Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.3862461668\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.00000 | −0.357771 | −0.178885 | − | 0.983870i | \(-0.557249\pi\) | ||||
−0.178885 | + | 0.983870i | \(0.557249\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.0000 | −0.712663 | −0.356332 | − | 0.934360i | \(-0.615973\pi\) | ||||
−0.356332 | + | 0.934360i | \(0.615973\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.0426692 | −0.0213346 | − | 0.999772i | \(-0.506792\pi\) | ||||
−0.0213346 | + | 0.999772i | \(0.506792\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0000 | −0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 36.0000 | 0.513605 | 0.256802 | − | 0.966464i | \(-0.417331\pi\) | ||||
0.256802 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76.0000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −114.000 | −1.03351 | −0.516753 | − | 0.856134i | \(-0.672859\pi\) | ||||
−0.516753 | + | 0.856134i | \(0.672859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −109.000 | −0.872000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 0.0384197 | 0.0192099 | − | 0.999815i | \(-0.493885\pi\) | ||||
0.0192099 | + | 0.999815i | \(0.493885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 256.000 | 1.48319 | 0.741596 | − | 0.670847i | \(-0.234069\pi\) | ||||
0.741596 | + | 0.670847i | \(0.234069\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −78.0000 | −0.411456 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −86.0000 | −0.382117 | −0.191058 | − | 0.981579i | \(-0.561192\pi\) | ||||
−0.191058 | + | 0.981579i | \(0.561192\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.00000 | −0.0246351 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −160.000 | −0.609459 | −0.304729 | − | 0.952439i | \(-0.598566\pi\) | ||||
−0.304729 | + | 0.952439i | \(0.598566\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −220.000 | −0.780225 | −0.390113 | − | 0.920767i | \(-0.627564\pi\) | ||||
−0.390113 | + | 0.920767i | \(0.627564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −36.0000 | −0.119257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −308.000 | −0.955881 | −0.477941 | − | 0.878392i | \(-0.658617\pi\) | ||||
−0.477941 | + | 0.878392i | \(0.658617\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 108.000 | 0.296530 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 258.000 | 0.668661 | 0.334330 | − | 0.942456i | \(-0.391490\pi\) | ||||
0.334330 | + | 0.942456i | \(0.391490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 104.000 | 0.254970 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 228.000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −264.000 | −0.582540 | −0.291270 | − | 0.956641i | \(-0.594078\pi\) | ||||
−0.291270 | + | 0.956641i | \(0.594078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −606.000 | −1.27197 | −0.635986 | − | 0.771700i | \(-0.719407\pi\) | ||||
−0.635986 | + | 0.771700i | \(0.719407\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | 0.0152658 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −520.000 | −0.948181 | −0.474090 | − | 0.880476i | \(-0.657223\pi\) | ||||
−0.474090 | + | 0.880476i | \(0.657223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −342.000 | −0.596695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −286.000 | −0.478056 | −0.239028 | − | 0.971013i | \(-0.576829\pi\) | ||||
−0.239028 | + | 0.971013i | \(0.576829\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 530.000 | 0.849751 | 0.424875 | − | 0.905252i | \(-0.360318\pi\) | ||||
0.424875 | + | 0.905252i | \(0.360318\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −327.000 | −0.503449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −44.0000 | −0.0626631 | −0.0313316 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313316 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1012.00 | −1.33833 | −0.669165 | − | 0.743114i | \(-0.733348\pi\) | ||||
−0.669165 | + | 0.743114i | \(0.733348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −144.000 | −0.183753 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0000 | 0.0221816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −768.000 | −0.914695 | −0.457347 | − | 0.889288i | \(-0.651200\pi\) | ||||
−0.457347 | + | 0.889288i | \(0.651200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 768.000 | 0.856321 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −304.000 | −0.328313 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −222.000 | −0.232378 | −0.116189 | − | 0.993227i | \(-0.537068\pi\) | ||||
−0.116189 | + | 0.993227i | \(0.537068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −234.000 | −0.237554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 320.000 | 0.315259 | 0.157630 | − | 0.987498i | \(-0.449615\pi\) | ||||
0.157630 | + | 0.987498i | \(0.449615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 592.000 | 0.566325 | 0.283163 | − | 0.959072i | \(-0.408616\pi\) | ||||
0.283163 | + | 0.959072i | \(0.408616\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1782.00 | 1.61002 | 0.805011 | − | 0.593259i | \(-0.202159\pi\) | ||||
0.805011 | + | 0.593259i | \(0.202159\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 230.000 | 0.202110 | 0.101055 | − | 0.994881i | \(-0.467778\pi\) | ||||
0.101055 | + | 0.994881i | \(0.467778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −258.000 | −0.220615 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1718.00 | −1.43023 | −0.715114 | − | 0.699007i | \(-0.753625\pi\) | ||||
−0.715114 | + | 0.699007i | \(0.753625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 456.000 | 0.369758 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.0000 | −0.0142231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −655.000 | −0.492111 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −480.000 | −0.351871 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 936.000 | 0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2444.00 | −1.70764 | −0.853819 | − | 0.520571i | \(-0.825719\pi\) | ||||
−0.853819 | + | 0.520571i | \(0.825719\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −660.000 | −0.450463 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1996.00 | −1.33123 | −0.665616 | − | 0.746295i | \(-0.731831\pi\) | ||||
−0.665616 | + | 0.746295i | \(0.731831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −108.000 | −0.0688530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1746.00 | −1.08884 | −0.544419 | − | 0.838813i | \(-0.683250\pi\) | ||||
−0.544419 | + | 0.838813i | \(0.683250\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1804.00 | −1.10081 | −0.550407 | − | 0.834896i | \(-0.685528\pi\) | ||||
−0.550407 | + | 0.834896i | \(0.685528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −924.000 | −0.551878 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 52.0000 | 0.0304088 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.0000 | −0.0137455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2814.00 | −1.54719 | −0.773597 | − | 0.633678i | \(-0.781544\pi\) | ||||
−0.773597 | + | 0.633678i | \(0.781544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −792.000 | −0.426835 | −0.213417 | − | 0.976961i | \(-0.568459\pi\) | ||||
−0.213417 | + | 0.976961i | \(0.568459\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 324.000 | 0.171202 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1024.00 | −0.530643 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2778.00 | 1.41216 | 0.706078 | − | 0.708134i | \(-0.250463\pi\) | ||||
0.706078 | + | 0.708134i | \(0.250463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 774.000 | 0.386052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2880.00 | 1.38392 | 0.691960 | − | 0.721936i | \(-0.256747\pi\) | ||||
0.691960 | + | 0.721936i | \(0.256747\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 312.000 | 0.147207 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1060.00 | 0.491169 | 0.245585 | − | 0.969375i | \(-0.421020\pi\) | ||||
0.245585 | + | 0.969375i | \(0.421020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2193.00 | −0.998179 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 684.000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1440.00 | 0.632839 | 0.316420 | − | 0.948619i | \(-0.397519\pi\) | ||||
0.316420 | + | 0.948619i | \(0.397519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −792.000 | −0.336330 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1210.00 | 0.505249 | 0.252625 | − | 0.967564i | \(-0.418706\pi\) | ||||
0.252625 | + | 0.967564i | \(0.418706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1618.00 | −0.664447 | −0.332224 | − | 0.943201i | \(-0.607799\pi\) | ||||
−0.332224 | + | 0.943201i | \(0.607799\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1818.00 | −0.734374 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 344.000 | 0.136710 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −936.000 | −0.366027 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4018.00 | 1.52216 | 0.761079 | − | 0.648659i | \(-0.224670\pi\) | ||||
0.761079 | + | 0.648659i | \(0.224670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3382.00 | 1.26136 | 0.630678 | − | 0.776045i | \(-0.282777\pi\) | ||||
0.630678 | + | 0.776045i | \(0.282777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.0000 | 0.00881372 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4302.00 | −1.55586 | −0.777931 | − | 0.628350i | \(-0.783731\pi\) | ||||
−0.777931 | + | 0.628350i | \(0.783731\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2640.00 | 0.940425 | 0.470213 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470213 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1560.00 | −0.547432 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 640.000 | 0.218047 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1026.00 | −0.344502 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1976.00 | −0.653985 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3396.00 | 1.10801 | 0.554005 | − | 0.832513i | \(-0.313099\pi\) | ||||
0.554005 | + | 0.832513i | \(0.313099\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −858.000 | −0.276006 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 880.000 | 0.279142 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1590.00 | 0.490604 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −72.0000 | −0.0219151 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3480.00 | −1.04501 | −0.522507 | − | 0.852635i | \(-0.675003\pi\) | ||||
−0.522507 | + | 0.852635i | \(0.675003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −981.000 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1504.00 | 0.439753 | 0.219877 | − | 0.975528i | \(-0.429435\pi\) | ||||
0.219877 | + | 0.975528i | \(0.429435\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5122.00 | −1.47804 | −0.739020 | − | 0.673683i | \(-0.764711\pi\) | ||||
−0.739020 | + | 0.673683i | \(0.764711\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1630.00 | 0.458304 | 0.229152 | − | 0.973391i | \(-0.426405\pi\) | ||||
0.229152 | + | 0.973391i | \(0.426405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1232.00 | 0.341986 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −132.000 | −0.0361786 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2522.00 | −0.682572 | −0.341286 | − | 0.939960i | \(-0.610862\pi\) | ||||
−0.341286 | + | 0.939960i | \(0.610862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3022.00 | −0.807735 | −0.403867 | − | 0.914817i | \(-0.632334\pi\) | ||||
−0.403867 | + | 0.914817i | \(0.632334\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −152.000 | −0.0391560 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3036.00 | −0.772685 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3480.00 | −0.875122 | −0.437561 | − | 0.899189i | \(-0.644158\pi\) | ||||
−0.437561 | + | 0.899189i | \(0.644158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2964.00 | 0.736542 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −432.000 | −0.106090 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3496.00 | −0.848539 | −0.424269 | − | 0.905536i | \(-0.639469\pi\) | ||||
−0.424269 | + | 0.905536i | \(0.639469\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 54.0000 | 0.0128066 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5058.00 | −1.18589 | −0.592946 | − | 0.805242i | \(-0.702035\pi\) | ||||
−0.592946 | + | 0.805242i | \(0.702035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1032.00 | −0.239227 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2304.00 | −0.528099 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3596.00 | −0.815063 | −0.407532 | − | 0.913191i | \(-0.633610\pi\) | ||||
−0.407532 | + | 0.913191i | \(0.633610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2424.00 | 0.543349 | 0.271674 | − | 0.962389i | \(-0.412423\pi\) | ||||
0.271674 | + | 0.962389i | \(0.412423\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2834.00 | 0.621442 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3634.00 | 0.788252 | 0.394126 | − | 0.919056i | \(-0.371047\pi\) | ||||
0.394126 | + | 0.919056i | \(0.371047\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2304.00 | 0.494397 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2970.00 | −0.630517 | −0.315259 | − | 0.949006i | \(-0.602091\pi\) | ||||
−0.315259 | + | 0.949006i | \(0.602091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7028.00 | 1.47622 | 0.738112 | − | 0.674679i | \(-0.235718\pi\) | ||||
0.738112 | + | 0.674679i | \(0.235718\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −912.000 | −0.189552 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3617.00 | −0.736210 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −666.000 | −0.134164 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 528.000 | 0.105277 | 0.0526384 | − | 0.998614i | \(-0.483237\pi\) | ||||
0.0526384 | + | 0.998614i | \(0.483237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1056.00 | 0.208416 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −702.000 | −0.137152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 228.000 | 0.0440989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 960.000 | 0.182015 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2424.00 | 0.455075 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4300.00 | −0.799394 | −0.399697 | − | 0.916647i | \(-0.630885\pi\) | ||||
−0.399697 | + | 0.916647i | \(0.630885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1776.00 | 0.326968 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4580.00 | 0.835074 | 0.417537 | − | 0.908660i | \(-0.362893\pi\) | ||||
0.417537 | + | 0.908660i | \(0.362893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2266.00 | −0.409207 | −0.204604 | − | 0.978845i | \(-0.565591\pi\) | ||||
−0.204604 | + | 0.978845i | \(0.565591\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7926.00 | −1.40432 | −0.702159 | − | 0.712021i | \(-0.747780\pi\) | ||||
−0.702159 | + | 0.712021i | \(0.747780\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −156.000 | −0.0273803 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5346.00 | 0.929547 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2736.00 | 0.471316 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 218.000 | 0.0372076 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 690.000 | 0.116688 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4132.00 | −0.686149 | −0.343074 | − | 0.939308i | \(-0.611468\pi\) | ||||
−0.343074 | + | 0.939308i | \(0.611468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −774.000 | −0.127372 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2080.00 | 0.339231 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3622.00 | −0.585469 | −0.292734 | − | 0.956194i | \(-0.594565\pi\) | ||||
−0.292734 | + | 0.956194i | \(0.594565\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5154.00 | −0.825743 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6656.00 | −1.05702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1368.00 | 0.213480 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10254.0 | −1.58635 | −0.793175 | − | 0.608994i | \(-0.791574\pi\) | ||||
−0.793175 | + | 0.608994i | \(0.791574\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8178.00 | 1.25432 | 0.627161 | − | 0.778890i | \(-0.284217\pi\) | ||||
0.627161 | + | 0.778890i | \(0.284217\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.0000 | −0.00821170 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9932.00 | −1.49753 | −0.748763 | − | 0.662837i | \(-0.769352\pi\) | ||||
−0.748763 | + | 0.662837i | \(0.769352\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1144.00 | 0.171034 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6546.00 | 0.962353 | 0.481176 | − | 0.876624i | \(-0.340210\pi\) | ||||
0.481176 | + | 0.876624i | \(0.340210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1083.00 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1965.00 | −0.284121 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2120.00 | −0.304016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12176.0 | 1.73183 | 0.865916 | − | 0.500190i | \(-0.166737\pi\) | ||||
0.865916 | + | 0.500190i | \(0.166737\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1440.00 | −0.203153 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8210.00 | −1.13967 | −0.569836 | − | 0.821758i | \(-0.692993\pi\) | ||||
−0.569836 | + | 0.821758i | \(0.692993\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2808.00 | 0.386679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.00163934 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6908.00 | 0.936254 | 0.468127 | − | 0.883661i | \(-0.344929\pi\) | ||||
0.468127 | + | 0.883661i | \(0.344929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7332.00 | −0.985905 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10248.0 | 1.36723 | 0.683614 | − | 0.729844i | \(-0.260407\pi\) | ||||
0.683614 | + | 0.729844i | \(0.260407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1980.00 | −0.260075 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −274.000 | −0.0357130 | −0.0178565 | − | 0.999841i | \(-0.505684\pi\) | ||||
−0.0178565 | + | 0.999841i | \(0.505684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4104.00 | −0.530814 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5988.00 | −0.768587 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 176.000 | 0.0224190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10010.0 | 1.26546 | 0.632730 | − | 0.774373i | \(-0.281934\pi\) | ||||
0.632730 | + | 0.774373i | \(0.281934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1998.00 | 0.248816 | 0.124408 | − | 0.992231i | \(-0.460297\pi\) | ||||
0.124408 | + | 0.992231i | \(0.460297\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −512.000 | −0.0632867 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −324.000 | −0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2236.00 | 0.272320 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12842.0 | 1.55256 | 0.776279 | − | 0.630390i | \(-0.217105\pi\) | ||||
0.776279 | + | 0.630390i | \(0.217105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5238.00 | −0.628641 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4048.00 | 0.478816 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5412.00 | −0.635556 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10400.0 | 1.21259 | 0.606293 | − | 0.795242i | \(-0.292656\pi\) | ||||
0.606293 | + | 0.795242i | \(0.292656\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15586.0 | 1.80431 | 0.902156 | − | 0.431410i | \(-0.141984\pi\) | ||||
0.902156 | + | 0.431410i | \(0.141984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2772.00 | −0.318627 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3924.00 | −0.447863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 156.000 | 0.0175565 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8066.00 | 0.901451 | 0.450726 | − | 0.892663i | \(-0.351165\pi\) | ||||
0.450726 | + | 0.892663i | \(0.351165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5222.00 | 0.579569 | 0.289784 | − | 0.957092i | \(-0.406416\pi\) | ||||
0.289784 | + | 0.957092i | \(0.406416\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −72.0000 | −0.00793594 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8664.00 | −0.948410 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10920.0 | 1.18721 | 0.593603 | − | 0.804758i | \(-0.297705\pi\) | ||||
0.593603 | + | 0.804758i | \(0.297705\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1650.00 | 0.176961 | 0.0884807 | − | 0.996078i | \(-0.471799\pi\) | ||||
0.0884807 | + | 0.996078i | \(0.471799\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3072.00 | 0.327251 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8442.00 | −0.893273 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11858.0 | 1.24636 | 0.623178 | − | 0.782080i | \(-0.285841\pi\) | ||||
0.623178 | + | 0.782080i | \(0.285841\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4160.00 | 0.434339 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2376.00 | −0.246433 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17894.0 | −1.83161 | −0.915805 | − | 0.401623i | \(-0.868446\pi\) | ||||
−0.915805 | + | 0.401623i | \(0.868446\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 972.000 | 0.0988433 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2088.00 | 0.210950 | 0.105475 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105475 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13532.0 | 1.35828 | 0.679142 | − | 0.734007i | \(-0.262352\pi\) | ||||
0.679142 | + | 0.734007i | \(0.262352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3072.00 | −0.306367 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6344.00 | −0.628620 | −0.314310 | − | 0.949320i | \(-0.601773\pi\) | ||||
−0.314310 | + | 0.949320i | \(0.601773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8334.00 | 0.815309 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5720.00 | 0.556038 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8284.00 | −0.800202 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2322.00 | 0.222887 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9948.00 | −0.948926 | −0.474463 | − | 0.880275i | \(-0.657358\pi\) | ||||
−0.474463 | + | 0.880275i | \(0.657358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 172.000 | 0.0163046 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 888.000 | 0.0831382 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20144.0 | 1.87436 | 0.937178 | − | 0.348850i | \(-0.113428\pi\) | ||||
0.937178 | + | 0.348850i | \(0.113428\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8640.00 | 0.799007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10530.0 | 0.967846 | 0.483923 | − | 0.875111i | \(-0.339212\pi\) | ||||
0.483923 | + | 0.875111i | \(0.339212\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 216.000 | 0.0197326 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 936.000 | 0.0849900 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5548.00 | −0.497721 | −0.248860 | − | 0.968539i | \(-0.580056\pi\) | ||||
−0.248860 | + | 0.968539i | \(0.580056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3180.00 | 0.283577 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2152.00 | 0.190761 | 0.0953807 | − | 0.995441i | \(-0.469593\pi\) | ||||
0.0953807 | + | 0.995441i | \(0.469593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1280.00 | −0.112791 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6579.00 | −0.576299 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19780.0 | 1.72246 | 0.861231 | − | 0.508214i | \(-0.169694\pi\) | ||||
0.861231 | + | 0.508214i | \(0.169694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2052.00 | 0.176604 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2368.00 | −0.202615 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8008.00 | 0.681221 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4320.00 | 0.365370 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23052.0 | −1.93844 | −0.969219 | − | 0.246199i | \(-0.920818\pi\) | ||||
−0.969219 | + | 0.246199i | \(0.920818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13364.0 | 1.11734 | 0.558668 | − | 0.829391i | \(-0.311313\pi\) | ||||
0.558668 | + | 0.829391i | \(0.311313\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9216.00 | 0.761775 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 829.000 | 0.0681351 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2376.00 | −0.194180 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 320.000 | 0.0260051 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7128.00 | −0.576019 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3630.00 | 0.291706 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9766.00 | −0.776106 | −0.388053 | − | 0.921637i | \(-0.626852\pi\) | ||||
−0.388053 | + | 0.921637i | \(0.626852\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4854.00 | −0.383619 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −920.000 | −0.0723091 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3768.00 | 0.294530 | 0.147265 | − | 0.989097i | \(-0.452953\pi\) | ||||
0.147265 | + | 0.989097i | \(0.452953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5454.00 | −0.423991 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 456.000 | 0.0352564 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1032.00 | 0.0789297 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1618.00 | 0.123082 | 0.0615412 | − | 0.998105i | \(-0.480398\pi\) | ||||
0.0615412 | + | 0.998105i | \(0.480398\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 440.000 | 0.0332916 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2808.00 | −0.211326 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5768.00 | 0.431780 | 0.215890 | − | 0.976418i | \(-0.430735\pi\) | ||||
0.215890 | + | 0.976418i | \(0.430735\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6872.00 | 0.511694 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8114.00 | −0.597815 | −0.298907 | − | 0.954282i | \(-0.596622\pi\) | ||||
−0.298907 | + | 0.954282i | \(0.596622\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7816.00 | 0.572836 | 0.286418 | − | 0.958105i | \(-0.407535\pi\) | ||||
0.286418 | + | 0.958105i | \(0.407535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12054.0 | 0.878819 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12426.0 | 0.901217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18278.0 | 1.31876 | 0.659379 | − | 0.751811i | \(-0.270819\pi\) | ||||
0.659379 | + | 0.751811i | \(0.270819\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10146.0 | 0.728244 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6708.00 | −0.476530 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 72.0000 | 0.00508860 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24960.0 | 1.75504 | 0.877521 | − | 0.479539i | \(-0.159196\pi\) | ||||
0.877521 | + | 0.479539i | \(0.159196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19456.0 | 1.36107 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12906.0 | −0.898277 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10892.0 | −0.754268 | −0.377134 | − | 0.926159i | \(-0.623090\pi\) | ||||
−0.377134 | + | 0.926159i | \(0.623090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7920.00 | 0.542955 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20022.0 | −1.36574 | −0.682869 | − | 0.730541i | \(-0.739268\pi\) | ||||
−0.682869 | + | 0.730541i | \(0.739268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10370.0 | −0.703829 | −0.351914 | − | 0.936032i | \(-0.614469\pi\) | ||||
−0.351914 | + | 0.936032i | \(0.614469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4680.00 | −0.316060 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2620.00 | 0.176063 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8992.00 | 0.601275 | 0.300638 | − | 0.953738i | \(-0.402801\pi\) | ||||
0.300638 | + | 0.953738i | \(0.402801\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 616.000 | 0.0407867 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12318.0 | 0.811614 | 0.405807 | − | 0.913959i | \(-0.366991\pi\) | ||||
0.405807 | + | 0.913959i | \(0.366991\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1920.00 | 0.125889 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26026.0 | −1.69816 | −0.849082 | − | 0.528261i | \(-0.822844\pi\) | ||||
−0.849082 | + | 0.528261i | \(0.822844\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18332.0 | 1.19035 | 0.595174 | − | 0.803597i | \(-0.297083\pi\) | ||||
0.595174 | + | 0.803597i | \(0.297083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3078.00 | −0.198898 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9881.00 | 0.632384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5928.00 | −0.377578 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3096.00 | −0.196257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10572.0 | 0.666980 | 0.333490 | − | 0.942754i | \(-0.391774\pi\) | ||||
0.333490 | + | 0.942754i | \(0.391774\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10188.0 | 0.639710 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9776.00 | 0.610943 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2574.00 | −0.159352 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24822.0 | 1.52950 | 0.764750 | − | 0.644327i | \(-0.222862\pi\) | ||||
0.764750 | + | 0.644327i | \(0.222862\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6620.00 | 0.406014 | 0.203007 | − | 0.979177i | \(-0.434929\pi\) | ||||
0.203007 | + | 0.979177i | \(0.434929\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2640.00 | 0.161163 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15956.0 | −0.969544 | −0.484772 | − | 0.874641i | \(-0.661097\pi\) | ||||
−0.484772 | + | 0.874641i | \(0.661097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6864.00 | 0.415155 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30802.0 | −1.84590 | −0.922952 | − | 0.384915i | \(-0.874231\pi\) | ||||
−0.922952 | + | 0.384915i | \(0.874231\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7984.00 | 0.476276 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4770.00 | 0.283250 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12714.0 | −0.751543 | −0.375772 | − | 0.926712i | \(-0.622622\pi\) | ||||
−0.375772 | + | 0.926712i | \(0.622622\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5822.00 | −0.342586 | −0.171293 | − | 0.985220i | \(-0.554795\pi\) | ||||
−0.171293 | + | 0.985220i | \(0.554795\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −216.000 | −0.0126527 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −684.000 | −0.0397070 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10440.0 | −0.603339 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15756.0 | 0.906488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28510.0 | 1.63296 | 0.816478 | − | 0.577376i | \(-0.195923\pi\) | ||||
0.816478 | + | 0.577376i | \(0.195923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2943.00 | −0.167816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21864.0 | 1.24121 | 0.620607 | − | 0.784122i | \(-0.286886\pi\) | ||||
0.620607 | + | 0.784122i | \(0.286886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4512.00 | 0.253892 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17862.0 | −1.00069 | −0.500344 | − | 0.865826i | \(-0.666793\pi\) | ||||
−0.500344 | + | 0.865826i | \(0.666793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6984.00 | 0.389555 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15366.0 | −0.853347 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −516.000 | −0.0285313 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6068.00 | 0.334063 | 0.167032 | − | 0.985952i | \(-0.446582\pi\) | ||||
0.167032 | + | 0.985952i | \(0.446582\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7216.00 | 0.393840 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5760.00 | −0.313021 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4890.00 | 0.264602 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7734.00 | 0.416703 | 0.208352 | − | 0.978054i | \(-0.433190\pi\) | ||||
0.208352 | + | 0.978054i | \(0.433190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6536.00 | −0.350654 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3696.00 | 0.197446 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19902.0 | 1.05421 | 0.527105 | − | 0.849800i | \(-0.323277\pi\) | ||||
0.527105 | + | 0.849800i | \(0.323277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −396.000 | −0.0208877 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29184.0 | −1.53289 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −208.000 | −0.0108794 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7566.00 | −0.394083 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12160.0 | −0.630725 | −0.315363 | − | 0.948971i | \(-0.602126\pi\) | ||||
−0.315363 | + | 0.948971i | \(0.602126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9066.00 | −0.466346 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −654.000 | −0.0335020 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3088.00 | −0.157534 | −0.0787672 | − | 0.996893i | \(-0.525098\pi\) | ||||
−0.0787672 | + | 0.996893i | \(0.525098\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7920.00 | −0.400727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10178.0 | −0.512869 | −0.256435 | − | 0.966562i | \(-0.582548\pi\) | ||||
−0.256435 | + | 0.966562i | \(0.582548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13520.0 | 0.675734 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5840.00 | −0.290701 | −0.145350 | − | 0.989380i | \(-0.546431\pi\) | ||||
−0.145350 | + | 0.989380i | \(0.546431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −456.000 | −0.0226067 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14414.0 | −0.711707 | −0.355854 | − | 0.934542i | \(-0.615810\pi\) | ||||
−0.355854 | + | 0.934542i | \(0.615810\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11256.0 | 0.553541 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9108.00 | −0.446110 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12608.0 | −0.612613 | −0.306307 | − | 0.951933i | \(-0.599093\pi\) | ||||
−0.306307 | + | 0.951933i | \(0.599093\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10440.0 | −0.505252 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3168.00 | 0.152709 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22606.0 | 1.08538 | 0.542688 | − | 0.839935i | \(-0.317407\pi\) | ||||
0.542688 | + | 0.839935i | \(0.317407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8892.00 | 0.425243 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5952.00 | −0.283521 | −0.141761 | − | 0.989901i | \(-0.545276\pi\) | ||||
−0.141761 | + | 0.989901i | \(0.545276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1296.00 | −0.0612510 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 528.000 | 0.0248566 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14138.0 | −0.662977 | −0.331489 | − | 0.943459i | \(-0.607551\pi\) | ||||
−0.331489 | + | 0.943459i | \(0.607551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10488.0 | −0.489904 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12616.0 | −0.587019 | −0.293510 | − | 0.955956i | \(-0.594823\pi\) | ||||
−0.293510 | + | 0.955956i | \(0.594823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27904.0 | −1.29334 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12160.0 | −0.559278 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7436.00 | 0.340693 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 162.000 | 0.00739388 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11112.0 | −0.505228 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12292.0 | 0.556750 | 0.278375 | − | 0.960472i | \(-0.410204\pi\) | ||||
0.278375 | + | 0.960472i | \(0.410204\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15174.0 | −0.684675 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1212.00 | 0.0542741 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3096.00 | −0.138118 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20784.0 | 0.923723 | 0.461861 | − | 0.886952i | \(-0.347182\pi\) | ||||
0.461861 | + | 0.886952i | \(0.347182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11088.0 | −0.490945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6912.00 | −0.304898 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13780.0 | −0.605586 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10788.0 | −0.470577 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13574.0 | −0.589909 | −0.294955 | − | 0.955511i | \(-0.595305\pi\) | ||||
−0.294955 | + | 0.955511i | \(0.595305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32308.0 | −1.39887 | −0.699437 | − | 0.714694i | \(-0.746566\pi\) | ||||
−0.699437 | + | 0.714694i | \(0.746566\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7272.00 | 0.313703 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11520.0 | −0.495126 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16720.0 | −0.715984 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2390.00 | −0.101598 | −0.0507988 | − | 0.998709i | \(-0.516177\pi\) | ||||
−0.0507988 | + | 0.998709i | \(0.516177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28020.0 | 1.18677 | 0.593387 | − | 0.804917i | \(-0.297790\pi\) | ||||
0.593387 | + | 0.804917i | \(0.297790\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8502.00 | 0.358790 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34006.0 | 1.42987 | 0.714936 | − | 0.699190i | \(-0.246456\pi\) | ||||
0.714936 | + | 0.699190i | \(0.246456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6310.00 | 0.264361 | 0.132181 | − | 0.991226i | \(-0.457802\pi\) | ||||
0.132181 | + | 0.991226i | \(0.457802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10902.0 | 0.455098 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4240.00 | −0.175726 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6912.00 | 0.285440 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16524.0 | 0.679943 | 0.339971 | − | 0.940436i | \(-0.389583\pi\) | ||||
0.339971 | + | 0.940436i | \(0.389583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24353.0 | −0.998524 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8910.00 | −0.364029 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8772.00 | 0.357119 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21084.0 | 0.852298 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9804.00 | 0.394920 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36662.0 | −1.47161 | −0.735805 | − | 0.677194i | \(-0.763196\pi\) | ||||
−0.735805 | + | 0.677194i | \(0.763196\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2736.00 | −0.109438 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42000.0 | 1.67409 | 0.837044 | − | 0.547136i | \(-0.184282\pi\) | ||||
0.837044 | + | 0.547136i | \(0.184282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28388.0 | −1.12757 | −0.563787 | − | 0.825920i | \(-0.690656\pi\) | ||||
−0.563787 | + | 0.825920i | \(0.690656\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23918.0 | 0.943428 | 0.471714 | − | 0.881752i | \(-0.343636\pi\) | ||||
0.471714 | + | 0.881752i | \(0.343636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5760.00 | −0.226411 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10851.0 | −0.425051 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1144.00 | 0.0446577 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1040.00 | 0.0404582 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1998.00 | −0.0774594 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2346.00 | −0.0903293 | −0.0451646 | − | 0.998980i | \(-0.514381\pi\) | ||||
−0.0451646 | + | 0.998980i | \(0.514381\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1584.00 | 0.0607816 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51876.0 | −1.98382 | −0.991911 | − | 0.126937i | \(-0.959485\pi\) | ||||
−0.991911 | + | 0.126937i | \(0.959485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11372.0 | −0.433407 | −0.216703 | − | 0.976237i | \(-0.569530\pi\) | ||||
−0.216703 | + | 0.976237i | \(0.569530\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3168.00 | 0.120329 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38764.0 | −1.46738 | −0.733691 | − | 0.679483i | \(-0.762204\pi\) | ||||
−0.733691 | + | 0.679483i | \(0.762204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2106.00 | −0.0791848 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23408.0 | −0.877177 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4840.00 | −0.180764 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 684.000 | 0.0254605 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1536.00 | 0.0569838 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9288.00 | 0.343427 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6472.00 | 0.237720 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11212.0 | −0.410461 | −0.205231 | − | 0.978714i | \(-0.565794\pi\) | ||||
−0.205231 | + | 0.978714i | \(0.565794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2880.00 | 0.105086 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1458.00 | 0.0530249 | 0.0265125 | − | 0.999648i | \(-0.491560\pi\) | ||||
0.0265125 | + | 0.999648i | \(0.491560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26312.0 | 0.953779 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7272.00 | 0.262738 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38608.0 | −1.38581 | −0.692906 | − | 0.721028i | \(-0.743670\pi\) | ||||
−0.692906 | + | 0.721028i | \(0.743670\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12900.0 | −0.461530 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 572.000 | 0.0203983 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9374.00 | 0.333206 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5328.00 | 0.188775 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7376.00 | −0.260494 | −0.130247 | − | 0.991482i | \(-0.541577\pi\) | ||||
−0.130247 | + | 0.991482i | \(0.541577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13740.0 | 0.482130 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3744.00 | 0.130954 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24878.0 | 0.867373 | 0.433687 | − | 0.901064i | \(-0.357212\pi\) | ||||
0.433687 | + | 0.901064i | \(0.357212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6798.00 | −0.236256 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26148.0 | 0.905845 | 0.452923 | − | 0.891550i | \(-0.350381\pi\) | ||||
0.452923 | + | 0.891550i | \(0.350381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18240.0 | 0.629879 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18350.0 | 0.629667 | 0.314834 | − | 0.949147i | \(-0.398051\pi\) | ||||
0.314834 | + | 0.949147i | \(0.398051\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1060.00 | −0.0362582 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23778.0 | −0.810783 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −57510.0 | −1.95481 | −0.977404 | − | 0.211381i | \(-0.932204\pi\) | ||||
−0.977404 | + | 0.211381i | \(0.932204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16072.0 | −0.544584 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −468.000 | −0.0158080 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35745.0 | 1.19986 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16038.0 | 0.536674 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13528.0 | −0.451276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33364.0 | −1.10953 | −0.554764 | − | 0.832008i | \(-0.687192\pi\) | ||||
−0.554764 | + | 0.832008i | \(0.687192\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8208.00 | 0.272114 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26892.0 | −0.888780 | −0.444390 | − | 0.895833i | \(-0.646580\pi\) | ||||
−0.444390 | + | 0.895833i | \(0.646580\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 654.000 | 0.0214818 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31970.0 | −1.04689 | −0.523445 | − | 0.852060i | \(-0.675353\pi\) | ||||
−0.523445 | + | 0.852060i | \(0.675353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19968.0 | 0.651869 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2070.00 | 0.0673700 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19728.0 | 0.640107 | 0.320054 | − | 0.947399i | \(-0.396299\pi\) | ||||
0.320054 | + | 0.947399i | \(0.396299\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17208.0 | 0.556642 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25080.0 | 0.806368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21400.0 | −0.685967 | −0.342984 | − | 0.939341i | \(-0.611438\pi\) | ||||
−0.342984 | + | 0.939341i | \(0.611438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12396.0 | −0.396148 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10560.0 | −0.336457 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4754.00 | 0.151014 | 0.0755069 | − | 0.997145i | \(-0.475943\pi\) | ||||
0.0755069 | + | 0.997145i | \(0.475943\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2322.00 | −0.0735384 |
(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 | 1176.4.a.j.1.1 | 1 | ||
4.3 | odd | 2 | 2352.4.a.h.1.1 | 1 | |||
7.6 | odd | 2 | 168.4.a.c.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 504.4.a.b.1.1 | 1 | |||
28.27 | even | 2 | 336.4.a.j.1.1 | 1 | |||
56.13 | odd | 2 | 1344.4.a.s.1.1 | 1 | |||
56.27 | even | 2 | 1344.4.a.e.1.1 | 1 | |||
84.83 | odd | 2 | 1008.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.c.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
336.4.a.j.1.1 | 1 | 28.27 | even | 2 | |||
504.4.a.b.1.1 | 1 | 21.20 | even | 2 | |||
1008.4.a.i.1.1 | 1 | 84.83 | odd | 2 | |||
1176.4.a.j.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1344.4.a.e.1.1 | 1 | 56.27 | even | 2 | |||
1344.4.a.s.1.1 | 1 | 56.13 | odd | 2 | |||
2352.4.a.h.1.1 | 1 | 4.3 | odd | 2 |