Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,8,Mod(1,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("360.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.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: | \(112.458609174\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 360.1 |
$q$-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 | ||||||||
\(5\) | −125.000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 776.000 | 0.855103 | 0.427552 | − | 0.903991i | \(-0.359376\pi\) | ||||
0.427552 | + | 0.903991i | \(0.359376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 124.000 | 0.0280897 | 0.0140449 | − | 0.999901i | \(-0.495529\pi\) | ||||
0.0140449 | + | 0.999901i | \(0.495529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13082.0 | −1.65148 | −0.825738 | − | 0.564053i | \(-0.809241\pi\) | ||||
−0.825738 | + | 0.564053i | \(0.809241\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15950.0 | 0.787389 | 0.393695 | − | 0.919241i | \(-0.371197\pi\) | ||||
0.393695 | + | 0.919241i | \(0.371197\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20516.0 | −0.686207 | −0.343103 | − | 0.939298i | \(-0.611478\pi\) | ||||
−0.343103 | + | 0.939298i | \(0.611478\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 29224.0 | 0.500832 | 0.250416 | − | 0.968138i | \(-0.419433\pi\) | ||||
0.250416 | + | 0.968138i | \(0.419433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 221482. | 1.68634 | 0.843171 | − | 0.537646i | \(-0.180686\pi\) | ||||
0.843171 | + | 0.537646i | \(0.180686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −109760. | −0.661726 | −0.330863 | − | 0.943679i | \(-0.607340\pi\) | ||||
−0.330863 | + | 0.943679i | \(0.607340\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −97000.0 | −0.382414 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 73422.0 | 0.238298 | 0.119149 | − | 0.992876i | \(-0.461983\pi\) | ||||
0.119149 | + | 0.992876i | \(0.461983\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12762.0 | −0.0289185 | −0.0144592 | − | 0.999895i | \(-0.504603\pi\) | ||||
−0.0144592 | + | 0.999895i | \(0.504603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 290548. | 0.557286 | 0.278643 | − | 0.960395i | \(-0.410115\pi\) | ||||
0.278643 | + | 0.960395i | \(0.410115\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.26915e6 | −1.78308 | −0.891541 | − | 0.452941i | \(-0.850375\pi\) | ||||
−0.891541 | + | 0.452941i | \(0.850375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −221367. | −0.268798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 395778. | 0.365162 | 0.182581 | − | 0.983191i | \(-0.441555\pi\) | ||||
0.182581 | + | 0.983191i | \(0.441555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15500.0 | −0.0125621 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −421492. | −0.267182 | −0.133591 | − | 0.991037i | \(-0.542651\pi\) | ||||
−0.133591 | + | 0.991037i | \(0.542651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.12225e6 | −1.19713 | −0.598566 | − | 0.801073i | \(-0.704263\pi\) | ||||
−0.598566 | + | 0.801073i | \(0.704263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.63525e6 | 0.738563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.13287e6 | −1.27257 | −0.636283 | − | 0.771456i | \(-0.719529\pi\) | ||||
−0.636283 | + | 0.771456i | \(0.719529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.37655e6 | 1.78279 | 0.891394 | − | 0.453230i | \(-0.149728\pi\) | ||||
0.891394 | + | 0.453230i | \(0.149728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.98547e6 | 1.49995 | 0.749973 | − | 0.661468i | \(-0.230066\pi\) | ||||
0.749973 | + | 0.661468i | \(0.230066\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 96224.0 | 0.0240196 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.86750e6 | 0.882543 | 0.441272 | − | 0.897374i | \(-0.354528\pi\) | ||||
0.441272 | + | 0.897374i | \(0.354528\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.19020e6 | 1.18831 | 0.594157 | − | 0.804349i | \(-0.297486\pi\) | ||||
0.594157 | + | 0.804349i | \(0.297486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.99375e6 | −0.352131 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.12439e6 | −0.169065 | −0.0845325 | − | 0.996421i | \(-0.526940\pi\) | ||||
−0.0845325 | + | 0.996421i | \(0.526940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.01516e7 | −1.41218 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.56450e6 | 0.306881 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.96810e6 | 1.10895 | 0.554474 | − | 0.832201i | \(-0.312919\pi\) | ||||
0.554474 | + | 0.832201i | \(0.312919\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −425166. | −0.0410614 | −0.0205307 | − | 0.999789i | \(-0.506536\pi\) | ||||
−0.0205307 | + | 0.999789i | \(0.506536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.06209e6 | 0.636800 | 0.318400 | − | 0.947957i | \(-0.396855\pi\) | ||||
0.318400 | + | 0.947957i | \(0.396855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.82186e7 | −1.43771 | −0.718855 | − | 0.695160i | \(-0.755333\pi\) | ||||
−0.718855 | + | 0.695160i | \(0.755333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.27869e7 | 1.68536 | 0.842679 | − | 0.538416i | \(-0.180977\pi\) | ||||
0.842679 | + | 0.538416i | \(0.180977\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 700398. | 0.0456636 | 0.0228318 | − | 0.999739i | \(-0.492732\pi\) | ||||
0.0228318 | + | 0.999739i | \(0.492732\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65300e6 | −0.223979 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.23772e7 | 0.673299 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.94718e7 | −0.999211 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.95312e6 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.69868e7 | 1.60226 | 0.801132 | − | 0.598488i | \(-0.204231\pi\) | ||||
0.801132 | + | 0.598488i | \(0.204231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.86042e7 | 1.88897 | 0.944484 | − | 0.328559i | \(-0.106563\pi\) | ||||
0.944484 | + | 0.328559i | \(0.106563\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.59204e7 | −0.586778 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.45152e7 | 0.814542 | 0.407271 | − | 0.913307i | \(-0.366480\pi\) | ||||
0.407271 | + | 0.913307i | \(0.366480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.14944e7 | −0.678848 | −0.339424 | − | 0.940633i | \(-0.610232\pi\) | ||||
−0.339424 | + | 0.940633i | \(0.610232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.62217e6 | −0.0463895 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.76852e7 | −0.754155 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.56239e7 | −0.386935 | −0.193467 | − | 0.981107i | \(-0.561973\pi\) | ||||
−0.193467 | + | 0.981107i | \(0.561973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.83038e7 | 1.85082 | 0.925408 | − | 0.378972i | \(-0.123722\pi\) | ||||
0.925408 | + | 0.378972i | \(0.123722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.37200e7 | 0.295933 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.52688e7 | −1.34604 | −0.673019 | − | 0.739625i | \(-0.735003\pi\) | ||||
−0.673019 | + | 0.739625i | \(0.735003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.26778e7 | 0.428263 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.07845e7 | −0.195049 | −0.0975246 | − | 0.995233i | \(-0.531092\pi\) | ||||
−0.0975246 | + | 0.995233i | \(0.531092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.90065e7 | −0.648081 | −0.324041 | − | 0.946043i | \(-0.605041\pi\) | ||||
−0.324041 | + | 0.946043i | \(0.605041\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.08390e8 | 1.72737 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.39258e7 | 0.498159 | 0.249080 | − | 0.968483i | \(-0.419872\pi\) | ||||
0.249080 | + | 0.968483i | \(0.419872\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.21250e7 | 0.171021 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.44958e8 | 1.88911 | 0.944553 | − | 0.328358i | \(-0.106495\pi\) | ||||
0.944553 | + | 0.328358i | \(0.106495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.39247e8 | 1.74547 | 0.872733 | − | 0.488199i | \(-0.162346\pi\) | ||||
0.872733 | + | 0.488199i | \(0.162346\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.17775e6 | −0.106570 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.97780e6 | 0.0221175 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.42946e7 | 0.252285 | 0.126143 | − | 0.992012i | \(-0.459740\pi\) | ||||
0.126143 | + | 0.992012i | \(0.459740\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.04825e8 | 1.04958 | 0.524790 | − | 0.851232i | \(-0.324144\pi\) | ||||
0.524790 | + | 0.851232i | \(0.324144\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.05566e8 | 1.91567 | 0.957833 | − | 0.287324i | \(-0.0927657\pi\) | ||||
0.957833 | + | 0.287324i | \(0.0927657\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.56329e7 | 0.410480 | 0.205240 | − | 0.978712i | \(-0.434202\pi\) | ||||
0.205240 | + | 0.978712i | \(0.434202\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.71870e8 | 1.44200 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.59525e6 | 0.0129327 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.54398e6 | −0.0192754 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.19090e7 | −0.0872743 | −0.0436372 | − | 0.999047i | \(-0.513895\pi\) | ||||
−0.0436372 | + | 0.999047i | \(0.513895\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.63185e7 | −0.249226 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.51738e7 | −0.565844 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.08658e8 | −1.30035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.68668e8 | −1.01851 | −0.509255 | − | 0.860616i | \(-0.670079\pi\) | ||||
−0.509255 | + | 0.860616i | \(0.670079\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.05791e8 | 0.600286 | 0.300143 | − | 0.953894i | \(-0.402966\pi\) | ||||
0.300143 | + | 0.953894i | \(0.402966\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.48457e8 | −1.91746 | −0.958728 | − | 0.284324i | \(-0.908231\pi\) | ||||
−0.958728 | + | 0.284324i | \(0.908231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.21828e8 | 1.14887 | 0.574434 | − | 0.818551i | \(-0.305222\pi\) | ||||
0.574434 | + | 0.818551i | \(0.305222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.58644e8 | 0.797418 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.89900e8 | 1.37359 | 0.686794 | − | 0.726852i | \(-0.259018\pi\) | ||||
0.686794 | + | 0.726852i | \(0.259018\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.63833e7 | −0.397530 | −0.198765 | − | 0.980047i | \(-0.563693\pi\) | ||||
−0.198765 | + | 0.980047i | \(0.563693\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.76709e7 | 0.120210 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.68390e8 | 1.13325 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.84765e8 | −1.13666 | −0.568328 | − | 0.822802i | \(-0.692410\pi\) | ||||
−0.568328 | + | 0.822802i | \(0.692410\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.62378e6 | 0.0140682 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.45535e7 | 0.310717 | 0.155359 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155359 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.69755e7 | 0.203769 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.57270e7 | 0.222792 | 0.111396 | − | 0.993776i | \(-0.464468\pi\) | ||||
0.111396 | + | 0.993776i | \(0.464468\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.94722e7 | −0.163306 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.81943e8 | −0.883136 | −0.441568 | − | 0.897228i | \(-0.645578\pi\) | ||||
−0.441568 | + | 0.897228i | \(0.645578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.09940e8 | 0.945987 | 0.472993 | − | 0.881066i | \(-0.343173\pi\) | ||||
0.472993 | + | 0.881066i | \(0.343173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.93750e6 | 0.00561794 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.25764e8 | −0.920924 | −0.460462 | − | 0.887680i | \(-0.652316\pi\) | ||||
−0.460462 | + | 0.887680i | \(0.652316\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.96310e8 | 0.796662 | 0.398331 | − | 0.917242i | \(-0.369590\pi\) | ||||
0.398331 | + | 0.917242i | \(0.369590\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.00092e8 | 1.31159 | 0.655794 | − | 0.754940i | \(-0.272334\pi\) | ||||
0.655794 | + | 0.754940i | \(0.272334\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.90331e6 | −0.0247283 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.55936e8 | −0.380018 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.07288e8 | −0.249180 | −0.124590 | − | 0.992208i | \(-0.539762\pi\) | ||||
−0.124590 | + | 0.992208i | \(0.539762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.26865e7 | 0.119487 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.82308e8 | −0.827113 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.25465e8 | 0.476537 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.65281e8 | 0.535374 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.06445e8 | 1.59071 | 0.795354 | − | 0.606145i | \(-0.207285\pi\) | ||||
0.795354 | + | 0.606145i | \(0.207285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.60964e7 | −0.0680460 | −0.0340230 | − | 0.999421i | \(-0.510832\pi\) | ||||
−0.0340230 | + | 0.999421i | \(0.510832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.31349e8 | −0.979433 | −0.489717 | − | 0.871882i | \(-0.662900\pi\) | ||||
−0.489717 | + | 0.871882i | \(0.662900\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.18418e7 | −0.0208791 | −0.0104396 | − | 0.999946i | \(-0.503323\pi\) | ||||
−0.0104396 | + | 0.999946i | \(0.503323\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.74638e7 | 0.0473688 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.27230e8 | −0.540312 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.04406e8 | −0.330295 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.84862e8 | −1.52472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.74592e8 | −0.567755 | −0.283877 | − | 0.958861i | \(-0.591621\pi\) | ||||
−0.283877 | + | 0.958861i | \(0.591621\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.91608e8 | 0.569109 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.66536e8 | 0.237030 | 0.118515 | − | 0.992952i | \(-0.462187\pi\) | ||||
0.118515 | + | 0.992952i | \(0.462187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.36102e7 | −0.0185877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.10850e8 | −1.08495 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.31438e8 | −0.425842 | −0.212921 | − | 0.977069i | \(-0.568298\pi\) | ||||
−0.212921 | + | 0.977069i | \(0.568298\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.29412e6 | −0.00540736 | −0.00270368 | − | 0.999996i | \(-0.500861\pi\) | ||||
−0.00270368 | + | 0.999996i | \(0.500861\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.90007e7 | 0.0592912 | 0.0296456 | − | 0.999560i | \(-0.490562\pi\) | ||||
0.0296456 | + | 0.999560i | \(0.490562\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.72069e8 | −0.797287 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.14432e9 | 1.30532 | 0.652658 | − | 0.757653i | \(-0.273654\pi\) | ||||
0.652658 | + | 0.757653i | \(0.273654\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.72965e8 | −0.529120 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.23183e8 | −0.670796 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.58047e8 | 0.589304 | 0.294652 | − | 0.955605i | \(-0.404796\pi\) | ||||
0.294652 | + | 0.955605i | \(0.404796\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.07124e8 | 0.312252 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.89487e8 | −0.887480 | −0.443740 | − | 0.896156i | \(-0.646349\pi\) | ||||
−0.443740 | + | 0.896156i | \(0.646349\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.89743e9 | −2.78495 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.40167e8 | 0.226608 | 0.113304 | − | 0.993560i | \(-0.463857\pi\) | ||||
0.113304 | + | 0.993560i | \(0.463857\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.54872e7 | 0.0413708 | 0.0206854 | − | 0.999786i | \(-0.493415\pi\) | ||||
0.0206854 | + | 0.999786i | \(0.493415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.20280e7 | −0.0107419 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.34802e8 | −0.632917 | −0.316458 | − | 0.948606i | \(-0.602494\pi\) | ||||
−0.316458 | + | 0.948606i | \(0.602494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.66123e8 | 0.394350 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.83438e8 | −0.394685 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.23610e8 | 0.660625 | 0.330312 | − | 0.943872i | \(-0.392846\pi\) | ||||
0.330312 | + | 0.943872i | \(0.392846\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.84193e8 | −0.297539 | −0.148770 | − | 0.988872i | \(-0.547531\pi\) | ||||
−0.148770 | + | 0.988872i | \(0.547531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.43588e9 | 1.09282 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.10433e6 | 0.00669372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.97006e9 | −1.42379 | −0.711897 | − | 0.702284i | \(-0.752164\pi\) | ||||
−0.711897 | + | 0.702284i | \(0.752164\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.27078e8 | −0.228468 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.73774e8 | −0.531430 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.66755e9 | −1.77159 | −0.885794 | − | 0.464078i | \(-0.846386\pi\) | ||||
−0.885794 | + | 0.464078i | \(0.846386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.63075e8 | −0.498402 | −0.249201 | − | 0.968452i | \(-0.580168\pi\) | ||||
−0.249201 | + | 0.968452i | \(0.580168\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.49219e8 | 0.157478 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.64687e9 | −1.02367 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.70874e8 | 0.403618 | 0.201809 | − | 0.979425i | \(-0.435318\pi\) | ||||
0.201809 | + | 0.979425i | \(0.435318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.38362e9 | −0.819048 | −0.409524 | − | 0.912299i | \(-0.634305\pi\) | ||||
−0.409524 | + | 0.912299i | \(0.634305\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.99560e8 | −0.343675 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.86303e9 | 1.05098 | 0.525489 | − | 0.850801i | \(-0.323883\pi\) | ||||
0.525489 | + | 0.850801i | \(0.323883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.57996e8 | 0.195644 | 0.0978218 | − | 0.995204i | \(-0.468812\pi\) | ||||
0.0978218 | + | 0.995204i | \(0.468812\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.40549e8 | 0.0756081 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.31697e9 | 1.20797 | 0.603987 | − | 0.796994i | \(-0.293578\pi\) | ||||
0.603987 | + | 0.796994i | \(0.293578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.58249e6 | −0.000812311 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.26895e9 | 0.631547 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.21599e9 | −1.08608 | −0.543039 | − | 0.839708i | \(-0.682726\pi\) | ||||
−0.543039 | + | 0.839708i | \(0.682726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.52028e9 | −1.19810 | −0.599052 | − | 0.800710i | \(-0.704456\pi\) | ||||
−0.599052 | + | 0.800710i | \(0.704456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.53493e9 | 0.718711 | 0.359355 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359355 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.53046e9 | 0.695364 | 0.347682 | − | 0.937613i | \(-0.386969\pi\) | ||||
0.347682 | + | 0.937613i | \(0.386969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43111e9 | −1.08818 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.60280e7 | 0.0156540 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.20562e8 | −0.137241 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.06870e9 | −1.27579 | −0.637897 | − | 0.770122i | \(-0.720196\pi\) | ||||
−0.637897 | + | 0.770122i | \(0.720196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.60507e8 | −0.393543 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.24601e9 | −0.495937 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.08947e9 | −1.21208 | −0.606041 | − | 0.795433i | \(-0.707243\pi\) | ||||
−0.606041 | + | 0.795433i | \(0.707243\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.55851e9 | 0.594189 | 0.297095 | − | 0.954848i | \(-0.403982\pi\) | ||||
0.297095 | + | 0.954848i | \(0.403982\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.53264e9 | 1.32781 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.17220e9 | 1.52447 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.26641e8 | 0.0816559 | 0.0408279 | − | 0.999166i | \(-0.487000\pi\) | ||||
0.0408279 | + | 0.999166i | \(0.487000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.93458e8 | 0.348066 | 0.174033 | − | 0.984740i | \(-0.444320\pi\) | ||||
0.174033 | + | 0.984740i | \(0.444320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.31458e7 | 0.0183632 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.41773e9 | 0.812635 | 0.406317 | − | 0.913732i | \(-0.366813\pi\) | ||||
0.406317 | + | 0.913732i | \(0.366813\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.86872e9 | 1.28261 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.82761e8 | −0.284785 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.57375e8 | −0.0500862 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.43295e9 | −1.99287 | −0.996433 | − | 0.0843875i | \(-0.973107\pi\) | ||||
−0.996433 | + | 0.0843875i | \(0.973107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.45552e9 | 0.750564 | 0.375282 | − | 0.926911i | \(-0.377546\pi\) | ||||
0.375282 | + | 0.926911i | \(0.377546\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.75067e9 | −0.521036 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.55078e9 | −0.749167 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.66952e8 | 0.0477582 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.27732e9 | 0.642963 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.74495e7 | −0.00755047 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.81566e9 | 1.03605 | 0.518023 | − | 0.855367i | \(-0.326668\pi\) | ||||
0.518023 | + | 0.855367i | \(0.326668\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.84836e9 | −0.753715 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.11439e9 | 0.291128 | 0.145564 | − | 0.989349i | \(-0.453500\pi\) | ||||
0.145564 | + | 0.989349i | \(0.453500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.54392e9 | −1.15718 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.00118e9 | 0.754666 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.64478e9 | −0.893671 | −0.446835 | − | 0.894616i | \(-0.647449\pi\) | ||||
−0.446835 | + | 0.894616i | \(0.647449\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.80095e9 | −0.920345 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.31668e9 | 0.310957 | 0.155478 | − | 0.987839i | \(-0.450308\pi\) | ||||
0.155478 | + | 0.987839i | \(0.450308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.75498e7 | −0.0204214 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.15078e9 | −0.261878 | −0.130939 | − | 0.991390i | \(-0.541799\pi\) | ||||
−0.130939 | + | 0.991390i | \(0.541799\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.33459e8 | −0.187352 | −0.0936759 | − | 0.995603i | \(-0.529862\pi\) | ||||
−0.0936759 | + | 0.995603i | \(0.529862\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.56625e8 | 0.100166 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.44998e9 | −0.314229 | −0.157115 | − | 0.987580i | \(-0.550219\pi\) | ||||
−0.157115 | + | 0.987580i | \(0.550219\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.80359e9 | 1.01613 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.90765e7 | 0.0102573 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.30473e9 | 1.28657 | 0.643284 | − | 0.765627i | \(-0.277571\pi\) | ||||
0.643284 | + | 0.765627i | \(0.277571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.25184e9 | 0.454081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.95526e9 | 1.17276 | 0.586381 | − | 0.810036i | \(-0.300552\pi\) | ||||
0.586381 | + | 0.810036i | \(0.300552\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.54715e9 | −0.301109 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.72932e9 | 0.708983 | 0.354491 | − | 0.935059i | \(-0.384654\pi\) | ||||
0.354491 | + | 0.935059i | \(0.384654\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.66326e9 | 1.06416 | 0.532078 | − | 0.846695i | \(-0.321411\pi\) | ||||
0.532078 | + | 0.846695i | \(0.321411\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.43397e9 | 0.446861 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.42376e9 | 0.984329 | 0.492164 | − | 0.870502i | \(-0.336206\pi\) | ||||
0.492164 | + | 0.870502i | \(0.336206\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.66030e10 | 2.94472 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.55053e9 | −0.447217 | −0.223608 | − | 0.974679i | \(-0.571784\pi\) | ||||
−0.223608 | + | 0.974679i | \(0.571784\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.54132e9 | 1.12116 | 0.560580 | − | 0.828101i | \(-0.310578\pi\) | ||||
0.560580 | + | 0.828101i | \(0.310578\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.17083e10 | −1.98416 | −0.992079 | − | 0.125612i | \(-0.959911\pi\) | ||||
−0.992079 | + | 0.125612i | \(0.959911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.72530e8 | −0.144568 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.17108e9 | 0.187633 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.85340e9 | 0.293675 | 0.146838 | − | 0.989161i | \(-0.453091\pi\) | ||||
0.146838 | + | 0.989161i | \(0.453091\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.62335e9 | −0.716554 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.89592e9 | 0.443914 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.84313e9 | 1.47615 | 0.738074 | − | 0.674720i | \(-0.235735\pi\) | ||||
0.738074 | + | 0.674720i | \(0.235735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.73935e9 | 0.999723 | 0.499861 | − | 0.866105i | \(-0.333384\pi\) | ||||
0.499861 | + | 0.866105i | \(0.333384\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.26180e9 | −1.19925 | −0.599625 | − | 0.800281i | \(-0.704684\pi\) | ||||
−0.599625 | + | 0.800281i | \(0.704684\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.22650e7 | −0.00750507 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.55833e9 | −0.359551 | −0.179776 | − | 0.983708i | \(-0.557537\pi\) | ||||
−0.179776 | + | 0.983708i | \(0.557537\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.07553e9 | −0.844772 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.90633e9 | −1.21227 | −0.606136 | − | 0.795361i | \(-0.707281\pi\) | ||||
−0.606136 | + | 0.795361i | \(0.707281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.57591e9 | −0.750950 | −0.375475 | − | 0.926833i | \(-0.622520\pi\) | ||||
−0.375475 | + | 0.926833i | \(0.622520\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.99005e9 | 0.262415 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.47259e9 | 0.844574 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.63159e8 | −0.0336271 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.92812e9 | 0.496744 | 0.248372 | − | 0.968665i | \(-0.420104\pi\) | ||||
0.248372 | + | 0.968665i | \(0.420104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.25393e10 | 1.55315 | 0.776576 | − | 0.630023i | \(-0.216955\pi\) | ||||
0.776576 | + | 0.630023i | \(0.216955\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.73524e9 | 0.948265 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.72047e9 | −0.326717 | −0.163358 | − | 0.986567i | \(-0.552233\pi\) | ||||
−0.163358 | + | 0.986567i | \(0.552233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.06440e9 | −0.364274 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.17757e9 | −0.603057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.85887e9 | −0.790823 | −0.395412 | − | 0.918504i | \(-0.629398\pi\) | ||||
−0.395412 | + | 0.918504i | \(0.629398\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.68680e9 | 0.303590 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.03554e8 | −0.0227701 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.76168e9 | −0.193158 | −0.0965791 | − | 0.995325i | \(-0.530790\pi\) | ||||
−0.0965791 | + | 0.995325i | \(0.530790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50633e9 | −0.163522 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.29929e8 | −0.0351117 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.49745e9 | −0.263169 | −0.131585 | − | 0.991305i | \(-0.542006\pi\) | ||||
−0.131585 | + | 0.991305i | \(0.542006\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.20763e9 | −0.331414 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.02771e8 | 0.0207460 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.33572e9 | 0.836358 | 0.418179 | − | 0.908365i | \(-0.362669\pi\) | ||||
0.418179 | + | 0.908365i | \(0.362669\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.48018e9 | 0.544530 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.46066e9 | 0.337268 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.99428e10 | 1.92494 | 0.962468 | − | 0.271396i | \(-0.0874852\pi\) | ||||
0.962468 | + | 0.271396i | \(0.0874852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.63424e9 | 0.438801 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.63020e10 | 1.52889 | 0.764446 | − | 0.644687i | \(-0.223012\pi\) | ||||
0.764446 | + | 0.644687i | \(0.223012\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.88476e8 | −0.0357460 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.63178e10 | −1.48732 | −0.743662 | − | 0.668556i | \(-0.766913\pi\) | ||||
−0.743662 | + | 0.668556i | \(0.766913\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.49757e10 | 1.33945 | 0.669725 | − | 0.742609i | \(-0.266412\pi\) | ||||
0.669725 | + | 0.742609i | \(0.266412\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.95299e9 | 0.173042 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.41376e10 | −1.22939 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.72538e9 | −0.751700 | −0.375850 | − | 0.926681i | \(-0.622649\pi\) | ||||
−0.375850 | + | 0.926681i | \(0.622649\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.78797e9 | −0.827710 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.69261e9 | 0.393168 | 0.196584 | − | 0.980487i | \(-0.437015\pi\) | ||||
0.196584 | + | 0.980487i | \(0.437015\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.02825e10 | 1.66831 | 0.834153 | − | 0.551533i | \(-0.185957\pi\) | ||||
0.834153 | + | 0.551533i | \(0.185957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.76826e10 | 1.44116 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.51396e9 | 0.441245 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.96632e10 | −1.55924 | −0.779618 | − | 0.626255i | \(-0.784587\pi\) | ||||
−0.779618 | + | 0.626255i | \(0.784587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.23325e10 | 0.960337 | 0.480169 | − | 0.877176i | \(-0.340575\pi\) | ||||
0.480169 | + | 0.877176i | \(0.340575\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.71500e9 | −0.132345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.61825e8 | 0.0198441 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.66692e8 | 0.0500780 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.15861e9 | 0.601966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.92456e9 | −0.652642 | −0.326321 | − | 0.945259i | \(-0.605809\pi\) | ||||
−0.326321 | + | 0.945259i | \(0.605809\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.43509e8 | 0.0390471 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.77633e10 | 1.97704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.07737e9 | −0.0753806 | −0.0376903 | − | 0.999289i | \(-0.512000\pi\) | ||||
−0.0376903 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.02430e10 | −1.40398 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.18198e8 | 0.0421331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.83473e9 | −0.191525 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.40339e7 | −0.00159589 | −0.000797947 | − | 1.00000i | \(-0.500254\pi\) | ||||
−0.000797947 | 1.00000i | \(0.500254\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.45618e10 | −1.61691 | −0.808456 | − | 0.588556i | \(-0.799697\pi\) | ||||
−0.808456 | + | 0.588556i | \(0.799697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.34806e9 | 0.0872286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.96088e9 | −0.382414 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.96936e10 | −1.24201 | −0.621005 | − | 0.783807i | \(-0.713275\pi\) | ||||
−0.621005 | + | 0.783807i | \(0.713275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.62460e10 | −1.64121 | −0.820604 | − | 0.571497i | \(-0.806363\pi\) | ||||
−0.820604 | + | 0.571497i | \(0.806363\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.66841e10 | −1.64052 | −0.820262 | − | 0.571988i | \(-0.806172\pi\) | ||||
−0.820262 | + | 0.571988i | \(0.806172\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.66586e9 | 0.406364 | 0.203182 | − | 0.979141i | \(-0.434872\pi\) | ||||
0.203182 | + | 0.979141i | \(0.434872\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.53080e9 | −0.211649 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.87581e9 | 0.289831 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.93131e10 | −1.12898 | −0.564490 | − | 0.825440i | \(-0.690927\pi\) | ||||
−0.564490 | + | 0.825440i | \(0.690927\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.18044e10 | 1.84375 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.35488e10 | −0.772505 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.51101e10 | −0.854429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.14568e9 | 0.119347 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.38350e10 | 1.31490 | 0.657451 | − | 0.753497i | \(-0.271635\pi\) | ||||
0.657451 | + | 0.753497i | \(0.271635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.28013e10 | −1.23745 | −0.618723 | − | 0.785609i | \(-0.712350\pi\) | ||||
−0.618723 | + | 0.785609i | \(0.712350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.27333e10 | −1.22373 | −0.611866 | − | 0.790961i | \(-0.709581\pi\) | ||||
−0.611866 | + | 0.790961i | \(0.709581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.04541e9 | 0.0553668 | 0.0276834 | − | 0.999617i | \(-0.491187\pi\) | ||||
0.0276834 | + | 0.999617i | \(0.491187\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.24072e9 | −0.222784 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.79570e8 | 0.0247904 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.09842e10 | 2.10161 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.51562e9 | −0.0764828 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.09543e10 | −1.04900 | −0.524498 | − | 0.851412i | \(-0.675747\pi\) | ||||
−0.524498 | + | 0.851412i | \(0.675747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.44270e9 | −0.415974 | −0.207987 | − | 0.978132i | \(-0.566691\pi\) | ||||
−0.207987 | + | 0.978132i | \(0.566691\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.96174e10 | 0.958911 | 0.479455 | − | 0.877566i | \(-0.340834\pi\) | ||||
0.479455 | + | 0.877566i | \(0.340834\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.06979e10 | 0.514713 | 0.257356 | − | 0.966317i | \(-0.417149\pi\) | ||||
0.257356 | + | 0.966317i | \(0.417149\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.87018e10 | 1.37010 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.60379e10 | 1.22356 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.81197e10 | −0.844834 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.43099e10 | −1.11590 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.31266e9 | 0.287525 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.74059e10 | −0.780596 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.17099e10 | −1.41114 | −0.705569 | − | 0.708641i | \(-0.749308\pi\) | ||||
−0.705569 | + | 0.708641i | \(0.749308\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.00203e10 | −1.31553 | −0.657766 | − | 0.753223i | \(-0.728498\pi\) | ||||
−0.657766 | + | 0.753223i | \(0.728498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.67584e8 | 0.0333794 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.77169e10 | 1.61526 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.17761e10 | −0.500494 | −0.250247 | − | 0.968182i | \(-0.580512\pi\) | ||||
−0.250247 | + | 0.968182i | \(0.580512\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.03361e10 | −2.94423 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.14722e9 | 0.0476596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.88395e10 | −0.770928 | −0.385464 | − | 0.922723i | \(-0.625959\pi\) | ||||
−0.385464 | + | 0.922723i | \(0.625959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.54157e9 | 0.184451 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.47225e8 | −0.00989126 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.45667e9 | −0.0975568 | −0.0487784 | − | 0.998810i | \(-0.515533\pi\) | ||||
−0.0487784 | + | 0.998810i | \(0.515533\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.10769e10 | −1.21583 | −0.607916 | − | 0.794001i | \(-0.707994\pi\) | ||||
−0.607916 | + | 0.794001i | \(0.707994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.72957e8 | −0.0144833 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.82161e10 | 0.696998 | 0.348499 | − | 0.937309i | \(-0.386691\pi\) | ||||
0.348499 | + | 0.937309i | \(0.386691\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.52199e10 | −2.47713 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.90305e10 | 1.46076 | 0.730380 | − | 0.683041i | \(-0.239343\pi\) | ||||
0.730380 | + | 0.683041i | \(0.239343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.03682e9 | −0.112825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.90238e10 | 0.696518 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.54654e10 | −0.562119 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.31032e10 | −0.469386 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.22959e10 | 0.437289 | 0.218645 | − | 0.975805i | \(-0.429836\pi\) | ||||
0.218645 | + | 0.975805i | \(0.429836\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.44806e8 | −0.0155921 | −0.00779603 | − | 0.999970i | \(-0.502482\pi\) | ||||
−0.00779603 | + | 0.999970i | \(0.502482\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.66796e10 | −0.580486 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.57833e10 | −0.541459 | −0.270730 | − | 0.962655i | \(-0.587265\pi\) | ||||
−0.270730 | + | 0.962655i | \(0.587265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.39425e8 | −0.00474898 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.45516e10 | 0.824409 | 0.412204 | − | 0.911091i | \(-0.364759\pi\) | ||||
0.412204 | + | 0.911091i | \(0.364759\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.56958e10 | −0.856712 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.49097e9 | 0.279107 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.56393e10 | 1.48964 | 0.744819 | − | 0.667266i | \(-0.232536\pi\) | ||||
0.744819 | + | 0.667266i | \(0.232536\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.70411e9 | −0.183572 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.18036e10 | 1.33592 | 0.667960 | − | 0.744197i | \(-0.267168\pi\) | ||||
0.667960 | + | 0.744197i | \(0.267168\pi\) | |||||||
\(998\) | 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 | 360.8.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 40.8.a.a.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 80.8.a.c.1.1 | 1 | |||
15.2 | even | 4 | 200.8.c.d.49.2 | 2 | |||
15.8 | even | 4 | 200.8.c.d.49.1 | 2 | |||
15.14 | odd | 2 | 200.8.a.g.1.1 | 1 | |||
24.5 | odd | 2 | 320.8.a.g.1.1 | 1 | |||
24.11 | even | 2 | 320.8.a.b.1.1 | 1 | |||
60.23 | odd | 4 | 400.8.c.h.49.2 | 2 | |||
60.47 | odd | 4 | 400.8.c.h.49.1 | 2 | |||
60.59 | even | 2 | 400.8.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.8.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
80.8.a.c.1.1 | 1 | 12.11 | even | 2 | |||
200.8.a.g.1.1 | 1 | 15.14 | odd | 2 | |||
200.8.c.d.49.1 | 2 | 15.8 | even | 4 | |||
200.8.c.d.49.2 | 2 | 15.2 | even | 4 | |||
320.8.a.b.1.1 | 1 | 24.11 | even | 2 | |||
320.8.a.g.1.1 | 1 | 24.5 | odd | 2 | |||
360.8.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
400.8.a.g.1.1 | 1 | 60.59 | even | 2 | |||
400.8.c.h.49.1 | 2 | 60.47 | odd | 4 | |||
400.8.c.h.49.2 | 2 | 60.23 | odd | 4 |