\pi\) | |||||||
\(422\) | 1.78084e14 | 0.647748 | ||||||||
\(423\) | 7.93996e13 | 0.285067 | ||||||||
\(424\) | −5.22384e14 | −1.85130 | ||||||||
\(425\) | 1.11049e13 | 0.0388484 | ||||||||
\(426\) | −1.48452e14 | −0.512666 | ||||||||
\(427\) | 1.44431e13 | 0.0492387 | ||||||||
\(428\) | 1.83794e13 | 0.0618573 | ||||||||
\(429\) | −5.99666e13 | −0.199248 | ||||||||
\(430\) | 3.44517e14 | 1.13014 | ||||||||
\(431\) | 7.24476e13 | 0.234638 | 0.117319 | − | 0.993094i | \(-0.462570\pi\) | ||||
0.117319 | + | 0.993094i | \(0.462570\pi\) | |||||||
\(432\) | 5.57178e13 | 0.178169 | ||||||||
\(433\) | 3.43810e14 | 1.08551 | 0.542756 | − | 0.839890i | \(-0.317381\pi\) | ||||
0.542756 | + | 0.839890i | \(0.317381\pi\) | |||||||
\(434\) | 6.70208e14 | 2.08937 | ||||||||
\(435\) | 2.14079e14 | 0.658996 | ||||||||
\(436\) | 3.31253e13 | 0.100689 | ||||||||
\(437\) | −2.27010e14 | −0.681393 | ||||||||
\(438\) | −2.32120e14 | −0.688026 | ||||||||
\(439\) | −1.03638e14 | −0.303364 | −0.151682 | − | 0.988429i | \(-0.548469\pi\) | ||||
−0.151682 | + | 0.988429i | \(0.548469\pi\) | |||||||
\(440\) | 2.48864e14 | 0.719404 | ||||||||
\(441\) | 3.27123e13 | 0.0933896 | ||||||||
\(442\) | −1.69724e14 | −0.478544 | ||||||||
\(443\) | 3.73050e13 | 0.103883 | 0.0519417 | − | 0.998650i | \(-0.483459\pi\) | ||||
0.0519417 | + | 0.998650i | \(0.483459\pi\) | |||||||
\(444\) | 1.58438e13 | 0.0435764 | ||||||||
\(445\) | −6.79910e14 | −1.84702 | ||||||||
\(446\) | 1.96032e14 | 0.526000 | ||||||||
\(447\) | 2.67462e14 | 0.708876 | ||||||||
\(448\) | 4.57861e14 | 1.19868 | ||||||||
\(449\) | 2.04923e14 | 0.529952 | 0.264976 | − | 0.964255i | \(-0.414636\pi\) | ||||
0.264976 | + | 0.964255i | \(0.414636\pi\) | |||||||
\(450\) | −4.97376e12 | −0.0127062 | ||||||||
\(451\) | −4.09745e14 | −1.03405 | ||||||||
\(452\) | −1.91779e13 | −0.0478124 | ||||||||
\(453\) | 8.57612e13 | 0.211228 | ||||||||
\(454\) | 5.73370e14 | 1.39517 | ||||||||
\(455\) | 2.42119e14 | 0.582058 | ||||||||
\(456\) | −1.39964e14 | −0.332436 | ||||||||
\(457\) | −2.24389e14 | −0.526577 | −0.263289 | − | 0.964717i | \(-0.584807\pi\) | ||||
−0.263289 | + | 0.964717i | \(0.584807\pi\) | |||||||
\(458\) | −1.90167e14 | −0.440935 | ||||||||
\(459\) | −8.25863e13 | −0.189207 | ||||||||
\(460\) | 3.81529e13 | 0.0863693 | ||||||||
\(461\) | −4.58977e14 | −1.02668 | −0.513340 | − | 0.858185i | \(-0.671592\pi\) | ||||
−0.513340 | + | 0.858185i | \(0.671592\pi\) | |||||||
\(462\) | 1.94996e14 | 0.431017 | ||||||||
\(463\) | 2.09824e14 | 0.458310 | 0.229155 | − | 0.973390i | \(-0.426404\pi\) | ||||
0.229155 | + | 0.973390i | \(0.426404\pi\) | |||||||
\(464\) | 4.80167e14 | 1.03644 | ||||||||
\(465\) | 5.28256e14 | 1.12682 | ||||||||
\(466\) | −2.90304e14 | −0.611970 | ||||||||
\(467\) | 7.64430e14 | 1.59256 | 0.796278 | − | 0.604931i | \(-0.206799\pi\) | ||||
0.796278 | + | 0.604931i | \(0.206799\pi\) | |||||||
\(468\) | −5.66818e12 | −0.0116706 | ||||||||
\(469\) | 3.16638e14 | 0.644337 | ||||||||
\(470\) | −4.18220e14 | −0.841137 | ||||||||
\(471\) | −3.33571e14 | −0.663091 | ||||||||
\(472\) | 6.83557e13 | 0.134306 | ||||||||
\(473\) | −4.04677e14 | −0.785909 | ||||||||
\(474\) | −1.06160e13 | −0.0203789 | ||||||||
\(475\) | 1.16230e13 | 0.0220548 | ||||||||
\(476\) | −4.11517e13 | −0.0771879 | ||||||||
\(477\) | −3.22617e14 | −0.598186 | ||||||||
\(478\) | −3.40825e13 | −0.0624710 | ||||||||
\(479\) | −5.73863e14 | −1.03983 | −0.519915 | − | 0.854218i | \(-0.674036\pi\) | ||||
−0.519915 | + | 0.854218i | \(0.674036\pi\) | |||||||
\(480\) | 4.55201e13 | 0.0815411 | ||||||||
\(481\) | 3.09908e14 | 0.548826 | ||||||||
\(482\) | 1.74736e14 | 0.305931 | ||||||||
\(483\) | 4.60714e14 | 0.797484 | ||||||||
\(484\) | 2.15778e13 | 0.0369281 | ||||||||
\(485\) | 5.13161e14 | 0.868308 | ||||||||
\(486\) | 3.69897e13 | 0.0618843 | ||||||||
\(487\) | −1.01994e15 | −1.68719 | −0.843597 | − | 0.536976i | \(-0.819566\pi\) | ||||
−0.843597 | + | 0.536976i | \(0.819566\pi\) | |||||||
\(488\) | 2.74475e13 | 0.0448945 | ||||||||
\(489\) | 1.08048e14 | 0.174750 | ||||||||
\(490\) | −1.72305e14 | −0.275562 | ||||||||
\(491\) | −6.75363e14 | −1.06804 | −0.534022 | − | 0.845471i | \(-0.679320\pi\) | ||||
−0.534022 | + | 0.845471i | \(0.679320\pi\) | |||||||
\(492\) | −3.87301e13 | −0.0605676 | ||||||||
\(493\) | −7.11715e14 | −1.10065 | ||||||||
\(494\) | −1.77643e14 | −0.271675 | ||||||||
\(495\) | 1.53695e14 | 0.232451 | ||||||||
\(496\) | 1.18485e15 | 1.77220 | ||||||||
\(497\) | −7.04053e14 | −1.04147 | ||||||||
\(498\) | −9.10969e13 | −0.133273 | ||||||||
\(499\) | 5.97022e14 | 0.863848 | 0.431924 | − | 0.901910i | \(-0.357835\pi\) | ||||
0.431924 | + | 0.901910i | \(0.357835\pi\) | |||||||
\(500\) | 4.74828e13 | 0.0679519 | ||||||||
\(501\) | 2.11768e14 | 0.299746 | ||||||||
\(502\) | −4.06625e14 | −0.569278 | ||||||||
\(503\) | −1.01245e15 | −1.40201 | −0.701005 | − | 0.713156i | \(-0.747265\pi\) | ||||
−0.701005 | + | 0.713156i | \(0.747265\pi\) | |||||||
\(504\) | 2.84054e14 | 0.389074 | ||||||||
\(505\) | 1.20274e15 | 1.62955 | ||||||||
\(506\) | 6.01033e14 | 0.805509 | ||||||||
\(507\) | 3.24624e14 | 0.430365 | ||||||||
\(508\) | −4.67858e13 | −0.0613570 | ||||||||
\(509\) | −1.31283e15 | −1.70318 | −0.851591 | − | 0.524207i | \(-0.824362\pi\) | ||||
−0.851591 | + | 0.524207i | \(0.824362\pi\) | |||||||
\(510\) | 4.35005e14 | 0.558288 | ||||||||
\(511\) | −1.10086e15 | −1.39770 | ||||||||
\(512\) | 8.62460e14 | 1.08331 | ||||||||
\(513\) | −8.64396e13 | −0.107416 | ||||||||
\(514\) | −9.92292e14 | −1.21995 | ||||||||
\(515\) | −1.34099e15 | −1.63113 | ||||||||
\(516\) | −3.82510e13 | −0.0460330 | ||||||||
\(517\) | 4.91251e14 | 0.584932 | ||||||||
\(518\) | −1.00774e15 | −1.18723 | ||||||||
\(519\) | 1.56458e14 | 0.182380 | ||||||||
\(520\) | 4.60120e14 | 0.530704 | ||||||||
\(521\) | 1.32049e15 | 1.50704 | 0.753522 | − | 0.657423i | \(-0.228353\pi\) | ||||
0.753522 | + | 0.657423i | \(0.228353\pi\) | |||||||
\(522\) | 3.18771e14 | 0.359990 | ||||||||
\(523\) | 1.46506e15 | 1.63718 | 0.818591 | − | 0.574377i | \(-0.194756\pi\) | ||||
0.818591 | + | 0.574377i | \(0.194756\pi\) | |||||||
\(524\) | 1.12787e14 | 0.124720 | ||||||||
\(525\) | −2.35886e13 | −0.0258123 | ||||||||
\(526\) | −1.49707e15 | −1.62114 | ||||||||
\(527\) | −1.75621e15 | −1.88200 | ||||||||
\(528\) | 3.44729e14 | 0.365588 | ||||||||
\(529\) | 4.67241e14 | 0.490382 | ||||||||
\(530\) | 1.69932e15 | 1.76505 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −4.30717e13 | −0.0438206 | ||||||||
\(533\) | −7.57569e14 | −0.762821 | ||||||||
\(534\) | −1.01241e15 | −1.00897 | ||||||||
\(535\) | −9.21417e14 | −0.908888 | ||||||||
\(536\) | 6.01735e14 | 0.587488 | ||||||||
\(537\) | 1.07302e15 | 1.03693 | ||||||||
\(538\) | −1.53718e15 | −1.47036 | ||||||||
\(539\) | 2.02393e14 | 0.191627 | ||||||||
\(540\) | 1.45276e13 | 0.0136154 | ||||||||
\(541\) | −1.07000e15 | −0.992654 | −0.496327 | − | 0.868136i | \(-0.665318\pi\) | ||||
−0.496327 | + | 0.868136i | \(0.665318\pi\) | |||||||
\(542\) | −5.82885e14 | −0.535287 | ||||||||
\(543\) | 7.63701e14 | 0.694263 | ||||||||
\(544\) | −1.51334e14 | −0.136189 | ||||||||
\(545\) | −1.66067e15 | −1.47946 | ||||||||
\(546\) | 3.60524e14 | 0.317961 | ||||||||
\(547\) | −1.56936e15 | −1.37022 | −0.685111 | − | 0.728439i | \(-0.740246\pi\) | ||||
−0.685111 | + | 0.728439i | \(0.740246\pi\) | |||||||
\(548\) | −1.57574e14 | −0.136204 | ||||||||
\(549\) | 1.69512e13 | 0.0145061 | ||||||||
\(550\) | −3.07730e13 | −0.0260720 | ||||||||
\(551\) | −7.44923e14 | −0.624852 | ||||||||
\(552\) | 8.75534e14 | 0.727123 | ||||||||
\(553\) | −5.03477e13 | −0.0413991 | ||||||||
\(554\) | 1.63197e14 | 0.132864 | ||||||||
\(555\) | −7.94297e14 | −0.640282 | ||||||||
\(556\) | −1.28773e13 | −0.0102781 | ||||||||
\(557\) | −1.18643e15 | −0.937647 | −0.468823 | − | 0.883292i | \(-0.655322\pi\) | ||||
−0.468823 | + | 0.883292i | \(0.655322\pi\) | |||||||
\(558\) | 7.86592e14 | 0.615547 | ||||||||
\(559\) | −7.48199e14 | −0.579765 | ||||||||
\(560\) | −1.39187e15 | −1.06798 | ||||||||
\(561\) | −5.10967e14 | −0.388237 | ||||||||
\(562\) | −1.67856e15 | −1.26296 | ||||||||
\(563\) | 1.77729e15 | 1.32422 | 0.662112 | − | 0.749405i | \(-0.269660\pi\) | ||||
0.662112 | + | 0.749405i | \(0.269660\pi\) | |||||||
\(564\) | 4.64342e13 | 0.0342612 | ||||||||
\(565\) | 9.61449e14 | 0.702522 | ||||||||
\(566\) | −1.95482e15 | −1.41454 | ||||||||
\(567\) | 1.75428e14 | 0.125716 | ||||||||
\(568\) | −1.33797e15 | −0.949579 | ||||||||
\(569\) | −4.24631e14 | −0.298466 | −0.149233 | − | 0.988802i | \(-0.547680\pi\) | ||||
−0.149233 | + | 0.988802i | \(0.547680\pi\) | |||||||
\(570\) | 4.55302e14 | 0.316948 | ||||||||
\(571\) | −2.59400e15 | −1.78843 | −0.894214 | − | 0.447641i | \(-0.852264\pi\) | ||||
−0.894214 | + | 0.447641i | \(0.852264\pi\) | |||||||
\(572\) | −3.50694e13 | −0.0239470 | ||||||||
\(573\) | −1.48499e15 | −1.00432 | ||||||||
\(574\) | 2.46342e15 | 1.65015 | ||||||||
\(575\) | −7.27069e13 | −0.0482394 | ||||||||
\(576\) | 5.37369e14 | 0.353142 | ||||||||
\(577\) | −1.60915e15 | −1.04744 | −0.523721 | − | 0.851890i | \(-0.675457\pi\) | ||||
−0.523721 | + | 0.851890i | \(0.675457\pi\) | |||||||
\(578\) | 4.99945e13 | 0.0322343 | ||||||||
\(579\) | −3.50023e13 | −0.0223545 | ||||||||
\(580\) | 1.25197e14 | 0.0792025 | ||||||||
\(581\) | −4.32037e14 | −0.270740 | ||||||||
\(582\) | 7.64114e14 | 0.474332 | ||||||||
\(583\) | −1.99605e15 | −1.22743 | ||||||||
\(584\) | −2.09205e15 | −1.27439 | ||||||||
\(585\) | 2.84164e14 | 0.171479 | ||||||||
\(586\) | −9.74592e14 | −0.582620 | ||||||||
\(587\) | −5.57425e14 | −0.330124 | −0.165062 | − | 0.986283i | \(-0.552782\pi\) | ||||
−0.165062 | + | 0.986283i | \(0.552782\pi\) | |||||||
\(588\) | 1.91307e13 | 0.0112242 | ||||||||
\(589\) | −1.83815e15 | −1.06843 | ||||||||
\(590\) | −2.22361e14 | −0.128048 | ||||||||
\(591\) | −1.37597e15 | −0.785016 | ||||||||
\(592\) | −1.78156e15 | −1.00701 | ||||||||
\(593\) | 7.68689e14 | 0.430477 | 0.215238 | − | 0.976562i | \(-0.430947\pi\) | ||||
0.215238 | + | 0.976562i | \(0.430947\pi\) | |||||||
\(594\) | 2.28857e14 | 0.126981 | ||||||||
\(595\) | 2.06306e15 | 1.13415 | ||||||||
\(596\) | 1.56416e14 | 0.0851975 | ||||||||
\(597\) | 1.43496e15 | 0.774427 | ||||||||
\(598\) | 1.11124e15 | 0.594224 | ||||||||
\(599\) | −9.18042e14 | −0.486424 | −0.243212 | − | 0.969973i | \(-0.578201\pi\) | ||||
−0.243212 | + | 0.969973i | \(0.578201\pi\) | |||||||
\(600\) | −4.48275e13 | −0.0235349 | ||||||||
\(601\) | 2.37400e15 | 1.23501 | 0.617505 | − | 0.786567i | \(-0.288143\pi\) | ||||
0.617505 | + | 0.786567i | \(0.288143\pi\) | |||||||
\(602\) | 2.43295e15 | 1.25416 | ||||||||
\(603\) | 3.71624e14 | 0.189827 | ||||||||
\(604\) | 5.01545e13 | 0.0253867 | ||||||||
\(605\) | −1.08176e15 | −0.542597 | ||||||||
\(606\) | 1.79092e15 | 0.890177 | ||||||||
\(607\) | 2.78400e15 | 1.37130 | 0.685648 | − | 0.727933i | \(-0.259519\pi\) | ||||
0.685648 | + | 0.727933i | \(0.259519\pi\) | |||||||
\(608\) | −1.58395e14 | −0.0773163 | ||||||||
\(609\) | 1.51181e15 | 0.731310 | ||||||||
\(610\) | −8.92867e13 | −0.0428028 | ||||||||
\(611\) | 9.08263e14 | 0.431504 | ||||||||
\(612\) | −4.82978e13 | −0.0227402 | ||||||||
\(613\) | 2.31529e15 | 1.08037 | 0.540185 | − | 0.841546i | \(-0.318354\pi\) | ||||
0.540185 | + | 0.841546i | \(0.318354\pi\) | |||||||
\(614\) | 2.09521e15 | 0.968952 | ||||||||
\(615\) | 1.94166e15 | 0.889938 | ||||||||
\(616\) | 1.75746e15 | 0.798346 | ||||||||
\(617\) | 7.90650e13 | 0.0355972 | 0.0177986 | − | 0.999842i | \(-0.494334\pi\) | ||||
0.0177986 | + | 0.999842i | \(0.494334\pi\) | |||||||
\(618\) | −1.99679e15 | −0.891036 | ||||||||
\(619\) | 1.54696e15 | 0.684197 | 0.342099 | − | 0.939664i | \(-0.388862\pi\) | ||||
0.342099 | + | 0.939664i | \(0.388862\pi\) | |||||||
\(620\) | 3.08933e14 | 0.135428 | ||||||||
\(621\) | 5.40718e14 | 0.234945 | ||||||||
\(622\) | −3.29823e15 | −1.42047 | ||||||||
\(623\) | −4.80147e15 | −2.04970 | ||||||||
\(624\) | 6.37363e14 | 0.269694 | ||||||||
\(625\) | −2.47467e15 | −1.03795 | ||||||||
\(626\) | 1.98981e15 | 0.827280 | ||||||||
\(627\) | −5.34807e14 | −0.220407 | ||||||||
\(628\) | −1.95078e14 | −0.0796947 | ||||||||
\(629\) | 2.64068e15 | 1.06939 | ||||||||
\(630\) | −9.24027e14 | −0.370947 | ||||||||
\(631\) | −3.12319e15 | −1.24290 | −0.621452 | − | 0.783452i | \(-0.713457\pi\) | ||||
−0.621452 | + | 0.783452i | \(0.713457\pi\) | |||||||
\(632\) | −9.56801e13 | −0.0377466 | ||||||||
\(633\) | 9.91248e14 | 0.387670 | ||||||||
\(634\) | 4.53690e14 | 0.175901 | ||||||||
\(635\) | 2.34552e15 | 0.901537 | ||||||||
\(636\) | −1.88672e14 | −0.0718940 | ||||||||
\(637\) | 3.74200e14 | 0.141363 | ||||||||
\(638\) | 1.97226e15 | 0.738669 | ||||||||
\(639\) | −8.26313e14 | −0.306825 | ||||||||
\(640\) | −2.44683e15 | −0.900771 | ||||||||
\(641\) | 3.29251e15 | 1.20173 | 0.600867 | − | 0.799349i | \(-0.294822\pi\) | ||||
0.600867 | + | 0.799349i | \(0.294822\pi\) | |||||||
\(642\) | −1.37202e15 | −0.496499 | ||||||||
\(643\) | −4.86563e15 | −1.74574 | −0.872869 | − | 0.487955i | \(-0.837743\pi\) | ||||
−0.872869 | + | 0.487955i | \(0.837743\pi\) | |||||||
\(644\) | 2.69433e14 | 0.0958469 | ||||||||
\(645\) | 1.91764e15 | 0.676378 | ||||||||
\(646\) | −1.51367e15 | −0.529362 | ||||||||
\(647\) | 2.31233e15 | 0.801817 | 0.400909 | − | 0.916118i | \(-0.368694\pi\) | ||||
0.400909 | + | 0.916118i | \(0.368694\pi\) | |||||||
\(648\) | 3.33380e14 | 0.114624 | ||||||||
\(649\) | 2.61190e14 | 0.0890454 | ||||||||
\(650\) | −5.68956e13 | −0.0192333 | ||||||||
\(651\) | 3.73050e15 | 1.25047 | ||||||||
\(652\) | 6.31882e13 | 0.0210027 | ||||||||
\(653\) | −3.09718e15 | −1.02081 | −0.510404 | − | 0.859935i | \(-0.670504\pi\) | ||||
−0.510404 | + | 0.859935i | \(0.670504\pi\) | |||||||
\(654\) | −2.47280e15 | −0.808186 | ||||||||
\(655\) | −5.65437e15 | −1.83255 | ||||||||
\(656\) | 4.35503e15 | 1.39965 | ||||||||
\(657\) | −1.29202e15 | −0.411775 | ||||||||
\(658\) | −2.95344e15 | −0.933438 | ||||||||
\(659\) | −8.36963e14 | −0.262323 | −0.131162 | − | 0.991361i | \(-0.541871\pi\) | ||||
−0.131162 | + | 0.991361i | \(0.541871\pi\) | |||||||
\(660\) | 8.98834e13 | 0.0279375 | ||||||||
\(661\) | −6.02877e14 | −0.185832 | −0.0929160 | − | 0.995674i | \(-0.529619\pi\) | ||||
−0.0929160 | + | 0.995674i | \(0.529619\pi\) | |||||||
\(662\) | 4.42645e14 | 0.135312 | ||||||||
\(663\) | −9.44716e14 | −0.286403 | ||||||||
\(664\) | −8.21038e14 | −0.246853 | ||||||||
\(665\) | 2.15932e15 | 0.643870 | ||||||||
\(666\) | −1.18274e15 | −0.349768 | ||||||||
\(667\) | 4.65982e15 | 1.36671 | ||||||||
\(668\) | 1.23846e14 | 0.0360255 | ||||||||
\(669\) | 1.09115e15 | 0.314805 | ||||||||
\(670\) | −1.95745e15 | −0.560116 | ||||||||
\(671\) | 1.04878e14 | 0.0297653 | ||||||||
\(672\) | 3.21459e14 | 0.0904888 | ||||||||
\(673\) | 2.95976e15 | 0.826369 | 0.413185 | − | 0.910647i | \(-0.364416\pi\) | ||||
0.413185 | + | 0.910647i | \(0.364416\pi\) | |||||||
\(674\) | −3.19109e15 | −0.883711 | ||||||||
\(675\) | −2.76849e13 | −0.00760452 | ||||||||
\(676\) | 1.89845e14 | 0.0517241 | ||||||||
\(677\) | 1.61475e15 | 0.436382 | 0.218191 | − | 0.975906i | \(-0.429984\pi\) | ||||
0.218191 | + | 0.975906i | \(0.429984\pi\) | |||||||
\(678\) | 1.43163e15 | 0.383767 | ||||||||
\(679\) | 3.62390e15 | 0.963590 | ||||||||
\(680\) | 3.92062e15 | 1.03408 | ||||||||
\(681\) | 3.19148e15 | 0.834994 | ||||||||
\(682\) | 4.86670e15 | 1.26305 | ||||||||
\(683\) | 4.94165e15 | 1.27221 | 0.636104 | − | 0.771603i | \(-0.280545\pi\) | ||||
0.636104 | + | 0.771603i | \(0.280545\pi\) | |||||||
\(684\) | −5.05513e13 | −0.0129099 | ||||||||
\(685\) | 7.89966e15 | 2.00129 | ||||||||
\(686\) | 3.12630e15 | 0.785684 | ||||||||
\(687\) | −1.05850e15 | −0.263894 | ||||||||
\(688\) | 4.30116e15 | 1.06377 | ||||||||
\(689\) | −3.69046e15 | −0.905472 | ||||||||
\(690\) | −2.84811e15 | −0.693246 | ||||||||
\(691\) | −3.06757e15 | −0.740738 | −0.370369 | − | 0.928885i | \(-0.620769\pi\) | ||||
−0.370369 | + | 0.928885i | \(0.620769\pi\) | |||||||
\(692\) | 9.14989e13 | 0.0219196 | ||||||||
\(693\) | 1.08538e15 | 0.257959 | ||||||||
\(694\) | −6.27012e15 | −1.47842 | ||||||||
\(695\) | 6.45578e14 | 0.151019 | ||||||||
\(696\) | 2.87302e15 | 0.666788 | ||||||||
\(697\) | −6.45514e15 | −1.48636 | ||||||||
\(698\) | −3.38520e15 | −0.773355 | ||||||||
\(699\) | −1.61588e15 | −0.366257 | ||||||||
\(700\) | −1.37950e13 | −0.00310229 | ||||||||
\(701\) | 5.24474e15 | 1.17024 | 0.585120 | − | 0.810947i | \(-0.301047\pi\) | ||||
0.585120 | + | 0.810947i | \(0.301047\pi\) | |||||||
\(702\) | 4.23130e14 | 0.0936741 | ||||||||
\(703\) | 2.76389e15 | 0.607108 | ||||||||
\(704\) | 3.32474e15 | 0.724616 | ||||||||
\(705\) | −2.32789e15 | −0.503411 | ||||||||
\(706\) | 2.69435e15 | 0.578135 | ||||||||
\(707\) | 8.49364e15 | 1.80837 | ||||||||
\(708\) | 2.46883e13 | 0.00521566 | ||||||||
\(709\) | 8.25422e15 | 1.73030 | 0.865151 | − | 0.501512i | \(-0.167223\pi\) | ||||
0.865151 | + | 0.501512i | \(0.167223\pi\) | |||||||
\(710\) | 4.35243e15 | 0.905337 | ||||||||
\(711\) | −5.90907e13 | −0.0121965 | ||||||||
\(712\) | −9.12464e15 | −1.86886 | ||||||||
\(713\) | 1.14985e16 | 2.33694 | ||||||||
\(714\) | 3.07197e15 | 0.619551 | ||||||||
\(715\) | 1.75814e15 | 0.351860 | ||||||||
\(716\) | 6.27520e14 | 0.124625 | ||||||||
\(717\) | −1.89710e14 | −0.0373882 | ||||||||
\(718\) | −3.16907e15 | −0.619794 | ||||||||
\(719\) | −4.62022e15 | −0.896715 | −0.448357 | − | 0.893854i | \(-0.647991\pi\) | ||||
−0.448357 | + | 0.893854i | \(0.647991\pi\) | |||||||
\(720\) | −1.63357e15 | −0.314636 | ||||||||
\(721\) | −9.47000e15 | −1.81011 | ||||||||
\(722\) | 3.50126e15 | 0.664155 | ||||||||
\(723\) | 9.72610e14 | 0.183096 | ||||||||
\(724\) | 4.46624e14 | 0.0834412 | ||||||||
\(725\) | −2.38584e14 | −0.0442366 | ||||||||
\(726\) | −1.61078e15 | −0.296405 | ||||||||
\(727\) | 3.01603e14 | 0.0550803 | 0.0275402 | − | 0.999621i | \(-0.491233\pi\) | ||||
0.0275402 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(728\) | 3.24933e15 | 0.588940 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 6.80544e15 | 1.21501 | ||||||||
\(731\) | −6.37530e15 | −1.12968 | ||||||||
\(732\) | 9.91332e12 | 0.00174345 | ||||||||
\(733\) | 5.27949e15 | 0.921552 | 0.460776 | − | 0.887517i | \(-0.347571\pi\) | ||||
0.460776 | + | 0.887517i | \(0.347571\pi\) | |||||||
\(734\) | −1.01579e16 | −1.75984 | ||||||||
\(735\) | −9.59080e14 | −0.164920 | ||||||||
\(736\) | 9.90829e14 | 0.169111 | ||||||||
\(737\) | 2.29926e15 | 0.389508 | ||||||||
\(738\) | 2.89120e15 | 0.486147 | ||||||||
\(739\) | 3.18645e15 | 0.531818 | 0.265909 | − | 0.963998i | \(-0.414328\pi\) | ||||
0.265909 | + | 0.963998i | \(0.414328\pi\) | |||||||
\(740\) | −4.64518e14 | −0.0769534 | ||||||||
\(741\) | −9.88795e14 | −0.162595 | ||||||||
\(742\) | 1.20004e16 | 1.95873 | ||||||||
\(743\) | −1.56705e15 | −0.253889 | −0.126944 | − | 0.991910i | \(-0.540517\pi\) | ||||
−0.126944 | + | 0.991910i | \(0.540517\pi\) | |||||||
\(744\) | 7.08940e15 | 1.14014 | ||||||||
\(745\) | −7.84162e15 | −1.25183 | ||||||||
\(746\) | 5.86616e15 | 0.929588 | ||||||||
\(747\) | −5.07062e14 | −0.0797623 | ||||||||
\(748\) | −2.98822e14 | −0.0466609 | ||||||||
\(749\) | −6.50697e15 | −1.00862 | ||||||||
\(750\) | −3.54459e15 | −0.545418 | ||||||||
\(751\) | 2.59659e15 | 0.396629 | 0.198314 | − | 0.980138i | \(-0.436453\pi\) | ||||
0.198314 | + | 0.980138i | \(0.436453\pi\) | |||||||
\(752\) | −5.22133e15 | −0.791740 | ||||||||
\(753\) | −2.26335e15 | −0.340706 | ||||||||
\(754\) | 3.64646e15 | 0.544916 | ||||||||
\(755\) | −2.51440e15 | −0.373015 | ||||||||
\(756\) | 1.02593e14 | 0.0151094 | ||||||||
\(757\) | −5.34562e14 | −0.0781575 | −0.0390788 | − | 0.999236i | \(-0.512442\pi\) | ||||
−0.0390788 | + | 0.999236i | \(0.512442\pi\) | |||||||
\(758\) | 1.08027e15 | 0.156802 | ||||||||
\(759\) | 3.34546e15 | 0.482087 | ||||||||
\(760\) | 4.10354e15 | 0.587062 | ||||||||
\(761\) | 9.47799e15 | 1.34617 | 0.673086 | − | 0.739564i | \(-0.264968\pi\) | ||||
0.673086 | + | 0.739564i | \(0.264968\pi\) | |||||||
\(762\) | 3.49256e15 | 0.492484 | ||||||||
\(763\) | −1.17275e16 | −1.64181 | ||||||||
\(764\) | −8.68445e14 | −0.120706 | ||||||||
\(765\) | 2.42132e15 | 0.334129 | ||||||||
\(766\) | −6.10560e15 | −0.836508 | ||||||||
\(767\) | 4.82910e14 | 0.0656888 | ||||||||
\(768\) | 8.85519e14 | 0.119595 | ||||||||
\(769\) | −6.04843e15 | −0.811050 | −0.405525 | − | 0.914084i | \(-0.632911\pi\) | ||||
−0.405525 | + | 0.914084i | \(0.632911\pi\) | |||||||
\(770\) | −5.71701e15 | −0.761150 | ||||||||
\(771\) | −5.52328e15 | −0.730126 | ||||||||
\(772\) | −2.04699e13 | −0.00268671 | ||||||||
\(773\) | −1.02296e15 | −0.133313 | −0.0666564 | − | 0.997776i | \(-0.521233\pi\) | ||||
−0.0666564 | + | 0.997776i | \(0.521233\pi\) | |||||||
\(774\) | 2.85544e15 | 0.369485 | ||||||||
\(775\) | −5.88724e14 | −0.0756401 | ||||||||
\(776\) | 6.88681e15 | 0.878575 | ||||||||
\(777\) | −5.60926e15 | −0.710542 | ||||||||
\(778\) | 4.88494e15 | 0.614428 | ||||||||
\(779\) | −6.75632e15 | −0.843829 | ||||||||
\(780\) | 1.66183e14 | 0.0206095 | ||||||||
\(781\) | −5.11246e15 | −0.629577 | ||||||||
\(782\) | 9.46869e15 | 1.15785 | ||||||||
\(783\) | 1.77434e15 | 0.215450 | ||||||||
\(784\) | −2.15116e15 | −0.259379 | ||||||||
\(785\) | 9.77985e15 | 1.17098 | ||||||||
\(786\) | −8.41955e15 | −1.00107 | ||||||||
\(787\) | 7.90190e15 | 0.932976 | 0.466488 | − | 0.884528i | \(-0.345519\pi\) | ||||
0.466488 | + | 0.884528i | \(0.345519\pi\) | |||||||
\(788\) | −8.04691e14 | −0.0943485 | ||||||||
\(789\) | −8.33294e15 | −0.970230 | ||||||||
\(790\) | 3.11247e14 | 0.0359879 | ||||||||
\(791\) | 6.78968e15 | 0.779612 | ||||||||
\(792\) | 2.06265e15 | 0.235199 | ||||||||
\(793\) | 1.93907e14 | 0.0219579 | ||||||||
\(794\) | 6.87841e15 | 0.773527 | ||||||||
\(795\) | 9.45870e15 | 1.05636 | ||||||||
\(796\) | 8.39186e14 | 0.0930757 | ||||||||
\(797\) | 1.68582e15 | 0.185690 | 0.0928452 | − | 0.995681i | \(-0.470404\pi\) | ||||
0.0928452 | + | 0.995681i | \(0.470404\pi\) | |||||||
\(798\) | 3.21530e15 | 0.351727 | ||||||||
\(799\) | 7.73918e15 | 0.840791 | ||||||||
\(800\) | −5.07306e13 | −0.00547363 | ||||||||
\(801\) | −5.63526e15 | −0.603858 | ||||||||
\(802\) | 5.66587e15 | 0.602986 | ||||||||
\(803\) | −7.99382e15 | −0.844927 | ||||||||
\(804\) | 2.17331e14 | 0.0228147 | ||||||||
\(805\) | −1.35075e16 | −1.40831 | ||||||||
\(806\) | 8.99794e15 | 0.931752 | ||||||||
\(807\) | −8.55622e15 | −0.879990 | ||||||||
\(808\) | 1.61412e16 | 1.64882 | ||||||||
\(809\) | 2.09869e15 | 0.212927 | 0.106463 | − | 0.994317i | \(-0.466047\pi\) | ||||
0.106463 | + | 0.994317i | \(0.466047\pi\) | |||||||
\(810\) | −1.08449e15 | −0.109284 | ||||||||
\(811\) | −1.42566e16 | −1.42692 | −0.713461 | − | 0.700695i | \(-0.752873\pi\) | ||||
−0.713461 | + | 0.700695i | \(0.752873\pi\) | |||||||
\(812\) | 8.84129e14 | 0.0878936 | ||||||||
\(813\) | −3.24444e15 | −0.320363 | ||||||||
\(814\) | −7.31767e15 | −0.717692 | ||||||||
\(815\) | −3.16782e15 | −0.308599 | ||||||||
\(816\) | 5.43088e15 | 0.525502 | ||||||||
\(817\) | −6.67275e15 | −0.641333 | ||||||||
\(818\) | −8.82758e15 | −0.842749 | ||||||||
\(819\) | 2.00674e15 | 0.190296 | ||||||||
\(820\) | 1.13551e15 | 0.106959 | ||||||||
\(821\) | 1.05580e16 | 0.987856 | 0.493928 | − | 0.869503i | \(-0.335561\pi\) | ||||
0.493928 | + | 0.869503i | \(0.335561\pi\) | |||||||
\(822\) | 1.17629e16 | 1.09325 | ||||||||
\(823\) | 1.15070e16 | 1.06234 | 0.531169 | − | 0.847266i | \(-0.321753\pi\) | ||||
0.531169 | + | 0.847266i | \(0.321753\pi\) | |||||||
\(824\) | −1.79967e16 | −1.65041 | ||||||||
\(825\) | −1.71288e14 | −0.0156038 | ||||||||
\(826\) | −1.57030e15 | −0.142099 | ||||||||
\(827\) | −4.73492e15 | −0.425630 | −0.212815 | − | 0.977093i | \(-0.568263\pi\) | ||||
−0.212815 | + | 0.977093i | \(0.568263\pi\) | |||||||
\(828\) | 3.16220e14 | 0.0282373 | ||||||||
\(829\) | −1.24379e16 | −1.10331 | −0.551654 | − | 0.834073i | \(-0.686003\pi\) | ||||
−0.551654 | + | 0.834073i | \(0.686003\pi\) | |||||||
\(830\) | 2.67084e15 | 0.235352 | ||||||||
\(831\) | 9.08382e14 | 0.0795175 | ||||||||
\(832\) | 6.14704e15 | 0.534550 | ||||||||
\(833\) | 3.18851e15 | 0.275448 | ||||||||
\(834\) | 9.61289e14 | 0.0824975 | ||||||||
\(835\) | −6.20877e15 | −0.529334 | ||||||||
\(836\) | −3.12764e14 | −0.0264900 | ||||||||
\(837\) | 4.37831e15 | 0.368398 | ||||||||
\(838\) | −1.53512e16 | −1.28322 | ||||||||
\(839\) | −7.25098e15 | −0.602152 | −0.301076 | − | 0.953600i | \(-0.597346\pi\) | ||||
−0.301076 | + | 0.953600i | \(0.597346\pi\) | |||||||
\(840\) | −8.32807e15 | −0.687081 | ||||||||
\(841\) | 3.09044e15 | 0.253304 | ||||||||
\(842\) | 1.14304e16 | 0.930772 | ||||||||
\(843\) | −9.34319e15 | −0.755864 | ||||||||
\(844\) | 5.79698e14 | 0.0465927 | ||||||||
\(845\) | −9.51754e15 | −0.759998 | ||||||||
\(846\) | −3.46631e15 | −0.274999 | ||||||||
\(847\) | −7.63931e15 | −0.602137 | ||||||||
\(848\) | 2.12153e16 | 1.66139 | ||||||||
\(849\) | −1.08809e16 | −0.846586 | ||||||||
\(850\) | −4.84799e14 | −0.0374764 | ||||||||
\(851\) | −1.72893e16 | −1.32790 | ||||||||
\(852\) | −4.83241e14 | −0.0368762 | ||||||||
\(853\) | −4.88298e15 | −0.370225 | −0.185112 | − | 0.982717i | \(-0.559265\pi\) | ||||
−0.185112 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(854\) | −6.30535e14 | −0.0474997 | ||||||||
\(855\) | 2.53429e15 | 0.189689 | ||||||||
\(856\) | −1.23658e16 | −0.919635 | ||||||||
\(857\) | 1.27260e16 | 0.940366 | 0.470183 | − | 0.882569i | \(-0.344188\pi\) | ||||
0.470183 | + | 0.882569i | \(0.344188\pi\) | |||||||
\(858\) | 2.61793e15 | 0.192211 | ||||||||
\(859\) | −7.72016e15 | −0.563202 | −0.281601 | − | 0.959532i | \(-0.590865\pi\) | ||||
−0.281601 | + | 0.959532i | \(0.590865\pi\) | |||||||
\(860\) | 1.12147e15 | 0.0812915 | ||||||||
\(861\) | 1.37118e16 | 0.987593 | ||||||||
\(862\) | −3.16281e15 | −0.226351 | ||||||||
\(863\) | −2.00729e16 | −1.42742 | −0.713708 | − | 0.700443i | \(-0.752986\pi\) | ||||
−0.713708 | + | 0.700443i | \(0.752986\pi\) | |||||||
\(864\) | 3.77281e14 | 0.0266588 | ||||||||
\(865\) | −4.58713e15 | −0.322071 | ||||||||
\(866\) | −1.50095e16 | −1.04717 | ||||||||
\(867\) | 2.78278e14 | 0.0192919 | ||||||||
\(868\) | 2.18166e15 | 0.150289 | ||||||||
\(869\) | −3.65598e14 | −0.0250262 | ||||||||
\(870\) | −9.34593e15 | −0.635721 | ||||||||
\(871\) | 4.25105e15 | 0.287340 | ||||||||
\(872\) | −2.22868e16 | −1.49695 | ||||||||
\(873\) | 4.25320e15 | 0.283882 | ||||||||
\(874\) | 9.91048e15 | 0.657328 | ||||||||
\(875\) | −1.68106e16 | −1.10800 | ||||||||
\(876\) | −7.55595e14 | −0.0494899 | ||||||||
\(877\) | 2.56450e16 | 1.66919 | 0.834594 | − | 0.550866i | \(-0.185703\pi\) | ||||
0.834594 | + | 0.550866i | \(0.185703\pi\) | |||||||
\(878\) | 4.52447e15 | 0.292649 | ||||||||
\(879\) | −5.42475e15 | −0.348691 | ||||||||
\(880\) | −1.01070e16 | −0.645606 | ||||||||
\(881\) | 1.81453e16 | 1.15185 | 0.575925 | − | 0.817502i | \(-0.304642\pi\) | ||||
0.575925 | + | 0.817502i | \(0.304642\pi\) | |||||||
\(882\) | −1.42810e15 | −0.0900912 | ||||||||
\(883\) | −1.47084e16 | −0.922107 | −0.461054 | − | 0.887372i | \(-0.652528\pi\) | ||||
−0.461054 | + | 0.887372i | \(0.652528\pi\) | |||||||
\(884\) | −5.52485e14 | −0.0344218 | ||||||||
\(885\) | −1.23770e15 | −0.0766353 | ||||||||
\(886\) | −1.62861e15 | −0.100214 | ||||||||
\(887\) | 6.28753e15 | 0.384503 | 0.192252 | − | 0.981346i | \(-0.438421\pi\) | ||||
0.192252 | + | 0.981346i | \(0.438421\pi\) | |||||||
\(888\) | −1.06598e16 | −0.647853 | ||||||||
\(889\) | 1.65639e16 | 1.00047 | ||||||||
\(890\) | 2.96825e16 | 1.78178 | ||||||||
\(891\) | 1.27386e15 | 0.0759967 | ||||||||
\(892\) | 6.38123e14 | 0.0378353 | ||||||||
\(893\) | 8.10028e15 | 0.477328 | ||||||||
\(894\) | −1.16764e16 | −0.683840 | ||||||||
\(895\) | −3.14595e16 | −1.83116 | ||||||||
\(896\) | −1.72793e16 | −0.999616 | ||||||||
\(897\) | 6.18535e15 | 0.355636 | ||||||||
\(898\) | −8.94624e15 | −0.511235 | ||||||||
\(899\) | 3.77316e16 | 2.14302 | ||||||||
\(900\) | −1.61905e13 | −0.000913961 0 | ||||||||
\(901\) | −3.14459e16 | −1.76432 | ||||||||
\(902\) | 1.78880e16 | 0.997531 | ||||||||
\(903\) | 1.35422e16 | 0.750598 | ||||||||
\(904\) | 1.29030e16 | 0.710828 | ||||||||
\(905\) | −2.23907e16 | −1.22603 | ||||||||
\(906\) | −3.74403e15 | −0.203767 | ||||||||
\(907\) | −2.27848e16 | −1.23255 | −0.616275 | − | 0.787531i | \(-0.711359\pi\) | ||||
−0.616275 | + | 0.787531i | \(0.711359\pi\) | |||||||
\(908\) | 1.86643e15 | 0.100355 | ||||||||
\(909\) | 9.96858e15 | 0.532760 | ||||||||
\(910\) | −1.05701e16 | −0.561501 | ||||||||
\(911\) | −1.34480e16 | −0.710078 | −0.355039 | − | 0.934852i | \(-0.615532\pi\) | ||||
−0.355039 | + | 0.934852i | \(0.615532\pi\) | |||||||
\(912\) | 5.68427e15 | 0.298334 | ||||||||
\(913\) | −3.13723e15 | −0.163665 | ||||||||
\(914\) | 9.79603e15 | 0.507980 | ||||||||
\(915\) | −4.96986e14 | −0.0256170 | ||||||||
\(916\) | −6.19029e14 | −0.0317165 | ||||||||
\(917\) | −3.99307e16 | −2.03365 | ||||||||
\(918\) | 3.60543e15 | 0.182525 | ||||||||
\(919\) | −1.66171e16 | −0.836217 | −0.418109 | − | 0.908397i | \(-0.637307\pi\) | ||||
−0.418109 | + | 0.908397i | \(0.637307\pi\) | |||||||
\(920\) | −2.56695e16 | −1.28406 | ||||||||
\(921\) | 1.16623e16 | 0.579906 | ||||||||
\(922\) | 2.00373e16 | 0.990420 | ||||||||
\(923\) | −9.45231e15 | −0.464439 | ||||||||
\(924\) | 6.34749e14 | 0.0310032 | ||||||||
\(925\) | 8.85217e14 | 0.0429804 | ||||||||
\(926\) | −9.16017e15 | −0.442123 | ||||||||
\(927\) | −1.11145e16 | −0.533275 | ||||||||
\(928\) | 3.25135e15 | 0.155078 | ||||||||
\(929\) | −1.95972e16 | −0.929197 | −0.464598 | − | 0.885522i | \(-0.653801\pi\) | ||||
−0.464598 | + | 0.885522i | \(0.653801\pi\) | |||||||
\(930\) | −2.30618e16 | −1.08702 | ||||||||
\(931\) | 3.33728e15 | 0.156376 | ||||||||
\(932\) | −9.44995e14 | −0.0440192 | ||||||||
\(933\) | −1.83585e16 | −0.850137 | ||||||||
\(934\) | −3.33723e16 | −1.53631 | ||||||||
\(935\) | 1.49809e16 | 0.685603 | ||||||||
\(936\) | 3.81358e15 | 0.173507 | ||||||||
\(937\) | 3.08038e16 | 1.39327 | 0.696637 | − | 0.717423i | \(-0.254679\pi\) | ||||
0.696637 | + | 0.717423i | \(0.254679\pi\) | |||||||
\(938\) | −1.38233e16 | −0.621580 | ||||||||
\(939\) | 1.10756e16 | 0.495117 | ||||||||
\(940\) | −1.36139e15 | −0.0605032 | ||||||||
\(941\) | 8.75412e15 | 0.386785 | 0.193392 | − | 0.981121i | \(-0.438051\pi\) | ||||
0.193392 | + | 0.981121i | \(0.438051\pi\) | |||||||
\(942\) | 1.45625e16 | 0.639671 | ||||||||
\(943\) | 4.22638e16 | 1.84567 | ||||||||
\(944\) | −2.77610e15 | −0.120528 | ||||||||
\(945\) | −5.14330e15 | −0.222007 | ||||||||
\(946\) | 1.76668e16 | 0.758152 | ||||||||
\(947\) | 4.88945e15 | 0.208610 | 0.104305 | − | 0.994545i | \(-0.466738\pi\) | ||||
0.104305 | + | 0.994545i | \(0.466738\pi\) | |||||||
\(948\) | −3.45572e13 | −0.00146586 | ||||||||
\(949\) | −1.47796e16 | −0.623303 | ||||||||
\(950\) | −5.07419e14 | −0.0212758 | ||||||||
\(951\) | 2.52532e15 | 0.105275 | ||||||||
\(952\) | 2.76871e16 | 1.14756 | ||||||||
\(953\) | 4.11751e15 | 0.169677 | 0.0848386 | − | 0.996395i | \(-0.472963\pi\) | ||||
0.0848386 | + | 0.996395i | \(0.472963\pi\) | |||||||
\(954\) | 1.40843e16 | 0.577059 | ||||||||
\(955\) | 4.35378e16 | 1.77357 | ||||||||
\(956\) | −1.10945e14 | −0.00449356 | ||||||||
\(957\) | 1.09779e16 | 0.442084 | ||||||||
\(958\) | 2.50528e16 | 1.00311 | ||||||||
\(959\) | 5.57867e16 | 2.22090 | ||||||||
\(960\) | −1.57549e16 | −0.623627 | ||||||||
\(961\) | 6.76972e16 | 2.66436 | ||||||||
\(962\) | −1.35295e16 | −0.529442 | ||||||||
\(963\) | −7.63693e15 | −0.297149 | ||||||||
\(964\) | 5.68798e14 | 0.0220057 | ||||||||
\(965\) | 1.02622e15 | 0.0394766 | ||||||||
\(966\) | −2.01131e16 | −0.769318 | ||||||||
\(967\) | 3.95380e15 | 0.150373 | 0.0751864 | − | 0.997169i | \(-0.476045\pi\) | ||||
0.0751864 | + | 0.997169i | \(0.476045\pi\) | |||||||
\(968\) | −1.45176e16 | −0.549012 | ||||||||
\(969\) | −8.42538e15 | −0.316817 | ||||||||
\(970\) | −2.24028e16 | −0.837641 | ||||||||
\(971\) | −5.07440e16 | −1.88660 | −0.943299 | − | 0.331945i | \(-0.892295\pi\) | ||||
−0.943299 | + | 0.331945i | \(0.892295\pi\) | |||||||
\(972\) | 1.20408e14 | 0.00445136 | ||||||||
\(973\) | 4.55902e15 | 0.167591 | ||||||||
\(974\) | 4.45270e16 | 1.62761 | ||||||||
\(975\) | −3.16691e14 | −0.0115109 | ||||||||
\(976\) | −1.11471e15 | −0.0402892 | ||||||||
\(977\) | −1.65424e16 | −0.594536 | −0.297268 | − | 0.954794i | \(-0.596075\pi\) | ||||
−0.297268 | + | 0.954794i | \(0.596075\pi\) | |||||||
\(978\) | −4.71700e15 | −0.168578 | ||||||||
\(979\) | −3.48657e16 | −1.23906 | ||||||||
\(980\) | −5.60885e14 | −0.0198212 | ||||||||
\(981\) | −1.37641e16 | −0.483690 | ||||||||
\(982\) | 2.94840e16 | 1.03032 | ||||||||
\(983\) | −4.79624e16 | −1.66670 | −0.833348 | − | 0.552749i | \(-0.813579\pi\) | ||||
−0.833348 | + | 0.552749i | \(0.813579\pi\) | |||||||
\(984\) | 2.60578e16 | 0.900460 | ||||||||
\(985\) | 4.03417e16 | 1.38629 | ||||||||
\(986\) | 3.10710e16 | 1.06177 | ||||||||
\(987\) | −1.64394e16 | −0.558651 | ||||||||
\(988\) | −5.78263e14 | −0.0195417 | ||||||||
\(989\) | 4.17410e16 | 1.40276 | ||||||||
\(990\) | −6.70979e15 | −0.224241 | ||||||||
\(991\) | −4.09919e16 | −1.36236 | −0.681182 | − | 0.732114i | \(-0.738534\pi\) | ||||
−0.681182 | + | 0.732114i | \(0.738534\pi\) | |||||||
\(992\) | 8.02296e15 | 0.265168 | ||||||||
\(993\) | 2.46384e15 | 0.0809827 | ||||||||
\(994\) | 3.07365e16 | 1.00468 | ||||||||
\(995\) | −4.20710e16 | −1.36759 | ||||||||
\(996\) | −2.96538e14 | −0.00958636 | ||||||||
\(997\) | −6.55021e15 | −0.210587 | −0.105294 | − | 0.994441i | \(-0.533578\pi\) | ||||
−0.105294 | + | 0.994441i | \(0.533578\pi\) | |||||||
\(998\) | −2.60639e16 | −0.833338 | ||||||||
\(999\) | −6.58332e15 | −0.209332 |
(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 | 177.12.a.a.1.8 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.a.1.8 | ✓ | 26 | 1.1 | even | 1 | trivial |