Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
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, 0, 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("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.6 | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.i.2591.5 |
$q$-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 | ||||||||
\(5\) | 2.64388i | 1.18238i | 0.806532 | + | 0.591190i | \(0.201342\pi\) | ||||
−0.806532 | + | 0.591190i | \(0.798658\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.12083 | 1.24248 | 0.621238 | − | 0.783622i | \(-0.286630\pi\) | ||||
0.621238 | + | 0.783622i | \(0.286630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.86886 | −1.35038 | −0.675190 | − | 0.737644i | \(-0.735938\pi\) | ||||
−0.675190 | + | 0.737644i | \(0.735938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.03749i | − 0.494165i | −0.968994 | − | 0.247083i | \(-0.920528\pi\) | ||||
0.968994 | − | 0.247083i | \(-0.0794719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.16827i | − 0.956268i | −0.878287 | − | 0.478134i | \(-0.841313\pi\) | ||||
0.878287 | − | 0.478134i | \(-0.158687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.48754 | 1.97829 | 0.989145 | − | 0.146945i | \(-0.0469440\pi\) | ||||
0.989145 | + | 0.146945i | \(0.0469440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.99011 | −0.398022 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.54751i | 0.287365i | 0.989624 | + | 0.143682i | \(0.0458943\pi\) | ||||
−0.989624 | + | 0.143682i | \(0.954106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 0.248395i | − 0.0446131i | −0.999751 | − | 0.0223066i | \(-0.992899\pi\) | ||||
0.999751 | − | 0.0223066i | \(-0.00710099\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.64388 | −0.446898 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.88909 | 1.29696 | 0.648479 | − | 0.761232i | \(-0.275405\pi\) | ||||
0.648479 | + | 0.761232i | \(0.275405\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00821i | 0.313629i | 0.987628 | + | 0.156815i | \(0.0501225\pi\) | ||||
−0.987628 | + | 0.156815i | \(0.949877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.547808i | 0.0835399i | 0.999127 | + | 0.0417700i | \(0.0132997\pi\) | ||||
−0.999127 | + | 0.0417700i | \(0.986700\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.59422 | 0.378406 | 0.189203 | − | 0.981938i | \(-0.439410\pi\) | ||||
0.189203 | + | 0.981938i | \(0.439410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.5632i | − 1.58832i | −0.607707 | − | 0.794161i | \(-0.707910\pi\) | ||||
0.607707 | − | 0.794161i | \(-0.292090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.8950i | 1.46908i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.4330 | −1.61864 | −0.809322 | − | 0.587365i | \(-0.800165\pi\) | ||||
−0.809322 | + | 0.587365i | \(0.800165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.2962 | 1.83044 | 0.915218 | − | 0.402959i | \(-0.132018\pi\) | ||||
0.915218 | + | 0.402959i | \(0.132018\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 12.8727i | − 1.59666i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.52832i | − 0.797561i | −0.917046 | − | 0.398781i | \(-0.869433\pi\) | ||||
0.917046 | − | 0.398781i | \(-0.130567\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.95273 | 0.706459 | 0.353229 | − | 0.935537i | \(-0.385084\pi\) | ||||
0.353229 | + | 0.935537i | \(0.385084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.7079 | 1.37031 | 0.685156 | − | 0.728396i | \(-0.259734\pi\) | ||||
0.685156 | + | 0.728396i | \(0.259734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.12083i | 0.469612i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.47832i | 0.841376i | 0.907205 | + | 0.420688i | \(0.138211\pi\) | ||||
−0.907205 | + | 0.420688i | \(0.861789\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.94011 | 0.432483 | 0.216241 | − | 0.976340i | \(-0.430620\pi\) | ||||
0.216241 | + | 0.976340i | \(0.430620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.38690 | 0.584291 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 12.9230i | − 1.36984i | −0.728619 | − | 0.684920i | \(-0.759837\pi\) | ||||
0.728619 | − | 0.684920i | \(-0.240163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 4.86886i | − 0.510395i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.0204 | 1.13067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.64630 | −0.573295 | −0.286648 | − | 0.958036i | \(-0.592541\pi\) | ||||
−0.286648 | + | 0.958036i | \(0.592541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4.71066i | − 0.468729i | −0.972149 | − | 0.234364i | \(-0.924699\pi\) | ||||
0.972149 | − | 0.234364i | \(-0.0753008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.6158i | 1.93280i | 0.257038 | + | 0.966401i | \(0.417253\pi\) | ||||
−0.257038 | + | 0.966401i | \(0.582747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.10360 | −0.396710 | −0.198355 | − | 0.980130i | \(-0.563560\pi\) | ||||
−0.198355 | + | 0.980130i | \(0.563560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.48792 | 0.812995 | 0.406497 | − | 0.913652i | \(-0.366750\pi\) | ||||
0.406497 | + | 0.913652i | \(0.366750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.60719i | 0.527480i | 0.964594 | + | 0.263740i | \(0.0849561\pi\) | ||||
−0.964594 | + | 0.263740i | \(0.915044\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.0839i | 2.33909i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.03749 | 0.186777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.98124 | 0.543749 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.95779i | 0.711766i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 16.0322i | − 1.42263i | −0.702875 | − | 0.711313i | \(-0.748101\pi\) | ||||
0.702875 | − | 0.711313i | \(-0.251899\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.05016 | 0.179123 | 0.0895615 | − | 0.995981i | \(-0.471453\pi\) | ||||
0.0895615 | + | 0.995981i | \(0.471453\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.16827 | 0.361435 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.4115i | 0.889517i | 0.895650 | + | 0.444759i | \(0.146711\pi\) | ||||
−0.895650 | + | 0.444759i | \(0.853289\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0177i | 1.10415i | 0.833795 | + | 0.552074i | \(0.186163\pi\) | ||||
−0.833795 | + | 0.552074i | \(0.813837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.0637 | −1.67781 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.09142 | −0.339774 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 22.5842i | − 1.85017i | −0.379758 | − | 0.925086i | \(-0.623993\pi\) | ||||
0.379758 | − | 0.925086i | \(-0.376007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.7533i | 1.93302i | 0.256638 | + | 0.966508i | \(0.417385\pi\) | ||||
−0.256638 | + | 0.966508i | \(0.582615\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.656728 | 0.0527497 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.78100 | 0.142139 | 0.0710696 | − | 0.997471i | \(-0.477359\pi\) | ||||
0.0710696 | + | 0.997471i | \(0.477359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.48754i | 0.747723i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.78773i | − 0.688308i | −0.938913 | − | 0.344154i | \(-0.888166\pi\) | ||||
0.938913 | − | 0.344154i | \(-0.111834\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.35719 | 0.259787 | 0.129893 | − | 0.991528i | \(-0.458536\pi\) | ||||
0.129893 | + | 0.991528i | \(0.458536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7058 | 0.823524 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.7408i | 1.27278i | 0.771369 | + | 0.636388i | \(0.219572\pi\) | ||||
−0.771369 | + | 0.636388i | \(0.780428\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1.99011i | − 0.150438i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1125 | −0.980074 | −0.490037 | − | 0.871702i | \(-0.663017\pi\) | ||||
−0.490037 | + | 0.871702i | \(0.663017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1190 | −0.752136 | −0.376068 | − | 0.926592i | \(-0.622724\pi\) | ||||
−0.376068 | + | 0.926592i | \(0.622724\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.8578i | 1.53350i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.39617i | − 0.613989i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.11278 | −0.514663 | −0.257331 | − | 0.966323i | \(-0.582843\pi\) | ||||
−0.257331 | + | 0.966323i | \(0.582843\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.21790 | 0.663519 | 0.331759 | − | 0.943364i | \(-0.392358\pi\) | ||||
0.331759 | + | 0.943364i | \(0.392358\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.43379i | 0.600883i | 0.953800 | + | 0.300441i | \(0.0971340\pi\) | ||||
−0.953800 | + | 0.300441i | \(0.902866\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.742006i | 0.0525994i | 0.999654 | + | 0.0262997i | \(0.00837242\pi\) | ||||
−0.999654 | + | 0.0262997i | \(0.991628\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.54751 | −0.108614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.30946 | −0.370829 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 17.1767i | − 1.18814i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.66439i | 0.527639i | 0.964572 | + | 0.263819i | \(0.0849823\pi\) | ||||
−0.964572 | + | 0.263819i | \(0.915018\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.44834 | −0.0987759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.248395 | 0.0168622 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.92028i | 0.667310i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.3982i | 1.09810i | 0.835788 | + | 0.549052i | \(0.185011\pi\) | ||||
−0.835788 | + | 0.549052i | \(0.814989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.6099 | −0.969692 | −0.484846 | − | 0.874599i | \(-0.661124\pi\) | ||||
−0.484846 | + | 0.874599i | \(0.661124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1027 | −1.32842 | −0.664212 | − | 0.747544i | \(-0.731233\pi\) | ||||
−0.664212 | + | 0.747544i | \(0.731233\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4.91623i | − 0.322073i | −0.986948 | − | 0.161036i | \(-0.948516\pi\) | ||||
0.986948 | − | 0.161036i | \(-0.0514837\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.85881i | 0.447419i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3618 | 1.38178 | 0.690890 | − | 0.722960i | \(-0.257219\pi\) | ||||
0.690890 | + | 0.722960i | \(0.257219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.87880 | 0.378687 | 0.189344 | − | 0.981911i | \(-0.439364\pi\) | ||||
0.189344 | + | 0.981911i | \(0.439364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.64388i | − 0.168911i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.2947i | 1.29132i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0745 | 0.699016 | 0.349508 | − | 0.936933i | \(-0.386349\pi\) | ||||
0.349508 | + | 0.936933i | \(0.386349\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 39.0965 | 2.45798 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.7076i | 0.730299i | 0.930949 | + | 0.365150i | \(0.118982\pi\) | ||||
−0.930949 | + | 0.365150i | \(0.881018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.88909i | 0.490204i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.5702 | −0.713451 | −0.356726 | − | 0.934209i | \(-0.616107\pi\) | ||||
−0.356726 | + | 0.934209i | \(0.616107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.5716 | 1.87800 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 18.6358i | − 1.13625i | −0.822944 | − | 0.568123i | \(-0.807670\pi\) | ||||
0.822944 | − | 0.568123i | \(-0.192330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.2036i | 0.680571i | 0.940322 | + | 0.340286i | \(0.110524\pi\) | ||||
−0.940322 | + | 0.340286i | \(0.889476\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.20091 | −0.494533 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.2418 | −1.75697 | −0.878485 | − | 0.477769i | \(-0.841446\pi\) | ||||
−0.878485 | + | 0.477769i | \(0.841446\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 11.6928i | − 0.697534i | −0.937209 | − | 0.348767i | \(-0.886600\pi\) | ||||
0.937209 | − | 0.348767i | \(-0.113400\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 18.3784i | − 1.09248i | −0.837628 | − | 0.546242i | \(-0.816058\pi\) | ||||
0.837628 | − | 0.546242i | \(-0.183942\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00821 | −0.118541 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8486 | 0.755801 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.2299i | 1.29868i | 0.760497 | + | 0.649341i | \(0.224955\pi\) | ||||
−0.760497 | + | 0.649341i | \(0.775045\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 32.8715i | − 1.91385i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −46.1935 | −2.67144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.547808 | −0.0315751 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.7974i | 2.16427i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.2640i | 0.985306i | 0.870226 | + | 0.492653i | \(0.163973\pi\) | ||||
−0.870226 | + | 0.492653i | \(0.836027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.80882 | 0.215978 | 0.107989 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107989 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.6882 | 1.45198 | 0.725991 | − | 0.687705i | \(-0.241382\pi\) | ||||
0.725991 | + | 0.687705i | \(0.241382\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.32114i | 0.355030i | 0.984118 | + | 0.177515i | \(0.0568059\pi\) | ||||
−0.984118 | + | 0.177515i | \(0.943194\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.37701i | 0.357044i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.49284 | −0.472554 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.68958 | 0.537481 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.59422i | 0.143024i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 3.46340i | − 0.190366i | −0.995460 | − | 0.0951829i | \(-0.969656\pi\) | ||||
0.995460 | − | 0.0951829i | \(-0.0303436\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.2601 | 0.943020 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.11720 | −0.278752 | −0.139376 | − | 0.990240i | \(-0.544510\pi\) | ||||
−0.139376 | + | 0.990240i | \(0.544510\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.02359i | − 0.0554308i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.8628 | 1.44207 | 0.721034 | − | 0.692900i | \(-0.243667\pi\) | ||||
0.721034 | + | 0.692900i | \(0.243667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.9241 | −1.06651 | −0.533256 | − | 0.845954i | \(-0.679032\pi\) | ||||
−0.533256 | + | 0.845954i | \(0.679032\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 28.8604i | − 1.53608i | −0.640401 | − | 0.768041i | \(-0.721232\pi\) | ||||
0.640401 | − | 0.768041i | \(-0.278768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.7383i | 0.835302i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.1252 | 1.37883 | 0.689417 | − | 0.724365i | \(-0.257867\pi\) | ||||
0.689417 | + | 0.724365i | \(0.257867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.62549 | 0.0855522 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.9544i | 1.62023i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 17.4489i | − 0.910827i | −0.890280 | − | 0.455414i | \(-0.849491\pi\) | ||||
0.890280 | − | 0.455414i | \(-0.150509\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5632 | 0.600330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.0226 | 1.08851 | 0.544254 | − | 0.838920i | \(-0.316813\pi\) | ||||
0.544254 | + | 0.838920i | \(0.316813\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.53459i | − 0.388051i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6392i | 1.47110i | 0.677471 | + | 0.735549i | \(0.263076\pi\) | ||||
−0.677471 | + | 0.735549i | \(0.736924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.16718 | 0.417323 | 0.208662 | − | 0.977988i | \(-0.433089\pi\) | ||||
0.208662 | + | 0.977988i | \(0.433089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.8950 | −0.555260 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.2176i | 1.32929i | 0.747161 | + | 0.664643i | \(0.231416\pi\) | ||||
−0.747161 | + | 0.664643i | \(0.768584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 19.3308i | − 0.977601i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.7718 | −0.994827 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3245 | 0.819304 | 0.409652 | − | 0.912242i | \(-0.365650\pi\) | ||||
0.409652 | + | 0.912242i | \(0.365650\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.4029i | 1.01887i | 0.860509 | + | 0.509435i | \(0.170146\pi\) | ||||
−0.860509 | + | 0.509435i | \(0.829854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.20940i | 0.0602446i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.5096 | 1.61144 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0523 | 1.18931 | 0.594654 | − | 0.803982i | \(-0.297289\pi\) | ||||
0.594654 | + | 0.803982i | \(0.297289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 12.4330i | − 0.611790i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4172i | 0.511359i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.79478 | −0.380800 | −0.190400 | − | 0.981707i | \(-0.560978\pi\) | ||||
−0.190400 | + | 0.981707i | \(0.560978\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7294 | 1.49766 | 0.748830 | − | 0.662762i | \(-0.230616\pi\) | ||||
0.748830 | + | 0.662762i | \(0.230616\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.05484i | 0.196689i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.2962i | 0.691840i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.3139 | 0.785814 | 0.392907 | − | 0.919578i | \(-0.371469\pi\) | ||||
0.392907 | + | 0.919578i | \(0.371469\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.02836 | −0.289705 | −0.144852 | − | 0.989453i | \(-0.546271\pi\) | ||||
−0.144852 | + | 0.989453i | \(0.546271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 39.5467i | − 1.89177i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.2529i | 1.20526i | 0.798022 | + | 0.602629i | \(0.205880\pi\) | ||||
−0.798022 | + | 0.602629i | \(0.794120\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.6419 | −1.26580 | −0.632898 | − | 0.774235i | \(-0.718135\pi\) | ||||
−0.632898 | + | 0.774235i | \(0.718135\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.1670 | 1.61967 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.22348i | 0.340897i | 0.985367 | + | 0.170449i | \(0.0545217\pi\) | ||||
−0.985367 | + | 0.170449i | \(0.945478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.27548i | 0.389677i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.8727 | 0.603481 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.2788 | −1.83738 | −0.918692 | − | 0.394974i | \(-0.870754\pi\) | ||||
−0.918692 | + | 0.394974i | \(0.870754\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 18.0976i | − 0.842892i | −0.906854 | − | 0.421446i | \(-0.861523\pi\) | ||||
0.906854 | − | 0.421446i | \(-0.138477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.4913i | 1.32410i | 0.749458 | + | 0.662052i | \(0.230314\pi\) | ||||
−0.749458 | + | 0.662052i | \(0.769686\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.9125 | −1.47673 | −0.738366 | − | 0.674400i | \(-0.764402\pi\) | ||||
−0.738366 | + | 0.674400i | \(0.764402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.52832 | 0.301450 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.25742i | 0.103796i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.29533i | 0.380616i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.73828 | 0.170806 | 0.0854031 | − | 0.996346i | \(-0.472782\pi\) | ||||
0.0854031 | + | 0.996346i | \(0.472782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.4109 | −1.75139 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 14.9282i | − 0.677853i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3.85953i | − 0.174892i | −0.996169 | − | 0.0874461i | \(-0.972129\pi\) | ||||
0.996169 | − | 0.0874461i | \(-0.0278706\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.428753 | −0.0193494 | −0.00967468 | − | 0.999953i | \(-0.503080\pi\) | ||||
−0.00967468 | + | 0.999953i | \(0.503080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.15303 | 0.142006 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.95273i | 0.267016i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.9296i | 1.78749i | 0.448571 | + | 0.893747i | \(0.351933\pi\) | ||||
−0.448571 | + | 0.893747i | \(0.648067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.19899 | −0.0980479 | −0.0490239 | − | 0.998798i | \(-0.515611\pi\) | ||||
−0.0490239 | + | 0.998798i | \(0.515611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4544 | 0.554215 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 16.5978i | − 0.735684i | −0.929888 | − | 0.367842i | \(-0.880097\pi\) | ||||
0.929888 | − | 0.367842i | \(-0.119903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.7079i | 0.517929i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −51.8619 | −2.28531 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.6903 | 0.470161 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 41.1482i | − 1.80274i | −0.433053 | − | 0.901368i | \(-0.642564\pi\) | ||||
0.433053 | − | 0.901368i | \(-0.357436\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5857i | 0.637790i | 0.947790 | + | 0.318895i | \(0.103312\pi\) | ||||
−0.947790 | + | 0.318895i | \(0.896688\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.506104 | −0.0220462 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 67.0135 | 2.91363 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 9.77768i | − 0.423518i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 10.8494i | − 0.469062i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.12083 | −0.177497 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.2868 | 1.17315 | 0.586575 | − | 0.809895i | \(-0.300476\pi\) | ||||
0.586575 | + | 0.809895i | \(0.300476\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.4410i | 0.961269i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 31.2511i | − 1.33620i | −0.744071 | − | 0.668100i | \(-0.767108\pi\) | ||||
0.744071 | − | 0.668100i | \(-0.232892\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.45043 | 0.274797 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.47832 | −0.318010 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 32.1278i | − 1.36130i | −0.732610 | − | 0.680648i | \(-0.761698\pi\) | ||||
0.732610 | − | 0.680648i | \(-0.238302\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 2.66720i | − 0.112811i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.62528 | −0.194933 | −0.0974663 | − | 0.995239i | \(-0.531074\pi\) | ||||
−0.0974663 | + | 0.995239i | \(0.531074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.8248 | −0.623682 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 26.5383i | − 1.11254i | −0.831000 | − | 0.556272i | \(-0.812231\pi\) | ||||
0.831000 | − | 0.556272i | \(-0.187769\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 30.6374i | − 1.28213i | −0.767485 | − | 0.641067i | \(-0.778492\pi\) | ||||
0.767485 | − | 0.641067i | \(-0.221508\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.8813 | −0.787403 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.0588 | −1.62604 | −0.813019 | − | 0.582238i | \(-0.802177\pi\) | ||||
−0.813019 | + | 0.582238i | \(0.802177\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.94011i | 0.163463i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 47.6498i | − 1.97345i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.80587 | 0.322183 | 0.161091 | − | 0.986940i | \(-0.448499\pi\) | ||||
0.161091 | + | 0.986940i | \(0.448499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03538 | −0.0426621 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 41.6924i | − 1.71210i | −0.516892 | − | 0.856051i | \(-0.672911\pi\) | ||||
0.516892 | − | 0.856051i | \(-0.327089\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.38690i | 0.220841i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.38483 | 0.342595 | 0.171297 | − | 0.985219i | \(-0.445204\pi\) | ||||
0.171297 | + | 0.985219i | \(0.445204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.3188 | 0.828820 | 0.414410 | − | 0.910090i | \(-0.363988\pi\) | ||||
0.414410 | + | 0.910090i | \(0.363988\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.8137i | 0.642918i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 27.8127i | − 1.12888i | −0.825473 | − | 0.564442i | \(-0.809091\pi\) | ||||
0.825473 | − | 0.564442i | \(-0.190909\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.6309 | −0.510991 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.65547 | −0.147643 | −0.0738214 | − | 0.997271i | \(-0.523519\pi\) | ||||
−0.0738214 | + | 0.997271i | \(0.523519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 21.3637i | − 0.860070i | −0.902812 | − | 0.430035i | \(-0.858501\pi\) | ||||
0.902812 | − | 0.430035i | \(-0.141499\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.48661i | 0.0597520i | 0.999554 | + | 0.0298760i | \(0.00951124\pi\) | ||||
−0.999554 | + | 0.0298760i | \(0.990489\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.9230 | 0.517750 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9900 | −1.23960 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 16.0740i | − 0.640912i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 10.2236i | − 0.406995i | −0.979075 | − | 0.203497i | \(-0.934769\pi\) | ||||
0.979075 | − | 0.203497i | \(-0.0652308\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.3872 | 1.68208 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.86886 | 0.192911 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.36460i | 0.290884i | 0.989367 | + | 0.145442i | \(0.0464605\pi\) | ||||
−0.989367 | + | 0.145442i | \(0.953540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0823i | 0.791967i | 0.918258 | + | 0.395983i | \(0.129596\pi\) | ||||
−0.918258 | + | 0.395983i | \(0.870404\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.1276 | 0.830610 | 0.415305 | − | 0.909682i | \(-0.363675\pi\) | ||||
0.415305 | + | 0.909682i | \(0.363675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.2345 | −2.01113 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.3880i | 1.89357i | 0.321867 | + | 0.946785i | \(0.395690\pi\) | ||||
−0.321867 | + | 0.946785i | \(0.604310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.42037i | 0.211791i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8453 | 0.656198 | 0.328099 | − | 0.944643i | \(-0.393592\pi\) | ||||
0.328099 | + | 0.944643i | \(0.393592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.7271 | −1.00067 | −0.500334 | − | 0.865832i | \(-0.666790\pi\) | ||||
−0.500334 | + | 0.865832i | \(0.666790\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.0204i | 0.427354i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6820i | 0.568490i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 58.9120 | 2.27427 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.545897 | −0.0210428 | −0.0105214 | − | 0.999945i | \(-0.503349\pi\) | ||||
−0.0105214 | + | 0.999945i | \(0.503349\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 40.6066i | − 1.56064i | −0.625382 | − | 0.780318i | \(-0.715057\pi\) | ||||
0.625382 | − | 0.780318i | \(-0.284943\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 5.64630i | − 0.216685i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.25283 | −0.124466 | −0.0622330 | − | 0.998062i | \(-0.519822\pi\) | ||||
−0.0622330 | + | 0.998062i | \(0.519822\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.5269 | −1.05175 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 56.2994i | 2.14484i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.9406i | 1.32920i | 0.747198 | + | 0.664602i | \(0.231399\pi\) | ||||
−0.747198 | + | 0.664602i | \(0.768601\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −34.4173 | −1.30552 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.09171 | 0.154985 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.09751i | 0.268069i | 0.990977 | + | 0.134035i | \(0.0427934\pi\) | ||||
−0.990977 | + | 0.134035i | \(0.957207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 32.8839i | − 1.24024i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.71066 | 0.177163 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.0565 | −1.61702 | −0.808510 | − | 0.588482i | \(-0.799726\pi\) | ||||
−0.808510 | + | 0.588482i | \(0.799726\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.35666i | − 0.0882577i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 53.0462i | − 1.98381i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.9861 | 0.409714 | 0.204857 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204857 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.6158 | −0.730531 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 3.07971i | − 0.114377i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 10.6945i | − 0.396637i | −0.980138 | − | 0.198319i | \(-0.936452\pi\) | ||||
0.980138 | − | 0.198319i | \(-0.0635481\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.11616 | 0.0412825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.3535 | 0.604029 | 0.302015 | − | 0.953303i | \(-0.402341\pi\) | ||||
0.302015 | + | 0.953303i | \(0.402341\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 26.9021i | − 0.990951i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 33.0891i | − 1.21720i | −0.793476 | − | 0.608601i | \(-0.791731\pi\) | ||||
0.793476 | − | 0.608601i | \(-0.208269\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.9244 | 1.06113 | 0.530566 | − | 0.847644i | \(-0.321979\pi\) | ||||
0.530566 | + | 0.847644i | \(0.321979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 59.7100 | 2.18761 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.10360i | − 0.149942i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.3341i | 0.669020i | 0.942392 | + | 0.334510i | \(0.108571\pi\) | ||||
−0.942392 | + | 0.334510i | \(0.891429\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −62.8009 | −2.28556 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.8508 | 0.539761 | 0.269880 | − | 0.962894i | \(-0.413016\pi\) | ||||
0.269880 | + | 0.962894i | \(0.413016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.52709i | 0.272857i | 0.990650 | + | 0.136428i | \(0.0435624\pi\) | ||||
−0.990650 | + | 0.136428i | \(0.956438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.48792i | 0.307283i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 60.5348 | 2.18578 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.6002 | 1.78863 | 0.894314 | − | 0.447440i | \(-0.147664\pi\) | ||||
0.894314 | + | 0.447440i | \(0.147664\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 45.5457i | − 1.63817i | −0.573676 | − | 0.819083i | \(-0.694483\pi\) | ||||
0.573676 | − | 0.819083i | \(-0.305517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.494334i | 0.0177570i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.37076 | 0.299914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.5302 | 0.877758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.70875i | 0.168063i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 24.5359i | − 0.874610i | −0.899313 | − | 0.437305i | \(-0.855933\pi\) | ||||
0.899313 | − | 0.437305i | \(-0.144067\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.60719 | −0.199369 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −69.6060 | −2.47178 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.2974i | 0.896080i | 0.894013 | + | 0.448040i | \(0.147878\pi\) | ||||
−0.894013 | + | 0.448040i | \(0.852122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 5.28571i | − 0.186995i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.2465 | 1.70258 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.0839 | −0.884093 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 23.3260i | − 0.820099i | −0.912063 | − | 0.410050i | \(-0.865511\pi\) | ||||
0.912063 | − | 0.410050i | \(-0.134489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.8400i | 1.29363i | 0.762648 | + | 0.646814i | \(0.223899\pi\) | ||||
−0.762648 | + | 0.646814i | \(0.776101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.2337 | 0.813841 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.28341 | 0.0798865 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.7705i | 1.91150i | 0.294175 | + | 0.955752i | \(0.404955\pi\) | ||||
−0.294175 | + | 0.955752i | \(0.595045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 43.9701i | − 1.53270i | −0.642423 | − | 0.766350i | \(-0.722071\pi\) | ||||
0.642423 | − | 0.766350i | \(-0.277929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.0167 | −0.835142 | −0.417571 | − | 0.908644i | \(-0.637118\pi\) | ||||
−0.417571 | + | 0.908644i | \(0.637118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.23391 | 0.216513 | 0.108256 | − | 0.994123i | \(-0.465473\pi\) | ||||
0.108256 | + | 0.994123i | \(0.465473\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.03749i | 0.0705950i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.87601i | 0.307167i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.7221 | −0.473738 | −0.236869 | − | 0.971542i | \(-0.576121\pi\) | ||||
−0.236869 | + | 0.971542i | \(0.576121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6052 | 0.917422 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.3049i | 0.973718i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.98124i | 0.205518i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 74.8481 | 2.56576 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.8815 | −1.26280 | −0.631400 | − | 0.775457i | \(-0.717519\pi\) | ||||
−0.631400 | + | 0.775457i | \(0.717519\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.35611i | 0.217120i | 0.994090 | + | 0.108560i | \(0.0346240\pi\) | ||||
−0.994090 | + | 0.108560i | \(0.965376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.3449i | 0.864755i | 0.901693 | + | 0.432378i | \(0.142325\pi\) | ||||
−0.901693 | + | 0.432378i | \(0.857675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.9486 | −0.610976 | −0.305488 | − | 0.952196i | \(-0.598820\pi\) | ||||
−0.305488 | + | 0.952196i | \(0.598820\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.2606 | −1.50491 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 30.8169i | 1.04539i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.7855i | 1.07701i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.95779 | −0.269022 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.0001 | −0.810427 | −0.405213 | − | 0.914222i | \(-0.632803\pi\) | ||||
−0.405213 | + | 0.914222i | \(0.632803\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.1921i | 1.25303i | 0.779408 | + | 0.626516i | \(0.215520\pi\) | ||||
−0.779408 | + | 0.626516i | \(0.784480\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 48.2212i | − 1.62277i | −0.584511 | − | 0.811386i | \(-0.698714\pi\) | ||||
0.584511 | − | 0.811386i | \(-0.301286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.900487 | −0.0302354 | −0.0151177 | − | 0.999886i | \(-0.504812\pi\) | ||||
−0.0151177 | + | 0.999886i | \(0.504812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.0322 | 0.537702 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 10.8134i | − 0.361857i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 34.6679i | − 1.15882i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.384393 | 0.0128202 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.5599 | −0.784894 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 26.7533i | − 0.889311i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7.11861i | − 0.236370i | −0.992992 | − | 0.118185i | \(-0.962292\pi\) | ||||
0.992992 | − | 0.118185i | \(-0.0377075\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.7843 | −1.78195 | −0.890977 | − | 0.454049i | \(-0.849979\pi\) | ||||
−0.890977 | + | 0.454049i | \(0.849979\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.2365 | 0.537350 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.05016i | 0.0677021i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.4104i | 1.95977i | 0.199563 | + | 0.979885i | \(0.436048\pi\) | ||||
−0.199563 | + | 0.979885i | \(0.563952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.9830 | −0.953987 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.7002 | −0.516218 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.3649i | 1.06186i | 0.847416 | + | 0.530930i | \(0.178157\pi\) | ||||
−0.847416 | + | 0.530930i | \(0.821843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.16827i | 0.136610i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.1985 | 0.725968 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.8314 | −0.484521 | −0.242260 | − | 0.970211i | \(-0.577889\pi\) | ||||
−0.242260 | + | 0.970211i | \(0.577889\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.1324i | 0.721494i | 0.932664 | + | 0.360747i | \(0.117478\pi\) | ||||
−0.932664 | + | 0.360747i | \(0.882522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.0530i | 0.620450i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.12874 | −0.296644 | −0.148322 | − | 0.988939i | \(-0.547387\pi\) | ||||
−0.148322 | + | 0.988939i | \(0.547387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.0044 | −1.85044 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 4.40579i | − 0.142718i | −0.997451 | − | 0.0713588i | \(-0.977266\pi\) | ||||
0.997451 | − | 0.0713588i | \(-0.0227335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 18.8054i | − 0.608527i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.4115 | −0.336206 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9383 | 0.998010 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.3710i | 0.784531i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.7941i | 0.636536i | 0.948001 | + | 0.318268i | \(0.103101\pi\) | ||||
−0.948001 | + | 0.318268i | \(0.896899\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.61141 | −0.147987 | −0.0739936 | − | 0.997259i | \(-0.523574\pi\) | ||||
−0.0739936 | + | 0.997259i | \(0.523574\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.0177 | −0.417328 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 15.0782i | − 0.482395i | −0.970476 | − | 0.241197i | \(-0.922460\pi\) | ||||
0.970476 | − | 0.241197i | \(-0.0775401\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 53.2536i | − 1.70199i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.7616 | −1.14062 | −0.570308 | − | 0.821431i | \(-0.693176\pi\) | ||||
−0.570308 | + | 0.821431i | \(0.693176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.2980 | −0.710472 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.19735i | 0.165266i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.8448i | 1.64690i | 0.567387 | + | 0.823451i | \(0.307954\pi\) | ||||
−0.567387 | + | 0.823451i | \(0.692046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.96178 | −0.0621925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.7850 | 1.35501 | 0.677507 | − | 0.735516i | \(-0.263060\pi\) | ||||
0.677507 | + | 0.735516i | \(0.263060\pi\) | |||||||
\(998\) | 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.h.i.2591.6 | yes | 24 | |
3.2 | odd | 2 | inner | 6048.2.h.i.2591.19 | yes | 24 | |
4.3 | odd | 2 | inner | 6048.2.h.i.2591.20 | yes | 24 | |
12.11 | even | 2 | inner | 6048.2.h.i.2591.5 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.i.2591.5 | ✓ | 24 | 12.11 | even | 2 | inner | |
6048.2.h.i.2591.6 | yes | 24 | 1.1 | even | 1 | trivial | |
6048.2.h.i.2591.19 | yes | 24 | 3.2 | odd | 2 | inner | |
6048.2.h.i.2591.20 | yes | 24 | 4.3 | odd | 2 | inner |