Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.4 | ||
Root | \(-1.19566 - 0.755240i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.e.3025.17 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.16969i | − 1.41753i | −0.705446 | − | 0.708764i | \(-0.749253\pi\) | ||||
0.705446 | − | 0.708764i | \(-0.250747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.44696i | 1.64232i | 0.570699 | + | 0.821160i | \(0.306673\pi\) | ||||
−0.570699 | + | 0.821160i | \(0.693327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.61205i | 1.00180i | 0.865504 | + | 0.500902i | \(0.166998\pi\) | ||||
−0.865504 | + | 0.500902i | \(0.833002\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.27628 | −0.794616 | −0.397308 | − | 0.917685i | \(-0.630055\pi\) | ||||
−0.397308 | + | 0.917685i | \(0.630055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.20627i | − 0.735569i | −0.929911 | − | 0.367785i | \(-0.880116\pi\) | ||||
0.929911 | − | 0.367785i | \(-0.119884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.673274 | 0.140387 | 0.0701936 | − | 0.997533i | \(-0.477638\pi\) | ||||
0.0701936 | + | 0.997533i | \(0.477638\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.04692 | −1.00938 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.85127i | 0.529468i | 0.964322 | + | 0.264734i | \(0.0852841\pi\) | ||||
−0.964322 | + | 0.264734i | \(0.914716\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.71845 | −0.667854 | −0.333927 | − | 0.942599i | \(-0.608374\pi\) | ||||
−0.333927 | + | 0.942599i | \(0.608374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.16969i | − 0.535775i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 11.9988i | − 1.97260i | −0.164971 | − | 0.986298i | \(-0.552753\pi\) | ||||
0.164971 | − | 0.986298i | \(-0.447247\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.44602 | 1.16287 | 0.581436 | − | 0.813592i | \(-0.302491\pi\) | ||||
0.581436 | + | 0.813592i | \(0.302491\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 12.5741i | − 1.91753i | −0.284195 | − | 0.958766i | \(-0.591726\pi\) | ||||
0.284195 | − | 0.958766i | \(-0.408274\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.06341 | −0.592710 | −0.296355 | − | 0.955078i | \(-0.595771\pi\) | ||||
−0.296355 | + | 0.955078i | \(0.595771\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.291601i | 0.0400545i | 0.999799 | + | 0.0200272i | \(0.00637529\pi\) | ||||
−0.999799 | + | 0.0200272i | \(0.993625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.2652 | 2.32803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 0.0209587i | − 0.00272859i | −0.999999 | − | 0.00136430i | \(-0.999566\pi\) | ||||
0.999999 | − | 0.00136430i | \(-0.000434269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.34034i | − 0.683760i | −0.939744 | − | 0.341880i | \(-0.888936\pi\) | ||||
0.939744 | − | 0.341880i | \(-0.111064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.4491 | 1.42008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.20714i | 0.758323i | 0.925331 | + | 0.379161i | \(0.123787\pi\) | ||||
−0.925331 | + | 0.379161i | \(0.876213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5050 | 1.84010 | 0.920050 | − | 0.391801i | \(-0.128148\pi\) | ||||
0.920050 | + | 0.391801i | \(0.128148\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.35371 | 0.158440 | 0.0792198 | − | 0.996857i | \(-0.474757\pi\) | ||||
0.0792198 | + | 0.996857i | \(0.474757\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.44696i | 0.620738i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0846 | 1.24711 | 0.623555 | − | 0.781779i | \(-0.285688\pi\) | ||||
0.623555 | + | 0.781779i | \(0.285688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.6442i | 1.49765i | 0.662768 | + | 0.748824i | \(0.269381\pi\) | ||||
−0.662768 | + | 0.748824i | \(0.730619\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.3848i | 1.12639i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.93965 | 0.629601 | 0.314801 | − | 0.949158i | \(-0.398062\pi\) | ||||
0.314801 | + | 0.949158i | \(0.398062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.61205i | 0.378646i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.1629 | −1.04269 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.60073 | 0.974807 | 0.487403 | − | 0.873177i | \(-0.337944\pi\) | ||||
0.487403 | + | 0.873177i | \(0.337944\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 14.2123i | − 1.41418i | −0.707124 | − | 0.707090i | \(-0.750008\pi\) | ||||
0.707124 | − | 0.707090i | \(-0.249992\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.69321 | −0.166837 | −0.0834187 | − | 0.996515i | \(-0.526584\pi\) | ||||
−0.0834187 | + | 0.996515i | \(0.526584\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.6644i | 1.12764i | 0.825897 | + | 0.563821i | \(0.190669\pi\) | ||||
−0.825897 | + | 0.563821i | \(0.809331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 14.0521i | − 1.34595i | −0.739667 | − | 0.672973i | \(-0.765017\pi\) | ||||
0.739667 | − | 0.672973i | \(-0.234983\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9455 | 1.40596 | 0.702979 | − | 0.711211i | \(-0.251853\pi\) | ||||
0.702979 | + | 0.711211i | \(0.251853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.13407i | − 0.199003i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.27628 | −0.300336 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.6693 | −1.69721 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.148729i | 0.0133028i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.07216 | −0.361346 | −0.180673 | − | 0.983543i | \(-0.557828\pi\) | ||||
−0.180673 | + | 0.983543i | \(0.557828\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 17.8643i | − 1.56081i | −0.625275 | − | 0.780404i | \(-0.715013\pi\) | ||||
0.625275 | − | 0.780404i | \(-0.284987\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.20627i | − 0.278019i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.1351 | 1.80569 | 0.902847 | − | 0.429963i | \(-0.141473\pi\) | ||||
0.902847 | + | 0.429963i | \(0.141473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 7.39359i | − 0.627116i | −0.949569 | − | 0.313558i | \(-0.898479\pi\) | ||||
0.949569 | − | 0.313558i | \(-0.101521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.6747 | −1.64528 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.03764 | 0.750535 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.0541i | 1.06944i | 0.845030 | + | 0.534719i | \(0.179582\pi\) | ||||
−0.845030 | + | 0.534719i | \(0.820418\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6477 | 1.43615 | 0.718073 | − | 0.695968i | \(-0.245024\pi\) | ||||
0.718073 | + | 0.695968i | \(0.245024\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.7863i | 0.946701i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00087i | 0.239495i | 0.992804 | + | 0.119748i | \(0.0382085\pi\) | ||||
−0.992804 | + | 0.119748i | \(0.961791\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.673274 | 0.0530614 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 0.871148i | − 0.0682335i | −0.999418 | − | 0.0341168i | \(-0.989138\pi\) | ||||
0.999418 | − | 0.0341168i | \(-0.0108618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.49952 | 0.580330 | 0.290165 | − | 0.956977i | \(-0.406290\pi\) | ||||
0.290165 | + | 0.956977i | \(0.406290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0469224 | −0.00360941 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.652919i | − 0.0496405i | −0.999692 | − | 0.0248203i | \(-0.992099\pi\) | ||||
0.999692 | − | 0.0248203i | \(-0.00790135\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.04692 | −0.381511 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.43263i | 0.331310i | 0.986184 | + | 0.165655i | \(0.0529738\pi\) | ||||
−0.986184 | + | 0.165655i | \(0.947026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 21.9779i | − 1.63360i | −0.576920 | − | 0.816801i | \(-0.695746\pi\) | ||||
0.576920 | − | 0.816801i | \(-0.304254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −38.0326 | −2.79621 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 17.8458i | − 1.30501i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.67327 | −0.482861 | −0.241430 | − | 0.970418i | \(-0.577617\pi\) | ||||
−0.241430 | + | 0.970418i | \(0.577617\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.0305 | 1.80174 | 0.900868 | − | 0.434092i | \(-0.142931\pi\) | ||||
0.900868 | + | 0.434092i | \(0.142931\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.77971i | − 0.269293i | −0.990894 | − | 0.134646i | \(-0.957010\pi\) | ||||
0.990894 | − | 0.134646i | \(-0.0429899\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.18059 | 0.509019 | 0.254509 | − | 0.967070i | \(-0.418086\pi\) | ||||
0.254509 | + | 0.967070i | \(0.418086\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.85127i | 0.200120i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 23.6016i | − 1.64840i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.4644 | 1.20804 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.30442i | 0.365171i | 0.983190 | + | 0.182586i | \(0.0584467\pi\) | ||||
−0.983190 | + | 0.182586i | \(0.941553\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.8560 | −2.71816 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.71845 | −0.252425 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 11.8341i | − 0.796048i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.62678 | −0.309832 | −0.154916 | − | 0.987928i | \(-0.549511\pi\) | ||||
−0.154916 | + | 0.987928i | \(0.549511\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 9.92356i | − 0.658650i | −0.944217 | − | 0.329325i | \(-0.893179\pi\) | ||||
0.944217 | − | 0.329325i | \(-0.106821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.32546i | 0.153671i | 0.997044 | + | 0.0768355i | \(0.0244816\pi\) | ||||
−0.997044 | + | 0.0768355i | \(0.975518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.23031 | 0.211625 | 0.105812 | − | 0.994386i | \(-0.466256\pi\) | ||||
0.105812 | + | 0.994386i | \(0.466256\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8797i | 0.840182i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.48961 | −0.225724 | −0.112862 | − | 0.993611i | \(-0.536002\pi\) | ||||
−0.112862 | + | 0.993611i | \(0.536002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.77778 | 0.629842 | 0.314921 | − | 0.949118i | \(-0.398022\pi\) | ||||
0.314921 | + | 0.949118i | \(0.398022\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.16969i | − 0.202504i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5812 | 0.736896 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 25.2169i | − 1.59168i | −0.605509 | − | 0.795838i | \(-0.707031\pi\) | ||||
0.605509 | − | 0.795838i | \(-0.292969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.66729i | 0.230561i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.12920 | −0.382329 | −0.191165 | − | 0.981558i | \(-0.561226\pi\) | ||||
−0.191165 | + | 0.981558i | \(0.561226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 11.9988i | − 0.745572i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.27084 | −0.0783635 | −0.0391818 | − | 0.999232i | \(-0.512475\pi\) | ||||
−0.0391818 | + | 0.999232i | \(0.512475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.924284 | 0.0567783 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 19.8081i | − 1.20772i | −0.797091 | − | 0.603859i | \(-0.793629\pi\) | ||||
0.797091 | − | 0.603859i | \(-0.206371\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1532 | −1.46720 | −0.733600 | − | 0.679581i | \(-0.762162\pi\) | ||||
−0.733600 | + | 0.679581i | \(0.762162\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 27.4904i | − 1.65773i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.31816i | 0.0792005i | 0.999216 | + | 0.0396003i | \(0.0126084\pi\) | ||||
−0.999216 | + | 0.0396003i | \(0.987392\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.7284 | −1.47517 | −0.737587 | − | 0.675252i | \(-0.764035\pi\) | ||||
−0.737587 | + | 0.675252i | \(0.764035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 18.6573i | − 1.10906i | −0.832163 | − | 0.554532i | \(-0.812897\pi\) | ||||
0.832163 | − | 0.554532i | \(-0.187103\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.44602 | 0.439525 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.26596 | −0.368586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4030i | 0.841431i | 0.907193 | + | 0.420715i | \(0.138221\pi\) | ||||
−0.907193 | + | 0.420715i | \(0.861779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0664326 | −0.00386786 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.43190i | 0.140640i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 12.5741i | − 0.724759i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.9272 | −0.969249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 27.3734i | − 1.56228i | −0.624353 | − | 0.781142i | \(-0.714637\pi\) | ||||
0.624353 | − | 0.781142i | \(-0.285363\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.9767 | −1.58641 | −0.793206 | − | 0.608953i | \(-0.791590\pi\) | ||||
−0.793206 | + | 0.608953i | \(0.791590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.5228 | 1.55568 | 0.777841 | − | 0.628461i | \(-0.216315\pi\) | ||||
0.777841 | + | 0.628461i | \(0.216315\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.73928i | − 0.0976879i | −0.998806 | − | 0.0488440i | \(-0.984446\pi\) | ||||
0.998806 | − | 0.0488440i | \(-0.0155537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.5307 | −0.869555 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.5047i | 0.584495i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 18.2297i | − 1.01120i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.06341 | −0.224023 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 13.7965i | − 0.758323i | −0.925331 | − | 0.379161i | \(-0.876212\pi\) | ||||
0.925331 | − | 0.379161i | \(-0.123788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.6747 | 1.07494 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.96903 | −0.107260 | −0.0536300 | − | 0.998561i | \(-0.517079\pi\) | ||||
−0.0536300 | + | 0.998561i | \(0.517079\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 20.2542i | − 1.09683i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.4183i | 1.14979i | 0.818226 | + | 0.574897i | \(0.194958\pi\) | ||||
−0.818226 | + | 0.574897i | \(0.805042\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.2315i | 1.29708i | 0.761180 | + | 0.648541i | \(0.224620\pi\) | ||||
−0.761180 | + | 0.648541i | \(0.775380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.1659 | −1.07332 | −0.536662 | − | 0.843797i | \(-0.680315\pi\) | ||||
−0.536662 | + | 0.843797i | \(0.680315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 49.1459i | − 2.60839i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.8643 | −1.04840 | −0.524198 | − | 0.851597i | \(-0.675635\pi\) | ||||
−0.524198 | + | 0.851597i | \(0.675635\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.71982 | 0.458938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.29083i | − 0.224592i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −37.1713 | −1.94033 | −0.970163 | − | 0.242454i | \(-0.922048\pi\) | ||||
−0.970163 | + | 0.242454i | \(0.922048\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.291601i | 0.0151392i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.6106i | 1.22251i | 0.791433 | + | 0.611256i | \(0.209335\pi\) | ||||
−0.791433 | + | 0.611256i | \(0.790665\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.2989 | −0.530422 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.2051i | 0.781034i | 0.920596 | + | 0.390517i | \(0.127704\pi\) | ||||
−0.920596 | + | 0.390517i | \(0.872296\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.26331 | −0.0645522 | −0.0322761 | − | 0.999479i | \(-0.510276\pi\) | ||||
−0.0322761 | + | 0.999479i | \(0.510276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.2652 | 0.879914 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 12.3813i | − 0.627754i | −0.949464 | − | 0.313877i | \(-0.898372\pi\) | ||||
0.949464 | − | 0.313877i | \(-0.101628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.20584 | −0.111554 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 35.1346i | − 1.76781i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.0272i | 0.954948i | 0.878646 | + | 0.477474i | \(0.158447\pi\) | ||||
−0.878646 | + | 0.477474i | \(0.841553\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.06885 | −0.303064 | −0.151532 | − | 0.988452i | \(-0.548421\pi\) | ||||
−0.151532 | + | 0.988452i | \(0.548421\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 13.4312i | − 0.669058i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 65.3572 | 3.23963 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.9491 | 1.43144 | 0.715720 | − | 0.698387i | \(-0.246099\pi\) | ||||
0.715720 | + | 0.698387i | \(0.246099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 0.0209587i | − 0.00103131i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 43.2480 | 2.12296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.30387i | 0.210258i | 0.994459 | + | 0.105129i | \(0.0335255\pi\) | ||||
−0.994459 | + | 0.105129i | \(0.966474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 18.0243i | − 0.878453i | −0.898376 | − | 0.439226i | \(-0.855253\pi\) | ||||
0.898376 | − | 0.439226i | \(-0.144747\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.5351 | 0.802073 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.34034i | − 0.258437i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.0189 | −0.530760 | −0.265380 | − | 0.964144i | \(-0.585497\pi\) | ||||
−0.265380 | + | 0.964144i | \(0.585497\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.0881 | 0.532861 | 0.266430 | − | 0.963854i | \(-0.414156\pi\) | ||||
0.266430 | + | 0.963854i | \(0.414156\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.15870i | − 0.103265i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.6928 | 1.56034 | 0.780171 | − | 0.625567i | \(-0.215132\pi\) | ||||
0.780171 | + | 0.625567i | \(0.215132\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.6225i | 1.12234i | 0.827700 | + | 0.561171i | \(0.189649\pi\) | ||||
−0.827700 | + | 0.561171i | \(0.810351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 18.8268i | − 0.892477i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.75599 | −0.413220 | −0.206610 | − | 0.978423i | \(-0.566243\pi\) | ||||
−0.206610 | + | 0.978423i | \(0.566243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.5581i | 1.90981i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.4491 | 0.536741 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8326 | 0.740618 | 0.370309 | − | 0.928909i | \(-0.379252\pi\) | ||||
0.370309 | + | 0.928909i | \(0.379252\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.1188i | 1.68222i | 0.540865 | + | 0.841109i | \(0.318097\pi\) | ||||
−0.540865 | + | 0.841109i | \(0.681903\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.28903 | −0.385224 | −0.192612 | − | 0.981275i | \(-0.561696\pi\) | ||||
−0.192612 | + | 0.981275i | \(0.561696\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.7640i | 1.05339i | 0.850053 | + | 0.526697i | \(0.176570\pi\) | ||||
−0.850053 | + | 0.526697i | \(0.823430\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.20714i | 0.286619i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 68.4906 | 3.14920 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.1818i | 0.742472i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.1931 | 1.74509 | 0.872543 | − | 0.488537i | \(-0.162469\pi\) | ||||
0.872543 | + | 0.488537i | \(0.162469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.3404 | 1.97615 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 30.4313i | − 1.38182i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.84028 | −0.400591 | −0.200296 | − | 0.979735i | \(-0.564190\pi\) | ||||
−0.200296 | + | 0.979735i | \(0.564190\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.9660i | 1.30722i | 0.756833 | + | 0.653608i | \(0.226746\pi\) | ||||
−0.756833 | + | 0.653608i | \(0.773254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9.34157i | − 0.420723i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5050 | 0.695492 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.417929i | 0.0187091i | 0.999956 | + | 0.00935453i | \(0.00297768\pi\) | ||||
−0.999956 | + | 0.00935453i | \(0.997022\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.3133 | 0.459848 | 0.229924 | − | 0.973209i | \(-0.426152\pi\) | ||||
0.229924 | + | 0.973209i | \(0.426152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −45.0487 | −2.00464 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.2340i | 0.985505i | 0.870169 | + | 0.492753i | \(0.164009\pi\) | ||||
−0.870169 | + | 0.492753i | \(0.835991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35371 | 0.0598845 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.36696i | 0.236497i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 22.1332i | − 0.973418i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3079 | −1.28400 | −0.642001 | − | 0.766704i | \(-0.721896\pi\) | ||||
−0.642001 | + | 0.766704i | \(0.721896\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.15302i | − 0.0504181i | −0.999682 | − | 0.0252090i | \(-0.991975\pi\) | ||||
0.999682 | − | 0.0252090i | \(-0.00802514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.1827 | 0.530687 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5467 | −0.980291 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.8954i | 1.16497i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.9726 | 1.59846 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.44696i | 0.234617i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 34.3825i | − 1.47822i | −0.673586 | − | 0.739109i | \(-0.735247\pi\) | ||||
0.673586 | − | 0.739109i | \(-0.264753\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.5407 | −1.90792 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1388i | 0.732802i | 0.930457 | + | 0.366401i | \(0.119410\pi\) | ||||
−0.930457 | + | 0.366401i | \(0.880590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.14195 | 0.389460 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0846 | 0.471363 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.0976i | 1.23290i | 0.787393 | + | 0.616452i | \(0.211430\pi\) | ||||
−0.787393 | + | 0.616452i | \(0.788570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.4183 | 1.92099 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 31.6652i | − 1.33453i | −0.744821 | − | 0.667264i | \(-0.767465\pi\) | ||||
0.744821 | − | 0.667264i | \(-0.232535\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 47.3727i | − 1.99298i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.16080 | 0.258274 | 0.129137 | − | 0.991627i | \(-0.458779\pi\) | ||||
0.129137 | + | 0.991627i | \(0.458779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 41.0313i | − 1.71711i | −0.512724 | − | 0.858553i | \(-0.671364\pi\) | ||||
0.512724 | − | 0.858553i | \(-0.328636\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.39796 | −0.141705 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.4290 | −1.05862 | −0.529311 | − | 0.848428i | \(-0.677550\pi\) | ||||
−0.529311 | + | 0.848428i | \(0.677550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6442i | 0.566058i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.58834 | −0.0657822 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.55639i | 0.146788i | 0.997303 | + | 0.0733939i | \(0.0233830\pi\) | ||||
−0.997303 | + | 0.0733939i | \(0.976617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.9224i | 0.491253i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.57142 | 0.105596 | 0.0527978 | − | 0.998605i | \(-0.483186\pi\) | ||||
0.0527978 | + | 0.998605i | \(0.483186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3848i | 0.425735i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.8400 | 0.892357 | 0.446178 | − | 0.894944i | \(-0.352785\pi\) | ||||
0.446178 | + | 0.894944i | \(0.352785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.8140 | −1.78721 | −0.893606 | − | 0.448853i | \(-0.851833\pi\) | ||||
−0.893606 | + | 0.448853i | \(0.851833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 59.1760i | 2.40585i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.9012 | −0.726588 | −0.363294 | − | 0.931675i | \(-0.618348\pi\) | ||||
−0.363294 | + | 0.931675i | \(0.618348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 14.6773i | − 0.593778i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.8902i | 0.641798i | 0.947113 | + | 0.320899i | \(0.103985\pi\) | ||||
−0.947113 | + | 0.320899i | \(0.896015\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.8402 | 0.838994 | 0.419497 | − | 0.907757i | \(-0.362206\pi\) | ||||
0.419497 | + | 0.907757i | \(0.362206\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.4914i | 1.26575i | 0.774255 | + | 0.632873i | \(0.218125\pi\) | ||||
−0.774255 | + | 0.632873i | \(0.781875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.93965 | 0.237967 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.7632 | −0.990527 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.3116i | 1.56746i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.6786 | 0.425109 | 0.212555 | − | 0.977149i | \(-0.431822\pi\) | ||||
0.212555 | + | 0.977149i | \(0.431822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9075i | 0.512218i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.61205i | 0.143115i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.7669 | 0.978232 | 0.489116 | − | 0.872219i | \(-0.337319\pi\) | ||||
0.489116 | + | 0.872219i | \(0.337319\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 11.5834i | − 0.456805i | −0.973567 | − | 0.228402i | \(-0.926650\pi\) | ||||
0.973567 | − | 0.228402i | \(-0.0733502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.1155 | 1.18396 | 0.591981 | − | 0.805952i | \(-0.298346\pi\) | ||||
0.591981 | + | 0.805952i | \(0.298346\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.114161 | 0.00448122 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 45.7814i | − 1.79157i | −0.444491 | − | 0.895783i | \(-0.646616\pi\) | ||||
0.444491 | − | 0.895783i | \(-0.353384\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −56.6242 | −2.21249 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 34.3446i | − 1.33788i | −0.743318 | − | 0.668938i | \(-0.766749\pi\) | ||||
0.743318 | − | 0.668938i | \(-0.233251\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.5119i | 1.03120i | 0.856831 | + | 0.515598i | \(0.172430\pi\) | ||||
−0.856831 | + | 0.515598i | \(0.827570\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.1629 | −0.394100 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.91969i | 0.0743305i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.0886 | 1.12295 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.2427 | −1.01158 | −0.505790 | − | 0.862657i | \(-0.668799\pi\) | ||||
−0.505790 | + | 0.862657i | \(0.668799\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.23458i | − 0.124315i | −0.998066 | − | 0.0621576i | \(-0.980202\pi\) | ||||
0.998066 | − | 0.0621576i | \(-0.0197981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.60073 | 0.368442 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 0.708911i | − 0.0271257i | −0.999908 | − | 0.0135629i | \(-0.995683\pi\) | ||||
0.999908 | − | 0.0135629i | \(-0.00431733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 66.9917i | − 2.55962i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.05328 | −0.0401267 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0071i | 1.48390i | 0.670454 | + | 0.741951i | \(0.266099\pi\) | ||||
−0.670454 | + | 0.741951i | \(0.733901\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.4354 | −0.888955 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.3953 | −0.924037 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 16.2448i | − 0.613559i | −0.951781 | − | 0.306779i | \(-0.900749\pi\) | ||||
0.951781 | − | 0.306779i | \(-0.0992514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.4715 | −1.45098 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 14.2123i | − 0.534510i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1720i | 0.945354i | 0.881236 | + | 0.472677i | \(0.156712\pi\) | ||||
−0.881236 | + | 0.472677i | \(0.843288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.50354 | −0.0937581 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 62.3626i | 2.33223i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.92289 | 0.295474 | 0.147737 | − | 0.989027i | \(-0.452801\pi\) | ||||
0.147737 | + | 0.989027i | \(0.452801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.69321 | −0.0630586 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 14.3901i | − 0.534436i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.10313 | 0.226353 | 0.113176 | − | 0.993575i | \(-0.463898\pi\) | ||||
0.113176 | + | 0.993575i | \(0.463898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 41.1963i | 1.52370i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 26.6568i | − 0.984591i | −0.870428 | − | 0.492296i | \(-0.836158\pi\) | ||||
0.870428 | − | 0.492296i | \(-0.163842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −33.8100 | −1.24541 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 9.27736i | − 0.341273i | −0.985334 | − | 0.170637i | \(-0.945418\pi\) | ||||
0.985334 | − | 0.170637i | \(-0.0545824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.6494 | −0.464062 | −0.232031 | − | 0.972708i | \(-0.574537\pi\) | ||||
−0.232031 | + | 0.972708i | \(0.574537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41.3776 | 1.51596 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6644i | 0.426209i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.10625 | 0.259311 | 0.129655 | − | 0.991559i | \(-0.458613\pi\) | ||||
0.129655 | + | 0.991559i | \(0.458613\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 55.9376i | − 2.03578i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.6019i | 1.25763i | 0.777556 | + | 0.628814i | \(0.216459\pi\) | ||||
−0.777556 | + | 0.628814i | \(0.783541\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.7114 | −0.787039 | −0.393520 | − | 0.919316i | \(-0.628743\pi\) | ||||
−0.393520 | + | 0.919316i | \(0.628743\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 14.0521i | − 0.508720i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.0757040 | 0.00273351 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.94161 | −0.214260 | −0.107130 | − | 0.994245i | \(-0.534166\pi\) | ||||
−0.107130 | + | 0.994245i | \(0.534166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.14102i | 0.0410398i | 0.999789 | + | 0.0205199i | \(0.00653215\pi\) | ||||
−0.999789 | + | 0.0205199i | \(0.993468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.7667 | 0.674121 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 23.8740i | − 0.855374i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 84.4548i | 3.02203i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.51181 | 0.339491 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 42.2224i | − 1.50507i | −0.658555 | − | 0.752533i | \(-0.728832\pi\) | ||||
0.658555 | − | 0.752533i | \(-0.271168\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.9455 | 0.531402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.2896 | 0.684993 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 37.0441i | − 1.31217i | −0.754687 | − | 0.656085i | \(-0.772211\pi\) | ||||
0.754687 | − | 0.656085i | \(-0.227789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.3129 | 0.470976 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.37359i | 0.260208i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.13407i | − 0.0752160i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.7803 | 0.660279 | 0.330140 | − | 0.943932i | \(-0.392904\pi\) | ||||
0.330140 | + | 0.943932i | \(0.392904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 54.4054i | − 1.91043i | −0.295909 | − | 0.955216i | \(-0.595623\pi\) | ||||
0.295909 | − | 0.955216i | \(-0.404377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.76127 | −0.0967229 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.3160 | −1.41048 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7178i | 0.932458i | 0.884664 | + | 0.466229i | \(0.154388\pi\) | ||||
−0.884664 | + | 0.466229i | \(0.845612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5033 | 0.540412 | 0.270206 | − | 0.962802i | \(-0.412908\pi\) | ||||
0.270206 | + | 0.962802i | \(0.412908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 16.0053i | − 0.556559i | −0.960500 | − | 0.278279i | \(-0.910236\pi\) | ||||
0.960500 | − | 0.278279i | \(-0.0897641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.1590i | 1.60317i | 0.597881 | + | 0.801585i | \(0.296009\pi\) | ||||
−0.597881 | + | 0.801585i | \(0.703991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.27628 | −0.113517 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 23.7711i | − 0.822634i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.38306 | 0.151320 | 0.0756601 | − | 0.997134i | \(-0.475894\pi\) | ||||
0.0756601 | + | 0.997134i | \(0.475894\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.8703 | 0.719664 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.148729i | 0.00511644i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.6693 | −0.641486 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 8.07850i | − 0.276927i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 15.5653i | − 0.532946i | −0.963842 | − | 0.266473i | \(-0.914142\pi\) | ||||
0.963842 | − | 0.266473i | \(-0.0858583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.2023 | 1.03169 | 0.515846 | − | 0.856681i | \(-0.327478\pi\) | ||||
0.515846 | + | 0.856681i | \(0.327478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 6.32139i | − 0.215683i | −0.994168 | − | 0.107841i | \(-0.965606\pi\) | ||||
0.994168 | − | 0.107841i | \(-0.0343939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.8902 | −1.22172 | −0.610858 | − | 0.791740i | \(-0.709175\pi\) | ||||
−0.610858 | + | 0.791740i | \(0.709175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.06955 | −0.0703668 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.3771i | 2.04815i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.4205 | −0.759690 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.148729i | 0.00502797i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.3677i | 1.09298i | 0.837466 | + | 0.546490i | \(0.184036\pi\) | ||||
−0.837466 | + | 0.546490i | \(0.815964\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.1052 | −1.11534 | −0.557670 | − | 0.830062i | \(-0.688305\pi\) | ||||
−0.557670 | + | 0.830062i | \(0.688305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7891i | 0.665957i | 0.942934 | + | 0.332979i | \(0.108054\pi\) | ||||
−0.942934 | + | 0.332979i | \(0.891946\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.843244 | −0.0283133 | −0.0141567 | − | 0.999900i | \(-0.504506\pi\) | ||||
−0.0141567 | + | 0.999900i | \(0.504506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.07216 | −0.136576 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.0284i | 0.435979i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.0500 | 0.469641 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 10.6023i | − 0.353607i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 0.955367i | − 0.0318279i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −69.6629 | −2.31567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.01198i | 0.299238i | 0.988744 | + | 0.149619i | \(0.0478047\pi\) | ||||
−0.988744 | + | 0.149619i | \(0.952195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.53535 | −0.0508685 | −0.0254343 | − | 0.999676i | \(-0.508097\pi\) | ||||
−0.0254343 | + | 0.999676i | \(0.508097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −74.3195 | −2.45962 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 17.8643i | − 0.589930i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.4581 | 0.740826 | 0.370413 | − | 0.928867i | \(-0.379216\pi\) | ||||
0.370413 | + | 0.928867i | \(0.379216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 56.0047i | 1.84342i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 60.5572i | 1.99111i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.2178 | 1.64759 | 0.823797 | − | 0.566885i | \(-0.191852\pi\) | ||||
0.823797 | + | 0.566885i | \(0.191852\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3.20627i | − 0.105081i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −56.5655 | −1.84989 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.9114 | 0.389130 | 0.194565 | − | 0.980890i | \(-0.437670\pi\) | ||||
0.194565 | + | 0.980890i | \(0.437670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 59.5916i | − 1.94263i | −0.237795 | − | 0.971315i | \(-0.576425\pi\) | ||||
0.237795 | − | 0.971315i | \(-0.423575\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.01321 | 0.163252 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.69613i | − 0.152604i | −0.997085 | − | 0.0763018i | \(-0.975689\pi\) | ||||
0.997085 | − | 0.0763018i | \(-0.0243113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.88966i | 0.158725i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.9727 | −1.26245 | −0.631224 | − | 0.775600i | \(-0.717447\pi\) | ||||
−0.631224 | + | 0.775600i | \(0.717447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.1522i | 0.684469i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.1351 | 0.682488 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.1731 | −0.553971 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 79.3390i | − 2.55401i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.5025 | −1.30247 | −0.651236 | − | 0.758875i | \(-0.725749\pi\) | ||||
−0.651236 | + | 0.758875i | \(0.725749\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 5.76542i | − 0.185021i | −0.995712 | − | 0.0925105i | \(-0.970511\pi\) | ||||
0.995712 | − | 0.0925105i | \(-0.0294892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 7.39359i | − 0.237028i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.3362 | 0.330684 | 0.165342 | − | 0.986236i | \(-0.447127\pi\) | ||||
0.165342 | + | 0.986236i | \(0.447127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.3530i | 1.03401i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.9663 | 0.732512 | 0.366256 | − | 0.930514i | \(-0.380639\pi\) | ||||
0.366256 | + | 0.930514i | \(0.380639\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9805 | −0.381730 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 8.46581i | − 0.269197i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.74450 | 0.182480 | 0.0912400 | − | 0.995829i | \(-0.470917\pi\) | ||||
0.0912400 | + | 0.995829i | \(0.470917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 22.7602i | − 0.721548i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.7098i | 1.89103i | 0.325580 | + | 0.945515i | \(0.394441\pi\) | ||||
−0.325580 | + | 0.945515i | \(0.605559\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.c.e.3025.4 | 20 | ||
3.2 | odd | 2 | inner | 6048.2.c.e.3025.18 | 20 | ||
4.3 | odd | 2 | 1512.2.c.e.757.17 | yes | 20 | ||
8.3 | odd | 2 | 1512.2.c.e.757.18 | yes | 20 | ||
8.5 | even | 2 | inner | 6048.2.c.e.3025.17 | 20 | ||
12.11 | even | 2 | 1512.2.c.e.757.4 | yes | 20 | ||
24.5 | odd | 2 | inner | 6048.2.c.e.3025.3 | 20 | ||
24.11 | even | 2 | 1512.2.c.e.757.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.e.757.3 | ✓ | 20 | 24.11 | even | 2 | ||
1512.2.c.e.757.4 | yes | 20 | 12.11 | even | 2 | ||
1512.2.c.e.757.17 | yes | 20 | 4.3 | odd | 2 | ||
1512.2.c.e.757.18 | yes | 20 | 8.3 | odd | 2 | ||
6048.2.c.e.3025.3 | 20 | 24.5 | odd | 2 | inner | ||
6048.2.c.e.3025.4 | 20 | 1.1 | even | 1 | trivial | ||
6048.2.c.e.3025.17 | 20 | 8.5 | even | 2 | inner | ||
6048.2.c.e.3025.18 | 20 | 3.2 | odd | 2 | inner |