Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,6,Mod(1,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("630.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.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: | \(101.041806482\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 630.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 187.000 | 0.465972 | 0.232986 | − | 0.972480i | \(-0.425150\pi\) | ||||
0.232986 | + | 0.972480i | \(0.425150\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 627.000 | 1.02899 | 0.514493 | − | 0.857495i | \(-0.327980\pi\) | ||||
0.514493 | + | 0.857495i | \(0.327980\pi\) | |||||||
\(14\) | −196.000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1813.00 | −1.52151 | −0.760756 | − | 0.649038i | \(-0.775172\pi\) | ||||
−0.760756 | + | 0.649038i | \(0.775172\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 258.000 | 0.163959 | 0.0819796 | − | 0.996634i | \(-0.473876\pi\) | ||||
0.0819796 | + | 0.996634i | \(0.473876\pi\) | |||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 748.000 | 0.329492 | ||||||||
\(23\) | −2970.00 | −1.17068 | −0.585338 | − | 0.810789i | \(-0.699038\pi\) | ||||
−0.585338 | + | 0.810789i | \(0.699038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2508.00 | 0.727602 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −784.000 | −0.188982 | ||||||||
\(29\) | −1299.00 | −0.286823 | −0.143412 | − | 0.989663i | \(-0.545807\pi\) | ||||
−0.143412 | + | 0.989663i | \(0.545807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1916.00 | 0.358089 | 0.179045 | − | 0.983841i | \(-0.442699\pi\) | ||||
0.179045 | + | 0.983841i | \(0.442699\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7252.00 | −1.07587 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6578.00 | 0.789932 | 0.394966 | − | 0.918696i | \(-0.370756\pi\) | ||||
0.394966 | + | 0.918696i | \(0.370756\pi\) | |||||||
\(38\) | 1032.00 | 0.115937 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −6676.00 | −0.620236 | −0.310118 | − | 0.950698i | \(-0.600368\pi\) | ||||
−0.310118 | + | 0.950698i | \(0.600368\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3178.00 | 0.262109 | 0.131055 | − | 0.991375i | \(-0.458164\pi\) | ||||
0.131055 | + | 0.991375i | \(0.458164\pi\) | |||||||
\(44\) | 2992.00 | 0.232986 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11880.0 | −0.827793 | ||||||||
\(47\) | 22001.0 | 1.45277 | 0.726387 | − | 0.687286i | \(-0.241198\pi\) | ||||
0.726387 | + | 0.687286i | \(0.241198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 2500.00 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10032.0 | 0.514493 | ||||||||
\(53\) | −26168.0 | −1.27962 | −0.639810 | − | 0.768533i | \(-0.720987\pi\) | ||||
−0.639810 | + | 0.768533i | \(0.720987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4675.00 | −0.208389 | ||||||||
\(56\) | −3136.00 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5196.00 | −0.202815 | ||||||||
\(59\) | −3932.00 | −0.147056 | −0.0735281 | − | 0.997293i | \(-0.523426\pi\) | ||||
−0.0735281 | + | 0.997293i | \(0.523426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48740.0 | −1.67711 | −0.838554 | − | 0.544819i | \(-0.816598\pi\) | ||||
−0.838554 | + | 0.544819i | \(0.816598\pi\) | |||||||
\(62\) | 7664.00 | 0.253207 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −15675.0 | −0.460176 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −44832.0 | −1.22012 | −0.610058 | − | 0.792357i | \(-0.708854\pi\) | ||||
−0.610058 | + | 0.792357i | \(0.708854\pi\) | |||||||
\(68\) | −29008.0 | −0.760756 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4900.00 | 0.119523 | ||||||||
\(71\) | −63736.0 | −1.50051 | −0.750255 | − | 0.661148i | \(-0.770069\pi\) | ||||
−0.750255 | + | 0.661148i | \(0.770069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 60470.0 | 1.32811 | 0.664053 | − | 0.747685i | \(-0.268835\pi\) | ||||
0.664053 | + | 0.747685i | \(0.268835\pi\) | |||||||
\(74\) | 26312.0 | 0.558566 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4128.00 | 0.0819796 | ||||||||
\(77\) | −9163.00 | −0.176121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −43721.0 | −0.788174 | −0.394087 | − | 0.919073i | \(-0.628939\pi\) | ||||
−0.394087 | + | 0.919073i | \(0.628939\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −26704.0 | −0.438573 | ||||||||
\(83\) | −97276.0 | −1.54992 | −0.774962 | − | 0.632008i | \(-0.782231\pi\) | ||||
−0.774962 | + | 0.632008i | \(0.782231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 45325.0 | 0.680441 | ||||||||
\(86\) | 12712.0 | 0.185339 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 11968.0 | 0.164746 | ||||||||
\(89\) | −45560.0 | −0.609689 | −0.304845 | − | 0.952402i | \(-0.598605\pi\) | ||||
−0.304845 | + | 0.952402i | \(0.598605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30723.0 | −0.388920 | ||||||||
\(92\) | −47520.0 | −0.585338 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 88004.0 | 1.02727 | ||||||||
\(95\) | −6450.00 | −0.0733248 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −57295.0 | −0.618283 | −0.309142 | − | 0.951016i | \(-0.600042\pi\) | ||||
−0.309142 | + | 0.951016i | \(0.600042\pi\) | |||||||
\(98\) | 9604.00 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 44970.0 | 0.438651 | 0.219326 | − | 0.975652i | \(-0.429614\pi\) | ||||
0.219326 | + | 0.975652i | \(0.429614\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −101405. | −0.941817 | −0.470908 | − | 0.882182i | \(-0.656074\pi\) | ||||
−0.470908 | + | 0.882182i | \(0.656074\pi\) | |||||||
\(104\) | 40128.0 | 0.363801 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −104672. | −0.904828 | ||||||||
\(107\) | 166002. | 1.40170 | 0.700848 | − | 0.713311i | \(-0.252805\pi\) | ||||
0.700848 | + | 0.713311i | \(0.252805\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8289.00 | 0.0668245 | 0.0334123 | − | 0.999442i | \(-0.489363\pi\) | ||||
0.0334123 | + | 0.999442i | \(0.489363\pi\) | |||||||
\(110\) | −18700.0 | −0.147353 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12544.0 | −0.0944911 | ||||||||
\(113\) | −263206. | −1.93910 | −0.969549 | − | 0.244898i | \(-0.921245\pi\) | ||||
−0.969549 | + | 0.244898i | \(0.921245\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 74250.0 | 0.523542 | ||||||||
\(116\) | −20784.0 | −0.143412 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15728.0 | −0.103984 | ||||||||
\(119\) | 88837.0 | 0.575078 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −126082. | −0.782870 | ||||||||
\(122\) | −194960. | −1.18589 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 30656.0 | 0.179045 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 30052.0 | 0.165335 | 0.0826674 | − | 0.996577i | \(-0.473656\pi\) | ||||
0.0826674 | + | 0.996577i | \(0.473656\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −62700.0 | −0.325394 | ||||||||
\(131\) | 120050. | 0.611201 | 0.305600 | − | 0.952160i | \(-0.401143\pi\) | ||||
0.305600 | + | 0.952160i | \(0.401143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12642.0 | −0.0619707 | ||||||||
\(134\) | −179328. | −0.862752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −116032. | −0.537936 | ||||||||
\(137\) | −31776.0 | −0.144643 | −0.0723216 | − | 0.997381i | \(-0.523041\pi\) | ||||
−0.0723216 | + | 0.997381i | \(0.523041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −200162. | −0.878708 | −0.439354 | − | 0.898314i | \(-0.644793\pi\) | ||||
−0.439354 | + | 0.898314i | \(0.644793\pi\) | |||||||
\(140\) | 19600.0 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −254944. | −1.06102 | ||||||||
\(143\) | 117249. | 0.479478 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32475.0 | 0.128271 | ||||||||
\(146\) | 241880. | 0.939113 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 105248. | 0.394966 | ||||||||
\(149\) | −309642. | −1.14260 | −0.571300 | − | 0.820741i | \(-0.693561\pi\) | ||||
−0.571300 | + | 0.820741i | \(0.693561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −208657. | −0.744716 | −0.372358 | − | 0.928089i | \(-0.621451\pi\) | ||||
−0.372358 | + | 0.928089i | \(0.621451\pi\) | |||||||
\(152\) | 16512.0 | 0.0579683 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −36652.0 | −0.124536 | ||||||||
\(155\) | −47900.0 | −0.160142 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36010.0 | 0.116593 | 0.0582967 | − | 0.998299i | \(-0.481433\pi\) | ||||
0.0582967 | + | 0.998299i | \(0.481433\pi\) | |||||||
\(158\) | −174884. | −0.557324 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | 145530. | 0.442474 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 175670. | 0.517879 | 0.258940 | − | 0.965893i | \(-0.416627\pi\) | ||||
0.258940 | + | 0.965893i | \(0.416627\pi\) | |||||||
\(164\) | −106816. | −0.310118 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −389104. | −1.09596 | ||||||||
\(167\) | 157413. | 0.436767 | 0.218383 | − | 0.975863i | \(-0.429922\pi\) | ||||
0.218383 | + | 0.975863i | \(0.429922\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21836.0 | 0.0588107 | ||||||||
\(170\) | 181300. | 0.481144 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 50848.0 | 0.131055 | ||||||||
\(173\) | 23471.0 | 0.0596233 | 0.0298117 | − | 0.999556i | \(-0.490509\pi\) | ||||
0.0298117 | + | 0.999556i | \(0.490509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −30625.0 | −0.0755929 | ||||||||
\(176\) | 47872.0 | 0.116493 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −182240. | −0.431116 | ||||||||
\(179\) | −612228. | −1.42817 | −0.714086 | − | 0.700058i | \(-0.753158\pi\) | ||||
−0.714086 | + | 0.700058i | \(0.753158\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 528832. | 1.19983 | 0.599917 | − | 0.800062i | \(-0.295200\pi\) | ||||
0.599917 | + | 0.800062i | \(0.295200\pi\) | |||||||
\(182\) | −122892. | −0.275008 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −190080. | −0.413897 | ||||||||
\(185\) | −164450. | −0.353268 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −339031. | −0.708982 | ||||||||
\(188\) | 352016. | 0.726387 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25800.0 | −0.0518484 | ||||||||
\(191\) | −540369. | −1.07178 | −0.535892 | − | 0.844287i | \(-0.680024\pi\) | ||||
−0.535892 | + | 0.844287i | \(0.680024\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 960320. | 1.85576 | 0.927882 | − | 0.372874i | \(-0.121628\pi\) | ||||
0.927882 | + | 0.372874i | \(0.121628\pi\) | |||||||
\(194\) | −229180. | −0.437192 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −761944. | −1.39881 | −0.699403 | − | 0.714728i | \(-0.746551\pi\) | ||||
−0.699403 | + | 0.714728i | \(0.746551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 125084. | 0.223908 | 0.111954 | − | 0.993713i | \(-0.464289\pi\) | ||||
0.111954 | + | 0.993713i | \(0.464289\pi\) | |||||||
\(200\) | 40000.0 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 179880. | 0.310173 | ||||||||
\(203\) | 63651.0 | 0.108409 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 166900. | 0.277378 | ||||||||
\(206\) | −405620. | −0.665965 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 160512. | 0.257246 | ||||||||
\(209\) | 48246.0 | 0.0764004 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 627547. | 0.970376 | 0.485188 | − | 0.874410i | \(-0.338751\pi\) | ||||
0.485188 | + | 0.874410i | \(0.338751\pi\) | |||||||
\(212\) | −418688. | −0.639810 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 664008. | 0.991149 | ||||||||
\(215\) | −79450.0 | −0.117219 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −93884.0 | −0.135345 | ||||||||
\(218\) | 33156.0 | 0.0472521 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −74800.0 | −0.104195 | ||||||||
\(221\) | −1.13675e6 | −1.56561 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.22110e6 | −1.64433 | −0.822166 | − | 0.569248i | \(-0.807234\pi\) | ||||
−0.822166 | + | 0.569248i | \(0.807234\pi\) | |||||||
\(224\) | −50176.0 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.05282e6 | −1.37115 | ||||||||
\(227\) | −390547. | −0.503047 | −0.251524 | − | 0.967851i | \(-0.580932\pi\) | ||||
−0.251524 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −712124. | −0.897360 | −0.448680 | − | 0.893692i | \(-0.648106\pi\) | ||||
−0.448680 | + | 0.893692i | \(0.648106\pi\) | |||||||
\(230\) | 297000. | 0.370200 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −83136.0 | −0.101407 | ||||||||
\(233\) | −561576. | −0.677671 | −0.338835 | − | 0.940846i | \(-0.610033\pi\) | ||||
−0.338835 | + | 0.940846i | \(0.610033\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −550025. | −0.649700 | ||||||||
\(236\) | −62912.0 | −0.0735281 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 355348. | 0.406641 | ||||||||
\(239\) | 1.36084e6 | 1.54103 | 0.770515 | − | 0.637421i | \(-0.219999\pi\) | ||||
0.770515 | + | 0.637421i | \(0.219999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 530050. | 0.587860 | 0.293930 | − | 0.955827i | \(-0.405037\pi\) | ||||
0.293930 | + | 0.955827i | \(0.405037\pi\) | |||||||
\(242\) | −504328. | −0.553573 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −779840. | −0.838554 | ||||||||
\(245\) | −60025.0 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 161766. | 0.168712 | ||||||||
\(248\) | 122624. | 0.126604 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −990330. | −0.992192 | −0.496096 | − | 0.868268i | \(-0.665234\pi\) | ||||
−0.496096 | + | 0.868268i | \(0.665234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −555390. | −0.545503 | ||||||||
\(254\) | 120208. | 0.116909 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.81643e6 | 1.71548 | 0.857740 | − | 0.514083i | \(-0.171868\pi\) | ||||
0.857740 | + | 0.514083i | \(0.171868\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −322322. | −0.298566 | ||||||||
\(260\) | −250800. | −0.230088 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 480200. | 0.432184 | ||||||||
\(263\) | 1.95847e6 | 1.74594 | 0.872968 | − | 0.487777i | \(-0.162192\pi\) | ||||
0.872968 | + | 0.487777i | \(0.162192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 654200. | 0.572263 | ||||||||
\(266\) | −50568.0 | −0.0438199 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −717312. | −0.610058 | ||||||||
\(269\) | −218034. | −0.183715 | −0.0918573 | − | 0.995772i | \(-0.529280\pi\) | ||||
−0.0918573 | + | 0.995772i | \(0.529280\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.26265e6 | 1.04438 | 0.522192 | − | 0.852828i | \(-0.325114\pi\) | ||||
0.522192 | + | 0.852828i | \(0.325114\pi\) | |||||||
\(272\) | −464128. | −0.380378 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −127104. | −0.102278 | ||||||||
\(275\) | 116875. | 0.0931944 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.10264e6 | −0.863443 | −0.431721 | − | 0.902007i | \(-0.642094\pi\) | ||||
−0.431721 | + | 0.902007i | \(0.642094\pi\) | |||||||
\(278\) | −800648. | −0.621340 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 78400.0 | 0.0597614 | ||||||||
\(281\) | 998213. | 0.754149 | 0.377075 | − | 0.926183i | \(-0.376930\pi\) | ||||
0.377075 | + | 0.926183i | \(0.376930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −386371. | −0.286773 | −0.143387 | − | 0.989667i | \(-0.545799\pi\) | ||||
−0.143387 | + | 0.989667i | \(0.545799\pi\) | |||||||
\(284\) | −1.01978e6 | −0.750255 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 468996. | 0.339042 | ||||||||
\(287\) | 327124. | 0.234427 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.86711e6 | 1.31500 | ||||||||
\(290\) | 129900. | 0.0907014 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 967520. | 0.664053 | ||||||||
\(293\) | 783571. | 0.533224 | 0.266612 | − | 0.963804i | \(-0.414096\pi\) | ||||
0.266612 | + | 0.963804i | \(0.414096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 98300.0 | 0.0657656 | ||||||||
\(296\) | 420992. | 0.279283 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.23857e6 | −0.807940 | ||||||||
\(299\) | −1.86219e6 | −1.20461 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −155722. | −0.0990681 | ||||||||
\(302\) | −834628. | −0.526594 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 66048.0 | 0.0409898 | ||||||||
\(305\) | 1.21850e6 | 0.750025 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.81773e6 | 1.70629 | 0.853147 | − | 0.521670i | \(-0.174691\pi\) | ||||
0.853147 | + | 0.521670i | \(0.174691\pi\) | |||||||
\(308\) | −146608. | −0.0880604 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −191600. | −0.113238 | ||||||||
\(311\) | 847398. | 0.496806 | 0.248403 | − | 0.968657i | \(-0.420094\pi\) | ||||
0.248403 | + | 0.968657i | \(0.420094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 364955. | 0.210561 | 0.105281 | − | 0.994443i | \(-0.466426\pi\) | ||||
0.105281 | + | 0.994443i | \(0.466426\pi\) | |||||||
\(314\) | 144040. | 0.0824440 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −699536. | −0.394087 | ||||||||
\(317\) | −1.93744e6 | −1.08288 | −0.541439 | − | 0.840740i | \(-0.682120\pi\) | ||||
−0.541439 | + | 0.840740i | \(0.682120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −242913. | −0.133652 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 582120. | 0.312876 | ||||||||
\(323\) | −467754. | −0.249466 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 391875. | 0.205797 | ||||||||
\(326\) | 702680. | 0.366196 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −427264. | −0.219286 | ||||||||
\(329\) | −1.07805e6 | −0.549097 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −61460.0 | −0.0308335 | −0.0154167 | − | 0.999881i | \(-0.504907\pi\) | ||||
−0.0154167 | + | 0.999881i | \(0.504907\pi\) | |||||||
\(332\) | −1.55642e6 | −0.774962 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 629652. | 0.308841 | ||||||||
\(335\) | 1.12080e6 | 0.545652 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.74116e6 | −1.79445 | −0.897225 | − | 0.441574i | \(-0.854420\pi\) | ||||
−0.897225 | + | 0.441574i | \(0.854420\pi\) | |||||||
\(338\) | 87344.0 | 0.0415854 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 725200. | 0.340221 | ||||||||
\(341\) | 358292. | 0.166860 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 203392. | 0.0926697 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 93884.0 | 0.0421601 | ||||||||
\(347\) | −211334. | −0.0942206 | −0.0471103 | − | 0.998890i | \(-0.515001\pi\) | ||||
−0.0471103 | + | 0.998890i | \(0.515001\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.39558e6 | 1.49228 | 0.746140 | − | 0.665789i | \(-0.231905\pi\) | ||||
0.746140 | + | 0.665789i | \(0.231905\pi\) | |||||||
\(350\) | −122500. | −0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 191488. | 0.0823730 | ||||||||
\(353\) | 3.88094e6 | 1.65768 | 0.828838 | − | 0.559489i | \(-0.189003\pi\) | ||||
0.828838 | + | 0.559489i | \(0.189003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.59340e6 | 0.671049 | ||||||||
\(356\) | −728960. | −0.304845 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.44891e6 | −1.00987 | ||||||||
\(359\) | −3.24210e6 | −1.32767 | −0.663836 | − | 0.747878i | \(-0.731073\pi\) | ||||
−0.663836 | + | 0.747878i | \(0.731073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.40954e6 | −0.973117 | ||||||||
\(362\) | 2.11533e6 | 0.848411 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −491568. | −0.194460 | ||||||||
\(365\) | −1.51175e6 | −0.593947 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.44430e6 | 0.559749 | 0.279874 | − | 0.960037i | \(-0.409707\pi\) | ||||
0.279874 | + | 0.960037i | \(0.409707\pi\) | |||||||
\(368\) | −760320. | −0.292669 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −657800. | −0.249798 | ||||||||
\(371\) | 1.28223e6 | 0.483651 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.43542e6 | 1.27852 | 0.639260 | − | 0.768991i | \(-0.279241\pi\) | ||||
0.639260 | + | 0.768991i | \(0.279241\pi\) | |||||||
\(374\) | −1.35612e6 | −0.501326 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.40806e6 | 0.513633 | ||||||||
\(377\) | −814473. | −0.295137 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.68635e6 | −0.603044 | −0.301522 | − | 0.953459i | \(-0.597495\pi\) | ||||
−0.301522 | + | 0.953459i | \(0.597495\pi\) | |||||||
\(380\) | −103200. | −0.0366624 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.16148e6 | −0.757865 | ||||||||
\(383\) | −2.64354e6 | −0.920850 | −0.460425 | − | 0.887699i | \(-0.652303\pi\) | ||||
−0.460425 | + | 0.887699i | \(0.652303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 229075. | 0.0787637 | ||||||||
\(386\) | 3.84128e6 | 1.31222 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −916720. | −0.309142 | ||||||||
\(389\) | 452099. | 0.151481 | 0.0757407 | − | 0.997128i | \(-0.475868\pi\) | ||||
0.0757407 | + | 0.997128i | \(0.475868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.38461e6 | 1.78120 | ||||||||
\(392\) | 153664. | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.04778e6 | −0.989105 | ||||||||
\(395\) | 1.09302e6 | 0.352482 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.95530e6 | −0.622641 | −0.311321 | − | 0.950305i | \(-0.600771\pi\) | ||||
−0.311321 | + | 0.950305i | \(0.600771\pi\) | |||||||
\(398\) | 500336. | 0.158327 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 4.76737e6 | 1.48053 | 0.740266 | − | 0.672314i | \(-0.234700\pi\) | ||||
0.740266 | + | 0.672314i | \(0.234700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.20133e6 | 0.368469 | ||||||||
\(404\) | 719520. | 0.219326 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 254604. | 0.0766567 | ||||||||
\(407\) | 1.23009e6 | 0.368086 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.13199e6 | −1.22138 | −0.610690 | − | 0.791870i | \(-0.709108\pi\) | ||||
−0.610690 | + | 0.791870i | \(0.709108\pi\) | |||||||
\(410\) | 667600. | 0.196136 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.62248e6 | −0.470908 | ||||||||
\(413\) | 192668. | 0.0555820 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.43190e6 | 0.693147 | ||||||||
\(416\) | 642048. | 0.181901 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 192984. | 0.0540232 | ||||||||
\(419\) | −190512. | −0.0530136 | −0.0265068 | − | 0.999649i | \(-0.508438\pi\) | ||||
−0.0265068 | + | 0.999649i | \(0.508438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.19186e6 | −1.42764 | −0.713818 | − | 0.700332i | \(-0.753035\pi\) | ||||
−0.713818 | + | 0.700332i | \(0.753035\pi\) | |||||||
\(422\) | 2.51019e6 | 0.686160 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.67475e6 | −0.452414 | ||||||||
\(425\) | −1.13312e6 | −0.304302 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.38826e6 | 0.633887 | ||||||||
\(428\) | 2.65603e6 | 0.700848 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −317800. | −0.0828863 | ||||||||
\(431\) | 4.21781e6 | 1.09369 | 0.546845 | − | 0.837234i | \(-0.315829\pi\) | ||||
0.546845 | + | 0.837234i | \(0.315829\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.86027e6 | −1.24578 | −0.622890 | − | 0.782310i | \(-0.714041\pi\) | ||||
−0.622890 | + | 0.782310i | \(0.714041\pi\) | |||||||
\(434\) | −375536. | −0.0957034 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 132624. | 0.0334123 | ||||||||
\(437\) | −766260. | −0.191943 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.03113e6 | −0.503011 | −0.251505 | − | 0.967856i | \(-0.580926\pi\) | ||||
−0.251505 | + | 0.967856i | \(0.580926\pi\) | |||||||
\(440\) | −299200. | −0.0736767 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.54700e6 | −1.10706 | ||||||||
\(443\) | −2.84199e6 | −0.688038 | −0.344019 | − | 0.938963i | \(-0.611789\pi\) | ||||
−0.344019 | + | 0.938963i | \(0.611789\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.13900e6 | 0.272661 | ||||||||
\(446\) | −4.88440e6 | −1.16272 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −200704. | −0.0472456 | ||||||||
\(449\) | 4.59682e6 | 1.07607 | 0.538037 | − | 0.842921i | \(-0.319166\pi\) | ||||
0.538037 | + | 0.842921i | \(0.319166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.24841e6 | −0.289012 | ||||||||
\(452\) | −4.21130e6 | −0.969549 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.56219e6 | −0.355708 | ||||||||
\(455\) | 768075. | 0.173930 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.93367e6 | 1.10504 | 0.552522 | − | 0.833498i | \(-0.313665\pi\) | ||||
0.552522 | + | 0.833498i | \(0.313665\pi\) | |||||||
\(458\) | −2.84850e6 | −0.634530 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.18800e6 | 0.261771 | ||||||||
\(461\) | 4.75667e6 | 1.04244 | 0.521220 | − | 0.853422i | \(-0.325477\pi\) | ||||
0.521220 | + | 0.853422i | \(0.325477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.08619e6 | 0.885862 | 0.442931 | − | 0.896556i | \(-0.353939\pi\) | ||||
0.442931 | + | 0.896556i | \(0.353939\pi\) | |||||||
\(464\) | −332544. | −0.0717058 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.24630e6 | −0.479186 | ||||||||
\(467\) | 4.15932e6 | 0.882531 | 0.441266 | − | 0.897377i | \(-0.354530\pi\) | ||||
0.441266 | + | 0.897377i | \(0.354530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.19677e6 | 0.461160 | ||||||||
\(470\) | −2.20010e6 | −0.459407 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −251648. | −0.0519922 | ||||||||
\(473\) | 594286. | 0.122136 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 161250. | 0.0327918 | ||||||||
\(476\) | 1.42139e6 | 0.287539 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.44335e6 | 1.08967 | ||||||||
\(479\) | 3.36040e6 | 0.669195 | 0.334597 | − | 0.942361i | \(-0.391400\pi\) | ||||
0.334597 | + | 0.942361i | \(0.391400\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.12441e6 | 0.812828 | ||||||||
\(482\) | 2.12020e6 | 0.415680 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.01731e6 | −0.391435 | ||||||||
\(485\) | 1.43238e6 | 0.276505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.05243e6 | 1.34746 | 0.673730 | − | 0.738977i | \(-0.264691\pi\) | ||||
0.673730 | + | 0.738977i | \(0.264691\pi\) | |||||||
\(488\) | −3.11936e6 | −0.592947 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −240100. | −0.0451754 | ||||||||
\(491\) | 83937.0 | 0.0157127 | 0.00785633 | − | 0.999969i | \(-0.497499\pi\) | ||||
0.00785633 | + | 0.999969i | \(0.497499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.35509e6 | 0.436405 | ||||||||
\(494\) | 647064. | 0.119297 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 490496. | 0.0895223 | ||||||||
\(497\) | 3.12306e6 | 0.567140 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.10526e6 | −1.27741 | −0.638703 | − | 0.769454i | \(-0.720529\pi\) | ||||
−0.638703 | + | 0.769454i | \(0.720529\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.96132e6 | −0.701586 | ||||||||
\(503\) | −2.89147e6 | −0.509564 | −0.254782 | − | 0.966999i | \(-0.582004\pi\) | ||||
−0.254782 | + | 0.966999i | \(0.582004\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.12425e6 | −0.196171 | ||||||||
\(506\) | −2.22156e6 | −0.385729 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 480832. | 0.0826674 | ||||||||
\(509\) | −1.03548e6 | −0.177153 | −0.0885764 | − | 0.996069i | \(-0.528232\pi\) | ||||
−0.0885764 | + | 0.996069i | \(0.528232\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.96303e6 | −0.501977 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.26572e6 | 1.21303 | ||||||||
\(515\) | 2.53513e6 | 0.421193 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.11419e6 | 0.676952 | ||||||||
\(518\) | −1.28929e6 | −0.211118 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.00320e6 | −0.162697 | ||||||||
\(521\) | 7.49715e6 | 1.21005 | 0.605023 | − | 0.796208i | \(-0.293164\pi\) | ||||
0.605023 | + | 0.796208i | \(0.293164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.53223e6 | 0.564670 | 0.282335 | − | 0.959316i | \(-0.408891\pi\) | ||||
0.282335 | + | 0.959316i | \(0.408891\pi\) | |||||||
\(524\) | 1.92080e6 | 0.305600 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.83390e6 | 1.23456 | ||||||||
\(527\) | −3.47371e6 | −0.544837 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.38456e6 | 0.370483 | ||||||||
\(530\) | 2.61680e6 | 0.404651 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −202272. | −0.0309854 | ||||||||
\(533\) | −4.18585e6 | −0.638213 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.15005e6 | −0.626858 | ||||||||
\(536\) | −2.86925e6 | −0.431376 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −872136. | −0.129906 | ||||||||
\(539\) | 448987. | 0.0665674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.99188e6 | −0.733281 | −0.366641 | − | 0.930363i | \(-0.619492\pi\) | ||||
−0.366641 | + | 0.930363i | \(0.619492\pi\) | |||||||
\(542\) | 5.05061e6 | 0.738491 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.85651e6 | −0.268968 | ||||||||
\(545\) | −207225. | −0.0298848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.12634e6 | 0.732553 | 0.366277 | − | 0.930506i | \(-0.380632\pi\) | ||||
0.366277 | + | 0.930506i | \(0.380632\pi\) | |||||||
\(548\) | −508416. | −0.0723216 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 467500. | 0.0658984 | ||||||||
\(551\) | −335142. | −0.0470273 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.14233e6 | 0.297902 | ||||||||
\(554\) | −4.41055e6 | −0.610546 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.20259e6 | −0.439354 | ||||||||
\(557\) | −8.86866e6 | −1.21121 | −0.605606 | − | 0.795765i | \(-0.707069\pi\) | ||||
−0.605606 | + | 0.795765i | \(0.707069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.99261e6 | 0.269707 | ||||||||
\(560\) | 313600. | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.99285e6 | 0.533264 | ||||||||
\(563\) | −9.07277e6 | −1.20634 | −0.603169 | − | 0.797613i | \(-0.706096\pi\) | ||||
−0.603169 | + | 0.797613i | \(0.706096\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.58015e6 | 0.867191 | ||||||||
\(566\) | −1.54548e6 | −0.202779 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.07910e6 | −0.530510 | ||||||||
\(569\) | −2.08310e6 | −0.269730 | −0.134865 | − | 0.990864i | \(-0.543060\pi\) | ||||
−0.134865 | + | 0.990864i | \(0.543060\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.46368e6 | −0.701286 | −0.350643 | − | 0.936509i | \(-0.614037\pi\) | ||||
−0.350643 | + | 0.936509i | \(0.614037\pi\) | |||||||
\(572\) | 1.87598e6 | 0.239739 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.30850e6 | 0.165765 | ||||||||
\(575\) | −1.85625e6 | −0.234135 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.66246e6 | 0.958140 | 0.479070 | − | 0.877777i | \(-0.340974\pi\) | ||||
0.479070 | + | 0.877777i | \(0.340974\pi\) | |||||||
\(578\) | 7.46845e6 | 0.929845 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 519600. | 0.0641356 | ||||||||
\(581\) | 4.76652e6 | 0.585816 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.89342e6 | −0.596267 | ||||||||
\(584\) | 3.87008e6 | 0.469556 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.13428e6 | 0.377046 | ||||||||
\(587\) | 1.57465e7 | 1.88620 | 0.943100 | − | 0.332510i | \(-0.107896\pi\) | ||||
0.943100 | + | 0.332510i | \(0.107896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 494328. | 0.0587120 | ||||||||
\(590\) | 393200. | 0.0465033 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.68397e6 | 0.197483 | ||||||||
\(593\) | 1.62409e7 | 1.89658 | 0.948292 | − | 0.317398i | \(-0.102809\pi\) | ||||
0.948292 | + | 0.317398i | \(0.102809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.22093e6 | −0.257183 | ||||||||
\(596\) | −4.95427e6 | −0.571300 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.44876e6 | −0.851787 | ||||||||
\(599\) | 1.90793e6 | 0.217268 | 0.108634 | − | 0.994082i | \(-0.465352\pi\) | ||||
0.108634 | + | 0.994082i | \(0.465352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.52970e6 | 0.398613 | 0.199306 | − | 0.979937i | \(-0.436131\pi\) | ||||
0.199306 | + | 0.979937i | \(0.436131\pi\) | |||||||
\(602\) | −622888. | −0.0700517 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.33851e6 | −0.372358 | ||||||||
\(605\) | 3.15205e6 | 0.350110 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.37799e6 | 0.372123 | 0.186061 | − | 0.982538i | \(-0.440428\pi\) | ||||
0.186061 | + | 0.982538i | \(0.440428\pi\) | |||||||
\(608\) | 264192. | 0.0289842 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.87400e6 | 0.530348 | ||||||||
\(611\) | 1.37946e7 | 1.49488 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.20412e6 | 0.129425 | 0.0647127 | − | 0.997904i | \(-0.479387\pi\) | ||||
0.0647127 | + | 0.997904i | \(0.479387\pi\) | |||||||
\(614\) | 1.12709e7 | 1.20653 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −586432. | −0.0622681 | ||||||||
\(617\) | 5.47330e6 | 0.578810 | 0.289405 | − | 0.957207i | \(-0.406543\pi\) | ||||
0.289405 | + | 0.957207i | \(0.406543\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.22662e6 | 0.338471 | 0.169236 | − | 0.985576i | \(-0.445870\pi\) | ||||
0.169236 | + | 0.985576i | \(0.445870\pi\) | |||||||
\(620\) | −766400. | −0.0800712 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.38959e6 | 0.351295 | ||||||||
\(623\) | 2.23244e6 | 0.230441 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.45982e6 | 0.148889 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 576160. | 0.0582967 | ||||||||
\(629\) | −1.19259e7 | −1.20189 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.36282e7 | 1.36259 | 0.681297 | − | 0.732007i | \(-0.261416\pi\) | ||||
0.681297 | + | 0.732007i | \(0.261416\pi\) | |||||||
\(632\) | −2.79814e6 | −0.278662 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.74975e6 | −0.765711 | ||||||||
\(635\) | −751300. | −0.0739399 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50543e6 | 0.146998 | ||||||||
\(638\) | −971652. | −0.0945059 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | 1.92472e7 | 1.85021 | 0.925106 | − | 0.379710i | \(-0.123976\pi\) | ||||
0.925106 | + | 0.379710i | \(0.123976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.28399e7 | −1.22472 | −0.612358 | − | 0.790580i | \(-0.709779\pi\) | ||||
−0.612358 | + | 0.790580i | \(0.709779\pi\) | |||||||
\(644\) | 2.32848e6 | 0.221237 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.87102e6 | −0.176399 | ||||||||
\(647\) | −2.00233e7 | −1.88050 | −0.940251 | − | 0.340481i | \(-0.889410\pi\) | ||||
−0.940251 | + | 0.340481i | \(0.889410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −735284. | −0.0685241 | ||||||||
\(650\) | 1.56750e6 | 0.145520 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.81072e6 | 0.258940 | ||||||||
\(653\) | 7.23655e6 | 0.664124 | 0.332062 | − | 0.943258i | \(-0.392256\pi\) | ||||
0.332062 | + | 0.943258i | \(0.392256\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00125e6 | −0.273337 | ||||||||
\(656\) | −1.70906e6 | −0.155059 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.31220e6 | −0.388270 | ||||||||
\(659\) | −1.42474e7 | −1.27798 | −0.638989 | − | 0.769216i | \(-0.720647\pi\) | ||||
−0.638989 | + | 0.769216i | \(0.720647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.49265e7 | 1.32878 | 0.664391 | − | 0.747385i | \(-0.268691\pi\) | ||||
0.664391 | + | 0.747385i | \(0.268691\pi\) | |||||||
\(662\) | −245840. | −0.0218026 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.22566e6 | −0.547981 | ||||||||
\(665\) | 316050. | 0.0277142 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.85803e6 | 0.335777 | ||||||||
\(668\) | 2.51861e6 | 0.218383 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.48320e6 | 0.385835 | ||||||||
\(671\) | −9.11438e6 | −0.781485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.55062e7 | −1.31967 | −0.659837 | − | 0.751409i | \(-0.729375\pi\) | ||||
−0.659837 | + | 0.751409i | \(0.729375\pi\) | |||||||
\(674\) | −1.49646e7 | −1.26887 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 349376. | 0.0294053 | ||||||||
\(677\) | 7.80065e6 | 0.654122 | 0.327061 | − | 0.945003i | \(-0.393942\pi\) | ||||
0.327061 | + | 0.945003i | \(0.393942\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.80745e6 | 0.233689 | ||||||||
\(680\) | 2.90080e6 | 0.240572 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.43317e6 | 0.117988 | ||||||||
\(683\) | −1.58547e7 | −1.30049 | −0.650243 | − | 0.759727i | \(-0.725333\pi\) | ||||
−0.650243 | + | 0.759727i | \(0.725333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 794400. | 0.0646864 | ||||||||
\(686\) | −470596. | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 813568. | 0.0655274 | ||||||||
\(689\) | −1.64073e7 | −1.31671 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.03656e7 | 1.62257 | 0.811284 | − | 0.584652i | \(-0.198769\pi\) | ||||
0.811284 | + | 0.584652i | \(0.198769\pi\) | |||||||
\(692\) | 375536. | 0.0298117 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −845336. | −0.0666240 | ||||||||
\(695\) | 5.00405e6 | 0.392970 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.21036e7 | 0.943696 | ||||||||
\(698\) | 1.35823e7 | 1.05520 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −490000. | −0.0377964 | ||||||||
\(701\) | −2.48036e7 | −1.90643 | −0.953213 | − | 0.302300i | \(-0.902246\pi\) | ||||
−0.953213 | + | 0.302300i | \(0.902246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.69712e6 | 0.129517 | ||||||||
\(704\) | 765952. | 0.0582465 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.55237e7 | 1.17215 | ||||||||
\(707\) | −2.20353e6 | −0.165795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.81917e7 | 1.35912 | 0.679560 | − | 0.733620i | \(-0.262171\pi\) | ||||
0.679560 | + | 0.733620i | \(0.262171\pi\) | |||||||
\(710\) | 6.37360e6 | 0.474503 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.91584e6 | −0.215558 | ||||||||
\(713\) | −5.69052e6 | −0.419207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.93122e6 | −0.214429 | ||||||||
\(716\) | −9.79565e6 | −0.714086 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.29684e7 | −0.938806 | ||||||||
\(719\) | 1.66202e7 | 1.19899 | 0.599493 | − | 0.800380i | \(-0.295369\pi\) | ||||
0.599493 | + | 0.800380i | \(0.295369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.96884e6 | 0.355973 | ||||||||
\(722\) | −9.63814e6 | −0.688098 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.46131e6 | 0.599917 | ||||||||
\(725\) | −811875. | −0.0573646 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.57591e7 | −1.10585 | −0.552925 | − | 0.833231i | \(-0.686489\pi\) | ||||
−0.552925 | + | 0.833231i | \(0.686489\pi\) | |||||||
\(728\) | −1.96627e6 | −0.137504 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.04700e6 | −0.419984 | ||||||||
\(731\) | −5.76171e6 | −0.398803 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.15238e6 | −0.147965 | −0.0739827 | − | 0.997260i | \(-0.523571\pi\) | ||||
−0.0739827 | + | 0.997260i | \(0.523571\pi\) | |||||||
\(734\) | 5.77721e6 | 0.395802 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.04128e6 | −0.206948 | ||||||||
\(737\) | −8.38358e6 | −0.568540 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.27267e7 | −1.53083 | −0.765413 | − | 0.643540i | \(-0.777465\pi\) | ||||
−0.765413 | + | 0.643540i | \(0.777465\pi\) | |||||||
\(740\) | −2.63120e6 | −0.176634 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.12893e6 | 0.341993 | ||||||||
\(743\) | −1.21153e7 | −0.805123 | −0.402561 | − | 0.915393i | \(-0.631880\pi\) | ||||
−0.402561 | + | 0.915393i | \(0.631880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.74105e6 | 0.510986 | ||||||||
\(746\) | 1.37417e7 | 0.904050 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.42450e6 | −0.354491 | ||||||||
\(749\) | −8.13410e6 | −0.529791 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.07590e7 | −1.34310 | −0.671549 | − | 0.740961i | \(-0.734371\pi\) | ||||
−0.671549 | + | 0.740961i | \(0.734371\pi\) | |||||||
\(752\) | 5.63226e6 | 0.363193 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.25789e6 | −0.208693 | ||||||||
\(755\) | 5.21642e6 | 0.333047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.86222e7 | −1.18111 | −0.590556 | − | 0.806997i | \(-0.701091\pi\) | ||||
−0.590556 | + | 0.806997i | \(0.701091\pi\) | |||||||
\(758\) | −6.74539e6 | −0.426417 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −412800. | −0.0259242 | ||||||||
\(761\) | −2.65336e7 | −1.66087 | −0.830434 | − | 0.557117i | \(-0.811907\pi\) | ||||
−0.830434 | + | 0.557117i | \(0.811907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −406161. | −0.0252573 | ||||||||
\(764\) | −8.64590e6 | −0.535892 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.05742e7 | −0.651139 | ||||||||
\(767\) | −2.46536e6 | −0.151319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.01595e7 | −1.22931 | −0.614657 | − | 0.788794i | \(-0.710706\pi\) | ||||
−0.614657 | + | 0.788794i | \(0.710706\pi\) | |||||||
\(770\) | 916300. | 0.0556943 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.53651e7 | 0.927882 | ||||||||
\(773\) | 5.86488e6 | 0.353029 | 0.176514 | − | 0.984298i | \(-0.443518\pi\) | ||||
0.176514 | + | 0.984298i | \(0.443518\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.19750e6 | 0.0716178 | ||||||||
\(776\) | −3.66688e6 | −0.218596 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.80840e6 | 0.107114 | ||||||||
\(779\) | −1.72241e6 | −0.101693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.19186e7 | −0.699196 | ||||||||
\(782\) | 2.15384e7 | 1.25950 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | −900250. | −0.0521422 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.63347e6 | −0.0940100 | −0.0470050 | − | 0.998895i | \(-0.514968\pi\) | ||||
−0.0470050 | + | 0.998895i | \(0.514968\pi\) | |||||||
\(788\) | −1.21911e7 | −0.699403 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.37210e6 | 0.249243 | ||||||||
\(791\) | 1.28971e7 | 0.732910 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.05600e7 | −1.72572 | ||||||||
\(794\) | −7.82121e6 | −0.440274 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00134e6 | 0.111954 | ||||||||
\(797\) | −2.07673e7 | −1.15807 | −0.579034 | − | 0.815303i | \(-0.696570\pi\) | ||||
−0.579034 | + | 0.815303i | \(0.696570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.98878e7 | −2.21041 | ||||||||
\(800\) | 640000. | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.90695e7 | 1.04689 | ||||||||
\(803\) | 1.13079e7 | 0.618860 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.63825e6 | −0.197880 | ||||||||
\(806\) | 4.80533e6 | 0.260547 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.87808e6 | 0.155087 | ||||||||
\(809\) | −3.53936e6 | −0.190131 | −0.0950656 | − | 0.995471i | \(-0.530306\pi\) | ||||
−0.0950656 | + | 0.995471i | \(0.530306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.11480e7 | −1.12906 | −0.564530 | − | 0.825412i | \(-0.690943\pi\) | ||||
−0.564530 | + | 0.825412i | \(0.690943\pi\) | |||||||
\(812\) | 1.01842e6 | 0.0542045 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.92034e6 | 0.260276 | ||||||||
\(815\) | −4.39175e6 | −0.231603 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 819924. | 0.0429753 | ||||||||
\(818\) | −1.65280e7 | −0.863646 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.67040e6 | 0.138689 | ||||||||
\(821\) | −265389. | −0.0137412 | −0.00687061 | − | 0.999976i | \(-0.502187\pi\) | ||||
−0.00687061 | + | 0.999976i | \(0.502187\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.09261e7 | 1.59157 | 0.795785 | − | 0.605579i | \(-0.207058\pi\) | ||||
0.795785 | + | 0.605579i | \(0.207058\pi\) | |||||||
\(824\) | −6.48992e6 | −0.332982 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 770672. | 0.0393024 | ||||||||
\(827\) | 2.84152e7 | 1.44473 | 0.722367 | − | 0.691510i | \(-0.243054\pi\) | ||||
0.722367 | + | 0.691510i | \(0.243054\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.33547e7 | −1.68566 | −0.842832 | − | 0.538177i | \(-0.819113\pi\) | ||||
−0.842832 | + | 0.538177i | \(0.819113\pi\) | |||||||
\(830\) | 9.72760e6 | 0.490129 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.56819e6 | 0.128623 | ||||||||
\(833\) | −4.35301e6 | −0.217359 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.93532e6 | −0.195328 | ||||||||
\(836\) | 771936. | 0.0382002 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −762048. | −0.0374863 | ||||||||
\(839\) | 5.66205e6 | 0.277695 | 0.138848 | − | 0.990314i | \(-0.455660\pi\) | ||||
0.138848 | + | 0.990314i | \(0.455660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.88237e7 | −0.917732 | ||||||||
\(842\) | −2.07674e7 | −1.00949 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.00408e7 | 0.485188 | ||||||||
\(845\) | −545900. | −0.0263009 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.17802e6 | 0.295897 | ||||||||
\(848\) | −6.69901e6 | −0.319905 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.53250e6 | −0.215174 | ||||||||
\(851\) | −1.95367e7 | −0.924754 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.19983e7 | 1.03518 | 0.517592 | − | 0.855628i | \(-0.326829\pi\) | ||||
0.517592 | + | 0.855628i | \(0.326829\pi\) | |||||||
\(854\) | 9.55304e6 | 0.448226 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.06241e7 | 0.495574 | ||||||||
\(857\) | 2.17568e7 | 1.01191 | 0.505956 | − | 0.862559i | \(-0.331140\pi\) | ||||
0.505956 | + | 0.862559i | \(0.331140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.09384e7 | −1.89299 | −0.946494 | − | 0.322721i | \(-0.895402\pi\) | ||||
−0.946494 | + | 0.322721i | \(0.895402\pi\) | |||||||
\(860\) | −1.27120e6 | −0.0586095 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.68712e7 | 0.773355 | ||||||||
\(863\) | −5.65597e6 | −0.258512 | −0.129256 | − | 0.991611i | \(-0.541259\pi\) | ||||
−0.129256 | + | 0.991611i | \(0.541259\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −586775. | −0.0266644 | ||||||||
\(866\) | −1.94411e7 | −0.880899 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.50214e6 | −0.0676725 | ||||||||
\(869\) | −8.17583e6 | −0.367267 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.81097e7 | −1.25548 | ||||||||
\(872\) | 530496. | 0.0236260 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.06504e6 | −0.135724 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.61067e7 | 1.14618 | 0.573089 | − | 0.819493i | \(-0.305745\pi\) | ||||
0.573089 | + | 0.819493i | \(0.305745\pi\) | |||||||
\(878\) | −8.12454e6 | −0.355682 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.19680e6 | −0.0520973 | ||||||||
\(881\) | −1.44294e6 | −0.0626339 | −0.0313170 | − | 0.999510i | \(-0.509970\pi\) | ||||
−0.0313170 | + | 0.999510i | \(0.509970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.52432e7 | −0.657921 | −0.328960 | − | 0.944344i | \(-0.606698\pi\) | ||||
−0.328960 | + | 0.944344i | \(0.606698\pi\) | |||||||
\(884\) | −1.81880e7 | −0.782807 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.13679e7 | −0.486517 | ||||||||
\(887\) | 3.31500e7 | 1.41473 | 0.707366 | − | 0.706847i | \(-0.249883\pi\) | ||||
0.707366 | + | 0.706847i | \(0.249883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.47255e6 | −0.0624907 | ||||||||
\(890\) | 4.55600e6 | 0.192801 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.95376e7 | −0.822166 | ||||||||
\(893\) | 5.67626e6 | 0.238195 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.53057e7 | 0.638698 | ||||||||
\(896\) | −802816. | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.83873e7 | 0.760899 | ||||||||
\(899\) | −2.48888e6 | −0.102708 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.74426e7 | 1.94696 | ||||||||
\(902\) | −4.99365e6 | −0.204363 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.68452e7 | −0.685575 | ||||||||
\(905\) | −1.32208e7 | −0.536582 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.16963e7 | 0.472096 | 0.236048 | − | 0.971741i | \(-0.424148\pi\) | ||||
0.236048 | + | 0.971741i | \(0.424148\pi\) | |||||||
\(908\) | −6.24875e6 | −0.251524 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.07230e6 | 0.122987 | ||||||||
\(911\) | −2.89321e7 | −1.15501 | −0.577503 | − | 0.816389i | \(-0.695973\pi\) | ||||
−0.577503 | + | 0.816389i | \(0.695973\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.81906e7 | −0.722221 | ||||||||
\(914\) | 1.97347e7 | 0.781384 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.13940e7 | −0.448680 | ||||||||
\(917\) | −5.88245e6 | −0.231012 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.57838e7 | −1.78823 | −0.894115 | − | 0.447838i | \(-0.852194\pi\) | ||||
−0.894115 | + | 0.447838i | \(0.852194\pi\) | |||||||
\(920\) | 4.75200e6 | 0.185100 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.90267e7 | 0.737116 | ||||||||
\(923\) | −3.99625e7 | −1.54400 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.11125e6 | 0.157986 | ||||||||
\(926\) | 1.63448e7 | 0.626399 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.33018e6 | −0.0507036 | ||||||||
\(929\) | −2.46947e7 | −0.938782 | −0.469391 | − | 0.882990i | \(-0.655526\pi\) | ||||
−0.469391 | + | 0.882990i | \(0.655526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 619458. | 0.0234227 | ||||||||
\(932\) | −8.98522e6 | −0.338835 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.66373e7 | 0.624044 | ||||||||
\(935\) | 8.47578e6 | 0.317067 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.98926e7 | −0.740187 | −0.370094 | − | 0.928994i | \(-0.620674\pi\) | ||||
−0.370094 | + | 0.928994i | \(0.620674\pi\) | |||||||
\(938\) | 8.78707e6 | 0.326090 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.80040e6 | −0.324850 | ||||||||
\(941\) | 3.73454e7 | 1.37488 | 0.687438 | − | 0.726243i | \(-0.258735\pi\) | ||||
0.687438 | + | 0.726243i | \(0.258735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.98277e7 | 0.726095 | ||||||||
\(944\) | −1.00659e6 | −0.0367641 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.37714e6 | 0.0863630 | ||||||||
\(947\) | −5.10396e7 | −1.84941 | −0.924703 | − | 0.380689i | \(-0.875687\pi\) | ||||
−0.924703 | + | 0.380689i | \(0.875687\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.79147e7 | 1.36660 | ||||||||
\(950\) | 645000. | 0.0231873 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.68557e6 | 0.203321 | ||||||||
\(953\) | −254832. | −0.00908912 | −0.00454456 | − | 0.999990i | \(-0.501447\pi\) | ||||
−0.00454456 | + | 0.999990i | \(0.501447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.35092e7 | 0.479316 | ||||||||
\(956\) | 2.17734e7 | 0.770515 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.34416e7 | 0.473192 | ||||||||
\(959\) | 1.55702e6 | 0.0546700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.49581e7 | −0.871772 | ||||||||
\(962\) | 1.64976e7 | 0.574756 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.48080e6 | 0.293930 | ||||||||
\(965\) | −2.40080e7 | −0.829923 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.17012e7 | 0.402405 | 0.201203 | − | 0.979550i | \(-0.435515\pi\) | ||||
0.201203 | + | 0.979550i | \(0.435515\pi\) | |||||||
\(968\) | −8.06925e6 | −0.276786 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.72950e6 | 0.195518 | ||||||||
\(971\) | −3.59080e7 | −1.22220 | −0.611101 | − | 0.791553i | \(-0.709273\pi\) | ||||
−0.611101 | + | 0.791553i | \(0.709273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.80794e6 | 0.332120 | ||||||||
\(974\) | 2.82097e7 | 0.952799 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.24774e7 | −0.419277 | ||||||||
\(977\) | 5.50592e7 | 1.84541 | 0.922706 | − | 0.385504i | \(-0.125972\pi\) | ||||
0.922706 | + | 0.385504i | \(0.125972\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.51972e6 | −0.284098 | ||||||||
\(980\) | −960400. | −0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 335748. | 0.0111105 | ||||||||
\(983\) | 1.81317e7 | 0.598488 | 0.299244 | − | 0.954177i | \(-0.403266\pi\) | ||||
0.299244 | + | 0.954177i | \(0.403266\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.90486e7 | 0.625565 | ||||||||
\(986\) | 9.42035e6 | 0.308585 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.58826e6 | 0.0843558 | ||||||||
\(989\) | −9.43866e6 | −0.306845 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.02908e7 | −0.656318 | −0.328159 | − | 0.944623i | \(-0.606428\pi\) | ||||
−0.328159 | + | 0.944623i | \(0.606428\pi\) | |||||||
\(992\) | 1.96198e6 | 0.0633018 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.24923e7 | 0.401028 | ||||||||
\(995\) | −3.12710e6 | −0.100135 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.75390e7 | 1.51465 | 0.757325 | − | 0.653038i | \(-0.226506\pi\) | ||||
0.757325 | + | 0.653038i | \(0.226506\pi\) | |||||||
\(998\) | −2.84211e7 | −0.903262 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 630.6.a.i.1.1 | 1 | ||
3.2 | odd | 2 | 70.6.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 560.6.a.e.1.1 | 1 | |||
15.2 | even | 4 | 350.6.c.g.99.1 | 2 | |||
15.8 | even | 4 | 350.6.c.g.99.2 | 2 | |||
15.14 | odd | 2 | 350.6.a.l.1.1 | 1 | |||
21.20 | even | 2 | 490.6.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.6.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
350.6.a.l.1.1 | 1 | 15.14 | odd | 2 | |||
350.6.c.g.99.1 | 2 | 15.2 | even | 4 | |||
350.6.c.g.99.2 | 2 | 15.8 | even | 4 | |||
490.6.a.g.1.1 | 1 | 21.20 | even | 2 | |||
560.6.a.e.1.1 | 1 | 12.11 | even | 2 | |||
630.6.a.i.1.1 | 1 | 1.1 | even | 1 | trivial |