Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8032,2,Mod(1,8032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8032 = 2^{5} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8032.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1358429035\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8032.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.513479 | −0.296457 | −0.148229 | − | 0.988953i | \(-0.547357\pi\) | ||||
−0.148229 | + | 0.988953i | \(0.547357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.65851 | 1.63614 | 0.818068 | − | 0.575121i | \(-0.195045\pi\) | ||||
0.818068 | + | 0.575121i | \(0.195045\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.146814 | −0.0554905 | −0.0277453 | − | 0.999615i | \(-0.508833\pi\) | ||||
−0.0277453 | + | 0.999615i | \(0.508833\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.73634 | −0.912113 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.10614 | −0.333512 | −0.166756 | − | 0.985998i | \(-0.553329\pi\) | ||||
−0.166756 | + | 0.985998i | \(0.553329\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.53847 | −1.53610 | −0.768048 | − | 0.640392i | \(-0.778772\pi\) | ||||
−0.768048 | + | 0.640392i | \(0.778772\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.87857 | −0.485045 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.13916 | 1.00389 | 0.501947 | − | 0.864898i | \(-0.332617\pi\) | ||||
0.501947 | + | 0.864898i | \(0.332617\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.16367 | −0.955212 | −0.477606 | − | 0.878574i | \(-0.658495\pi\) | ||||
−0.477606 | + | 0.878574i | \(0.658495\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0753860 | 0.0164506 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.90373 | 1.85656 | 0.928278 | − | 0.371888i | \(-0.121290\pi\) | ||||
0.928278 | + | 0.371888i | \(0.121290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.38472 | 1.67694 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.94549 | 0.566860 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.49912 | −0.464075 | −0.232037 | − | 0.972707i | \(-0.574539\pi\) | ||||
−0.232037 | + | 0.972707i | \(0.574539\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5175 | 1.88899 | 0.944497 | − | 0.328521i | \(-0.106550\pi\) | ||||
0.944497 | + | 0.328521i | \(0.106550\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.567977 | 0.0988722 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.537121 | −0.0907901 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.89054 | −0.639601 | −0.319800 | − | 0.947485i | \(-0.603616\pi\) | ||||
−0.319800 | + | 0.947485i | \(0.603616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.84389 | 0.455387 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.80331 | −0.437804 | −0.218902 | − | 0.975747i | \(-0.570247\pi\) | ||||
−0.218902 | + | 0.975747i | \(0.570247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.32039 | 1.11635 | 0.558175 | − | 0.829723i | \(-0.311502\pi\) | ||||
0.558175 | + | 0.829723i | \(0.311502\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.0109 | −1.49234 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.06109 | −0.592371 | −0.296185 | − | 0.955131i | \(-0.595715\pi\) | ||||
−0.296185 | + | 0.955131i | \(0.595715\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97845 | −0.996921 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.12537 | −0.297612 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.79452 | −0.933299 | −0.466649 | − | 0.884442i | \(-0.654539\pi\) | ||||
−0.466649 | + | 0.884442i | \(0.654539\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.04681 | −0.545672 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.13796 | 0.283180 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.3028 | 1.73188 | 0.865938 | − | 0.500151i | \(-0.166722\pi\) | ||||
0.865938 | + | 0.500151i | \(0.166722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.86321 | 0.494634 | 0.247317 | − | 0.968935i | \(-0.420451\pi\) | ||||
0.247317 | + | 0.968935i | \(0.420451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.401733 | 0.0506136 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.2626 | −2.51326 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0938 | −1.47750 | −0.738748 | − | 0.673981i | \(-0.764583\pi\) | ||||
−0.738748 | + | 0.673981i | \(0.764583\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.57188 | −0.550389 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.607392 | −0.0720842 | −0.0360421 | − | 0.999350i | \(-0.511475\pi\) | ||||
−0.0360421 | + | 0.999350i | \(0.511475\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.61197 | 0.188667 | 0.0943335 | − | 0.995541i | \(-0.469928\pi\) | ||||
0.0943335 | + | 0.995541i | \(0.469928\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.30538 | −0.497142 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.162396 | 0.0185068 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.403251 | 0.0453693 | 0.0226846 | − | 0.999743i | \(-0.492779\pi\) | ||||
0.0226846 | + | 0.999743i | \(0.492779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.69657 | 0.744063 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.41012 | 0.593838 | 0.296919 | − | 0.954903i | \(-0.404041\pi\) | ||||
0.296919 | + | 0.954903i | \(0.404041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.1432 | 1.64251 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.28324 | 0.137578 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.27215 | 0.558847 | 0.279423 | − | 0.960168i | \(-0.409857\pi\) | ||||
0.279423 | + | 0.960168i | \(0.409857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.813126 | 0.0852388 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.40050 | −0.560006 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.2329 | −1.56286 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2094 | 1.23968 | 0.619839 | − | 0.784729i | \(-0.287198\pi\) | ||||
0.619839 | + | 0.784729i | \(0.287198\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.02676 | 0.304201 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.30614 | 0.726988 | 0.363494 | − | 0.931596i | \(-0.381584\pi\) | ||||
0.363494 | + | 0.931596i | \(0.381584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.35535 | 0.921810 | 0.460905 | − | 0.887450i | \(-0.347525\pi\) | ||||
0.460905 | + | 0.887450i | \(0.347525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.275801 | 0.0269154 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.651858 | −0.0630175 | −0.0315087 | − | 0.999503i | \(-0.510031\pi\) | ||||
−0.0315087 | + | 0.999503i | \(0.510031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4705 | −1.57759 | −0.788795 | − | 0.614657i | \(-0.789294\pi\) | ||||
−0.788795 | + | 0.614657i | \(0.789294\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.99771 | 0.189614 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.08521 | 0.196160 | 0.0980801 | − | 0.995179i | \(-0.468730\pi\) | ||||
0.0980801 | + | 0.995179i | \(0.468730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.5744 | 3.03758 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.1551 | 1.40109 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.607687 | −0.0557066 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.77646 | −0.888770 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.43944 | 0.129790 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.3830 | 1.10757 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.77618 | −0.246346 | −0.123173 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123173 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.75887 | −0.330950 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.5711 | 1.44782 | 0.723910 | − | 0.689894i | \(-0.242343\pi\) | ||||
0.723910 | + | 0.689894i | \(0.242343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.611286 | 0.0530052 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.7761 | 0.927460 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.3014 | 1.05098 | 0.525490 | − | 0.850800i | \(-0.323882\pi\) | ||||
0.525490 | + | 0.850800i | \(0.323882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1736 | 1.03255 | 0.516276 | − | 0.856422i | \(-0.327318\pi\) | ||||
0.516276 | + | 0.856422i | \(0.327318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.08528 | 0.175613 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.12630 | 0.512307 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.14306 | −0.759289 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.58329 | 0.295544 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.332666 | 0.0272531 | 0.0136265 | − | 0.999907i | \(-0.495662\pi\) | ||||
0.0136265 | + | 0.999907i | \(0.495662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8096 | 0.961054 | 0.480527 | − | 0.876980i | \(-0.340445\pi\) | ||||
0.480527 | + | 0.876980i | \(0.340445\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.3261 | −0.915665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 38.4783 | 3.09065 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5185 | 0.839466 | 0.419733 | − | 0.907648i | \(-0.362124\pi\) | ||||
0.419733 | + | 0.907648i | \(0.362124\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.48884 | 0.276683 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.30719 | −0.103021 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.925899 | −0.0725220 | −0.0362610 | − | 0.999342i | \(-0.511545\pi\) | ||||
−0.0362610 | + | 0.999342i | \(0.511545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.07795 | 0.161768 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.06548 | −0.314596 | −0.157298 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157298 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.6747 | 1.35959 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.3932 | 0.871262 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.9829 | 1.29118 | 0.645592 | − | 0.763682i | \(-0.276611\pi\) | ||||
0.645592 | + | 0.763682i | \(0.276611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.23099 | −0.0930545 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.83071 | −0.513427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.3149 | −0.770970 | −0.385485 | − | 0.922714i | \(-0.625966\pi\) | ||||
−0.385485 | + | 0.922714i | \(0.625966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.04859 | 0.375259 | 0.187629 | − | 0.982240i | \(-0.439920\pi\) | ||||
0.187629 | + | 0.982240i | \(0.439920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.98368 | −0.146638 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.2336 | −1.04647 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.57847 | −0.334811 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.432440 | −0.0314553 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1335 | −0.733232 | −0.366616 | − | 0.930372i | \(-0.619484\pi\) | ||||
−0.366616 | + | 0.930372i | \(0.619484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.97497 | 0.358106 | 0.179053 | − | 0.983839i | \(-0.442697\pi\) | ||||
0.179053 | + | 0.983839i | \(0.442697\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.4044 | 0.745075 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.61719 | −0.542703 | −0.271351 | − | 0.962480i | \(-0.587471\pi\) | ||||
−0.271351 | + | 0.962480i | \(0.587471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0875 | 1.06952 | 0.534761 | − | 0.845004i | \(-0.320402\pi\) | ||||
0.534761 | + | 0.845004i | \(0.320402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.20993 | 0.438015 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.366906 | 0.0257517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.2560 | −0.716307 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.3636 | −1.69339 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.60559 | 0.318575 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3372 | 1.26239 | 0.631193 | − | 0.775626i | \(-0.282566\pi\) | ||||
0.631193 | + | 0.775626i | \(0.282566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.311883 | 0.0213699 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 26.7818 | 1.82650 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.54411 | −0.104821 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.827714 | −0.0559317 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.9246 | −1.54208 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2459 | 1.69059 | 0.845295 | − | 0.534300i | \(-0.179425\pi\) | ||||
0.845295 | + | 0.534300i | \(0.179425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.9434 | −1.52956 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.7417 | −0.978440 | −0.489220 | − | 0.872160i | \(-0.662718\pi\) | ||||
−0.489220 | + | 0.872160i | \(0.662718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.9195 | 1.31632 | 0.658158 | − | 0.752880i | \(-0.271336\pi\) | ||||
0.658158 | + | 0.752880i | \(0.271336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0833871 | −0.00548647 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.1824 | −1.45322 | −0.726609 | − | 0.687051i | \(-0.758905\pi\) | ||||
−0.726609 | + | 0.687051i | \(0.758905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.8575 | −0.969199 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.207061 | −0.0134501 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.6759 | −1.27273 | −0.636364 | − | 0.771389i | \(-0.719562\pi\) | ||||
−0.636364 | + | 0.771389i | \(0.719562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4588 | 1.57553 | 0.787765 | − | 0.615975i | \(-0.211238\pi\) | ||||
0.787765 | + | 0.615975i | \(0.211238\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.2750 | −0.787443 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −25.5307 | −1.63110 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.0604 | 1.46730 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.77798 | −0.176048 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.84873 | −0.619184 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.77570 | −0.486933 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.4609 | 1.15156 | 0.575778 | − | 0.817606i | \(-0.304699\pi\) | ||||
0.575778 | + | 0.817606i | \(0.304699\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.571186 | 0.0354918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.83844 | 0.423289 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9493 | 0.798491 | 0.399245 | − | 0.916844i | \(-0.369272\pi\) | ||||
0.399245 | + | 0.916844i | \(0.369272\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.8578 | −1.52700 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.70714 | −0.165674 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.366421 | −0.0223411 | −0.0111705 | − | 0.999938i | \(-0.503556\pi\) | ||||
−0.0111705 | + | 0.999938i | \(0.503556\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4672 | −0.635838 | −0.317919 | − | 0.948118i | \(-0.602984\pi\) | ||||
−0.317919 | + | 0.948118i | \(0.602984\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.417523 | −0.0252697 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.27463 | −0.559281 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.3880 | −1.34517 | −0.672583 | − | 0.740022i | \(-0.734815\pi\) | ||||
−0.672583 | + | 0.740022i | \(0.734815\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −28.7794 | −1.72298 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.1397 | 1.38040 | 0.690199 | − | 0.723620i | \(-0.257523\pi\) | ||||
0.690199 | + | 0.723620i | \(0.257523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.2230 | 1.32102 | 0.660510 | − | 0.750817i | \(-0.270340\pi\) | ||||
0.660510 | + | 0.750817i | \(0.270340\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.82175 | 0.463321 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.411566 | 0.0242940 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.132645 | 0.00780262 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.26928 | −0.367511 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1071 | −0.648883 | −0.324442 | − | 0.945906i | \(-0.605176\pi\) | ||||
−0.324442 | + | 0.945906i | \(0.605176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.6684 | 2.83359 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.25811 | −0.189055 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −49.3131 | −2.85185 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07474 | −0.0619468 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.75155 | −0.215521 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.1336 | 0.809289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7401 | 0.841260 | 0.420630 | − | 0.907232i | \(-0.361809\pi\) | ||||
0.420630 | + | 0.907232i | \(0.361809\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.80377 | −0.273277 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.2075 | −1.25927 | −0.629636 | − | 0.776891i | \(-0.716796\pi\) | ||||
−0.629636 | + | 0.776891i | \(0.716796\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.49330 | −0.0844062 | −0.0422031 | − | 0.999109i | \(-0.513438\pi\) | ||||
−0.0422031 | + | 0.999109i | \(0.513438\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.46975 | 0.0828108 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.2510 | −0.575752 | −0.287876 | − | 0.957668i | \(-0.592949\pi\) | ||||
−0.287876 | + | 0.957668i | \(0.592949\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.76436 | 0.154775 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.334715 | 0.0186820 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.2341 | −0.958932 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −46.4385 | −2.57595 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.45726 | 0.467688 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.596225 | 0.0328709 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.63251 | −0.199661 | −0.0998305 | − | 0.995004i | \(-0.531830\pi\) | ||||
−0.0998305 | + | 0.995004i | \(0.531830\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.6458 | 0.583388 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −44.2454 | −2.41739 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.1260 | 1.25975 | 0.629877 | − | 0.776695i | \(-0.283105\pi\) | ||||
0.629877 | + | 0.776695i | \(0.283105\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.07071 | −0.0581531 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6337 | −0.630003 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.05223 | 0.110810 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.7263 | −0.900512 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.28619 | −0.283778 | −0.141889 | − | 0.989883i | \(-0.545318\pi\) | ||||
−0.141889 | + | 0.989883i | \(0.545318\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.46261 | 0.399464 | 0.199732 | − | 0.979851i | \(-0.435993\pi\) | ||||
0.199732 | + | 0.979851i | \(0.435993\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.3135 | −0.870751 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3630 | 0.551566 | 0.275783 | − | 0.961220i | \(-0.411063\pi\) | ||||
0.275783 | + | 0.961220i | \(0.411063\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.22215 | −0.117940 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.312035 | 0.0165146 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.1864 | 1.75151 | 0.875754 | − | 0.482757i | \(-0.160365\pi\) | ||||
0.875754 | + | 0.482757i | \(0.160365\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.66382 | −0.0875693 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.02001 | 0.263482 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.89742 | 0.308685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.2801 | −0.902013 | −0.451007 | − | 0.892521i | \(-0.648935\pi\) | ||||
−0.451007 | + | 0.892521i | \(0.648935\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.67081 | 0.399326 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.997531 | 0.0517892 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.8035 | 1.07716 | 0.538581 | − | 0.842574i | \(-0.318960\pi\) | ||||
0.538581 | + | 0.842574i | \(0.318960\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.35843 | −0.328348 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8413 | 0.712863 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.9226 | −1.02336 | −0.511679 | − | 0.859177i | \(-0.670976\pi\) | ||||
−0.511679 | + | 0.859177i | \(0.670976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.42551 | 0.0730311 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.2040 | −0.623595 | −0.311798 | − | 0.950149i | \(-0.600931\pi\) | ||||
−0.311798 | + | 0.950149i | \(0.600931\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.594129 | 0.0302796 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.0311 | −1.01824 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.64158 | 0.488848 | 0.244424 | − | 0.969669i | \(-0.421401\pi\) | ||||
0.244424 | + | 0.969669i | \(0.421401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.8539 | 1.86378 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.50890 | −0.429217 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.47530 | 0.0742304 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3447 | −0.669754 | −0.334877 | − | 0.942262i | \(-0.608695\pi\) | ||||
−0.334877 | + | 0.942262i | \(0.608695\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.313883 | −0.0157138 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.5500 | 1.42572 | 0.712860 | − | 0.701307i | \(-0.247400\pi\) | ||||
0.712860 | + | 0.701307i | \(0.247400\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −58.2507 | −2.90168 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.4995 | 1.21739 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.30346 | 0.213315 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.6542 | −0.526818 | −0.263409 | − | 0.964684i | \(-0.584847\pi\) | ||||
−0.263409 | + | 0.964684i | \(0.584847\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.31651 | −0.311570 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.95304 | −0.0961027 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.7930 | 0.971600 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.25089 | −0.306107 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.3383 | 0.944740 | 0.472370 | − | 0.881400i | \(-0.343399\pi\) | ||||
0.472370 | + | 0.881400i | \(0.343399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.9152 | 1.50672 | 0.753358 | − | 0.657610i | \(-0.228433\pi\) | ||||
0.753358 | + | 0.657610i | \(0.228433\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.1125 | 0.540309 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 34.7057 | 1.68347 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.567174 | −0.0274475 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.14573 | −0.151877 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1973 | −0.635693 | −0.317847 | − | 0.948142i | \(-0.602960\pi\) | ||||
−0.317847 | + | 0.948142i | \(0.602960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.45262 | −0.165922 | −0.0829611 | − | 0.996553i | \(-0.526438\pi\) | ||||
−0.0829611 | + | 0.996553i | \(0.526438\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.69477 | 0.225097 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.0722 | −1.77340 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.2950 | 1.01636 | 0.508178 | − | 0.861252i | \(-0.330319\pi\) | ||||
0.508178 | + | 0.861252i | \(0.330319\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.0954 | 0.909304 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4198 | 1.30275 | 0.651377 | − | 0.758754i | \(-0.274192\pi\) | ||||
0.651377 | + | 0.758754i | \(0.274192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.2882 | 0.914350 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.170817 | −0.00807937 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.4545 | −1.95636 | −0.978180 | − | 0.207757i | \(-0.933384\pi\) | ||||
−0.978180 | + | 0.207757i | \(0.933384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.10084 | 0.146013 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.06400 | −0.284911 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.97483 | 0.139462 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.6703 | −1.66859 | −0.834293 | − | 0.551321i | \(-0.814124\pi\) | ||||
−0.834293 | + | 0.551321i | \(0.814124\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.1919 | 0.569067 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7995 | 0.502982 | 0.251491 | − | 0.967860i | \(-0.419079\pi\) | ||||
0.251491 | + | 0.967860i | \(0.419079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.6864 | 1.75144 | 0.875718 | − | 0.482824i | \(-0.160389\pi\) | ||||
0.875718 | + | 0.482824i | \(0.160389\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.7578 | −0.916246 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.7099 | −1.28226 | −0.641131 | − | 0.767432i | \(-0.721534\pi\) | ||||
−0.641131 | + | 0.767432i | \(0.721534\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.77555 | 0.0819871 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.40102 | −0.248866 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.09735 | −0.372316 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.9112 | −1.60184 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.5921 | 0.851274 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.3872 | 0.565984 | 0.282992 | − | 0.959122i | \(-0.408673\pi\) | ||||
0.282992 | + | 0.959122i | \(0.408673\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.5477 | 0.982488 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.671216 | 0.0305414 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.6683 | 2.02828 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.5896 | 1.74866 | 0.874331 | − | 0.485331i | \(-0.161301\pi\) | ||||
0.874331 | + | 0.485331i | \(0.161301\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.475430 | 0.0214997 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.5864 | −0.477756 | −0.238878 | − | 0.971050i | \(-0.576780\pi\) | ||||
−0.238878 | + | 0.971050i | \(0.576780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3442 | −0.465882 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.0734 | 0.497714 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0891737 | 0.00399999 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.40586 | 0.152467 | 0.0762336 | − | 0.997090i | \(-0.475711\pi\) | ||||
0.0762336 | + | 0.997090i | \(0.475711\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.08754 | 0.0932644 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.0841 | 1.20762 | 0.603809 | − | 0.797129i | \(-0.293649\pi\) | ||||
0.603809 | + | 0.797129i | \(0.293649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.7296 | 1.18945 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.07559 | −0.403061 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.13933 | −0.272121 | −0.136060 | − | 0.990701i | \(-0.543444\pi\) | ||||
−0.136060 | + | 0.990701i | \(0.543444\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.236660 | −0.0104692 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.2641 | −0.541472 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.2267 | 1.50821 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.49211 | 0.197563 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.72035 | −0.382781 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.900655 | 0.0394584 | 0.0197292 | − | 0.999805i | \(-0.493720\pi\) | ||||
0.0197292 | + | 0.999805i | \(0.493720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7590 | −1.12636 | −0.563182 | − | 0.826333i | \(-0.690423\pi\) | ||||
−0.563182 | + | 0.826333i | \(0.690423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.632090 | 0.0275867 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.5335 | 1.89635 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.2763 | 2.44680 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.4010 | −1.57967 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.5261 | 0.672509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.38483 | −0.103105 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.29647 | 0.228560 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.71911 | 0.332485 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.555268 | −0.0238728 | −0.0119364 | − | 0.999929i | \(-0.503800\pi\) | ||||
−0.0119364 | + | 0.999929i | \(0.503800\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.59234 | −0.111248 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −60.2576 | −2.58115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.3057 | −1.29578 | −0.647890 | − | 0.761734i | \(-0.724348\pi\) | ||||
−0.647890 | + | 0.761734i | \(0.724348\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5711 | −0.451162 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4055 | 0.443290 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0592030 | −0.00251757 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.30865 | 0.310235 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.66320 | 0.324700 | 0.162350 | − | 0.986733i | \(-0.448093\pi\) | ||||
0.162350 | + | 0.986733i | \(0.448093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.5438 | −1.71482 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.35095 | 0.0992572 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.4275 | −0.692337 | −0.346169 | − | 0.938172i | \(-0.612518\pi\) | ||||
−0.346169 | + | 0.938172i | \(0.612518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.62877 | 0.320945 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.983151 | −0.0412885 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.7236 | 0.575325 | 0.287663 | − | 0.957732i | \(-0.407122\pi\) | ||||
0.287663 | + | 0.957732i | \(0.407122\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6548 | −0.613285 | −0.306643 | − | 0.951825i | \(-0.599206\pi\) | ||||
−0.306643 | + | 0.951825i | \(0.599206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.20332 | 0.217372 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 74.6552 | 3.11334 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.3647 | −1.38899 | −0.694495 | − | 0.719498i | \(-0.744372\pi\) | ||||
−0.694495 | + | 0.719498i | \(0.744372\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.55454 | −0.106163 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.794282 | −0.0329524 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.51565 | 0.311267 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 55.4453 | 2.29238 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.6944 | −1.43199 | −0.715996 | − | 0.698104i | \(-0.754027\pi\) | ||||
−0.715996 | + | 0.698104i | \(0.754027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.7913 | −1.80439 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.91127 | 0.160888 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.1688 | −1.52634 | −0.763171 | − | 0.646197i | \(-0.776358\pi\) | ||||
−0.763171 | + | 0.646197i | \(0.776358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.22323 | −0.0911436 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.74709 | −0.317067 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.4568 | −1.12185 | −0.560927 | − | 0.827865i | \(-0.689555\pi\) | ||||
−0.560927 | + | 0.827865i | \(0.689555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6136 | −0.432936 | −0.216468 | − | 0.976290i | \(-0.569454\pi\) | ||||
−0.216468 | + | 0.976290i | \(0.569454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.0928 | 1.34764 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.7673 | −1.45415 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.6277 | 1.73021 | 0.865103 | − | 0.501594i | \(-0.167253\pi\) | ||||
0.865103 | + | 0.501594i | \(0.167253\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.188398 | −0.00763429 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.4922 | 0.909938 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.6046 | 1.39767 | 0.698834 | − | 0.715284i | \(-0.253703\pi\) | ||||
0.698834 | + | 0.715284i | \(0.253703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.26622 | 0.212354 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.90255 | 0.157111 | 0.0785554 | − | 0.996910i | \(-0.474969\pi\) | ||||
0.0785554 | + | 0.996910i | \(0.474969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.70819 | 0.350012 | 0.175006 | − | 0.984567i | \(-0.444006\pi\) | ||||
0.175006 | + | 0.984567i | \(0.444006\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.2258 | 1.05241 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.774026 | −0.0310107 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.37988 | 0.135195 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.36487 | −0.0944439 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.1036 | −0.642091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.90155 | −0.314556 | −0.157278 | − | 0.987554i | \(-0.550272\pi\) | ||||
−0.157278 | + | 0.987554i | \(0.550272\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.41578 | −0.374244 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.1567 | −0.403056 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.6499 | 1.53137 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.66203 | 0.0657489 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2276 | −1.58889 | −0.794447 | − | 0.607333i | \(-0.792239\pi\) | ||||
−0.794447 | + | 0.607333i | \(0.792239\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.3566 | 1.70982 | 0.854909 | − | 0.518778i | \(-0.173613\pi\) | ||||
0.854909 | + | 0.518778i | \(0.173613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.7519 | −0.541479 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.8168 | 0.779078 | 0.389539 | − | 0.921010i | \(-0.372634\pi\) | ||||
0.389539 | + | 0.921010i | \(0.372634\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.7147 | −0.577602 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.792870 | 0.0310750 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.18807 | −0.242158 | −0.121079 | − | 0.992643i | \(-0.538635\pi\) | ||||
−0.121079 | + | 0.992643i | \(0.538635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 60.6255 | 2.36883 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.41090 | −0.172086 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.5381 | 0.644233 | 0.322116 | − | 0.946700i | \(-0.395606\pi\) | ||||
0.322116 | + | 0.946700i | \(0.395606\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.3680 | −0.597747 | −0.298874 | − | 0.954293i | \(-0.596611\pi\) | ||||
−0.298874 | + | 0.954293i | \(0.596611\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.7713 | 0.457160 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.23640 | 0.0867238 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.2515 | −0.861580 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9632 | −0.501188 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.27324 | −0.164967 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.1903 | −0.546995 | −0.273498 | − | 0.961873i | \(-0.588181\pi\) | ||||
−0.273498 | + | 0.961873i | \(0.588181\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.6971 | 0.950592 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6816 | −0.487394 | −0.243697 | − | 0.969851i | \(-0.578360\pi\) | ||||
−0.243697 | + | 0.969851i | \(0.578360\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.79251 | −0.0687904 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.56955 | 0.290066 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.9509 | −0.839927 | −0.419964 | − | 0.907541i | \(-0.637957\pi\) | ||||
−0.419964 | + | 0.907541i | \(0.637957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.0048 | 1.71955 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.2282 | −0.390231 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37.6313 | 1.43364 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.23221 | 0.313168 | 0.156584 | − | 0.987665i | \(-0.449952\pi\) | ||||
0.156584 | + | 0.987665i | \(0.449952\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.444371 | −0.0168803 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 44.5373 | 1.68940 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.6034 | −0.439508 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.3902 | 0.430817 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.72402 | −0.216193 | −0.108097 | − | 0.994140i | \(-0.534476\pi\) | ||||
−0.108097 | + | 0.994140i | \(0.534476\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.1989 | 0.610955 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.62904 | 0.287326 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.07264 | −0.0403410 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.810559 | 0.0304412 | 0.0152206 | − | 0.999884i | \(-0.495155\pi\) | ||||
0.0152206 | + | 0.999884i | \(0.495155\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.10343 | −0.0413819 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 93.6447 | 3.50702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.4132 | 0.838204 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.1032 | 0.377310 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.4465 | 0.464176 | 0.232088 | − | 0.972695i | \(-0.425444\pi\) | ||||
0.232088 | + | 0.972695i | \(0.425444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.37350 | −0.0511517 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.5591 | −0.467078 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.9544 | −0.778227 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.7123 | 0.916529 | 0.458264 | − | 0.888816i | \(-0.348471\pi\) | ||||
0.458264 | + | 0.888816i | \(0.348471\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.7867 | −0.510620 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.3003 | 1.12070 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.98022 | 0.110077 | 0.0550386 | − | 0.998484i | \(-0.482472\pi\) | ||||
0.0550386 | + | 0.998484i | \(0.482472\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.1095 | 0.483551 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.3774 | 0.492763 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.3734 | −0.565520 | −0.282760 | − | 0.959191i | \(-0.591250\pi\) | ||||
−0.282760 | + | 0.959191i | \(0.591250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.8410 | −0.434991 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.6367 | −1.30738 | −0.653691 | − | 0.756762i | \(-0.726780\pi\) | ||||
−0.653691 | + | 0.756762i | \(0.726780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.21706 | 0.0445898 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.8039 | −0.541647 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0957019 | 0.00349687 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.4970 | 1.11285 | 0.556426 | − | 0.830897i | \(-0.312172\pi\) | ||||
0.556426 | + | 0.830897i | \(0.312172\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.513479 | −0.0187122 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.2057 | 1.57242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.1242 | −0.440661 | −0.220331 | − | 0.975425i | \(-0.570714\pi\) | ||||
−0.220331 | + | 0.975425i | \(0.570714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.05711 | 0.183562 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.4881 | −0.815194 | −0.407597 | − | 0.913162i | \(-0.633633\pi\) | ||||
−0.407597 | + | 0.913162i | \(0.633633\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.41810 | 0.0875412 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.4368 | −1.49815 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −73.6772 | −2.66033 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.1763 | −1.16031 | −0.580153 | − | 0.814507i | \(-0.697007\pi\) | ||||
−0.580153 | + | 0.814507i | \(0.697007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.47926 | −0.341387 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3506 | 1.27147 | 0.635737 | − | 0.771906i | \(-0.280696\pi\) | ||||
0.635737 | + | 0.771906i | \(0.280696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 88.1860 | 3.16773 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.293292 | −0.0105218 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.6721 | 0.418196 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.671858 | 0.0240410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.36113 | −0.263065 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.4820 | 1.37348 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.3310 | −1.93669 | −0.968346 | − | 0.249613i | \(-0.919696\pi\) | ||||
−0.968346 | + | 0.249613i | \(0.919696\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.64922 | −0.236718 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.306138 | −0.0108850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.3963 | −0.759805 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7640 | 0.452691 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.5327 | −0.691884 | −0.345942 | − | 0.938256i | \(-0.612441\pi\) | ||||
−0.345942 | + | 0.938256i | \(0.612441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.8095 | −0.594677 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.4264 | −0.509731 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.78306 | −0.0629228 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.78238 | −0.168557 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.188150 | 0.00662318 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.62037 | −0.303076 | −0.151538 | − | 0.988451i | \(-0.548423\pi\) | ||||
−0.151538 | + | 0.988451i | \(0.548423\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.8093 | −1.15209 | −0.576045 | − | 0.817418i | \(-0.695405\pi\) | ||||
−0.576045 | + | 0.817418i | \(0.695405\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.37470 | 0.188499 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.38741 | −0.118656 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.4797 | −1.06635 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.22499 | −0.0777474 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.7721 | −0.375949 | −0.187975 | − | 0.982174i | \(-0.560192\pi\) | ||||
−0.187975 | + | 0.982174i | \(0.560192\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.811789 | −0.0282972 | −0.0141486 | − | 0.999900i | \(-0.504504\pi\) | ||||
−0.0141486 | + | 0.999900i | \(0.504504\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.76233 | 0.165803 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.5287 | −0.400891 | −0.200446 | − | 0.979705i | \(-0.564239\pi\) | ||||
−0.200446 | + | 0.979705i | \(0.564239\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.1809 | 0.631450 | 0.315725 | − | 0.948851i | \(-0.397752\pi\) | ||||
0.315725 | + | 0.948851i | \(0.397752\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.4958 | 0.398784 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.8849 | −1.00080 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.8736 | −0.514723 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.9791 | 1.07079 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.8944 | 0.410640 | 0.205320 | − | 0.978695i | \(-0.434176\pi\) | ||||
0.205320 | + | 0.978695i | \(0.434176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7544 | −0.784635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.8817 | −0.409229 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.6631 | 2.22448 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.43532 | 0.0493183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.4110 | −0.391626 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.6403 | −1.18745 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.98122 | −0.170554 | −0.0852769 | − | 0.996357i | \(-0.527177\pi\) | ||||
−0.0852769 | + | 0.996357i | \(0.527177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 41.6823 | 1.42550 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.0481 | −0.958104 | −0.479052 | − | 0.877787i | \(-0.659019\pi\) | ||||
−0.479052 | + | 0.877787i | \(0.659019\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.7436 | 1.83371 | 0.916855 | − | 0.399221i | \(-0.130719\pi\) | ||||
0.916855 | + | 0.399221i | \(0.130719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.211330 | −0.00720212 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.84177 | −0.198856 | −0.0994281 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994281 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 62.1321 | 2.11255 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.0681102 | −0.00231314 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.446050 | −0.0151312 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 66.9814 | 2.26958 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −33.4091 | −1.13073 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.81800 | −0.0614597 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.6192 | −0.865097 | −0.432549 | − | 0.901611i | \(-0.642386\pi\) | ||||
−0.432549 | + | 0.901611i | \(0.642386\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.70326 | 0.192366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.46664 | 0.318939 | 0.159470 | − | 0.987203i | \(-0.449022\pi\) | ||||
0.159470 | + | 0.987203i | \(0.449022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.2535 | 0.681586 | 0.340793 | − | 0.940138i | \(-0.389305\pi\) | ||||
0.340793 | + | 0.940138i | \(0.389305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.9902 | −0.840037 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.7078 | 0.728875 | 0.364438 | − | 0.931228i | \(-0.381261\pi\) | ||||
0.364438 | + | 0.931228i | \(0.381261\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.407582 | 0.0136699 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.40731 | −0.248154 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.9090 | 0.565840 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.7371 | −1.26141 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.3212 | 0.845451 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.2844 | −0.876634 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.1236 | −0.936933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.551855 | 0.0183646 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.4703 | 0.613974 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.1616 | −1.66559 | −0.832794 | − | 0.553583i | \(-0.813260\pi\) | ||||
−0.832794 | + | 0.553583i | \(0.813260\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.9921 | −0.663096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.8879 | −0.526390 | −0.263195 | − | 0.964743i | \(-0.584776\pi\) | ||||
−0.263195 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.98432 | −0.198052 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.25732 | −0.239920 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.43287 | −0.0803403 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.65979 | 0.285660 | 0.142830 | − | 0.989747i | \(-0.454380\pi\) | ||||
0.142830 | + | 0.989747i | \(0.454380\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.56872 | −0.249398 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.36403 | 0.110728 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.6211 | −1.07257 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.5994 | −0.840795 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.5223 | 1.62477 | 0.812387 | − | 0.583118i | \(-0.198168\pi\) | ||||
0.812387 | + | 0.583118i | \(0.198168\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.0560 | 0.952271 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.4031 | 0.373320 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.7504 | −0.547797 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.8046 | −0.712325 | −0.356163 | − | 0.934424i | \(-0.615915\pi\) | ||||
−0.356163 | + | 0.934424i | \(0.615915\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.766778 | 0.0250228 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.4317 | 1.28544 | 0.642718 | − | 0.766103i | \(-0.277807\pi\) | ||||
0.642718 | + | 0.766103i | \(0.277807\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.9599 | −0.812807 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.58209 | −0.0514653 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.4145 | 0.500904 | 0.250452 | − | 0.968129i | \(-0.419421\pi\) | ||||
0.250452 | + | 0.968129i | \(0.419421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.92786 | −0.289811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.26366 | 0.170686 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.2434 | 0.526175 | 0.263087 | − | 0.964772i | \(-0.415259\pi\) | ||||
0.263087 | + | 0.964772i | \(0.415259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −37.0734 | −1.19967 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.41944 | −0.0458841 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.80602 | −0.0583194 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79.6172 | 2.56830 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.78370 | 0.0574790 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.2010 | 0.585910 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.8299 | −1.21653 | −0.608264 | − | 0.793735i | \(-0.708134\pi\) | ||||
−0.608264 | + | 0.793735i | \(0.708134\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.84936 | 0.284282 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.4728 | 1.13838 | 0.569189 | − | 0.822207i | \(-0.307257\pi\) | ||||
0.569189 | + | 0.822207i | \(0.307257\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.78726 | −0.0572968 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.8452 | 0.763658 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.9898 | −1.69529 | −0.847647 | − | 0.530561i | \(-0.821981\pi\) | ||||
−0.847647 | + | 0.530561i | \(0.821981\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.83171 | −0.186382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.0689 | 1.43894 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.2492 | 0.645850 | 0.322925 | − | 0.946425i | \(-0.395334\pi\) | ||||
0.322925 | + | 0.946425i | \(0.395334\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.8676 | −0.887936 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.306149 | −0.00974483 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 65.1788 | 2.07256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.5315 | −1.70049 | −0.850243 | − | 0.526391i | \(-0.823545\pi\) | ||||
−0.850243 | + | 0.526391i | \(0.823545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.86522 | 0.0591910 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 55.1976 | 1.74988 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.0483 | −1.45837 | −0.729183 | − | 0.684319i | \(-0.760099\pi\) | ||||
−0.729183 | + | 0.684319i | \(0.760099\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.4595 | −0.362564 |
(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 | 8032.2.a.i.1.13 | yes | 30 | |
4.3 | odd | 2 | 8032.2.a.h.1.18 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8032.2.a.h.1.18 | ✓ | 30 | 4.3 | odd | 2 | ||
8032.2.a.i.1.13 | yes | 30 | 1.1 | even | 1 | trivial |