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 | 237.28 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.19 |
$q$-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 | \(0.0547870\pi\) | ||||
−0.985224 | + | 0.171270i | \(0.945213\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.87533i | − | 1.73310i | −0.499090 | − | 0.866550i | \(-0.666332\pi\) | ||
0.499090 | − | 0.866550i | \(-0.333668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.92807i | − | 1.10671i | −0.832946 | − | 0.553354i | \(-0.813348\pi\) | ||
0.832946 | − | 0.553354i | \(-0.186652\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.64800 | 0.882667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.95085i | 1.49274i | 0.665533 | + | 0.746368i | \(0.268204\pi\) | ||||
−0.665533 | + | 0.746368i | \(0.731796\pi\) | |||||||
\(12\) | 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 | \(-0.660294\pi\) | ||
0.482562 | − | 0.875862i | \(-0.339706\pi\) | |||||||
\(24\) | 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 | \(0.0487746\pi\) | ||||
−0.988283 | + | 0.152631i | \(0.951225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.62019i | − | 1.36863i | −0.729188 | − | 0.684313i | \(-0.760102\pi\) | ||
0.729188 | − | 0.684313i | \(-0.239898\pi\) | |||||||
\(32\) | 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 | \(-0.997686\pi\) | ||
0.999974 | − | 0.00727042i | \(-0.00231427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.25584i | − | 0.361223i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.48344i | − | 0.387849i | −0.981016 | − | 0.193924i | \(-0.937878\pi\) | ||
0.981016 | − | 0.193924i | \(-0.0621217\pi\) | |||||||
\(42\) | 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 | \(0.144649\pi\) | ||||
−0.898512 | + | 0.438949i | \(0.855351\pi\) | |||||||
\(62\) | 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 | \(-0.834764\pi\) | ||
0.868264 | − | 0.496102i | \(-0.165236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.16000i | 0.838014i | 0.907983 | + | 0.419007i | \(0.137622\pi\) | ||||
−0.907983 | + | 0.419007i | \(0.862378\pi\) | |||||||
\(74\) | 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 | \(-0.843190\pi\) | ||
0.881090 | − | 0.472948i | \(-0.156810\pi\) | |||||||
\(80\) | 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 | \(-0.952357\pi\) | ||
0.988820 | − | 0.149116i | \(-0.0476427\pi\) | |||||||
\(98\) | 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 | \(-0.882354\pi\) | ||
0.932473 | − | 0.361240i | \(-0.117646\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.87296i | 0.370963i | 0.982648 | + | 0.185481i | \(0.0593844\pi\) | ||||
−0.982648 | + | 0.185481i | \(0.940616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0524761 | 0.00498082 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.26006i | 0.494825i | 0.968910 | + | 0.247413i | \(0.0795803\pi\) | ||||
−0.968910 | + | 0.247413i | \(0.920420\pi\) | |||||||
\(114\) | 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 | \(-0.723579\pi\) | ||
0.646046 | − | 0.763298i | \(-0.276421\pi\) | |||||||
\(132\) | 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 | \(-0.848671\pi\) | ||
0.889103 | − | 0.457707i | \(-0.151329\pi\) | |||||||
\(140\) | 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 | \(0.165058\pi\) | ||||
−0.868541 | + | 0.495618i | \(0.834942\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.3831i | 0.886171i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.5213i | 1.43322i | 0.697475 | + | 0.716609i | \(0.254307\pi\) | ||||
−0.697475 | + | 0.716609i | \(0.745693\pi\) | |||||||
\(168\) | 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 | \(0.319846\pi\) | ||||
−0.536236 | + | 0.844068i | \(0.680154\pi\) | |||||||
\(174\) | 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 | \(-0.940465\pi\) | ||
0.982560 | − | 0.185945i | \(-0.0595347\pi\) | |||||||
\(182\) | 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 | \(0.210749\pi\) | ||||
−0.788711 | + | 0.614764i | \(0.789251\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.74211 | −0.626035 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.16663i | 0.653095i | 0.945181 | + | 0.326548i | \(0.105885\pi\) | ||||
−0.945181 | + | 0.326548i | \(0.894115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.96742i | − | 0.352131i | −0.984378 | − | 0.176066i | \(-0.943663\pi\) | ||
0.984378 | − | 0.176066i | \(-0.0563371\pi\) | |||||||
\(200\) | 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 | \(0.190077\pi\) | ||||
−0.826944 | + | 0.562284i | \(0.809923\pi\) | |||||||
\(212\) | 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 | \(-0.781734\pi\) | ||
0.773975 | − | 0.633217i | \(-0.218266\pi\) | |||||||
\(228\) | 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 | \(-0.809862\pi\) | ||
0.826838 | − | 0.562441i | \(-0.190138\pi\) | |||||||
\(234\) | 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 | \(-0.655556\pi\) | ||
0.469473 | − | 0.882947i | \(-0.344444\pi\) | |||||||
\(242\) | 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 | \(0.178821\pi\) | ||||
−0.846307 | + | 0.532695i | \(0.821179\pi\) | |||||||
\(270\) | 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 | \(-0.862944\pi\) | ||
0.908726 | − | 0.417394i | \(-0.137056\pi\) | |||||||
\(278\) | 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 | \(-0.694319\pi\) | ||
0.573254 | − | 0.819378i | \(-0.305681\pi\) | |||||||
\(284\) | 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 | \(-0.714127\pi\) | ||
0.623100 | − | 0.782142i | \(-0.285873\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.2054i | 1.48122i | 0.671935 | + | 0.740610i | \(0.265463\pi\) | ||||
−0.671935 | + | 0.740610i | \(0.734537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.0475 | −1.69299 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 11.8975i | − | 0.668227i | −0.942533 | − | 0.334114i | \(-0.891563\pi\) | ||
0.942533 | − | 0.334114i | \(-0.108437\pi\) | |||||||
\(318\) | 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 | \(-0.578265\pi\) | ||
0.243408 | − | 0.969924i | \(-0.421735\pi\) | |||||||
\(338\) | 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 | \(0.120825\pi\) | ||||
−0.928820 | + | 0.370532i | \(0.879175\pi\) | |||||||
\(348\) | 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 | \(0.251637\pi\) | ||||
−0.703462 | + | 0.710733i | \(0.748363\pi\) | |||||||
\(368\) | 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 | \(-0.893749\pi\) | ||
0.944805 | − | 0.327633i | \(-0.106251\pi\) | |||||||
\(380\) | 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 | \(-0.795267\pi\) | ||
0.800187 | − | 0.599750i | \(-0.204733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.16201 | 0.158298 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5266i | 0.825297i | 0.910890 | + | 0.412648i | \(0.135396\pi\) | ||||
−0.910890 | + | 0.412648i | \(0.864604\pi\) | |||||||
\(402\) | 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 | \(0.167670\pi\) | ||||
−0.864445 | + | 0.502727i | \(0.832330\pi\) | |||||||
\(420\) | 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 | \(0.0693727\pi\) | ||||
−0.976345 | + | 0.216219i | \(0.930627\pi\) | |||||||
\(432\) | 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 | \(0.0150256\pi\) | ||||
−0.998886 | + | 0.0471868i | \(0.984974\pi\) | |||||||
\(440\) | 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 | \(0.381212\pi\) | ||||
−0.364583 | + | 0.931171i | \(0.618788\pi\) | |||||||
\(450\) | 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 | \(-0.961771\pi\) | ||
0.992797 | − | 0.119810i | \(-0.0382287\pi\) | |||||||
\(480\) | 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 | \(0.261920\pi\) | ||||
−0.680137 | + | 0.733085i | \(0.738080\pi\) | |||||||
\(488\) | 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 | \(-0.910166\pi\) | ||
0.960439 | − | 0.278489i | \(-0.0898337\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.9886 | −0.490934 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 31.5232i | − | 1.40555i | −0.711413 | − | 0.702774i | \(-0.751944\pi\) | ||
0.711413 | − | 0.702774i | \(-0.248056\pi\) | |||||||
\(504\) | 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 | \(-0.904975\pi\) | ||
0.955770 | − | 0.294114i | \(-0.0950245\pi\) | |||||||
\(522\) | 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 | \(-0.860965\pi\) | ||
0.906113 | − | 0.423036i | \(-0.139035\pi\) | |||||||
\(542\) | 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 | \(-0.928822\pi\) | ||
0.975103 | − | 0.221753i | \(-0.0711777\pi\) | |||||||
\(548\) | 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 | \(0.173687\pi\) | ||||
−0.854788 | + | 0.518978i | \(0.826313\pi\) | |||||||
\(572\) | 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 | \(-0.936159\pi\) | ||
0.979955 | − | 0.199219i | \(-0.0638406\pi\) | |||||||
\(602\) | 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 | \(-0.862776\pi\) | ||
0.908505 | − | 0.417873i | \(-0.137224\pi\) | |||||||
\(608\) | 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 | \(-0.873467\pi\) | ||
0.922026 | − | 0.387129i | \(-0.126533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.18242i | − | 0.0877188i | −0.999038 | − | 0.0438594i | \(-0.986035\pi\) | ||
0.999038 | − | 0.0438594i | \(-0.0139654\pi\) | |||||||
\(620\) | 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 | \(0.187897\pi\) | ||||
−0.830776 | + | 0.556607i | \(0.812103\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8432i | 0.545924i | 0.962025 | + | 0.272962i | \(0.0880033\pi\) | ||||
−0.962025 | + | 0.272962i | \(0.911997\pi\) | |||||||
\(644\) | 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 | \(0.0342728\pi\) | ||||
−0.994209 | + | 0.107463i | \(0.965727\pi\) | |||||||
\(654\) | 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 | \(0.0289429\pi\) | ||||
−0.995869 | + | 0.0908016i | \(0.971057\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 33.5703i | − | 1.29212i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.39320i | 0.0535450i | 0.999642 | + | 0.0267725i | \(0.00852297\pi\) | ||||
−0.999642 | + | 0.0267725i | \(0.991477\pi\) | |||||||
\(678\) | 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 | \(-0.749482\pi\) | ||
0.705956 | − | 0.708256i | \(-0.250518\pi\) | |||||||
\(684\) | 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 | \(-0.770278\pi\) | ||
0.750688 | − | 0.660657i | \(-0.229722\pi\) | |||||||
\(692\) | 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 | \(0.362808\pi\) | ||||
−0.417781 | + | 0.908548i | \(0.637192\pi\) | |||||||
\(710\) | 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 | \(0.0585430\pi\) | ||||
−0.983135 | + | 0.182883i | \(0.941457\pi\) | |||||||
\(720\) | 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 | \(0.00281422\pi\) | ||||
−0.999961 | + | 0.00884102i | \(0.997186\pi\) | |||||||
\(744\) | 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 | \(-0.786078\pi\) | ||
0.782543 | − | 0.622597i | \(-0.213922\pi\) | |||||||
\(752\) | 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 | \(0.228638\pi\) | ||||
−0.752933 | + | 0.658097i | \(0.771362\pi\) | |||||||
\(788\) | 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 | \(0.0187777\pi\) | ||||
−0.998260 | + | 0.0589575i | \(0.981222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.9645i | − | 1.05220i | −0.850424 | − | 0.526098i | \(-0.823655\pi\) | ||
0.850424 | − | 0.526098i | \(-0.176345\pi\) | |||||||
\(812\) | 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 | \(-0.654929\pi\) | ||
0.467733 | − | 0.883870i | \(-0.345071\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.4677i | 1.20147i | 0.799449 | + | 0.600734i | \(0.205125\pi\) | ||||
−0.799449 | + | 0.600734i | \(0.794875\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.4266 | 1.02450 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.8530i | 1.83788i | 0.394400 | + | 0.918939i | \(0.370953\pi\) | ||||
−0.394400 | + | 0.918939i | \(0.629047\pi\) | |||||||
\(828\) | 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 | \(-0.872875\pi\) | ||
0.921304 | − | 0.388843i | \(-0.127125\pi\) | |||||||
\(840\) | 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 | \(0.257733\pi\) | ||||
−0.689721 | + | 0.724075i | \(0.742267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 18.6783i | − | 0.638783i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.4900i | 1.48559i | 0.669520 | + | 0.742794i | \(0.266500\pi\) | ||||
−0.669520 | + | 0.742794i | \(0.733500\pi\) | |||||||
\(858\) | 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 | \(-0.792434\pi\) | ||
0.794819 | − | 0.606847i | \(-0.207566\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.18512i | − | 0.107432i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.4598i | 1.19467i | 0.801992 | + | 0.597335i | \(0.203774\pi\) | ||||
−0.801992 | + | 0.597335i | \(0.796226\pi\) | |||||||
\(882\) | 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 | \(-0.570281\pi\) | ||
0.219006 | − | 0.975723i | \(-0.429719\pi\) | |||||||
\(888\) | 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 | \(-0.843890\pi\) | ||
0.882129 | − | 0.471008i | \(-0.156110\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.2950 | −1.10433 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.65666i | − | 0.253676i | −0.991923 | − | 0.126838i | \(-0.959517\pi\) | ||
0.991923 | − | 0.126838i | \(-0.0404829\pi\) | |||||||
\(912\) | 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 | \(0.103958\pi\) | ||||
−0.947140 | + | 0.320820i | \(0.896042\pi\) | |||||||
\(930\) | 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 | \(0.125853\pi\) | ||||
−0.922851 | + | 0.385158i | \(0.874147\pi\) | |||||||
\(942\) | 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 | \(0.122339\pi\) | ||||
−0.927046 | + | 0.374948i | \(0.877661\pi\) | |||||||
\(948\) | 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 | \(0.128230\pi\) | ||||
−0.919949 | + | 0.392039i | \(0.871770\pi\) | |||||||
\(984\) | 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 | \(0.0988639\pi\) | ||||
−0.952153 | + | 0.305621i | \(0.901136\pi\) | |||||||
\(992\) | 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 | \(0.00988028\pi\) | ||||
−0.999518 | + | 0.0310348i | \(0.990120\pi\) | |||||||
\(998\) | 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.237.28 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.19 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.19 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.28 | yes | 46 | 1.1 | even | 1 | trivial |