Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (of order \(2\), degree \(1\), 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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 46 x^{14} + 1311 x^{12} + 24382 x^{10} + 338077 x^{8} + 3338772 x^{6} + 24662556 x^{4} + \cdots + 362673936 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{84}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.11 | ||
Root | \(-1.45110 + 3.51338i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.5.b.d.319.14 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 19.1142i | − 0.764569i | −0.924045 | − | 0.382285i | \(-0.875137\pi\) | ||||
0.924045 | − | 0.382285i | \(-0.124863\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.40010i | 0.130614i | 0.997865 | + | 0.0653071i | \(0.0208027\pi\) | ||||
−0.997865 | + | 0.0653071i | \(0.979197\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −67.7877 | −0.560229 | −0.280114 | − | 0.959967i | \(-0.590372\pi\) | ||||
−0.280114 | + | 0.959967i | \(0.590372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 154.346i | 0.913290i | 0.889649 | + | 0.456645i | \(0.150949\pi\) | ||||
−0.889649 | + | 0.456645i | \(0.849051\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 99.3205i | − 0.441424i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 284.063 | 0.982918 | 0.491459 | − | 0.870901i | \(-0.336464\pi\) | ||||
0.491459 | + | 0.870901i | \(0.336464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 434.548 | 1.20373 | 0.601866 | − | 0.798597i | \(-0.294424\pi\) | ||||
0.601866 | + | 0.798597i | \(0.294424\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 33.2559i | 0.0754102i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 462.698i | − 0.874666i | −0.899300 | − | 0.437333i | \(-0.855923\pi\) | ||||
0.899300 | − | 0.437333i | \(-0.144077\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 259.646 | 0.415434 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 350.108i | − 0.416300i | −0.978097 | − | 0.208150i | \(-0.933256\pi\) | ||||
0.978097 | − | 0.208150i | \(-0.0667442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 88.4523i | 0.0920420i | 0.998940 | + | 0.0460210i | \(0.0146541\pi\) | ||||
−0.998940 | + | 0.0460210i | \(0.985346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −352.235 | −0.323448 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 122.333 | 0.0998637 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1636.60i | − 1.19547i | −0.801694 | − | 0.597734i | \(-0.796068\pi\) | ||||
0.801694 | − | 0.597734i | \(-0.203932\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 802.006i | 0.527288i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 395.726 | 0.235411 | 0.117706 | − | 0.993049i | \(-0.462446\pi\) | ||||
0.117706 | + | 0.993049i | \(0.462446\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −350.192 | −0.189396 | −0.0946978 | − | 0.995506i | \(-0.530188\pi\) | ||||
−0.0946978 | + | 0.995506i | \(0.530188\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 516.084i | − 0.254856i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 2459.53i | − 1.11341i | −0.830709 | − | 0.556707i | \(-0.812065\pi\) | ||||
0.830709 | − | 0.556707i | \(-0.187935\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2360.04 | 0.982940 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1476.04 | 0.567488 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3827.15i | − 1.36246i | −0.732069 | − | 0.681230i | \(-0.761445\pi\) | ||||
0.732069 | − | 0.681230i | \(-0.238555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1295.71i | 0.428334i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2257.98 | 0.694975 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1754.25 | −0.503951 | −0.251975 | − | 0.967734i | \(-0.581080\pi\) | ||||
−0.251975 | + | 0.967734i | \(0.581080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2335.10i | − 0.627546i | −0.949498 | − | 0.313773i | \(-0.898407\pi\) | ||||
0.949498 | − | 0.313773i | \(-0.101593\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 172.803i | 0.0435381i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2950.21 | 0.698274 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2198.93 | −0.489848 | −0.244924 | − | 0.969542i | \(-0.578763\pi\) | ||||
−0.244924 | + | 0.969542i | \(0.578763\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2404.25i | − 0.504989i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4463.62i | 0.885463i | 0.896654 | + | 0.442732i | \(0.145991\pi\) | ||||
−0.896654 | + | 0.442732i | \(0.854009\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2592.13 | 0.486420 | 0.243210 | − | 0.969974i | \(-0.421800\pi\) | ||||
0.243210 | + | 0.969974i | \(0.421800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1349.16 | 0.239851 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 433.848i | − 0.0731738i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2040.82i | 0.327002i | 0.986543 | + | 0.163501i | \(0.0522788\pi\) | ||||
−0.986543 | + | 0.163501i | \(0.947721\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5245.36 | −0.761411 | −0.380706 | − | 0.924696i | \(-0.624319\pi\) | ||||
−0.380706 | + | 0.924696i | \(0.624319\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 5429.65i | − 0.751509i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1819.22i | − 0.240351i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14320.4 | 1.80790 | 0.903952 | − | 0.427635i | \(-0.140653\pi\) | ||||
0.903952 | + | 0.427635i | \(0.140653\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −987.830 | −0.119289 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 459.612i | 0.0531405i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 8306.04i | − 0.920337i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16844.8 | 1.79029 | 0.895145 | − | 0.445776i | \(-0.147072\pi\) | ||||
0.895145 | + | 0.445776i | \(0.147072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1830.27 | −0.186743 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 8909.06i | − 0.873352i | −0.899619 | − | 0.436676i | \(-0.856156\pi\) | ||||
0.899619 | − | 0.436676i | \(-0.143844\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19586.8i | 1.84624i | 0.384507 | + | 0.923122i | \(0.374371\pi\) | ||||
−0.384507 | + | 0.923122i | \(0.625629\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 635.661 | 0.0576563 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13789.3 | 1.20441 | 0.602207 | − | 0.798340i | \(-0.294288\pi\) | ||||
0.602207 | + | 0.798340i | \(0.294288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 13179.9i | − 1.10933i | −0.832074 | − | 0.554665i | \(-0.812847\pi\) | ||||
0.832074 | − | 0.554665i | \(-0.187153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 8504.00i | − 0.690204i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2732.48 | −0.213993 | −0.106997 | − | 0.994259i | \(-0.534123\pi\) | ||||
−0.106997 | + | 0.994259i | \(0.534123\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8844.13 | −0.668743 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4167.34i | 0.304430i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1818.03i | 0.128383i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10045.8 | −0.686144 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2056.25 | 0.135915 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 16909.3i | − 1.08220i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 23919.4i | − 1.48301i | −0.670949 | − | 0.741503i | \(-0.734113\pi\) | ||||
0.670949 | − | 0.741503i | \(-0.265887\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1819.65 | −0.109348 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 25059.5 | 1.46026 | 0.730129 | − | 0.683309i | \(-0.239460\pi\) | ||||
0.730129 | + | 0.683309i | \(0.239460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2781.15i | 0.157225i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 2681.65i | − 0.147141i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 528.551 | 0.0281609 | 0.0140804 | − | 0.999901i | \(-0.495518\pi\) | ||||
0.0140804 | + | 0.999901i | \(0.495518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −24051.5 | −1.24484 | −0.622419 | − | 0.782684i | \(-0.713850\pi\) | ||||
−0.622419 | + | 0.782684i | \(0.713850\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 12780.1i | − 0.642830i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 10462.8i | − 0.511651i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6692.06 | −0.318290 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12263.1 | 0.567501 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5229.61i | 0.235557i | 0.993040 | + | 0.117779i | \(0.0375773\pi\) | ||||
−0.993040 | + | 0.117779i | \(0.962423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 26586.7i | 1.16603i | 0.812460 | + | 0.583017i | \(0.198128\pi\) | ||||
−0.812460 | + | 0.583017i | \(0.801872\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7669.71 | 0.327639 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1690.70 | 0.0703725 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10616.7i | 0.430717i | 0.976535 | + | 0.215359i | \(0.0690920\pi\) | ||||
−0.976535 | + | 0.215359i | \(0.930908\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 19886.5i | − 0.786617i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2961.32 | 0.114244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13539.3 | −0.509589 | −0.254794 | − | 0.966995i | \(-0.582008\pi\) | ||||
−0.254794 | + | 0.966995i | \(0.582008\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6732.70i | 0.247299i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 31228.7i | 1.11975i | 0.828577 | + | 0.559876i | \(0.189151\pi\) | ||||
−0.828577 | + | 0.559876i | \(0.810849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4738.29 | 0.165901 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11732.8 | 0.401244 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 42767.2i | 1.42895i | 0.699659 | + | 0.714477i | \(0.253335\pi\) | ||||
−0.699659 | + | 0.714477i | \(0.746665\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1661.76i | 0.0542615i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9115.36 | −0.290956 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16667.9 | 0.520206 | 0.260103 | − | 0.965581i | \(-0.416244\pi\) | ||||
0.260103 | + | 0.965581i | \(0.416244\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23689.5i | 0.723101i | 0.932353 | + | 0.361550i | \(0.117752\pi\) | ||||
−0.932353 | + | 0.361550i | \(0.882248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 12133.5i | − 0.362314i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31282.3 | −0.914019 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19256.0 | −0.550659 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 897.909i | 0.0251367i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 67099.3i | − 1.83929i | −0.392747 | − | 0.919647i | \(-0.628475\pi\) | ||||
0.392747 | − | 0.919647i | \(-0.371525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11239.9 | −0.301750 | −0.150875 | − | 0.988553i | \(-0.548209\pi\) | ||||
−0.150875 | + | 0.988553i | \(0.548209\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15329.7 | 0.403149 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14984.6i | 0.386113i | 0.981188 | + | 0.193056i | \(0.0618400\pi\) | ||||
−0.981188 | + | 0.193056i | \(0.938160\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 71104.7i | 1.79553i | 0.440477 | + | 0.897764i | \(0.354809\pi\) | ||||
−0.440477 | + | 0.897764i | \(0.645191\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11426.0 | −0.282814 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2240.73 | 0.0543747 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 7564.01i | − 0.179988i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 12492.9i | − 0.291555i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29457.0 | −0.674365 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −60965.8 | −1.36937 | −0.684686 | − | 0.728838i | \(-0.740061\pi\) | ||||
−0.684686 | + | 0.728838i | \(0.740061\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23193.7i | 0.511222i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6693.66i | 0.144806i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −566.104 | −0.0120220 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13469.1 | 0.280835 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 43844.0i | 0.897689i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 87167.1i | 1.75284i | 0.481545 | + | 0.876422i | \(0.340076\pi\) | ||||
−0.481545 | + | 0.876422i | \(0.659924\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7010.44 | 0.138478 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14968.7 | −0.290492 | −0.145246 | − | 0.989396i | \(-0.546397\pi\) | ||||
−0.145246 | + | 0.989396i | \(0.546397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 78306.4i | 1.49323i | 0.665257 | + | 0.746615i | \(0.268322\pi\) | ||||
−0.665257 | + | 0.746615i | \(0.731678\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 2254.34i | − 0.0422469i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −54896.5 | −1.01119 | −0.505595 | − | 0.862771i | \(-0.668727\pi\) | ||||
−0.505595 | + | 0.862771i | \(0.668727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −47012.1 | −0.851283 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10604.4i | 0.188795i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 66861.2i | − 1.17052i | −0.810846 | − | 0.585259i | \(-0.800993\pi\) | ||||
0.810846 | − | 0.585259i | \(-0.199007\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −99876.4 | −1.71961 | −0.859803 | − | 0.510626i | \(-0.829414\pi\) | ||||
−0.859803 | + | 0.510626i | \(0.829414\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 45110.3i | − 0.751526i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 67070.7i | 1.09936i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27255.7 | −0.439601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18469.6 | 0.293164 | 0.146582 | − | 0.989199i | \(-0.453173\pi\) | ||||
0.146582 | + | 0.989199i | \(0.453173\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31365.2i | 0.490013i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 28213.3i | − 0.433884i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12430.9 | 0.188208 | 0.0941040 | − | 0.995562i | \(-0.470001\pi\) | ||||
0.0941040 | + | 0.995562i | \(0.470001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10474.4 | 0.156145 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 9452.93i | − 0.138767i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 50546.1i | − 0.730762i | −0.930858 | − | 0.365381i | \(-0.880939\pi\) | ||||
0.930858 | − | 0.365381i | \(-0.119061\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −73153.1 | −1.04170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 74411.0 | 1.04379 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 88678.2i | 1.22550i | 0.790278 | + | 0.612748i | \(0.209936\pi\) | ||||
−0.790278 | + | 0.612748i | \(0.790064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 18805.0i | − 0.256056i | −0.991771 | − | 0.128028i | \(-0.959135\pi\) | ||||
0.991771 | − | 0.128028i | \(-0.0408647\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5132.92 | −0.0688714 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17600.8 | −0.232738 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 37803.3i | − 0.492686i | −0.969183 | − | 0.246343i | \(-0.920771\pi\) | ||||
0.969183 | − | 0.246343i | \(-0.0792289\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2388.21i | 0.0306807i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25583.9 | 0.324006 | 0.162003 | − | 0.986790i | \(-0.448205\pi\) | ||||
0.162003 | + | 0.986790i | \(0.448205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −42546.3 | −0.531237 | −0.265619 | − | 0.964078i | \(-0.585576\pi\) | ||||
−0.265619 | + | 0.964078i | \(0.585576\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 43159.5i | − 0.531357i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2532.69i | 0.0307481i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2829.08 | −0.0338726 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 87528.3 | 1.03362 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 101982.i | − 1.18793i | −0.804492 | − | 0.593963i | \(-0.797562\pi\) | ||||
0.804492 | − | 0.593963i | \(-0.202438\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33531.2i | 0.385305i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9510.34 | −0.107816 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 71415.7 | 0.798824 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2241.27i | − 0.0247378i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 46292.9i | − 0.504230i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −44633.7 | −0.479803 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −170124. | −1.80505 | −0.902523 | − | 0.430642i | \(-0.858287\pi\) | ||||
−0.902523 | + | 0.430642i | \(0.858287\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 101776.i | 1.06593i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 41592.7i | − 0.430028i | −0.976611 | − | 0.215014i | \(-0.931020\pi\) | ||||
0.976611 | − | 0.215014i | \(-0.0689797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 121687. | 1.24210 | 0.621049 | − | 0.783772i | \(-0.286707\pi\) | ||||
0.621049 | + | 0.783772i | \(0.286707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3302.99 | 0.0332879 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 126498.i | 1.25882i | 0.777073 | + | 0.629411i | \(0.216704\pi\) | ||||
−0.777073 | + | 0.629411i | \(0.783296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23733.0i | 0.233223i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 71651.5 | 0.695368 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 123439. | 1.18317 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40075.3i | 0.379411i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 68485.0i | − 0.640471i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15741.3 | 0.145428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33699.5 | 0.307586 | 0.153793 | − | 0.988103i | \(-0.450851\pi\) | ||||
0.153793 | + | 0.988103i | \(0.450851\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 44188.1i | − 0.398489i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 42030.8i | 0.374523i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 92980.8 | 0.818717 | 0.409358 | − | 0.912374i | \(-0.365753\pi\) | ||||
0.409358 | + | 0.912374i | \(0.365753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14198.4 | −0.123549 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 5995.98i | − 0.0515645i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30471.1i | 0.259000i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −45955.4 | −0.386099 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6718.56 | −0.0557978 | −0.0278989 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0278989 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 79498.6i | − 0.652693i | −0.945250 | − | 0.326346i | \(-0.894182\pi\) | ||||
0.945250 | − | 0.326346i | \(-0.105818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21654.2i | 0.175763i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 45108.7 | 0.362002 | 0.181001 | − | 0.983483i | \(-0.442066\pi\) | ||||
0.181001 | + | 0.983483i | \(0.442066\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 85318.7 | 0.676998 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9446.78i | 0.0741220i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 171192.i | − 1.32829i | −0.747602 | − | 0.664147i | \(-0.768795\pi\) | ||||
0.747602 | − | 0.664147i | \(-0.231205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 58510.5 | 0.448972 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −52199.7 | −0.396145 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 49546.6i | − 0.371902i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 197479.i | 1.46618i | 0.680130 | + | 0.733091i | \(0.261923\pi\) | ||||
−0.680130 | + | 0.733091i | \(0.738077\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10684.6 | 0.0784704 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24494.1 | 0.177957 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 78469.2i | − 0.564003i | −0.959414 | − | 0.282002i | \(-0.909002\pi\) | ||||
0.959414 | − | 0.282002i | \(-0.0909984\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 87863.5i | − 0.624807i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 54037.9 | 0.380203 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −248236. | −1.72817 | −0.864086 | − | 0.503344i | \(-0.832103\pi\) | ||||
−0.864086 | + | 0.503344i | \(0.832103\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 124289.i | − 0.856214i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 75091.5i | 0.511910i | 0.966689 | + | 0.255955i | \(0.0823898\pi\) | ||||
−0.966689 | + | 0.255955i | \(0.917610\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8292.67 | −0.0559465 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9455.19 | −0.0631319 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 280557.i | − 1.85405i | −0.375000 | − | 0.927025i | \(-0.622357\pi\) | ||||
0.375000 | − | 0.927025i | \(-0.377643\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 131436.i | − 0.859725i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 130213. | 0.843081 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39008.8 | 0.250016 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 225848.i | − 1.43296i | −0.697605 | − | 0.716482i | \(-0.745751\pi\) | ||||
0.697605 | − | 0.716482i | \(-0.254249\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14451.3i | 0.0907737i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 165029. | 1.02629 | 0.513147 | − | 0.858301i | \(-0.328480\pi\) | ||||
0.513147 | + | 0.858301i | \(0.328480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13652.3 | −0.0840611 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 13934.3i | − 0.0849522i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 110941.i | 0.669735i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29698.0 | −0.177534 | −0.0887669 | − | 0.996052i | \(-0.528293\pi\) | ||||
−0.0887669 | + | 0.996052i | \(0.528293\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2746.43 | 0.0162587 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11227.4i | − 0.0658231i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 100261.i | 0.582152i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −124975. | −0.718708 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 100933. | 0.574918 | 0.287459 | − | 0.957793i | \(-0.407190\pi\) | ||||
0.287459 | + | 0.957793i | \(0.407190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 211728.i | 1.19457i | 0.802028 | + | 0.597287i | \(0.203755\pi\) | ||||
−0.802028 | + | 0.597287i | \(0.796245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 66407.4i | − 0.371138i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 73755.9 | 0.408337 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14944.9 | 0.0819665 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 54366.1i | − 0.295402i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 147606.i | 0.794603i | 0.917688 | + | 0.397302i | \(0.130053\pi\) | ||||
−0.917688 | + | 0.397302i | \(0.869947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 98534.8 | 0.525550 | 0.262775 | − | 0.964857i | \(-0.415362\pi\) | ||||
0.262775 | + | 0.964857i | \(0.415362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34772.9 | −0.183765 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 201064.i | − 1.05286i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 27484.6i | − 0.142613i | −0.997454 | − | 0.0713067i | \(-0.977283\pi\) | ||||
0.997454 | − | 0.0713067i | \(-0.0227169\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 63721.0 | 0.327647 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −53561.9 | −0.272928 | −0.136464 | − | 0.990645i | \(-0.543574\pi\) | ||||
−0.136464 | + | 0.990645i | \(0.543574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 273724.i | − 1.38227i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27173.8i | 0.135999i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 69100.4 | 0.342758 | 0.171379 | − | 0.985205i | \(-0.445178\pi\) | ||||
0.171379 | + | 0.985205i | \(0.445178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26825.4 | −0.131884 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 138149.i | 0.673210i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 18881.6i | 0.0912045i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 115106. | 0.551146 | 0.275573 | − | 0.961280i | \(-0.411132\pi\) | ||||
0.275573 | + | 0.961280i | \(0.411132\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 39853.0 | 0.189163 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 108198.i | 0.509119i | 0.967057 | + | 0.254559i | \(0.0819304\pi\) | ||||
−0.967057 | + | 0.254559i | \(0.918070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 63779.4i | 0.297522i | 0.988873 | + | 0.148761i | \(0.0475285\pi\) | ||||
−0.988873 | + | 0.148761i | \(0.952472\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8785.13 | 0.0406296 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −392929. | −1.80169 | −0.900844 | − | 0.434142i | \(-0.857052\pi\) | ||||
−0.900844 | + | 0.434142i | \(0.857052\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 14073.3i | − 0.0639811i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 55166.2i | 0.248675i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23738.7 | 0.106105 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 112829. | 0.500071 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 103333.i | − 0.454153i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 249509.i | 1.08746i | 0.839259 | + | 0.543732i | \(0.182989\pi\) | ||||
−0.839259 | + | 0.543732i | \(0.817011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 252602. | 1.09181 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15387.4 | 0.0659587 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 321976.i | − 1.36880i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 401706.i | − 1.69375i | −0.531789 | − | 0.846877i | \(-0.678480\pi\) | ||||
0.531789 | − | 0.846877i | \(-0.321520\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −70352.1 | −0.294211 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 110571. | 0.458645 | 0.229322 | − | 0.973351i | \(-0.426349\pi\) | ||||
0.229322 | + | 0.973351i | \(0.426349\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 99452.9i | − 0.409189i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34984.1i | 0.142778i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28567.6 | −0.115654 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −186945. | −0.750779 | −0.375390 | − | 0.926867i | \(-0.622491\pi\) | ||||
−0.375390 | + | 0.926867i | \(0.622491\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 162269.i | 0.646489i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 439468.i | − 1.73697i | −0.495719 | − | 0.868483i | \(-0.665095\pi\) | ||||
0.495719 | − | 0.868483i | \(-0.334905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −170290. | −0.667738 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24620.9 | 0.0957828 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 339847.i | 1.31174i | 0.754874 | + | 0.655870i | \(0.227698\pi\) | ||||
−0.754874 | + | 0.655870i | \(0.772302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16589.9i | 0.0635334i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 60965.3 | 0.231658 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 374387. | 1.41158 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 166726.i | 0.623767i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 222225.i | 0.825007i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 107168. | 0.394812 | 0.197406 | − | 0.980322i | \(-0.436748\pi\) | ||||
0.197406 | + | 0.980322i | \(0.436748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 372679. | 1.36248 | 0.681242 | − | 0.732058i | \(-0.261440\pi\) | ||||
0.681242 | + | 0.732058i | \(0.261440\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8634.76i | 0.0313279i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25126.1i | 0.0904697i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 65751.1 | 0.234959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −47364.8 | −0.167984 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 61078.8i | 0.214999i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 263573.i | − 0.920858i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 86609.0 | 0.300341 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −159981. | −0.550671 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 105010.i | 0.358785i | 0.983778 | + | 0.179393i | \(0.0574132\pi\) | ||||
−0.983778 | + | 0.179393i | \(0.942587\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 123094.i | 0.417482i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −251924. | −0.848159 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 556117. | 1.85862 | 0.929311 | − | 0.369298i | \(-0.120402\pi\) | ||||
0.929311 | + | 0.369298i | \(0.120402\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 63047.7i | − 0.209182i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 152139.i | − 0.501114i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13061.5 | −0.0427112 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −162548. | −0.527709 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 336211.i | 1.08368i | 0.840481 | + | 0.541841i | \(0.182273\pi\) | ||||
−0.840481 | + | 0.541841i | \(0.817727\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 54050.8i | − 0.172973i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −100057. | −0.317923 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −558606. | −1.76234 | −0.881168 | − | 0.472803i | \(-0.843242\pi\) | ||||
−0.881168 | + | 0.472803i | \(0.843242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 52229.2i | 0.163613i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4665.67i | 0.0145127i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 190223. | 0.587542 | 0.293771 | − | 0.955876i | \(-0.405090\pi\) | ||||
0.293771 | + | 0.955876i | \(0.405090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 72652.1 | 0.222831 | 0.111416 | − | 0.993774i | \(-0.464462\pi\) | ||||
0.111416 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 348658.i | − 1.06192i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 120138.i | − 0.363366i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −294340. | −0.884091 | −0.442046 | − | 0.896993i | \(-0.645747\pi\) | ||||
−0.442046 | + | 0.896993i | \(0.645747\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −58404.2 | −0.174216 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 33570.8i | − 0.0994512i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 259434.i | 0.763289i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 79655.6 | 0.232758 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −189152. | −0.548953 | −0.274477 | − | 0.961594i | \(-0.588505\pi\) | ||||
−0.274477 | + | 0.961594i | \(0.588505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38436.7i | 0.110794i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 77862.5i | 0.222922i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −50118.2 | −0.142523 | −0.0712617 | − | 0.997458i | \(-0.522703\pi\) | ||||
−0.0712617 | + | 0.997458i | \(0.522703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34750.3 | 0.0981578 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 369471.i | 1.03665i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 142995.i | 0.398536i | 0.979945 | + | 0.199268i | \(0.0638564\pi\) | ||||
−0.979945 | + | 0.199268i | \(0.936144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −582870. | −1.61370 | −0.806849 | − | 0.590757i | \(-0.798829\pi\) | ||||
−0.806849 | + | 0.590757i | \(0.798829\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −59371.0 | −0.163283 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 192018.i | 0.524605i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 44407.7i | − 0.120526i | −0.998183 | − | 0.0602630i | \(-0.980806\pi\) | ||||
0.998183 | − | 0.0602630i | \(-0.0191939\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11643.2 | 0.0313933 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 379619. | 1.01687 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 108875.i | 0.289738i | 0.989451 | + | 0.144869i | \(0.0462761\pi\) | ||||
−0.989451 | + | 0.144869i | \(0.953724\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 39303.7i | − 0.103916i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −698860. | −1.83578 | −0.917888 | − | 0.396839i | \(-0.870107\pi\) | ||||
−0.917888 | + | 0.396839i | \(0.870107\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 441728. | 1.15285 | 0.576427 | − | 0.817149i | \(-0.304447\pi\) | ||||
0.576427 | + | 0.817149i | \(0.304447\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 64914.8i | − 0.168330i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 91652.0i | 0.236138i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −160930. | −0.411981 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −153063. | −0.389345 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 464897.i | − 1.17505i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 649021.i | − 1.63005i | −0.579428 | − | 0.815023i | \(-0.696724\pi\) | ||||
0.579428 | − | 0.815023i | \(-0.303276\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −316788. | −0.790608 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −457201. | −1.13386 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 364263.i | 0.897710i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 120518.i | 0.295154i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −774491. | −1.88495 | −0.942477 | − | 0.334272i | \(-0.891510\pi\) | ||||
−0.942477 | + | 0.334272i | \(0.891510\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 611676. | 1.47945 | 0.739723 | − | 0.672911i | \(-0.234956\pi\) | ||||
0.739723 | + | 0.672911i | \(0.234956\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 34781.3i | 0.0836038i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 518940.i | 1.23968i | 0.784729 | + | 0.619838i | \(0.212802\pi\) | ||||
−0.784729 | + | 0.619838i | \(0.787198\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 118917. | 0.282327 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2941.56 | −0.00694090 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 648450.i | 1.52072i | 0.649500 | + | 0.760362i | \(0.274978\pi\) | ||||
−0.649500 | + | 0.760362i | \(0.725022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 478993.i | − 1.11647i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 69987.6 | 0.162140 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −611892. | −1.40898 | −0.704489 | − | 0.709715i | \(-0.748824\pi\) | ||||
−0.704489 | + | 0.709715i | \(0.748824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 157591.i | 0.360684i | 0.983604 | + | 0.180342i | \(0.0577205\pi\) | ||||
−0.983604 | + | 0.180342i | \(0.942280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 227820.i | 0.518281i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 53159.5 | 0.120209 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −161995. | −0.364124 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 452934.i | 1.01200i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 158291.i | 0.351569i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −96816.9 | −0.213757 | −0.106879 | − | 0.994272i | \(-0.534086\pi\) | ||||
−0.106879 | + | 0.994272i | \(0.534086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36427.3 | 0.0799502 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 50973.9i | 0.111217i | 0.998453 | + | 0.0556084i | \(0.0177098\pi\) | ||||
−0.998453 | + | 0.0556084i | \(0.982290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 107809.i | 0.233837i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −77779.9 | −0.167715 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 179552. | 0.384901 | 0.192451 | − | 0.981307i | \(-0.438356\pi\) | ||||
0.192451 | + | 0.981307i | \(0.438356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10102.9i | − 0.0215309i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 406892.i | 0.862116i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 590706. | 1.24432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −189721. | −0.397338 | −0.198669 | − | 0.980067i | \(-0.563662\pi\) | ||||
−0.198669 | + | 0.980067i | \(0.563662\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 11713.9i | − 0.0243913i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 459726.i | 0.951765i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 112411. | 0.231390 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −285251. | −0.583811 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 499395.i | 1.01627i | 0.861278 | + | 0.508133i | \(0.169664\pi\) | ||||
−0.861278 | + | 0.508133i | \(0.830336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 711179.i | − 1.43902i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −244282. | −0.491488 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 57018.9 | 0.114072 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 328533.i | 0.653561i | 0.945100 | + | 0.326781i | \(0.105964\pi\) | ||||
−0.945100 | + | 0.326781i | \(0.894036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 55102.2i | 0.109001i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40926.8 | 0.0805060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −199988. | −0.391193 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 347421.i | − 0.675799i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 70795.6i | 0.136946i | 0.997653 | + | 0.0684728i | \(0.0218126\pi\) | ||||
−0.997653 | + | 0.0684728i | \(0.978187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −125357. | −0.241146 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −518973. | −0.992815 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 90904.2i | − 0.172945i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 264078.i | 0.499646i | 0.968291 | + | 0.249823i | \(0.0803725\pi\) | ||||
−0.968291 | + | 0.249823i | \(0.919627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −99476.8 | −0.186160 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 216452.i | − 0.402859i | −0.979503 | − | 0.201430i | \(-0.935441\pi\) | ||||
0.979503 | − | 0.201430i | \(-0.0645587\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 234400.i | − 0.433894i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 149060. | 0.274427 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 515590. | 0.944094 | 0.472047 | − | 0.881573i | \(-0.343515\pi\) | ||||
0.472047 | + | 0.881573i | \(0.343515\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 348510.i | 0.634714i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 622349.i | 1.12734i | 0.825999 | + | 0.563672i | \(0.190612\pi\) | ||||
−0.825999 | + | 0.563672i | \(0.809388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 99960.0 | 0.180100 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −141625. | −0.253804 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 88253.1i | 0.157314i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 583086.i | − 1.03384i | −0.856034 | − | 0.516919i | \(-0.827079\pi\) | ||||
0.856034 | − | 0.516919i | \(-0.172921\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 95970.8 | 0.169258 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 508185. | 0.891513 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 884570.i | 1.54362i | 0.635853 | + | 0.771810i | \(0.280649\pi\) | ||||
−0.635853 | + | 0.771810i | \(0.719351\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 162979.i | 0.282909i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −343529. | −0.593190 | −0.296595 | − | 0.955003i | \(-0.595851\pi\) | ||||
−0.296595 | + | 0.955003i | \(0.595851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 84352.9 | 0.144894 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 146601.i | − 0.250503i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 270762.i | − 0.460253i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −694796. | −1.17491 | −0.587455 | − | 0.809257i | \(-0.699870\pi\) | ||||
−0.587455 | + | 0.809257i | \(0.699870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 64593.1 | 0.108662 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 49585.9i | − 0.0829850i | −0.999139 | − | 0.0414925i | \(-0.986789\pi\) | ||||
0.999139 | − | 0.0414925i | \(-0.0132113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22966.3i | 0.0382373i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 54426.5 | 0.0901505 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 171962. | 0.283372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 302578.i | − 0.496062i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 49118.9i | − 0.0801170i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 202931. | 0.329313 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −557614. | −0.900293 | −0.450147 | − | 0.892955i | \(-0.648628\pi\) | ||||
−0.450147 | + | 0.892955i | \(0.648628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 262645.i | − 0.421906i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 17488.1i | − 0.0279506i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 360414. | 0.573132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −380114. | −0.601423 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 459192.i | − 0.722899i | −0.932392 | − | 0.361449i | \(-0.882282\pi\) | ||||
0.932392 | − | 0.361449i | \(-0.117718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 698663.i | − 1.09439i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 386651. | 0.602634 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −175715. | −0.272506 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 56603.3i | − 0.0873474i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 460785.i | 0.707541i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −594379. | −0.908168 | −0.454084 | − | 0.890959i | \(-0.650033\pi\) | ||||
−0.454084 | + | 0.890959i | \(0.650033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.17014e6 | 1.77908 | 0.889541 | − | 0.456855i | \(-0.151024\pi\) | ||||
0.889541 | + | 0.456855i | \(0.151024\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 97713.7i | − 0.147834i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 258793.i | 0.389616i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −152175. | −0.227982 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26671.4 | −0.0397629 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 63648.5i | − 0.0944282i | −0.998885 | − | 0.0472141i | \(-0.984966\pi\) | ||||
0.998885 | − | 0.0472141i | \(-0.0150343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 79834.3i | 0.117866i | 0.998262 | + | 0.0589331i | \(0.0187699\pi\) | ||||
−0.998262 | + | 0.0589331i | \(0.981230\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −91456.4 | −0.134371 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 242691. | 0.354848 | 0.177424 | − | 0.984134i | \(-0.443224\pi\) | ||||
0.177424 | + | 0.984134i | \(0.443224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 417062.i | − 0.606864i | −0.952853 | − | 0.303432i | \(-0.901867\pi\) | ||||
0.952853 | − | 0.303432i | \(-0.0981326\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 196432.i | − 0.284452i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 670400. | 0.966149 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 596914. | 0.856128 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12409.5i | 0.0177135i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31642.8i | 0.0449522i | 0.999747 | + | 0.0224761i | \(0.00715497\pi\) | ||||
−0.999747 | + | 0.0224761i | \(0.992845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 584705. | 0.826694 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 132938. | 0.187065 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 90568.8i | − 0.126843i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 64294.3i | − 0.0896202i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −221077. | −0.306710 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −757251. | −1.04564 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.10273e6i | − 1.51555i | −0.652513 | − | 0.757777i | \(-0.726285\pi\) | ||||
0.652513 | − | 0.757777i | \(-0.273715\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 224263.i | − 0.306779i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 505940. | 0.688870 | 0.344435 | − | 0.938810i | \(-0.388071\pi\) | ||||
0.344435 | + | 0.938810i | \(0.388071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 741942. | 1.00550 | 0.502752 | − | 0.864431i | \(-0.332321\pi\) | ||||
0.502752 | + | 0.864431i | \(0.332321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13160.2i | 0.0177524i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 536150.i | − 0.719888i | −0.932974 | − | 0.359944i | \(-0.882796\pi\) | ||||
0.932974 | − | 0.359944i | \(-0.117204\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 817462. | 1.09253 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14700.3 | −0.0195564 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 138343.i | − 0.183196i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 339396.i | − 0.447373i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 454811. | 0.596763 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 108221. | 0.141350 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 59941.4i | − 0.0779341i | −0.999240 | − | 0.0389671i | \(-0.987593\pi\) | ||||
0.999240 | − | 0.0389671i | \(-0.0124067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 529916.i | − 0.685850i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −828350. | −1.06724 | −0.533620 | − | 0.845724i | \(-0.679169\pi\) | ||||
−0.533620 | + | 0.845724i | \(0.679169\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −245690. | −0.315113 | −0.157556 | − | 0.987510i | \(-0.550362\pi\) | ||||
−0.157556 | + | 0.987510i | \(0.550362\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 174233.i | 0.222456i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 758015.i | 0.963453i | 0.876322 | + | 0.481726i | \(0.159990\pi\) | ||||
−0.876322 | + | 0.481726i | \(0.840010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 153087. | 0.193702 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −49417.2 | −0.0622476 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.06878e6i | − 1.34025i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 318594.i | − 0.397733i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 371087. | 0.461201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30967.9 | 0.0383171 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.08715e6i | − 1.33919i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 11646.0i | − 0.0142824i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 452807. | 0.552861 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −520331. | −0.632506 | −0.316253 | − | 0.948675i | \(-0.602425\pi\) | ||||
−0.316253 | + | 0.948675i | \(0.602425\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 240545.i | − 0.291117i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.10094e6i | − 1.32656i | −0.748370 | − | 0.663282i | \(-0.769163\pi\) | ||||
0.748370 | − | 0.663282i | \(-0.230837\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 355571. | 0.426564 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −231923. | −0.277014 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 160383.i | 0.190731i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 990050.i | 1.17227i | 0.810215 | + | 0.586133i | \(0.199350\pi\) | ||||
−0.810215 | + | 0.586133i | \(0.800650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −883989. | −1.04214 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −688942. | −0.808685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 424936.i | − 0.496638i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 528844.i | 0.615415i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 112392. | 0.130228 | 0.0651140 | − | 0.997878i | \(-0.479259\pi\) | ||||
0.0651140 | + | 0.997878i | \(0.479259\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.02555e6 | 1.18320 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 216122.i | − 0.248277i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 368063.i | 0.421017i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −293444. | −0.334231 | −0.167115 | − | 0.985937i | \(-0.553445\pi\) | ||||
−0.167115 | + | 0.985937i | \(0.553445\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 632304. | 0.717125 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 531934.i | − 0.600729i | −0.953825 | − | 0.300364i | \(-0.902892\pi\) | ||||
0.953825 | − | 0.300364i | \(-0.0971083\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 183102.i | − 0.205906i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17162.8 | 0.0192188 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −378760. | −0.422342 | −0.211171 | − | 0.977449i | \(-0.567728\pi\) | ||||
−0.211171 | + | 0.977449i | \(0.567728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 400085.i | 0.444243i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 657301.i | 0.726781i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.75746e6 | 1.93508 | 0.967539 | − | 0.252721i | \(-0.0813256\pi\) | ||||
0.967539 | + | 0.252721i | \(0.0813256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.28255e6 | −1.40627 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 123320.i | 0.134651i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3382.78i | 0.00367821i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 915697. | 0.991528 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 372312. | 0.401471 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 214842.i | 0.230709i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59833.4i | 0.0639868i | 0.999488 | + | 0.0319934i | \(0.0101856\pi\) | ||||
−0.999488 | + | 0.0319934i | \(0.989814\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 641408. | 0.683104 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 687930. | 0.729635 | 0.364817 | − | 0.931079i | \(-0.381131\pi\) | ||||
0.364817 | + | 0.931079i | \(0.381131\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 153932.i | − 0.162594i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 208238.i | 0.219053i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.20414e6 | 1.26150 | 0.630752 | − | 0.775985i | \(-0.282747\pi\) | ||||
0.630752 | + | 0.775985i | \(0.282747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −970746. | −1.01284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 355858.i | − 0.369776i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 202530.i | 0.209596i | 0.994494 | + | 0.104798i | \(0.0334196\pi\) | ||||
−0.994494 | + | 0.104798i | \(0.966580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 286420. | 0.295210 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 81793.9 | 0.0839628 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 162033.i | 0.165658i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 762037.i | 0.775941i | 0.921672 | + | 0.387970i | \(0.126824\pi\) | ||||
−0.921672 | + | 0.387970i | \(0.873176\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 175108. | 0.177585 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.35911e6 | 1.37281 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 75700.5i | − 0.0761567i | −0.999275 | − | 0.0380784i | \(-0.987876\pi\) | ||||
0.999275 | − | 0.0380784i | \(-0.0121237\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 229608.i | − 0.230068i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.5.b.d.319.11 | yes | 16 | |
3.2 | odd | 2 | 1152.5.b.m.703.12 | 16 | |||
4.3 | odd | 2 | inner | 384.5.b.d.319.3 | ✓ | 16 | |
8.3 | odd | 2 | inner | 384.5.b.d.319.14 | yes | 16 | |
8.5 | even | 2 | inner | 384.5.b.d.319.6 | yes | 16 | |
12.11 | even | 2 | 1152.5.b.m.703.11 | 16 | |||
16.3 | odd | 4 | 768.5.g.j.511.1 | 8 | |||
16.5 | even | 4 | 768.5.g.h.511.4 | 8 | |||
16.11 | odd | 4 | 768.5.g.h.511.8 | 8 | |||
16.13 | even | 4 | 768.5.g.j.511.5 | 8 | |||
24.5 | odd | 2 | 1152.5.b.m.703.6 | 16 | |||
24.11 | even | 2 | 1152.5.b.m.703.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.b.d.319.3 | ✓ | 16 | 4.3 | odd | 2 | inner | |
384.5.b.d.319.6 | yes | 16 | 8.5 | even | 2 | inner | |
384.5.b.d.319.11 | yes | 16 | 1.1 | even | 1 | trivial | |
384.5.b.d.319.14 | yes | 16 | 8.3 | odd | 2 | inner | |
768.5.g.h.511.4 | 8 | 16.5 | even | 4 | |||
768.5.g.h.511.8 | 8 | 16.11 | odd | 4 | |||
768.5.g.j.511.1 | 8 | 16.3 | odd | 4 | |||
768.5.g.j.511.5 | 8 | 16.13 | even | 4 | |||
1152.5.b.m.703.5 | 16 | 24.11 | even | 2 | |||
1152.5.b.m.703.6 | 16 | 24.5 | odd | 2 | |||
1152.5.b.m.703.11 | 16 | 12.11 | even | 2 | |||
1152.5.b.m.703.12 | 16 | 3.2 | odd | 2 |