Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,8,Mod(1,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("32.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.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: | \(9.99632081549\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{15}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 15 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.87298\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.1 |
$q$-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 | ||||||||
\(3\) | 61.9677 | 1.32508 | 0.662539 | − | 0.749028i | \(-0.269479\pi\) | ||||
0.662539 | + | 0.749028i | \(0.269479\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 70.0000 | 0.250440 | 0.125220 | − | 0.992129i | \(-0.460036\pi\) | ||||
0.125220 | + | 0.992129i | \(0.460036\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1115.42 | 1.22912 | 0.614561 | − | 0.788869i | \(-0.289333\pi\) | ||||
0.614561 | + | 0.788869i | \(0.289333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1653.00 | 0.755830 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7250.22 | −1.64239 | −0.821196 | − | 0.570646i | \(-0.806693\pi\) | ||||
−0.821196 | + | 0.570646i | \(0.806693\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13758.0 | 1.73682 | 0.868408 | − | 0.495851i | \(-0.165144\pi\) | ||||
0.868408 | + | 0.495851i | \(0.165144\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4337.74 | 0.331852 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16994.0 | 0.838927 | 0.419464 | − | 0.907772i | \(-0.362218\pi\) | ||||
0.419464 | + | 0.907772i | \(0.362218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34020.3 | 1.13789 | 0.568945 | − | 0.822376i | \(-0.307352\pi\) | ||||
0.568945 | + | 0.822376i | \(0.307352\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 69120.0 | 1.62868 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −32347.2 | −0.554356 | −0.277178 | − | 0.960819i | \(-0.589399\pi\) | ||||
−0.277178 | + | 0.960819i | \(0.589399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −73225.0 | −0.937280 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −33090.8 | −0.323544 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34190.0 | 0.260319 | 0.130160 | − | 0.991493i | \(-0.458451\pi\) | ||||
0.130160 | + | 0.991493i | \(0.458451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −120465. | −0.726266 | −0.363133 | − | 0.931737i | \(-0.618293\pi\) | ||||
−0.363133 | + | 0.931737i | \(0.618293\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −449280. | −2.17630 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 78079.3 | 0.307821 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35206.0 | 0.114264 | 0.0571322 | − | 0.998367i | \(-0.481804\pi\) | ||||
0.0571322 | + | 0.998367i | \(0.481804\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 852552. | 2.30141 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −484550. | −1.09798 | −0.548991 | − | 0.835828i | \(-0.684988\pi\) | ||||
−0.548991 | + | 0.835828i | \(0.684988\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −672040. | −1.28901 | −0.644504 | − | 0.764601i | \(-0.722936\pi\) | ||||
−0.644504 | + | 0.764601i | \(0.722936\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 115710. | 0.189290 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.20688e6 | −1.69560 | −0.847799 | − | 0.530318i | \(-0.822073\pi\) | ||||
−0.847799 | + | 0.530318i | \(0.822073\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 420617. | 0.510741 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.05308e6 | 1.11164 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 851702. | 0.785818 | 0.392909 | − | 0.919577i | \(-0.371469\pi\) | ||||
0.392909 | + | 0.919577i | \(0.371469\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −507516. | −0.411320 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.10816e6 | 1.50779 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 695464. | 0.440852 | 0.220426 | − | 0.975404i | \(-0.429255\pi\) | ||||
0.220426 | + | 0.975404i | \(0.429255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 71630.0 | 0.0404055 | 0.0202028 | − | 0.999796i | \(-0.493569\pi\) | ||||
0.0202028 | + | 0.999796i | \(0.493569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.84379e6 | 0.929007 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 963060. | 0.434967 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −307298. | −0.124824 | −0.0624120 | − | 0.998050i | \(-0.519879\pi\) | ||||
−0.0624120 | + | 0.998050i | \(0.519879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00448e6 | −0.734564 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −757370. | −0.251133 | −0.125566 | − | 0.992085i | \(-0.540075\pi\) | ||||
−0.125566 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.91204e6 | 1.17699 | 0.588496 | − | 0.808500i | \(-0.299720\pi\) | ||||
0.588496 | + | 0.808500i | \(0.299720\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.53759e6 | −1.24197 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.08704e6 | −2.01870 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 314548. | 0.0717782 | 0.0358891 | − | 0.999356i | \(-0.488574\pi\) | ||||
0.0358891 | + | 0.999356i | \(0.488574\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.66567e6 | −1.18455 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.53649e6 | −0.294955 | −0.147478 | − | 0.989065i | \(-0.547115\pi\) | ||||
−0.147478 | + | 0.989065i | \(0.547115\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.18958e6 | 0.210101 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.11868e6 | 0.344943 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.51063e6 | −0.377501 | −0.188750 | − | 0.982025i | \(-0.560444\pi\) | ||||
−0.188750 | + | 0.982025i | \(0.560444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.53459e7 | 2.13476 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.46496e6 | −0.962359 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.38142e6 | 0.284973 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −50094.0 | −0.00557294 | −0.00278647 | − | 0.999996i | \(-0.500887\pi\) | ||||
−0.00278647 | + | 0.999996i | \(0.500887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.19846e7 | −1.24137 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50354e7 | 1.45208 | 0.726039 | − | 0.687653i | \(-0.241359\pi\) | ||||
0.726039 | + | 0.687653i | \(0.241359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.99917e7 | −1.80268 | −0.901340 | − | 0.433113i | \(-0.857415\pi\) | ||||
−0.901340 | + | 0.433113i | \(0.857415\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.83840e6 | 0.407886 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.75102e6 | 0.690582 | 0.345291 | − | 0.938496i | \(-0.387780\pi\) | ||||
0.345291 | + | 0.938496i | \(0.387780\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.78070e7 | 1.31704 | 0.658518 | − | 0.752565i | \(-0.271184\pi\) | ||||
0.658518 | + | 0.752565i | \(0.271184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.18164e6 | 0.151409 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.88499e7 | −1.22895 | −0.614475 | − | 0.788936i | \(-0.710632\pi\) | ||||
−0.614475 | + | 0.788936i | \(0.710632\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.26430e6 | −0.138833 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.27420e7 | 1.31274 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.89554e7 | 1.03114 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.30786e7 | 1.69745 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.00265e7 | −1.45491 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.05945e7 | −0.485172 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.31235e7 | 1.43490 | 0.717452 | − | 0.696608i | \(-0.245308\pi\) | ||||
0.717452 | + | 0.696608i | \(0.245308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.16448e7 | −1.70804 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.63468e7 | 1.02395 | 0.511974 | − | 0.859001i | \(-0.328915\pi\) | ||||
0.511974 | + | 0.859001i | \(0.328915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.79469e7 | 1.39861 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.31635e6 | −0.0810283 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.88745e7 | −0.627125 | −0.313563 | − | 0.949568i | \(-0.601523\pi\) | ||||
−0.313563 | + | 0.949568i | \(0.601523\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.08848e7 | −0.343771 | −0.171886 | − | 0.985117i | \(-0.554986\pi\) | ||||
−0.171886 | + | 0.985117i | \(0.554986\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.47878e7 | −2.24680 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.97486e7 | −2.85253 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.39330e6 | 0.0651942 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.60647e7 | 0.676771 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.44462e7 | −0.853078 | −0.426539 | − | 0.904469i | \(-0.640267\pi\) | ||||
−0.426539 | + | 0.904469i | \(0.640267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.30493e7 | 0.308438 | 0.154219 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154219 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.80911e7 | 0.634086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.43257e6 | −0.181886 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.04587e7 | −0.421919 | −0.210960 | − | 0.977495i | \(-0.567659\pi\) | ||||
−0.210960 | + | 0.977495i | \(0.567659\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.27780e7 | 1.04127 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.60806e7 | −0.681371 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.07978e7 | 0.195290 | 0.0976448 | − | 0.995221i | \(-0.468869\pi\) | ||||
0.0976448 | + | 0.995221i | \(0.468869\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.14496e7 | −0.545031 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.58122e7 | 0.927303 | 0.463652 | − | 0.886018i | \(-0.346539\pi\) | ||||
0.463652 | + | 0.886018i | \(0.346539\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.26534e8 | 2.01653 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.62355e7 | 0.860051 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.94250e6 | −0.131310 | −0.0656550 | − | 0.997842i | \(-0.520914\pi\) | ||||
−0.0656550 | + | 0.997842i | \(0.520914\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.16766e7 | −1.15203 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.30963e7 | 0.584163 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.39334e7 | −1.22415 | −0.612074 | − | 0.790800i | \(-0.709665\pi\) | ||||
−0.612074 | + | 0.790800i | \(0.709665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.62269e7 | 1.20621 | 0.603103 | − | 0.797663i | \(-0.293931\pi\) | ||||
0.603103 | + | 0.797663i | \(0.293931\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.43875e6 | 0.0535404 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.46442e6 | 0.0286163 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23210e8 | −1.37785 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.69101e7 | −0.397675 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.06875e8 | 1.10984 | 0.554919 | − | 0.831905i | \(-0.312749\pi\) | ||||
0.554919 | + | 0.831905i | \(0.312749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.34693e8 | 1.34863 | 0.674317 | − | 0.738442i | \(-0.264438\pi\) | ||||
0.674317 | + | 0.738442i | \(0.264438\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.96786e7 | 0.576365 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.36611e7 | 0.872826 | 0.436413 | − | 0.899747i | \(-0.356249\pi\) | ||||
0.436413 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.37621e7 | −0.483605 | −0.241802 | − | 0.970326i | \(-0.577739\pi\) | ||||
−0.241802 | + | 0.970326i | \(0.577739\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.90426e7 | −0.165401 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.81362e7 | 0.319964 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.39185e7 | −0.274978 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.34699e7 | −0.418999 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.46655e8 | −1.86886 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.26710e8 | 0.928586 | 0.464293 | − | 0.885682i | \(-0.346308\pi\) | ||||
0.464293 | + | 0.885682i | \(0.346308\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.69325e7 | −0.332771 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.70428e7 | −0.322819 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.34369e8 | −0.892670 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.42420e8 | 1.55961 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.33803e8 | 1.45706 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00325e8 | 1.20967 | 0.604836 | − | 0.796350i | \(-0.293239\pi\) | ||||
0.604836 | + | 0.796350i | \(0.293239\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.21041e8 | −0.708424 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.46632e8 | −1.39946 | −0.699728 | − | 0.714410i | \(-0.746695\pi\) | ||||
−0.699728 | + | 0.714410i | \(0.746695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.24690e8 | −1.23640 | −0.618201 | − | 0.786020i | \(-0.712138\pi\) | ||||
−0.618201 | + | 0.786020i | \(0.712138\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.01136e8 | −2.67494 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.49045e8 | −1.28983 | −0.644914 | − | 0.764256i | \(-0.723107\pi\) | ||||
−0.644914 | + | 0.764256i | \(0.723107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.44819e7 | −0.424645 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.94918e7 | 0.0951116 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.04740e8 | 0.496273 | 0.248136 | − | 0.968725i | \(-0.420182\pi\) | ||||
0.248136 | + | 0.968725i | \(0.420182\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.04571e7 | 0.370258 | 0.185129 | − | 0.982714i | \(-0.440730\pi\) | ||||
0.185129 | + | 0.982714i | \(0.440730\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.78719e8 | −1.24608 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.94432e7 | 0.127910 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.68051e8 | 1.97630 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.52128e7 | −0.390839 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.60093e8 | 0.639021 | 0.319511 | − | 0.947583i | \(-0.396482\pi\) | ||||
0.319511 | + | 0.947583i | \(0.396482\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.34524e8 | 0.910470 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.37156e7 | 0.278400 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.76666e8 | 0.649213 | 0.324607 | − | 0.945849i | \(-0.394768\pi\) | ||||
0.324607 | + | 0.945849i | \(0.394768\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.92694e7 | 0.140445 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.65161e7 | 0.196757 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.49243e8 | 1.18381 | 0.591906 | − | 0.806007i | \(-0.298376\pi\) | ||||
0.591906 | + | 0.806007i | \(0.298376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.96191e7 | 0.196800 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.55578e8 | −0.500218 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.91355e8 | 0.599387 | 0.299693 | − | 0.954036i | \(-0.403116\pi\) | ||||
0.299693 | + | 0.954036i | \(0.403116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.62669e8 | −1.71736 | −0.858678 | − | 0.512516i | \(-0.828714\pi\) | ||||
−0.858678 | + | 0.512516i | \(0.828714\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.50953e8 | 2.82872 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.30898e8 | 1.53938 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.25734e8 | −1.48623 | −0.743116 | − | 0.669162i | \(-0.766653\pi\) | ||||
−0.743116 | + | 0.669162i | \(0.766653\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.99129e8 | −0.548934 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.24101e7 | −0.114024 | −0.0570122 | − | 0.998373i | \(-0.518157\pi\) | ||||
−0.0570122 | + | 0.998373i | \(0.518157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.44052e7 | −0.247596 | −0.123798 | − | 0.992307i | \(-0.539507\pi\) | ||||
−0.123798 | + | 0.992307i | \(0.539507\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.47571e8 | 0.377611 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.40476e8 | −1.34955 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.21543e8 | −0.296201 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.10421e6 | −0.00738458 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.01296e8 | 0.932027 | 0.466014 | − | 0.884778i | \(-0.345690\pi\) | ||||
0.466014 | + | 0.884778i | \(0.345690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.86825e7 | 0.110407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.39916e8 | 0.531387 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.45032e8 | −0.962814 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.49606e8 | −1.58435 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.31710e8 | 1.92412 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.01410e6 | 0.0101191 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.71076e8 | 0.534697 | 0.267348 | − | 0.963600i | \(-0.413853\pi\) | ||||
0.267348 | + | 0.963600i | \(0.413853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.23884e9 | −2.38869 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.12911e8 | −0.778387 | −0.389193 | − | 0.921156i | \(-0.627246\pi\) | ||||
−0.389193 | + | 0.921156i | \(0.627246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.81101e8 | −0.333823 | −0.166911 | − | 0.985972i | \(-0.553379\pi\) | ||||
−0.166911 | + | 0.985972i | \(0.553379\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.29065e8 | 0.232660 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.48850e8 | 1.32034 | 0.660172 | − | 0.751114i | \(-0.270483\pi\) | ||||
0.660172 | + | 0.751114i | \(0.270483\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.47885e8 | −0.427546 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.42281e8 | 0.915075 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.78141e8 | 0.954607 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00743e9 | −1.62788 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.10346e9 | 1.74517 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.34618e9 | −2.08410 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.59530e8 | −0.241793 | −0.120897 | − | 0.992665i | \(-0.538577\pi\) | ||||
−0.120897 | + | 0.992665i | \(0.538577\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.81955e7 | 0.0863644 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.15109e7 | −0.0312609 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.50578e8 | −0.783636 | −0.391818 | − | 0.920043i | \(-0.628154\pi\) | ||||
−0.391818 | + | 0.920043i | \(0.628154\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.16809e9 | −1.62846 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.73400e8 | 1.19281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.49431e8 | −0.601359 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.40314e8 | −0.183964 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.20856e9 | −1.55279 | −0.776397 | − | 0.630244i | \(-0.782955\pi\) | ||||
−0.776397 | + | 0.630244i | \(0.782955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.10448e8 | 0.139081 | 0.0695404 | − | 0.997579i | \(-0.477847\pi\) | ||||
0.0695404 | + | 0.997579i | \(0.477847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.55263e8 | −0.561937 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.42950e8 | 0.777975 | 0.388988 | − | 0.921243i | \(-0.372825\pi\) | ||||
0.388988 | + | 0.921243i | \(0.372825\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.30159e7 | −0.0628936 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.17463e9 | 1.36635 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.97988e8 | 0.225844 | 0.112922 | − | 0.993604i | \(-0.463979\pi\) | ||||
0.112922 | + | 0.993604i | \(0.463979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.63508e8 | 0.294794 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.04981e9 | 2.24926 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.73843e8 | 0.294765 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.68287e8 | 0.283315 | 0.141657 | − | 0.989916i | \(-0.454757\pi\) | ||||
0.141657 | + | 0.989916i | \(0.454757\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.00961e8 | −0.829887 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.50005e8 | 0.965866 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.72832e8 | 0.471765 | 0.235883 | − | 0.971782i | \(-0.424202\pi\) | ||||
0.235883 | + | 0.971782i | \(0.424202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.56517e8 | −0.642890 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.70386e8 | 0.452126 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.27673e9 | 1.20465 | 0.602324 | − | 0.798251i | \(-0.294241\pi\) | ||||
0.602324 | + | 0.798251i | \(0.294241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.05259e9 | 1.90136 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.29377e8 | −0.663371 | −0.331685 | − | 0.943390i | \(-0.607617\pi\) | ||||
−0.331685 | + | 0.943390i | \(0.607617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.66093e8 | −0.505563 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.11088e9 | −0.974271 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.29163e8 | 0.455791 | 0.227896 | − | 0.973686i | \(-0.426815\pi\) | ||||
0.227896 | + | 0.973686i | \(0.426815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.49708e8 | −0.465064 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.63265e9 | 1.35681 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.20184e7 | 0.0179761 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.59191e9 | −1.27688 | −0.638442 | − | 0.769670i | \(-0.720421\pi\) | ||||
−0.638442 | + | 0.769670i | \(0.720421\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.35148e9 | 1.85326 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.03748e9 | −0.803480 | −0.401740 | − | 0.915754i | \(-0.631594\pi\) | ||||
−0.401740 | + | 0.915754i | \(0.631594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.65736e9 | −1.26139 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.96597e8 | −0.296659 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.55251e8 | −0.187667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.08439e8 | −0.367458 | −0.183729 | − | 0.982977i | \(-0.558817\pi\) | ||||
−0.183729 | + | 0.982977i | \(0.558817\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.16961e9 | −0.830989 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.75734e8 | 0.541861 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.07554e8 | −0.0738685 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.74508e8 | −0.455523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.96853e8 | −0.197148 | −0.0985739 | − | 0.995130i | \(-0.531428\pi\) | ||||
−0.0985739 | + | 0.995130i | \(0.531428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.73091e8 | 0.570259 | 0.285130 | − | 0.958489i | \(-0.407963\pi\) | ||||
0.285130 | + | 0.958489i | \(0.407963\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.99498e9 | −1.28158 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.24439e9 | −0.786310 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.98975e7 | 0.0496633 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.18119e9 | −3.77983 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.90031e9 | 1.74491 | 0.872457 | − | 0.488691i | \(-0.162525\pi\) | ||||
0.872457 | + | 0.488691i | \(0.162525\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.46197e9 | 1.45739 | 0.728695 | − | 0.684838i | \(-0.240127\pi\) | ||||
0.728695 | + | 0.684838i | \(0.240127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.48307e8 | 0.0863874 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.10046e9 | −0.630796 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.88969e9 | 1.06602 | 0.533009 | − | 0.846110i | \(-0.321061\pi\) | ||||
0.533009 | + | 0.846110i | \(0.321061\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.95280e8 | 0.386033 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.14187e8 | 0.117052 | 0.0585261 | − | 0.998286i | \(-0.481360\pi\) | ||||
0.0585261 | + | 0.998286i | \(0.481360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.75744e8 | −0.0945411 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.13455e9 | −1.13039 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.48824e9 | −1.29727 | −0.648635 | − | 0.761100i | \(-0.724660\pi\) | ||||
−0.648635 | + | 0.761100i | \(0.724660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.51310e9 | 1.80332 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.08635e8 | 0.408704 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.07422e9 | 0.534628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.18777e9 | 1.07225 | 0.536123 | − | 0.844140i | \(-0.319888\pi\) | ||||
0.536123 | + | 0.844140i | \(0.319888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.62345e8 | −0.271430 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.48625e9 | −0.706541 | −0.353271 | − | 0.935521i | \(-0.614930\pi\) | ||||
−0.353271 | + | 0.935521i | \(0.614930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.59340e9 | −1.21433 | −0.607164 | − | 0.794576i | \(-0.707693\pi\) | ||||
−0.607164 | + | 0.794576i | \(0.707693\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.22547e8 | −0.241013 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.84718e9 | 0.839266 | 0.419633 | − | 0.907694i | \(-0.362159\pi\) | ||||
0.419633 | + | 0.907694i | \(0.362159\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.42766e8 | −0.153424 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.26778e9 | −0.559076 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.87244e9 | 2.11706 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.49114e9 | −1.06652 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.40786e9 | 0.593945 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.45543e9 | −1.43657 | −0.718287 | − | 0.695747i | \(-0.755073\pi\) | ||||
−0.718287 | + | 0.695747i | \(0.755073\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.84364e8 | 0.198456 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.23584e9 | −0.902869 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.50658e6 | −0.00139569 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.63187e9 | 1.42488 | 0.712442 | − | 0.701731i | \(-0.247589\pi\) | ||||
0.712442 | + | 0.701731i | \(0.247589\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.69116e8 | 0.258774 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.32674e9 | −0.505827 | −0.252914 | − | 0.967489i | \(-0.581389\pi\) | ||||
−0.252914 | + | 0.967489i | \(0.581389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.81025e8 | 0.218389 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.38924e8 | −0.310888 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.44785e8 | −0.308673 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.32010e8 | 0.0835901 | 0.0417950 | − | 0.999126i | \(-0.486692\pi\) | ||||
0.0417950 | + | 0.999126i | \(0.486692\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.45856e9 | 1.22875 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.22500e9 | 0.429187 | 0.214594 | − | 0.976703i | \(-0.431157\pi\) | ||||
0.214594 | + | 0.976703i | \(0.431157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.05248e9 | 0.363658 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.84103e9 | 2.67205 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.54747e8 | 0.220070 | 0.110035 | − | 0.993928i | \(-0.464904\pi\) | ||||
0.110035 | + | 0.993928i | \(0.464904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.36357e9 | 1.44667 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.12576e9 | −0.368158 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.39942e9 | −0.451462 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.75018e9 | 2.78484 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.54146e8 | −0.173996 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.39015e8 | −0.0740445 | −0.0370222 | − | 0.999314i | \(-0.511787\pi\) | ||||
−0.0370222 | + | 0.999314i | \(0.511787\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.76480e9 | −1.76209 | −0.881045 | − | 0.473032i | \(-0.843159\pi\) | ||||
−0.881045 | + | 0.473032i | \(0.843159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.06131e9 | −1.52653 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.04719e9 | −0.609285 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.35849e9 | −0.692690 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.14960e9 | 0.333209 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.66644e9 | −1.90699 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.12571e8 | 0.172949 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.82084e9 | −1.62209 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.04957e9 | −0.838837 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.89419e9 | 1.60042 | 0.800210 | − | 0.599720i | \(-0.204722\pi\) | ||||
0.800210 | + | 0.599720i | \(0.204722\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.96296e9 | 1.59832 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.24649e9 | 0.329838 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.11664e9 | −0.291714 | −0.145857 | − | 0.989306i | \(-0.546594\pi\) | ||||
−0.145857 | + | 0.989306i | \(0.546594\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.18404e8 | 0.0305397 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.16315e9 | 0.296215 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.50853e8 | 0.0882241 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.52715e8 | 0.0379188 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.94322e9 | −0.721656 | −0.360828 | − | 0.932632i | \(-0.617506\pi\) | ||||
−0.360828 | + | 0.932632i | \(0.617506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.24593e9 | −2.23877 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.63506e9 | −1.82576 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.84572e8 | 0.138057 | 0.0690285 | − | 0.997615i | \(-0.478010\pi\) | ||||
0.0690285 | + | 0.997615i | \(0.478010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.31949e9 | −0.307778 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.31960e9 | −1.45596 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.40531e9 | −1.68519 | −0.842597 | − | 0.538544i | \(-0.818975\pi\) | ||||
−0.842597 | + | 0.538544i | \(0.818975\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.06829e8 | 0.0689715 | 0.0344858 | − | 0.999405i | \(-0.489021\pi\) | ||||
0.0344858 | + | 0.999405i | \(0.489021\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.62280e9 | 1.47062 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.36862e9 | 0.519587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.60748e8 | −0.0781786 | −0.0390893 | − | 0.999236i | \(-0.512446\pi\) | ||||
−0.0390893 | + | 0.999236i | \(0.512446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.34662e9 | 1.78705 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.71383e9 | −0.362536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.17503e9 | −1.29062 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.59194e9 | 0.328761 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.35297e9 | 1.29641 | 0.648206 | − | 0.761465i | \(-0.275520\pi\) | ||||
0.648206 | + | 0.761465i | \(0.275520\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.09826e9 | −0.826411 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.80397e9 | 1.15656 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.89548e9 | 1.75177 | 0.875886 | − | 0.482517i | \(-0.160277\pi\) | ||||
0.875886 | + | 0.482517i | \(0.160277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.32688e9 | 0.258239 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.33151e9 | −0.640813 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.27230e9 | 1.00232 | 0.501160 | − | 0.865355i | \(-0.332907\pi\) | ||||
0.501160 | + | 0.865355i | \(0.332907\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.96322e9 | 0.368899 | 0.184449 | − | 0.982842i | \(-0.440950\pi\) | ||||
0.184449 | + | 0.982842i | \(0.440950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.07964e8 | −0.0943457 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.31550e9 | 0.425110 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.98364e9 | 1.26742 | 0.633712 | − | 0.773569i | \(-0.281531\pi\) | ||||
0.633712 | + | 0.773569i | \(0.281531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.36321e9 | 0.423977 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.66043e10 | −2.94494 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.02824e9 | 0.180295 | 0.0901476 | − | 0.995928i | \(-0.471266\pi\) | ||||
0.0901476 | + | 0.995928i | \(0.471266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.10185e9 | −0.364367 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.41933e8 | 0.0243267 | 0.0121634 | − | 0.999926i | \(-0.496128\pi\) | ||||
0.0121634 | + | 0.999926i | \(0.496128\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.00946e9 | 1.18787 | 0.593933 | − | 0.804515i | \(-0.297574\pi\) | ||||
0.593933 | + | 0.804515i | \(0.297574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07039e9 | 0.179359 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.80040e9 | −0.463994 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.97909e9 | 0.815774 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.52846e10 | −2.47639 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.98291e8 | 0.0958595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.69697e8 | 0.106115 | 0.0530573 | − | 0.998591i | \(-0.483103\pi\) | ||||
0.0530573 | + | 0.998591i | \(0.483103\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.85193e9 | 1.23045 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.31864e9 | 0.359357 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.78685e9 | 0.887062 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.25193e9 | −0.189814 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.05455e10 | 1.58149 | 0.790743 | − | 0.612148i | \(-0.209694\pi\) | ||||
0.790743 | + | 0.612148i | \(0.209694\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.39491e9 | 1.09697 | 0.548485 | − | 0.836160i | \(-0.315205\pi\) | ||||
0.548485 | + | 0.836160i | \(0.315205\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.91514e9 | −0.427760 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.79266e9 | −1.13115 | −0.565575 | − | 0.824697i | \(-0.691346\pi\) | ||||
−0.565575 | + | 0.824697i | \(0.691346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.04227e9 | −0.724052 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.32656e9 | −1.18286 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.23260e10 | −1.73232 | −0.866159 | − | 0.499768i | \(-0.833419\pi\) | ||||
−0.866159 | + | 0.499768i | \(0.833419\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.84427e9 | 0.256437 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.46661e9 | 0.889606 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.03521e10 | 1.40906 | 0.704532 | − | 0.709672i | \(-0.251157\pi\) | ||||
0.704532 | + | 0.709672i | \(0.251157\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.58143e9 | −0.347661 | −0.173830 | − | 0.984776i | \(-0.555614\pi\) | ||||
−0.173830 | + | 0.984776i | \(0.555614\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.44883e10 | 1.93072 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.65628e9 | 0.350266 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.10595e9 | −0.144309 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.24137e10 | 1.60291 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.19334e8 | −0.0663617 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.53171e9 | −0.825989 | −0.412995 | − | 0.910734i | \(-0.635517\pi\) | ||||
−0.412995 | + | 0.910734i | \(0.635517\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.42307e9 | 0.303252 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.13228e10 | −1.40247 | −0.701233 | − | 0.712932i | \(-0.747367\pi\) | ||||
−0.701233 | + | 0.712932i | \(0.747367\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.58758e7 | −0.00684983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.52832e10 | −1.85439 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.30342e10 | 1.56535 | 0.782676 | − | 0.622429i | \(-0.213854\pi\) | ||||
0.782676 | + | 0.622429i | \(0.213854\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.32122e9 | −0.157057 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.39235e10 | −1.63833 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.17177e10 | 1.36482 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.79137e9 | −0.206544 | −0.103272 | − | 0.994653i | \(-0.532931\pi\) | ||||
−0.103272 | + | 0.994653i | \(0.532931\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.33679e10 | −1.52579 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.61937e8 | −0.0860939 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.23444e9 | −0.921127 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.54327e10 | −1.70912 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.08521e10 | 1.18987 | 0.594937 | − | 0.803772i | \(-0.297177\pi\) | ||||
0.594937 | + | 0.803772i | \(0.297177\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19772e9 | 0.130020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.23515e9 | −0.562687 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.67708e10 | 1.78478 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.12248e9 | −0.750532 | −0.375266 | − | 0.926917i | \(-0.622449\pi\) | ||||
−0.375266 | + | 0.926917i | \(0.622449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.19948e8 | 0.0542521 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.89671e9 | 0.402610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.98240e9 | −0.714387 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.49051e9 | 0.657600 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.34850e9 | −0.536638 | −0.268319 | − | 0.963330i | \(-0.586468\pi\) | ||||
−0.268319 | + | 0.963330i | \(0.586468\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.22991e10 | −2.21571 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.98574e9 | 0.490621 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.50356e9 | −0.243992 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.41219e9 | −0.715445 | −0.357722 | − | 0.933828i | \(-0.616447\pi\) | ||||
−0.357722 | + | 0.933828i | \(0.616447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.88078e9 | −0.466598 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.14206e10 | −1.08138 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.23085e10 | −1.15436 | −0.577182 | − | 0.816615i | \(-0.695848\pi\) | ||||
−0.577182 | + | 0.816615i | \(0.695848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.82453e9 | 0.169490 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.22798e9 | 0.205010 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.11431e10 | −1.01567 | −0.507833 | − | 0.861455i | \(-0.669553\pi\) | ||||
−0.507833 | + | 0.861455i | \(0.669553\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.90041e10 | 2.61876 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.48011e9 | 0.490150 | 0.245075 | − | 0.969504i | \(-0.421187\pi\) | ||||
0.245075 | + | 0.969504i | \(0.421187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.41123e9 | −0.213645 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.53982e9 | −0.222936 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.76106e9 | 0.848810 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.76351e9 | 0.668834 | 0.334417 | − | 0.942425i | \(-0.391461\pi\) | ||||
0.334417 | + | 0.942425i | \(0.391461\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.92062e9 | 0.846752 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.13450e8 | 0.0772450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.58618e9 | 0.468036 | 0.234018 | − | 0.972232i | \(-0.424813\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424813\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.45329e10 | 1.20644 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.26117e10 | −1.03736 | −0.518679 | − | 0.854969i | \(-0.673576\pi\) | ||||
−0.518679 | + | 0.854969i | \(0.673576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.98622e10 | 1.61880 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.96638e9 | 0.158800 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.56819e9 | 0.765678 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.33475e10 | 1.05842 | 0.529208 | − | 0.848492i | \(-0.322489\pi\) | ||||
0.529208 | + | 0.848492i | \(0.322489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.09476e10 | 0.860258 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.75882e8 | −0.0136959 | −0.00684797 | − | 0.999977i | \(-0.502180\pi\) | ||||
−0.00684797 | + | 0.999977i | \(0.502180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.82107e9 | 0.680715 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.43344e9 | 0.186100 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.64845e10 | −1.24938 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.49110e9 | 0.412459 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.13137e9 | −0.0842248 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.43211e9 | −0.105665 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.27829e10 | −0.934802 | −0.467401 | − | 0.884046i | \(-0.654809\pi\) | ||||
−0.467401 | + | 0.884046i | \(0.654809\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.16418e10 | 1.56864 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.10255e10 | −1.51053 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.85486e8 | 0.0701769 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.69446e9 | 0.260775 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.22622e10 | 1.55763 | 0.778814 | − | 0.627255i | \(-0.215822\pi\) | ||||
0.778814 | + | 0.627255i | \(0.215822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.05098e10 | −1.42248 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.15007e9 | −0.285326 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.83632e10 | −1.93308 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.52564e9 | −0.170642 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.18578e10 | 0.794234 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.37057e10 | 1.57410 | 0.787050 | − | 0.616889i | \(-0.211607\pi\) | ||||
0.787050 | + | 0.616889i | \(0.211607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.02345e10 | 1.33205 | 0.666025 | − | 0.745930i | \(-0.267995\pi\) | ||||
0.666025 | + | 0.745930i | \(0.267995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.48673e10 | −2.27563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.55847e8 | 0.0489083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.28630e10 | −1.46675 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.53668e10 | 1.61351 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.64348e10 | −1.66715 | −0.833575 | − | 0.552407i | \(-0.813710\pi\) | ||||
−0.833575 | + | 0.552407i | \(0.813710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.73175e10 | −1.70821 | −0.854104 | − | 0.520102i | \(-0.825894\pi\) | ||||
−0.854104 | + | 0.520102i | \(0.825894\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.28985e10 | 2.03980 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.63558e10 | 1.00555 | 0.502773 | − | 0.864418i | \(-0.332313\pi\) | ||||
0.502773 | + | 0.864418i | \(0.332313\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.74626e9 | −0.411266 | −0.205633 | − | 0.978629i | \(-0.565925\pi\) | ||||
−0.205633 | + | 0.978629i | \(0.565925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.25785e10 | −1.96937 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.14797e9 | 0.428474 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.90686e9 | 0.232233 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.98629e9 | 0.234979 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.37908e10 | 0.806161 | 0.403080 | − | 0.915165i | \(-0.367940\pi\) | ||||
0.403080 | + | 0.915165i | \(0.367940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.60809e10 | −0.932234 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.62806e9 | −0.151091 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.85738e9 | 0.505018 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.68965e10 | 2.08638 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.85007e9 | −0.328084 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.13881e9 | −0.0633431 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.09615e9 | −0.391472 | −0.195736 | − | 0.980657i | \(-0.562710\pi\) | ||||
−0.195736 | + | 0.980657i | \(0.562710\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.93649e9 | 0.215391 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.09501e10 | −1.13698 | −0.568490 | − | 0.822690i | \(-0.692472\pi\) | ||||
−0.568490 | + | 0.822690i | \(0.692472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.36920e10 | −0.737040 | −0.368520 | − | 0.929620i | \(-0.620135\pi\) | ||||
−0.368520 | + | 0.929620i | \(0.620135\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.34921e10 | −1.78826 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.83553e10 | 1.50174 | 0.750872 | − | 0.660447i | \(-0.229633\pi\) | ||||
0.750872 | + | 0.660447i | \(0.229633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.25975e8 | −0.0328852 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.53172e9 | −0.392489 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.28055e9 | −0.117888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.22781e9 | −0.216796 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.28054e7 | −0.00421220 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.18173e10 | −0.596335 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.71632e10 | −1.35982 | −0.679912 | − | 0.733294i | \(-0.737982\pi\) | ||||
−0.679912 | + | 0.733294i | \(0.737982\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.48674e10 | 1.23501 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.39431e10 | 0.686978 | 0.343489 | − | 0.939157i | \(-0.388391\pi\) | ||||
0.343489 | + | 0.939157i | \(0.388391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.30370e10 | −1.61487 | −0.807437 | − | 0.589954i | \(-0.799146\pi\) | ||||
−0.807437 | + | 0.589954i | \(0.799146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.01674e9 | 0.146297 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.66589e10 | −0.801521 | −0.400760 | − | 0.916183i | \(-0.631254\pi\) | ||||
−0.400760 | + | 0.916183i | \(0.631254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.69466e10 | 1.76367 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.10774e10 | 1.94550 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.10585e10 | −1.92940 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.57533e9 | −0.306575 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.75776e10 | −1.27580 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.11871e9 | −0.189061 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.44738e10 | 0.659244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.64514e10 | −2.09938 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.73588e9 | 0.302082 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.81507e10 | −0.807731 | −0.403865 | − | 0.914818i | \(-0.632334\pi\) | ||||
−0.403865 | + | 0.914818i | \(0.632334\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.48535e10 | 1.09752 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.78139e10 | 0.780630 | 0.390315 | − | 0.920681i | \(-0.372366\pi\) | ||||
0.390315 | + | 0.920681i | \(0.372366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.11399e10 | 0.484433 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.10712e8 | 0.0134086 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.93877e10 | 1.25856 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.94899e10 | 0.828333 | 0.414166 | − | 0.910201i | \(-0.364073\pi\) | ||||
0.414166 | + | 0.910201i | \(0.364073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.67980e10 | 0.708514 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.04199e10 | −0.436171 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.57796e9 | −0.107098 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.30462e10 | −1.36252 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.36640e10 | −1.37756 | −0.688780 | − | 0.724971i | \(-0.741853\pi\) | ||||
−0.688780 | + | 0.724971i | \(0.741853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.43095e10 | 0.581167 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.55872e10 | −1.03142 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.62472e9 | −0.345068 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.56214e10 | 1.81167 | 0.905837 | − | 0.423626i | \(-0.139243\pi\) | ||||
0.905837 | + | 0.423626i | \(0.139243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.12224e10 | −0.442341 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.00373e10 | 1.95763 | 0.978814 | − | 0.204752i | \(-0.0656388\pi\) | ||||
0.978814 | + | 0.204752i | \(0.0656388\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56738e10 | 0.608673 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.58371e9 | −0.0995937 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.19677e10 | 1.22317 | 0.611584 | − | 0.791180i | \(-0.290533\pi\) | ||||
0.611584 | + | 0.791180i | \(0.290533\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.38219e10 | 2.04422 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.64045e10 | 1.74956 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.10999e10 | −1.16395 | −0.581974 | − | 0.813208i | \(-0.697719\pi\) | ||||
−0.581974 | + | 0.813208i | \(0.697719\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.48125e9 | 0.277947 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.53609e10 | −0.566532 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.10530e10 | −0.770813 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.30007e10 | −0.472537 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.44654e10 | 0.521963 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.42851e9 | 0.337752 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.30176e10 | 1.88550 | 0.942751 | − | 0.333497i | \(-0.108229\pi\) | ||||
0.942751 | + | 0.333497i | \(0.108229\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.58261e10 | 1.26493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.84951e10 | 1.69993 | 0.849964 | − | 0.526841i | \(-0.176624\pi\) | ||||
0.849964 | + | 0.526841i | \(0.176624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.21411e10 | −0.422537 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.24281e10 | −2.15707 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.30489e9 | −0.0790714 | −0.0395357 | − | 0.999218i | \(-0.512588\pi\) | ||||
−0.0395357 | + | 0.999218i | \(0.512588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.82026e10 | 0.620004 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.94349e10 | 0.995455 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.41653e10 | −0.811438 | −0.405719 | − | 0.913998i | \(-0.632979\pi\) | ||||
−0.405719 | + | 0.913998i | \(0.632979\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.55628e9 | 0.218590 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.34198e10 | −2.76159 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.17386e10 | 0.714569 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.22086e10 | −1.70406 | −0.852029 | − | 0.523495i | \(-0.824628\pi\) | ||||
−0.852029 | + | 0.523495i | \(0.824628\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.88572e9 | −0.320395 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.76335e9 | −0.121114 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.83024e9 | 0.250232 | 0.125116 | − | 0.992142i | \(-0.460070\pi\) | ||||
0.125116 | + | 0.992142i | \(0.460070\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.16499e9 | −0.0369696 |
(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 | 32.8.a.c.1.2 | yes | 2 | |
3.2 | odd | 2 | 288.8.a.k.1.2 | 2 | |||
4.3 | odd | 2 | inner | 32.8.a.c.1.1 | ✓ | 2 | |
8.3 | odd | 2 | 64.8.a.i.1.2 | 2 | |||
8.5 | even | 2 | 64.8.a.i.1.1 | 2 | |||
12.11 | even | 2 | 288.8.a.k.1.1 | 2 | |||
16.3 | odd | 4 | 256.8.b.i.129.1 | 4 | |||
16.5 | even | 4 | 256.8.b.i.129.2 | 4 | |||
16.11 | odd | 4 | 256.8.b.i.129.4 | 4 | |||
16.13 | even | 4 | 256.8.b.i.129.3 | 4 | |||
24.5 | odd | 2 | 576.8.a.bk.1.2 | 2 | |||
24.11 | even | 2 | 576.8.a.bk.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.8.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | inner | |
32.8.a.c.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
64.8.a.i.1.1 | 2 | 8.5 | even | 2 | |||
64.8.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
256.8.b.i.129.1 | 4 | 16.3 | odd | 4 | |||
256.8.b.i.129.2 | 4 | 16.5 | even | 4 | |||
256.8.b.i.129.3 | 4 | 16.13 | even | 4 | |||
256.8.b.i.129.4 | 4 | 16.11 | odd | 4 | |||
288.8.a.k.1.1 | 2 | 12.11 | even | 2 | |||
288.8.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
576.8.a.bk.1.1 | 2 | 24.11 | even | 2 | |||
576.8.a.bk.1.2 | 2 | 24.5 | odd | 2 |