Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,8,Mod(1,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.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: | \(179.933774679\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{46}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 46 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 72) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.78233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 437.552 | 1.56543 | 0.782717 | − | 0.622378i | \(-0.213833\pi\) | ||||
0.782717 | + | 0.622378i | \(0.213833\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1722.21 | 1.89776 | 0.948882 | − | 0.315630i | \(-0.102216\pi\) | ||||
0.948882 | + | 0.315630i | \(0.102216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4226.62 | −0.957456 | −0.478728 | − | 0.877963i | \(-0.658902\pi\) | ||||
−0.478728 | + | 0.877963i | \(0.658902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6638.83 | 0.838088 | 0.419044 | − | 0.907966i | \(-0.362365\pi\) | ||||
0.419044 | + | 0.907966i | \(0.362365\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −34165.6 | −1.68662 | −0.843311 | − | 0.537426i | \(-0.819397\pi\) | ||||
−0.843311 | + | 0.537426i | \(0.819397\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20358.1 | 0.680925 | 0.340462 | − | 0.940258i | \(-0.389416\pi\) | ||||
0.340462 | + | 0.940258i | \(0.389416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −45985.9 | −0.788093 | −0.394047 | − | 0.919090i | \(-0.628925\pi\) | ||||
−0.394047 | + | 0.919090i | \(0.628925\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 113327. | 1.45058 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 51462.3 | 0.391828 | 0.195914 | − | 0.980621i | \(-0.437233\pi\) | ||||
0.195914 | + | 0.980621i | \(0.437233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −15184.8 | −0.0915469 | −0.0457734 | − | 0.998952i | \(-0.514575\pi\) | ||||
−0.0457734 | + | 0.998952i | \(0.514575\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 753555. | 2.97082 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 384588. | 1.24821 | 0.624107 | − | 0.781339i | \(-0.285463\pi\) | ||||
0.624107 | + | 0.781339i | \(0.285463\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −602282. | −1.36476 | −0.682380 | − | 0.730998i | \(-0.739055\pi\) | ||||
−0.682380 | + | 0.730998i | \(0.739055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 248405. | 0.476455 | 0.238227 | − | 0.971209i | \(-0.423434\pi\) | ||||
0.238227 | + | 0.971209i | \(0.423434\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 718924. | 1.01004 | 0.505022 | − | 0.863106i | \(-0.331484\pi\) | ||||
0.505022 | + | 0.863106i | \(0.331484\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.14246e6 | 2.60151 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.39480e6 | 1.28690 | 0.643450 | − | 0.765488i | \(-0.277502\pi\) | ||||
0.643450 | + | 0.765488i | \(0.277502\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.84937e6 | −1.49883 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.19713e6 | 0.758857 | 0.379429 | − | 0.925221i | \(-0.376121\pi\) | ||||
0.379429 | + | 0.925221i | \(0.376121\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −764413. | −0.431195 | −0.215598 | − | 0.976482i | \(-0.569170\pi\) | ||||
−0.215598 | + | 0.976482i | \(0.569170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.90483e6 | 1.31197 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.54127e6 | 1.03226 | 0.516131 | − | 0.856510i | \(-0.327372\pi\) | ||||
0.516131 | + | 0.856510i | \(0.327372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.66313e6 | 1.54623 | 0.773114 | − | 0.634267i | \(-0.218698\pi\) | ||||
0.773114 | + | 0.634267i | \(0.218698\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −339311. | −0.102086 | −0.0510432 | − | 0.998696i | \(-0.516255\pi\) | ||||
−0.0510432 | + | 0.998696i | \(0.516255\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.27912e6 | −1.81703 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 328624. | 0.0749902 | 0.0374951 | − | 0.999297i | \(-0.488062\pi\) | ||||
0.0374951 | + | 0.999297i | \(0.488062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.77607e6 | 0.340947 | 0.170474 | − | 0.985362i | \(-0.445470\pi\) | ||||
0.170474 | + | 0.985362i | \(0.445470\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.49492e7 | −2.64029 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 582340. | 0.0875612 | 0.0437806 | − | 0.999041i | \(-0.486060\pi\) | ||||
0.0437806 | + | 0.999041i | \(0.486060\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.14334e7 | 1.59049 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.90771e6 | 1.06594 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.28652e6 | −0.365625 | −0.182812 | − | 0.983148i | \(-0.558520\pi\) | ||||
−0.182812 | + | 0.983148i | \(0.558520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.54549e6 | 0.342414 | 0.171207 | − | 0.985235i | \(-0.445233\pi\) | ||||
0.171207 | + | 0.985235i | \(0.445233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.24694e7 | −1.12438 | −0.562192 | − | 0.827007i | \(-0.690042\pi\) | ||||
−0.562192 | + | 0.827007i | \(0.690042\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.77904e7 | −1.40392 | −0.701962 | − | 0.712214i | \(-0.747692\pi\) | ||||
−0.701962 | + | 0.712214i | \(0.747692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −668188. | −0.0494204 | −0.0247102 | − | 0.999695i | \(-0.507866\pi\) | ||||
−0.0247102 | + | 0.999695i | \(0.507866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.59643e7 | −1.04082 | −0.520408 | − | 0.853918i | \(-0.674220\pi\) | ||||
−0.520408 | + | 0.853918i | \(0.674220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.01212e7 | −1.23371 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.88402e7 | −3.20081 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.62284e6 | −0.0832772 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.54025e7 | 0.705354 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.97232e7 | 1.72081 | 0.860403 | − | 0.509615i | \(-0.170212\pi\) | ||||
0.860403 | + | 0.509615i | \(0.170212\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.07841e6 | 0.236233 | 0.118116 | − | 0.993000i | \(-0.462314\pi\) | ||||
0.118116 | + | 0.993000i | \(0.462314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.50608e7 | 1.29223 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.87491e7 | 0.955216 | 0.477608 | − | 0.878573i | \(-0.341504\pi\) | ||||
0.477608 | + | 0.878573i | \(0.341504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.65405e7 | 1.46987 | 0.734935 | − | 0.678138i | \(-0.237213\pi\) | ||||
0.734935 | + | 0.678138i | \(0.237213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.80598e7 | −0.802433 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.25174e7 | 0.613381 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.10645e7 | 0.769330 | 0.384665 | − | 0.923056i | \(-0.374317\pi\) | ||||
0.384665 | + | 0.923056i | \(0.374317\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.42377e7 | 0.336528 | 0.168264 | − | 0.985742i | \(-0.446184\pi\) | ||||
0.168264 | + | 0.985742i | \(0.446184\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.64414e6 | −0.143311 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.35878e7 | 1.51760 | 0.758800 | − | 0.651324i | \(-0.225786\pi\) | ||||
0.758800 | + | 0.651324i | \(0.225786\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.91973e7 | −1.49562 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.10928e7 | −1.46665 | −0.733324 | − | 0.679880i | \(-0.762032\pi\) | ||||
−0.733324 | + | 0.679880i | \(0.762032\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.11778e8 | 1.85716 | 0.928581 | − | 0.371130i | \(-0.121029\pi\) | ||||
0.928581 | + | 0.371130i | \(0.121029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.86745e7 | −0.297608 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.97788e7 | −1.31829 | −0.659147 | − | 0.752014i | \(-0.729083\pi\) | ||||
−0.659147 | + | 0.752014i | \(0.729083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.95172e8 | 2.75286 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.65667e7 | −0.606862 | −0.303431 | − | 0.952853i | \(-0.598132\pi\) | ||||
−0.303431 | + | 0.952853i | \(0.598132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.73507e7 | 0.844242 | 0.422121 | − | 0.906539i | \(-0.361286\pi\) | ||||
0.422121 | + | 0.906539i | \(0.361286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.68277e8 | 1.95400 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.44405e8 | 1.61487 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.95557e7 | 0.306920 | 0.153460 | − | 0.988155i | \(-0.450958\pi\) | ||||
0.153460 | + | 0.988155i | \(0.450958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.23751e8 | −1.23908 | −0.619540 | − | 0.784965i | \(-0.712681\pi\) | ||||
−0.619540 | + | 0.784965i | \(0.712681\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.28755e7 | −0.213177 | −0.106588 | − | 0.994303i | \(-0.533993\pi\) | ||||
−0.106588 | + | 0.994303i | \(0.533993\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.69164e7 | −0.781837 | −0.390918 | − | 0.920425i | \(-0.627842\pi\) | ||||
−0.390918 | + | 0.920425i | \(0.627842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.86287e7 | 0.743598 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.63530e8 | −2.13644 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.60459e7 | −0.651956 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.82685e7 | 0.280448 | 0.140224 | − | 0.990120i | \(-0.455218\pi\) | ||||
0.140224 | + | 0.990120i | \(0.455218\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.08690e8 | 0.745858 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.61514e7 | −0.173734 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.26820e8 | −1.41354 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.07224e8 | 1.25133 | 0.625667 | − | 0.780090i | \(-0.284827\pi\) | ||||
0.625667 | + | 0.780090i | \(0.284827\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.07779e8 | 1.17899 | 0.589497 | − | 0.807770i | \(-0.299326\pi\) | ||||
0.589497 | + | 0.807770i | \(0.299326\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.86435e8 | −1.02589 | −0.512947 | − | 0.858420i | \(-0.671446\pi\) | ||||
−0.512947 | + | 0.858420i | \(0.671446\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.55106e7 | 0.0803309 | 0.0401654 | − | 0.999193i | \(-0.487212\pi\) | ||||
0.0401654 | + | 0.999193i | \(0.487212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.14566e8 | 1.58116 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.74511e8 | 0.826856 | 0.413428 | − | 0.910537i | \(-0.364331\pi\) | ||||
0.413428 | + | 0.910537i | \(0.364331\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.69055e7 | −0.353914 | −0.176957 | − | 0.984219i | \(-0.556625\pi\) | ||||
−0.176957 | + | 0.984219i | \(0.556625\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.37435e8 | 4.07249 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.35154e8 | 0.570675 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.99888e8 | 0.797865 | 0.398933 | − | 0.916980i | \(-0.369381\pi\) | ||||
0.398933 | + | 0.916980i | \(0.369381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.94365e8 | 0.754565 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.96410e8 | −0.721769 | −0.360884 | − | 0.932611i | \(-0.617525\pi\) | ||||
−0.360884 | + | 0.932611i | \(0.617525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.62339e8 | 2.36882 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.80764e8 | −1.29066 | −0.645328 | − | 0.763905i | \(-0.723279\pi\) | ||||
−0.645328 | + | 0.763905i | \(0.723279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.10295e8 | 2.01456 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.47962e8 | −1.40316 | −0.701581 | − | 0.712590i | \(-0.747522\pi\) | ||||
−0.701581 | + | 0.712590i | \(0.747522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.62567e8 | 0.496180 | 0.248090 | − | 0.968737i | \(-0.420197\pi\) | ||||
0.248090 | + | 0.968737i | \(0.420197\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.78989e8 | −1.38887 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.52029e8 | −0.712477 | −0.356239 | − | 0.934395i | \(-0.615941\pi\) | ||||
−0.356239 | + | 0.934395i | \(0.615941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.40349e7 | 0.145279 | 0.0726393 | − | 0.997358i | \(-0.476858\pi\) | ||||
0.0726393 | + | 0.997358i | \(0.476858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.76782e8 | 1.51272 | 0.756361 | − | 0.654155i | \(-0.226976\pi\) | ||||
0.756361 | + | 0.654155i | \(0.226976\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.03725e9 | −2.58999 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.56949e8 | 1.84469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.67850e8 | −1.31885 | −0.659427 | − | 0.751769i | \(-0.729201\pi\) | ||||
−0.659427 | + | 0.751769i | \(0.729201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.23807e8 | 1.18794 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.05293e8 | −0.660492 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.27806e8 | 0.904199 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.34471e8 | −0.675007 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12785e8 | 0.419718 | 0.209859 | − | 0.977732i | \(-0.432699\pi\) | ||||
0.209859 | + | 0.977732i | \(0.432699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.52178e8 | 0.852408 | 0.426204 | − | 0.904627i | \(-0.359851\pi\) | ||||
0.426204 | + | 0.904627i | \(0.359851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.42763e8 | −1.55346 | −0.776730 | − | 0.629834i | \(-0.783123\pi\) | ||||
−0.776730 | + | 0.629834i | \(0.783123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.02806e8 | 0.181264 | 0.0906318 | − | 0.995884i | \(-0.471111\pi\) | ||||
0.0906318 | + | 0.995884i | \(0.471111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.17512e8 | −0.375159 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.95546e8 | −1.14846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.52356e8 | 1.21571 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.23814e9 | 1.91683 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.55210e8 | −0.689944 | −0.344972 | − | 0.938613i | \(-0.612112\pi\) | ||||
−0.344972 | + | 0.938613i | \(0.612112\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.11194e9 | 1.61594 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.38644e8 | 0.197331 | 0.0986655 | − | 0.995121i | \(-0.468543\pi\) | ||||
0.0986655 | + | 0.995121i | \(0.468543\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.41805e7 | 0.0876522 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.27144e9 | 3.03929 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.99476e8 | −1.02719 | −0.513597 | − | 0.858032i | \(-0.671687\pi\) | ||||
−0.513597 | + | 0.858032i | \(0.671687\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.15205e8 | −1.15247 | −0.576234 | − | 0.817284i | \(-0.695478\pi\) | ||||
−0.576234 | + | 0.817284i | \(0.695478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.76398e8 | −0.818448 | −0.409224 | − | 0.912434i | \(-0.634201\pi\) | ||||
−0.409224 | + | 0.912434i | \(0.634201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.04036e9 | 2.42052 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.99641e8 | −0.455869 | −0.227934 | − | 0.973676i | \(-0.573197\pi\) | ||||
−0.227934 | + | 0.973676i | \(0.573197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.79421e8 | −0.536342 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.48466e8 | −0.159809 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.15569e8 | 0.438846 | 0.219423 | − | 0.975630i | \(-0.429582\pi\) | ||||
0.219423 | + | 0.975630i | \(0.429582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.40213e9 | 2.44223 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.54100e8 | −0.652624 | −0.326312 | − | 0.945262i | \(-0.605806\pi\) | ||||
−0.326312 | + | 0.945262i | \(0.605806\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.41649e8 | 0.328387 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.68523e8 | −0.630782 | −0.315391 | − | 0.948962i | \(-0.602136\pi\) | ||||
−0.315391 | + | 0.948962i | \(0.602136\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.38983e8 | 0.672107 | 0.336054 | − | 0.941843i | \(-0.390908\pi\) | ||||
0.336054 | + | 0.941843i | \(0.390908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.18499e9 | −2.84443 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.04715e7 | 0.0348598 | 0.0174299 | − | 0.999848i | \(-0.494452\pi\) | ||||
0.0174299 | + | 0.999848i | \(0.494452\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.57114e9 | 1.32922 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.43790e8 | 0.117392 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.87564e9 | 1.50447 | 0.752233 | − | 0.658897i | \(-0.228977\pi\) | ||||
0.752233 | + | 0.658897i | \(0.228977\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.96483e8 | 0.771728 | 0.385864 | − | 0.922556i | \(-0.373903\pi\) | ||||
0.385864 | + | 0.922556i | \(0.373903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.00809e8 | −0.0767244 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.62551e9 | −1.19511 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.01806e8 | 0.0735772 | 0.0367886 | − | 0.999323i | \(-0.488287\pi\) | ||||
0.0367886 | + | 0.999323i | \(0.488287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.06171e9 | 1.44013 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.77124e8 | 0.533730 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.61886e9 | 1.07513 | 0.537564 | − | 0.843223i | \(-0.319345\pi\) | ||||
0.537564 | + | 0.843223i | \(0.319345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.76813e9 | −1.15486 | −0.577428 | − | 0.816441i | \(-0.695944\pi\) | ||||
−0.577428 | + | 0.816441i | \(0.695944\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.87187e9 | −2.44658 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.31648e9 | −0.818307 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.37116e8 | 0.262982 | 0.131491 | − | 0.991317i | \(-0.458024\pi\) | ||||
0.131491 | + | 0.991317i | \(0.458024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.69007e8 | 0.573613 | 0.286807 | − | 0.957989i | \(-0.407406\pi\) | ||||
0.286807 | + | 0.957989i | \(0.407406\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.36185e8 | −0.536632 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.86918e8 | −0.500331 | −0.250166 | − | 0.968203i | \(-0.580485\pi\) | ||||
−0.250166 | + | 0.968203i | \(0.580485\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.47780e9 | 1.35411 | 0.677053 | − | 0.735934i | \(-0.263257\pi\) | ||||
0.677053 | + | 0.735934i | \(0.263257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.54804e8 | 0.137071 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.68169e7 | 0.0504765 | 0.0252382 | − | 0.999681i | \(-0.491966\pi\) | ||||
0.0252382 | + | 0.999681i | \(0.491966\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.54562e9 | 1.30670 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.00272e9 | 2.48981 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.53320e9 | 1.73166 | 0.865828 | − | 0.500341i | \(-0.166792\pi\) | ||||
0.865828 | + | 0.500341i | \(0.166792\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.88532e7 | −0.0279780 | −0.0139890 | − | 0.999902i | \(-0.504453\pi\) | ||||
−0.0139890 | + | 0.999902i | \(0.504453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.28948e9 | −1.07202 | −0.536011 | − | 0.844211i | \(-0.680069\pi\) | ||||
−0.536011 | + | 0.844211i | \(0.680069\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.76508e9 | −1.71067 | −0.855333 | − | 0.518079i | \(-0.826647\pi\) | ||||
−0.855333 | + | 0.518079i | \(0.826647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.37660e9 | 1.95899 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.04992e9 | −0.456185 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.30711e9 | 0.987736 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.15354e9 | −0.895320 | −0.447660 | − | 0.894204i | \(-0.647743\pi\) | ||||
−0.447660 | + | 0.894204i | \(0.647743\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.55321e9 | 1.04611 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.43803e9 | −0.572361 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.64683e8 | −0.182308 | −0.0911540 | − | 0.995837i | \(-0.529056\pi\) | ||||
−0.0911540 | + | 0.995837i | \(0.529056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.88216e8 | 0.300511 | 0.150255 | − | 0.988647i | \(-0.451990\pi\) | ||||
0.150255 | + | 0.988647i | \(0.451990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.75824e9 | −0.660866 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.03088e9 | 2.93438 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.30040e9 | −1.54938 | −0.774688 | − | 0.632344i | \(-0.782093\pi\) | ||||
−0.774688 | + | 0.632344i | \(0.782093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.47920e9 | −1.91968 | −0.959840 | − | 0.280547i | \(-0.909484\pi\) | ||||
−0.959840 | + | 0.280547i | \(0.909484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.55134e9 | 0.536027 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.25720e9 | −0.422562 | −0.211281 | − | 0.977425i | \(-0.567764\pi\) | ||||
−0.211281 | + | 0.977425i | \(0.567764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.84364e8 | −0.193736 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.45600e9 | −1.76015 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.03862e9 | −0.967073 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.69281e8 | −0.269295 | −0.134648 | − | 0.990894i | \(-0.542990\pi\) | ||||
−0.134648 | + | 0.990894i | \(0.542990\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.30165e7 | −0.0253752 | −0.0126876 | − | 0.999920i | \(-0.504039\pi\) | ||||
−0.0126876 | + | 0.999920i | \(0.504039\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.18798e8 | 0.154405 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.29012e9 | −0.378909 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.99845e9 | −1.14379 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.78424e9 | −2.19775 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.05535e9 | −2.49083 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.05014e8 | −0.245734 | −0.122867 | − | 0.992423i | \(-0.539209\pi\) | ||||
−0.122867 | + | 0.992423i | \(0.539209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.92367e8 | −0.0773643 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.61326e9 | 0.682696 | 0.341348 | − | 0.939937i | \(-0.389116\pi\) | ||||
0.341348 | + | 0.939937i | \(0.389116\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.04767e9 | 0.266806 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.65959e8 | 0.142314 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.06824e9 | 1.97827 | 0.989136 | − | 0.147006i | \(-0.0469637\pi\) | ||||
0.989136 | + | 0.147006i | \(0.0469637\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.64912e9 | 0.399311 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.55851e9 | 1.31274 | 0.656371 | − | 0.754439i | \(-0.272091\pi\) | ||||
0.656371 | + | 0.754439i | \(0.272091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.98519e9 | −1.62933 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.82207e9 | −0.642207 | −0.321104 | − | 0.947044i | \(-0.604054\pi\) | ||||
−0.321104 | + | 0.947044i | \(0.604054\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.20632e9 | 1.39511 | 0.697554 | − | 0.716533i | \(-0.254272\pi\) | ||||
0.697554 | + | 0.716533i | \(0.254272\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.21143e9 | −1.14319 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.43205e9 | −1.17720 | −0.588598 | − | 0.808426i | \(-0.700320\pi\) | ||||
−0.588598 | + | 0.808426i | \(0.700320\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.05876e9 | 0.647038 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.89527e9 | −1.23215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.08447e9 | 0.629431 | 0.314715 | − | 0.949186i | \(-0.398091\pi\) | ||||
0.314715 | + | 0.949186i | \(0.398091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.09134e8 | −0.0623365 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.83257e8 | −0.134553 | −0.0672764 | − | 0.997734i | \(-0.521431\pi\) | ||||
−0.0672764 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.57457e10 | −5.01066 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.24846e9 | 0.997787 | 0.498893 | − | 0.866663i | \(-0.333740\pi\) | ||||
0.498893 | + | 0.866663i | \(0.333740\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.00032e9 | −0.751682 | −0.375841 | − | 0.926684i | \(-0.622646\pi\) | ||||
−0.375841 | + | 0.926684i | \(0.622646\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.10075e8 | −0.130365 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.52401e9 | −0.458069 | −0.229034 | − | 0.973418i | \(-0.573557\pi\) | ||||
−0.229034 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.77281e9 | 0.846506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.17565e9 | 0.206142 | 0.103071 | − | 0.994674i | \(-0.467133\pi\) | ||||
0.103071 | + | 0.994674i | \(0.467133\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.05146e9 | −1.03720 | −0.518599 | − | 0.855017i | \(-0.673546\pi\) | ||||
−0.518599 | + | 0.855017i | \(0.673546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.38449e9 | −1.59035 | −0.795176 | − | 0.606378i | \(-0.792622\pi\) | ||||
−0.795176 | + | 0.606378i | \(0.792622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.00291e9 | 0.166171 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.11424e9 | −0.346396 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.31397e10 | −2.10527 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.21509e9 | −0.667889 | −0.333945 | − | 0.942593i | \(-0.608380\pi\) | ||||
−0.333945 | + | 0.942593i | \(0.608380\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.73810e10 | 2.69381 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.42234e10 | 2.18029 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.96210e9 | −1.49399 | −0.746995 | − | 0.664829i | \(-0.768504\pi\) | ||||
−0.746995 | + | 0.664829i | \(0.768504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.98296e9 | 1.03586 | 0.517930 | − | 0.855423i | \(-0.326703\pi\) | ||||
0.517930 | + | 0.855423i | \(0.326703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.65100e9 | −1.11059 | −0.555294 | − | 0.831654i | \(-0.687394\pi\) | ||||
−0.555294 | + | 0.831654i | \(0.687394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.05983e9 | −0.726573 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.57145e9 | 1.34518 | 0.672592 | − | 0.740014i | \(-0.265181\pi\) | ||||
0.672592 | + | 0.740014i | \(0.265181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.65962e9 | 0.369807 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.13794e9 | −1.10768 | −0.553842 | − | 0.832622i | \(-0.686839\pi\) | ||||
−0.553842 | + | 0.832622i | \(0.686839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.82041e9 | −1.32259 | −0.661294 | − | 0.750127i | \(-0.729992\pi\) | ||||
−0.661294 | + | 0.750127i | \(0.729992\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.53409e10 | 2.02291 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.36654e9 | −0.308797 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.23089e9 | 0.412851 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.93826e9 | 0.498026 | 0.249013 | − | 0.968500i | \(-0.419894\pi\) | ||||
0.249013 | + | 0.968500i | \(0.419894\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.66884e9 | 0.949882 | 0.474941 | − | 0.880018i | \(-0.342469\pi\) | ||||
0.474941 | + | 0.880018i | \(0.342469\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.66008e9 | −0.693870 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.65167e9 | −0.918933 | −0.459466 | − | 0.888195i | \(-0.651959\pi\) | ||||
−0.459466 | + | 0.888195i | \(0.651959\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.25792e10 | 1.49533 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.25981e9 | 1.07854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.58561e10 | −1.82820 | −0.914098 | − | 0.405493i | \(-0.867100\pi\) | ||||
−0.914098 | + | 0.405493i | \(0.867100\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.03639e10 | 2.30098 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.05773e10 | 2.30183 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.61910e9 | −0.616104 | −0.308052 | − | 0.951370i | \(-0.599677\pi\) | ||||
−0.308052 | + | 0.951370i | \(0.599677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.82946e9 | 0.849940 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.10608e9 | 0.649822 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.34254e10 | 1.41471 | 0.707353 | − | 0.706860i | \(-0.249889\pi\) | ||||
0.707353 | + | 0.706860i | \(0.249889\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.98288e8 | 0.0721475 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.22776e10 | −1.25616 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.63313e10 | 1.63858 | 0.819292 | − | 0.573377i | \(-0.194367\pi\) | ||||
0.819292 | + | 0.573377i | \(0.194367\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.14749e10 | −2.13382 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.83205e9 | 0.568379 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.33823e9 | −0.418738 | −0.209369 | − | 0.977837i | \(-0.567141\pi\) | ||||
−0.209369 | + | 0.977837i | \(0.567141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.48692e9 | −0.803599 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.43119e9 | 0.696939 | 0.348469 | − | 0.937320i | \(-0.386702\pi\) | ||||
0.348469 | + | 0.937320i | \(0.386702\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.07410e10 | −0.988345 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.03186e9 | 0.458641 | 0.229321 | − | 0.973351i | \(-0.426350\pi\) | ||||
0.229321 | + | 0.973351i | \(0.426350\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.63121e10 | −1.45898 | −0.729491 | − | 0.683990i | \(-0.760243\pi\) | ||||
−0.729491 | + | 0.683990i | \(0.760243\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.35923e10 | 1.20433 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.06388e10 | −2.66432 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.07632e10 | −1.78877 | −0.894385 | − | 0.447299i | \(-0.852386\pi\) | ||||
−0.894385 | + | 0.447299i | \(0.852386\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.22975e9 | 0.526813 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.85677e9 | −0.323138 | −0.161569 | − | 0.986861i | \(-0.551655\pi\) | ||||
−0.161569 | + | 0.986861i | \(0.551655\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.80368e9 | 0.148358 | 0.0741792 | − | 0.997245i | \(-0.476366\pi\) | ||||
0.0741792 | + | 0.997245i | \(0.476366\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.15076e9 | −0.0937882 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.94756e9 | 0.635989 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.33349e9 | 0.264336 | 0.132168 | − | 0.991227i | \(-0.457806\pi\) | ||||
0.132168 | + | 0.991227i | \(0.457806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.11920e10 | 0.871526 | 0.435763 | − | 0.900062i | \(-0.356479\pi\) | ||||
0.435763 | + | 0.900062i | \(0.356479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.72084e9 | −0.132796 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.22613e10 | −0.929299 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.97093e10 | −1.48045 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.21985e10 | 2.37570 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.19525e9 | 0.160536 | 0.0802679 | − | 0.996773i | \(-0.474422\pi\) | ||||
0.0802679 | + | 0.996773i | \(0.474422\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.74938e10 | −1.97522 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.07481e9 | −0.361380 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.43541e9 | −0.380302 | −0.190151 | − | 0.981755i | \(-0.560898\pi\) | ||||
−0.190151 | + | 0.981755i | \(0.560898\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.45625e10 | −1.70356 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.43414e9 | 0.0977433 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.46529e10 | −2.34129 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.89544e9 | −0.657075 | −0.328538 | − | 0.944491i | \(-0.606556\pi\) | ||||
−0.328538 | + | 0.944491i | \(0.606556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.00426e10 | −0.661111 | −0.330556 | − | 0.943787i | \(-0.607236\pi\) | ||||
−0.330556 | + | 0.943787i | \(0.607236\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.54823e10 | −2.29594 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.05706e9 | 0.324430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.07209e10 | 1.93746 | 0.968731 | − | 0.248112i | \(-0.0798100\pi\) | ||||
0.968731 | + | 0.248112i | \(0.0798100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.01255e10 | 1.25848 | 0.629241 | − | 0.777210i | \(-0.283366\pi\) | ||||
0.629241 | + | 0.777210i | \(0.283366\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.55472e10 | −0.955832 | −0.477916 | − | 0.878405i | \(-0.658608\pi\) | ||||
−0.477916 | + | 0.878405i | \(0.658608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.42396e10 | −0.868077 | −0.434038 | − | 0.900894i | \(-0.642912\pi\) | ||||
−0.434038 | + | 0.900894i | \(0.642912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.31982e10 | −4.38776 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.89088e10 | 2.90726 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.17959e9 | 0.185868 | 0.0929338 | − | 0.995672i | \(-0.470375\pi\) | ||||
0.0929338 | + | 0.995672i | \(0.470375\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.46015e10 | −0.846470 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.17104e9 | −0.465885 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.79486e9 | −0.158040 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.76856e10 | −0.983709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.62326e9 | 0.255051 | 0.127525 | − | 0.991835i | \(-0.459297\pi\) | ||||
0.127525 | + | 0.991835i | \(0.459297\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.13062e10 | 1.15631 | 0.578153 | − | 0.815929i | \(-0.303774\pi\) | ||||
0.578153 | + | 0.815929i | \(0.303774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.86988e9 | 0.423635 | 0.211818 | − | 0.977309i | \(-0.432062\pi\) | ||||
0.211818 | + | 0.977309i | \(0.432062\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.55483e9 | −0.0823465 | −0.0411732 | − | 0.999152i | \(-0.513110\pi\) | ||||
−0.0411732 | + | 0.999152i | \(0.513110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.92829e10 | −2.06370 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.38897e9 | −0.0717999 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.68711e10 | 0.865126 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.65264e10 | 1.33860 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.34828e10 | 1.17558 | 0.587790 | − | 0.809014i | \(-0.299998\pi\) | ||||
0.587790 | + | 0.809014i | \(0.299998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.10488e9 | 0.0544378 | 0.0272189 | − | 0.999629i | \(-0.491335\pi\) | ||||
0.0272189 | + | 0.999629i | \(0.491335\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.52780e10 | −0.746800 | −0.373400 | − | 0.927670i | \(-0.621808\pi\) | ||||
−0.373400 | + | 0.927670i | \(0.621808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.13521e10 | 0.546189 | 0.273094 | − | 0.961987i | \(-0.411953\pi\) | ||||
0.273094 | + | 0.961987i | \(0.411953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.84117e10 | 3.26568 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.46359e10 | 0.687764 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.03754e10 | −0.950002 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.81445e8 | −0.0358707 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.76540e10 | −2.17052 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.94694e10 | 1.32160 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.41214e9 | 0.107344 | 0.0536718 | − | 0.998559i | \(-0.482908\pi\) | ||||
0.0536718 | + | 0.998559i | \(0.482908\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.63158e10 | −1.15319 | −0.576597 | − | 0.817029i | \(-0.695620\pi\) | ||||
−0.576597 | + | 0.817029i | \(0.695620\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.50679e9 | −0.326442 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.04683e10 | 0.448314 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.35629e10 | 1.00144 | 0.500719 | − | 0.865610i | \(-0.333069\pi\) | ||||
0.500719 | + | 0.865610i | \(0.333069\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.09577e10 | 1.29588 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.35840e10 | 1.81064 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.08846e9 | 0.0854618 | 0.0427309 | − | 0.999087i | \(-0.486394\pi\) | ||||
0.0427309 | + | 0.999087i | \(0.486394\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.36163e10 | 1.77143 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.31847e10 | 2.52797 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.67845e10 | 1.46075 | 0.730376 | − | 0.683045i | \(-0.239345\pi\) | ||||
0.730376 | + | 0.683045i | \(0.239345\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.19271e9 | −0.359650 | −0.179825 | − | 0.983699i | \(-0.557553\pi\) | ||||
−0.179825 | + | 0.983699i | \(0.557553\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.76965e10 | 1.07556 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.30566e10 | 0.499581 | 0.249791 | − | 0.968300i | \(-0.419638\pi\) | ||||
0.249791 | + | 0.968300i | \(0.419638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.25263e9 | −0.0855574 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.42599e10 | 0.907954 | 0.453977 | − | 0.891013i | \(-0.350005\pi\) | ||||
0.453977 | + | 0.891013i | \(0.350005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.29322e10 | 0.480462 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.95118e10 | 1.81278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72820e10 | −0.991619 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.41476e10 | −1.93970 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.37434e10 | 0.488766 | 0.244383 | − | 0.969679i | \(-0.421415\pi\) | ||||
0.244383 | + | 0.969679i | \(0.421415\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.37656e9 | 0.223521 | 0.111761 | − | 0.993735i | \(-0.464351\pi\) | ||||
0.111761 | + | 0.993735i | \(0.464351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.01523e10 | 2.78947 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.35347e10 | 1.49350 | 0.746748 | − | 0.665107i | \(-0.231614\pi\) | ||||
0.746748 | + | 0.665107i | \(0.231614\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.46133e9 | −0.0838361 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.03387e10 | −0.682946 | −0.341473 | − | 0.939892i | \(-0.610926\pi\) | ||||
−0.341473 | + | 0.939892i | \(0.610926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00092e10 | −0.333714 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.14232e10 | −0.375491 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.03245e10 | 1.64256 | 0.821280 | − | 0.570525i | \(-0.193260\pi\) | ||||
0.821280 | + | 0.570525i | \(0.193260\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.80304e10 | −1.22391 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.65066e10 | 0.847073 | 0.423537 | − | 0.905879i | \(-0.360789\pi\) | ||||
0.423537 | + | 0.905879i | \(0.360789\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 576.8.a.bq.1.2 | 2 | ||
3.2 | odd | 2 | 576.8.a.bd.1.1 | 2 | |||
4.3 | odd | 2 | 576.8.a.bp.1.2 | 2 | |||
8.3 | odd | 2 | 144.8.a.l.1.1 | 2 | |||
8.5 | even | 2 | 72.8.a.f.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 576.8.a.bc.1.1 | 2 | |||
24.5 | odd | 2 | 72.8.a.g.1.2 | yes | 2 | ||
24.11 | even | 2 | 144.8.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.8.a.f.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
72.8.a.g.1.2 | yes | 2 | 24.5 | odd | 2 | ||
144.8.a.l.1.1 | 2 | 8.3 | odd | 2 | |||
144.8.a.n.1.2 | 2 | 24.11 | even | 2 | |||
576.8.a.bc.1.1 | 2 | 12.11 | even | 2 | |||
576.8.a.bd.1.1 | 2 | 3.2 | odd | 2 | |||
576.8.a.bp.1.2 | 2 | 4.3 | odd | 2 | |||
576.8.a.bq.1.2 | 2 | 1.1 | even | 1 | trivial |