Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,8,Mod(129,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.129");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(79.9705665239\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.50765497344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 101x^{4} + 2512x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.2 | ||
Root | \(6.65206i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.129 |
Dual form | 256.8.b.l.129.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 51.2165i | − 1.09518i | −0.836747 | − | 0.547590i | \(-0.815545\pi\) | ||||
0.836747 | − | 0.547590i | \(-0.184455\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 145.477i | 0.520473i | 0.965545 | + | 0.260237i | \(0.0838006\pi\) | ||||
−0.965545 | + | 0.260237i | \(0.916199\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 192.521 | 0.212146 | 0.106073 | − | 0.994358i | \(-0.466172\pi\) | ||||
0.106073 | + | 0.994358i | \(0.466172\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −436.129 | −0.199419 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5081.41i | − 1.15109i | −0.817770 | − | 0.575546i | \(-0.804790\pi\) | ||||
0.817770 | − | 0.575546i | \(-0.195210\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9384.12i | 1.18465i | 0.805697 | + | 0.592327i | \(0.201791\pi\) | ||||
−0.805697 | + | 0.592327i | \(0.798209\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7450.81 | 0.570012 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17222.6 | −0.850211 | −0.425105 | − | 0.905144i | \(-0.639763\pi\) | ||||
−0.425105 | + | 0.905144i | \(0.639763\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17236.8i | 0.576527i | 0.957551 | + | 0.288263i | \(0.0930779\pi\) | ||||
−0.957551 | + | 0.288263i | \(0.906922\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 9860.23i | − 0.232337i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18418.0 | −0.315642 | −0.157821 | − | 0.987468i | \(-0.550447\pi\) | ||||
−0.157821 | + | 0.987468i | \(0.550447\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 56961.5 | 0.729107 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 89673.5i | − 0.876780i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 58384.4i | 0.444533i | 0.974986 | + | 0.222266i | \(0.0713455\pi\) | ||||
−0.974986 | + | 0.222266i | \(0.928655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 99913.3 | 0.602362 | 0.301181 | − | 0.953567i | \(-0.402619\pi\) | ||||
0.301181 | + | 0.953567i | \(0.402619\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −260252. | −1.26065 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 28007.3i | 0.110416i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 484307.i | 1.57186i | 0.618314 | + | 0.785931i | \(0.287816\pi\) | ||||
−0.618314 | + | 0.785931i | \(0.712184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 480622. | 1.29741 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −569425. | −1.29031 | −0.645153 | − | 0.764053i | \(-0.723206\pi\) | ||||
−0.645153 | + | 0.764053i | \(0.723206\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 18958.6i | 0.0363636i | 0.999835 | + | 0.0181818i | \(0.00578776\pi\) | ||||
−0.999835 | + | 0.0181818i | \(0.994212\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 63446.6i | − 0.103792i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.22220e6 | −1.71712 | −0.858558 | − | 0.512717i | \(-0.828639\pi\) | ||||
−0.858558 | + | 0.512717i | \(0.828639\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −786479. | −0.954994 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 882079.i | 0.931133i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.64310e6i | 1.51600i | 0.652257 | + | 0.757998i | \(0.273822\pi\) | ||||
−0.652257 | + | 0.757998i | \(0.726178\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 739227. | 0.599113 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 882809. | 0.631400 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 63612.4i | − 0.0403236i | −0.999797 | − | 0.0201618i | \(-0.993582\pi\) | ||||
0.999797 | − | 0.0201618i | \(-0.00641814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.39333e6i | − 0.785960i | −0.919547 | − | 0.392980i | \(-0.871444\pi\) | ||||
0.919547 | − | 0.392980i | \(-0.128556\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −83963.7 | −0.0423058 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.36517e6 | −0.616581 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.02319e6i | 1.22802i | 0.789300 | + | 0.614008i | \(0.210444\pi\) | ||||
−0.789300 | + | 0.614008i | \(0.789556\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 943304.i | 0.345685i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.28271e6 | 1.08850 | 0.544250 | − | 0.838923i | \(-0.316814\pi\) | ||||
0.544250 | + | 0.838923i | \(0.316814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.52034e6 | 1.36001 | 0.680003 | − | 0.733210i | \(-0.261979\pi\) | ||||
0.680003 | + | 0.733210i | \(0.261979\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 2.91737e6i | − 0.798504i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 978276.i | − 0.244199i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.18742e6 | 0.727352 | 0.363676 | − | 0.931525i | \(-0.381521\pi\) | ||||
0.363676 | + | 0.931525i | \(0.381521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.54657e6 | −1.15965 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.31201e6i | 1.40367i | 0.712342 | + | 0.701833i | \(0.247635\pi\) | ||||
−0.712342 | + | 0.701833i | \(0.752365\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.50548e6i | − 0.442512i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.99024e6 | 0.486843 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.55637e6 | 0.534739 | 0.267369 | − | 0.963594i | \(-0.413846\pi\) | ||||
0.267369 | + | 0.963594i | \(0.413846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.80664e6i | 0.251319i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 5.11721e6i | − 0.659695i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.50756e6 | −0.300067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.36320e7 | 1.51656 | 0.758281 | − | 0.651928i | \(-0.226040\pi\) | ||||
0.758281 | + | 0.651928i | \(0.226040\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.21615e6i | 0.229549i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 2.80336e6i | − 0.270741i | −0.990795 | − | 0.135371i | \(-0.956778\pi\) | ||||
0.990795 | − | 0.135371i | \(-0.0432225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.87446e7 | 1.69023 | 0.845116 | − | 0.534582i | \(-0.179531\pi\) | ||||
0.845116 | + | 0.534582i | \(0.179531\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.43443e6 | 0.120926 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.61604e7i | 1.27529i | 0.770331 | + | 0.637644i | \(0.220091\pi\) | ||||
−0.770331 | + | 0.637644i | \(0.779909\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.51664e7i | − 1.12173i | −0.827906 | − | 0.560867i | \(-0.810468\pi\) | ||||
0.827906 | − | 0.560867i | \(-0.189532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.48045e7 | 1.72147 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.70281e6 | 0.502197 | 0.251099 | − | 0.967962i | \(-0.419208\pi\) | ||||
0.251099 | + | 0.967962i | \(0.419208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.67939e6i | − 0.164283i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 4.09268e6i | − 0.236242i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.31570e6 | −0.180368 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.33357e6 | −0.325012 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.91639e7i | 1.41312i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.96519e7i | 0.899954i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.30616e6 | 0.316502 | 0.158251 | − | 0.987399i | \(-0.449415\pi\) | ||||
0.158251 | + | 0.987399i | \(0.449415\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 970993. | 0.0398246 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.64805e7i | 0.640504i | 0.947332 | + | 0.320252i | \(0.103768\pi\) | ||||
−0.947332 | + | 0.320252i | \(0.896232\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.31844e6i | 0.122308i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.30454e7 | 0.456341 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.74046e7 | −1.57506 | −0.787532 | − | 0.616273i | \(-0.788642\pi\) | ||||
−0.787532 | + | 0.616273i | \(0.788642\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.60622e7i | 1.45476i | 0.686233 | + | 0.727382i | \(0.259263\pi\) | ||||
−0.686233 | + | 0.727382i | \(0.740737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.25968e7i | 1.88055i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.76846e7 | 1.36365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.49357e6 | −0.231368 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.02807e7i | 1.04589i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1.97163e7i | − 0.488285i | −0.969739 | − | 0.244142i | \(-0.921494\pi\) | ||||
0.969739 | − | 0.244142i | \(-0.0785064\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.53585e7 | −1.30847 | −0.654237 | − | 0.756289i | \(-0.727010\pi\) | ||||
−0.654237 | + | 0.756289i | \(0.727010\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.51125e6 | 0.169548 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.45351e7i | 0.313513i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.33244e7i | 0.687248i | 0.939107 | + | 0.343624i | \(0.111655\pi\) | ||||
−0.939107 | + | 0.343624i | \(0.888345\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.41537e7 | 1.66029 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.54584e6 | −0.0669620 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.57147e6i | 0.0645938i | 0.999478 | + | 0.0322969i | \(0.0102822\pi\) | ||||
−0.999478 | + | 0.0322969i | \(0.989718\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 3.78606e7i | − 0.656136i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.16844e8 | 1.94133 | 0.970667 | − | 0.240429i | \(-0.0772882\pi\) | ||||
0.970667 | + | 0.240429i | \(0.0772882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.53132e7 | −0.403407 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 7.51747e6i | − 0.114970i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2.83019e7i | − 0.415579i | −0.978174 | − | 0.207790i | \(-0.933373\pi\) | ||||
0.978174 | − | 0.207790i | \(-0.0666270\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.09663e7 | 0.154677 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.25800e6 | −0.0441616 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 7.62530e7i | − 0.993737i | −0.867826 | − | 0.496868i | \(-0.834483\pi\) | ||||
0.867826 | − | 0.496868i | \(-0.165517\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.39175e7i | 0.675857i | 0.941172 | + | 0.337929i | \(0.109726\pi\) | ||||
−0.941172 | + | 0.337929i | \(0.890274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.13616e7 | −0.860768 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.04554e7 | −0.818113 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.75149e7i | 0.978670i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.72640e7i | − 0.186005i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.12934e7 | −0.636498 | −0.318249 | − | 0.948007i | \(-0.603095\pi\) | ||||
−0.318249 | + | 0.948007i | \(0.603095\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.41428e6 | −0.0642239 | −0.0321120 | − | 0.999484i | \(-0.510223\pi\) | ||||
−0.0321120 | + | 0.999484i | \(0.510223\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.99193e7i | 0.675267i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.33319e8i | 1.24240i | 0.783653 | + | 0.621198i | \(0.213354\pi\) | ||||
−0.783653 | + | 0.621198i | \(0.786646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.76933e8 | 1.59156 | 0.795780 | − | 0.605585i | \(-0.207061\pi\) | ||||
0.795780 | + | 0.605585i | \(0.207061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.54837e8 | 1.34490 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.12402e7i | 0.0943057i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 8.28380e7i | − 0.671570i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.03261e6 | 0.0629449 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.75873e7 | 0.663635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.12921e8i | 0.827532i | 0.910383 | + | 0.413766i | \(0.135787\pi\) | ||||
−0.910383 | + | 0.413766i | \(0.864213\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 1.68129e8i | − 1.19210i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.75803e6 | −0.0189263 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.92354e7 | 0.127788 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2.31516e8i | − 1.48945i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.61619e8i | − 1.00721i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.09574e8 | −1.86938 | −0.934689 | − | 0.355465i | \(-0.884322\pi\) | ||||
−0.934689 | + | 0.355465i | \(0.884322\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.48425e7 | −0.145398 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 8.20252e7i | − 0.465433i | −0.972545 | − | 0.232716i | \(-0.925239\pi\) | ||||
0.972545 | − | 0.232716i | \(-0.0747614\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.46442e7i | 0.465772i | 0.972504 | + | 0.232886i | \(0.0748169\pi\) | ||||
−0.972504 | + | 0.232886i | \(0.925183\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.01039e7 | −0.267442 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.29590e8 | 1.18907 | 0.594535 | − | 0.804069i | \(-0.297336\pi\) | ||||
0.594535 | + | 0.804069i | \(0.297336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.77802e8i | − 0.893713i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.63249e8i | − 0.796582i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.29560e7 | 0.203531 | 0.101766 | − | 0.994808i | \(-0.467551\pi\) | ||||
0.101766 | + | 0.994808i | \(0.467551\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.01479e8 | −0.466999 | −0.233499 | − | 0.972357i | \(-0.575018\pi\) | ||||
−0.233499 | + | 0.972357i | \(0.575018\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.79601e7i | 0.393246i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.14414e8i | − 0.497049i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.61752e8 | −0.682985 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.74496e8 | 1.53727 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.44611e8i | − 0.577223i | −0.957446 | − | 0.288612i | \(-0.906806\pi\) | ||||
0.957446 | − | 0.288612i | \(-0.0931936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.35893e7i | 0.363333i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.28322e8 | −0.484630 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.87026e8 | −1.05477 | −0.527383 | − | 0.849628i | \(-0.676827\pi\) | ||||
−0.527383 | + | 0.849628i | \(0.676827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.32390e7i | 0.333464i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2.54631e7i | − 0.0886481i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.41676e8 | −0.819197 | −0.409598 | − | 0.912266i | \(-0.634331\pi\) | ||||
−0.409598 | + | 0.912266i | \(0.634331\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.39033e8 | −0.789035 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.82145e8i | − 0.585635i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.32948e7i | 0.260907i | 0.991454 | + | 0.130453i | \(0.0416433\pi\) | ||||
−0.991454 | + | 0.130453i | \(0.958357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.13948e8 | −0.958221 | −0.479110 | − | 0.877755i | \(-0.659041\pi\) | ||||
−0.479110 | + | 0.877755i | \(0.659041\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.25295e7 | 0.275240 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.89445e8i | − 0.839269i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.19831e8i | 1.18685i | 0.804890 | + | 0.593425i | \(0.202224\pi\) | ||||
−0.804890 | + | 0.593425i | \(0.797776\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.35751e7 | −0.120122 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.77038e8 | −1.01371 | −0.506854 | − | 0.862032i | \(-0.669192\pi\) | ||||
−0.506854 | + | 0.862032i | \(0.669192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7.46059e7i | − 0.195668i | −0.995203 | − | 0.0978341i | \(-0.968809\pi\) | ||||
0.995203 | − | 0.0978341i | \(-0.0311915\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.28428e8i | 0.328627i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.09626e8 | −0.273733 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.13722e8 | −0.277142 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 6.98186e8i | − 1.66091i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.39379e8i | 1.02048i | 0.860033 | + | 0.510238i | \(0.170443\pi\) | ||||
−0.860033 | + | 0.510238i | \(0.829557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.25413e6 | 0.0209874 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.55668e8 | −1.00925 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.72837e8i | − 0.373927i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.64992e6i | 0.00771437i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.43578e8 | −0.296510 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.02698e8 | 0.409071 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 5.09082e8i | − 1.00416i | −0.864821 | − | 0.502081i | \(-0.832568\pi\) | ||||
0.864821 | − | 0.502081i | \(-0.167432\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 9.60034e8i | − 1.85111i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.36937e8 | −0.258143 | −0.129072 | − | 0.991635i | \(-0.541200\pi\) | ||||
−0.129072 | + | 0.991635i | \(0.541200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.83418e8 | −0.338094 | −0.169047 | − | 0.985608i | \(-0.554069\pi\) | ||||
−0.169047 | + | 0.985608i | \(0.554069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1.22148e7i | − 0.0220190i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.69406e8i | 1.35659i | 0.734790 | + | 0.678294i | \(0.237281\pi\) | ||||
−0.734790 | + | 0.678294i | \(0.762719\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.96675e8 | 0.511698 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.27678e8 | 1.39667 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.96862e8i | − 0.490169i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.34534e8i | 0.863740i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.76770e8 | −1.22850 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.35298e8 | −0.364278 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.19278e8i | 0.180785i | 0.995906 | + | 0.0903926i | \(0.0288122\pi\) | ||||
−0.995906 | + | 0.0903926i | \(0.971188\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.11220e8i | − 0.313459i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.39804e8 | −0.639150 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.92823e8 | −0.843763 | −0.421882 | − | 0.906651i | \(-0.638630\pi\) | ||||
−0.421882 | + | 0.906651i | \(0.638630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 3.94511e8i | − 0.549996i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 5.07701e8i | − 0.693374i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.09962e8 | −0.414743 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.37229e8 | −0.179920 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.05723e8i | 0.906736i | 0.891323 | + | 0.453368i | \(0.149778\pi\) | ||||
−0.891323 | + | 0.453368i | \(0.850222\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.96668e8i | 0.499503i | 0.968310 | + | 0.249751i | \(0.0803489\pi\) | ||||
−0.968310 | + | 0.249751i | \(0.919651\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.41507e8 | 1.03868 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.96190e7 | 0.0237392 | 0.0118696 | − | 0.999930i | \(-0.496222\pi\) | ||||
0.0118696 | + | 0.999930i | \(0.496222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.77558e8i | 0.566535i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.69818e8i | 0.197536i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.71544e9 | −1.95680 | −0.978398 | − | 0.206732i | \(-0.933717\pi\) | ||||
−0.978398 | + | 0.206732i | \(0.933717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.96764e8 | 0.667617 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.24383e8i | 0.355947i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.57604e8i | 0.707847i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.54817e8 | −0.163489 | −0.0817444 | − | 0.996653i | \(-0.526049\pi\) | ||||
−0.0817444 | + | 0.996653i | \(0.526049\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.48342e8 | 0.257311 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.16330e8i | 0.321612i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.92398e9i | − 1.91964i | −0.280613 | − | 0.959821i | \(-0.590538\pi\) | ||||
0.280613 | − | 0.959821i | \(-0.409462\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00650e9 | 0.985612 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.47886e8 | −0.526618 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.57142e9i | − 1.48270i | −0.671116 | − | 0.741352i | \(-0.734185\pi\) | ||||
0.671116 | − | 0.741352i | \(-0.265815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 3.74196e8i | − 0.346626i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.75347e8 | 0.796131 | 0.398065 | − | 0.917357i | \(-0.369682\pi\) | ||||
0.398065 | + | 0.917357i | \(0.369682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.42316e8 | 0.127099 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 8.26839e6i | − 0.00725157i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.37884e8i | 0.118765i | 0.998235 | + | 0.0593827i | \(0.0189132\pi\) | ||||
−0.998235 | + | 0.0593827i | \(0.981087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.17205e8 | 0.268362 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.44075e8 | 0.701467 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.63696e8i | 0.378568i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.71487e9i | − 1.37551i | −0.725941 | − | 0.687757i | \(-0.758595\pi\) | ||||
0.725941 | − | 0.687757i | \(-0.241405\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.69959e8 | 0.133949 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.96564e8 | 0.384565 | 0.192283 | − | 0.981340i | \(-0.438411\pi\) | ||||
0.192283 | + | 0.981340i | \(0.438411\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.37599e8i | 0.713591i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 8.06898e8i | − 0.603567i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.46096e9 | 1.80936 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.96571e9 | 1.42065 | 0.710325 | − | 0.703874i | \(-0.248548\pi\) | ||||
0.710325 | + | 0.703874i | \(0.248548\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.42790e9i | 1.72498i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.22467e7i | − 0.00855448i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.06373e9 | −0.730571 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.35914e9 | 1.59323 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.31255e8i | 0.153583i | 0.997047 | + | 0.0767913i | \(0.0244675\pi\) | ||||
−0.997047 | + | 0.0767913i | \(0.975532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.73476e9i | 1.78621i | 0.449851 | + | 0.893103i | \(0.351477\pi\) | ||||
−0.449851 | + | 0.893103i | \(0.648523\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.33036e8 | 0.342425 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.81023e8 | −0.619895 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.68245e8i | − 0.166738i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.44224e9i | − 1.49344i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.59396e8 | 0.396712 | 0.198356 | − | 0.980130i | \(-0.436440\pi\) | ||||
0.198356 | + | 0.980130i | \(0.436440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.84454e9 | −1.09189 | −0.545946 | − | 0.837820i | \(-0.683830\pi\) | ||||
−0.545946 | + | 0.837820i | \(0.683830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.35011e8i | 0.253389i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.17467e8i | − 0.181976i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.34127e9 | 1.32077 | 0.660384 | − | 0.750928i | \(-0.270394\pi\) | ||||
0.660384 | + | 0.750928i | \(0.270394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.43006e8 | 0.190444 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1.69165e9i | − 0.924483i | −0.886754 | − | 0.462241i | \(-0.847045\pi\) | ||||
0.886754 | − | 0.462241i | \(-0.152955\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.17369e8i | 0.278317i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.00980e9 | −0.534760 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.05472e9 | −1.59261 | −0.796304 | − | 0.604897i | \(-0.793214\pi\) | ||||
−0.796304 | + | 0.604897i | \(0.793214\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.89348e9i | 1.48526i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.83527e9i | 1.43301i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.62823e8 | −0.130805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.90086e8 | −0.191185 | −0.0955924 | − | 0.995421i | \(-0.530475\pi\) | ||||
−0.0955924 | + | 0.995421i | \(0.530475\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.54441e9i | 0.745448i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.36426e9i | 0.648550i | 0.945963 | + | 0.324275i | \(0.105120\pi\) | ||||
−0.945963 | + | 0.324275i | \(0.894880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.33810e9 | 0.626551 | 0.313276 | − | 0.949662i | \(-0.398574\pi\) | ||||
0.313276 | + | 0.949662i | \(0.398574\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.44435e8 | 0.343354 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.60450e8i | 0.0729005i | 0.999335 | + | 0.0364503i | \(0.0116051\pi\) | ||||
−0.999335 | + | 0.0364503i | \(0.988395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.82027e8i | 0.260518i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.70676e9 | 0.752660 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.63364e7 | 0.0418578 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.81835e8i | 0.420350i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 7.16602e8i | − 0.302318i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.56265e9 | 1.06541 | 0.532704 | − | 0.846302i | \(-0.321176\pi\) | ||||
0.532704 | + | 0.846302i | \(0.321176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.54479e9 | −1.86211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.81605e8i | 0.0733355i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.98315e9i | 0.789330i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.63335e9 | 1.81779 | 0.908895 | − | 0.417024i | \(-0.136927\pi\) | ||||
0.908895 | + | 0.417024i | \(0.136927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.82918e8 | 0.0707418 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 1.84615e9i | − 0.703854i | −0.936028 | − | 0.351927i | \(-0.885527\pi\) | ||||
0.936028 | − | 0.351927i | \(-0.114473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.00553e9i | − 0.377947i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.22398e8 | −0.119474 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.31989e8 | 0.230920 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.12844e9i | 1.84771i | 0.382746 | + | 0.923854i | \(0.374978\pi\) | ||||
−0.382746 | + | 0.923854i | \(0.625022\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5.98436e9i | − 2.12611i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.60493e9 | −0.912657 | −0.456328 | − | 0.889811i | \(-0.650836\pi\) | ||||
−0.456328 | + | 0.889811i | \(0.650836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.07824e8 | 0.140914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.29645e9i | 0.441803i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.90571e9i | 1.98500i | 0.122261 | + | 0.992498i | \(0.460985\pi\) | ||||
−0.122261 | + | 0.992498i | \(0.539015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.70257e8 | 0.288519 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.54569e9 | 0.505487 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.72691e9i | 0.879721i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.21050e9i | 1.97656i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.44952e9 | −0.455134 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.11569e9 | 0.345629 | 0.172815 | − | 0.984954i | \(-0.444714\pi\) | ||||
0.172815 | + | 0.984954i | \(0.444714\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.12256e8i | − 0.126012i | −0.998013 | − | 0.0630059i | \(-0.979931\pi\) | ||||
0.998013 | − | 0.0630059i | \(-0.0200687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 5.61653e8i | − 0.169399i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.72076e9 | −0.512135 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.06560e9 | −0.900370 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.77432e7i | 0.00804129i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 5.34355e9i | − 1.52857i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.35096e9 | −0.663753 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.90541e9 | −1.08832 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.99642e9i | 1.09929i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.94914e8i | 0.215839i | 0.994160 | + | 0.107919i | \(0.0344189\pi\) | ||||
−0.994160 | + | 0.107919i | \(0.965581\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.76147e9 | 0.740185 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.20636e9 | 0.583833 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 5.28117e9i | − 1.37967i | −0.723967 | − | 0.689834i | \(-0.757683\pi\) | ||||
0.723967 | − | 0.689834i | \(-0.242317\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.07672e8i | 0.156735i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00636e9 | −0.256285 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.13644e8 | 0.154305 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.60848e9i | 0.895980i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.63862e9i | − 1.38254i | −0.722594 | − | 0.691272i | \(-0.757050\pi\) | ||||
0.722594 | − | 0.691272i | \(-0.242950\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.77910e8 | −0.0430783 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.48221e9 | 1.07182 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7.06564e9i | − 1.66868i | −0.551252 | − | 0.834338i | \(-0.685850\pi\) | ||||
0.551252 | − | 0.834338i | \(-0.314150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.12058e9i | 0.261380i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.06783e9 | −0.246015 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.40034e9 | −1.00137 | −0.500684 | − | 0.865630i | \(-0.666918\pi\) | ||||
−0.500684 | + | 0.865630i | \(0.666918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4.60968e9i | − 1.03620i | −0.855319 | − | 0.518101i | \(-0.826639\pi\) | ||||
0.855319 | − | 0.518101i | \(-0.173361\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.13923e9i | 0.697079i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.04912e9 | −0.230137 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.61376e9 | 0.566436 | 0.283218 | − | 0.959056i | \(-0.408598\pi\) | ||||
0.283218 | + | 0.959056i | \(0.408598\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.28517e8i | 0.0703368i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.40771e9i | 0.297781i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.34925e9 | 1.74505 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.95390e8 | 0.122958 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.25292e9i | 1.27600i | 0.770038 | + | 0.637998i | \(0.220237\pi\) | ||||
−0.770038 | + | 0.637998i | \(0.779763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.72219e9i | 0.347278i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.82813e9 | 1.36065 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.05058e9 | 1.19153 | 0.595765 | − | 0.803158i | \(-0.296849\pi\) | ||||
0.595765 | + | 0.803158i | \(0.296849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.82357e8i | − 0.0938770i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 9.06189e9i | − 1.74304i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.42695e9 | −1.79216 | −0.896081 | − | 0.443891i | \(-0.853598\pi\) | ||||
−0.896081 | + | 0.443891i | \(0.853598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.75834e9 | 0.330401 | 0.165200 | − | 0.986260i | \(-0.447173\pi\) | ||||
0.165200 | + | 0.986260i | \(0.447173\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 1.31850e9i | − 0.244889i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 9.21387e8i | − 0.169160i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.23873e9 | −1.31372 | −0.656859 | − | 0.754013i | \(-0.728115\pi\) | ||||
−0.656859 | + | 0.754013i | \(0.728115\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.75683e8 | 0.103282 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.14693e10i | − 2.03419i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.25590e8i | − 0.0220213i | −0.999939 | − | 0.0110107i | \(-0.996495\pi\) | ||||
0.999939 | − | 0.0110107i | \(-0.00350487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.24267e9 | −0.735490 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.80957e9 | −0.310153 | −0.155077 | − | 0.987902i | \(-0.549562\pi\) | ||||
−0.155077 | + | 0.987902i | \(0.549562\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 9.74012e9i | − 1.65062i | −0.564680 | − | 0.825310i | \(-0.691000\pi\) | ||||
0.564680 | − | 0.825310i | \(-0.309000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.65160e9i | 0.276749i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.84674e8 | 0.113442 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.59122e9 | 0.260705 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.48592e9i | − 0.726800i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 8.34100e9i | − 1.33641i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.98157e9 | −0.630887 | −0.315444 | − | 0.948944i | \(-0.602153\pi\) | ||||
−0.315444 | + | 0.948944i | \(0.602153\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.78340e9 | 0.906296 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.06288e9i | 0.164731i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 7.38041e9i | − 1.13134i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.43168e9 | −0.217067 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.99235e9 | 0.598723 | 0.299361 | − | 0.954140i | \(-0.403226\pi\) | ||||
0.299361 | + | 0.954140i | \(0.403226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.07939e10i | 1.60118i | 0.599213 | + | 0.800589i | \(0.295480\pi\) | ||||
−0.599213 | + | 0.800589i | \(0.704520\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.41257e8i | 0.0207277i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.19085e9 | −0.318015 | −0.159008 | − | 0.987277i | \(-0.550829\pi\) | ||||
−0.159008 | + | 0.987277i | \(0.550829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.23241e8 | −0.0464162 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 9.85168e8i | − 0.139951i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.30043e9i | − 0.182763i | −0.995816 | − | 0.0913817i | \(-0.970872\pi\) | ||||
0.995816 | − | 0.0913817i | \(-0.0291283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.39754e9 | −0.333365 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.97145e9 | −0.271210 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.49570e9i | 0.203585i | 0.994806 | + | 0.101793i | \(0.0324578\pi\) | ||||
−0.994806 | + | 0.101793i | \(0.967542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 4.45984e9i | − 0.600640i | −0.953839 | − | 0.300320i | \(-0.902907\pi\) | ||||
0.953839 | − | 0.300320i | \(-0.0970934\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.27753e9 | −1.10307 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.82756e8 | −0.0636578 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.07532e9i | − 0.140313i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.58553e10i | 2.04731i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.08010e9 | −0.904712 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.93326e9 | −0.876768 | −0.438384 | − | 0.898788i | \(-0.644449\pi\) | ||||
−0.438384 | + | 0.898788i | \(0.644449\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 5.10794e9i | − 0.639267i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.17696e10i | 1.45781i | 0.684613 | + | 0.728907i | \(0.259971\pi\) | ||||
−0.684613 | + | 0.728907i | \(0.740029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.62445e9 | 0.321732 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.20104e9 | −0.509732 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.18271e10i | − 1.42039i | −0.704006 | − | 0.710194i | \(-0.748607\pi\) | ||||
0.704006 | − | 0.710194i | \(-0.251393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 6.89627e9i | − 0.819779i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.33518e9 | 0.510104 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.54190e10 | −1.79593 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 5.64930e9i | − 0.651361i | −0.945480 | − | 0.325680i | \(-0.894407\pi\) | ||||
0.945480 | − | 0.325680i | \(-0.105593\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.26654e8i | 0.0486978i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.70098e9 | −0.757166 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.80695e9 | 1.09703 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.17588e10i | − 1.30225i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.07474e9i | 0.556417i | 0.960521 | + | 0.278208i | \(0.0897406\pi\) | ||||
−0.960521 | + | 0.278208i | \(0.910259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.34790e9 | −0.906220 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.10637e9 | −0.978777 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5.39705e8i | − 0.0574365i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.79283e10i | 1.88919i | 0.328232 | + | 0.944597i | \(0.393547\pi\) | ||||
−0.328232 | + | 0.944597i | \(0.606453\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.39013e9 | −0.145048 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.84020e9 | −0.190131 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.93700e9i | 0.709742i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.20005e9i | − 0.222903i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.11920e10 | −1.12294 | −0.561468 | − | 0.827498i | \(-0.689763\pi\) | ||||
−0.561468 | + | 0.827498i | \(0.689763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.60873e9 | 0.358575 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.19739e9i | 0.511448i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.32566e9i | 0.324112i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.52463e10 | 1.47161 | 0.735805 | − | 0.677193i | \(-0.236804\pi\) | ||||
0.735805 | + | 0.677193i | \(0.236804\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.62535e9 | −0.728976 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3.26516e8i | − 0.0309167i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.33611e10i | − 1.25308i | −0.779389 | − | 0.626541i | \(-0.784470\pi\) | ||||
0.779389 | − | 0.626541i | \(-0.215530\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.85990e9 | −0.544358 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.53621e10 | 1.41356 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.12829e9i | − 0.102841i | −0.998677 | − | 0.0514203i | \(-0.983625\pi\) | ||||
0.998677 | − | 0.0514203i | \(-0.0163748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.28439e9i | 0.747991i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.70680e7 | 0.00152659 | 0.000763295 | − | 1.00000i | \(-0.499757\pi\) | ||||
0.000763295 | 1.00000i | \(0.499757\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.86826e9 | 0.254139 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 3.18898e9i | − 0.279917i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.11120e9i | 0.270547i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.70601e10 | −1.46974 | −0.734871 | − | 0.678207i | \(-0.762757\pi\) | ||||
−0.734871 | + | 0.678207i | \(0.762757\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.40648e9 | −0.632163 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 8.05338e9i | − 0.681026i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22318e9i | 0.102484i | 0.998686 | + | 0.0512418i | \(0.0163179\pi\) | ||||
−0.998686 | + | 0.0512418i | \(0.983682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.79332e9 | 0.397915 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.82094e9 | −0.643299 | −0.321649 | − | 0.946859i | \(-0.604237\pi\) | ||||
−0.321649 | + | 0.946859i | \(0.604237\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.91984e9i | − 0.237971i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.09271e9i | 0.0882452i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.96946e8 | 0.0477696 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.17810e9 | −0.648500 | −0.324250 | − | 0.945971i | \(-0.605112\pi\) | ||||
−0.324250 | + | 0.945971i | \(0.605112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.47005e10i | 1.15516i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.07643e10i | − 0.838218i | −0.907936 | − | 0.419109i | \(-0.862343\pi\) | ||||
0.907936 | − | 0.419109i | \(-0.137657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.69122e9 | 0.439187 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.77537e9 | 0.365203 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 9.81507e9i | − 0.743896i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.66808e10i | − 1.25296i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.23553e9 | 0.389758 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.84792e9 | −0.357694 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.74535e10i | 1.27635i | 0.769890 | + | 0.638177i | \(0.220311\pi\) | ||||
−0.769890 | + | 0.638177i | \(0.779689\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.23778e10i | 0.897168i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.48295e9 | 0.106539 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.30752e10 | 0.931091 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.22424e10i | 0.864135i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.19624e8i | 0.00836976i | 0.999991 | + | 0.00418488i | \(0.00133209\pi\) | ||||
−0.999991 | + | 0.00418488i | \(0.998668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.10494e10 | 1.45991 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.55103e9 | −0.106637 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.29697e10i | − 1.56549i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 5.15837e8i | − 0.0348520i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.26607e9 | 0.285740 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.68783e9 | 0.244879 | 0.122439 | − | 0.992476i | \(-0.460928\pi\) | ||||
0.122439 | + | 0.992476i | \(0.460928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.94079e9i | 0.325254i | 0.986688 | + | 0.162627i | \(0.0519968\pi\) | ||||
−0.986688 | + | 0.162627i | \(0.948003\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.60793e10i | 1.04942i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.19567e8 | −0.0336194 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.26786e8 | −0.0209646 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 7.87925e8i | − 0.0501177i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 9.73545e9i | − 0.613981i | −0.951713 | − | 0.306990i | \(-0.900678\pi\) | ||||
0.951713 | − | 0.306990i | \(-0.0993219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.04183e9 | 0.502869 | 0.251435 | − | 0.967874i | \(-0.419098\pi\) | ||||
0.251435 | + | 0.967874i | \(0.419098\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.48243e10 | −0.919151 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.48354e10i | − 1.52687i | −0.645885 | − | 0.763435i | \(-0.723512\pi\) | ||||
0.645885 | − | 0.763435i | \(-0.276488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.35472e8i | 0.0570282i | 0.999593 | + | 0.0285141i | \(0.00907756\pi\) | ||||
−0.999593 | + | 0.0285141i | \(0.990922\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.15023e10 | 1.29981 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.35452e10 | 0.811946 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.69981e10i | 1.01041i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 8.95958e9i | − 0.528139i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.51816e9 | −0.556399 | −0.278199 | − | 0.960523i | \(-0.589738\pi\) | ||||
−0.278199 | + | 0.960523i | \(0.589738\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.38411e10 | 0.802391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.93106e10i | 1.11019i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 3.68248e9i | − 0.209962i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.21934e9 | −0.0689499 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.82105e9 | −0.214292 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.91995e9i | − 0.496146i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.66989e10i | − 0.921228i | −0.887601 | − | 0.460614i | \(-0.847629\pi\) | ||||
0.887601 | − | 0.460614i | \(-0.152371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.09362e9 | 0.0598389 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.60352e10 | 0.870243 | 0.435121 | − | 0.900372i | \(-0.356705\pi\) | ||||
0.435121 | + | 0.900372i | \(0.356705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.41808e10i | 1.30165i | 0.759227 | + | 0.650826i | \(0.225577\pi\) | ||||
−0.759227 | + | 0.650826i | \(0.774423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.61465e9i | 0.299786i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.03439e9 | 0.319592 | 0.159796 | − | 0.987150i | \(-0.448916\pi\) | ||||
0.159796 | + | 0.987150i | \(0.448916\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.11727e9 | 0.216298 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.82445e9i | 0.303520i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 1.61966e10i | − 0.837249i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.83700e10 | −1.45478 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.94533e9 | −0.302431 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.78340e9i | 0.190921i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.87528e9i | 0.194001i | 0.995284 | + | 0.0970007i | \(0.0309249\pi\) | ||||
−0.995284 | + | 0.0970007i | \(0.969075\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.25035e10 | 1.11761 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.37191e10 | 1.66135 | 0.830673 | − | 0.556760i | \(-0.187956\pi\) | ||||
0.830673 | + | 0.556760i | \(0.187956\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.25227e10i | 1.58973i | 0.606784 | + | 0.794867i | \(0.292459\pi\) | ||||
−0.606784 | + | 0.794867i | \(0.707541\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 4.73964e8i | − 0.0229850i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.17993e10 | 0.567704 | 0.283852 | − | 0.958868i | \(-0.408388\pi\) | ||||
0.283852 | + | 0.958868i | \(0.408388\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.40659e9 | 0.0671444 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.81844e10i | 1.33486i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.10668e10i | − 0.989963i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.10930e10 | 0.517214 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.85208e9 | −0.409517 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.83338e9i | 0.267770i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2.82983e10i | − 1.28892i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.86936e8 | 0.00844862 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.84375e9 | −0.351766 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.60172e10i | 0.712788i | 0.934336 | + | 0.356394i | \(0.115994\pi\) | ||||
−0.934336 | + | 0.356394i | \(0.884006\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.22263e9i | 0.0539908i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.42391e9 | 0.369147 | 0.184574 | − | 0.982819i | \(-0.440910\pi\) | ||||
0.184574 | + | 0.982819i | \(0.440910\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.71554e10 | 1.61575 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.03815e10i | − 0.448007i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.17284e9i | 0.135880i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.03951e10 | 1.71682 | 0.858408 | − | 0.512967i | \(-0.171454\pi\) | ||||
0.858408 | + | 0.512967i | \(0.171454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.60734e10 | −1.09974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.08053e10i | 1.28950i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.75868e10i | 1.14606i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.17507e9 | −0.337064 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.24836e9 | 0.255688 | 0.127844 | − | 0.991794i | \(-0.459194\pi\) | ||||
0.127844 | + | 0.991794i | \(0.459194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.35564e10i | − 0.550580i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.01346e9i | 0.282713i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.27314e10 | −0.509372 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.33715e10 | −1.32522 | −0.662608 | − | 0.748966i | \(-0.730551\pi\) | ||||
−0.662608 | + | 0.748966i | \(0.730551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.39403e9i | 0.370273i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.63777e10i | 0.640749i | 0.947291 | + | 0.320375i | \(0.103809\pi\) | ||||
−0.947291 | + | 0.320375i | \(0.896191\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.04877e10 | 0.407275 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.51151e9 | 0.0968107 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 9.07481e9i | − 0.347226i | −0.984814 | − | 0.173613i | \(-0.944456\pi\) | ||||
0.984814 | − | 0.173613i | \(-0.0555442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.24194e10i | 1.61114i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.94063e10 | 1.48571 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.87187e10 | 0.700569 | 0.350284 | − | 0.936643i | \(-0.386085\pi\) | ||||
0.350284 | + | 0.936643i | \(0.386085\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 8.91676e9i | − 0.331280i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.51947e10i | − 0.560401i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.12636e9 | −0.334143 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.75299e10 | −0.637160 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 7.04800e9i | − 0.254316i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 9.33128e8i | − 0.0334269i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.29498e10 | −0.816182 | −0.408091 | − | 0.912941i | \(-0.633805\pi\) | ||||
−0.408091 | + | 0.912941i | \(0.633805\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.52042e10 | −0.536823 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.95632e9i | 0.173737i | 0.996220 | + | 0.0868684i | \(0.0276860\pi\) | ||||
−0.996220 | + | 0.0868684i | \(0.972314\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.86791e9i | 0.308622i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.73769e10 | 0.945951 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.14703e10 | −1.07962 | −0.539809 | − | 0.841787i | \(-0.681504\pi\) | ||||
−0.539809 | + | 0.841787i | \(0.681504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.80714e10i | − 0.615533i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.61450e9i | 0.223695i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.75291e10 | −0.924389 | −0.462195 | − | 0.886778i | \(-0.652938\pi\) | ||||
−0.462195 | + | 0.886778i | \(0.652938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.93948e10 | −0.646635 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.20512e10i | 0.398950i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.49179e8i | − 0.0114779i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.41201e10 | 1.76645 | 0.883224 | − | 0.468951i | \(-0.155368\pi\) | ||||
0.883224 | + | 0.468951i | \(0.155368\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.10901e9 | 0.197992 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.57396e10i | 0.828365i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.70649e10i | − 0.545343i | −0.962107 | − | 0.272672i | \(-0.912093\pi\) | ||||
0.962107 | − | 0.272672i | \(-0.0879072\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.34295e10 | 1.37818 |
(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 | 256.8.b.l.129.2 | 6 | ||
4.3 | odd | 2 | 256.8.b.k.129.5 | 6 | |||
8.3 | odd | 2 | 256.8.b.k.129.2 | 6 | |||
8.5 | even | 2 | inner | 256.8.b.l.129.5 | 6 | ||
16.3 | odd | 4 | 128.8.a.c.1.1 | yes | 3 | ||
16.5 | even | 4 | 128.8.a.d.1.1 | yes | 3 | ||
16.11 | odd | 4 | 128.8.a.b.1.3 | yes | 3 | ||
16.13 | even | 4 | 128.8.a.a.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.8.a.a.1.3 | ✓ | 3 | 16.13 | even | 4 | ||
128.8.a.b.1.3 | yes | 3 | 16.11 | odd | 4 | ||
128.8.a.c.1.1 | yes | 3 | 16.3 | odd | 4 | ||
128.8.a.d.1.1 | yes | 3 | 16.5 | even | 4 | ||
256.8.b.k.129.2 | 6 | 8.3 | odd | 2 | |||
256.8.b.k.129.5 | 6 | 4.3 | odd | 2 | |||
256.8.b.l.129.2 | 6 | 1.1 | even | 1 | trivial | ||
256.8.b.l.129.5 | 6 | 8.5 | even | 2 | inner |