Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.19 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.28 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 0.593296i | − | 0.342540i | −0.985224 | − | 0.171270i | \(-0.945213\pi\) | ||
0.985224 | − | 0.171270i | \(-0.0547870\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.87533i | 1.73310i | 0.499090 | + | 0.866550i | \(0.333668\pi\) | ||||
−0.499090 | + | 0.866550i | \(0.666332\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.92807i | 1.10671i | 0.832946 | + | 0.553354i | \(0.186652\pi\) | ||||
−0.832946 | + | 0.553354i | \(0.813348\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.64800 | 0.882667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.95085i | − | 1.49274i | −0.665533 | − | 0.746368i | \(-0.731796\pi\) | ||
0.665533 | − | 0.746368i | \(-0.268204\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.80221 | −1.05454 | −0.527272 | − | 0.849697i | \(-0.676785\pi\) | ||||
−0.527272 | + | 0.849697i | \(0.676785\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.29922 | 0.593656 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.88587 | + | 2.94479i | 0.699926 | + | 0.714216i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.82016 | 0.417573 | 0.208787 | − | 0.977961i | \(-0.433049\pi\) | ||||
0.208787 | + | 0.977961i | \(0.433049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73721 | 0.379091 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.40097i | 1.75172i | 0.482562 | + | 0.875862i | \(0.339706\pi\) | ||||
−0.482562 | + | 0.875862i | \(0.660294\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.0182 | −2.00364 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.35094i | − | 0.644888i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.64389i | − | 0.305262i | −0.988283 | − | 0.152631i | \(-0.951225\pi\) | ||
0.988283 | − | 0.152631i | \(-0.0487746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.62019i | 1.36863i | 0.729188 | + | 0.684313i | \(0.239898\pi\) | ||||
−0.729188 | + | 0.684313i | \(0.760102\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.93732 | −0.511321 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.3473 | −1.91804 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0884485i | 0.0145408i | 0.999974 | + | 0.00727042i | \(0.00231427\pi\) | ||||
−0.999974 | + | 0.00727042i | \(0.997686\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.25584i | 0.361223i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.48344i | 0.387849i | 0.981016 | + | 0.193924i | \(0.0621217\pi\) | ||||
−0.981016 | + | 0.193924i | \(0.937878\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2661 | 1.56557 | 0.782785 | − | 0.622292i | \(-0.213798\pi\) | ||||
0.782785 | + | 0.622292i | \(0.213798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.2619i | 1.52975i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.02570 | −0.149614 | −0.0748070 | − | 0.997198i | \(-0.523834\pi\) | ||||
−0.0748070 | + | 0.997198i | \(0.523834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.57361 | −0.224802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.74713 | − | 1.71217i | 0.244647 | − | 0.239752i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.471127 | 0.0647143 | 0.0323571 | − | 0.999476i | \(-0.489699\pi\) | ||||
0.0323571 | + | 0.999476i | \(0.489699\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.1862 | 2.58706 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.07989i | − | 0.143035i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.85661i | − | 0.877898i | −0.898512 | − | 0.438949i | \(-0.855351\pi\) | ||
0.898512 | − | 0.438949i | \(-0.144649\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.75354i | 0.976854i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 14.7348i | − | 1.82763i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9279 | −1.57939 | −0.789696 | − | 0.613499i | \(-0.789762\pi\) | ||||
−0.789696 | + | 0.613499i | \(0.789762\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.98426 | 0.600035 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.36046i | 0.992204i | 0.868264 | + | 0.496102i | \(0.165236\pi\) | ||||
−0.868264 | + | 0.496102i | \(0.834764\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.16000i | − | 0.838014i | −0.907983 | − | 0.419007i | \(-0.862378\pi\) | ||
0.907983 | − | 0.419007i | \(-0.137622\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.94375i | 0.686325i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.4964 | 1.65202 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.40731i | 0.945896i | 0.881090 | + | 0.472948i | \(0.156810\pi\) | ||||
−0.881090 | + | 0.472948i | \(0.843190\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.95590 | 0.661767 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.81612 | 0.309110 | 0.154555 | − | 0.987984i | \(-0.450606\pi\) | ||||
0.154555 | + | 0.987984i | \(0.450606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.4120 | + | 11.1837i | −1.23781 | + | 1.21304i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.975310 | −0.104564 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.6865 | −1.34476 | −0.672381 | − | 0.740206i | \(-0.734728\pi\) | ||||
−0.672381 | + | 0.740206i | \(0.734728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 11.1331i | − | 1.16707i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.52103 | 0.468809 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.05372i | 0.723697i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.93724i | 0.298232i | 0.988820 | + | 0.149116i | \(0.0476427\pi\) | ||||
−0.988820 | + | 0.149116i | \(0.952357\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 13.1098i | − | 1.31759i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.5736 | −1.25112 | −0.625562 | − | 0.780174i | \(-0.715130\pi\) | ||||
−0.625562 | + | 0.780174i | \(0.715130\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.918766 | −0.0905287 | −0.0452644 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452644 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.73228i | 0.657003i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.47339i | 0.722480i | 0.932473 | + | 0.361240i | \(0.117646\pi\) | ||||
−0.932473 | + | 0.361240i | \(0.882354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.87296i | − | 0.370963i | −0.982648 | − | 0.185481i | \(-0.940616\pi\) | ||
0.982648 | − | 0.185481i | \(-0.0593844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0524761 | 0.00498082 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.26006i | − | 0.494825i | −0.968910 | − | 0.247413i | \(-0.920420\pi\) | ||
0.968910 | − | 0.247413i | \(-0.0795803\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32.5566 | −3.03591 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.0683 | −0.930810 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.62255 | + | 8.45003i | −0.790428 | + | 0.774613i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.5109 | −1.22826 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.47342 | 0.132854 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 19.4472i | − | 1.73941i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.46239 | 0.750915 | 0.375458 | − | 0.926840i | \(-0.377486\pi\) | ||||
0.375458 | + | 0.926840i | \(0.377486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.09085i | − | 0.536270i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4727i | 1.52660i | 0.646046 | + | 0.763298i | \(0.276421\pi\) | ||||
−0.646046 | + | 0.763298i | \(0.723579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.32956i | 0.462132i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.9860 | 1.11766 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.30666 | 0.197071 | 0.0985357 | − | 0.995134i | \(-0.468584\pi\) | ||||
0.0985357 | + | 0.995134i | \(0.468584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7926i | 0.915413i | 0.889103 | + | 0.457707i | \(0.151329\pi\) | ||||
−0.889103 | + | 0.457707i | \(0.848671\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.608545i | 0.0512487i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.8242i | 1.57415i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.37060 | 0.529049 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.933619i | 0.0770036i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.8742 | −1.13662 | −0.568311 | − | 0.822814i | \(-0.692403\pi\) | ||||
−0.568311 | + | 0.822814i | \(0.692403\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1809 | −0.909891 | −0.454945 | − | 0.890519i | \(-0.650341\pi\) | ||||
−0.454945 | + | 0.890519i | \(0.650341\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.64178 | + | 7.79780i | 0.617801 | + | 0.630415i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29.5308 | −2.37197 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.01139 | 0.160527 | 0.0802633 | − | 0.996774i | \(-0.474424\pi\) | ||||
0.0802633 | + | 0.996774i | \(0.474424\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 0.279518i | − | 0.0221672i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.5987 | −1.93865 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12.6552i | − | 0.991235i | −0.868541 | − | 0.495618i | \(-0.834942\pi\) | ||
0.868541 | − | 0.495618i | \(-0.165058\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 11.3831i | − | 0.886171i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.5213i | − | 1.43322i | −0.697475 | − | 0.716609i | \(-0.745693\pi\) | ||
0.697475 | − | 0.716609i | \(-0.254307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.45680 | 0.112061 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.81978 | 0.368578 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.2040i | − | 1.68814i | −0.536236 | − | 0.844068i | \(-0.680154\pi\) | ||
0.536236 | − | 0.844068i | \(-0.319846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 29.3340i | − | 2.21744i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 0.593296i | − | 0.0445949i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.3235 | −1.36957 | −0.684783 | − | 0.728747i | \(-0.740103\pi\) | ||||
−0.684783 | + | 0.728747i | \(0.740103\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00327i | 0.371890i | 0.982560 | + | 0.185945i | \(0.0595347\pi\) | ||||
−0.982560 | + | 0.185945i | \(0.940465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.06800 | −0.300715 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.342767 | −0.0252008 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.5792 | − | 14.2875i | 1.06614 | − | 1.04480i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.81179 | 0.713702 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.52982 | 0.255409 | 0.127704 | − | 0.991812i | \(-0.459239\pi\) | ||||
0.127704 | + | 0.991812i | \(0.459239\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 17.0812i | − | 1.22953i | −0.788711 | − | 0.614764i | \(-0.789251\pi\) | ||
0.788711 | − | 0.614764i | \(-0.210749\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.74211 | −0.626035 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.16663i | − | 0.653095i | −0.945181 | − | 0.326548i | \(-0.894115\pi\) | ||
0.945181 | − | 0.326548i | \(-0.105885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.96742i | 0.352131i | 0.984378 | + | 0.176066i | \(0.0563371\pi\) | ||||
−0.984378 | + | 0.176066i | \(0.943663\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.67005i | 0.541004i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.81342 | 0.337836 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.62417 | −0.672181 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.2458i | 1.54619i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 9.01133i | − | 0.623327i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.3353i | − | 1.12457i | −0.826944 | − | 0.562284i | \(-0.809923\pi\) | ||
0.826944 | − | 0.562284i | \(-0.190077\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.96023 | 0.339869 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 39.7847i | 2.71329i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.3125 | −1.51467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.24800 | −0.287053 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.9727 | − | 11.1967i | −0.738102 | − | 0.753171i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.02994 | −0.403795 | −0.201897 | − | 0.979407i | \(-0.564711\pi\) | ||||
−0.201897 | + | 0.979407i | \(0.564711\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.5282 | −1.76854 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0807i | 1.26643i | 0.773975 | + | 0.633217i | \(0.218266\pi\) | ||||
−0.773975 | + | 0.633217i | \(0.781734\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.92975 | −0.656176 | −0.328088 | − | 0.944647i | \(-0.606404\pi\) | ||||
−0.328088 | + | 0.944647i | \(0.606404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.60068i | − | 0.565883i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.1706i | 1.12488i | 0.826838 | + | 0.562441i | \(0.190138\pi\) | ||||
−0.826838 | + | 0.562441i | \(0.809862\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 3.97493i | − | 0.259296i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.98802 | 0.324007 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.30844 | 0.278690 | 0.139345 | − | 0.990244i | \(-0.455500\pi\) | ||||
0.139345 | + | 0.990244i | \(0.455500\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.4140i | 1.76589i | 0.469473 | + | 0.882947i | \(0.344444\pi\) | ||||
−0.469473 | + | 0.882947i | \(0.655556\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 13.5864i | − | 0.871569i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.09828i | − | 0.389605i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92063 | −0.440349 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.67080i | − | 0.105882i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.84664 | 0.432156 | 0.216078 | − | 0.976376i | \(-0.430673\pi\) | ||||
0.216078 | + | 0.976376i | \(0.430673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.5919 | 2.61486 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.63524 | + | 6.77071i | 0.415515 | + | 0.423998i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2578 | 1.26364 | 0.631822 | − | 0.775113i | \(-0.282307\pi\) | ||||
0.631822 | + | 0.775113i | \(0.282307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.258984 | −0.0160925 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 4.35301i | − | 0.269444i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.14819 | −0.0708001 | −0.0354001 | − | 0.999373i | \(-0.511271\pi\) | ||||
−0.0354001 | + | 0.999373i | \(0.511271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82577i | 0.112156i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.52682i | 0.460634i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.4737i | − | 1.06539i | −0.846307 | − | 0.532695i | \(-0.821179\pi\) | ||
0.846307 | − | 0.532695i | \(-0.178821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.871087 | −0.0529148 | −0.0264574 | − | 0.999650i | \(-0.508423\pi\) | ||||
−0.0264574 | + | 0.999650i | \(0.508423\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.60525 | −0.399768 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 49.5985i | 2.99090i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.8936i | 0.834787i | 0.908726 | + | 0.417394i | \(0.137056\pi\) | ||||
−0.908726 | + | 0.417394i | \(0.862944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.1783i | 1.20804i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.08777 | 0.363166 | 0.181583 | − | 0.983376i | \(-0.441878\pi\) | ||||
0.181583 | + | 0.983376i | \(0.441878\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.5681i | 1.63876i | 0.573254 | + | 0.819378i | \(0.305681\pi\) | ||||
−0.573254 | + | 0.819378i | \(0.694319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.18495 | 0.247895 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.27171 | −0.429235 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.343546 | + | 16.9965i | −0.0202086 | + | 0.999796i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.74265 | 0.102156 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.36853 | −0.313633 | −0.156816 | − | 0.987628i | \(-0.550123\pi\) | ||||
−0.156816 | + | 0.987628i | \(0.550123\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.87533i | 0.225631i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.5900 | −0.962647 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 31.9423i | − | 1.84727i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.0600i | 1.73263i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.45989i | 0.428560i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.5716 | 1.52149 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5224 | 0.885910 | 0.442955 | − | 0.896544i | \(-0.353930\pi\) | ||||
0.442955 | + | 0.896544i | \(0.353930\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.545100i | 0.0310097i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.5865i | 1.56428i | 0.623100 | + | 0.782142i | \(0.285873\pi\) | ||||
−0.623100 | + | 0.782142i | \(0.714127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 26.2054i | − | 1.48122i | −0.671935 | − | 0.740610i | \(-0.734537\pi\) | ||
0.671935 | − | 0.740610i | \(-0.265463\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.0475 | −1.69299 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.8975i | 0.668227i | 0.942533 | + | 0.334114i | \(0.108437\pi\) | ||||
−0.942533 | + | 0.334114i | \(0.891563\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.13862 | −0.455675 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.43393 | 0.247478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.25274 | + | 5.35999i | 0.292270 | + | 0.298238i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.0913 | 2.11292 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.29781 | −0.127069 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.00333i | − | 0.165579i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.4502 | −1.17901 | −0.589505 | − | 0.807764i | \(-0.700677\pi\) | ||||
−0.589505 | + | 0.807764i | \(0.700677\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.234212i | 0.0128347i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 50.0998i | − | 2.73724i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.6109i | 1.93985i | 0.243408 | + | 0.969924i | \(0.421735\pi\) | ||||
−0.243408 | + | 0.969924i | \(0.578265\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.12077 | −0.169497 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.7264 | 2.04300 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.8889i | 0.857918i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.3157i | 1.03992i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.8045i | − | 0.741064i | −0.928820 | − | 0.370532i | \(-0.879175\pi\) | ||
0.928820 | − | 0.370532i | \(-0.120825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.43255 | −0.183740 | −0.0918701 | − | 0.995771i | \(-0.529284\pi\) | ||||
−0.0918701 | + | 0.995771i | \(0.529284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7410i | 0.680062i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.17223 | −0.222065 | −0.111033 | − | 0.993817i | \(-0.535416\pi\) | ||||
−0.111033 | + | 0.993817i | \(0.535416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.3996 | −1.71959 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.01337 | + | 5.11573i | 0.265336 | + | 0.270753i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.5274 | 1.40006 | 0.700032 | − | 0.714112i | \(-0.253169\pi\) | ||||
0.700032 | + | 0.714112i | \(0.253169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6870 | −0.825632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.01595i | 0.420728i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.7474 | 1.45236 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 27.2314i | − | 1.42147i | −0.703462 | − | 0.710733i | \(-0.748363\pi\) | ||
0.703462 | − | 0.710733i | \(-0.251637\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.57616i | 0.342341i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.37949i | 0.0716198i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.7377 | 0.814869 | 0.407434 | − | 0.913234i | \(-0.366424\pi\) | ||||
0.407434 | + | 0.913234i | \(0.366424\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.5379 | −0.595815 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.25040i | 0.321912i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.7567i | 0.655267i | 0.944805 | + | 0.327633i | \(0.106251\pi\) | ||||
−0.944805 | + | 0.327633i | \(0.893749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 5.02070i | − | 0.257218i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.1510 | 1.89833 | 0.949164 | − | 0.314782i | \(-0.101931\pi\) | ||||
0.949164 | + | 0.314782i | \(0.101931\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 56.1785i | 2.86312i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.1847 | 1.38188 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.1313 | 1.57842 | 0.789209 | − | 0.614125i | \(-0.210491\pi\) | ||||
0.789209 | + | 0.614125i | \(0.210491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.7391 | + | 24.2441i | −1.25111 | + | 1.22608i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.3665 | 0.522920 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.5811 | −1.63933 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8999i | 1.19950i | 0.800187 | + | 0.599750i | \(0.204733\pi\) | ||||
−0.800187 | + | 0.599750i | \(0.795267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.16201 | 0.158298 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 16.5266i | − | 0.825297i | −0.910890 | − | 0.412648i | \(-0.864604\pi\) | ||
0.910890 | − | 0.412648i | \(-0.135396\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 28.9736i | − | 1.44328i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 23.0811i | 1.14691i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.437895 | 0.0217057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.42032 | −0.0702305 | −0.0351152 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351152 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.36853i | − | 0.0675047i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.92807i | 0.144081i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.9134i | 0.535719i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.40318 | 0.313565 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 20.5811i | − | 1.00545i | −0.864445 | − | 0.502727i | \(-0.832330\pi\) | ||
0.864445 | − | 0.502727i | \(-0.167670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0994 | −1.27201 | −0.636003 | − | 0.771687i | \(-0.719413\pi\) | ||||
−0.636003 | + | 0.771687i | \(0.719413\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.71606 | −0.132059 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28.9112 | − | 29.5014i | −1.40240 | − | 1.43103i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0766 | 0.971577 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.1683 | 0.539210 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.97767i | − | 0.432439i | −0.976345 | − | 0.216219i | \(-0.930627\pi\) | ||
0.976345 | − | 0.216219i | \(-0.0693727\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.45697 | 0.310302 | 0.155151 | − | 0.987891i | \(-0.450414\pi\) | ||||
0.155151 | + | 0.987891i | \(0.450414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.77965i | − | 0.181220i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.2911i | 0.731473i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.97734i | − | 0.0943735i | −0.998886 | − | 0.0471868i | \(-0.984974\pi\) | ||
0.998886 | − | 0.0471868i | \(-0.0150256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.16693 | −0.198425 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.5708 | −1.45246 | −0.726230 | − | 0.687452i | \(-0.758729\pi\) | ||||
−0.726230 | + | 0.687452i | \(0.758729\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 49.1642i | − | 2.33061i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.23153i | 0.389338i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 39.4623i | − | 1.86234i | −0.364583 | − | 0.931171i | \(-0.618788\pi\) | ||
0.364583 | − | 0.931171i | \(-0.381212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.2952 | 0.578956 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.63360i | 0.311674i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.1446 | 2.02265 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.5916 | −0.729344 | −0.364672 | − | 0.931136i | \(-0.618819\pi\) | ||||
−0.364672 | + | 0.931136i | \(0.618819\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.86779 | − | 9.67035i | 0.460589 | − | 0.451373i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.7521 | 1.10625 | 0.553123 | − | 0.833100i | \(-0.313436\pi\) | ||||
0.553123 | + | 0.833100i | \(0.313436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.8449 | 1.43349 | 0.716743 | − | 0.697338i | \(-0.245632\pi\) | ||||
0.716743 | + | 0.697338i | \(0.245632\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.5205i | 0.812493i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 42.2503 | 1.95511 | 0.977555 | − | 0.210683i | \(-0.0675687\pi\) | ||||
0.977555 | + | 0.210683i | \(0.0675687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 37.8538i | − | 1.74792i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.19335i | − | 0.0549867i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 50.8260i | − | 2.33698i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.2347 | −0.836666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.24754 | 0.0571211 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.24436i | 0.239621i | 0.992797 | + | 0.119810i | \(0.0382287\pi\) | ||||
−0.992797 | + | 0.119810i | \(0.961771\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.336300i | − | 0.0153340i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.5943i | 0.664063i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.3828 | −0.516866 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.3556i | − | 1.46617i | −0.680137 | − | 0.733085i | \(-0.738080\pi\) | ||
0.680137 | − | 0.733085i | \(-0.261920\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.50831 | −0.339537 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.9506 | 1.08088 | 0.540438 | − | 0.841384i | \(-0.318258\pi\) | ||||
0.540438 | + | 0.841384i | \(0.318258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.84089 | − | 4.74403i | 0.218023 | − | 0.213661i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 50.8050 | 2.28351 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.4800 | −1.09808 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4420i | 0.556979i | 0.960439 | + | 0.278489i | \(0.0898337\pi\) | ||||
−0.960439 | + | 0.278489i | \(0.910166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.9886 | −0.490934 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.5232i | 1.40555i | 0.711413 | + | 0.702774i | \(0.248056\pi\) | ||||
−0.711413 | + | 0.702774i | \(0.751944\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 48.7270i | − | 2.16833i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 0.864311i | − | 0.0383854i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.7227 | −0.874195 | −0.437097 | − | 0.899414i | \(-0.643993\pi\) | ||||
−0.437097 | + | 0.899414i | \(0.643993\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.9650 | 0.927437 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 6.09924i | − | 0.269288i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 3.56052i | − | 0.156895i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.07809i | 0.223334i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.1735 | −0.578254 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.4265i | 0.588228i | 0.955770 | + | 0.294114i | \(0.0950245\pi\) | ||||
−0.955770 | + | 0.294114i | \(0.904975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.84227 | 0.168011 | 0.0840054 | − | 0.996465i | \(-0.473229\pi\) | ||||
0.0840054 | + | 0.996465i | \(0.473229\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.4037 | −0.759562 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.4398 | + | 21.9909i | −0.977495 | + | 0.957937i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −47.5764 | −2.06854 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.64800 | 0.114913 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 9.44258i | − | 0.409003i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.9618 | −1.25213 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.8713i | 0.469131i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.79072i | 0.335570i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6791i | 0.846071i | 0.906113 | + | 0.423036i | \(0.139035\pi\) | ||||
−0.906113 | + | 0.423036i | \(0.860965\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.96842 | 0.127387 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.0090 | 0.642915 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3727i | 0.443505i | 0.975103 | + | 0.221753i | \(0.0711777\pi\) | ||||
−0.975103 | + | 0.221753i | \(0.928822\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 18.1563i | − | 0.774892i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.99213i | − | 0.127469i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.6172 | −1.04683 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.203362i | 0.00863226i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.8749 | 1.30821 | 0.654105 | − | 0.756404i | \(-0.273045\pi\) | ||||
0.654105 | + | 0.756404i | \(0.273045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.0340 | −1.65096 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.47670 | − | 8.64977i | −0.357887 | − | 0.365194i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.0945 | 1.68978 | 0.844890 | − | 0.534940i | \(-0.179666\pi\) | ||||
0.844890 | + | 0.534940i | \(0.179666\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.3845 | 0.857582 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.4393i | 0.732383i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.7366 | −1.79161 | −0.895806 | − | 0.444446i | \(-0.853400\pi\) | ||||
−0.895806 | + | 0.444446i | \(0.853400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 24.8026i | − | 1.03796i | −0.854788 | − | 0.518978i | \(-0.826313\pi\) | ||
0.854788 | − | 0.518978i | \(-0.173687\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.09423i | − | 0.0874876i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 84.1626i | − | 3.50982i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.7144 | 1.07051 | 0.535253 | − | 0.844692i | \(-0.320216\pi\) | ||||
0.535253 | + | 0.844692i | \(0.320216\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.1342 | −0.421162 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.24582i | 0.342094i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.33248i | − | 0.0966014i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 39.0178i | − | 1.61319i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.9337 | 1.23550 | 0.617748 | − | 0.786376i | \(-0.288045\pi\) | ||||
0.617748 | + | 0.786376i | \(0.288045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.8700i | 0.571502i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.43852 | −0.223711 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.7668 | 0.565336 | 0.282668 | − | 0.959218i | \(-0.408781\pi\) | ||||
0.282668 | + | 0.959218i | \(0.408781\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.7467 | − | 33.4153i | −1.34248 | − | 1.36989i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.94715 | 0.120619 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.413974 | −0.0169145 | −0.00845727 | − | 0.999964i | \(-0.502692\pi\) | ||||
−0.00845727 | + | 0.999964i | \(0.502692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.76784i | 0.398438i | 0.979955 | + | 0.199219i | \(0.0638406\pi\) | ||||
−0.979955 | + | 0.199219i | \(0.936159\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −34.2330 | −1.39408 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 52.3591i | − | 2.12870i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.5906i | 0.835746i | 0.908505 | + | 0.417873i | \(0.137224\pi\) | ||||
−0.908505 | + | 0.417873i | \(0.862776\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 2.85578i | − | 0.115722i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.89993 | 0.157774 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2067 | 0.775749 | 0.387875 | − | 0.921712i | \(-0.373209\pi\) | ||||
0.387875 | + | 0.921712i | \(0.373209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.70998i | 0.230249i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.2322i | 0.774257i | 0.922026 | + | 0.387129i | \(0.126533\pi\) | ||||
−0.922026 | + | 0.387129i | \(0.873467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.18242i | 0.0877188i | 0.999038 | + | 0.0438594i | \(0.0139654\pi\) | ||||
−0.999038 | + | 0.0438594i | \(0.986035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.1511 | 1.12967 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 37.1469i | − | 1.48826i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.2732 | 1.01093 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.34639 | −0.213514 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.260462 | + | 0.255251i | −0.0103853 | + | 0.0101775i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.7845 | −1.98189 | −0.990944 | − | 0.134277i | \(-0.957129\pi\) | ||||
−0.990944 | + | 0.134277i | \(0.957129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.69167 | −0.385209 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.7945i | 1.30141i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.98321 | 0.237064 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.1385i | 0.875786i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 28.1843i | − | 1.11321i | −0.830776 | − | 0.556607i | \(-0.812103\pi\) | ||
0.830776 | − | 0.556607i | \(-0.187897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 13.8432i | − | 0.545924i | −0.962025 | − | 0.272962i | \(-0.911997\pi\) | ||
0.962025 | − | 0.272962i | \(-0.0880033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.6041 | 0.929410 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.5492 | 0.571989 | 0.285995 | − | 0.958231i | \(-0.407676\pi\) | ||||
0.285995 | + | 0.958231i | \(0.407676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.95085i | − | 0.194338i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.2379i | 0.518834i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 5.49220i | − | 0.214926i | −0.994209 | − | 0.107463i | \(-0.965727\pi\) | ||
0.994209 | − | 0.107463i | \(-0.0342728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −67.7125 | −2.64575 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 18.9597i | − | 0.739687i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.2140 | −0.631608 | −0.315804 | − | 0.948824i | \(-0.602274\pi\) | ||||
−0.315804 | + | 0.948824i | \(0.602274\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.42581 | 0.366621 | 0.183311 | − | 0.983055i | \(-0.441319\pi\) | ||||
0.183311 | + | 0.983055i | \(0.441319\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.64296 | + | 6.51004i | −0.257991 | + | 0.252829i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.6538 | −0.800921 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8102 | 0.534734 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.57754i | 0.138316i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9460 | −1.31047 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.71120i | − | 0.181603i | −0.995869 | − | 0.0908016i | \(-0.971057\pi\) | ||
0.995869 | − | 0.0908016i | \(-0.0289429\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 33.5703i | 1.29212i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.39320i | − | 0.0535450i | −0.999642 | − | 0.0267725i | \(-0.991477\pi\) | ||
0.999642 | − | 0.0267725i | \(-0.00852297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.60046 | −0.330055 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.3205 | 0.433803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.0195i | 1.41651i | 0.705956 | + | 0.708256i | \(0.250518\pi\) | ||||
−0.705956 | + | 0.708256i | \(0.749482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.93908i | 0.341545i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.89128i | 0.224766i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.79132 | −0.0682440 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.7332i | 1.32131i | 0.750688 | + | 0.660657i | \(0.229722\pi\) | ||||
−0.750688 | + | 0.660657i | \(0.770278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 38.3866 | 1.45819 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.8248 | −1.58650 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.31322 | + | 7.16689i | −0.277008 | + | 0.271465i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.1872 | 0.385316 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.88392 | 0.184463 | 0.0922316 | − | 0.995738i | \(-0.470600\pi\) | ||||
0.0922316 | + | 0.995738i | \(0.470600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.160991i | 0.00607187i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.35831 | −0.0888192 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 36.8166i | − | 1.38463i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 48.3839i | − | 1.81710i | −0.417781 | − | 0.908548i | \(-0.637192\pi\) | ||
0.417781 | − | 0.908548i | \(-0.362808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.2626i | 0.834911i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −64.0170 | −2.39746 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −72.9498 | −2.72817 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 2.55618i | − | 0.0954623i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 9.80772i | − | 0.365766i | −0.983135 | − | 0.182883i | \(-0.941457\pi\) | ||
0.983135 | − | 0.182883i | \(-0.0585430\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.69022i | − | 0.100189i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.2646 | 0.604888 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.4688i | 0.611634i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5244 | 0.538680 | 0.269340 | − | 0.963045i | \(-0.413194\pi\) | ||||
0.269340 | + | 0.963045i | \(0.413194\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.80694 | 0.363220 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.6267 | + | 30.2316i | 1.09578 | + | 1.11816i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1472 | 0.707216 | 0.353608 | − | 0.935394i | \(-0.384955\pi\) | ||||
0.353608 | + | 0.935394i | \(0.384955\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.61808 | −0.133455 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 64.0039i | 2.35761i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.7662 | −1.35247 | −0.676233 | − | 0.736688i | \(-0.736389\pi\) | ||||
−0.676233 | + | 0.736688i | \(0.736389\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.10598i | 0.150837i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 0.481977i | − | 0.0176820i | −0.999961 | − | 0.00884102i | \(-0.997186\pi\) | ||
0.999961 | − | 0.00884102i | \(-0.00281422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 53.7673i | − | 1.96988i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.45710 | 0.272841 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.8826 | −0.799574 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.1238i | 1.24519i | 0.782543 | + | 0.622597i | \(0.213922\pi\) | ||||
−0.782543 | + | 0.622597i | \(0.786078\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.06208i | − | 0.148030i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 43.3298i | − | 1.57693i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2759 | −0.555212 | −0.277606 | − | 0.960695i | \(-0.589541\pi\) | ||||
−0.277606 | + | 0.960695i | \(0.589541\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 24.6763i | − | 0.895694i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.2701 | 1.38729 | 0.693645 | − | 0.720317i | \(-0.256004\pi\) | ||||
0.693645 | + | 0.720317i | \(0.256004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3403 | 0.410547 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.2190 | + | 29.6144i | −1.09257 | + | 1.07071i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.80221 | −0.137290 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.8202 | 1.43595 | 0.717976 | − | 0.696068i | \(-0.245069\pi\) | ||||
0.717976 | + | 0.696068i | \(0.245069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 12.0189i | − | 0.432848i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.8048 | 0.784265 | 0.392133 | − | 0.919909i | \(-0.371737\pi\) | ||||
0.392133 | + | 0.919909i | \(0.371737\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 76.3405i | − | 2.74223i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.153654i | 0.00551231i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.52027i | 0.161955i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.3914 | 1.48110 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.50855 | −0.196860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.79481i | 0.278209i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.9239i | − | 1.31619i | −0.752933 | − | 0.658097i | \(-0.771362\pi\) | ||
0.752933 | − | 0.658097i | \(-0.228638\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.681214i | 0.0242518i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4018 | 0.547627 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.0702i | 0.925782i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.08322 | 0.0384180 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.7539 | 1.76237 | 0.881187 | − | 0.472768i | \(-0.156745\pi\) | ||||
0.881187 | + | 0.472768i | \(0.156745\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.96004 | − | 3.02047i | −0.104719 | − | 0.106857i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.5937 | −1.18698 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.4480 | −1.25093 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 95.3280i | − | 3.35987i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.3671 | −0.364938 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.35385i | − | 0.117915i | −0.998260 | − | 0.0589575i | \(-0.981222\pi\) | ||
0.998260 | − | 0.0589575i | \(-0.0187777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.9645i | 1.05220i | 0.850424 | + | 0.526098i | \(0.176345\pi\) | ||||
−0.850424 | + | 0.526098i | \(0.823655\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.516812i | 0.0181254i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 49.0433 | 1.71791 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.6860 | 0.653741 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 29.4806i | − | 1.03013i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.6512i | 1.76774i | 0.467733 | + | 0.883870i | \(0.345071\pi\) | ||||
−0.467733 | + | 0.883870i | \(0.654929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34.4677i | − | 1.20147i | −0.799449 | − | 0.600734i | \(-0.794875\pi\) | ||
0.799449 | − | 0.600734i | \(-0.205125\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.4266 | 1.02450 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 52.8530i | − | 1.83788i | −0.394400 | − | 0.918939i | \(-0.629047\pi\) | ||
0.394400 | − | 0.918939i | \(-0.370953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.8961 | −1.59404 | −0.797019 | − | 0.603954i | \(-0.793591\pi\) | ||||
−0.797019 | + | 0.603954i | \(0.793591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.24304 | 0.285948 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.54124 | − | 4.63396i | −0.157345 | − | 0.160557i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 71.7760 | 2.48391 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.5348 | 0.882611 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5261i | 0.777686i | 0.921304 | + | 0.388843i | \(0.127125\pi\) | ||||
−0.921304 | + | 0.388843i | \(0.872875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.2976 | 0.906815 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 3.61185i | − | 0.124399i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.64557i | 0.194213i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 39.5608i | − | 1.35933i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.3561 | 0.561339 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.743054 | −0.0254716 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.2949i | − | 1.44815i | −0.689721 | − | 0.724075i | \(-0.742267\pi\) | ||
0.689721 | − | 0.724075i | \(-0.257733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.6783i | 0.638783i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 43.4900i | − | 1.48559i | −0.669520 | − | 0.742794i | \(-0.733500\pi\) | ||
0.669520 | − | 0.742794i | \(-0.266500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.7871 | −0.811606 | −0.405803 | − | 0.913961i | \(-0.633008\pi\) | ||||
−0.405803 | + | 0.913961i | \(0.633008\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.31427i | 0.147030i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.34212 | 0.215888 | 0.107944 | − | 0.994157i | \(-0.465573\pi\) | ||||
0.107944 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 86.0477 | 2.92571 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0840 | + | 0.203824i | 0.342470 | + | 0.00692223i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.6233 | 1.41197 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.1545 | 1.66554 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.77782i | 0.263239i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 56.9427 | 1.92501 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.9426i | 1.21369i | 0.794819 | + | 0.606847i | \(0.207566\pi\) | ||||
−0.794819 | + | 0.606847i | \(0.792434\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.18512i | 0.107432i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.4598i | − | 1.19467i | −0.801992 | − | 0.597335i | \(-0.796226\pi\) | ||
0.801992 | − | 0.597335i | \(-0.203774\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.0617 | −1.11262 | −0.556308 | − | 0.830976i | \(-0.687782\pi\) | ||||
−0.556308 | + | 0.830976i | \(0.687782\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.29922 | 0.0772874 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 58.1191i | 1.95145i | 0.219006 | + | 0.975723i | \(0.429719\pi\) | ||||
−0.219006 | + | 0.975723i | \(0.570281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.7785i | 0.831044i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 29.4868i | − | 0.987844i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.86694 | −0.0624748 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 71.0098i | − | 2.37360i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.9512 | −0.632763 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5267 | 0.417790 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.35961 | + | 1.38737i | 0.0452952 | + | 0.0462200i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.8345 | 0.593494 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.3893 | −0.644523 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.3702i | 0.942016i | 0.882129 | + | 0.471008i | \(0.156110\pi\) | ||||
−0.882129 | + | 0.471008i | \(0.843890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.2950 | −1.10433 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.65666i | 0.253676i | 0.991923 | + | 0.126838i | \(0.0404829\pi\) | ||||
−0.991923 | + | 0.126838i | \(0.959517\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.9422i | − | 0.461419i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 15.7648i | − | 0.521169i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −51.1613 | −1.68950 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.8360 | 1.38004 | 0.690021 | − | 0.723790i | \(-0.257601\pi\) | ||||
0.690021 | + | 0.723790i | \(0.257601\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 9.20938i | − | 0.303459i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 31.7882i | − | 1.04632i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 0.886094i | − | 0.0291346i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.43289 | −0.0799067 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.5569i | − | 0.641640i | −0.947140 | − | 0.320820i | \(-0.896042\pi\) | ||
0.947140 | − | 0.320820i | \(-0.103958\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.86423 | −0.0938714 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.3669 | 0.535829 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 55.3687 | + | 56.4992i | 1.81075 | + | 1.84772i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.9555 | −1.07661 | −0.538305 | − | 0.842750i | \(-0.680935\pi\) | ||||
−0.538305 | + | 0.842750i | \(0.680935\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.5476 | −0.507376 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 23.6300i | − | 0.770316i | −0.922851 | − | 0.385158i | \(-0.874147\pi\) | ||
0.922851 | − | 0.385158i | \(-0.125853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.8634 | −0.679404 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38.0239i | 1.23692i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 23.0768i | − | 0.749896i | −0.927046 | − | 0.374948i | \(-0.877661\pi\) | ||
0.927046 | − | 0.374948i | \(-0.122339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.2238i | 0.883722i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.05871 | 0.228894 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.2644 | 0.915575 | 0.457787 | − | 0.889062i | \(-0.348642\pi\) | ||||
0.457787 | + | 0.889062i | \(0.348642\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.6792i | 0.442649i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.82861i | 0.156087i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.75407i | 0.218100i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0673 | −0.873140 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.7895i | 0.637709i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 66.1952 | 2.13090 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.8946 | −1.34724 | −0.673620 | − | 0.739078i | \(-0.735262\pi\) | ||||
−0.673620 | + | 0.739078i | \(0.735262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.18006 | − | 3.11643i | 0.102158 | − | 0.100114i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1614 | 1.12838 | 0.564192 | − | 0.825643i | \(-0.309188\pi\) | ||||
0.564192 | + | 0.825643i | \(0.309188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.6014 | −1.01310 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 22.5994i | − | 0.723760i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.7177 | 0.790789 | 0.395395 | − | 0.918511i | \(-0.370608\pi\) | ||||
0.395395 | + | 0.918511i | \(0.370608\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.8087i | 2.00737i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 10.2556i | − | 0.327436i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 24.5831i | − | 0.784078i | −0.919949 | − | 0.392039i | \(-0.871770\pi\) | ||
0.919949 | − | 0.392039i | \(-0.128230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.5237 | 1.13188 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.78186 | −0.0567174 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 86.2455i | 2.74245i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 19.2420i | − | 0.611241i | −0.952153 | − | 0.305621i | \(-0.901136\pi\) | ||
0.952153 | − | 0.305621i | \(-0.0988639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.7263i | 0.403858i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.2504 | −0.610279 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.95987i | − | 0.0620696i | −0.999518 | − | 0.0310348i | \(-0.990120\pi\) | ||
0.999518 | − | 0.0310348i | \(-0.00988028\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.296385 | 0.00937722 |
(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 | 4012.2.b.b.237.19 | ✓ | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.28 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.19 | ✓ | 46 | 1.1 | even | 1 | trivial | |
4012.2.b.b.237.28 | yes | 46 | 17.16 | even | 2 | inner |