Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.3 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.g.3025.22 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.11390i | − 1.39258i | −0.717760 | − | 0.696290i | \(-0.754833\pi\) | ||||
0.717760 | − | 0.696290i | \(-0.245167\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.37402i | 0.715793i | 0.933761 | + | 0.357897i | \(0.116506\pi\) | ||||
−0.933761 | + | 0.357897i | \(0.883494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.09044i | − 0.302434i | −0.988501 | − | 0.151217i | \(-0.951681\pi\) | ||||
0.988501 | − | 0.151217i | \(-0.0483192\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.69300 | −0.895684 | −0.447842 | − | 0.894113i | \(-0.647807\pi\) | ||||
−0.447842 | + | 0.894113i | \(0.647807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.08263i | 0.248372i | 0.992259 | + | 0.124186i | \(0.0396320\pi\) | ||||
−0.992259 | + | 0.124186i | \(0.960368\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.87366 | 1.01623 | 0.508114 | − | 0.861290i | \(-0.330343\pi\) | ||||
0.508114 | + | 0.861290i | \(0.330343\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69640 | −0.939280 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1.59607i | − 0.296382i | −0.988959 | − | 0.148191i | \(-0.952655\pi\) | ||||
0.988959 | − | 0.148191i | \(-0.0473451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.45516 | −1.33899 | −0.669493 | − | 0.742818i | \(-0.733489\pi\) | ||||
−0.669493 | + | 0.742818i | \(0.733489\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.11390i | 0.526346i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.61410i | 0.758554i | 0.925283 | + | 0.379277i | \(0.123827\pi\) | ||||
−0.925283 | + | 0.379277i | \(0.876173\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.0380616 | 0.00594422 | 0.00297211 | − | 0.999996i | \(-0.499054\pi\) | ||||
0.00297211 | + | 0.999996i | \(0.499054\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.0608i | − 1.68675i | −0.537323 | − | 0.843377i | \(-0.680564\pi\) | ||||
0.537323 | − | 0.843377i | \(-0.319436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.337175 | 0.0491821 | 0.0245910 | − | 0.999698i | \(-0.492172\pi\) | ||||
0.0245910 | + | 0.999698i | \(0.492172\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.14672i | 1.11904i | 0.828818 | + | 0.559519i | \(0.189014\pi\) | ||||
−0.828818 | + | 0.559519i | \(0.810986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.39246 | 0.996799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.0761i | 1.96274i | 0.192129 | + | 0.981370i | \(0.438461\pi\) | ||||
−0.192129 | + | 0.981370i | \(0.561539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.53745i | − 0.708998i | −0.935056 | − | 0.354499i | \(-0.884651\pi\) | ||||
0.935056 | − | 0.354499i | \(-0.115349\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.39553 | −0.421163 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.70421i | 0.941219i | 0.882342 | + | 0.470609i | \(0.155966\pi\) | ||||
−0.882342 | + | 0.470609i | \(0.844034\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5472 | −1.60776 | −0.803878 | − | 0.594794i | \(-0.797234\pi\) | ||||
−0.803878 | + | 0.594794i | \(0.797234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.6727 | −1.71731 | −0.858656 | − | 0.512553i | \(-0.828700\pi\) | ||||
−0.858656 | + | 0.512553i | \(0.828700\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.37402i | − 0.270544i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.18122 | −0.582932 | −0.291466 | − | 0.956581i | \(-0.594143\pi\) | ||||
−0.291466 | + | 0.956581i | \(0.594143\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.138321i | − 0.0151827i | −0.999971 | − | 0.00759136i | \(-0.997584\pi\) | ||||
0.999971 | − | 0.00759136i | \(-0.00241643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.4996i | 1.24731i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9531 | 1.26703 | 0.633514 | − | 0.773731i | \(-0.281612\pi\) | ||||
0.633514 | + | 0.773731i | \(0.281612\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.09044i | 0.114309i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.37121 | 0.345879 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.30202 | −0.538339 | −0.269169 | − | 0.963093i | \(-0.586749\pi\) | ||||
−0.269169 | + | 0.963093i | \(0.586749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.0753369i | − 0.00749630i | −0.999993 | − | 0.00374815i | \(-0.998807\pi\) | ||||
0.999993 | − | 0.00374815i | \(-0.00119308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.3347 | −1.51097 | −0.755487 | − | 0.655163i | \(-0.772600\pi\) | ||||
−0.755487 | + | 0.655163i | \(0.772600\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.03726i | − 0.390297i | −0.980774 | − | 0.195148i | \(-0.937481\pi\) | ||||
0.980774 | − | 0.195148i | \(-0.0625189\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2335i | 1.17176i | 0.810399 | + | 0.585879i | \(0.199251\pi\) | ||||
−0.810399 | + | 0.585879i | \(0.800749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1934 | 1.05299 | 0.526495 | − | 0.850178i | \(-0.323506\pi\) | ||||
0.526495 | + | 0.850178i | \(0.323506\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 15.1761i | − 1.41518i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.69300 | 0.338537 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.36404 | 0.487640 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 0.945386i | − 0.0845579i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.43139 | 0.215751 | 0.107876 | − | 0.994164i | \(-0.465595\pi\) | ||||
0.107876 | + | 0.994164i | \(0.465595\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.83723i | 0.772112i | 0.922475 | + | 0.386056i | \(0.126163\pi\) | ||||
−0.922475 | + | 0.386056i | \(0.873837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.08263i | − 0.0938760i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1478 | −0.952422 | −0.476211 | − | 0.879331i | \(-0.657990\pi\) | ||||
−0.476211 | + | 0.879331i | \(0.657990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 17.2724i | − 1.46502i | −0.680755 | − | 0.732511i | \(-0.738348\pi\) | ||||
0.680755 | − | 0.732511i | \(-0.261652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.58872 | 0.216480 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.97000 | −0.412736 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7236i | 1.12428i | 0.827042 | + | 0.562140i | \(0.190022\pi\) | ||||
−0.827042 | + | 0.562140i | \(0.809978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8195 | 1.04324 | 0.521620 | − | 0.853178i | \(-0.325328\pi\) | ||||
0.521620 | + | 0.853178i | \(0.325328\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.2146i | 1.86465i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.1418i | 1.68730i | 0.536892 | + | 0.843651i | \(0.319598\pi\) | ||||
−0.536892 | + | 0.843651i | \(0.680402\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.87366 | −0.384098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.386568i | 0.0302784i | 0.999885 | + | 0.0151392i | \(0.00481914\pi\) | ||||
−0.999885 | + | 0.0151392i | \(0.995181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.4336 | −1.11690 | −0.558451 | − | 0.829537i | \(-0.688604\pi\) | ||||
−0.558451 | + | 0.829537i | \(0.688604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8109 | 0.908534 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9493i | 1.06055i | 0.847826 | + | 0.530274i | \(0.177911\pi\) | ||||
−0.847826 | + | 0.530274i | \(0.822089\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.69640 | 0.355014 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.6569i | 0.796537i | 0.917269 | + | 0.398269i | \(0.130389\pi\) | ||||
−0.917269 | + | 0.398269i | \(0.869611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.63866i | 0.493448i | 0.969086 | + | 0.246724i | \(0.0793540\pi\) | ||||
−0.969086 | + | 0.246724i | \(0.920646\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.3679 | 1.05635 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.76724i | − 0.641124i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.81148 | 0.709934 | 0.354967 | − | 0.934879i | \(-0.384492\pi\) | ||||
0.354967 | + | 0.934879i | \(0.384492\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4539 | 1.25636 | 0.628180 | − | 0.778068i | \(-0.283800\pi\) | ||||
0.628180 | + | 0.778068i | \(0.283800\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.6871i | 1.97262i | 0.164888 | + | 0.986312i | \(0.447274\pi\) | ||||
−0.164888 | + | 0.986312i | \(0.552726\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.29804 | −0.659121 | −0.329560 | − | 0.944134i | \(-0.606901\pi\) | ||||
−0.329560 | + | 0.944134i | \(0.606901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.59607i | 0.112022i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 0.118520i | − 0.00827780i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.57018 | −0.177783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 16.3068i | − 1.12260i | −0.827611 | − | 0.561302i | \(-0.810301\pi\) | ||||
0.827611 | − | 0.561302i | \(-0.189699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −34.4422 | −2.34894 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.45516 | 0.506089 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.02699i | 0.270885i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8846 | 1.26461 | 0.632304 | − | 0.774720i | \(-0.282109\pi\) | ||||
0.632304 | + | 0.774720i | \(0.282109\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9709i | 0.860907i | 0.902613 | + | 0.430454i | \(0.141646\pi\) | ||||
−0.902613 | + | 0.430454i | \(0.858354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5.92552i | − 0.391569i | −0.980647 | − | 0.195785i | \(-0.937275\pi\) | ||||
0.980647 | − | 0.195785i | \(-0.0627253\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2093 | −0.799861 | −0.399930 | − | 0.916546i | \(-0.630966\pi\) | ||||
−0.399930 | + | 0.916546i | \(0.630966\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1.04993i | − 0.0684900i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.5273 | 1.45717 | 0.728585 | − | 0.684956i | \(-0.240178\pi\) | ||||
0.728585 | + | 0.684956i | \(0.240178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1826 | −1.04241 | −0.521206 | − | 0.853431i | \(-0.674518\pi\) | ||||
−0.521206 | + | 0.853431i | \(0.674518\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.11390i | − 0.198940i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.18054 | 0.0751162 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.88454i | 0.434548i | 0.976111 | + | 0.217274i | \(0.0697166\pi\) | ||||
−0.976111 | + | 0.217274i | \(0.930283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5702i | 0.727409i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.70139 | 0.168508 | 0.0842541 | − | 0.996444i | \(-0.473149\pi\) | ||||
0.0842541 | + | 0.996444i | \(0.473149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.61410i | − 0.286707i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5500 | 0.835527 | 0.417763 | − | 0.908556i | \(-0.362814\pi\) | ||||
0.417763 | + | 0.908556i | \(0.362814\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.3681 | 1.55835 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.41522i | 0.391143i | 0.980689 | + | 0.195571i | \(0.0626562\pi\) | ||||
−0.980689 | + | 0.195571i | \(0.937344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5096 | 0.881397 | 0.440698 | − | 0.897655i | \(-0.354731\pi\) | ||||
0.440698 | + | 0.897655i | \(0.354731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 11.1493i | − 0.672330i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 25.3175i | − 1.52118i | −0.649231 | − | 0.760591i | \(-0.724909\pi\) | ||||
0.649231 | − | 0.760591i | \(-0.275091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.719979 | 0.0429504 | 0.0214752 | − | 0.999769i | \(-0.493164\pi\) | ||||
0.0214752 | + | 0.999769i | \(0.493164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.3262i | − 0.673275i | −0.941634 | − | 0.336637i | \(-0.890710\pi\) | ||||
0.941634 | − | 0.336637i | \(-0.109290\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0380616 | −0.00224670 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.36176 | −0.197751 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.2567i | 0.891304i | 0.895206 | + | 0.445652i | \(0.147028\pi\) | ||||
−0.895206 | + | 0.445652i | \(0.852972\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 46.9455 | 2.73327 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 5.31443i | − 0.307342i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0608i | 0.637533i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.2431 | −0.987337 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.5497i | 1.45820i | 0.684409 | + | 0.729098i | \(0.260060\pi\) | ||||
−0.684409 | + | 0.729098i | \(0.739940\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00328 | 0.170300 | 0.0851501 | − | 0.996368i | \(-0.472863\pi\) | ||||
0.0851501 | + | 0.996368i | \(0.472863\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.53962 | −0.313118 | −0.156559 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156559 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.1705i | 1.80688i | 0.428718 | + | 0.903439i | \(0.358966\pi\) | ||||
−0.428718 | + | 0.903439i | \(0.641034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.78909 | 0.212148 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.99815i | − 0.222463i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.12114i | 0.284070i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.337175 | −0.0185891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9617i | 1.37202i | 0.727592 | + | 0.686010i | \(0.240639\pi\) | ||||
−0.727592 | + | 0.686010i | \(0.759361\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.9902 | 1.31072 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.7899 | 0.969076 | 0.484538 | − | 0.874770i | \(-0.338988\pi\) | ||||
0.484538 | + | 0.874770i | \(0.338988\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 17.6987i | − 0.958437i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.08108i | 0.111718i | 0.998439 | + | 0.0558591i | \(0.0177898\pi\) | ||||
−0.998439 | + | 0.0558591i | \(0.982210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.11683i | 0.380955i | 0.981692 | + | 0.190477i | \(0.0610036\pi\) | ||||
−0.981692 | + | 0.190477i | \(0.938996\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.9449 | −1.54058 | −0.770290 | − | 0.637694i | \(-0.779889\pi\) | ||||
−0.770290 | + | 0.637694i | \(0.779889\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42.1847i | 2.23893i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0190 | −0.528780 | −0.264390 | − | 0.964416i | \(-0.585171\pi\) | ||||
−0.264390 | + | 0.964416i | \(0.585171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8279 | 0.938311 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 45.6894i | 2.39149i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.4662 | −1.64252 | −0.821261 | − | 0.570552i | \(-0.806729\pi\) | ||||
−0.821261 | + | 0.570552i | \(0.806729\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 8.14672i | − 0.422956i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 31.8121i | − 1.64717i | −0.567193 | − | 0.823585i | \(-0.691970\pi\) | ||||
0.567193 | − | 0.823585i | \(-0.308030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.74042 | −0.0896360 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 15.2806i | − 0.784911i | −0.919771 | − | 0.392456i | \(-0.871626\pi\) | ||||
0.919771 | − | 0.392456i | \(-0.128374\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.0555 | 0.973691 | 0.486845 | − | 0.873488i | \(-0.338147\pi\) | ||||
0.486845 | + | 0.873488i | \(0.338147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.39246 | −0.376755 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3.69055i | − 0.187118i | −0.995614 | − | 0.0935591i | \(-0.970176\pi\) | ||||
0.995614 | − | 0.0935591i | \(-0.0298244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.9984 | −0.910219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.1338i | 0.811780i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 14.8184i | − 0.743715i | −0.928290 | − | 0.371857i | \(-0.878721\pi\) | ||||
0.928290 | − | 0.371857i | \(-0.121279\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.80006 | 0.0898908 | 0.0449454 | − | 0.998989i | \(-0.485689\pi\) | ||||
0.0449454 | + | 0.998989i | \(0.485689\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.12940i | 0.404954i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9540 | −0.542968 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.6731 | −1.26945 | −0.634727 | − | 0.772736i | \(-0.718888\pi\) | ||||
−0.634727 | + | 0.772736i | \(0.718888\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 15.0761i | − 0.741846i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.430719 | −0.0211431 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 17.3661i | − 0.848392i | −0.905571 | − | 0.424196i | \(-0.860557\pi\) | ||||
0.905571 | − | 0.424196i | \(-0.139443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4837i | 1.48568i | 0.669468 | + | 0.742841i | \(0.266522\pi\) | ||||
−0.669468 | + | 0.742841i | \(0.733478\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.3438 | 0.841298 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.53745i | 0.267976i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.49698 | −0.457453 | −0.228727 | − | 0.973491i | \(-0.573456\pi\) | ||||
−0.228727 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.6935 | 1.23475 | 0.617376 | − | 0.786668i | \(-0.288196\pi\) | ||||
0.617376 | + | 0.786668i | \(0.288196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.27637i | 0.252403i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.0047 | −0.525227 | −0.262614 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262614 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 32.0650i | − 1.52346i | −0.647897 | − | 0.761728i | \(-0.724351\pi\) | ||||
0.647897 | − | 0.761728i | \(-0.275649\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 37.2208i | − 1.76444i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.5474 | −0.780922 | −0.390461 | − | 0.920619i | \(-0.627684\pi\) | ||||
−0.390461 | + | 0.920619i | \(0.627684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0903588i | 0.00425483i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.39553 | 0.159185 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.9067 | −1.25864 | −0.629321 | − | 0.777145i | \(-0.716667\pi\) | ||||
−0.629321 | + | 0.777145i | \(0.716667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.9351i | 1.34764i | 0.738895 | + | 0.673821i | \(0.235348\pi\) | ||||
−0.738895 | + | 0.673821i | \(0.764652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3287 | −0.480017 | −0.240009 | − | 0.970771i | \(-0.577150\pi\) | ||||
−0.240009 | + | 0.970771i | \(0.577150\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.1113i | 1.02319i | 0.859227 | + | 0.511595i | \(0.170945\pi\) | ||||
−0.859227 | + | 0.511595i | \(0.829055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7.70421i | − 0.355747i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.2585 | 1.20737 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.08446i | − 0.233291i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.77499 | −0.263866 | −0.131933 | − | 0.991259i | \(-0.542118\pi\) | ||||
−0.131933 | + | 0.991259i | \(0.542118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.03140 | 0.229412 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5100i | 0.749680i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5566 | −0.568993 | −0.284497 | − | 0.958677i | \(-0.591826\pi\) | ||||
−0.284497 | + | 0.958677i | \(0.591826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.9548i | 0.945677i | 0.881149 | + | 0.472839i | \(0.156771\pi\) | ||||
−0.881149 | + | 0.472839i | \(0.843229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.89428i | 0.265465i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.5472 | 0.607675 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 13.0152i | − 0.582641i | −0.956626 | − | 0.291320i | \(-0.905905\pi\) | ||||
0.956626 | − | 0.291320i | \(-0.0940946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.9100 | −1.02150 | −0.510752 | − | 0.859728i | \(-0.670633\pi\) | ||||
−0.510752 | + | 0.859728i | \(0.670633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.234592 | −0.0104392 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 24.5703i | − 1.08906i | −0.838741 | − | 0.544530i | \(-0.816708\pi\) | ||||
0.838741 | − | 0.544530i | \(-0.183292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6727 | 0.649083 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 47.7508i | 2.10415i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.800460i | 0.0352042i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.51316 | −0.0662929 | −0.0331465 | − | 0.999451i | \(-0.510553\pi\) | ||||
−0.0331465 | + | 0.999451i | \(0.510553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.202190i | 0.00884117i | 0.999990 | + | 0.00442059i | \(0.00140712\pi\) | ||||
−0.999990 | + | 0.00442059i | \(0.998593\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.5319 | 1.19931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.752559 | 0.0327199 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.0415038i | − 0.00179773i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.5716 | −0.543520 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.37402i | 0.102256i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 28.5045i | − 1.22550i | −0.790275 | − | 0.612752i | \(-0.790062\pi\) | ||||
0.790275 | − | 0.612752i | \(-0.209938\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.0940 | 1.63177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.9150i | 1.62113i | 0.585648 | + | 0.810565i | \(0.300840\pi\) | ||||
−0.585648 | + | 0.810565i | \(0.699160\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.72795 | 0.0736132 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.18122 | 0.220328 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 16.6109i | − 0.703828i | −0.936032 | − | 0.351914i | \(-0.885531\pi\) | ||||
0.936032 | − | 0.351914i | \(-0.114469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0611 | −0.510131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.84219i | 0.288364i | 0.989551 | + | 0.144182i | \(0.0460551\pi\) | ||||
−0.989551 | + | 0.144182i | \(0.953945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 34.8553i | − 1.46637i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3184 | 0.642180 | 0.321090 | − | 0.947049i | \(-0.395951\pi\) | ||||
0.321090 | + | 0.947049i | \(0.395951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.6853i | 1.53523i | 0.640911 | + | 0.767616i | \(0.278557\pi\) | ||||
−0.640911 | + | 0.767616i | \(0.721443\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.8886 | −0.954523 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.9150 | −0.995596 | −0.497798 | − | 0.867293i | \(-0.665858\pi\) | ||||
−0.497798 | + | 0.867293i | \(0.665858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.138321i | 0.00573852i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.3404 | −0.800999 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 45.0433i | − 1.85914i | −0.368651 | − | 0.929568i | \(-0.620180\pi\) | ||||
0.368651 | − | 0.929568i | \(-0.379820\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 8.07118i | − 0.332567i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.4524 | −0.552425 | −0.276212 | − | 0.961097i | \(-0.589079\pi\) | ||||
−0.276212 | + | 0.961097i | \(0.589079\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 11.4996i | − 0.471439i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.8377 | −0.892263 | −0.446132 | − | 0.894967i | \(-0.647199\pi\) | ||||
−0.446132 | + | 0.894967i | \(0.647199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.3704 | −0.667764 | −0.333882 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333882 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 16.7031i | − 0.679078i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.8256 | −1.17000 | −0.584998 | − | 0.811034i | \(-0.698905\pi\) | ||||
−0.584998 | + | 0.811034i | \(0.698905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 0.367669i | − 0.0148743i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 34.6397i | − 1.39908i | −0.714592 | − | 0.699541i | \(-0.753388\pi\) | ||||
0.714592 | − | 0.699541i | \(-0.246612\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.6359 | −1.55542 | −0.777711 | − | 0.628622i | \(-0.783619\pi\) | ||||
−0.777711 | + | 0.628622i | \(0.783619\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 25.9642i | − 1.04359i | −0.853071 | − | 0.521794i | \(-0.825263\pi\) | ||||
0.853071 | − | 0.521794i | \(-0.174737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.9531 | −0.478891 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.4258 | −1.05703 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 17.0399i | − 0.679425i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.94731 | −0.236759 | −0.118379 | − | 0.992968i | \(-0.537770\pi\) | ||||
−0.118379 | + | 0.992968i | \(0.537770\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 7.57112i | − 0.300451i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.09044i | − 0.0432048i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.7290 | 1.64820 | 0.824098 | − | 0.566447i | \(-0.191682\pi\) | ||||
0.824098 | + | 0.566447i | \(0.191682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 36.9825i | − 1.45845i | −0.684275 | − | 0.729224i | \(-0.739881\pi\) | ||||
0.684275 | − | 0.729224i | \(-0.260119\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.39044 | −0.0939778 | −0.0469889 | − | 0.998895i | \(-0.514963\pi\) | ||||
−0.0469889 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.7909 | −1.40492 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 27.1588i | − 1.06280i | −0.847120 | − | 0.531402i | \(-0.821665\pi\) | ||||
0.847120 | − | 0.531402i | \(-0.178335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.5183 | 1.07523 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.3343i | 1.61016i | 0.593169 | + | 0.805078i | \(0.297877\pi\) | ||||
−0.593169 | + | 0.805078i | \(0.702123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.44768i | 0.250786i | 0.992107 | + | 0.125393i | \(0.0400192\pi\) | ||||
−0.992107 | + | 0.125393i | \(0.959981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.37121 | −0.130730 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.77869i | − 0.301192i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1460 | 0.507496 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.1564 | −1.39373 | −0.696863 | − | 0.717204i | \(-0.745421\pi\) | ||||
−0.696863 | + | 0.717204i | \(0.745421\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 47.4088i | − 1.82207i | −0.412330 | − | 0.911035i | \(-0.635285\pi\) | ||||
0.412330 | − | 0.911035i | \(-0.364715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.30202 | 0.203473 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.55646i | 0.136084i | 0.997682 | + | 0.0680420i | \(0.0216752\pi\) | ||||
−0.997682 | + | 0.0680420i | \(0.978325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.7132i | 1.32632i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.88350 | 0.338435 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.6181i | 1.58323i | 0.611023 | + | 0.791613i | \(0.290758\pi\) | ||||
−0.611023 | + | 0.791613i | \(0.709242\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −53.7845 | −2.04016 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.140561 | −0.00532414 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.8945i | 1.31795i | 0.752166 | + | 0.658973i | \(0.229009\pi\) | ||||
−0.752166 | + | 0.658973i | \(0.770991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.99537 | −0.188404 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0753369i | 0.00283334i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.2296i | 1.84886i | 0.381357 | + | 0.924428i | \(0.375457\pi\) | ||||
−0.381357 | + | 0.924428i | \(0.624543\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.3339 | −1.36072 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 8.06103i | − 0.301466i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.9969 | 0.410117 | 0.205058 | − | 0.978750i | \(-0.434262\pi\) | ||||
0.205058 | + | 0.978750i | \(0.434262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3347 | 0.571095 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.49577i | 0.278386i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.03008 | −0.334907 | −0.167454 | − | 0.985880i | \(-0.553554\pi\) | ||||
−0.167454 | + | 0.985880i | \(0.553554\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.8474i | 1.51080i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.6840i | 1.53963i | 0.638265 | + | 0.769817i | \(0.279653\pi\) | ||||
−0.638265 | + | 0.769817i | \(0.720347\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.2899 | −0.673718 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.7320i | 1.27764i | 0.769358 | + | 0.638818i | \(0.220576\pi\) | ||||
−0.769358 | + | 0.638818i | \(0.779424\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.9173 | 0.583951 | 0.291975 | − | 0.956426i | \(-0.405687\pi\) | ||||
0.291975 | + | 0.956426i | \(0.405687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.7339 | 1.56565 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.03726i | 0.147518i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.7001 | −0.499925 | −0.249963 | − | 0.968255i | \(-0.580418\pi\) | ||||
−0.249963 | + | 0.968255i | \(0.580418\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 39.9188i | − 1.45279i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 27.3072i | − 0.992496i | −0.868181 | − | 0.496248i | \(-0.834711\pi\) | ||||
0.868181 | − | 0.496248i | \(-0.165289\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3078 | −0.663657 | −0.331829 | − | 0.943340i | \(-0.607666\pi\) | ||||
−0.331829 | + | 0.943340i | \(0.607666\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 12.2335i | − 0.442883i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.4396 | 0.593598 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3631 | −0.481884 | −0.240942 | − | 0.970540i | \(-0.577456\pi\) | ||||
−0.240942 | + | 0.970540i | \(0.577456\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.3918i | 1.41682i | 0.705799 | + | 0.708412i | \(0.250588\pi\) | ||||
−0.705799 | + | 0.708412i | \(0.749412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.0124 | 1.25768 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0412066i | 0.00147638i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 32.1613i | − 1.15082i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 65.8336 | 2.34970 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.3862i | 1.29703i | 0.761203 | + | 0.648514i | \(0.224609\pi\) | ||||
−0.761203 | + | 0.648514i | \(0.775391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.1934 | −0.397993 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.03826 | −0.214425 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 33.1598i | − 1.17458i | −0.809377 | − | 0.587290i | \(-0.800195\pi\) | ||||
0.809377 | − | 0.587290i | \(-0.199805\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.24519 | −0.0440516 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 34.8333i | − 1.22924i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.1761i | 0.534888i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.9173 | −1.57921 | −0.789604 | − | 0.613616i | \(-0.789714\pi\) | ||||
−0.789604 | + | 0.613616i | \(0.789714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 37.5222i | − 1.31758i | −0.752325 | − | 0.658792i | \(-0.771068\pi\) | ||||
0.752325 | − | 0.658792i | \(-0.228932\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.20374 | 0.0421650 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.9747 | 0.418943 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 0.214362i | − 0.00748129i | −0.999993 | − | 0.00374065i | \(-0.998809\pi\) | ||||
0.999993 | − | 0.00374065i | \(-0.00119069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.84153 | 0.168765 | 0.0843825 | − | 0.996433i | \(-0.473108\pi\) | ||||
0.0843825 | + | 0.996433i | \(0.473108\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 9.13088i | − 0.317512i | −0.987318 | − | 0.158756i | \(-0.949252\pi\) | ||||
0.987318 | − | 0.158756i | \(-0.0507483\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 22.8115i | − 0.792275i | −0.918191 | − | 0.396138i | \(-0.870350\pi\) | ||||
0.918191 | − | 0.396138i | \(-0.129650\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.69300 | −0.127955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.9447i | 1.55538i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.9537 | 1.31031 | 0.655154 | − | 0.755496i | \(-0.272604\pi\) | ||||
0.655154 | + | 0.755496i | \(0.272604\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4526 | 0.912157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 36.7781i | − 1.26521i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.36404 | −0.184311 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.4876i | 0.770864i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.9465i | 1.23078i | 0.788221 | + | 0.615392i | \(0.211002\pi\) | ||||
−0.788221 | + | 0.615392i | \(0.788998\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.9904 | 1.26357 | 0.631783 | − | 0.775145i | \(-0.282323\pi\) | ||||
0.631783 | + | 0.775145i | \(0.282323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 0.924367i | − 0.0315390i | −0.999876 | − | 0.0157695i | \(-0.994980\pi\) | ||||
0.999876 | − | 0.0157695i | \(-0.00501979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.2057 | 0.381445 | 0.190723 | − | 0.981644i | \(-0.438917\pi\) | ||||
0.190723 | + | 0.981644i | \(0.438917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 43.4369 | 1.47690 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 12.3003i | − 0.417259i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.40098 | 0.284656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.945386i | 0.0319599i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 38.6354i | − 1.30463i | −0.757950 | − | 0.652313i | \(-0.773799\pi\) | ||||
0.757950 | − | 0.652313i | \(-0.226201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.0860 | −1.58637 | −0.793184 | − | 0.608982i | \(-0.791578\pi\) | ||||
−0.793184 | + | 0.608982i | \(0.791578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.23864i | − 0.0753362i | −0.999290 | − | 0.0376681i | \(-0.988007\pi\) | ||||
0.999290 | − | 0.0376681i | \(-0.0119930\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.5911 | 1.90014 | 0.950071 | − | 0.312032i | \(-0.101010\pi\) | ||||
0.950071 | + | 0.312032i | \(0.101010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.43139 | −0.0815463 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.365036i | 0.0122155i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.1847 | 1.10924 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.8989i | 0.396852i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 30.0858i | − 1.00230i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.6721 | 0.687165 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0996i | 1.23187i | 0.787797 | + | 0.615935i | \(0.211222\pi\) | ||||
−0.787797 | + | 0.615935i | \(0.788778\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.3701 | 1.50318 | 0.751589 | − | 0.659632i | \(-0.229288\pi\) | ||||
0.751589 | + | 0.659632i | \(0.229288\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.328377 | 0.0108677 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 8.83723i | − 0.291831i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.8038 | −0.950148 | −0.475074 | − | 0.879946i | \(-0.657579\pi\) | ||||
−0.475074 | + | 0.879946i | \(0.657579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.7724i | 0.486240i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 21.6697i | − 0.712495i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.5518 | −1.49451 | −0.747254 | − | 0.664539i | \(-0.768628\pi\) | ||||
−0.747254 | + | 0.664539i | \(0.768628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.08263i | 0.0354818i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.3003 | −0.892817 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.3973 | −1.41773 | −0.708864 | − | 0.705346i | \(-0.750792\pi\) | ||||
−0.708864 | + | 0.705346i | \(0.750792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.5629i | 0.572534i | 0.958150 | + | 0.286267i | \(0.0924145\pi\) | ||||
−0.958150 | + | 0.286267i | \(0.907586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.185499 | 0.00604068 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 33.8968i | − 1.10150i | −0.834671 | − | 0.550749i | \(-0.814342\pi\) | ||||
0.834671 | − | 0.550749i | \(-0.185658\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.9997i | 0.519373i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.7021 | −1.38326 | −0.691628 | − | 0.722254i | \(-0.743106\pi\) | ||||
−0.691628 | + | 0.722254i | \(0.743106\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 30.5520i | − 0.988639i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1478 | 0.359982 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.5794 | 0.792883 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 54.3498i | − 1.74958i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.9796 | −0.771132 | −0.385566 | − | 0.922680i | \(-0.625994\pi\) | ||||
−0.385566 | + | 0.922680i | \(0.625994\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 13.2383i | − 0.424837i | −0.977179 | − | 0.212418i | \(-0.931866\pi\) | ||||
0.977179 | − | 0.212418i | \(-0.0681340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.2724i | 0.553726i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.7224 | 1.59076 | 0.795380 | − | 0.606110i | \(-0.207271\pi\) | ||||
0.795380 | + | 0.606110i | \(0.207271\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.3769i | 0.906929i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.8135 | −1.07848 | −0.539241 | − | 0.842151i | \(-0.681289\pi\) | ||||
−0.539241 | + | 0.842151i | \(0.681289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 86.2150 | 2.74704 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 53.9065i | − 1.71413i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.2781 | −1.15241 | −0.576206 | − | 0.817304i | \(-0.695468\pi\) | ||||
−0.576206 | + | 0.817304i | \(0.695468\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.9532i | 0.917879i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 22.7054i | − 0.719088i | −0.933128 | − | 0.359544i | \(-0.882932\pi\) | ||||
0.933128 | − | 0.359544i | \(-0.117068\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.c.g.3025.3 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.g.3025.21 | 24 | ||
4.3 | odd | 2 | 1512.2.c.f.757.23 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.f.757.24 | yes | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.g.3025.22 | 24 | ||
12.11 | even | 2 | 1512.2.c.f.757.2 | yes | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.g.3025.4 | 24 | ||
24.11 | even | 2 | 1512.2.c.f.757.1 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.1 | ✓ | 24 | 24.11 | even | 2 | ||
1512.2.c.f.757.2 | yes | 24 | 12.11 | even | 2 | ||
1512.2.c.f.757.23 | yes | 24 | 4.3 | odd | 2 | ||
1512.2.c.f.757.24 | yes | 24 | 8.3 | odd | 2 | ||
6048.2.c.g.3025.3 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.g.3025.4 | 24 | 24.5 | odd | 2 | inner | ||
6048.2.c.g.3025.21 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.g.3025.22 | 24 | 8.5 | even | 2 | inner |