Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
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([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (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: | \(32\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.11 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.c.5615.12 |
$q$-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 | ||||||||
\(5\) | −0.436221 | −0.195084 | −0.0975421 | − | 0.995231i | \(-0.531098\pi\) | ||||
−0.0975421 | + | 0.995231i | \(0.531098\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.73863i | 0.825727i | 0.910793 | + | 0.412863i | \(0.135471\pi\) | ||||
−0.910793 | + | 0.412863i | \(0.864529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.64657i | 0.456676i | 0.973582 | + | 0.228338i | \(0.0733291\pi\) | ||||
−0.973582 | + | 0.228338i | \(0.926671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.22231i | 1.26660i | 0.773908 | + | 0.633298i | \(0.218299\pi\) | ||||
−0.773908 | + | 0.633298i | \(0.781701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.99963 | 1.37641 | 0.688204 | − | 0.725517i | \(-0.258399\pi\) | ||||
0.688204 | + | 0.725517i | \(0.258399\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.68296 | −1.60201 | −0.801004 | − | 0.598659i | \(-0.795700\pi\) | ||||
−0.801004 | + | 0.598659i | \(0.795700\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80971 | −0.961942 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.94791 | 0.918804 | 0.459402 | − | 0.888228i | \(-0.348064\pi\) | ||||
0.459402 | + | 0.888228i | \(0.348064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.77950i | 1.75645i | 0.478248 | + | 0.878225i | \(0.341272\pi\) | ||||
−0.478248 | + | 0.878225i | \(0.658728\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 0.436221i | − 0.0737349i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.81676i | − 0.627472i | −0.949510 | − | 0.313736i | \(-0.898419\pi\) | ||||
0.949510 | − | 0.313736i | \(-0.101581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 9.74668i | − 1.52218i | −0.648649 | − | 0.761088i | \(-0.724666\pi\) | ||||
0.648649 | − | 0.761088i | \(-0.275334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.84195 | 1.34838 | 0.674192 | − | 0.738556i | \(-0.264492\pi\) | ||||
0.674192 | + | 0.738556i | \(0.264492\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.54668 | 0.663202 | 0.331601 | − | 0.943420i | \(-0.392411\pi\) | ||||
0.331601 | + | 0.943420i | \(0.392411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.94845 | −1.36652 | −0.683262 | − | 0.730173i | \(-0.739439\pi\) | ||||
−0.683262 | + | 0.730173i | \(0.739439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.19465i | − 0.161086i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.2892i | 1.73011i | 0.501681 | + | 0.865053i | \(0.332715\pi\) | ||||
−0.501681 | + | 0.865053i | \(0.667285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 6.26145i | − 0.801696i | −0.916145 | − | 0.400848i | \(-0.868716\pi\) | ||||
0.916145 | − | 0.400848i | \(-0.131284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.718269i | − 0.0890903i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.42171 | −1.15104 | −0.575522 | − | 0.817786i | \(-0.695201\pi\) | ||||
−0.575522 | + | 0.817786i | \(0.695201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.76751 | −1.15919 | −0.579595 | − | 0.814905i | \(-0.696789\pi\) | ||||
−0.579595 | + | 0.814905i | \(0.696789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.14079 | −1.06985 | −0.534924 | − | 0.844900i | \(-0.679660\pi\) | ||||
−0.534924 | + | 0.844900i | \(0.679660\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.73863 | −0.312095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 5.19984i | − 0.585028i | −0.956261 | − | 0.292514i | \(-0.905508\pi\) | ||||
0.956261 | − | 0.292514i | \(-0.0944917\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.227071i | − 0.0249243i | −0.999922 | − | 0.0124622i | \(-0.996033\pi\) | ||||
0.999922 | − | 0.0124622i | \(-0.00396693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.27808i | − 0.247093i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 2.46567i | − 0.261360i | −0.991425 | − | 0.130680i | \(-0.958284\pi\) | ||||
0.991425 | − | 0.130680i | \(-0.0417161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.64657 | −0.172607 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.61717 | −0.268516 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.37287 | −0.342463 | −0.171232 | − | 0.985231i | \(-0.554775\pi\) | ||||
−0.171232 | + | 0.985231i | \(0.554775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.20021 | 0.119425 | 0.0597125 | − | 0.998216i | \(-0.480982\pi\) | ||||
0.0597125 | + | 0.998216i | \(0.480982\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10.7004i | − 1.05434i | −0.849761 | − | 0.527169i | \(-0.823254\pi\) | ||||
0.849761 | − | 0.527169i | \(-0.176746\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.49655i | 0.144676i | 0.997380 | + | 0.0723382i | \(0.0230461\pi\) | ||||
−0.997380 | + | 0.0723382i | \(0.976954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 18.4352i | − 1.76578i | −0.469583 | − | 0.882888i | \(-0.655596\pi\) | ||||
0.469583 | − | 0.882888i | \(-0.344404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.25692i | 0.494529i | 0.968948 | + | 0.247265i | \(0.0795317\pi\) | ||||
−0.968948 | + | 0.247265i | \(0.920468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.35147 | 0.312526 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.22231 | −0.478729 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.49993 | 0.318175 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.27921 | 0.382744 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7677i | 1.75410i | 0.480396 | + | 0.877051i | \(0.340493\pi\) | ||||
−0.480396 | + | 0.877051i | \(0.659507\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.25252i | 0.808397i | 0.914671 | + | 0.404198i | \(0.132449\pi\) | ||||
−0.914671 | + | 0.404198i | \(0.867551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.99963i | 0.520234i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.53255i | − 0.216370i | −0.994131 | − | 0.108185i | \(-0.965496\pi\) | ||||
0.994131 | − | 0.108185i | \(-0.0345039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.7831 | 1.67798 | 0.838991 | − | 0.544146i | \(-0.183146\pi\) | ||||
0.838991 | + | 0.544146i | \(0.183146\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.50934 | −0.377090 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.15839 | −0.179244 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.16461 | −0.668871 | −0.334435 | − | 0.942419i | \(-0.608546\pi\) | ||||
−0.334435 | + | 0.942419i | \(0.608546\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8741i | 1.21044i | 0.796058 | + | 0.605220i | \(0.206915\pi\) | ||||
−0.796058 | + | 0.605220i | \(0.793085\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.26603i | − 0.342656i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.92207i | − 0.392824i | −0.980521 | − | 0.196412i | \(-0.937071\pi\) | ||||
0.980521 | − | 0.196412i | \(-0.0629290\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 7.68296i | − 0.605502i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.87250 | 0.459970 | 0.229985 | − | 0.973194i | \(-0.426132\pi\) | ||||
0.229985 | + | 0.973194i | \(0.426132\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.1181 | −1.71155 | −0.855777 | − | 0.517345i | \(-0.826920\pi\) | ||||
−0.855777 | + | 0.517345i | \(0.826920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2888 | 0.791447 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.1920 | −1.83928 | −0.919642 | − | 0.392758i | \(-0.871521\pi\) | ||||
−0.919642 | + | 0.392758i | \(0.871521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.80971i | − 0.363580i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 5.41287i | − 0.404577i | −0.979326 | − | 0.202288i | \(-0.935162\pi\) | ||||
0.979326 | − | 0.202288i | \(-0.0648378\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.19672i | 0.460598i | 0.973120 | + | 0.230299i | \(0.0739705\pi\) | ||||
−0.973120 | + | 0.230299i | \(0.926030\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.66495i | 0.122410i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.3020 | −1.04586 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6191 | −0.985444 | −0.492722 | − | 0.870187i | \(-0.663998\pi\) | ||||
−0.492722 | + | 0.870187i | \(0.663998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.89278 | 0.424172 | 0.212086 | − | 0.977251i | \(-0.431974\pi\) | ||||
0.212086 | + | 0.977251i | \(0.431974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.0323 | −1.35600 | −0.677998 | − | 0.735064i | \(-0.737152\pi\) | ||||
−0.677998 | + | 0.735064i | \(0.737152\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 5.91398i | − 0.419231i | −0.977784 | − | 0.209616i | \(-0.932779\pi\) | ||||
0.977784 | − | 0.209616i | \(-0.0672212\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.94791i | 0.347275i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.25171i | 0.296952i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.4307i | 1.13654i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9334 | −0.890369 | −0.445185 | − | 0.895439i | \(-0.646862\pi\) | ||||
−0.445185 | + | 0.895439i | \(0.646862\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.85705 | −0.263049 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.77950 | −0.663876 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.59890 | −0.578424 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 0.758557i | − 0.0507967i | −0.999677 | − | 0.0253984i | \(-0.991915\pi\) | ||||
0.999677 | − | 0.0253984i | \(-0.00808542\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.60986i | 0.239595i | 0.992798 | + | 0.119797i | \(0.0382245\pi\) | ||||
−0.992798 | + | 0.119797i | \(0.961776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.47625i | 0.229717i | 0.993382 | + | 0.114859i | \(0.0366415\pi\) | ||||
−0.993382 | + | 0.114859i | \(0.963358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.9786i | 1.50538i | 0.658376 | + | 0.752689i | \(0.271244\pi\) | ||||
−0.658376 | + | 0.752689i | \(0.728756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.98336 | −0.129380 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.4478 | −0.675813 | −0.337906 | − | 0.941180i | \(-0.609719\pi\) | ||||
−0.337906 | + | 0.941180i | \(0.609719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0939 | −0.650208 | −0.325104 | − | 0.945678i | \(-0.605399\pi\) | ||||
−0.325104 | + | 0.945678i | \(0.605399\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.436221 | 0.0278692 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.87880i | 0.628573i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 18.0568i | − 1.13974i | −0.821736 | − | 0.569868i | \(-0.806994\pi\) | ||||
0.821736 | − | 0.569868i | \(-0.193006\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 21.0408i | − 1.32282i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.77643i | 0.235567i | 0.993039 | + | 0.117784i | \(0.0375789\pi\) | ||||
−0.993039 | + | 0.117784i | \(0.962421\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.81676 | 0.237162 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.1460 | 1.18060 | 0.590298 | − | 0.807185i | \(-0.299010\pi\) | ||||
0.590298 | + | 0.807185i | \(0.299010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.33973 | 0.266587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9031 | −0.725747 | −0.362873 | − | 0.931838i | \(-0.618204\pi\) | ||||
−0.362873 | + | 0.931838i | \(0.618204\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4765i | 1.60833i | 0.594403 | + | 0.804167i | \(0.297388\pi\) | ||||
−0.594403 | + | 0.804167i | \(0.702612\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 13.1720i | − 0.794302i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.49587i | 0.570552i | 0.958445 | + | 0.285276i | \(0.0920852\pi\) | ||||
−0.958445 | + | 0.285276i | \(0.907915\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7754i | 1.00073i | 0.865813 | + | 0.500367i | \(0.166802\pi\) | ||||
−0.865813 | + | 0.500367i | \(0.833198\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6841 | −0.813437 | −0.406719 | − | 0.913554i | \(-0.633327\pi\) | ||||
−0.406719 | + | 0.913554i | \(0.633327\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.74668 | 0.575328 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.2725 | −0.604268 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.46088 | −0.552710 | −0.276355 | − | 0.961056i | \(-0.589127\pi\) | ||||
−0.276355 | + | 0.961056i | \(0.589127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 5.79703i | − 0.337516i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 12.6505i | − 0.731599i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.84195i | 0.509641i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.73138i | 0.156398i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4055 | 0.708019 | 0.354009 | − | 0.935242i | \(-0.384818\pi\) | ||||
0.354009 | + | 0.935242i | \(0.384818\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.70862 | 0.0968870 | 0.0484435 | − | 0.998826i | \(-0.484574\pi\) | ||||
0.0484435 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9889 | 0.677652 | 0.338826 | − | 0.940849i | \(-0.389970\pi\) | ||||
0.338826 | + | 0.940849i | \(0.389970\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.6470 | 1.38431 | 0.692155 | − | 0.721748i | \(-0.256661\pi\) | ||||
0.692155 | + | 0.721748i | \(0.256661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5505i | 0.758681i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.3319i | 1.74336i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 7.91952i | − 0.439296i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.54668i | 0.250667i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.66221 | 0.311223 | 0.155612 | − | 0.987818i | \(-0.450265\pi\) | ||||
0.155612 | + | 0.987818i | \(0.450265\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.10995 | 0.224551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.2480 | −1.75666 | −0.878331 | − | 0.478053i | \(-0.841343\pi\) | ||||
−0.878331 | + | 0.478053i | \(0.841343\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.7824 | −1.45035 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.3357i | 1.09168i | 0.837889 | + | 0.545840i | \(0.183789\pi\) | ||||
−0.837889 | + | 0.545840i | \(0.816211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.27539i | 0.442971i | 0.975164 | + | 0.221486i | \(0.0710906\pi\) | ||||
−0.975164 | + | 0.221486i | \(0.928909\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 8.23298i | − 0.438197i | −0.975703 | − | 0.219099i | \(-0.929688\pi\) | ||||
0.975703 | − | 0.219099i | \(-0.0703117\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.26080 | 0.226140 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.5802 | −0.558403 | −0.279202 | − | 0.960232i | \(-0.590070\pi\) | ||||
−0.279202 | + | 0.960232i | \(0.590070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.9955 | 0.894502 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.98741 | 0.208710 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 23.7595i | − 1.24023i | −0.784509 | − | 0.620117i | \(-0.787085\pi\) | ||||
0.784509 | − | 0.620117i | \(-0.212915\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 9.94845i | − 0.516498i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.1442i | − 0.628802i | −0.949290 | − | 0.314401i | \(-0.898196\pi\) | ||||
0.949290 | − | 0.314401i | \(-0.101804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.14708i | 0.419596i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.1386 | 1.65085 | 0.825426 | − | 0.564511i | \(-0.190935\pi\) | ||||
0.825426 | + | 0.564511i | \(0.190935\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.0530 | −1.53564 | −0.767819 | − | 0.640667i | \(-0.778658\pi\) | ||||
−0.767819 | + | 0.640667i | \(0.778658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.19465 | 0.0608849 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.8723 | 0.652652 | 0.326326 | − | 0.945257i | \(-0.394189\pi\) | ||||
0.326326 | + | 0.945257i | \(0.394189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 40.1228i | − 2.02910i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.26828i | 0.114130i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8323i | 1.04554i | 0.852473 | + | 0.522771i | \(0.175102\pi\) | ||||
−0.852473 | + | 0.522771i | \(0.824898\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 15.8270i | − 0.790361i | −0.918604 | − | 0.395180i | \(-0.870682\pi\) | ||||
0.918604 | − | 0.395180i | \(-0.129318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.1026 | −0.802129 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.4527 | 0.518120 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.95136 | −0.195382 | −0.0976910 | − | 0.995217i | \(-0.531146\pi\) | ||||
−0.0976910 | + | 0.995217i | \(0.531146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.2892 | −0.653919 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0990534i | 0.00486234i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 3.56977i | − 0.174395i | −0.996191 | − | 0.0871974i | \(-0.972209\pi\) | ||||
0.996191 | − | 0.0871974i | \(-0.0277911\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 16.3767i | − 0.798152i | −0.916918 | − | 0.399076i | \(-0.869331\pi\) | ||||
0.916918 | − | 0.399076i | \(-0.130669\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 25.1178i | − 1.21839i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.26145 | 0.303013 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.7503 | −1.38485 | −0.692426 | − | 0.721489i | \(-0.743458\pi\) | ||||
−0.692426 | + | 0.721489i | \(0.743458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6276 | −1.13547 | −0.567735 | − | 0.823212i | \(-0.692180\pi\) | ||||
−0.567735 | + | 0.823212i | \(0.692180\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −46.0949 | −2.20502 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 15.4891i | − 0.739255i | −0.929180 | − | 0.369628i | \(-0.879485\pi\) | ||||
0.929180 | − | 0.369628i | \(-0.120515\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 21.7640i | − 1.03404i | −0.855974 | − | 0.517019i | \(-0.827042\pi\) | ||||
0.855974 | − | 0.517019i | \(-0.172958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.07558i | 0.0509872i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.9358i | 1.36557i | 0.730621 | + | 0.682783i | \(0.239231\pi\) | ||||
−0.730621 | + | 0.682783i | \(0.760769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.6925 | 1.25690 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.718269 | 0.0336730 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.2466 | 1.22776 | 0.613882 | − | 0.789397i | \(-0.289607\pi\) | ||||
0.613882 | + | 0.789397i | \(0.289607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.47471 | −0.348132 | −0.174066 | − | 0.984734i | \(-0.555691\pi\) | ||||
−0.174066 | + | 0.984734i | \(0.555691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.09410i | − 0.376165i | −0.982153 | − | 0.188082i | \(-0.939773\pi\) | ||||
0.982153 | − | 0.188082i | \(-0.0602272\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 16.0617i | − 0.743246i | −0.928384 | − | 0.371623i | \(-0.878801\pi\) | ||||
0.928384 | − | 0.371623i | \(-0.121199\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 9.42171i | − 0.435054i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.2148i | 1.11340i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28.8565 | −1.32403 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.6989 | 1.44836 | 0.724181 | − | 0.689610i | \(-0.242218\pi\) | ||||
0.724181 | + | 0.689610i | \(0.242218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.28456 | 0.286551 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.47132 | 0.0668092 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.5363i | 1.38373i | 0.722025 | + | 0.691867i | \(0.243211\pi\) | ||||
−0.722025 | + | 0.691867i | \(0.756789\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.2201i | 1.86024i | 0.367259 | + | 0.930119i | \(0.380296\pi\) | ||||
−0.367259 | + | 0.930119i | \(0.619704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.8395i | 1.16375i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 9.76751i | − 0.438133i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.03676 | −0.180710 | −0.0903552 | − | 0.995910i | \(-0.528800\pi\) | ||||
−0.0903552 | + | 0.995910i | \(0.528800\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.2393 | −1.79418 | −0.897092 | − | 0.441845i | \(-0.854324\pi\) | ||||
−0.897092 | + | 0.441845i | \(0.854324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.523556 | −0.0232979 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.68050 | −0.429081 | −0.214540 | − | 0.976715i | \(-0.568825\pi\) | ||||
−0.214540 | + | 0.976715i | \(0.568825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 9.14079i | − 0.404365i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.66773i | 0.205685i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4517i | 0.547624i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.92629i | 0.172014i | 0.996295 | + | 0.0860069i | \(0.0274107\pi\) | ||||
−0.996295 | + | 0.0860069i | \(0.972589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.8709 | −0.912623 | −0.456311 | − | 0.889820i | \(-0.650830\pi\) | ||||
−0.456311 | + | 0.889820i | \(0.650830\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −51.0716 | −2.22471 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.0279 | 1.56643 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.0486 | 0.695141 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 0.652825i | − 0.0282241i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2.73863i | − 0.117961i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.18975i | 0.137138i | 0.997646 | + | 0.0685691i | \(0.0218434\pi\) | ||||
−0.997646 | + | 0.0685691i | \(0.978157\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.04185i | 0.344475i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9137 | −1.19350 | −0.596751 | − | 0.802426i | \(-0.703542\pi\) | ||||
−0.596751 | + | 0.802426i | \(0.703542\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.6856 | 1.26465 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.19984 | 0.221120 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.0025 | −0.593304 | −0.296652 | − | 0.954986i | \(-0.595870\pi\) | ||||
−0.296652 | + | 0.954986i | \(0.595870\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.5589i | 0.615775i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 13.8839i | − 0.585137i | −0.956245 | − | 0.292569i | \(-0.905490\pi\) | ||||
0.956245 | − | 0.292569i | \(-0.0945100\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 2.29318i | − 0.0964749i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.7512i | 0.618401i | 0.950997 | + | 0.309200i | \(0.100061\pi\) | ||||
−0.950997 | + | 0.309200i | \(0.899939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.28135 | −0.179169 | −0.0895845 | − | 0.995979i | \(-0.528554\pi\) | ||||
−0.0895845 | + | 0.995979i | \(0.528554\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.9528 | 1.54104 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1951 | 0.466059 | 0.233030 | − | 0.972470i | \(-0.425136\pi\) | ||||
0.233030 | + | 0.972470i | \(0.425136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.227071 | 0.00942051 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 27.2451i | − 1.12838i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.45377i | − 0.0600035i | −0.999550 | − | 0.0300018i | \(-0.990449\pi\) | ||||
0.999550 | − | 0.0300018i | \(-0.00955129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 58.6733i | 2.41759i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 13.1827i | − 0.541347i | −0.962671 | − | 0.270674i | \(-0.912754\pi\) | ||||
0.962671 | − | 0.270674i | \(-0.0872464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.27808 | 0.0933924 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.4852 | 0.591848 | 0.295924 | − | 0.955211i | \(-0.404372\pi\) | ||||
0.295924 | + | 0.955211i | \(0.404372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.7364 | −1.13139 | −0.565695 | − | 0.824614i | \(-0.691392\pi\) | ||||
−0.565695 | + | 0.824614i | \(0.691392\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.52674 | −0.0620709 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5137i | 0.751447i | 0.926732 | + | 0.375723i | \(0.122606\pi\) | ||||
−0.926732 | + | 0.375723i | \(0.877394\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.48643i | 0.302868i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 25.3069i | − 1.02213i | −0.859541 | − | 0.511067i | \(-0.829250\pi\) | ||||
0.859541 | − | 0.511067i | \(-0.170750\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.8249i | 1.92536i | 0.270647 | + | 0.962679i | \(0.412762\pi\) | ||||
−0.270647 | + | 0.962679i | \(0.587238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.22411 | −0.129588 | −0.0647939 | − | 0.997899i | \(-0.520639\pi\) | ||||
−0.0647939 | + | 0.997899i | \(0.520639\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.46567 | 0.0987848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.1819 | 0.887275 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.9323 | 0.794754 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 22.6025i | − 0.899791i | −0.893081 | − | 0.449896i | \(-0.851461\pi\) | ||||
0.893081 | − | 0.449896i | \(-0.148539\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 8.62311i | − 0.342198i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.64657i | − 0.0652394i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 15.4383i | − 0.609775i | −0.952388 | − | 0.304888i | \(-0.901381\pi\) | ||||
0.952388 | − | 0.304888i | \(-0.0986189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.41036 | −0.0556191 | −0.0278095 | − | 0.999613i | \(-0.508853\pi\) | ||||
−0.0278095 | + | 0.999613i | \(0.508853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.811574 | 0.0319063 | 0.0159531 | − | 0.999873i | \(-0.494922\pi\) | ||||
0.0159531 | + | 0.999873i | \(0.494922\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −36.3941 | −1.42860 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.82168 | 0.384352 | 0.192176 | − | 0.981360i | \(-0.438446\pi\) | ||||
0.192176 | + | 0.981360i | \(0.438446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 4.03615i | − 0.157705i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.1456i | 0.434170i | 0.976153 | + | 0.217085i | \(0.0696548\pi\) | ||||
−0.976153 | + | 0.217085i | \(0.930345\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 15.3989i | − 0.598947i | −0.954105 | − | 0.299474i | \(-0.903189\pi\) | ||||
0.954105 | − | 0.299474i | \(-0.0968111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 2.61717i | − 0.101489i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.0146 | −1.47193 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.1478 | 0.661982 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.4112 | 0.786795 | 0.393398 | − | 0.919368i | \(-0.371300\pi\) | ||||
0.393398 | + | 0.919368i | \(0.371300\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 50.5124 | 1.94135 | 0.970674 | − | 0.240401i | \(-0.0772789\pi\) | ||||
0.970674 | + | 0.240401i | \(0.0772789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 3.37287i | − 0.129439i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.3625i | 1.27658i | 0.769796 | + | 0.638291i | \(0.220358\pi\) | ||||
−0.769796 | + | 0.638291i | \(0.779642\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.10475i | 0.0422104i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 16.3808i | − 0.624059i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.3714 | −0.927133 | −0.463567 | − | 0.886062i | \(-0.653431\pi\) | ||||
−0.463567 | + | 0.886062i | \(0.653431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.62982 | −0.327348 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.9002 | 1.92798 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.1271 | 1.28896 | 0.644481 | − | 0.764620i | \(-0.277073\pi\) | ||||
0.644481 | + | 0.764620i | \(0.277073\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 22.8991i | − 0.863658i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.20021i | 0.0451384i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.8145i | 0.856818i | 0.903585 | + | 0.428409i | \(0.140926\pi\) | ||||
−0.903585 | + | 0.428409i | \(0.859074\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 75.1355i | − 2.81385i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.96707 | 0.0735642 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.18175 | −0.0813654 | −0.0406827 | − | 0.999172i | \(-0.512953\pi\) | ||||
−0.0406827 | + | 0.999172i | \(0.512953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7004 | 0.398502 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.7980 | −0.883837 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 15.3017i | − 0.567507i | −0.958897 | − | 0.283754i | \(-0.908420\pi\) | ||||
0.958897 | − | 0.283754i | \(-0.0915798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.1754i | 1.70786i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 15.8711i | − 0.586213i | −0.956080 | − | 0.293106i | \(-0.905311\pi\) | ||||
0.956080 | − | 0.293106i | \(-0.0946890\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 25.8025i | − 0.950449i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.1319 | −1.14521 | −0.572603 | − | 0.819833i | \(-0.694066\pi\) | ||||
−0.572603 | + | 0.819833i | \(0.694066\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.6629 | −0.537930 | −0.268965 | − | 0.963150i | \(-0.586682\pi\) | ||||
−0.268965 | + | 0.963150i | \(0.586682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.56158 | 0.130486 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.49655 | −0.0546826 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.46100i | 0.308746i | 0.988013 | + | 0.154373i | \(0.0493358\pi\) | ||||
−0.988013 | + | 0.154373i | \(0.950664\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 6.48842i | − 0.236138i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39.6473i | 1.44101i | 0.693451 | + | 0.720504i | \(0.256089\pi\) | ||||
−0.693451 | + | 0.720504i | \(0.743911\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 49.7301i | − 1.80271i | −0.433076 | − | 0.901357i | \(-0.642572\pi\) | ||||
0.433076 | − | 0.901357i | \(-0.357428\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.4352 | 0.667401 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.8816 | −0.790098 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.62877 | 0.202979 | 0.101489 | − | 0.994837i | \(-0.467639\pi\) | ||||
0.101489 | + | 0.994837i | \(0.467639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.3999 | 0.913570 | 0.456785 | − | 0.889577i | \(-0.349001\pi\) | ||||
0.456785 | + | 0.889577i | \(0.349001\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 47.0366i | − 1.68960i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 58.4764i | − 2.09514i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 26.7495i | − 0.957174i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.14711i | 0.0766338i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.5311 | 1.12396 | 0.561982 | − | 0.827150i | \(-0.310039\pi\) | ||||
0.561982 | + | 0.827150i | \(0.310039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.25692 | −0.186915 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.3099 | 0.366115 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.3724 | −1.32380 | −0.661899 | − | 0.749593i | \(-0.730249\pi\) | ||||
−0.661899 | + | 0.749593i | \(0.730249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7442i | 0.840010i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 25.0332i | − 0.883402i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.35147i | 0.118124i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.37230i | 0.153722i | 0.997042 | + | 0.0768610i | \(0.0244898\pi\) | ||||
−0.997042 | + | 0.0768610i | \(0.975510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.1067 | 1.02208 | 0.511038 | − | 0.859558i | \(-0.329261\pi\) | ||||
0.511038 | + | 0.859558i | \(0.329261\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.56171 | −0.0897328 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.0484 | 1.85593 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.1785 | 1.57674 | 0.788370 | − | 0.615201i | \(-0.210925\pi\) | ||||
0.788370 | + | 0.615201i | \(0.210925\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 30.6242i | − 1.06749i | −0.845644 | − | 0.533747i | \(-0.820783\pi\) | ||||
0.845644 | − | 0.533747i | \(-0.179217\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 12.0993i | − 0.420734i | −0.977623 | − | 0.210367i | \(-0.932534\pi\) | ||||
0.977623 | − | 0.210367i | \(-0.0674658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.2105i | 0.528283i | 0.964484 | + | 0.264142i | \(0.0850886\pi\) | ||||
−0.964484 | + | 0.264142i | \(0.914911\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 5.22231i | − 0.180942i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.64841 | 0.333897 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.2155 | 1.45744 | 0.728721 | − | 0.684811i | \(-0.240115\pi\) | ||||
0.728721 | + | 0.684811i | \(0.240115\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.51816 | −0.155799 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.48820 | −0.154399 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.49993i | 0.120259i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.3240i | 1.00521i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.2536i | 1.68641i | 0.537592 | + | 0.843205i | \(0.319334\pi\) | ||||
−0.537592 | + | 0.843205i | \(0.680666\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.9243i | 0.885557i | 0.896631 | + | 0.442779i | \(0.146007\pi\) | ||||
−0.896631 | + | 0.442779i | \(0.853993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.25940 | −0.315927 | −0.157963 | − | 0.987445i | \(-0.550493\pi\) | ||||
−0.157963 | + | 0.987445i | \(0.550493\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.21443 | 0.211542 | 0.105771 | − | 0.994391i | \(-0.466269\pi\) | ||||
0.105771 | + | 0.994391i | \(0.466269\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5531 | 0.358815 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.2404 | 0.483073 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 15.5135i | − 0.525655i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.27921i | 0.144664i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 15.1038i | − 0.510020i | −0.966938 | − | 0.255010i | \(-0.917921\pi\) | ||||
0.966938 | − | 0.255010i | \(-0.0820787\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 2.59677i | − 0.0874874i | −0.999043 | − | 0.0437437i | \(-0.986072\pi\) | ||||
0.999043 | − | 0.0437437i | \(-0.0139285\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.0661 | −0.372404 | −0.186202 | − | 0.982511i | \(-0.559618\pi\) | ||||
−0.186202 | + | 0.982511i | \(0.559618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.38595 | 0.247996 | 0.123998 | − | 0.992282i | \(-0.460428\pi\) | ||||
0.123998 | + | 0.992282i | \(0.460428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.7677 | −0.662989 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.2784 | 0.912837 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.36121i | 0.0789265i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.3881i | 1.61383i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 51.9539i | − 1.73084i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 2.70314i | − 0.0898555i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.58114 | −0.185319 | −0.0926594 | − | 0.995698i | \(-0.529537\pi\) | ||||
−0.0926594 | + | 0.995698i | \(0.529537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.02450 | 0.232732 | 0.116366 | − | 0.993206i | \(-0.462875\pi\) | ||||
0.116366 | + | 0.993206i | \(0.462875\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.621864 | 0.0205807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.25252 | −0.305545 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.7961i | 0.850935i | 0.904974 | + | 0.425468i | \(0.139890\pi\) | ||||
−0.904974 | + | 0.425468i | \(0.860110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 16.0829i | − 0.529374i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.3575i | 0.603591i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.1558i | 0.333201i | 0.986024 | + | 0.166600i | \(0.0532790\pi\) | ||||
−0.986024 | + | 0.166600i | \(0.946721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.99963 | −0.196630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.23882 | 0.204031 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.1504 | 0.625616 | 0.312808 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312808 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.3260 | 0.467016 | 0.233508 | − | 0.972355i | \(-0.424980\pi\) | ||||
0.233508 | + | 0.972355i | \(0.424980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.8833i | 2.43854i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7.67662i | − 0.249456i | −0.992191 | − | 0.124728i | \(-0.960194\pi\) | ||||
0.992191 | − | 0.124728i | \(-0.0398059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 15.0509i | − 0.488574i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 52.6546i | − 1.70565i | −0.522197 | − | 0.852825i | \(-0.674887\pi\) | ||||
0.522197 | − | 0.852825i | \(-0.325113\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.94095 | 0.192245 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.53255 | 0.0817803 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −64.6386 | −2.08512 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.57056 | −0.0827492 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 50.1578i | − 1.61297i | −0.591257 | − | 0.806483i | \(-0.701368\pi\) | ||||
0.591257 | − | 0.806483i | \(-0.298632\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.8144i | 1.75908i | 0.475828 | + | 0.879538i | \(0.342148\pi\) | ||||
−0.475828 | + | 0.879538i | \(0.657852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.7831i | 0.634217i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.0603583i | 0.00193103i | 1.00000 | 0.000965516i | \(0.000307333\pi\) | |||||
−1.00000 | 0.000965516i | \(0.999693\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.75254 | 0.215812 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.40354 | 0.236136 | 0.118068 | − | 0.993005i | \(-0.462330\pi\) | ||||
0.118068 | + | 0.993005i | \(0.462330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.30230 | 0.264533 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −67.9323 | −2.16012 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.6861i | 1.13361i | 0.823853 | + | 0.566803i | \(0.191820\pi\) | ||||
−0.823853 | + | 0.566803i | \(0.808180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.57981i | 0.0817853i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.4345i | 1.66062i | 0.557304 | + | 0.830308i | \(0.311836\pi\) | ||||
−0.557304 | + | 0.830308i | \(0.688164\pi\) | |||||||
\(998\) | 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.j.c.5615.11 | 32 | ||
3.2 | odd | 2 | inner | 6048.2.j.c.5615.22 | 32 | ||
4.3 | odd | 2 | 1512.2.j.c.323.14 | yes | 32 | ||
8.3 | odd | 2 | inner | 6048.2.j.c.5615.21 | 32 | ||
8.5 | even | 2 | 1512.2.j.c.323.20 | yes | 32 | ||
12.11 | even | 2 | 1512.2.j.c.323.19 | yes | 32 | ||
24.5 | odd | 2 | 1512.2.j.c.323.13 | ✓ | 32 | ||
24.11 | even | 2 | inner | 6048.2.j.c.5615.12 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.13 | ✓ | 32 | 24.5 | odd | 2 | ||
1512.2.j.c.323.14 | yes | 32 | 4.3 | odd | 2 | ||
1512.2.j.c.323.19 | yes | 32 | 12.11 | even | 2 | ||
1512.2.j.c.323.20 | yes | 32 | 8.5 | even | 2 | ||
6048.2.j.c.5615.11 | 32 | 1.1 | even | 1 | trivial | ||
6048.2.j.c.5615.12 | 32 | 24.11 | even | 2 | inner | ||
6048.2.j.c.5615.21 | 32 | 8.3 | odd | 2 | inner | ||
6048.2.j.c.5615.22 | 32 | 3.2 | odd | 2 | inner |