Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,6,Mod(1,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(1.28307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8.1 |
$q$-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 | ||||||||
\(3\) | 20.0000 | 1.28300 | 0.641500 | − | 0.767123i | \(-0.278312\pi\) | ||||
0.641500 | + | 0.767123i | \(0.278312\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −74.0000 | −1.32375 | −0.661876 | − | 0.749613i | \(-0.730240\pi\) | ||||
−0.661876 | + | 0.749613i | \(0.730240\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.0000 | −0.185125 | −0.0925627 | − | 0.995707i | \(-0.529506\pi\) | ||||
−0.0925627 | + | 0.995707i | \(0.529506\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 157.000 | 0.646091 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 124.000 | 0.308987 | 0.154493 | − | 0.987994i | \(-0.450625\pi\) | ||||
0.154493 | + | 0.987994i | \(0.450625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 478.000 | 0.784458 | 0.392229 | − | 0.919868i | \(-0.371704\pi\) | ||||
0.392229 | + | 0.919868i | \(0.371704\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1480.00 | −1.69837 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1198.00 | −1.00539 | −0.502695 | − | 0.864464i | \(-0.667658\pi\) | ||||
−0.502695 | + | 0.864464i | \(0.667658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3044.00 | 1.93446 | 0.967232 | − | 0.253894i | \(-0.0817115\pi\) | ||||
0.967232 | + | 0.253894i | \(0.0817115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −480.000 | −0.237516 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 184.000 | 0.0725268 | 0.0362634 | − | 0.999342i | \(-0.488454\pi\) | ||||
0.0362634 | + | 0.999342i | \(0.488454\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2351.00 | 0.752320 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1720.00 | −0.454066 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3282.00 | −0.724676 | −0.362338 | − | 0.932047i | \(-0.618021\pi\) | ||||
−0.362338 | + | 0.932047i | \(0.618021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5728.00 | −1.07053 | −0.535265 | − | 0.844684i | \(-0.679788\pi\) | ||||
−0.535265 | + | 0.844684i | \(0.679788\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2480.00 | 0.396430 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1776.00 | 0.245060 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10326.0 | 1.24002 | 0.620009 | − | 0.784595i | \(-0.287129\pi\) | ||||
0.620009 | + | 0.784595i | \(0.287129\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9560.00 | 1.00646 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8886.00 | −0.825556 | −0.412778 | − | 0.910832i | \(-0.635442\pi\) | ||||
−0.412778 | + | 0.910832i | \(0.635442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9188.00 | −0.757792 | −0.378896 | − | 0.925439i | \(-0.623696\pi\) | ||||
−0.378896 | + | 0.925439i | \(0.623696\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11618.0 | −0.855264 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23664.0 | 1.56258 | 0.781292 | − | 0.624165i | \(-0.214561\pi\) | ||||
0.781292 | + | 0.624165i | \(0.214561\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16231.0 | −0.965729 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −23960.0 | −1.28992 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11686.0 | 0.571447 | 0.285724 | − | 0.958312i | \(-0.407766\pi\) | ||||
0.285724 | + | 0.958312i | \(0.407766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9176.00 | −0.409022 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60880.0 | 2.48192 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16876.0 | 0.631160 | 0.315580 | − | 0.948899i | \(-0.397801\pi\) | ||||
0.315580 | + | 0.948899i | \(0.397801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18482.0 | −0.635952 | −0.317976 | − | 0.948099i | \(-0.603003\pi\) | ||||
−0.317976 | + | 0.948099i | \(0.603003\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3768.00 | −0.119608 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −35372.0 | −1.03843 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15532.0 | −0.422708 | −0.211354 | − | 0.977410i | \(-0.567787\pi\) | ||||
−0.211354 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3680.00 | 0.0930519 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −31960.0 | −0.752421 | −0.376210 | − | 0.926534i | \(-0.622773\pi\) | ||||
−0.376210 | + | 0.926534i | \(0.622773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4886.00 | −0.107312 | −0.0536558 | − | 0.998559i | \(-0.517087\pi\) | ||||
−0.0536558 | + | 0.998559i | \(0.517087\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 47020.0 | 0.965227 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2976.00 | −0.0572013 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 44560.0 | 0.803299 | 0.401650 | − | 0.915793i | \(-0.368437\pi\) | ||||
0.401650 | + | 0.915793i | \(0.368437\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −72551.0 | −1.22866 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 67364.0 | 1.07333 | 0.536664 | − | 0.843796i | \(-0.319684\pi\) | ||||
0.536664 | + | 0.843796i | \(0.319684\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 88652.0 | 1.33089 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −65640.0 | −0.929759 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 71994.0 | 0.963432 | 0.481716 | − | 0.876327i | \(-0.340014\pi\) | ||||
0.481716 | + | 0.876327i | \(0.340014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11472.0 | −0.145223 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −114560. | −1.37349 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −225256. | −2.56075 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 48866.0 | 0.527324 | 0.263662 | − | 0.964615i | \(-0.415070\pi\) | ||||
0.263662 | + | 0.964615i | \(0.415070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19468.0 | 0.199633 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 51606.0 | 0.503381 | 0.251690 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251690 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 180424. | 1.67572 | 0.837860 | − | 0.545886i | \(-0.183807\pi\) | ||||
0.837860 | + | 0.545886i | \(0.183807\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 35520.0 | 0.314412 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −65700.0 | −0.554761 | −0.277381 | − | 0.960760i | \(-0.589466\pi\) | ||||
−0.277381 | + | 0.960760i | \(0.589466\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −112706. | −0.908617 | −0.454308 | − | 0.890844i | \(-0.650114\pi\) | ||||
−0.454308 | + | 0.890844i | \(0.650114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 206520. | 1.59094 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −23502.0 | −0.173145 | −0.0865723 | − | 0.996246i | \(-0.527591\pi\) | ||||
−0.0865723 | + | 0.996246i | \(0.527591\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13616.0 | −0.0960075 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 75046.0 | 0.506831 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28752.0 | 0.186123 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −145675. | −0.904527 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −177720. | −1.05919 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 57276.0 | 0.327867 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −94592.0 | −0.520409 | −0.260205 | − | 0.965553i | \(-0.583790\pi\) | ||||
−0.260205 | + | 0.965553i | \(0.583790\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −183760. | −0.972247 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70292.0 | 0.357872 | 0.178936 | − | 0.983861i | \(-0.442735\pi\) | ||||
0.178936 | + | 0.983861i | \(0.442735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −73056.0 | −0.358119 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 127280. | 0.601071 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 277290. | 1.26221 | 0.631107 | − | 0.775696i | \(-0.282601\pi\) | ||||
0.631107 | + | 0.775696i | \(0.282601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −130308. | −0.572050 | −0.286025 | − | 0.958222i | \(-0.592334\pi\) | ||||
−0.286025 | + | 0.958222i | \(0.592334\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 473280. | 2.00480 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 59272.0 | 0.242387 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 242868. | 0.959291 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −324620. | −1.23903 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −401530. | −1.48167 | −0.740836 | − | 0.671685i | \(-0.765571\pi\) | ||||
−0.740836 | + | 0.671685i | \(0.765571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −75976.0 | −0.271165 | −0.135583 | − | 0.990766i | \(-0.543291\pi\) | ||||
−0.135583 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −188086. | −0.649573 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 423872. | 1.41712 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −394322. | −1.27674 | −0.638369 | − | 0.769730i | \(-0.720391\pi\) | ||||
−0.638369 | + | 0.769730i | \(0.720391\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 233720. | 0.733167 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4416.00 | −0.0134265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11724.0 | −0.0345626 | −0.0172813 | − | 0.999851i | \(-0.505501\pi\) | ||||
−0.0172813 | + | 0.999851i | \(0.505501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −183520. | −0.524775 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −551928. | −1.53141 | −0.765705 | − | 0.643192i | \(-0.777610\pi\) | ||||
−0.765705 | + | 0.643192i | \(0.777610\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −142809. | −0.384626 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 477908. | 1.24984 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 432894. | 1.09968 | 0.549840 | − | 0.835270i | \(-0.314689\pi\) | ||||
0.549840 | + | 0.835270i | \(0.314689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −56424.0 | −0.139274 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 337520. | 0.809779 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 559620. | 1.30545 | 0.652726 | − | 0.757594i | \(-0.273625\pi\) | ||||
0.652726 | + | 0.757594i | \(0.273625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 604710. | 1.37199 | 0.685995 | − | 0.727607i | \(-0.259367\pi\) | ||||
0.685995 | + | 0.727607i | \(0.259367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −369640. | −0.815927 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −764124. | −1.64148 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −148552. | −0.310652 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 41280.0 | 0.0840592 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −409152. | −0.811524 | −0.405762 | − | 0.913979i | \(-0.632994\pi\) | ||||
−0.405762 | + | 0.913979i | \(0.632994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 540866. | 1.04519 | 0.522596 | − | 0.852580i | \(-0.324963\pi\) | ||||
0.522596 | + | 0.852580i | \(0.324963\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −707440. | −1.33230 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −629898. | −1.15639 | −0.578195 | − | 0.815898i | \(-0.696243\pi\) | ||||
−0.578195 | + | 0.815898i | \(0.696243\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 283048. | 0.506673 | 0.253336 | − | 0.967378i | \(-0.418472\pi\) | ||||
0.253336 | + | 0.967378i | \(0.418472\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −310640. | −0.542335 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 78768.0 | 0.134156 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 657564. | 1.09283 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 28888.0 | 0.0468588 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 377456. | 0.597724 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 142756. | 0.220744 | 0.110372 | − | 0.993890i | \(-0.464796\pi\) | ||||
0.110372 | + | 0.993890i | \(0.464796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −639200. | −0.965357 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 679912. | 1.00313 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 137472. | 0.198182 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −97720.0 | −0.137681 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −572644. | −0.788686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 889696. | 1.19806 | 0.599031 | − | 0.800726i | \(-0.295553\pi\) | ||||
0.599031 | + | 0.800726i | \(0.295553\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 369107. | 0.486067 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.14316e6 | 1.47245 | 0.736226 | − | 0.676736i | \(-0.236606\pi\) | ||||
0.736226 | + | 0.676736i | \(0.236606\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −695786. | −0.876773 | −0.438386 | − | 0.898787i | \(-0.644450\pi\) | ||||
−0.438386 | + | 0.898787i | \(0.644450\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −59520.0 | −0.0733893 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −347126. | −0.418887 | −0.209444 | − | 0.977821i | \(-0.567165\pi\) | ||||
−0.209444 | + | 0.977821i | \(0.567165\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.75114e6 | −2.06847 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 891200. | 1.03063 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.64296e6 | −1.86051 | −0.930255 | − | 0.366912i | \(-0.880415\pi\) | ||||
−0.930255 | + | 0.366912i | \(0.880415\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.16744e6 | −1.29477 | −0.647383 | − | 0.762165i | \(-0.724137\pi\) | ||||
−0.647383 | + | 0.762165i | \(0.724137\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.03306e6 | −1.12230 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.20109e6 | 1.27839 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.45503e6 | 1.51751 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.34728e6 | 1.37708 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −790612. | −0.792098 | −0.396049 | − | 0.918229i | \(-0.629619\pi\) | ||||
−0.396049 | + | 0.918229i | \(0.629619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22816.0 | 0.0224098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.77304e6 | 1.70753 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −129790. | −0.122577 | −0.0612884 | − | 0.998120i | \(-0.519521\pi\) | ||||
−0.0612884 | + | 0.998120i | \(0.519521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −247824. | −0.229559 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −515274. | −0.468206 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 70888.0 | 0.0631951 | 0.0315975 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315975 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −864764. | −0.756455 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.43988e6 | 1.23608 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.79017e6 | 1.50839 | 0.754197 | − | 0.656649i | \(-0.228027\pi\) | ||||
0.754197 | + | 0.656649i | \(0.228027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.77362e6 | −1.46702 | −0.733511 | − | 0.679678i | \(-0.762120\pi\) | ||||
−0.733511 | + | 0.679678i | \(0.762120\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −229440. | −0.186321 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 291524. | 0.232457 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −275450. | −0.215697 | −0.107848 | − | 0.994167i | \(-0.534396\pi\) | ||||
−0.107848 | + | 0.994167i | \(0.534396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −899296. | −0.691659 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 594170. | 0.448895 | 0.224448 | − | 0.974486i | \(-0.427942\pi\) | ||||
0.224448 | + | 0.974486i | \(0.427942\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.09243e6 | 0.810824 | 0.405412 | − | 0.914134i | \(-0.367128\pi\) | ||||
0.405412 | + | 0.914134i | \(0.367128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.50512e6 | −3.28545 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 213264. | 0.152831 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15347.0 | 0.0108088 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 977320. | 0.676557 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 333654. | 0.227053 | 0.113527 | − | 0.993535i | \(-0.463785\pi\) | ||||
0.113527 | + | 0.993535i | \(0.463785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.24882e6 | −0.835500 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −213280. | −0.140300 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 87952.0 | 0.0568942 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 220512. | 0.140287 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.03212e6 | 0.645838 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.36767e6 | 0.841843 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.05997e6 | 0.641872 | 0.320936 | − | 0.947101i | \(-0.396003\pi\) | ||||
0.320936 | + | 0.947101i | \(0.396003\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.60848e6 | 2.14995 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.33649e6 | −0.783545 | −0.391773 | − | 0.920062i | \(-0.628138\pi\) | ||||
−0.391773 | + | 0.920062i | \(0.628138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.64419e6 | 0.948615 | 0.474308 | − | 0.880359i | \(-0.342698\pi\) | ||||
0.474308 | + | 0.880359i | \(0.342698\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 278832. | 0.158331 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.72370e6 | −0.963414 | −0.481707 | − | 0.876332i | \(-0.659983\pi\) | ||||
−0.481707 | + | 0.876332i | \(0.659983\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −406968. | −0.223915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.31400e6 | −0.711759 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.64671e6 | −1.94489 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.12378e6 | 0.590163 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.25412e6 | −1.16576 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −567936. | −0.289274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74963e6 | 1.37944 | 0.689722 | − | 0.724074i | \(-0.257733\pi\) | ||||
0.689722 | + | 0.724074i | \(0.257733\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.62118e6 | 0.801164 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.14937e6 | 0.559561 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.41489e6 | −1.63796 | −0.818978 | − | 0.573824i | \(-0.805459\pi\) | ||||
−0.818978 | + | 0.573824i | \(0.805459\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −470040. | −0.222145 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −710272. | −0.330780 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 792912. | 0.363906 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −272320. | −0.123178 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 730764. | 0.325802 | 0.162901 | − | 0.986642i | \(-0.447915\pi\) | ||||
0.162901 | + | 0.986642i | \(0.447915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.29749e6 | −1.00969 | −0.504847 | − | 0.863209i | \(-0.668451\pi\) | ||||
−0.504847 | + | 0.863209i | \(0.668451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −822160. | −0.356196 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.17072e6 | −0.500052 | −0.250026 | − | 0.968239i | \(-0.580439\pi\) | ||||
−0.250026 | + | 0.968239i | \(0.580439\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.36504e6 | 0.996019 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 575040. | 0.238796 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.88654e6 | 1.59157 | 0.795787 | − | 0.605577i | \(-0.207058\pi\) | ||||
0.795787 | + | 0.605577i | \(0.207058\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.78984e6 | 2.74215 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.91350e6 | −1.16051 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 361564. | 0.142054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 933040. | 0.361606 | 0.180803 | − | 0.983519i | \(-0.442130\pi\) | ||||
0.180803 | + | 0.983519i | \(0.442130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.39510e6 | −0.533384 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −280464. | −0.105789 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −392218. | −0.145967 | −0.0729836 | − | 0.997333i | \(-0.523252\pi\) | ||||
−0.0729836 | + | 0.997333i | \(0.523252\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.14552e6 | 0.420653 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.56880e6 | −0.568477 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.72930e6 | −1.69122 | −0.845608 | − | 0.533805i | \(-0.820762\pi\) | ||||
−0.845608 | + | 0.533805i | \(0.820762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.89184e6 | −0.667686 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.89734e6 | 0.660920 | 0.330460 | − | 0.943820i | \(-0.392796\pi\) | ||||
0.330460 | + | 0.943820i | \(0.392796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 220224. | 0.0757204 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.44252e6 | −0.489602 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.72295e6 | −1.24742 | −0.623711 | − | 0.781655i | \(-0.714376\pi\) | ||||
−0.623711 | + | 0.781655i | \(0.714376\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −220432. | −0.0729177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.40584e6 | 0.459150 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.29744e6 | −1.06337 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.33808e6 | 1.06297 | 0.531484 | − | 0.847068i | \(-0.321635\pi\) | ||||
0.531484 | + | 0.847068i | \(0.321635\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.46112e6 | −0.459466 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.27490e6 | 1.32759 | 0.663796 | − | 0.747913i | \(-0.268944\pi\) | ||||
0.663796 | + | 0.747913i | \(0.268944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.73798e6 | −0.839785 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.36877e6 | 1.62644 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.28042e6 | 0.383149 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.57319e6 | −0.760613 | −0.380306 | − | 0.924861i | \(-0.624181\pi\) | ||||
−0.380306 | + | 0.924861i | \(0.624181\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.54580e6 | 1.61942 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −405024. | −0.116844 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.98494e6 | −1.42082 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.60616e6 | −0.733941 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.26828e6 | 1.46600 | 0.732999 | − | 0.680230i | \(-0.238120\pi\) | ||||
0.732999 | + | 0.680230i | \(0.238120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −973354. | −0.267649 | −0.133824 | − | 0.991005i | \(-0.542726\pi\) | ||||
−0.133824 | + | 0.991005i | \(0.542726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.71525e6 | 1.00957 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.81650e6 | −0.756375 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 443568. | 0.117731 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.18544e6 | 0.310983 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.55736e6 | 0.922433 | 0.461216 | − | 0.887288i | \(-0.347413\pi\) | ||||
0.461216 | + | 0.887288i | \(0.347413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.95496e6 | −0.501092 | −0.250546 | − | 0.968105i | \(-0.580610\pi\) | ||||
−0.250546 | + | 0.968105i | \(0.580610\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.85736e6 | 1.23077 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 560096. | 0.140300 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.29681e6 | −0.816455 | −0.408228 | − | 0.912880i | \(-0.633853\pi\) | ||||
−0.408228 | + | 0.912880i | \(0.633853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.54827e6 | −0.623948 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.05820e6 | −1.22458 | −0.612289 | − | 0.790634i | \(-0.709751\pi\) | ||||
−0.612289 | + | 0.790634i | \(0.709751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.32756e6 | −1.27535 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.03060e6 | −1.90099 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.12730e6 | 0.497981 | 0.248990 | − | 0.968506i | \(-0.419901\pi\) | ||||
0.248990 | + | 0.968506i | \(0.419901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.10186e6 | −0.255086 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.51952e6 | −0.347905 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 848928. | 0.192239 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 289130. | 0.0647594 | 0.0323797 | − | 0.999476i | \(-0.489691\pi\) | ||||
0.0323797 | + | 0.999476i | \(0.489691\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.06056e6 | 0.456513 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.66870e6 | 0.584854 | 0.292427 | − | 0.956288i | \(-0.405537\pi\) | ||||
0.292427 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.58619e6 | 1.64464 | 0.822321 | − | 0.569024i | \(-0.192679\pi\) | ||||
0.822321 | + | 0.569024i | \(0.192679\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.47744e6 | 1.81816 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.41961e6 | −0.301216 | −0.150608 | − | 0.988594i | \(-0.548123\pi\) | ||||
−0.150608 | + | 0.988594i | \(0.548123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 372768. | 0.0782540 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.88644e6 | −1.63806 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.13931e6 | −0.234148 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.15644e6 | 1.45534 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.83470e6 | 0.369207 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.88406e6 | −0.375195 | −0.187597 | − | 0.982246i | \(-0.560070\pi\) | ||||
−0.187597 | + | 0.982246i | \(0.560070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.93583e6 | 0.972741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −88320.0 | −0.0172263 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.61608e6 | −0.698046 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.01388e6 | −1.14903 | −0.574516 | − | 0.818493i | \(-0.694810\pi\) | ||||
−0.574516 | + | 0.818493i | \(0.694810\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −234480. | −0.0443439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.29232e6 | 0.803504 | 0.401752 | − | 0.915749i | \(-0.368401\pi\) | ||||
0.401752 | + | 0.915749i | \(0.368401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.93184e6 | 0.728581 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.44063e6 | −0.264265 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 767040. | 0.139292 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.34509e6 | 0.241825 | 0.120912 | − | 0.992663i | \(-0.461418\pi\) | ||||
0.120912 | + | 0.992663i | \(0.461418\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.10386e7 | −1.96480 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 202008. | 0.0355999 | 0.0177999 | − | 0.999842i | \(-0.494334\pi\) | ||||
0.0177999 | + | 0.999842i | \(0.494334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.81884e6 | −0.666352 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.85618e6 | −0.493476 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.78344e6 | 1.67377 | 0.836887 | − | 0.547375i | \(-0.184373\pi\) | ||||
0.836887 | + | 0.547375i | \(0.184373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 117264. | 0.0198661 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.23568e6 | −0.878374 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.33514e7 | −2.21824 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.93434e6 | 0.482818 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.65788e6 | 1.41089 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.04830e7 | −1.69197 | −0.845985 | − | 0.533207i | \(-0.820987\pi\) | ||||
−0.845985 | + | 0.533207i | \(0.820987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.21017e6 | 0.992772 | 0.496386 | − | 0.868102i | \(-0.334660\pi\) | ||||
0.496386 | + | 0.868102i | \(0.334660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.12848e6 | −0.178688 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.86214e6 | 1.07630 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.40249e6 | −0.994740 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.64953e6 | 0.407787 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24751e6 | −0.647614 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.86180e6 | 0.734366 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.11924e7 | 1.67489 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.01264e6 | −0.298397 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.08088e6 | 0.746355 | 0.373178 | − | 0.927760i | \(-0.378268\pi\) | ||||
0.373178 | + | 0.927760i | \(0.378268\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.20942e7 | 1.76026 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.34024e6 | 1.20278 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.34687e6 | 0.478267 | 0.239133 | − | 0.970987i | \(-0.423137\pi\) | ||||
0.239133 | + | 0.970987i | \(0.423137\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.90167e6 | −0.410883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.99041e6 | −1.40186 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.06944e6 | −0.148711 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.52825e7 | −2.10601 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.00377e6 | 0.956520 | 0.478260 | − | 0.878218i | \(-0.341268\pi\) | ||||
0.478260 | + | 0.878218i | \(0.341268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.39186e6 | −0.594456 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.97104e6 | −0.398567 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.29819e7 | −1.72610 | −0.863052 | − | 0.505116i | \(-0.831450\pi\) | ||||
−0.863052 | + | 0.505116i | \(0.831450\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.73915e6 | 0.229200 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.74122e6 | 0.227456 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.89942e6 | 0.245946 | 0.122973 | − | 0.992410i | \(-0.460757\pi\) | ||||
0.122973 | + | 0.992410i | \(0.460757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.66300e6 | −0.213452 | −0.106726 | − | 0.994288i | \(-0.534037\pi\) | ||||
−0.106726 | + | 0.994288i | \(0.534037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.18304e6 | −1.04119 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 432584. | 0.0545633 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.77344e6 | 1.09706 | 0.548530 | − | 0.836131i | \(-0.315188\pi\) | ||||
0.548530 | + | 0.836131i | \(0.315188\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.08173e7 | 1.34098 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.61674e6 | −0.198700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.44906e6 | 0.176570 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.55340e6 | −0.670918 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.18393e6 | 0.620961 | 0.310480 | − | 0.950580i | \(-0.399510\pi\) | ||||
0.310480 | + | 0.950580i | \(0.399510\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.74360e7 | −2.07090 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.25980e7 | −1.48365 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.49858e6 | 0.992452 | 0.496226 | − | 0.868193i | \(-0.334719\pi\) | ||||
0.496226 | + | 0.868193i | \(0.334719\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.12765e6 | −0.246381 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.66096e6 | 0.650061 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.12471e7 | 1.28078 | 0.640388 | − | 0.768051i | \(-0.278773\pi\) | ||||
0.640388 | + | 0.768051i | \(0.278773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.46439e6 | −0.391238 | −0.195619 | − | 0.980680i | \(-0.562672\pi\) | ||||
−0.195619 | + | 0.980680i | \(0.562672\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.43852e6 | −0.273108 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.07799e7 | 1.19737 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −999712. | −0.110129 | −0.0550647 | − | 0.998483i | \(-0.517537\pi\) | ||||
−0.0550647 | + | 0.998483i | \(0.517537\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.57536e6 | 0.172122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.13114e7 | 1.22578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.81340e6 | 1.05480 | 0.527398 | − | 0.849619i | \(-0.323168\pi\) | ||||
0.527398 | + | 0.849619i | \(0.323168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.31513e7 | 1.40210 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.34745e6 | −0.565501 | −0.282751 | − | 0.959193i | \(-0.591247\pi\) | ||||
−0.282751 | + | 0.959193i | \(0.591247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.82768e6 | −0.716221 | −0.358110 | − | 0.933679i | \(-0.616579\pi\) | ||||
−0.358110 | + | 0.933679i | \(0.616579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −316480. | −0.0329319 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.72786e6 | −0.178356 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.15853e7 | −1.18633 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.54912e6 | 0.766880 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.23705e7 | −1.24670 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.60970e6 | −0.360909 | −0.180455 | − | 0.983583i | \(-0.557757\pi\) | ||||
−0.180455 | + | 0.983583i | \(0.557757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.85512e6 | 0.283214 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.99981e6 | 0.688893 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.75842e6 | −0.757573 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.01772e6 | −0.486132 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.33853e7 | −1.28672 | −0.643361 | − | 0.765563i | \(-0.722460\pi\) | ||||
−0.643361 | + | 0.765563i | \(0.722460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.91115e6 | −0.945358 | −0.472679 | − | 0.881235i | \(-0.656713\pi\) | ||||
−0.472679 | + | 0.881235i | \(0.656713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.35982e7 | 1.28701 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.78359e7 | −1.67508 | −0.837539 | − | 0.546378i | \(-0.816006\pi\) | ||||
−0.837539 | + | 0.546378i | \(0.816006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.09262e6 | 0.195020 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.74944e6 | 0.254268 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.32323e6 | −0.396758 | −0.198379 | − | 0.980125i | \(-0.563568\pi\) | ||||
−0.198379 | + | 0.980125i | \(0.563568\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.20161e6 | −0.473734 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −767102. | −0.0693330 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.97858e7 | 1.77476 | 0.887382 | − | 0.461035i | \(-0.152522\pi\) | ||||
0.887382 | + | 0.461035i | \(0.152522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57772e7 | 1.40451 | 0.702255 | − | 0.711925i | \(-0.252176\pi\) | ||||
0.702255 | + | 0.711925i | \(0.252176\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.14529e7 | −1.01188 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.40614e6 | 0.474060 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −603888. | −0.0525584 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.77939e7 | 1.53711 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.29177e6 | −0.196501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.78762e6 | 0.577670 | 0.288835 | − | 0.957379i | \(-0.406732\pi\) | ||||
0.288835 | + | 0.957379i | \(0.406732\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.04372e6 | −0.341603 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.49942e7 | −1.25734 | −0.628669 | − | 0.777673i | \(-0.716400\pi\) | ||||
−0.628669 | + | 0.777673i | \(0.716400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.17278e6 | −0.0976211 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.28631e7 | 1.88916 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.15580e7 | 0.948053 | 0.474026 | − | 0.880511i | \(-0.342800\pi\) | ||||
0.474026 | + | 0.880511i | \(0.342800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.05195e7 | −1.67086 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.39157e7 | −1.12490 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.58591e6 | 0.448276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −220156. | −0.0175402 | −0.00877012 | − | 0.999962i | \(-0.502792\pi\) | ||||
−0.00877012 | + | 0.999962i | \(0.502792\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −467232. | −0.0369572 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.64279e6 | 0.757253 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.06454e7 | 0.830006 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.94252e6 | −0.537433 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.78933e6 | 0.368111 | 0.184056 | − | 0.982916i | \(-0.441077\pi\) | ||||
0.184056 | + | 0.982916i | \(0.441077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.14323e7 | 2.39877 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.50227e7 | −2.65385 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.23854e6 | −0.0931886 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.26892e6 | 0.318935 | 0.159468 | − | 0.987203i | \(-0.449022\pi\) | ||||
0.159468 | + | 0.987203i | \(0.449022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.99592e6 | 0.519004 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.05395e6 | −0.0776421 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.38613e6 | −0.320860 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.28592e7 | −2.38704 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.61960e7 | −1.16838 | −0.584190 | − | 0.811617i | \(-0.698588\pi\) | ||||
−0.584190 | + | 0.811617i | \(0.698588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.33018e6 | −0.310218 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.33488e7 | −1.66119 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.71598e6 | −0.545188 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.53426e6 | 0.458522 | 0.229261 | − | 0.973365i | \(-0.426369\pi\) | ||||
0.229261 | + | 0.973365i | \(0.426369\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.03131e6 | −0.211257 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.10072e7 | 0.761876 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.31617e7 | 0.904800 | 0.452400 | − | 0.891815i | \(-0.350568\pi\) | ||||
0.452400 | + | 0.891815i | \(0.350568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.40219e7 | 1.64017 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.92597e6 | −0.130611 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.42348e7 | −0.958825 | −0.479412 | − | 0.877590i | \(-0.659150\pi\) | ||||
−0.479412 | + | 0.877590i | \(0.659150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.91006e7 | 1.94696 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.15835e7 | −1.43434 | −0.717168 | − | 0.696901i | \(-0.754562\pi\) | ||||
−0.717168 | + | 0.696901i | \(0.754562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.97132e7 | 1.96137 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.05761e7 | 0.693467 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.57680e6 | 0.102700 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.86594e7 | 1.20725 | 0.603625 | − | 0.797268i | \(-0.293722\pi\) | ||||
0.603625 | + | 0.797268i | \(0.293722\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.58122e7 | −1.01626 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.62222e6 | 0.358956 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.56681e6 | −0.162800 | −0.0813999 | − | 0.996682i | \(-0.525939\pi\) | ||||
−0.0813999 | + | 0.996682i | \(0.525939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 456320. | 0.0287518 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.59586e7 | −1.62487 | −0.812436 | − | 0.583051i | \(-0.801859\pi\) | ||||
−0.812436 | + | 0.583051i | \(0.801859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.70494e6 | 0.168208 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.39184e7 | 0.859874 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.06673e6 | 0.495118 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.53267e6 | 0.337380 | 0.168690 | − | 0.985669i | \(-0.446046\pi\) | ||||
0.168690 | + | 0.985669i | \(0.446046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.59580e6 | −0.157266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.32940e6 | 0.501378 | 0.250689 | − | 0.968068i | \(-0.419343\pi\) | ||||
0.250689 | + | 0.968068i | \(0.419343\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.34665e7 | −0.805381 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.95648e6 | −0.294524 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.70490e7 | −1.59701 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.96304e6 | −0.232488 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.64504e6 | 0.329051 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.91798e7 | 1.69009 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.36523e7 | −0.785719 | −0.392860 | − | 0.919598i | \(-0.628514\pi\) | ||||
−0.392860 | + | 0.919598i | \(0.628514\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.41776e6 | 0.0810793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 564048. | 0.0320535 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.83440e6 | −0.498877 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.72953e7 | −0.970532 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.54626e6 | −0.476574 | −0.238287 | − | 0.971195i | \(-0.576586\pi\) | ||||
−0.238287 | + | 0.971195i | \(0.576586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.83495e7 | −1.57101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.13031e7 | 0.622465 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −605864. | −0.0331578 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 326784. | 0.0177734 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.58035e7 | 1.93527 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.58484e6 | 0.407451 | 0.203725 | − | 0.979028i | \(-0.434695\pi\) | ||||
0.203725 | + | 0.979028i | \(0.434695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.18473e6 | 0.330194 | 0.165097 | − | 0.986277i | \(-0.447206\pi\) | ||||
0.165097 | + | 0.986277i | \(0.447206\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.54723e7 | −1.88219 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 867576. | 0.0457524 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.79683e7 | −1.46592 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.80110e6 | −0.0938273 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.78102e6 | −0.143995 | −0.0719973 | − | 0.997405i | \(-0.522937\pi\) | ||||
−0.0719973 | + | 0.997405i | \(0.522937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.63895e7 | 0.843461 | 0.421731 | − | 0.906721i | \(-0.361423\pi\) | ||||
0.421731 | + | 0.906721i | \(0.361423\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.83048e6 | 0.298242 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.29511e7 | 1.16692 | 0.583459 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583459 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.50136e6 | −0.176950 | −0.0884750 | − | 0.996078i | \(-0.528199\pi\) | ||||
−0.0884750 | + | 0.996078i | \(0.528199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.50900e6 | −0.276739 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.94447e7 | 0.970934 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.08427e7 | 2.02721 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.85216e6 | 0.486091 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.29668e6 | 0.259776 | 0.129888 | − | 0.991529i | \(-0.458538\pi\) | ||||
0.129888 | + | 0.991529i | \(0.458538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.73962e6 | −0.474845 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.18834e7 | 0.575933 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.05679e7 | 0.509150 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.49620e6 | 0.167451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.18486e7 | 1.04029 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.89998e6 | 0.0899344 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.02948e7 | −0.955021 | −0.477511 | − | 0.878626i | \(-0.658461\pi\) | ||||
−0.477511 | + | 0.878626i | \(0.658461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.53652e7 | −1.65448 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.82785e6 | −0.224544 | −0.112272 | − | 0.993678i | \(-0.535813\pi\) | ||||
−0.112272 | + | 0.993678i | \(0.535813\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.30210e7 | −0.602092 | −0.301046 | − | 0.953610i | \(-0.597336\pi\) | ||||
−0.301046 | + | 0.953610i | \(0.597336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.26528e6 | 0.196083 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.92387e7 | −1.79344 | −0.896721 | − | 0.442596i | \(-0.854058\pi\) | ||||
−0.896721 | + | 0.442596i | \(0.854058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.20342e7 | −1.45570 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 306940. | 0.0138677 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.52544e6 | 0.248209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.42430e6 | −0.331596 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.67196e6 | 0.340699 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.37462e6 | −0.0606965 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.34622e7 | 0.591041 | 0.295520 | − | 0.955336i | \(-0.404507\pi\) | ||||
0.295520 | + | 0.955336i | \(0.404507\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.67308e6 | 0.291309 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −917710. | −0.0398351 | −0.0199175 | − | 0.999802i | \(-0.506340\pi\) | ||||
−0.0199175 | + | 0.999802i | \(0.506340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.45488e7 | 1.05957 | 0.529784 | − | 0.848133i | \(-0.322273\pi\) | ||||
0.529784 | + | 0.848133i | \(0.322273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.49765e7 | −1.07195 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.61463e7 | −0.689070 | −0.344535 | − | 0.938773i | \(-0.611963\pi\) | ||||
−0.344535 | + | 0.938773i | \(0.611963\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.27021e6 | 0.0963410 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.99632e6 | −0.379639 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.20332e7 | 3.02276 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.14119e7 | −1.72809 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.75904e6 | 0.0729953 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.87993e7 | 0.775787 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.39998e7 | −0.574527 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.41024e6 | 0.179988 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.47485e7 | −1.81617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.03361e7 | −0.820824 | −0.410412 | − | 0.911900i | \(-0.634615\pi\) | ||||
−0.410412 | + | 0.911900i | \(0.634615\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.10214e6 | 0.325230 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.07726e7 | 0.430054 | 0.215027 | − | 0.976608i | \(-0.431016\pi\) | ||||
0.215027 | + | 0.976608i | \(0.431016\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.35314e6 | 0.331644 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.73534e7 | 1.08009 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.68701e6 | −0.0662512 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.18566e7 | 1.63484 | 0.817419 | − | 0.576043i | \(-0.195404\pi\) | ||||
0.817419 | + | 0.576043i | \(0.195404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.11994e7 | 0.823522 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.52769e7 | −0.590242 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.42764e7 | 0.932890 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.83266e7 | 1.08267 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.99845e7 | 1.13988 | 0.569939 | − | 0.821687i | \(-0.306967\pi\) | ||||
0.569939 | + | 0.821687i | \(0.306967\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.94072e7 | −1.86817 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.67298e7 | −1.00529 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.09928e7 | 0.411227 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.42402e7 | 0.529867 | 0.264934 | − | 0.964267i | \(-0.414650\pi\) | ||||
0.264934 | + | 0.964267i | \(0.414650\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.28837e7 | 1.21707 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.14546e7 | −1.52615 | −0.763077 | − | 0.646307i | \(-0.776313\pi\) | ||||
−0.763077 | + | 0.646307i | \(0.776313\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.63502e6 | −0.0598749 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.05472e6 | −0.111274 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.54079e7 | −0.558300 | −0.279150 | − | 0.960248i | \(-0.590053\pi\) | ||||
−0.279150 | + | 0.960248i | \(0.590053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.33551e6 | −0.0841813 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.44740e7 | −1.23606 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.06328e7 | −0.735912 | −0.367956 | − | 0.929843i | \(-0.619942\pi\) | ||||
−0.367956 | + | 0.929843i | \(0.619942\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.02772e7 | 1.07426 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.13936e6 | −0.287283 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.65496e6 | −0.233668 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.18083e6 | 0.146034 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.03149e7 | −0.358426 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.00241e7 | −1.38358 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.18724e7 | 0.408294 | 0.204147 | − | 0.978940i | \(-0.434558\pi\) | ||||
0.204147 | + | 0.978940i | \(0.434558\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.29342e7 | −2.49530 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.53222e6 | 0.0521523 | 0.0260761 | − | 0.999660i | \(-0.491699\pi\) | ||||
0.0260761 | + | 0.999660i | \(0.491699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.12739e6 | 0.105901 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.24756e7 | 0.757180 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.74321e7 | 0.584269 | 0.292135 | − | 0.956377i | \(-0.405635\pi\) | ||||
0.292135 | + | 0.956377i | \(0.405635\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.92726e6 | 0.297688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.76948e7 | −0.587049 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.23270e6 | 0.0736963 | 0.0368482 | − | 0.999321i | \(-0.488268\pi\) | ||||
0.0368482 | + | 0.999321i | \(0.488268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.66125e7 | 1.53078 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.13587e7 | −0.371139 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.69059e6 | −0.0549602 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.22501e7 | 0.719693 | 0.359847 | − | 0.933011i | \(-0.382829\pi\) | ||||
0.359847 | + | 0.933011i | \(0.382829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.49926e7 | 1.76983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.09456e7 | −0.670709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.32662e7 | 1.69712 | 0.848562 | − | 0.529095i | \(-0.177469\pi\) | ||||
0.848562 | + | 0.529095i | \(0.177469\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.77607e7 | −0.563050 |
(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 | 8.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 72.6.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 16.6.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 200.6.c.a.49.1 | 2 | |||
5.3 | odd | 4 | 200.6.c.a.49.2 | 2 | |||
5.4 | even | 2 | 200.6.a.a.1.1 | 1 | |||
7.2 | even | 3 | 392.6.i.b.361.1 | 2 | |||
7.3 | odd | 6 | 392.6.i.e.177.1 | 2 | |||
7.4 | even | 3 | 392.6.i.b.177.1 | 2 | |||
7.5 | odd | 6 | 392.6.i.e.361.1 | 2 | |||
7.6 | odd | 2 | 392.6.a.b.1.1 | 1 | |||
8.3 | odd | 2 | 64.6.a.g.1.1 | 1 | |||
8.5 | even | 2 | 64.6.a.a.1.1 | 1 | |||
11.10 | odd | 2 | 968.6.a.a.1.1 | 1 | |||
12.11 | even | 2 | 144.6.a.k.1.1 | 1 | |||
16.3 | odd | 4 | 256.6.b.d.129.1 | 2 | |||
16.5 | even | 4 | 256.6.b.f.129.1 | 2 | |||
16.11 | odd | 4 | 256.6.b.d.129.2 | 2 | |||
16.13 | even | 4 | 256.6.b.f.129.2 | 2 | |||
20.3 | even | 4 | 400.6.c.d.49.1 | 2 | |||
20.7 | even | 4 | 400.6.c.d.49.2 | 2 | |||
20.19 | odd | 2 | 400.6.a.l.1.1 | 1 | |||
24.5 | odd | 2 | 576.6.a.g.1.1 | 1 | |||
24.11 | even | 2 | 576.6.a.h.1.1 | 1 | |||
28.27 | even | 2 | 784.6.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.6.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
64.6.a.a.1.1 | 1 | 8.5 | even | 2 | |||
64.6.a.g.1.1 | 1 | 8.3 | odd | 2 | |||
72.6.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
144.6.a.k.1.1 | 1 | 12.11 | even | 2 | |||
200.6.a.a.1.1 | 1 | 5.4 | even | 2 | |||
200.6.c.a.49.1 | 2 | 5.2 | odd | 4 | |||
200.6.c.a.49.2 | 2 | 5.3 | odd | 4 | |||
256.6.b.d.129.1 | 2 | 16.3 | odd | 4 | |||
256.6.b.d.129.2 | 2 | 16.11 | odd | 4 | |||
256.6.b.f.129.1 | 2 | 16.5 | even | 4 | |||
256.6.b.f.129.2 | 2 | 16.13 | even | 4 | |||
392.6.a.b.1.1 | 1 | 7.6 | odd | 2 | |||
392.6.i.b.177.1 | 2 | 7.4 | even | 3 | |||
392.6.i.b.361.1 | 2 | 7.2 | even | 3 | |||
392.6.i.e.177.1 | 2 | 7.3 | odd | 6 | |||
392.6.i.e.361.1 | 2 | 7.5 | odd | 6 | |||
400.6.a.l.1.1 | 1 | 20.19 | odd | 2 | |||
400.6.c.d.49.1 | 2 | 20.3 | even | 4 | |||
400.6.c.d.49.2 | 2 | 20.7 | even | 4 | |||
576.6.a.g.1.1 | 1 | 24.5 | odd | 2 | |||
576.6.a.h.1.1 | 1 | 24.11 | even | 2 | |||
784.6.a.l.1.1 | 1 | 28.27 | even | 2 | |||
968.6.a.a.1.1 | 1 | 11.10 | odd | 2 |