Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,5,Mod(127,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, 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("768.127");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(79.3881316484\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{70}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.7 | ||
Root | \(0.500000 + 2.27039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.127 |
Dual form | 768.5.b.i.127.2 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | 38.1647i | 1.52659i | 0.646051 | + | 0.763294i | \(0.276419\pi\) | ||||
−0.646051 | + | 0.763294i | \(0.723581\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | −14.9385 | −0.123459 | −0.0617295 | − | 0.998093i | \(-0.519662\pi\) | ||||
−0.0617295 | + | 0.998093i | \(0.519662\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 281.909i | 1.66810i | 0.551687 | + | 0.834051i | \(0.313984\pi\) | ||||
−0.551687 | + | 0.834051i | \(0.686016\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 71.7400 | 0.198726 | 0.0993628 | − | 0.995051i | \(-0.468320\pi\) | ||||
0.0993628 | + | 0.995051i | \(0.468320\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 259.891i | − 0.589321i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 558.040i | 0.663543i | 0.943360 | + | 0.331771i | \(0.107646\pi\) | ||||
−0.943360 | + | 0.331771i | \(0.892354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1709.27i | 1.77864i | 0.457285 | + | 0.889320i | \(0.348822\pi\) | ||||
−0.457285 | + | 0.889320i | \(0.651178\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 77.6229 | 0.0712791 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1908.85 | −1.55824 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 210.427i | − 0.153708i | −0.997042 | − | 0.0768541i | \(-0.975512\pi\) | ||||
0.997042 | − | 0.0768541i | \(-0.0244876\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 1464.84i | − 0.963079i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35.0966 | 0.0208784 | 0.0104392 | − | 0.999946i | \(-0.496677\pi\) | ||||
0.0104392 | + | 0.999946i | \(0.496677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2340.97 | 1.26607 | 0.633036 | − | 0.774122i | \(-0.281809\pi\) | ||||
0.633036 | + | 0.774122i | \(0.281809\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1030.45i | 0.508863i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 193.166i | 0.0874449i | 0.999044 | + | 0.0437224i | \(0.0139217\pi\) | ||||
−0.999044 | + | 0.0437224i | \(0.986078\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −100.598 | −0.0418985 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2965.49 | 1.14013 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1962.98i | 0.698818i | 0.936970 | + | 0.349409i | \(0.113618\pi\) | ||||
−0.936970 | + | 0.349409i | \(0.886382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 570.125i | − 0.188471i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −372.772 | −0.114734 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4860.39 | 1.39626 | 0.698131 | − | 0.715970i | \(-0.254015\pi\) | ||||
0.698131 | + | 0.715970i | \(0.254015\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 478.284i | 0.128536i | 0.997933 | + | 0.0642682i | \(0.0204713\pi\) | ||||
−0.997933 | + | 0.0642682i | \(0.979529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1350.43i | 0.340245i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10759.0 | −2.54651 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4762.37 | −1.06090 | −0.530449 | − | 0.847717i | \(-0.677977\pi\) | ||||
−0.530449 | + | 0.847717i | \(0.677977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 3877.42i | − 0.814414i | ||||||||
\(70\) | 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 | \(-0.333395\pi\) | ||||
0.499833 | + | 0.866122i | \(0.333395\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4320.84 | 0.768149 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 747.166i | − 0.126019i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6615.84i | 1.06006i | 0.847979 | + | 0.530030i | \(0.177819\pi\) | ||||
−0.847979 | + | 0.530030i | \(0.822181\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6872.82 | 0.997651 | 0.498826 | − | 0.866702i | \(-0.333765\pi\) | ||||
0.498826 | + | 0.866702i | \(0.333765\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 21780.9i | − 3.01466i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2899.66i | − 0.383097i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5237.05 | 0.661160 | 0.330580 | − | 0.943778i | \(-0.392756\pi\) | ||||
0.330580 | + | 0.943778i | \(0.392756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14100.0 | −1.70269 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 8881.65i | − 1.02690i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | −403.341 | −0.0411530 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 15431.3i | − 1.51272i | −0.654154 | − | 0.756362i | \(-0.726975\pi\) | ||||
0.654154 | − | 0.756362i | \(-0.273025\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 14214.7 | 1.24157 | 0.620785 | − | 0.783981i | \(-0.286814\pi\) | ||||
0.620785 | + | 0.783981i | \(0.286814\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 283.406i | 0.0238537i | 0.999929 | + | 0.0119269i | \(0.00379652\pi\) | ||||
−0.999929 | + | 0.0119269i | \(0.996203\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −28478.9 | −2.15341 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7611.55i | 0.556034i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 28544.5i | − 2.01571i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14417.8 | −0.984758 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −182.367 | −0.0120541 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 7882.75i | − 0.504496i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8132.78i | 0.504233i | 0.967697 | + | 0.252117i | \(0.0811267\pi\) | ||||
−0.967697 | + | 0.252117i | \(0.918873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12164.0 | −0.730967 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9963.50 | −0.580590 | −0.290295 | − | 0.956937i | \(-0.593753\pi\) | ||||
−0.290295 | + | 0.956937i | \(0.593753\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3588.14i | 0.202846i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5354.36i | − 0.293792i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −34463.3 | −1.83618 | −0.918091 | − | 0.396369i | \(-0.870270\pi\) | ||||
−0.918091 | + | 0.396369i | \(0.870270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 37114.7 | 1.92095 | 0.960477 | − | 0.278361i | \(-0.0897910\pi\) | ||||
0.960477 | + | 0.278361i | \(0.0897910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1003.72i | − 0.0504863i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 4211.31i | − 0.205942i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21297.4 | −1.01296 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 522.725 | 0.0241901 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 15314.2i | − 0.689797i | −0.938640 | − | 0.344899i | \(-0.887913\pi\) | ||||
0.938640 | − | 0.344899i | \(-0.112087\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | −65233.9 | −2.71525 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 7662.12i | − 0.310849i | −0.987848 | − | 0.155425i | \(-0.950325\pi\) | ||||
0.987848 | − | 0.155425i | \(-0.0496745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 10199.9i | − 0.403463i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −37322.5 | −1.43985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8483.09 | −0.319285 | −0.159643 | − | 0.987175i | \(-0.551034\pi\) | ||||
−0.159643 | + | 0.987175i | \(0.551034\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2962.46i | 0.108814i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 1936.98 | 0.0662419 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1104.54i | 0.0369055i | 0.999830 | + | 0.0184527i | \(0.00587402\pi\) | ||||
−0.999830 | + | 0.0184527i | \(0.994126\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 41590.6i | − 1.35806i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25255.3 | −0.806132 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 35189.9 | 1.09828 | 0.549139 | − | 0.835731i | \(-0.314956\pi\) | ||||
0.549139 | + | 0.835731i | \(0.314956\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 30095.0i | − 0.918623i | −0.888275 | − | 0.459311i | \(-0.848096\pi\) | ||||
0.888275 | − | 0.459311i | \(-0.151904\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2485.24i | − 0.0742105i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8030.87 | 0.234649 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8525.55 | 0.243803 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 7017.05i | − 0.196440i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 15842.3i | − 0.434261i | −0.976143 | − | 0.217131i | \(-0.930330\pi\) | ||||
0.976143 | − | 0.217131i | \(-0.0696697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 49712.8 | 1.33461 | 0.667303 | − | 0.744786i | \(-0.267448\pi\) | ||||
0.667303 | + | 0.744786i | \(0.267448\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 55905.4 | 1.47023 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17445.4i | 0.449520i | 0.974414 | + | 0.224760i | \(0.0721598\pi\) | ||||
−0.974414 | + | 0.224760i | \(0.927840\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −27910.9 | −0.677301 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1339.45i | 0.0318727i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20147.7i | 0.470202i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1071.69 | −0.0245345 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 51764.4 | 1.16270 | 0.581348 | − | 0.813655i | \(-0.302525\pi\) | ||||
0.581348 | + | 0.813655i | \(0.302525\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21843.7i | 0.481469i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 89342.3i | 1.93277i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −85491.0 | −1.81552 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27681.1 | −0.577158 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 160888.i | − 3.29412i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 58417.9i | − 1.17472i | −0.809324 | − | 0.587362i | \(-0.800166\pi\) | ||||
0.809324 | − | 0.587362i | \(-0.199834\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22451.7 | −0.443491 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −60234.3 | −1.16894 | −0.584470 | − | 0.811415i | \(-0.698698\pi\) | ||||
−0.584470 | + | 0.811415i | \(0.698698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 31082.1i | − 0.592706i | −0.955078 | − | 0.296353i | \(-0.904229\pi\) | ||||
0.955078 | − | 0.296353i | \(-0.0957706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3882.39i | 0.0727570i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25930.7 | 0.477643 | 0.238821 | − | 0.971064i | \(-0.423239\pi\) | ||||
0.238821 | + | 0.971064i | \(0.423239\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7372.12 | −0.133492 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 34376.9i | − 0.612026i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4425.21i | 0.0774708i | 0.999250 | + | 0.0387354i | \(0.0123329\pi\) | ||||
−0.999250 | + | 0.0387354i | \(0.987667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −34491.1 | −0.593844 | −0.296922 | − | 0.954902i | \(-0.595960\pi\) | ||||
−0.296922 | + | 0.954902i | \(0.595960\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3839.31i | − 0.0639618i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20224.2i | 0.331495i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35712.2 | −0.575994 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21673.7 | 0.344022 | 0.172011 | − | 0.985095i | \(-0.444974\pi\) | ||||
0.172011 | + | 0.985095i | \(0.444974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 11147.3i | − 0.174152i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 10524.7 | 0.156895 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15067.1i | 0.221181i | ||||||||
\(262\) | 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 | ||||||||
\(267\) | −27212.5 | −0.381721 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 80644.9i | − 1.11448i | −0.830351 | − | 0.557240i | \(-0.811860\pi\) | ||||
0.830351 | − | 0.557240i | \(-0.188140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 49892.7i | − 0.679357i | −0.940542 | − | 0.339678i | \(-0.889682\pi\) | ||||
0.940542 | − | 0.339678i | \(-0.110318\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73265.6 | 0.983048 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12422.1 | 0.164259 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 13320.1i | − 0.173599i | −0.996226 | − | 0.0867996i | \(-0.972336\pi\) | ||||
0.996226 | − | 0.0867996i | \(-0.0276640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46150.4i | 0.592880i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18143.5 | 0.229778 | 0.114889 | − | 0.993378i | \(-0.463349\pi\) | ||||
0.114889 | + | 0.993378i | \(0.463349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 140931. | 1.75968 | 0.879840 | − | 0.475270i | \(-0.157650\pi\) | ||||
0.879840 | + | 0.475270i | \(0.157650\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 14226.7i | − 0.175152i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1755.39i | 0.0213113i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 242187. | 2.89971 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30180.9 | 0.356407 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 108058.i | 1.25870i | 0.777122 | + | 0.629350i | \(0.216679\pi\) | ||||
−0.777122 | + | 0.629350i | \(0.783321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 185495.i | 2.13152i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2095.82 | 0.0237597 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −210364. | −2.35304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 117086.i | 1.29232i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 80183.3i | 0.873371i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18253.6 | −0.196222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27092.9 | 0.287461 | 0.143730 | − | 0.989617i | \(-0.454090\pi\) | ||||
0.143730 | + | 0.989617i | \(0.454090\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 61227.2i | − 0.641250i | ||||||||
\(310\) | 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 | \(-0.152131\pi\) | ||||
0.887948 | + | 0.459945i | \(0.152131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −51538.8 | −0.519414 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 154121.i | 1.53371i | 0.641822 | + | 0.766854i | \(0.278179\pi\) | ||||
−0.641822 | + | 0.766854i | \(0.721821\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 8336.29i | − 0.0819203i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −73861.9 | −0.716821 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −40942.6 | −0.392437 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 234420.i | − 2.21937i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1472.62i | − 0.0137719i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9661.38 | −0.0892580 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 146508. | 1.33723 | 0.668613 | − | 0.743611i | \(-0.266889\pi\) | ||||
0.668613 | + | 0.743611i | \(0.266889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 5681.52i | − 0.0512361i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −24709.4 | −0.215012 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 25534.0i | − 0.219589i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 115057.i | 0.977967i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 147981. | 1.24327 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 125592. | 1.04304 | 0.521521 | − | 0.853239i | \(-0.325365\pi\) | ||||
0.521521 | + | 0.853239i | \(0.325365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 44311.9i | − 0.363806i | −0.983316 | − | 0.181903i | \(-0.941774\pi\) | ||||
0.983316 | − | 0.181903i | \(-0.0582257\pi\) | |||||||
\(350\) | 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. | 1.27307 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 148322.i | 1.16377i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 74917.3 | 0.568550 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 203312.i | 1.52608i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22943.3i | 0.170343i | 0.996366 | + | 0.0851714i | \(0.0271438\pi\) | ||||
−0.996366 | + | 0.0851714i | \(0.972856\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 947.607 | 0.00695946 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −98180.3 | −0.713307 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 214254.i | 1.53997i | 0.638062 | + | 0.769985i | \(0.279736\pi\) | ||||
−0.638062 | + | 0.769985i | \(0.720264\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 40960.0i | 0.291271i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −157317. | −1.10686 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 135220. | 0.941376 | 0.470688 | − | 0.882300i | \(-0.344006\pi\) | ||||
0.470688 | + | 0.882300i | \(0.344006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 42259.2i | − 0.291119i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 99667.3i | 0.679446i | 0.940525 | + | 0.339723i | \(0.110333\pi\) | ||||
−0.940525 | + | 0.339723i | \(0.889667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28515.4 | 0.192379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 63206.1 | 0.422024 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 83760.5i | 0.553529i | 0.960938 | + | 0.276764i | \(0.0892621\pi\) | ||||
−0.960938 | + | 0.276764i | \(0.910738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 425869.i | − 2.78562i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 51771.9 | 0.335204 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −252491. | −1.61828 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 222509.i | 1.41178i | 0.708322 | + | 0.705890i | \(0.249453\pi\) | ||||
−0.708322 | + | 0.705890i | \(0.750547\pi\) | |||||||
\(398\) | 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. | −2.96695 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27822.1i | 0.169621i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3143.46i | 0.0189767i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34233.7 | 0.204648 | 0.102324 | − | 0.994751i | \(-0.467372\pi\) | ||||
0.102324 | + | 0.994751i | \(0.467372\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 179077. | 1.06012 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 243097.i | 1.42521i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 262299.i | 1.52300i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −192854. | −1.10906 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −90685.6 | −0.516547 | −0.258274 | − | 0.966072i | \(-0.583154\pi\) | ||||
−0.258274 | + | 0.966072i | \(0.583154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 278121.i | 1.56917i | 0.620022 | + | 0.784584i | \(0.287124\pi\) | ||||
−0.620022 | + | 0.784584i | \(0.712876\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5215.48i | 0.0291483i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 474570. | 2.62738 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23921.8 | −0.131201 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21882.6i | 0.118901i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 183909.i | 0.990032i | 0.868884 | + | 0.495016i | \(0.164838\pi\) | ||||
−0.868884 | + | 0.495016i | \(0.835162\pi\) | |||||||
\(432\) | 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. | 0.584831 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 53533.1i | 0.280324i | ||||||||
\(438\) | 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. | −1.17427 | −0.587133 | − | 0.809491i | \(-0.699743\pi\) | ||||
−0.587133 | + | 0.809491i | \(0.699743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 199870.i | 1.00932i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | −524.291 | −0.00257762 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 221059.i | − 1.07724i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 538121.i | − 2.59931i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 303453. | 1.45298 | 0.726489 | − | 0.687179i | \(-0.241151\pi\) | ||||
0.726489 | + | 0.687179i | \(0.241151\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 80068.2 | 0.380045 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 147882.i | − 0.695849i | −0.937523 | − | 0.347924i | \(-0.886887\pi\) | ||||
0.937523 | − | 0.347924i | \(-0.113113\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 106150.i | − 0.495174i | −0.968866 | − | 0.247587i | \(-0.920362\pi\) | ||||
0.968866 | − | 0.247587i | \(-0.0796376\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 338965. | 1.56765 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −158470. | −0.726630 | −0.363315 | − | 0.931666i | \(-0.618355\pi\) | ||||
−0.363315 | + | 0.931666i | \(0.618355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 238195.i | − 1.08289i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39813.5i | 0.179469i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34970.6 | −0.156308 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −59655.0 | −0.264399 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 53000.4i | 0.232939i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 87871.4i | − 0.382981i | −0.981495 | − | 0.191490i | \(-0.938668\pi\) | ||||
0.981495 | − | 0.191490i | \(-0.0613320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 59321.2 | 0.256401 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 193933. | 0.831300 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 221673.i | − 0.942386i | ||||||||
\(486\) | 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. | 0.485088 | 0.242544 | − | 0.970140i | \(-0.422018\pi\) | ||||
0.242544 | + | 0.970140i | \(0.422018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 318478.i | − 1.31034i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 15393.4i | − 0.0628237i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 210259. | 0.851219 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 99656.8 | 0.400227 | 0.200113 | − | 0.979773i | \(-0.435869\pi\) | ||||
0.200113 | + | 0.979773i | \(0.435869\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 127908.i | 0.509591i | ||||||||
\(502\) | 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. | 1.02917 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 94288.3i | 0.363934i | 0.983305 | + | 0.181967i | \(0.0582463\pi\) | ||||
−0.983305 | + | 0.181967i | \(0.941754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 266446.i | 1.02039i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10064.8 | −0.0382448 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −449702. | −1.69555 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2885.61i | − 0.0107959i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 5739.38i | − 0.0213074i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 252399. | 0.929848 | 0.464924 | − | 0.885351i | \(-0.346082\pi\) | ||||
0.464924 | + | 0.885351i | \(0.346082\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −360986. | −1.31973 | −0.659867 | − | 0.751382i | \(-0.729388\pi\) | ||||
−0.659867 | + | 0.751382i | \(0.729388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 216111.i | 0.784076i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 975497.i | − 3.51240i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −276989. | −0.989809 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 131230. | 0.465421 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9894.05i | 0.0348273i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 542501.i | 1.89537i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −182852. | −0.634091 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1502.79 | 0.00517275 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 212815.i | 0.727123i | 0.931570 | + | 0.363561i | \(0.118439\pi\) | ||||
−0.931570 | + | 0.363561i | \(0.881561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 156378.i | 0.530367i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10816.1 | −0.0364148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 84823.3 | 0.283492 | 0.141746 | − | 0.989903i | \(-0.454728\pi\) | ||||
0.141746 | + | 0.989903i | \(0.454728\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12913.7i | 0.0428455i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40033.7i | 0.131863i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −330898. | −1.08204 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −41729.6 | −0.135475 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8677.73i | − 0.0279702i | −0.999902 | − | 0.0139851i | \(-0.995548\pi\) | ||||
0.999902 | − | 0.0139851i | \(-0.00445174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 659940.i | 2.11194i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44300.0 | −0.140760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 114230. | 0.360381 | 0.180190 | − | 0.983632i | \(-0.442329\pi\) | ||||
0.180190 | + | 0.983632i | \(0.442329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 181486.i | 0.568521i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36461.7i | 0.113415i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29567.0 | 0.0913236 | 0.0456618 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456618 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −229583. | −0.704155 | −0.352078 | − | 0.935971i | \(-0.614525\pi\) | ||||
−0.352078 | + | 0.935971i | \(0.614525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 82318.9i | 0.250721i | ||||||||
\(574\) | 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. | −0.770536 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 343751.i | 1.01834i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 29324.0i | − 0.0862754i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −290493. | −0.848835 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 548252. | 1.59112 | 0.795561 | − | 0.605873i | \(-0.207176\pi\) | ||||
0.795561 | + | 0.605873i | \(0.207176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 122623.i | 0.353461i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 1.08939e6 | 3.07717 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 174740.i | 0.490278i | ||||||||
\(598\) | 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 | \(-0.665776\pi\) | ||||
−0.497575 | + | 0.867421i | \(0.665776\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −128584. | −0.353633 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 550253.i | − 1.50332i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 333341.i | 0.904714i | 0.891837 | + | 0.452357i | \(0.149417\pi\) | ||||
−0.891837 | + | 0.452357i | \(0.850583\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 145029. | 0.391040 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −54455.2 | −0.145867 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 357269.i | 0.950768i | 0.879778 | + | 0.475384i | \(0.157691\pi\) | ||||
−0.879778 | + | 0.475384i | \(0.842309\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 6959.99i | − 0.0184017i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −271334. | −0.712744 | −0.356372 | − | 0.934344i | \(-0.615986\pi\) | ||||
−0.356372 | + | 0.934344i | \(0.615986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 383666. | 1.00132 | 0.500659 | − | 0.865645i | \(-0.333091\pi\) | ||||
0.500659 | + | 0.865645i | \(0.333091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 104690.i | − 0.271471i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 261936.i | 0.674869i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −218873. | −0.560315 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5568.66 | 0.0141650 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 120092.i | 0.303538i | ||||||||
\(630\) | 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. | −0.769757 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 28359.6i | − 0.0698911i | ||||||||
\(638\) | 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. | −0.250290 | −0.125145 | − | 0.992138i | \(-0.539940\pi\) | ||||
−0.125145 | + | 0.992138i | \(0.539940\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 464236.i | − 1.11589i | ||||||||
\(646\) | 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. | 1.04819 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 227855.i | − 0.534358i | −0.963647 | − | 0.267179i | \(-0.913909\pi\) | ||||
0.963647 | − | 0.267179i | \(-0.0860915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 380254.i | − 0.886322i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 143835. | 0.333222 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −182148. | −0.419423 | −0.209712 | − | 0.977763i | \(-0.567253\pi\) | ||||
−0.209712 | + | 0.977763i | \(0.567253\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 606405.i | 1.38791i | 0.720020 | + | 0.693953i | \(0.244132\pi\) | ||||
−0.720020 | + | 0.693953i | \(0.755868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 835999.i | 1.90186i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −136941. | −0.309663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −416415. | −0.935997 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 303548.i | 0.678228i | ||||||||
\(670\) | 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. | 0.256050 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 134998.i | − 0.294543i | −0.989096 | − | 0.147272i | \(-0.952951\pi\) | ||||
0.989096 | − | 0.147272i | \(-0.0470491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 290509.i | − 0.630115i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 312987. | 0.674888 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −566455. | −1.21429 | −0.607147 | − | 0.794589i | \(-0.707686\pi\) | ||||
−0.607147 | + | 0.794589i | \(0.707686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.31528e6i | − 2.80310i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 161507.i | 0.342199i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −553382. | −1.16570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 543725. | 1.13874 | 0.569368 | − | 0.822083i | \(-0.307188\pi\) | ||||
0.569368 | + | 0.822083i | \(0.307188\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 20173.5i | − 0.0420063i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.41647e6i | 2.93251i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20029.9 | −0.0412300 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −134740. | −0.275767 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 767758.i | 1.56239i | 0.624289 | + | 0.781193i | \(0.285389\pi\) | ||||
−0.624289 | + | 0.781193i | \(0.714611\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 15096.0i | − 0.0305458i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 38306.6 | 0.0770719 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 771811. | 1.54409 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 560272.i | 1.11457i | 0.830322 | + | 0.557284i | \(0.188157\pi\) | ||||
−0.830322 | + | 0.557284i | \(0.811843\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 178628.i | 0.353353i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.27548e6 | −2.50896 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 160724. | 0.314389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 22994.1i | − 0.0447278i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 759774.i | − 1.46969i | −0.678234 | − | 0.734846i | \(-0.737254\pi\) | ||||
0.678234 | − | 0.734846i | \(-0.262746\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −589347. | −1.13371 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 179221. | 0.342856 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 464035.i | − 0.882826i | ||||||||
\(726\) | 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 | ||||||||
\(731\) | −1.33601e6 | −2.50020 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 600287.i | − 1.11725i | −0.829420 | − | 0.558626i | \(-0.811329\pi\) | ||||
0.829420 | − | 0.558626i | \(-0.188671\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19949.6i | 0.0369284i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 71142.9 | 0.130977 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −116503. | −0.213327 | −0.106664 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106664 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 105088.i | − 0.191389i | ||||||||
\(742\) | 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. | 0.332550 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 710964.i | 1.26731i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 255543.i | − 0.453089i | −0.974001 | − | 0.226545i | \(-0.927257\pi\) | ||||
0.974001 | − | 0.226545i | \(-0.0727429\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −112620. | −0.198621 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.62364e6 | −2.84836 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 157849.i | − 0.275454i | −0.990470 | − | 0.137727i | \(-0.956020\pi\) | ||||
0.990470 | − | 0.137727i | \(-0.0439797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 57923.0i | 0.100547i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 436931. | 0.754474 | 0.377237 | − | 0.926117i | \(-0.376874\pi\) | ||||
0.377237 | + | 0.926117i | \(0.376874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14174.8 | −0.0243483 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 588085.i | − 1.00489i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | −54625.1 | −0.0918932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 143407.i | − 0.240000i | −0.992774 | − | 0.120000i | \(-0.961711\pi\) | ||||
0.992774 | − | 0.120000i | \(-0.0382895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.42134e6i | − 2.36643i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −54687.9 | −0.0905835 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2517.83 | 0.00414907 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62799.1i | 0.102956i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 78290.8i | − 0.127699i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 292423. | 0.474539 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 295695. | 0.477414 | 0.238707 | − | 0.971092i | \(-0.423276\pi\) | ||||
0.238707 | + | 0.971092i | \(0.423276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 205927.i | 0.330795i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 237843.i | 0.380134i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −134833. | −0.214412 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 389278. | 0.615922 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41548.0i | 0.0654084i | 0.999465 | + | 0.0327042i | \(0.0104119\pi\) | ||||
−0.999465 | + | 0.0327042i | \(0.989588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 110241.i | − 0.172683i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 141400. | 0.220387 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −79580.9 | −0.123418 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.42440e6i | − 2.19806i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 419043.i | 0.643445i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.20959e6 | −1.84817 | −0.924083 | − | 0.382191i | \(-0.875170\pi\) | ||||
−0.924083 | + | 0.382191i | \(0.875170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 212276. | 0.322744 | 0.161372 | − | 0.986894i | \(-0.448408\pi\) | ||||
0.161372 | + | 0.986894i | \(0.448408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 259250.i | 0.392227i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 323755.i | − 0.487417i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 167941. | 0.251601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −380699. | −0.567563 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.12848e6i | − 1.67420i | −0.547048 | − | 0.837101i | \(-0.684248\pi\) | ||||
0.547048 | − | 0.837101i | \(-0.315752\pi\) | |||||||
\(822\) | 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. | 0.675409 | 0.337705 | − | 0.941252i | \(-0.390349\pi\) | ||||
0.337705 | + | 0.941252i | \(0.390349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1.04514e6i | − 1.52077i | −0.649472 | − | 0.760386i | \(-0.725010\pi\) | ||||
0.649472 | − | 0.760386i | \(-0.274990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69213.3i | 0.100228i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 57412.3 | 0.0827399 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 939459. | 1.34743 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 239804.i | − 0.342300i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | −94276.5 | −0.132662 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.94304e6i | − 2.72125i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 721122.i | − 1.00518i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −732299. | −1.01595 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 157022. | 0.216822 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 445462.i | − 0.612227i | −0.951995 | − | 0.306113i | \(-0.900971\pi\) | ||||
0.951995 | − | 0.306113i | \(-0.0990286\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 73924.2i | 0.101124i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −255454. | −0.347817 | −0.173909 | − | 0.984762i | \(-0.555640\pi\) | ||||
−0.173909 | + | 0.984762i | \(0.555640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 549268. | 0.744386 | 0.372193 | − | 0.928155i | \(-0.378606\pi\) | ||||
0.372193 | + | 0.928155i | \(0.378606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 9121.27i | − 0.0123041i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 217330.i | − 0.291808i | −0.989299 | − | 0.145904i | \(-0.953391\pi\) | ||||
0.989299 | − | 0.145904i | \(-0.0466091\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42154.6 | −0.0563395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.25844e6 | −1.67415 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 98830.9i | − 0.130874i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.34256e6i | − 1.76969i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −156825. | −0.205772 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 394264. | 0.514957 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 467000.i | 0.607180i | 0.952803 | + | 0.303590i | \(0.0981853\pi\) | ||||
−0.952803 | + | 0.303590i | \(0.901815\pi\) | |||||||
\(878\) | 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. | −0.811890 | −0.405945 | − | 0.913898i | \(-0.633058\pi\) | ||||
−0.405945 | + | 0.913898i | \(0.633058\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 963862.i | − 1.23063i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | −10890.2 | −0.0137177 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13857.7i | 0.0173775i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.34301e6i | 1.67662i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.09308e6 | 1.35853 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −953842. | −1.18020 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.12029e6i | − 1.38000i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 608395.i | − 0.746123i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.14857e6 | 1.40236 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 374365. | 0.455072 | 0.227536 | − | 0.973770i | \(-0.426933\pi\) | ||||
0.227536 | + | 0.973770i | \(0.426933\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 416645.i | − 0.504241i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 790211.i | 0.952152i | 0.879404 | + | 0.476076i | \(0.157941\pi\) | ||||
−0.879404 | + | 0.476076i | \(0.842059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −102670. | −0.123169 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 94848.3 | 0.113289 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 498334.i | − 0.592628i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 1.18510e6 | 1.39108 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 174979.i | 0.204505i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | −7216.92 | −0.00832631 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 597221.i | 0.686075i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 325375.i | 0.372187i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 801226. | 0.912591 | 0.456295 | − | 0.889828i | \(-0.349176\pi\) | ||||
0.456295 | + | 0.889828i | \(0.349176\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −904040. | −1.02531 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 504479.i | 0.569724i | 0.958569 | + | 0.284862i | \(0.0919477\pi\) | ||||
−0.958569 | + | 0.284862i | \(0.908052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26189.4i | 0.0294512i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 267804. | 0.299884 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −170424. | −0.190034 | −0.0950169 | − | 0.995476i | \(-0.530291\pi\) | ||||
−0.0950169 | + | 0.995476i | \(0.530291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.50179e6i | 1.66755i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 800835.i | − 0.885486i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 352354. | 0.387965 | 0.193983 | − | 0.981005i | \(-0.437859\pi\) | ||||
0.193983 | + | 0.981005i | \(0.437859\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 604616. | 0.662938 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 43316.7i | 0.0472967i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1.72372e6i | − 1.87425i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.99809e6 | −2.16356 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 383798. | 0.413857 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.89727e6i | 2.03740i | ||||||||
\(966\) | 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. | 0.567408 | 0.283704 | − | 0.958912i | \(-0.408437\pi\) | ||||
0.283704 | + | 0.958912i | \(0.408437\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.85633e6i | 1.96078i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | −78233.9 | −0.0816262 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7651.96i | 0.00795123i | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 50202.0 | 0.0515331 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.74685e6i | 1.78593i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 564204.i | − 0.574498i | −0.957856 | − | 0.287249i | \(-0.907259\pi\) | ||||
0.957856 | − | 0.287249i | \(-0.0927407\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −761276. | −0.772047 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.28343e6 | 1.29636 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.31568e6i | − 1.32361i | −0.749678 | − | 0.661803i | \(-0.769792\pi\) | ||||
0.749678 | − | 0.661803i | \(-0.230208\pi\) | |||||||
\(998\) | 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 | 768.5.b.i.127.7 | 16 | ||
4.3 | odd | 2 | 768.5.b.h.127.15 | 16 | |||
8.3 | odd | 2 | inner | 768.5.b.i.127.2 | 16 | ||
8.5 | even | 2 | 768.5.b.h.127.10 | 16 | |||
16.3 | odd | 4 | 384.5.g.b.127.15 | yes | 16 | ||
16.5 | even | 4 | 384.5.g.a.127.10 | yes | 16 | ||
16.11 | odd | 4 | 384.5.g.a.127.2 | ✓ | 16 | ||
16.13 | even | 4 | 384.5.g.b.127.7 | yes | 16 | ||
48.5 | odd | 4 | 1152.5.g.f.127.13 | 16 | |||
48.11 | even | 4 | 1152.5.g.f.127.14 | 16 | |||
48.29 | odd | 4 | 1152.5.g.c.127.3 | 16 | |||
48.35 | even | 4 | 1152.5.g.c.127.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.g.a.127.2 | ✓ | 16 | 16.11 | odd | 4 | ||
384.5.g.a.127.10 | yes | 16 | 16.5 | even | 4 | ||
384.5.g.b.127.7 | yes | 16 | 16.13 | even | 4 | ||
384.5.g.b.127.15 | yes | 16 | 16.3 | odd | 4 | ||
768.5.b.h.127.10 | 16 | 8.5 | even | 2 | |||
768.5.b.h.127.15 | 16 | 4.3 | odd | 2 | |||
768.5.b.i.127.2 | 16 | 8.3 | odd | 2 | inner | ||
768.5.b.i.127.7 | 16 | 1.1 | even | 1 | trivial | ||
1152.5.g.c.127.3 | 16 | 48.29 | odd | 4 | |||
1152.5.g.c.127.4 | 16 | 48.35 | even | 4 | |||
1152.5.g.f.127.13 | 16 | 48.5 | odd | 4 | |||
1152.5.g.f.127.14 | 16 | 48.11 | even | 4 |