Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(77.2951891566\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.45753625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 41x^{2} - 30x - 20 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.05921\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.89070 | −1.09159 | −0.545797 | − | 0.837917i | \(-0.683773\pi\) | ||||
−0.545797 | + | 0.837917i | \(0.683773\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.74075 | −1.03591 | −0.517953 | − | 0.855409i | \(-0.673306\pi\) | ||||
−0.517953 | + | 0.855409i | \(0.673306\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.574737 | 0.191579 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.196821 | −0.0545884 | −0.0272942 | − | 0.999627i | \(-0.508689\pi\) | ||||
−0.0272942 | + | 0.999627i | \(0.508689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.89070 | 0.488176 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.46809 | 0.356063 | 0.178032 | − | 0.984025i | \(-0.443027\pi\) | ||||
0.178032 | + | 0.984025i | \(0.443027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.68154 | −0.615187 | −0.307593 | − | 0.951518i | \(-0.599524\pi\) | ||||
−0.307593 | + | 0.951518i | \(0.599524\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.18193 | 1.13079 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.81736 | −0.378945 | −0.189473 | − | 0.981886i | \(-0.560678\pi\) | ||||
−0.189473 | + | 0.981886i | \(0.560678\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.58544 | 0.882468 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.37946 | −0.256160 | −0.128080 | − | 0.991764i | \(-0.540881\pi\) | ||||
−0.128080 | + | 0.991764i | \(0.540881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.90411 | −1.06041 | −0.530205 | − | 0.847870i | \(-0.677885\pi\) | ||||
−0.530205 | + | 0.847870i | \(0.677885\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.74075 | 0.463271 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.57623 | 0.752328 | 0.376164 | − | 0.926553i | \(-0.377243\pi\) | ||||
0.376164 | + | 0.926553i | \(0.377243\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.372129 | 0.0595884 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.23428 | −0.192762 | −0.0963812 | − | 0.995344i | \(-0.530727\pi\) | ||||
−0.0963812 | + | 0.995344i | \(0.530727\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96514 | 0.452180 | 0.226090 | − | 0.974106i | \(-0.427406\pi\) | ||||
0.226090 | + | 0.974106i | \(0.427406\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.574737 | −0.0856768 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.30107 | −1.35670 | −0.678350 | − | 0.734739i | \(-0.737305\pi\) | ||||
−0.678350 | + | 0.734739i | \(0.737305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.511708 | 0.0731012 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.77571 | −0.388677 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.69388 | 0.370032 | 0.185016 | − | 0.982735i | \(-0.440766\pi\) | ||||
0.185016 | + | 0.982735i | \(0.440766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.06997 | 0.671535 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.2092 | −1.84988 | −0.924942 | − | 0.380108i | \(-0.875887\pi\) | ||||
−0.924942 | + | 0.380108i | \(0.875887\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.54027 | −0.965433 | −0.482716 | − | 0.875777i | \(-0.660350\pi\) | ||||
−0.482716 | + | 0.875777i | \(0.660350\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.57521 | −0.198458 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.196821 | 0.0244127 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6500 | −1.30111 | −0.650553 | − | 0.759461i | \(-0.725463\pi\) | ||||
−0.650553 | + | 0.759461i | \(0.725463\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.43607 | 0.413655 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.87672 | 0.816116 | 0.408058 | − | 0.912956i | \(-0.366206\pi\) | ||||
0.408058 | + | 0.912956i | \(0.366206\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4314 | −1.22090 | −0.610452 | − | 0.792053i | \(-0.709012\pi\) | ||||
−0.610452 | + | 0.792053i | \(0.709012\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.89070 | −0.218319 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.87328 | 0.210761 | 0.105380 | − | 0.994432i | \(-0.466394\pi\) | ||||
0.105380 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3939 | −1.15488 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.79397 | −0.635971 | −0.317986 | − | 0.948096i | \(-0.603006\pi\) | ||||
−0.317986 | + | 0.948096i | \(0.603006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.46809 | −0.159236 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.60815 | 0.279623 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.3060 | 1.83443 | 0.917214 | − | 0.398396i | \(-0.130433\pi\) | ||||
0.917214 | + | 0.398396i | \(0.130433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.539438 | 0.0565484 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.1629 | 1.15754 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.68154 | 0.275120 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.3188 | −1.86000 | −0.929998 | − | 0.367564i | \(-0.880192\pi\) | ||||
−0.929998 | + | 0.367564i | \(0.880192\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00039 | −0.497558 | −0.248779 | − | 0.968560i | \(-0.580029\pi\) | ||||
−0.248779 | + | 0.968560i | \(0.580029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.17856 | −0.904391 | −0.452195 | − | 0.891919i | \(-0.649359\pi\) | ||||
−0.452195 | + | 0.891919i | \(0.649359\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.18193 | −0.505704 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.8116 | −1.62524 | −0.812621 | − | 0.582792i | \(-0.801960\pi\) | ||||
−0.812621 | + | 0.582792i | \(0.801960\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.91076 | 0.949279 | 0.474639 | − | 0.880180i | \(-0.342578\pi\) | ||||
0.474639 | + | 0.880180i | \(0.342578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.65227 | −0.821238 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.6713 | 1.19202 | 0.596009 | − | 0.802978i | \(-0.296752\pi\) | ||||
0.596009 | + | 0.802978i | \(0.296752\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.81736 | 0.169470 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.113120 | −0.0104580 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.02366 | −0.368848 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.33365 | 0.210418 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4404 | 0.926437 | 0.463218 | − | 0.886244i | \(-0.346695\pi\) | ||||
0.463218 | + | 0.886244i | \(0.346695\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.60619 | −0.493597 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.9537 | −1.83073 | −0.915367 | − | 0.402621i | \(-0.868099\pi\) | ||||
−0.915367 | + | 0.402621i | \(0.868099\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.34942 | 0.637276 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.58544 | −0.394652 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.96083 | 0.252961 | 0.126481 | − | 0.991969i | \(-0.459632\pi\) | ||||
0.126481 | + | 0.991969i | \(0.459632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4253 | 1.39318 | 0.696589 | − | 0.717470i | \(-0.254700\pi\) | ||||
0.696589 | + | 0.717470i | \(0.254700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.5855 | 1.48097 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.37946 | 0.114558 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.967485 | −0.0797968 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.1836 | 1.57158 | 0.785790 | − | 0.618494i | \(-0.212257\pi\) | ||||
0.785790 | + | 0.618494i | \(0.212257\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.04992 | −0.736472 | −0.368236 | − | 0.929732i | \(-0.620038\pi\) | ||||
−0.368236 | + | 0.929732i | \(0.620038\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.843764 | 0.0682142 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.90411 | 0.474230 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.1894 | −1.45167 | −0.725837 | − | 0.687867i | \(-0.758547\pi\) | ||||
−0.725837 | + | 0.687867i | \(0.758547\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.09331 | −0.403925 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.98092 | 0.392552 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.34677 | −0.497117 | −0.248559 | − | 0.968617i | \(-0.579957\pi\) | ||||
−0.248559 | + | 0.968617i | \(0.579957\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.9261 | 1.07763 | 0.538817 | − | 0.842423i | \(-0.318871\pi\) | ||||
0.538817 | + | 0.842423i | \(0.318871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9613 | −0.997020 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.54118 | −0.117857 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.2172 | −1.84120 | −0.920598 | − | 0.390511i | \(-0.872299\pi\) | ||||
−0.920598 | + | 0.390511i | \(0.872299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.74075 | −0.207181 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.8654 | 2.01932 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.41972 | −0.106115 | −0.0530573 | − | 0.998591i | \(-0.516897\pi\) | ||||
−0.0530573 | + | 0.998591i | \(0.516897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.62889 | 0.418392 | 0.209196 | − | 0.977874i | \(-0.432915\pi\) | ||||
0.209196 | + | 0.977874i | \(0.432915\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.2564 | 1.05386 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.57623 | −0.336451 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.5675 | −0.914154 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.24259 | 0.162268 | 0.0811341 | − | 0.996703i | \(-0.474146\pi\) | ||||
0.0811341 | + | 0.996703i | \(0.474146\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.30699 | 0.669932 | 0.334966 | − | 0.942230i | \(-0.391275\pi\) | ||||
0.334966 | + | 0.942230i | \(0.391275\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.372129 | −0.0266487 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.3935 | −1.02549 | −0.512747 | − | 0.858540i | \(-0.671372\pi\) | ||||
−0.512747 | + | 0.858540i | \(0.671372\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.00915 | −0.213313 | −0.106657 | − | 0.994296i | \(-0.534015\pi\) | ||||
−0.106657 | + | 0.994296i | \(0.534015\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.1360 | 1.42028 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.78076 | 0.265358 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.23428 | 0.0862059 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.04450 | −0.0725980 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6428 | 1.07689 | 0.538447 | − | 0.842659i | \(-0.319011\pi\) | ||||
0.538447 | + | 0.842659i | \(0.319011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.0018 | −0.890868 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.96514 | −0.202221 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.1817 | 1.09848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.7226 | 1.33273 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.288950 | −0.0194369 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.21134 | −0.348977 | −0.174488 | − | 0.984659i | \(-0.555827\pi\) | ||||
−0.174488 | + | 0.984659i | \(0.555827\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.574737 | 0.0383158 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7838 | −0.914861 | −0.457430 | − | 0.889245i | \(-0.651230\pi\) | ||||
−0.457430 | + | 0.889245i | \(0.651230\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.5800 | 1.62429 | 0.812147 | − | 0.583453i | \(-0.198299\pi\) | ||||
0.812147 | + | 0.583453i | \(0.198299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.02886 | −0.525988 | −0.262994 | − | 0.964797i | \(-0.584710\pi\) | ||||
−0.262994 | + | 0.964797i | \(0.584710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.30107 | 0.606735 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.54181 | −0.230066 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.36215 | −0.0881102 | −0.0440551 | − | 0.999029i | \(-0.514028\pi\) | ||||
−0.0440551 | + | 0.999029i | \(0.514028\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.94349 | 0.189607 | 0.0948035 | − | 0.995496i | \(-0.469778\pi\) | ||||
0.0948035 | + | 0.995496i | \(0.469778\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.89538 | 0.378189 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.511708 | −0.0326918 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.527783 | 0.0335820 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.9547 | 0.694223 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7107 | −0.991651 | −0.495826 | − | 0.868422i | \(-0.665134\pi\) | ||||
−0.495826 | + | 0.868422i | \(0.665134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.77571 | 0.173821 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.90470 | −0.555460 | −0.277730 | − | 0.960659i | \(-0.589582\pi\) | ||||
−0.277730 | + | 0.960659i | \(0.589582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.5423 | −0.779341 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.792829 | −0.0490749 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.671733 | 0.0414208 | 0.0207104 | − | 0.999786i | \(-0.493407\pi\) | ||||
0.0207104 | + | 0.999786i | \(0.493407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.69388 | −0.165484 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.7203 | −2.00245 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.7105 | 1.62857 | 0.814283 | − | 0.580468i | \(-0.197130\pi\) | ||||
0.814283 | + | 0.580468i | \(0.197130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3089 | 1.35517 | 0.677584 | − | 0.735446i | \(-0.263027\pi\) | ||||
0.677584 | + | 0.735446i | \(0.263027\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.01991 | −0.0617280 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.9001 | −1.37593 | −0.687967 | − | 0.725742i | \(-0.741497\pi\) | ||||
−0.687967 | + | 0.725742i | \(0.741497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.39331 | −0.203152 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.3433 | 1.69082 | 0.845411 | − | 0.534117i | \(-0.179356\pi\) | ||||
0.845411 | + | 0.534117i | \(0.179356\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.0561 | −1.84609 | −0.923046 | − | 0.384690i | \(-0.874308\pi\) | ||||
−0.923046 | + | 0.384690i | \(0.874308\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.06997 | −0.300319 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.38286 | 0.199684 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8447 | −0.873219 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.6354 | 2.03036 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.84981 | −0.458591 | −0.229295 | − | 0.973357i | \(-0.573642\pi\) | ||||
−0.229295 | + | 0.973357i | \(0.573642\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.2092 | 0.827293 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.357695 | 0.0206860 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.12671 | −0.468416 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.45423 | 0.543131 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.54027 | 0.431755 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0601 | 0.574160 | 0.287080 | − | 0.957907i | \(-0.407315\pi\) | ||||
0.287080 | + | 0.957907i | \(0.407315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.3539 | 0.987228 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.3650 | 1.26820 | 0.634101 | − | 0.773250i | \(-0.281370\pi\) | ||||
0.634101 | + | 0.773250i | \(0.281370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.1486 | 1.02582 | 0.512910 | − | 0.858442i | \(-0.328567\pi\) | ||||
0.512910 | + | 0.858442i | \(0.328567\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.57521 | 0.0887531 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.51660 | −0.141346 | −0.0706732 | − | 0.997500i | \(-0.522515\pi\) | ||||
−0.0706732 | + | 0.997500i | \(0.522515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.7857 | 1.77411 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.93673 | −0.219045 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.196821 | −0.0109177 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.7383 | −1.03623 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.4919 | 1.40541 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.54546 | 0.414736 | 0.207368 | − | 0.978263i | \(-0.433510\pi\) | ||||
0.207368 | + | 0.978263i | \(0.433510\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.63013 | 0.144130 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.6500 | 0.581872 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0017 | 1.25298 | 0.626491 | − | 0.779429i | \(-0.284490\pi\) | ||||
0.626491 | + | 0.779429i | \(0.284490\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.9576 | −1.30120 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7828 | 0.960180 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.43607 | −0.184992 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.07466 | 0.218739 | 0.109370 | − | 0.994001i | \(-0.465117\pi\) | ||||
0.109370 | + | 0.994001i | \(0.465117\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.8075 | 1.27439 | 0.637193 | − | 0.770704i | \(-0.280095\pi\) | ||||
0.637193 | + | 0.770704i | \(0.280095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.902511 | −0.0481725 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.00060 | −0.372605 | −0.186302 | − | 0.982492i | \(-0.559650\pi\) | ||||
−0.186302 | + | 0.982492i | \(0.559650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.87672 | −0.364978 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.60752 | 0.402632 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.4700 | 1.92482 | 0.962408 | − | 0.271609i | \(-0.0875557\pi\) | ||||
0.962408 | + | 0.271609i | \(0.0875557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.8094 | −0.621545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4314 | 0.546005 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.1854 | 1.52346 | 0.761732 | − | 0.647892i | \(-0.224349\pi\) | ||||
0.761732 | + | 0.647892i | \(0.224349\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.709387 | −0.0369292 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.38324 | −0.383319 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0215 | −1.03667 | −0.518337 | − | 0.855176i | \(-0.673449\pi\) | ||||
−0.518337 | + | 0.855176i | \(0.673449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.89070 | 0.0976352 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.271508 | 0.0139833 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.18971 | −0.420677 | −0.210338 | − | 0.977629i | \(-0.567457\pi\) | ||||
−0.210338 | + | 0.977629i | \(0.567457\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.7397 | −1.01129 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.2852 | −1.03653 | −0.518263 | − | 0.855221i | \(-0.673421\pi\) | ||||
−0.518263 | + | 0.855221i | \(0.673421\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.70418 | 0.0866282 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0260 | 0.660443 | 0.330221 | − | 0.943904i | \(-0.392877\pi\) | ||||
0.330221 | + | 0.943904i | \(0.392877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.66804 | −0.134928 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 39.6171 | 1.99842 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.87328 | −0.0942552 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.593277 | −0.0297757 | −0.0148878 | − | 0.999889i | \(-0.504739\pi\) | ||||
−0.0148878 | + | 0.999889i | \(0.504739\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.8955 | −0.695647 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.04664 | −0.451768 | −0.225884 | − | 0.974154i | \(-0.572527\pi\) | ||||
−0.225884 | + | 0.974154i | \(0.572527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.16205 | 0.0578860 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.3939 | 0.516476 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7566 | 0.878008 | 0.439004 | − | 0.898485i | \(-0.355331\pi\) | ||||
0.439004 | + | 0.898485i | \(0.355331\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.59804 | −0.276131 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.9439 | 1.91631 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.79397 | 0.284415 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.0553 | −1.52079 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.43701 | 0.461028 | 0.230514 | − | 0.973069i | \(-0.425959\pi\) | ||||
0.230514 | + | 0.973069i | \(0.425959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2461 | −1.18168 | −0.590842 | − | 0.806787i | \(-0.701204\pi\) | ||||
−0.590842 | + | 0.806787i | \(0.701204\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.34567 | −0.259915 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.46809 | 0.0712126 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.6660 | 1.00010 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.61485 | 0.463131 | 0.231565 | − | 0.972819i | \(-0.425615\pi\) | ||||
0.231565 | + | 0.972819i | \(0.425615\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.44277 | −0.453791 | −0.226895 | − | 0.973919i | \(-0.572858\pi\) | ||||
−0.226895 | + | 0.973919i | \(0.572858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.60815 | −0.125051 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.87331 | 0.233122 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8211 | 0.850555 | 0.425278 | − | 0.905063i | \(-0.360176\pi\) | ||||
0.425278 | + | 0.905063i | \(0.360176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.294098 | 0.0140047 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.6167 | 0.836995 | 0.418497 | − | 0.908218i | \(-0.362557\pi\) | ||||
0.418497 | + | 0.908218i | \(0.362557\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.3060 | −0.820381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.2703 | −1.71553 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.01122 | −0.378073 | −0.189036 | − | 0.981970i | \(-0.560536\pi\) | ||||
−0.189036 | + | 0.981970i | \(0.560536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.1107 | 0.803929 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.539438 | −0.0252892 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.21578 | −0.384318 | −0.192159 | − | 0.981364i | \(-0.561549\pi\) | ||||
−0.192159 | + | 0.981364i | \(0.561549\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.73182 | 0.314214 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.47559 | −0.255024 | −0.127512 | − | 0.991837i | \(-0.540699\pi\) | ||||
−0.127512 | + | 0.991837i | \(0.540699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.1843 | −1.26336 | −0.631681 | − | 0.775228i | \(-0.717635\pi\) | ||||
−0.631681 | + | 0.775228i | \(0.717635\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.1629 | −0.517667 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.05376 | −0.326409 | −0.163205 | − | 0.986592i | \(-0.552183\pi\) | ||||
−0.163205 | + | 0.986592i | \(0.552183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.1890 | 1.34782 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.3907 | 1.58464 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.68154 | −0.123037 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.54827 | 0.0708905 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.31048 | −0.242642 | −0.121321 | − | 0.992613i | \(-0.538713\pi\) | ||||
−0.121321 | + | 0.992613i | \(0.538713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.900700 | −0.0410684 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.41742 | −0.428507 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.3188 | 0.831816 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8480 | −0.536884 | −0.268442 | − | 0.963296i | \(-0.586509\pi\) | ||||
−0.268442 | + | 0.963296i | \(0.586509\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.9998 | 0.542651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.3787 | 1.73201 | 0.866003 | − | 0.500038i | \(-0.166681\pi\) | ||||
0.866003 | + | 0.500038i | \(0.166681\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.02517 | −0.0912091 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.8474 | −0.845420 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.6869 | −0.478411 | −0.239205 | − | 0.970969i | \(-0.576887\pi\) | ||||
−0.239205 | + | 0.970969i | \(0.576887\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.3300 | −1.17634 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.5077 | 1.58321 | 0.791606 | − | 0.611032i | \(-0.209245\pi\) | ||||
0.791606 | + | 0.611032i | \(0.209245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.00039 | 0.222515 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.5058 | 1.08834 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.3976 | −0.948433 | −0.474216 | − | 0.880408i | \(-0.657269\pi\) | ||||
−0.474216 | + | 0.880408i | \(0.657269\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.5899 | 1.26474 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.2960 | −0.542883 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.17856 | 0.404456 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.7873 | 2.00984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.3712 | −0.848669 | −0.424334 | − | 0.905506i | \(-0.639492\pi\) | ||||
−0.424334 | + | 0.905506i | \(0.639492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.894305 | 0.0391052 | 0.0195526 | − | 0.999809i | \(-0.493776\pi\) | ||||
0.0195526 | + | 0.999809i | \(0.493776\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.18193 | 0.226158 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.66774 | −0.377573 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.6972 | −0.856400 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.16657 | −0.354399 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.242933 | 0.0105226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.8116 | 0.726831 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.68425 | 0.115834 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.1527 | 1.72630 | 0.863150 | − | 0.504948i | \(-0.168488\pi\) | ||||
0.863150 | + | 0.504948i | \(0.168488\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.6425 | −0.456715 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.91076 | −0.424530 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.49729 | −0.192290 | −0.0961451 | − | 0.995367i | \(-0.530651\pi\) | ||||
−0.0961451 | + | 0.995367i | \(0.530651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.33367 | −0.184957 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.69908 | 0.157586 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.13420 | −0.218329 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.65227 | 0.367269 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.9736 | 1.01580 | 0.507898 | − | 0.861417i | \(-0.330423\pi\) | ||||
0.507898 | + | 0.861417i | \(0.330423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.583603 | −0.0246838 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.3442 | 0.773116 | 0.386558 | − | 0.922265i | \(-0.373664\pi\) | ||||
0.386558 | + | 0.922265i | \(0.373664\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.6713 | −0.533087 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 28.4870 | 1.19634 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.70511 | 0.113404 | 0.0567020 | − | 0.998391i | \(-0.481942\pi\) | ||||
0.0567020 | + | 0.998391i | \(0.481942\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6593 | 0.571626 | 0.285813 | − | 0.958285i | \(-0.407736\pi\) | ||||
0.285813 | + | 0.958285i | \(0.407736\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.24006 | −0.177131 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.81736 | −0.0757891 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.23640 | 0.342886 | 0.171443 | − | 0.985194i | \(-0.445157\pi\) | ||||
0.171443 | + | 0.985194i | \(0.445157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.5967 | −0.731294 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.8798 | 0.658806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.113120 | 0.00467696 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.3766 | −0.923581 | −0.461791 | − | 0.886989i | \(-0.652793\pi\) | ||||
−0.461791 | + | 0.886989i | \(0.652793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.8321 | 0.652350 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.2138 | 1.11942 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.5253 | 1.82844 | 0.914218 | − | 0.405223i | \(-0.132806\pi\) | ||||
0.914218 | + | 0.405223i | \(0.132806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.02366 | 0.164954 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.68940 | 0.232851 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.9292 | −1.63146 | −0.815732 | − | 0.578430i | \(-0.803666\pi\) | ||||
−0.815732 | + | 0.578430i | \(0.803666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.9828 | −1.26381 | −0.631907 | − | 0.775044i | \(-0.717727\pi\) | ||||
−0.631907 | + | 0.775044i | \(0.717727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.12096 | −0.249265 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.5634 | 1.07817 | 0.539087 | − | 0.842250i | \(-0.318769\pi\) | ||||
0.539087 | + | 0.842250i | \(0.318769\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.14828 | −0.289663 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.83065 | 0.0740601 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.2647 | −1.14160 | −0.570801 | − | 0.821089i | \(-0.693367\pi\) | ||||
−0.570801 | + | 0.821089i | \(0.693367\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.33365 | −0.0941020 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.98722 | −0.160520 | −0.0802598 | − | 0.996774i | \(-0.525575\pi\) | ||||
−0.0802598 | + | 0.996774i | \(0.525575\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.6186 | −1.19047 | −0.595236 | − | 0.803551i | \(-0.702941\pi\) | ||||
−0.595236 | + | 0.803551i | \(0.702941\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.33338 | −0.334407 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −47.4313 | −1.90029 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.71831 | 0.267876 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.7749 | 1.38437 | 0.692183 | − | 0.721722i | \(-0.256649\pi\) | ||||
0.692183 | + | 0.721722i | \(0.256649\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.5758 | −1.17553 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4404 | −0.414315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.100715 | −0.00399047 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.95231 | 0.156351 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.0319 | 1.06770 | 0.533848 | − | 0.845580i | \(-0.320745\pi\) | ||||
0.533848 | + | 0.845580i | \(0.320745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3855 | 1.23772 | 0.618861 | − | 0.785500i | \(-0.287594\pi\) | ||||
0.618861 | + | 0.785500i | \(0.287594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.60619 | 0.220743 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.1624 | 1.69689 | 0.848444 | − | 0.529284i | \(-0.177540\pi\) | ||||
0.848444 | + | 0.529284i | \(0.177540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.5947 | −1.19910 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.89228 | 0.387115 | 0.193557 | − | 0.981089i | \(-0.437997\pi\) | ||||
0.193557 | + | 0.981089i | \(0.437997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.9537 | 0.818729 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.99532 | −0.233900 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.3139 | 0.479683 | 0.239842 | − | 0.970812i | \(-0.422904\pi\) | ||||
0.239842 | + | 0.970812i | \(0.422904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.4390 | −1.02836 | −0.514179 | − | 0.857683i | \(-0.671903\pi\) | ||||
−0.514179 | + | 0.857683i | \(0.671903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.546318 | 0.0212172 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.34942 | −0.284998 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.50698 | 0.0970706 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.85306 | 0.380941 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.6219 | 0.563632 | 0.281816 | − | 0.959469i | \(-0.409063\pi\) | ||||
0.281816 | + | 0.959469i | \(0.409063\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.58544 | 0.176494 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.1645 | 1.12088 | 0.560441 | − | 0.828195i | \(-0.310632\pi\) | ||||
0.560441 | + | 0.828195i | \(0.310632\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.2074 | 1.92678 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.0609 | 0.998657 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.7011 | −0.983427 | −0.491713 | − | 0.870757i | \(-0.663629\pi\) | ||||
−0.491713 | + | 0.870757i | \(0.663629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.96083 | −0.113128 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −46.4734 | −1.77307 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.530212 | −0.0201995 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.87725 | −0.0714139 | −0.0357070 | − | 0.999362i | \(-0.511368\pi\) | ||||
−0.0357070 | + | 0.999362i | \(0.511368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.4253 | −0.623048 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.81203 | −0.0686356 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.1801 | 0.574166 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.4735 | −1.49089 | −0.745447 | − | 0.666565i | \(-0.767764\pi\) | ||||
−0.745447 | + | 0.666565i | \(0.767764\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.2713 | −0.462822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.5855 | −0.662308 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7048 | 0.515423 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.7390 | −1.30465 | −0.652325 | − | 0.757939i | \(-0.726206\pi\) | ||||
−0.652325 | + | 0.757939i | \(0.726206\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.07665 | 0.0403774 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.7299 | 0.401837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.57542 | 0.0961807 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.7972 | −0.812897 | −0.406449 | − | 0.913674i | \(-0.633233\pi\) | ||||
−0.406449 | + | 0.913674i | \(0.633233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.1561 | 0.936864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.56525 | −0.206974 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.37946 | −0.0512320 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.0916 | −1.22730 | −0.613650 | − | 0.789578i | \(-0.710299\pi\) | ||||
−0.613650 | + | 0.789578i | \(0.710299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0353 | 0.742047 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.35308 | 0.161005 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.8016 | 1.39624 | 0.698118 | − | 0.715983i | \(-0.254021\pi\) | ||||
0.698118 | + | 0.715983i | \(0.254021\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.967485 | 0.0356862 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.8114 | 1.02306 | 0.511529 | − | 0.859266i | \(-0.329079\pi\) | ||||
0.511529 | + | 0.859266i | \(0.329079\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.997878 | −0.0366580 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.6766 | 0.831925 | 0.415963 | − | 0.909382i | \(-0.363445\pi\) | ||||
0.415963 | + | 0.909382i | \(0.363445\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.1836 | −0.702832 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.33001 | −0.121839 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.0765 | 1.68360 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.70546 | −0.0622330 | −0.0311165 | − | 0.999516i | \(-0.509906\pi\) | ||||
−0.0311165 | + | 0.999516i | \(0.509906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.7042 | 1.08248 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.04992 | 0.329360 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.27807 | −0.300872 | −0.150436 | − | 0.988620i | \(-0.548068\pi\) | ||||
−0.150436 | + | 0.988620i | \(0.548068\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.2064 | 0.514982 | 0.257491 | − | 0.966281i | \(-0.417104\pi\) | ||||
0.257491 | + | 0.966281i | \(0.417104\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.1629 | −0.983364 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.843764 | −0.0305063 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.79668 | 0.100982 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0174 | 1.11852 | 0.559258 | − | 0.828993i | \(-0.311086\pi\) | ||||
0.559258 | + | 0.828993i | \(0.311086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.8361 | 0.606337 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2223 | −0.439607 | −0.219803 | − | 0.975544i | \(-0.570542\pi\) | ||||
−0.219803 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.90411 | −0.212082 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.7137 | 0.850725 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.30977 | 0.118585 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.32544 | −0.226053 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.1894 | 0.649208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.68049 | 0.273780 | 0.136890 | − | 0.990586i | \(-0.456289\pi\) | ||||
0.136890 | + | 0.990586i | \(0.456289\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.27004 | −0.0452147 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.7289 | −1.23482 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.48408 | 0.0527014 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.09331 | 0.180641 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.14757 | −0.0406491 | −0.0203245 | − | 0.999793i | \(-0.506470\pi\) | ||||
−0.0203245 | + | 0.999793i | \(0.506470\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.6548 | −0.483071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.94637 | 0.351438 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.98092 | −0.175554 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −50.5014 | −1.77773 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.494854 | −0.0173982 | −0.00869908 | − | 0.999962i | \(-0.502769\pi\) | ||||
−0.00869908 | + | 0.999962i | \(0.502769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.7818 | 0.835091 | 0.417546 | − | 0.908656i | \(-0.362890\pi\) | ||||
0.417546 | + | 0.908656i | \(0.362890\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42.1793 | −1.47929 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.34677 | 0.222318 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.95113 | −0.278175 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.310035 | 0.0108335 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.7817 | −1.45819 | −0.729096 | − | 0.684412i | \(-0.760059\pi\) | ||||
−0.729096 | + | 0.684412i | \(0.760059\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3527 | 0.814023 | 0.407011 | − | 0.913423i | \(-0.366571\pi\) | ||||
0.407011 | + | 0.913423i | \(0.366571\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.2469 | −0.669280 | −0.334640 | − | 0.942346i | \(-0.608615\pi\) | ||||
−0.334640 | + | 0.942346i | \(0.608615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6334 | 0.612434 | 0.306217 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306217 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.2972 | 1.50196 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.751232 | 0.0260286 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9261 | −0.481932 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.0729 | −0.935778 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.8854 | 1.03176 | 0.515879 | − | 0.856662i | \(-0.327465\pi\) | ||||
0.515879 | + | 0.856662i | \(0.327465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0971 | −0.934382 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −53.5887 | −1.84569 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.9613 | 0.445881 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 58.7176 | 2.01518 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.31666 | −0.285091 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.78136 | 0.300668 | 0.150334 | − | 0.988635i | \(-0.451965\pi\) | ||||
0.150334 | + | 0.988635i | \(0.451965\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.54118 | 0.0527072 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.6711 | −0.876909 | −0.438454 | − | 0.898753i | \(-0.644474\pi\) | ||||
−0.438454 | + | 0.898753i | \(0.644474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.5338 | 1.41711 | 0.708557 | − | 0.705654i | \(-0.249346\pi\) | ||||
0.708557 | + | 0.705654i | \(0.249346\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.39596 | −0.217974 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.83297 | 0.0964353 | 0.0482177 | − | 0.998837i | \(-0.484646\pi\) | ||||
0.0482177 | + | 0.998837i | \(0.484646\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.2172 | 0.823408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.0669 | 0.953201 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.09615 | 0.0710253 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.5285 | −0.356336 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.74075 | 0.0926542 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.0319 | −0.879035 | −0.439518 | − | 0.898234i | \(-0.644851\pi\) | ||||
−0.439518 | + | 0.898234i | \(0.644851\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.8416 | 0.500595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.6862 | −1.26968 | −0.634841 | − | 0.772643i | \(-0.718934\pi\) | ||||
−0.634841 | + | 0.772643i | \(0.718934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.5341 | 1.59965 | 0.799825 | − | 0.600233i | \(-0.204926\pi\) | ||||
0.799825 | + | 0.600233i | \(0.204926\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.8654 | −0.903069 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.7310 | 1.60265 | 0.801326 | − | 0.598228i | \(-0.204128\pi\) | ||||
0.801326 | + | 0.598228i | \(0.204128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.6146 | −0.959701 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.9412 | 0.834624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.41972 | 0.0474559 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.676292 | −0.0225807 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.14450 | 0.271634 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.95484 | 0.131755 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.3651 | 0.511320 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.62889 | −0.187111 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.7132 | −1.11943 | −0.559714 | − | 0.828686i | \(-0.689089\pi\) | ||||
−0.559714 | + | 0.828686i | \(0.689089\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.87391 | −0.0953216 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.9640 | −1.29094 | −0.645468 | − | 0.763788i | \(-0.723338\pi\) | ||||
−0.645468 | + | 0.763788i | \(0.723338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.2564 | −0.471301 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 57.4289 | 1.89647 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5411 | 0.413692 | 0.206846 | − | 0.978374i | \(-0.433680\pi\) | ||||
0.206846 | + | 0.978374i | \(0.433680\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.0206 | −0.626750 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.35348 | −0.0445505 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.57623 | 0.150466 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.27526 | −0.173262 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.5557 | 0.871263 | 0.435631 | − | 0.900125i | \(-0.356525\pi\) | ||||
0.435631 | + | 0.900125i | \(0.356525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.37216 | −0.0449709 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.2854 | −1.38436 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.566670 | −0.0185123 | −0.00925615 | − | 0.999957i | \(-0.502946\pi\) | ||||
−0.00925615 | + | 0.999957i | \(0.502946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34.3136 | −1.11978 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.4578 | −0.373514 | −0.186757 | − | 0.982406i | \(-0.559798\pi\) | ||||
−0.186757 | + | 0.982406i | \(0.559798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.24313 | 0.0730464 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.5675 | 0.408822 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.2412 | −0.982707 | −0.491354 | − | 0.870960i | \(-0.663498\pi\) | ||||
−0.491354 | + | 0.870960i | \(0.663498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.05312 | 0.0666472 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.75813 | 0.154293 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.7753 | −1.35324 | −0.676618 | − | 0.736334i | \(-0.736555\pi\) | ||||
−0.676618 | + | 0.736334i | \(0.736555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.24259 | −0.0725685 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.11490 | −0.262044 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.85852 | 0.124468 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.66227 | −0.311362 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.30699 | −0.299603 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.9026 | 0.447078 | 0.223539 | − | 0.974695i | \(-0.428239\pi\) | ||||
0.223539 | + | 0.974695i | \(0.428239\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.44316 | 0.239109 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.24997 | 0.168480 | 0.0842398 | − | 0.996446i | \(-0.473154\pi\) | ||||
0.0842398 | + | 0.996446i | \(0.473154\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.0177 | −1.44320 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.372129 | 0.0119177 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.0523 | 1.69729 | 0.848646 | − | 0.528961i | \(-0.177418\pi\) | ||||
0.848646 | + | 0.528961i | \(0.177418\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.69608 | 0.181862 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.43729 | −0.0458425 | −0.0229212 | − | 0.999737i | \(-0.507297\pi\) | ||||
−0.0229212 | + | 0.999737i | \(0.507297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3935 | 0.458615 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −48.1975 | −1.53414 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.38872 | −0.171351 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.6101 | 0.718234 | 0.359117 | − | 0.933292i | \(-0.383078\pi\) | ||||
0.359117 | + | 0.933292i | \(0.383078\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.2662 | −0.452724 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.00915 | 0.0953965 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.0567 | 1.87034 | 0.935172 | − | 0.354194i | \(-0.115245\pi\) | ||||
0.935172 | + | 0.354194i | \(0.115245\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.9840 | 0.663906 |
(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 | 9680.2.a.cy.1.2 | 6 | ||
4.3 | odd | 2 | 4840.2.a.be.1.5 | 6 | |||
11.2 | odd | 10 | 880.2.bo.j.81.1 | 12 | |||
11.6 | odd | 10 | 880.2.bo.j.641.1 | 12 | |||
11.10 | odd | 2 | 9680.2.a.cx.1.2 | 6 | |||
44.35 | even | 10 | 440.2.y.b.81.3 | ✓ | 12 | ||
44.39 | even | 10 | 440.2.y.b.201.3 | yes | 12 | ||
44.43 | even | 2 | 4840.2.a.bf.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.b.81.3 | ✓ | 12 | 44.35 | even | 10 | ||
440.2.y.b.201.3 | yes | 12 | 44.39 | even | 10 | ||
880.2.bo.j.81.1 | 12 | 11.2 | odd | 10 | |||
880.2.bo.j.641.1 | 12 | 11.6 | odd | 10 | |||
4840.2.a.be.1.5 | 6 | 4.3 | odd | 2 | |||
4840.2.a.bf.1.5 | 6 | 44.43 | even | 2 | |||
9680.2.a.cx.1.2 | 6 | 11.10 | odd | 2 | |||
9680.2.a.cy.1.2 | 6 | 1.1 | even | 1 | trivial |