Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(127,384)]
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, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.127");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (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: | \( x^{16} - 8 x^{15} + 104 x^{14} - 588 x^{13} + 3846 x^{12} - 15796 x^{11} + 66992 x^{10} - 203224 x^{9} + \cdots + 2196513 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{86}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.15 | ||
Root | \(0.500000 - 2.27039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.127 |
Dual form | 384.5.g.b.127.7 |
$q$-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 | ||||||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 38.1647 | 1.52659 | 0.763294 | − | 0.646051i | \(-0.223581\pi\) | ||||
0.763294 | + | 0.646051i | \(0.223581\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 50.0160i | 1.02073i | 0.859957 | + | 0.510367i | \(0.170490\pi\) | ||||
−0.859957 | + | 0.510367i | \(0.829510\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 14.9385i | − 0.123459i | −0.998093 | − | 0.0617295i | \(-0.980338\pi\) | ||||
0.998093 | − | 0.0617295i | \(-0.0196616\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −281.909 | −1.66810 | −0.834051 | − | 0.551687i | \(-0.813984\pi\) | ||||
−0.834051 | + | 0.551687i | \(0.813984\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 198.310i | 0.881376i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −570.708 | −1.97477 | −0.987385 | − | 0.158340i | \(-0.949386\pi\) | ||||
−0.987385 | + | 0.158340i | \(0.949386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 71.7400i | − 0.198726i | −0.995051 | − | 0.0993628i | \(-0.968320\pi\) | ||||
0.995051 | − | 0.0993628i | \(-0.0316804\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −259.891 | −0.589321 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 746.211i | 1.41061i | 0.708906 | + | 0.705303i | \(0.249189\pi\) | ||||
−0.708906 | + | 0.705303i | \(0.750811\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 831.546 | 1.33047 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 140.296i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −558.040 | −0.663543 | −0.331771 | − | 0.943360i | \(-0.607646\pi\) | ||||
−0.331771 | + | 0.943360i | \(0.607646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 1709.27i | − 1.77864i | −0.457285 | − | 0.889320i | \(-0.651178\pi\) | ||||
0.457285 | − | 0.889320i | \(-0.348822\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 77.6229 | 0.0712791 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1908.85i | 1.55824i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −210.427 | −0.153708 | −0.0768541 | − | 0.997042i | \(-0.524488\pi\) | ||||
−0.0768541 | + | 0.997042i | \(0.524488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 1464.84i | − 0.963079i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −35.0966 | −0.0208784 | −0.0104392 | − | 0.999946i | \(-0.503323\pi\) | ||||
−0.0104392 | + | 0.999946i | \(0.503323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2340.97i | 1.26607i | 0.774122 | + | 0.633036i | \(0.218191\pi\) | ||||
−0.774122 | + | 0.633036i | \(0.781809\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1030.45 | −0.508863 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 193.166i | − 0.0874449i | −0.999044 | − | 0.0437224i | \(-0.986078\pi\) | ||||
0.999044 | − | 0.0437224i | \(-0.0139217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −100.598 | −0.0418985 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 2965.49i | − 1.14013i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1962.98 | 0.698818 | 0.349409 | − | 0.936970i | \(-0.386382\pi\) | ||||
0.349409 | + | 0.936970i | \(0.386382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 570.125i | − 0.188471i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 372.772 | 0.114734 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4860.39i | 1.39626i | 0.715970 | + | 0.698131i | \(0.245985\pi\) | ||||
−0.715970 | + | 0.698131i | \(0.754015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −478.284 | −0.128536 | −0.0642682 | − | 0.997933i | \(-0.520471\pi\) | ||||
−0.0642682 | + | 0.997933i | \(0.520471\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1350.43i | − 0.340245i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10759.0 | −2.54651 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4762.37i | 1.06090i | 0.847717 | + | 0.530449i | \(0.177977\pi\) | ||||
−0.847717 | + | 0.530449i | \(0.822023\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3877.42 | −0.814414 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 4203.83i | − 0.833928i | −0.908923 | − | 0.416964i | \(-0.863094\pi\) | ||||
0.908923 | − | 0.416964i | \(-0.136906\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5327.22 | −0.999666 | −0.499833 | − | 0.866122i | \(-0.666605\pi\) | ||||
−0.499833 | + | 0.866122i | \(0.666605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4320.84i | 0.768149i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 747.166 | 0.126019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6615.84i | − 1.06006i | −0.847979 | − | 0.530030i | \(-0.822181\pi\) | ||||
0.847979 | − | 0.530030i | \(-0.177819\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6872.82i | − 0.997651i | −0.866702 | − | 0.498826i | \(-0.833765\pi\) | ||||
0.866702 | − | 0.498826i | \(-0.166235\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21780.9 | −3.01466 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2899.66i | − 0.383097i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5237.05 | −0.661160 | −0.330580 | − | 0.943778i | \(-0.607244\pi\) | ||||
−0.330580 | + | 0.943778i | \(0.607244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 14100.0i | − 1.70269i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8881.65 | 1.02690 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 2737.93i | − 0.303372i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5808.32 | −0.617315 | −0.308658 | − | 0.951173i | \(-0.599880\pi\) | ||||
−0.308658 | + | 0.951173i | \(0.599880\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 403.341i | 0.0411530i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15431.3 | −1.51272 | −0.756362 | − | 0.654154i | \(-0.773025\pi\) | ||||
−0.756362 | + | 0.654154i | \(0.773025\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11783.2i | 1.11068i | 0.831624 | + | 0.555339i | \(0.187411\pi\) | ||||
−0.831624 | + | 0.555339i | \(0.812589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9918.65 | −0.899651 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14214.7i | 1.24157i | 0.783981 | + | 0.620785i | \(0.213186\pi\) | ||||
−0.783981 | + | 0.620785i | \(0.786814\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −283.406 | −0.0238537 | −0.0119269 | − | 0.999929i | \(-0.503797\pi\) | ||||
−0.0119269 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1093.41i | − 0.0887435i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4755.34 | 0.372413 | 0.186206 | − | 0.982511i | \(-0.440381\pi\) | ||||
0.186206 | + | 0.982511i | \(0.440381\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28478.9i | 2.15341i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7611.55 | 0.556034 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 28544.5i | − 2.01571i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14417.8 | 0.984758 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 182.367i | − 0.0120541i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7882.75 | 0.504496 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 8132.78i | − 0.504233i | −0.967697 | − | 0.252117i | \(-0.918873\pi\) | ||||
0.967697 | − | 0.252117i | \(-0.0811267\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12164.0 | −0.730967 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9963.50i | 0.580590i | 0.956937 | + | 0.290295i | \(0.0937534\pi\) | ||||
−0.956937 | + | 0.290295i | \(0.906247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3588.14 | 0.202846 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5354.36i | − 0.293792i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 34463.3 | 1.83618 | 0.918091 | − | 0.396369i | \(-0.129730\pi\) | ||||
0.918091 | + | 0.396369i | \(0.129730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37114.7i | 1.92095i | 0.278361 | + | 0.960477i | \(0.410209\pi\) | ||||
−0.278361 | + | 0.960477i | \(0.589791\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1003.72 | 0.0504863 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4211.31i | 0.205942i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21297.4 | −1.01296 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 522.725i | − 0.0241901i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15314.2 | −0.689797 | −0.344899 | − | 0.938640i | \(-0.612087\pi\) | ||||
−0.344899 | + | 0.938640i | \(0.612087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 42542.8i | 1.86583i | 0.360093 | + | 0.932916i | \(0.382745\pi\) | ||||
−0.360093 | + | 0.932916i | \(0.617255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15409.1 | 0.658256 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 65233.9i | − 2.71525i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7662.12 | 0.310849 | 0.155425 | − | 0.987848i | \(-0.450325\pi\) | ||||
0.155425 | + | 0.987848i | \(0.450325\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10199.9i | 0.403463i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −37322.5 | −1.43985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8483.09i | 0.319285i | 0.987175 | + | 0.159643i | \(0.0510342\pi\) | ||||
−0.987175 | + | 0.159643i | \(0.948966\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2962.46 | 0.108814 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 24615.9i | − 0.882638i | −0.897350 | − | 0.441319i | \(-0.854511\pi\) | ||||
0.897350 | − | 0.441319i | \(-0.145489\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 50911.9 | 1.78257 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1936.98i | 0.0662419i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1104.54 | −0.0369055 | −0.0184527 | − | 0.999830i | \(-0.505874\pi\) | ||||
−0.0184527 | + | 0.999830i | \(0.505874\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 41590.6i | 1.35806i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25255.3 | −0.806132 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 35189.9i | − 1.09828i | −0.835731 | − | 0.549139i | \(-0.814956\pi\) | ||||
0.835731 | − | 0.549139i | \(-0.185044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −30095.0 | −0.918623 | −0.459311 | − | 0.888275i | \(-0.651904\pi\) | ||||
−0.459311 | + | 0.888275i | \(0.651904\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2485.24i | − 0.0742105i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8030.87 | −0.234649 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8525.55i | 0.243803i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7017.05 | 0.196440 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15842.3i | 0.434261i | 0.976143 | + | 0.217131i | \(0.0696697\pi\) | ||||
−0.976143 | + | 0.217131i | \(0.930330\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 49712.8 | 1.33461 | 0.667303 | − | 0.744786i | \(-0.267448\pi\) | ||||
0.667303 | + | 0.744786i | \(0.267448\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 55905.4i | − 1.47023i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17445.4 | 0.449520 | 0.224760 | − | 0.974414i | \(-0.427840\pi\) | ||||
0.224760 | + | 0.974414i | \(0.427840\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 33628.6i | − 0.849187i | −0.905384 | − | 0.424593i | \(-0.860417\pi\) | ||||
0.905384 | − | 0.424593i | \(-0.139583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24746.0 | −0.612510 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 27910.9i | − 0.677301i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1339.45 | −0.0318727 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 20147.7i | − 0.470202i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1071.69 | −0.0245345 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 51764.4i | − 1.16270i | −0.813655 | − | 0.581348i | \(-0.802525\pi\) | ||||
0.813655 | − | 0.581348i | \(-0.197475\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21843.7 | 0.481469 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 89342.3i | 1.93277i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 85491.0 | 1.81552 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 27681.1i | − 0.577158i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 160888. | 3.29412 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 58417.9i | 1.17472i | 0.809324 | + | 0.587362i | \(0.199834\pi\) | ||||
−0.809324 | + | 0.587362i | \(0.800166\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22451.7 | −0.443491 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 60234.3i | 1.16894i | 0.811415 | + | 0.584470i | \(0.198698\pi\) | ||||
−0.811415 | + | 0.584470i | \(0.801302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −31082.1 | −0.592706 | −0.296353 | − | 0.955078i | \(-0.595771\pi\) | ||||
−0.296353 | + | 0.955078i | \(0.595771\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3882.39i | 0.0727570i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25930.7 | −0.477643 | −0.238821 | − | 0.971064i | \(-0.576761\pi\) | ||||
−0.238821 | + | 0.971064i | \(0.576761\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 7372.12i | − 0.133492i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34376.9 | 0.612026 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 4425.21i | − 0.0774708i | −0.999250 | − | 0.0387354i | \(-0.987667\pi\) | ||||
0.999250 | − | 0.0387354i | \(-0.0123329\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −34491.1 | −0.593844 | −0.296922 | − | 0.954902i | \(-0.595960\pi\) | ||||
−0.296922 | + | 0.954902i | \(0.595960\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3839.31 | −0.0639618 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20224.2i | 0.331495i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35712.2 | 0.575994 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21673.7i | 0.344022i | 0.985095 | + | 0.172011i | \(0.0550265\pi\) | ||||
−0.985095 | + | 0.172011i | \(0.944974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11147.3 | 0.174152 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 113177.i | − 1.74051i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10512.6 | 0.159164 | 0.0795819 | − | 0.996828i | \(-0.474641\pi\) | ||||
0.0795819 | + | 0.996828i | \(0.474641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 10524.7i | − 0.156895i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15067.1 | 0.221181 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 39630.6i | − 0.572954i | −0.958087 | − | 0.286477i | \(-0.907516\pi\) | ||||
0.958087 | − | 0.286477i | \(-0.0924841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 74916.6 | 1.06681 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 27212.5i | − 0.381721i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 80644.9 | 1.11448 | 0.557240 | − | 0.830351i | \(-0.311860\pi\) | ||||
0.557240 | + | 0.830351i | \(0.311860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 49892.7i | 0.679357i | 0.940542 | + | 0.339678i | \(0.110318\pi\) | ||||
−0.940542 | + | 0.339678i | \(0.889682\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73265.6 | 0.983048 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 12422.1i | − 0.164259i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13320.1 | −0.173599 | −0.0867996 | − | 0.996226i | \(-0.527664\pi\) | ||||
−0.0867996 | + | 0.996226i | \(0.527664\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46150.4i | 0.592880i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18143.5 | −0.229778 | −0.114889 | − | 0.993378i | \(-0.536651\pi\) | ||||
−0.114889 | + | 0.993378i | \(0.536651\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 140931.i | 1.75968i | 0.475270 | + | 0.879840i | \(0.342350\pi\) | ||||
−0.475270 | + | 0.879840i | \(0.657650\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14226.7 | 0.175152 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1755.39i | − 0.0213113i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 242187. | 2.89971 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 30180.9i | − 0.356407i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 108058. | 1.25870 | 0.629350 | − | 0.777122i | \(-0.283321\pi\) | ||||
0.629350 | + | 0.777122i | \(0.283321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 185495.i | 2.13152i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2095.82 | −0.0237597 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 210364.i | − 2.35304i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −117086. | −1.29232 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 80183.3i | − 0.873371i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18253.6 | −0.196222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 27092.9i | − 0.287461i | −0.989617 | − | 0.143730i | \(-0.954090\pi\) | ||||
0.989617 | − | 0.143730i | \(-0.0459098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −61227.2 | −0.641250 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 114935.i | − 1.18832i | −0.804348 | − | 0.594158i | \(-0.797485\pi\) | ||||
0.804348 | − | 0.594158i | \(-0.202515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −173983. | −1.77590 | −0.887948 | − | 0.459945i | \(-0.847869\pi\) | ||||
−0.887948 | + | 0.459945i | \(0.847869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 51538.8i | − 0.519414i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −154121. | −1.53371 | −0.766854 | − | 0.641822i | \(-0.778179\pi\) | ||||
−0.766854 | + | 0.641822i | \(0.778179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8336.29i | 0.0819203i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −73861.9 | −0.716821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40942.6i | 0.392437i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −234420. | −2.21937 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1472.62i | − 0.0137719i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9661.38 | 0.0892580 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 146508.i | 1.33723i | 0.743611 | + | 0.668613i | \(0.233111\pi\) | ||||
−0.743611 | + | 0.668613i | \(0.766889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5681.52 | 0.0512361 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 181755.i | 1.61955i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −156868. | −1.38126 | −0.690628 | − | 0.723210i | \(-0.742666\pi\) | ||||
−0.690628 | + | 0.723210i | \(0.742666\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24709.4i | 0.215012i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25534.0 | −0.219589 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 115057.i | 0.977967i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −147981. | −1.24327 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 125592.i | 1.04304i | 0.853239 | + | 0.521521i | \(0.174635\pi\) | ||||
−0.853239 | + | 0.521521i | \(0.825365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 44311.9 | 0.363806 | 0.181903 | − | 0.983316i | \(-0.441774\pi\) | ||||
0.181903 | + | 0.983316i | \(0.441774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 39550.8i | 0.321026i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −155580. | −1.24855 | −0.624273 | − | 0.781206i | \(-0.714605\pi\) | ||||
−0.624273 | + | 0.781206i | \(0.714605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 160438.i | − 1.27307i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 148322. | 1.16377 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 208069.i | − 1.61443i | −0.590259 | − | 0.807214i | \(-0.700974\pi\) | ||||
0.590259 | − | 0.807214i | \(-0.299026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 125174. | 0.960508 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 74917.3i | 0.568550i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −203312. | −1.52608 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 22943.3i | − 0.170343i | −0.996366 | − | 0.0851714i | \(-0.972856\pi\) | ||||
0.996366 | − | 0.0851714i | \(-0.0271438\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 947.607 | 0.00695946 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 98180.3i | 0.713307i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 214254. | 1.53997 | 0.769985 | − | 0.638062i | \(-0.220264\pi\) | ||||
0.769985 | + | 0.638062i | \(0.220264\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 40960.0i | 0.291271i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 157317. | 1.10686 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 135220.i | 0.941376i | 0.882300 | + | 0.470688i | \(0.155994\pi\) | ||||
−0.882300 | + | 0.470688i | \(0.844006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42259.2 | 0.291119 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 99667.3i | − 0.679446i | −0.940525 | − | 0.339723i | \(-0.889667\pi\) | ||||
0.940525 | − | 0.339723i | \(-0.110333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28515.4 | 0.192379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 63206.1i | − 0.422024i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 83760.5 | 0.553529 | 0.276764 | − | 0.960938i | \(-0.410738\pi\) | ||||
0.276764 | + | 0.960938i | \(0.410738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 425869.i | − 2.78562i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −51771.9 | −0.335204 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 252491.i | − 1.61828i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −222509. | −1.41178 | −0.705890 | − | 0.708322i | \(-0.749453\pi\) | ||||
−0.705890 | + | 0.708322i | \(0.749453\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18644.5i | 0.117113i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 119674. | 0.744237 | 0.372119 | − | 0.928185i | \(-0.378631\pi\) | ||||
0.372119 | + | 0.928185i | \(0.378631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 481860.i | 2.96695i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27822.1 | 0.169621 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3143.46i | 0.0189767i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34233.7 | −0.204648 | −0.102324 | − | 0.994751i | \(-0.532628\pi\) | ||||
−0.102324 | + | 0.994751i | \(0.532628\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 179077.i | 1.06012i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −243097. | −1.42521 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 262299.i | − 1.52300i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −192854. | −1.10906 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 90685.6i | 0.516547i | 0.966072 | + | 0.258274i | \(0.0831536\pi\) | ||||
−0.966072 | + | 0.258274i | \(0.916846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 278121. | 1.56917 | 0.784584 | − | 0.620022i | \(-0.212876\pi\) | ||||
0.784584 | + | 0.620022i | \(0.212876\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5215.48i | 0.0291483i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −474570. | −2.62738 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 23921.8i | − 0.131201i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21882.6 | −0.118901 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 183909.i | − 0.990032i | −0.868884 | − | 0.495016i | \(-0.835162\pi\) | ||||
0.868884 | − | 0.495016i | \(-0.164838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 119776. | 0.638843 | 0.319421 | − | 0.947613i | \(-0.396511\pi\) | ||||
0.319421 | + | 0.947613i | \(0.396511\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 110665.i | − 0.584831i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 53533.1 | 0.280324 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 288630.i | 1.49766i | 0.662763 | + | 0.748829i | \(0.269384\pi\) | ||||
−0.662763 | + | 0.748829i | \(0.730616\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2716.16 | 0.0139662 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 230448.i | − 1.17427i | −0.809491 | − | 0.587133i | \(-0.800257\pi\) | ||||
0.809491 | − | 0.587133i | \(-0.199743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −199870. | −1.00932 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 79574.8i | − 0.398255i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 73745.4 | 0.365799 | 0.182899 | − | 0.983132i | \(-0.441452\pi\) | ||||
0.182899 | + | 0.983132i | \(0.441452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 524.291i | 0.00257762i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −221059. | −1.07724 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 538121.i | − 2.59931i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −303453. | −1.45298 | −0.726489 | − | 0.687179i | \(-0.758849\pi\) | ||||
−0.726489 | + | 0.687179i | \(0.758849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 80068.2i | 0.380045i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 147882. | 0.695849 | 0.347924 | − | 0.937523i | \(-0.386887\pi\) | ||||
0.347924 | + | 0.937523i | \(0.386887\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 106150.i | 0.495174i | 0.968866 | + | 0.247587i | \(0.0796376\pi\) | ||||
−0.968866 | + | 0.247587i | \(0.920362\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 338965. | 1.56765 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 158470.i | 0.726630i | 0.931666 | + | 0.363315i | \(0.118355\pi\) | ||||
−0.931666 | + | 0.363315i | \(0.881645\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −238195. | −1.08289 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39813.5i | 0.179469i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34970.6 | 0.156308 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 59655.0i | − 0.264399i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −53000.4 | −0.232939 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 87871.4i | 0.382981i | 0.981495 | + | 0.191490i | \(0.0613320\pi\) | ||||
−0.981495 | + | 0.191490i | \(0.938668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 59321.2 | 0.256401 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 193933.i | − 0.831300i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −221673. | −0.942386 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11919.2i | 0.0502561i | 0.999684 | + | 0.0251281i | \(0.00799935\pi\) | ||||
−0.999684 | + | 0.0251281i | \(0.992001\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44079.4 | −0.184339 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 116945.i | 0.485088i | 0.970140 | + | 0.242544i | \(0.0779819\pi\) | ||||
−0.970140 | + | 0.242544i | \(0.922018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 318478. | 1.31034 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15393.4i | 0.0628237i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 210259. | 0.851219 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 99656.8i | − 0.400227i | −0.979773 | − | 0.200113i | \(-0.935869\pi\) | ||||
0.979773 | − | 0.200113i | \(-0.0641310\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 127908. | 0.509591 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 166780.i | 0.659186i | 0.944123 | + | 0.329593i | \(0.106912\pi\) | ||||
−0.944123 | + | 0.329593i | \(0.893088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −588931. | −2.30931 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 264546.i | 1.02917i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −94288.3 | −0.363934 | −0.181967 | − | 0.983305i | \(-0.558246\pi\) | ||||
−0.181967 | + | 0.983305i | \(0.558246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 266446.i | − 1.02039i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10064.8 | −0.0382448 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 449702.i | 1.69555i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2885.61 | −0.0107959 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 5739.38i | − 0.0213074i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −252399. | −0.929848 | −0.464924 | − | 0.885351i | \(-0.653918\pi\) | ||||
−0.464924 | + | 0.885351i | \(0.653918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 360986.i | − 1.31973i | −0.751382 | − | 0.659867i | \(-0.770612\pi\) | ||||
0.751382 | − | 0.659867i | \(-0.229388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −216111. | −0.784076 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 975497.i | 3.51240i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −276989. | −0.989809 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 131230.i | − 0.465421i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9894.05 | 0.0348273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 542501.i | 1.89537i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 182852. | 0.634091 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1502.79i | 0.00517275i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −212815. | −0.727123 | −0.363561 | − | 0.931570i | \(-0.618439\pi\) | ||||
−0.363561 | + | 0.931570i | \(0.618439\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 156378.i | − 0.530367i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10816.1 | −0.0364148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 84823.3i | − 0.283492i | −0.989903 | − | 0.141746i | \(-0.954728\pi\) | ||||
0.989903 | − | 0.141746i | \(-0.0452716\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12913.7 | 0.0428455 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40033.7i | 0.131863i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 330898. | 1.08204 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 41729.6i | − 0.135475i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8677.73 | 0.0279702 | 0.0139851 | − | 0.999902i | \(-0.495548\pi\) | ||||
0.0139851 | + | 0.999902i | \(0.495548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 659940.i | − 2.11194i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44300.0 | −0.140760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 114230.i | − 0.360381i | −0.983632 | − | 0.180190i | \(-0.942329\pi\) | ||||
0.983632 | − | 0.180190i | \(-0.0576714\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 181486. | 0.568521 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36461.7i | 0.113415i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29567.0 | −0.0913236 | −0.0456618 | − | 0.998957i | \(-0.514540\pi\) | ||||
−0.0456618 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 229583.i | − 0.704155i | −0.935971 | − | 0.352078i | \(-0.885475\pi\) | ||||
0.935971 | − | 0.352078i | \(-0.114525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −82318.9 | −0.250721 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 620508.i | 1.87677i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 522988. | 1.57087 | 0.785434 | − | 0.618945i | \(-0.212440\pi\) | ||||
0.785434 | + | 0.618945i | \(0.212440\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 258315.i | 0.770536i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 343751. | 1.01834 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 29324.0i | − 0.0862754i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 290493. | 0.848835 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 548252.i | 1.59112i | 0.605873 | + | 0.795561i | \(0.292824\pi\) | ||||
−0.605873 | + | 0.795561i | \(0.707176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −122623. | −0.353461 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 90649.0i | 0.259530i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 509890. | 1.45000 | 0.724998 | − | 0.688751i | \(-0.241841\pi\) | ||||
0.724998 | + | 0.688751i | \(0.241841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.08939e6i | − 3.07717i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 174740. | 0.490278 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 163569.i | − 0.455877i | −0.973676 | − | 0.227939i | \(-0.926801\pi\) | ||||
0.973676 | − | 0.227939i | \(-0.0731985\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 359449. | 0.995151 | 0.497575 | − | 0.867421i | \(-0.334224\pi\) | ||||
0.497575 | + | 0.867421i | \(0.334224\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 128584.i | − 0.353633i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 550253. | 1.50332 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 333341.i | − 0.904714i | −0.891837 | − | 0.452357i | \(-0.850583\pi\) | ||||
0.891837 | − | 0.452357i | \(-0.149417\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 145029. | 0.391040 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54455.2i | 0.145867i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 357269. | 0.950768 | 0.475384 | − | 0.879778i | \(-0.342309\pi\) | ||||
0.475384 | + | 0.879778i | \(0.342309\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 6959.99i | − 0.0184017i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 271334. | 0.712744 | 0.356372 | − | 0.934344i | \(-0.384014\pi\) | ||||
0.356372 | + | 0.934344i | \(0.384014\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 383666.i | 1.00132i | 0.865645 | + | 0.500659i | \(0.166909\pi\) | ||||
−0.865645 | + | 0.500659i | \(0.833091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 104690. | 0.271471 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 261936.i | − 0.674869i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −218873. | −0.560315 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 5568.66i | − 0.0141650i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 120092. | 0.303538 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 199171.i | − 0.500227i | −0.968216 | − | 0.250114i | \(-0.919532\pi\) | ||||
0.968216 | − | 0.250114i | \(-0.0804680\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 268976. | 0.671283 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 310385.i | − 0.769757i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28359.6 | 0.0698911 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 113503.i | 0.277976i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 46510.1 | 0.113196 | 0.0565980 | − | 0.998397i | \(-0.481975\pi\) | ||||
0.0565980 | + | 0.998397i | \(0.481975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 103482.i | 0.250290i | 0.992138 | + | 0.125145i | \(0.0399396\pi\) | ||||
−0.992138 | + | 0.125145i | \(0.960060\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −464236. | −1.11589 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 512475.i | − 1.22423i | −0.790767 | − | 0.612117i | \(-0.790318\pi\) | ||||
0.790767 | − | 0.612117i | \(-0.209682\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 72607.1 | 0.172381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 444224.i | 1.04819i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 227855. | 0.534358 | 0.267179 | − | 0.963647i | \(-0.413909\pi\) | ||||
0.267179 | + | 0.963647i | \(0.413909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 380254.i | 0.886322i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 143835. | 0.333222 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 182148.i | 0.419423i | 0.977763 | + | 0.209712i | \(0.0672525\pi\) | ||||
−0.977763 | + | 0.209712i | \(0.932747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 606405. | 1.38791 | 0.693953 | − | 0.720020i | \(-0.255868\pi\) | ||||
0.693953 | + | 0.720020i | \(0.255868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 835999.i | 1.90186i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 136941. | 0.309663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 416415.i | − 0.935997i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −303548. | −0.678228 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7144.86i | 0.0158690i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −635313. | −1.40268 | −0.701339 | − | 0.712828i | \(-0.747414\pi\) | ||||
−0.701339 | + | 0.712828i | \(0.747414\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 116663.i | − 0.256050i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −134998. | −0.294543 | −0.147272 | − | 0.989096i | \(-0.547049\pi\) | ||||
−0.147272 | + | 0.989096i | \(0.547049\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 290509.i | − 0.630115i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −312987. | −0.674888 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 566455.i | − 1.21429i | −0.794589 | − | 0.607147i | \(-0.792314\pi\) | ||||
0.794589 | − | 0.607147i | \(-0.207686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.31528e6 | 2.80310 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 161507.i | − 0.342199i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −553382. | −1.16570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 543725.i | − 1.13874i | −0.822083 | − | 0.569368i | \(-0.807188\pi\) | ||||
0.822083 | − | 0.569368i | \(-0.192812\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20173.5 | −0.0420063 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.41647e6i | 2.93251i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20029.9 | 0.0412300 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 134740.i | − 0.275767i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −767758. | −1.56239 | −0.781193 | − | 0.624289i | \(-0.785389\pi\) | ||||
−0.781193 | + | 0.624289i | \(0.785389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15096.0i | 0.0305458i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 38306.6 | 0.0770719 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 771811.i | − 1.54409i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 560272. | 1.11457 | 0.557284 | − | 0.830322i | \(-0.311843\pi\) | ||||
0.557284 | + | 0.830322i | \(0.311843\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 178628.i | 0.353353i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.27548e6 | 2.50896 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 160724.i | 0.314389i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22994.1 | 0.0447278 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 759774.i | 1.46969i | 0.678234 | + | 0.734846i | \(0.262746\pi\) | ||||
−0.678234 | + | 0.734846i | \(0.737254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −589347. | −1.13371 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 179221.i | − 0.342856i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −464035. | −0.882826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 472137.i | 0.893305i | 0.894708 | + | 0.446652i | \(0.147384\pi\) | ||||
−0.894708 | + | 0.446652i | \(0.852616\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.33601e6i | − 2.50020i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 600287. | 1.11725 | 0.558626 | − | 0.829420i | \(-0.311329\pi\) | ||||
0.558626 | + | 0.829420i | \(0.311329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 19949.6i | − 0.0369284i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 71142.9 | 0.130977 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 116503.i | 0.213327i | 0.994295 | + | 0.106664i | \(0.0340168\pi\) | ||||
−0.994295 | + | 0.106664i | \(0.965983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −105088. | −0.191389 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 362499.i | − 0.656642i | −0.944566 | − | 0.328321i | \(-0.893517\pi\) | ||||
0.944566 | − | 0.328321i | \(-0.106483\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −584462. | −1.05304 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 185566.i | 0.332550i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −710964. | −1.26731 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 255543.i | 0.453089i | 0.974001 | + | 0.226545i | \(0.0727429\pi\) | ||||
−0.974001 | + | 0.226545i | \(0.927257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −112620. | −0.198621 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.62364e6i | 2.84836i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −157849. | −0.275454 | −0.137727 | − | 0.990470i | \(-0.543980\pi\) | ||||
−0.137727 | + | 0.990470i | \(0.543980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 57923.0i | 0.100547i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −436931. | −0.754474 | −0.377237 | − | 0.926117i | \(-0.623126\pi\) | ||||
−0.377237 | + | 0.926117i | \(0.623126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 14174.8i | − 0.0243483i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 588085. | 1.00489 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.37019e6i | − 2.32911i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42172.0 | −0.0713135 | −0.0356568 | − | 0.999364i | \(-0.511352\pi\) | ||||
−0.0356568 | + | 0.999364i | \(0.511352\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54625.1i | 0.0918932i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −143407. | −0.240000 | −0.120000 | − | 0.992774i | \(-0.538289\pi\) | ||||
−0.120000 | + | 0.992774i | \(0.538289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.42134e6i | − 2.36643i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 54687.9 | 0.0905835 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2517.83i | 0.00414907i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62799.1 | −0.102956 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 78290.8i | 0.127699i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 292423. | 0.474539 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 295695.i | − 0.477414i | −0.971092 | − | 0.238707i | \(-0.923276\pi\) | ||||
0.971092 | − | 0.238707i | \(-0.0767235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 205927. | 0.330795 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 237843.i | 0.380134i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 134833. | 0.214412 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 389278.i | 0.615922i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41548.0 | −0.0654084 | −0.0327042 | − | 0.999465i | \(-0.510412\pi\) | ||||
−0.0327042 | + | 0.999465i | \(0.510412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 110241.i | 0.172683i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 141400. | 0.220387 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 79580.9i | 0.123418i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.42440e6 | −2.19806 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 419043.i | 0.643445i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.20959e6 | 1.84817 | 0.924083 | − | 0.382191i | \(-0.124830\pi\) | ||||
0.924083 | + | 0.382191i | \(0.124830\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 212276.i | 0.322744i | 0.986894 | + | 0.161372i | \(0.0515920\pi\) | ||||
−0.986894 | + | 0.161372i | \(0.948408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −259250. | −0.392227 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 323755.i | 0.487417i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 167941. | 0.251601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 380699.i | 0.567563i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.12848e6 | −1.67420 | −0.837101 | − | 0.547048i | \(-0.815752\pi\) | ||||
−0.837101 | + | 0.547048i | \(0.815752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 51078.0i | − 0.0754109i | −0.999289 | − | 0.0377055i | \(-0.987995\pi\) | ||||
0.999289 | − | 0.0377055i | \(-0.0120049\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 64547.0 | 0.0948349 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 461932.i | 0.675409i | 0.941252 | + | 0.337705i | \(0.109651\pi\) | ||||
−0.941252 | + | 0.337705i | \(0.890349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.04514e6 | 1.52077 | 0.760386 | − | 0.649472i | \(-0.225010\pi\) | ||||
0.760386 | + | 0.649472i | \(0.225010\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 69213.3i | − 0.100228i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 57412.3 | 0.0827399 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 939459.i | − 1.34743i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −239804. | −0.342300 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 765515.i | − 1.08750i | −0.839247 | − | 0.543751i | \(-0.817004\pi\) | ||||
0.839247 | − | 0.543751i | \(-0.182996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −395873. | −0.559711 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 94276.5i | − 0.132662i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.94304e6 | 2.72125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 721122.i | 1.00518i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −732299. | −1.01595 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 157022.i | − 0.216822i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −445462. | −0.612227 | −0.306113 | − | 0.951995i | \(-0.599029\pi\) | ||||
−0.306113 | + | 0.951995i | \(0.599029\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 73924.2i | 0.101124i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 255454. | 0.347817 | 0.173909 | − | 0.984762i | \(-0.444360\pi\) | ||||
0.173909 | + | 0.984762i | \(0.444360\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 549268.i | 0.744386i | 0.928155 | + | 0.372193i | \(0.121394\pi\) | ||||
−0.928155 | + | 0.372193i | \(0.878606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9121.27 | 0.0123041 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 217330.i | 0.291808i | 0.989299 | + | 0.145904i | \(0.0466091\pi\) | ||||
−0.989299 | + | 0.145904i | \(0.953391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42154.6 | −0.0563395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.25844e6i | 1.67415i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −98830.9 | −0.130874 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.34256e6i | − 1.76969i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 156825. | 0.205772 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 394264.i | 0.514957i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −467000. | −0.607180 | −0.303590 | − | 0.952803i | \(-0.598185\pi\) | ||||
−0.303590 | + | 0.952803i | \(0.598185\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 561487.i | 0.726711i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −916522. | −1.18084 | −0.590420 | − | 0.807096i | \(-0.701038\pi\) | ||||
−0.590420 | + | 0.807096i | \(0.701038\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 633021.i | 0.811890i | 0.913898 | + | 0.405945i | \(0.133058\pi\) | ||||
−0.913898 | + | 0.405945i | \(0.866942\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −963862. | −1.23063 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 666258.i | − 0.846828i | −0.905936 | − | 0.423414i | \(-0.860832\pi\) | ||||
0.905936 | − | 0.423414i | \(-0.139168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 406769. | 0.514688 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 10890.2i | − 0.0137177i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13857.7 | −0.0173775 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.34301e6i | − 1.67662i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.09308e6 | 1.35853 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 953842.i | 1.18020i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.12029e6 | −1.38000 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 608395.i | − 0.746123i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.14857e6 | −1.40236 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 374365.i | 0.455072i | 0.973770 | + | 0.227536i | \(0.0730670\pi\) | ||||
−0.973770 | + | 0.227536i | \(0.926933\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 416645. | 0.504241 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 790211.i | − 0.952152i | −0.879404 | − | 0.476076i | \(-0.842059\pi\) | ||||
0.879404 | − | 0.476076i | \(-0.157941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −102670. | −0.123169 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 94848.3i | − 0.113289i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −498334. | −0.592628 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00581e6i | 1.19093i | 0.803380 | + | 0.595466i | \(0.203033\pi\) | ||||
−0.803380 | + | 0.595466i | \(0.796967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 140779. | 0.165966 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.18510e6i | 1.39108i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −174979. | −0.204505 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 318146.i | − 0.370226i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −645243. | −0.747639 | −0.373820 | − | 0.927501i | \(-0.621952\pi\) | ||||
−0.373820 | + | 0.927501i | \(0.621952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7216.92i | 0.00832631i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 597221. | 0.686075 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 325375.i | 0.372187i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −801226. | −0.912591 | −0.456295 | − | 0.889828i | \(-0.650824\pi\) | ||||
−0.456295 | + | 0.889828i | \(0.650824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 904040.i | − 1.02531i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −504479. | −0.569724 | −0.284862 | − | 0.958569i | \(-0.591948\pi\) | ||||
−0.284862 | + | 0.958569i | \(0.591948\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 26189.4i | − 0.0294512i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 267804. | 0.299884 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 170424.i | 0.190034i | 0.995476 | + | 0.0950169i | \(0.0302905\pi\) | ||||
−0.995476 | + | 0.0950169i | \(0.969709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50179e6 | 1.66755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 800835.i | − 0.885486i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −352354. | −0.387965 | −0.193983 | − | 0.981005i | \(-0.562141\pi\) | ||||
−0.193983 | + | 0.981005i | \(0.562141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 604616.i | 0.662938i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −43316.7 | −0.0472967 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.72372e6i | 1.87425i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.99809e6 | −2.16356 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 383798.i | − 0.413857i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.89727e6 | 2.03740 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.37663e6i | 1.47219i | 0.676879 | + | 0.736094i | \(0.263332\pi\) | ||||
−0.676879 | + | 0.736094i | \(0.736668\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −212744. | −0.226574 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 534975.i | 0.567408i | 0.958912 | + | 0.283704i | \(0.0915633\pi\) | ||||
−0.958912 | + | 0.283704i | \(0.908437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.85633e6 | −1.96078 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 1.21808e6i | − 1.28135i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.19772e6 | −1.25477 | −0.627386 | − | 0.778708i | \(-0.715875\pi\) | ||||
−0.627386 | + | 0.778708i | \(0.715875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78233.9i | 0.0816262i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7651.96 | 0.00795123 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 149071.i | 0.154272i | 0.997021 | + | 0.0771360i | \(0.0245776\pi\) | ||||
−0.997021 | + | 0.0771360i | \(0.975422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 665799. | 0.686232 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 50202.0i | 0.0515331i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.74685e6 | −1.78593 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 564204.i | 0.574498i | 0.957856 | + | 0.287249i | \(0.0927407\pi\) | ||||
−0.957856 | + | 0.287249i | \(0.907259\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −761276. | −0.772047 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.28343e6i | − 1.29636i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.31568e6 | −1.32361 | −0.661803 | − | 0.749678i | \(-0.730208\pi\) | ||||
−0.661803 | + | 0.749678i | \(0.730208\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29522.0i | 0.0295812i |
(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.g.b.127.15 | yes | 16 | |
3.2 | odd | 2 | 1152.5.g.c.127.4 | 16 | |||
4.3 | odd | 2 | inner | 384.5.g.b.127.7 | yes | 16 | |
8.3 | odd | 2 | 384.5.g.a.127.10 | yes | 16 | ||
8.5 | even | 2 | 384.5.g.a.127.2 | ✓ | 16 | ||
12.11 | even | 2 | 1152.5.g.c.127.3 | 16 | |||
16.3 | odd | 4 | 768.5.b.h.127.10 | 16 | |||
16.5 | even | 4 | 768.5.b.h.127.15 | 16 | |||
16.11 | odd | 4 | 768.5.b.i.127.7 | 16 | |||
16.13 | even | 4 | 768.5.b.i.127.2 | 16 | |||
24.5 | odd | 2 | 1152.5.g.f.127.14 | 16 | |||
24.11 | even | 2 | 1152.5.g.f.127.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.g.a.127.2 | ✓ | 16 | 8.5 | even | 2 | ||
384.5.g.a.127.10 | yes | 16 | 8.3 | odd | 2 | ||
384.5.g.b.127.7 | yes | 16 | 4.3 | odd | 2 | inner | |
384.5.g.b.127.15 | yes | 16 | 1.1 | even | 1 | trivial | |
768.5.b.h.127.10 | 16 | 16.3 | odd | 4 | |||
768.5.b.h.127.15 | 16 | 16.5 | even | 4 | |||
768.5.b.i.127.2 | 16 | 16.13 | even | 4 | |||
768.5.b.i.127.7 | 16 | 16.11 | odd | 4 | |||
1152.5.g.c.127.3 | 16 | 12.11 | even | 2 | |||
1152.5.g.c.127.4 | 16 | 3.2 | odd | 2 | |||
1152.5.g.f.127.13 | 16 | 24.11 | even | 2 | |||
1152.5.g.f.127.14 | 16 | 24.5 | odd | 2 |