Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,10,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(197.773761087\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 3854x^{3} + 12258x^{2} + 2877633x + 16772643 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{29}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(43.8567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2126.01 | 1.52125 | 0.760623 | − | 0.649194i | \(-0.224894\pi\) | ||||
0.760623 | + | 0.649194i | \(0.224894\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1445.12 | −0.227490 | −0.113745 | − | 0.993510i | \(-0.536285\pi\) | ||||
−0.113745 | + | 0.993510i | \(0.536285\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20159.9 | −0.415166 | −0.207583 | − | 0.978217i | \(-0.566560\pi\) | ||||
−0.207583 | + | 0.978217i | \(0.566560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 150057. | 1.45717 | 0.728586 | − | 0.684955i | \(-0.240178\pi\) | ||||
0.728586 | + | 0.684955i | \(0.240178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 172206. | 0.878292 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 351448. | 1.02057 | 0.510283 | − | 0.860006i | \(-0.329541\pi\) | ||||
0.510283 | + | 0.860006i | \(0.329541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 584303. | 1.02860 | 0.514300 | − | 0.857610i | \(-0.328052\pi\) | ||||
0.514300 | + | 0.857610i | \(0.328052\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −117055. | −0.131342 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −289317. | −0.215575 | −0.107787 | − | 0.994174i | \(-0.534377\pi\) | ||||
−0.107787 | + | 0.994174i | \(0.534377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.56678e6 | 1.31419 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.55200e6 | 0.670022 | 0.335011 | − | 0.942214i | \(-0.391260\pi\) | ||||
0.335011 | + | 0.942214i | \(0.391260\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.90613e6 | −1.92653 | −0.963267 | − | 0.268546i | \(-0.913457\pi\) | ||||
−0.963267 | + | 0.268546i | \(0.913457\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.63295e6 | −0.239696 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.07234e6 | −0.346069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.78890e6 | 0.332358 | 0.166179 | − | 0.986096i | \(-0.446857\pi\) | ||||
0.166179 | + | 0.986096i | \(0.446857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.21546e7 | 0.841298 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.02647e7 | 0.567308 | 0.283654 | − | 0.958927i | \(-0.408453\pi\) | ||||
0.283654 | + | 0.958927i | \(0.408453\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.60796e6 | 0.160936 | 0.0804680 | − | 0.996757i | \(-0.474359\pi\) | ||||
0.0804680 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.39487e7 | 0.507082 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.06168e7 | −0.317362 | −0.158681 | − | 0.987330i | \(-0.550724\pi\) | ||||
−0.158681 | + | 0.987330i | \(0.550724\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.82652e7 | −0.948248 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.84673e7 | 0.589224 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.14129e7 | 0.720933 | 0.360466 | − | 0.932772i | \(-0.382618\pi\) | ||||
0.360466 | + | 0.932772i | \(0.382618\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.28601e7 | −0.631569 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.73285e7 | 0.593863 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.14005e7 | 0.982007 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.51926e8 | 1.40491 | 0.702454 | − | 0.711729i | \(-0.252087\pi\) | ||||
0.702454 | + | 0.711729i | \(0.252087\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.48144e6 | −0.0758302 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.19022e8 | 2.21672 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.97423e8 | 1.19691 | 0.598456 | − | 0.801156i | \(-0.295781\pi\) | ||||
0.598456 | + | 0.801156i | \(0.295781\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.34347e7 | −0.124462 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.32283e8 | −0.617791 | −0.308896 | − | 0.951096i | \(-0.599959\pi\) | ||||
−0.308896 | + | 0.951096i | \(0.599959\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50306e8 | −0.619474 | −0.309737 | − | 0.950822i | \(-0.600241\pi\) | ||||
−0.309737 | + | 0.950822i | \(0.600241\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.07909e8 | 0.758748 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.91335e7 | 0.0944463 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.92882e8 | −1.13485 | −0.567427 | − | 0.823423i | \(-0.692061\pi\) | ||||
−0.567427 | + | 0.823423i | \(0.692061\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.76638e7 | 0.110240 | 0.0551198 | − | 0.998480i | \(-0.482446\pi\) | ||||
0.0551198 | + | 0.998480i | \(0.482446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.47181e8 | 1.55253 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.06712e8 | 0.386837 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.00694e9 | −1.70118 | −0.850588 | − | 0.525832i | \(-0.823754\pi\) | ||||
−0.850588 | + | 0.525832i | \(0.823754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.16850e8 | −0.331493 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.02397e8 | −1.11228 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.24223e9 | 1.56475 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.13065e8 | 0.932508 | 0.466254 | − | 0.884651i | \(-0.345603\pi\) | ||||
0.466254 | + | 0.884651i | \(0.345603\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.32269e8 | −0.138389 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.06164e9 | 1.01515 | 0.507575 | − | 0.861607i | \(-0.330542\pi\) | ||||
0.507575 | + | 0.861607i | \(0.330542\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.08863e9 | 1.82849 | 0.914246 | − | 0.405160i | \(-0.132784\pi\) | ||||
0.914246 | + | 0.405160i | \(0.132784\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.48859e8 | −0.199803 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.01080e9 | −0.745487 | −0.372744 | − | 0.927934i | \(-0.621583\pi\) | ||||
−0.372744 | + | 0.927934i | \(0.621583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.42877e9 | −1.64804 | −0.824019 | − | 0.566562i | \(-0.808273\pi\) | ||||
−0.824019 | + | 0.566562i | \(0.808273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.06901e8 | 0.191887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.64111e9 | −0.946858 | −0.473429 | − | 0.880832i | \(-0.656984\pi\) | ||||
−0.473429 | + | 0.880832i | \(0.656984\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.15089e8 | −0.327943 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.84523e8 | 0.485724 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.07886e8 | −0.232169 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.95153e9 | −0.827637 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.31441e8 | 0.327535 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.30463e9 | 0.477960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.28568e8 | 0.282626 | 0.141313 | − | 0.989965i | \(-0.454868\pi\) | ||||
0.141313 | + | 0.989965i | \(0.454868\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.92245e8 | 0.0929165 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.06490e8 | −0.120595 | −0.0602975 | − | 0.998180i | \(-0.519205\pi\) | ||||
−0.0602975 | + | 0.998180i | \(0.519205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.44389e8 | −0.233997 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.12985e9 | 0.292764 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.35544e9 | −1.05631 | −0.528153 | − | 0.849149i | \(-0.677115\pi\) | ||||
−0.528153 | + | 0.849149i | \(0.677115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.87849e9 | 1.10846 | 0.554228 | − | 0.832365i | \(-0.313014\pi\) | ||||
0.554228 | + | 0.832365i | \(0.313014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.59963e8 | −0.183229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.02513e9 | −0.604968 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.42556e9 | 1.01927 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.09948e9 | −0.547471 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.24917e9 | 1.03869 | 0.519343 | − | 0.854566i | \(-0.326177\pi\) | ||||
0.519343 | + | 0.854566i | \(0.326177\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.69710e9 | 1.20484 | 0.602422 | − | 0.798178i | \(-0.294202\pi\) | ||||
0.602422 | + | 0.798178i | \(0.294202\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.30585e9 | 0.340189 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.10605e10 | −2.93073 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.53416e8 | 0.0989661 | 0.0494831 | − | 0.998775i | \(-0.484243\pi\) | ||||
0.0494831 | + | 0.998775i | \(0.484243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.35445e9 | 0.416231 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.18098e8 | 0.0490413 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.24666e9 | 1.02598 | 0.512992 | − | 0.858393i | \(-0.328537\pi\) | ||||
0.512992 | + | 0.858393i | \(0.328537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.47167e9 | −0.364637 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.32098e10 | −1.31423 | −0.657114 | − | 0.753791i | \(-0.728223\pi\) | ||||
−0.657114 | + | 0.753791i | \(0.728223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.19125e10 | 1.12335 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.83361e9 | 0.342867 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.06746e8 | −0.0514991 | −0.0257495 | − | 0.999668i | \(-0.508197\pi\) | ||||
−0.0257495 | + | 0.999668i | \(0.508197\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.70930e9 | −0.298966 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.40344e9 | 0.566962 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.46950e9 | 0.471012 | 0.235506 | − | 0.971873i | \(-0.424325\pi\) | ||||
0.235506 | + | 0.971873i | \(0.424325\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.92300e9 | 0.340938 | 0.170469 | − | 0.985363i | \(-0.445472\pi\) | ||||
0.170469 | + | 0.985363i | \(0.445472\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.23060e10 | 0.811125 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.05523e9 | 0.505598 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.08517e9 | −0.423704 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.67997e8 | −0.0437806 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.45071e10 | −0.788735 | −0.394367 | − | 0.918953i | \(-0.629036\pi\) | ||||
−0.394367 | + | 0.918953i | \(0.629036\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.02370e10 | 1.56867 | 0.784333 | − | 0.620340i | \(-0.213005\pi\) | ||||
0.784333 | + | 0.620340i | \(0.213005\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.58408e10 | 1.27982 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.70014e10 | 1.75033 | 0.875166 | − | 0.483823i | \(-0.160752\pi\) | ||||
0.875166 | + | 0.483823i | \(0.160752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.46975e9 | 0.247246 | 0.123623 | − | 0.992329i | \(-0.460549\pi\) | ||||
0.123623 | + | 0.992329i | \(0.460549\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.59913e10 | 0.691037 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.68795e9 | −0.152424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.18228e10 | 0.863015 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.89821e9 | −0.0718583 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.17795e10 | −0.427040 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.46026e10 | −1.89645 | −0.948226 | − | 0.317595i | \(-0.897125\pi\) | ||||
−0.948226 | + | 0.317595i | \(0.897125\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.07149e10 | −0.356682 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.67054e9 | 0.244823 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.43156e10 | 0.438268 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.21748e10 | −0.357654 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.27372e10 | 1.48714 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.33790e9 | −0.144543 | −0.0722717 | − | 0.997385i | \(-0.523025\pi\) | ||||
−0.0722717 | + | 0.997385i | \(0.523025\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.68406e10 | 0.438063 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.32409e10 | −1.33085 | −0.665425 | − | 0.746465i | \(-0.731750\pi\) | ||||
−0.665425 | + | 0.746465i | \(0.731750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.47725e10 | −0.835558 | −0.417779 | − | 0.908549i | \(-0.637191\pi\) | ||||
−0.417779 | + | 0.908549i | \(0.637191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.35982e9 | 0.0545286 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.88898e10 | 1.08672 | 0.543358 | − | 0.839501i | \(-0.317152\pi\) | ||||
0.543358 | + | 0.839501i | \(0.317152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.25714e10 | −0.482785 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.18234e10 | −0.655209 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.43988e10 | 0.880198 | 0.440099 | − | 0.897949i | \(-0.354943\pi\) | ||||
0.440099 | + | 0.897949i | \(0.354943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.37387e10 | −1.02615 | −0.513075 | − | 0.858344i | \(-0.671494\pi\) | ||||
−0.513075 | + | 0.858344i | \(0.671494\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.13521e10 | −1.44252 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.76786e10 | 1.49885 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.86077e9 | 0.0636468 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.51803e10 | −1.51362 | −0.756808 | − | 0.653638i | \(-0.773242\pi\) | ||||
−0.756808 | + | 0.653638i | \(0.773242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.83260e9 | 0.0894994 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.05217e10 | 0.896355 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.76361e10 | −1.25310 | −0.626548 | − | 0.779383i | \(-0.715533\pi\) | ||||
−0.626548 | + | 0.779383i | \(0.715533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.47543e9 | −0.0756082 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.67436e10 | 0.223341 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.12390e11 | 1.44853 | 0.724265 | − | 0.689522i | \(-0.242179\pi\) | ||||
0.724265 | + | 0.689522i | \(0.242179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.80442e10 | 1.09672 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.15623e10 | −0.982175 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.30872e11 | 1.52392 | 0.761960 | − | 0.647624i | \(-0.224237\pi\) | ||||
0.761960 | + | 0.647624i | \(0.224237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.12023e10 | 0.576670 | 0.288335 | − | 0.957530i | \(-0.406898\pi\) | ||||
0.288335 | + | 0.957530i | \(0.406898\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.75649e10 | −0.191387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.17460e10 | −0.545607 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.35027e10 | 0.750143 | 0.375072 | − | 0.926996i | \(-0.377618\pi\) | ||||
0.375072 | + | 0.926996i | \(0.377618\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.49941e10 | −0.642178 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.63145e10 | 0.825857 | 0.412929 | − | 0.910763i | \(-0.364506\pi\) | ||||
0.412929 | + | 0.910763i | \(0.364506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.02580e10 | 0.558439 | 0.279219 | − | 0.960227i | \(-0.409924\pi\) | ||||
0.279219 | + | 0.960227i | \(0.409924\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00621e11 | 0.903412 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.48337e10 | −0.129057 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.92803e9 | 0.0415559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.58583e10 | 0.538384 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.73424e11 | 1.37469 | 0.687344 | − | 0.726332i | \(-0.258777\pi\) | ||||
0.687344 | + | 0.726332i | \(0.258777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.94318e11 | 1.49387 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.07138e10 | −0.0798987 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.34139e10 | −0.314130 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.21394e9 | −0.0366114 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.59927e10 | 0.586098 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.22996e11 | 2.13721 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.83367e11 | −1.17814 | −0.589071 | − | 0.808081i | \(-0.700506\pi\) | ||||
−0.589071 | + | 0.808081i | \(0.700506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.69179e11 | 1.05568 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.67223e10 | 0.404436 | 0.202218 | − | 0.979341i | \(-0.435185\pi\) | ||||
0.202218 | + | 0.979341i | \(0.435185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.40731e11 | 0.828784 | 0.414392 | − | 0.910098i | \(-0.363994\pi\) | ||||
0.414392 | + | 0.910098i | \(0.363994\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.01576e10 | −0.115356 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.34125e11 | −0.746007 | −0.373004 | − | 0.927830i | \(-0.621672\pi\) | ||||
−0.373004 | + | 0.927830i | \(0.621672\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.14480e10 | −0.278170 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.18751e10 | −0.430407 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.05352e11 | 1.04976 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.85162e11 | 1.91500 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.96730e11 | −0.951496 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.53426e10 | 0.0721967 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.72093e11 | −0.788020 | −0.394010 | − | 0.919106i | \(-0.628912\pi\) | ||||
−0.394010 | + | 0.919106i | \(0.628912\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.48590e10 | 0.110786 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.19723e11 | 1.82080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.52423e11 | 1.06609 | 0.533046 | − | 0.846086i | \(-0.321047\pi\) | ||||
0.533046 | + | 0.846086i | \(0.321047\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.32930e11 | −0.546669 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.99707e11 | 0.799831 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.13614e11 | 0.443208 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.98222e10 | −0.189338 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.95517e11 | 1.46448 | 0.732238 | − | 0.681049i | \(-0.238476\pi\) | ||||
0.732238 | + | 0.681049i | \(0.238476\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.50336e10 | 0.162488 | 0.0812441 | − | 0.996694i | \(-0.474111\pi\) | ||||
0.0812441 | + | 0.996694i | \(0.474111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.97463e10 | 0.280433 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.82955e11 | 0.627130 | 0.313565 | − | 0.949567i | \(-0.398477\pi\) | ||||
0.313565 | + | 0.949567i | \(0.398477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.81235e11 | −0.939812 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.11387e10 | −0.134043 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.89461e10 | −0.187297 | −0.0936483 | − | 0.995605i | \(-0.529853\pi\) | ||||
−0.0936483 | + | 0.995605i | \(0.529853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.87222e10 | 0.0580195 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.58074e11 | −0.477837 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.19551e11 | −0.942373 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.40036e11 | −1.55391 | −0.776955 | − | 0.629556i | \(-0.783237\pi\) | ||||
−0.776955 | + | 0.629556i | \(0.783237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.73467e10 | 0.189103 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.98467e10 | −0.164005 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.12254e11 | 1.63773 | 0.818865 | − | 0.573986i | \(-0.194604\pi\) | ||||
0.818865 | + | 0.573986i | \(0.194604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.05675e11 | 0.275950 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.82944e11 | 0.976337 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.08851e11 | 1.01786 | 0.508931 | − | 0.860808i | \(-0.330041\pi\) | ||||
0.508931 | + | 0.860808i | \(0.330041\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.71140e10 | 0.163174 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.10228e11 | 1.44910 | 0.724549 | − | 0.689224i | \(-0.242048\pi\) | ||||
0.724549 | + | 0.689224i | \(0.242048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.19380e10 | 0.143676 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.36718e10 | 0.0536454 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.17629e10 | 0.203186 | 0.101593 | − | 0.994826i | \(-0.467606\pi\) | ||||
0.101593 | + | 0.994826i | \(0.467606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.01680e11 | −0.220009 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.29257e10 | −0.0696255 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.35270e11 | −1.72639 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.90677e11 | 0.587291 | 0.293646 | − | 0.955914i | \(-0.405131\pi\) | ||||
0.293646 | + | 0.955914i | \(0.405131\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.83955e10 | −0.135098 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.22231e10 | −0.0815456 | −0.0407728 | − | 0.999168i | \(-0.512982\pi\) | ||||
−0.0407728 | + | 0.999168i | \(0.512982\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.48648e12 | −2.80729 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.15176e10 | 0.169027 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.63840e10 | −0.137984 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.59030e11 | −0.457715 | −0.228857 | − | 0.973460i | \(-0.573499\pi\) | ||||
−0.228857 | + | 0.973460i | \(0.573499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.52791e11 | −0.609859 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.32085e11 | −0.223397 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.01334e11 | 0.167701 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.95157e11 | 0.639968 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.54680e11 | 1.35469 | 0.677346 | − | 0.735665i | \(-0.263130\pi\) | ||||
0.677346 | + | 0.735665i | \(0.263130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.85059e11 | −0.907675 | −0.453837 | − | 0.891085i | \(-0.649945\pi\) | ||||
−0.453837 | + | 0.891085i | \(0.649945\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.96570e10 | −0.105787 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.02089e11 | 1.34122 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.19552e11 | −0.319603 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.45036e11 | −0.349278 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.32751e12 | 1.85306 | 0.926532 | − | 0.376215i | \(-0.122775\pi\) | ||||
0.926532 | + | 0.376215i | \(0.122775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.21842e11 | −1.26026 | −0.630131 | − | 0.776489i | \(-0.716999\pi\) | ||||
−0.630131 | + | 0.776489i | \(0.716999\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.39470e11 | 0.588475 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.69049e11 | −0.221741 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.11660e11 | 0.528992 | 0.264496 | − | 0.964387i | \(-0.414794\pi\) | ||||
0.264496 | + | 0.964387i | \(0.414794\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.51058e11 | −0.316083 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.98623e10 | −0.123193 | −0.0615964 | − | 0.998101i | \(-0.519619\pi\) | ||||
−0.0615964 | + | 0.998101i | \(0.519619\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.14077e12 | −2.58791 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.06183e11 | 0.599686 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.41938e12 | −1.64812 | −0.824060 | − | 0.566503i | \(-0.808296\pi\) | ||||
−0.824060 | + | 0.566503i | \(0.808296\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.06935e11 | −0.235527 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.23465e11 | 0.695617 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.61025e11 | −0.504282 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.45069e12 | 1.55579 | 0.777897 | − | 0.628392i | \(-0.216287\pi\) | ||||
0.777897 | + | 0.628392i | \(0.216287\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.86774e11 | 0.196408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.12468e12 | −1.15978 | −0.579891 | − | 0.814694i | \(-0.696905\pi\) | ||||
−0.579891 | + | 0.814694i | \(0.696905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.05071e12 | −1.06260 | −0.531299 | − | 0.847184i | \(-0.678296\pi\) | ||||
−0.531299 | + | 0.847184i | \(0.678296\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.70590e12 | −1.69206 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.95982e12 | −1.90673 | −0.953366 | − | 0.301817i | \(-0.902407\pi\) | ||||
−0.953366 | + | 0.301817i | \(0.902407\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.85301e11 | −0.272286 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.10267e10 | 0.0571381 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.27361e10 | −0.0668152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.49977e12 | 1.35178 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.71710e11 | 0.240311 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.53456e12 | −1.33191 | −0.665954 | − | 0.745993i | \(-0.731975\pi\) | ||||
−0.665954 | + | 0.745993i | \(0.731975\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.68551e11 | 0.484302 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.38659e10 | 0.0283140 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.72858e12 | 1.41857 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.84071e11 | 0.389968 | 0.194984 | − | 0.980806i | \(-0.437535\pi\) | ||||
0.194984 | + | 0.980806i | \(0.437535\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.48979e11 | 0.592352 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.19993e11 | −0.481415 | −0.240708 | − | 0.970598i | \(-0.577380\pi\) | ||||
−0.240708 | + | 0.970598i | \(0.577380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.96895e11 | 0.683802 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.81205e11 | −0.210523 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.91165e11 | 0.140542 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.55499e10 | 0.0112273 | 0.00561364 | − | 0.999984i | \(-0.498213\pi\) | ||||
0.00561364 | + | 0.999984i | \(0.498213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.06999e12 | −0.758770 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.35355e12 | −0.942799 | −0.471400 | − | 0.881920i | \(-0.656251\pi\) | ||||
−0.471400 | + | 0.881920i | \(0.656251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.25705e12 | 1.54429 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.64916e11 | 0.648565 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.85998e11 | 0.585063 | 0.292532 | − | 0.956256i | \(-0.405502\pi\) | ||||
0.292532 | + | 0.956256i | \(0.405502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.17210e11 | 0.140925 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.10523e11 | 0.197954 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.44043e12 | 2.78159 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.14034e11 | 0.131758 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.91464e10 | −0.0297330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.02158e12 | −1.20205 | −0.601025 | − | 0.799231i | \(-0.705241\pi\) | ||||
−0.601025 | + | 0.799231i | \(0.705241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.78264e12 | 1.04185 | 0.520927 | − | 0.853601i | \(-0.325586\pi\) | ||||
0.520927 | + | 0.853601i | \(0.325586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.00454e11 | −0.172608 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.48149e12 | −1.96616 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.71745e12 | −0.953527 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.99679e11 | 0.327336 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.54029e12 | 0.826665 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.14898e12 | −1.13407 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.24029e11 | 0.271939 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.71424e11 | 0.393680 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.53295e12 | −0.769380 | −0.384690 | − | 0.923046i | \(-0.625692\pi\) | ||||
−0.384690 | + | 0.923046i | \(0.625692\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.98763e11 | 0.196841 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.16358e12 | −2.50707 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.82914e12 | 1.82877 | 0.914384 | − | 0.404848i | \(-0.132676\pi\) | ||||
0.914384 | + | 0.404848i | \(0.132676\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.96787e11 | 0.468303 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.49114e12 | 0.689185 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.67762e11 | 0.258169 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.52474e11 | 0.291907 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.93062e12 | 0.849861 | 0.424930 | − | 0.905226i | \(-0.360299\pi\) | ||||
0.424930 | + | 0.905226i | \(0.360299\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.41399e11 | 0.234511 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.73899e11 | −0.244626 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.31015e12 | −0.969064 | −0.484532 | − | 0.874774i | \(-0.661010\pi\) | ||||
−0.484532 | + | 0.874774i | \(0.661010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.48901e12 | −1.44040 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.22077e10 | −0.0252767 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.54228e12 | 0.616818 | 0.308409 | − | 0.951254i | \(-0.400203\pi\) | ||||
0.308409 | + | 0.951254i | \(0.400203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.11331e12 | −1.61931 | −0.809653 | − | 0.586909i | \(-0.800345\pi\) | ||||
−0.809653 | + | 0.586909i | \(0.800345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.17508e12 | −0.455376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.42611e11 | −0.283306 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.75851e12 | −1.03606 | −0.518029 | − | 0.855363i | \(-0.673334\pi\) | ||||
−0.518029 | + | 0.855363i | \(0.673334\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.44920e12 | 0.905670 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.88800e10 | −0.0250784 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.34881e11 | −0.299307 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.09310e12 | 0.738905 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.68695e12 | 1.62937 | 0.814684 | − | 0.579905i | \(-0.196910\pi\) | ||||
0.814684 | + | 0.579905i | \(0.196910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.78818e12 | −1.98163 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.99712e12 | 1.01055 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.97181e12 | −1.31899 | −0.659496 | − | 0.751708i | \(-0.729230\pi\) | ||||
−0.659496 | + | 0.751708i | \(0.729230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.07977e12 | −0.353186 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.43050e11 | 0.142747 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.21210e11 | 0.260635 | 0.130318 | − | 0.991472i | \(-0.458400\pi\) | ||||
0.130318 | + | 0.991472i | \(0.458400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.05981e11 | 0.283259 | 0.141630 | − | 0.989920i | \(-0.454766\pi\) | ||||
0.141630 | + | 0.989920i | \(0.454766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.29529e12 | 0.398970 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.14896e12 | −1.25904 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.71983e12 | −1.41116 | −0.705582 | − | 0.708628i | \(-0.749314\pi\) | ||||
−0.705582 | + | 0.708628i | \(0.749314\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.98724e11 | −0.0880018 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.59313e12 | −0.462450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.50974e12 | 1.00393 | 0.501964 | − | 0.864889i | \(-0.332611\pi\) | ||||
0.501964 | + | 0.864889i | \(0.332611\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.76765e12 | 0.498262 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.71750e12 | −0.477104 | −0.238552 | − | 0.971130i | \(-0.576673\pi\) | ||||
−0.238552 | + | 0.971130i | \(0.576673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.13938e12 | −1.40703 | −0.703514 | − | 0.710681i | \(-0.748387\pi\) | ||||
−0.703514 | + | 0.710681i | \(0.748387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.53755e11 | −0.0414874 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.45515e12 | 0.387002 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.23959e12 | −0.587095 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.54139e11 | −0.246552 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.33160e12 | 0.339193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.82848e12 | −1.46360 | −0.731802 | − | 0.681518i | \(-0.761320\pi\) | ||||
−0.731802 | + | 0.681518i | \(0.761320\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.42281e12 | −1.09492 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.76154e12 | 0.429943 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.74196e12 | −1.38176 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.67909e11 | −0.205930 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.81980e12 | −1.12763 | −0.563817 | − | 0.825900i | \(-0.690668\pi\) | ||||
−0.563817 | + | 0.825900i | \(0.690668\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.81149e12 | 1.57142 | 0.785711 | − | 0.618594i | \(-0.212297\pi\) | ||||
0.785711 | + | 0.618594i | \(0.212297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.21314e11 | 0.141349 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.47142e12 | −0.554468 | −0.277234 | − | 0.960802i | \(-0.589418\pi\) | ||||
−0.277234 | + | 0.960802i | \(0.589418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.84263e12 | −0.407696 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.15956e12 | 0.253034 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.66067e12 | −1.86398 | −0.931992 | − | 0.362478i | \(-0.881931\pi\) | ||||
−0.931992 | + | 0.362478i | \(0.881931\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.64200e11 | −0.183455 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.86158e11 | −0.206491 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.22504e12 | 0.872663 | 0.436332 | − | 0.899786i | \(-0.356277\pi\) | ||||
0.436332 | + | 0.899786i | \(0.356277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.23326e11 | 0.0658770 | 0.0329385 | − | 0.999457i | \(-0.489513\pi\) | ||||
0.0329385 | + | 0.999457i | \(0.489513\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.27171e12 | 0.858601 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.79518e12 | −0.355967 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.38335e11 | −0.144440 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.32370e11 | −0.0834522 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.06282e12 | −0.583270 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.71913e12 | 1.07464 | 0.537319 | − | 0.843379i | \(-0.319437\pi\) | ||||
0.537319 | + | 0.843379i | \(0.319437\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.36409e12 | 0.252916 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.54197e12 | 0.648031 | 0.324016 | − | 0.946052i | \(-0.394967\pi\) | ||||
0.324016 | + | 0.946052i | \(0.394967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.17498e12 | −0.212137 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.31251e12 | −0.768366 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.15530e12 | −0.203143 | −0.101571 | − | 0.994828i | \(-0.532387\pi\) | ||||
−0.101571 | + | 0.994828i | \(0.532387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.25970e12 | −1.60690 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.81658e12 | −0.482410 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.21429e12 | 1.05052 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.67044e12 | −0.612445 | −0.306222 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306222 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.91145e11 | 0.0314821 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.03717e13 | 1.68623 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.60751e12 | 0.578975 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.96007e12 | 0.627416 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.79947e12 | −1.06352 | −0.531758 | − | 0.846896i | \(-0.678468\pi\) | ||||
−0.531758 | + | 0.846896i | \(0.678468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.21387e12 | 0.341863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.82829e12 | −0.278736 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.53420e12 | −0.230937 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.40116e12 | 0.356873 | 0.178437 | − | 0.983951i | \(-0.442896\pi\) | ||||
0.178437 | + | 0.983951i | \(0.442896\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.57770e12 | −0.378285 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.86601e12 | 0.415312 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.43145e12 | −0.920305 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.59630e12 | 0.508183 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.47504e12 | −1.18266 | −0.591332 | − | 0.806428i | \(-0.701398\pi\) | ||||
−0.591332 | + | 0.806428i | \(0.701398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.01832e12 | −0.415964 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.35283e12 | −0.592447 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.55040e12 | 0.880536 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.63217e12 | −1.14608 | −0.573040 | − | 0.819527i | \(-0.694236\pi\) | ||||
−0.573040 | + | 0.819527i | \(0.694236\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.26801e12 | 0.164246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.13998e12 | −0.529700 | −0.264850 | − | 0.964290i | \(-0.585323\pi\) | ||||
−0.264850 | + | 0.964290i | \(0.585323\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.58952e12 | −0.832839 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.98004e12 | −0.496917 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.04729e13 | −1.29171 | −0.645856 | − | 0.763459i | \(-0.723499\pi\) | ||||
−0.645856 | + | 0.763459i | \(0.723499\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.10197e12 | 0.865360 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.13032e12 | 0.256446 | 0.128223 | − | 0.991745i | \(-0.459073\pi\) | ||||
0.128223 | + | 0.991745i | \(0.459073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.32858e13 | 1.58010 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.12722e11 | 0.0367465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.46074e12 | 0.169591 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.83639e11 | −0.112838 | −0.0564191 | − | 0.998407i | \(-0.517968\pi\) | ||||
−0.0564191 | + | 0.998407i | \(0.517968\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.70961e12 | −0.873886 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.63641e13 | 1.83286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.86648e12 | −0.317261 | −0.158631 | − | 0.987338i | \(-0.550708\pi\) | ||||
−0.158631 | + | 0.987338i | \(0.550708\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.72441e11 | 0.0516725 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.06618e13 | 1.15240 | 0.576198 | − | 0.817310i | \(-0.304536\pi\) | ||||
0.576198 | + | 0.817310i | \(0.304536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.50987e12 | 0.374913 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.90226e12 | 0.517511 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.37153e13 | 1.43095 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.89791e12 | 0.505059 | 0.252529 | − | 0.967589i | \(-0.418738\pi\) | ||||
0.252529 | + | 0.967589i | \(0.418738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.09853e12 | −0.723475 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.00025e13 | 1.00763 | 0.503816 | − | 0.863811i | \(-0.331929\pi\) | ||||
0.503816 | + | 0.863811i | \(0.331929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.54268e13 | −2.53183 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.43510e11 | −0.0436524 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.99769e12 | 0.583533 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.66681e12 | 0.256486 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.35624e12 | 0.128946 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.60177e12 | 0.150552 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.62330e12 | 0.615443 | 0.307721 | − | 0.951476i | \(-0.400433\pi\) | ||||
0.307721 | + | 0.951476i | \(0.400433\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.10360e12 | 0.836309 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.37161e12 | 0.215401 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.27975e13 | 2.04719 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.13158e12 | 0.633189 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.63840e12 | 0.846140 | 0.423070 | − | 0.906097i | \(-0.360952\pi\) | ||||
0.423070 | + | 0.906097i | \(0.360952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.73127e12 | −0.323889 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.60655e12 | −0.567059 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.03016e12 | 0.257185 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.88879e11 | 0.0746038 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.06007e13 | 0.879836 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.06927e12 | 0.662317 | 0.331159 | − | 0.943575i | \(-0.392560\pi\) | ||||
0.331159 | + | 0.943575i | \(0.392560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.14952e13 | −0.933089 | −0.466544 | − | 0.884498i | \(-0.654501\pi\) | ||||
−0.466544 | + | 0.884498i | \(0.654501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.14738e12 | 0.332941 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.96585e13 | 1.56077 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.10814e12 | 0.165539 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.42275e12 | −0.110498 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.53548e13 | −1.94767 | −0.973837 | − | 0.227248i | \(-0.927027\pi\) | ||||
−0.973837 | + | 0.227248i | \(0.927027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.35033e13 | −1.02598 | −0.512992 | − | 0.858394i | \(-0.671463\pi\) | ||||
−0.512992 | + | 0.858394i | \(0.671463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.19143e12 | −0.315006 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.32566e12 | 0.544593 | 0.272296 | − | 0.962213i | \(-0.412217\pi\) | ||||
0.272296 | + | 0.962213i | \(0.412217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.72332e12 | −0.126727 | −0.0633635 | − | 0.997991i | \(-0.520183\pi\) | ||||
−0.0633635 | + | 0.997991i | \(0.520183\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.95372e12 | 0.433095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.34482e13 | −0.967750 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.80840e13 | −1.99927 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.26453e12 | −0.370762 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.89755e13 | 1.32210 | 0.661051 | − | 0.750341i | \(-0.270111\pi\) | ||||
0.661051 | + | 0.750341i | \(0.270111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.99446e12 | −0.551071 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.99147e12 | 0.476809 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.53261e13 | 1.70889 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.82019e12 | 0.188280 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.88090e12 | 0.322415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.09619e12 | −0.0716480 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.14364e13 | −0.739638 | −0.369819 | − | 0.929104i | \(-0.620580\pi\) | ||||
−0.369819 | + | 0.929104i | \(0.620580\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.15028e12 | 0.521585 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.91509e12 | −0.247929 | −0.123965 | − | 0.992287i | \(-0.539561\pi\) | ||||
−0.123965 | + | 0.992287i | \(0.539561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.45009e13 | −1.53537 | −0.767685 | − | 0.640828i | \(-0.778591\pi\) | ||||
−0.767685 | + | 0.640828i | \(0.778591\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.20153e12 | −0.0745112 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.55511e12 | 0.586391 | 0.293195 | − | 0.956053i | \(-0.405281\pi\) | ||||
0.293195 | + | 0.956053i | \(0.405281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.28994e12 | −0.0783427 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.99170e11 | 0.0239923 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.92047e12 | 0.471153 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.96247e13 | 1.74410 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.33452e12 | 0.310836 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.88534e12 | −0.108731 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.71224e12 | −0.0977385 | −0.0488692 | − | 0.998805i | \(-0.515562\pi\) | ||||
−0.0488692 | + | 0.998805i | \(0.515562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.40473e13 | 0.793676 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.35035e12 | −0.522921 | −0.261461 | − | 0.965214i | \(-0.584204\pi\) | ||||
−0.261461 | + | 0.965214i | \(0.584204\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.69552e13 | −0.938598 | −0.469299 | − | 0.883039i | \(-0.655493\pi\) | ||||
−0.469299 | + | 0.883039i | \(0.655493\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.57398e13 | 0.862489 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.72616e13 | 0.936322 | 0.468161 | − | 0.883643i | \(-0.344917\pi\) | ||||
0.468161 | + | 0.883643i | \(0.344917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.19738e12 | −0.0642946 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.67818e11 | −0.0461295 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.20344e12 | −0.326438 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.37542e13 | 0.716525 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.51653e12 | −0.181363 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.52804e13 | −1.29082 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.45545e13 | 0.735760 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.22329e11 | −0.0211376 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.04663e13 | 0.518651 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.85379e12 | −0.385342 | −0.192671 | − | 0.981263i | \(-0.561715\pi\) | ||||
−0.192671 | + | 0.981263i | \(0.561715\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.96541e12 | 0.338384 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.85344e12 | −0.425872 | −0.212936 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212936 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.60898e11 | −0.0457677 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.61627e13 | 1.23392 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.87428e11 | 0.0274342 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.44239e13 | 0.667055 | 0.333527 | − | 0.942740i | \(-0.391761\pi\) | ||||
0.333527 | + | 0.942740i | \(0.391761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.48527e13 | −0.680201 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.98500e13 | −0.900227 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.72527e12 | 0.436781 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.37035e13 | 0.609497 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.42057e13 | 1.06622 | 0.533111 | − | 0.846045i | \(-0.321023\pi\) | ||||
0.533111 | + | 0.846045i | \(0.321023\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.23585e13 | −0.975369 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.40451e12 | 0.233501 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.50631e13 | −0.644558 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.32006e12 | 0.352613 | 0.176306 | − | 0.984335i | \(-0.443585\pi\) | ||||
0.176306 | + | 0.984335i | \(0.443585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.13992e13 | 0.478499 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.32963e13 | 0.968576 | 0.484288 | − | 0.874909i | \(-0.339079\pi\) | ||||
0.484288 | + | 0.874909i | \(0.339079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.96975e12 | −0.122297 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.63277e12 | −0.0666010 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.61981e12 | 0.146255 | 0.0731276 | − | 0.997323i | \(-0.476702\pi\) | ||||
0.0731276 | + | 0.997323i | \(0.476702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.25544e13 | −0.902680 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.08641e13 | −0.430708 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.39005e13 | −1.33134 | −0.665669 | − | 0.746248i | \(-0.731854\pi\) | ||||
−0.665669 | + | 0.746248i | \(0.731854\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.08422e13 | −1.19986 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.16729e12 | −0.160602 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.29415e12 | 0.240300 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.16919e13 | 2.71153 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.63189e12 | −0.248496 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.42840e13 | 2.38633 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.32172e13 | −0.853870 | −0.426935 | − | 0.904282i | \(-0.640407\pi\) | ||||
−0.426935 | + | 0.904282i | \(0.640407\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.66335e13 | 0.606077 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.45225e13 | 0.885274 | 0.442637 | − | 0.896701i | \(-0.354043\pi\) | ||||
0.442637 | + | 0.896701i | \(0.354043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.05001e12 | −0.252163 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.11981e13 | 1.10563 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.10059e13 | −1.08872 | −0.544362 | − | 0.838850i | \(-0.683228\pi\) | ||||
−0.544362 | + | 0.838850i | \(0.683228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.02999e13 | 0.706270 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.59352e13 | −0.549346 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.65150e11 | −0.0227211 | −0.0113605 | − | 0.999935i | \(-0.503616\pi\) | ||||
−0.0113605 | + | 0.999935i | \(0.503616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.86653e13 | 2.66269 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.24275e12 | 0.0416828 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.04384e12 | −0.0346938 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.23636e13 | −1.72464 | −0.862320 | − | 0.506364i | \(-0.830989\pi\) | ||||
−0.862320 | + | 0.506364i | \(0.830989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.39395e13 | −0.454964 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.16287e13 | 0.376122 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.66861e13 | −1.49644 | −0.748219 | − | 0.663451i | \(-0.769091\pi\) | ||||
−0.748219 | + | 0.663451i | \(0.769091\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.01358e12 | 0.0639623 |
(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 | 384.10.a.p.1.5 | yes | 5 | |
4.3 | odd | 2 | 384.10.a.l.1.5 | yes | 5 | ||
8.3 | odd | 2 | 384.10.a.m.1.1 | yes | 5 | ||
8.5 | even | 2 | 384.10.a.i.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.10.a.i.1.1 | ✓ | 5 | 8.5 | even | 2 | ||
384.10.a.l.1.5 | yes | 5 | 4.3 | odd | 2 | ||
384.10.a.m.1.1 | yes | 5 | 8.3 | odd | 2 | ||
384.10.a.p.1.5 | yes | 5 | 1.1 | even | 1 | trivial |