Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 13x^{7} + 8x^{6} + 56x^{5} - 15x^{4} - 81x^{3} + 2x^{2} + 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.460631\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-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 | ||||||||
\(3\) | −0.460631 | −0.265945 | −0.132973 | − | 0.991120i | \(-0.542452\pi\) | ||||
−0.132973 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.528623 | 0.236408 | 0.118204 | − | 0.992989i | \(-0.462286\pi\) | ||||
0.118204 | + | 0.992989i | \(0.462286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.88578 | −0.712756 | −0.356378 | − | 0.934342i | \(-0.615988\pi\) | ||||
−0.356378 | + | 0.934342i | \(0.615988\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.78782 | −0.929273 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.52080 | 1.36307 | 0.681537 | − | 0.731784i | \(-0.261312\pi\) | ||||
0.681537 | + | 0.731784i | \(0.261312\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.67304 | −1.29607 | −0.648033 | − | 0.761612i | \(-0.724408\pi\) | ||||
−0.648033 | + | 0.761612i | \(0.724408\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.243500 | −0.0628715 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.22703 | 1.75281 | 0.876406 | − | 0.481573i | \(-0.159935\pi\) | ||||
0.876406 | + | 0.481573i | \(0.159935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.05086 | −0.470500 | −0.235250 | − | 0.971935i | \(-0.575591\pi\) | ||||
−0.235250 | + | 0.971935i | \(0.575591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.868646 | 0.189554 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.329593 | −0.0687248 | −0.0343624 | − | 0.999409i | \(-0.510940\pi\) | ||||
−0.0343624 | + | 0.999409i | \(0.510940\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.72056 | −0.944111 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.66605 | 0.513081 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.05453 | −0.567211 | −0.283606 | − | 0.958941i | \(-0.591531\pi\) | ||||
−0.283606 | + | 0.958941i | \(0.591531\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.53069 | −1.35255 | −0.676276 | − | 0.736649i | \(-0.736407\pi\) | ||||
−0.676276 | + | 0.736649i | \(0.736407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.08242 | −0.362503 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.996865 | −0.168501 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.39234 | −1.37969 | −0.689846 | − | 0.723956i | \(-0.742322\pi\) | ||||
−0.689846 | + | 0.723956i | \(0.742322\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.15254 | 0.344683 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.74458 | −0.897153 | −0.448576 | − | 0.893744i | \(-0.648069\pi\) | ||||
−0.448576 | + | 0.893744i | \(0.648069\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.97486 | 0.606160 | 0.303080 | − | 0.952965i | \(-0.401985\pi\) | ||||
0.303080 | + | 0.952965i | \(0.401985\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.47371 | −0.219687 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.13084 | −0.456680 | −0.228340 | − | 0.973581i | \(-0.573330\pi\) | ||||
−0.228340 | + | 0.973581i | \(0.573330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.44385 | −0.491979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.32899 | −0.466152 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.78055 | −0.656659 | −0.328330 | − | 0.944563i | \(-0.606486\pi\) | ||||
−0.328330 | + | 0.944563i | \(0.606486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.38980 | 0.322241 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.944691 | 0.125127 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.57453 | 1.11631 | 0.558154 | − | 0.829737i | \(-0.311510\pi\) | ||||
0.558154 | + | 0.829737i | \(0.311510\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.95580 | −0.634526 | −0.317263 | − | 0.948338i | \(-0.602764\pi\) | ||||
−0.317263 | + | 0.948338i | \(0.602764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.25720 | 0.662345 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.47028 | −0.306400 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.60533 | −0.562630 | −0.281315 | − | 0.959615i | \(-0.590771\pi\) | ||||
−0.281315 | + | 0.959615i | \(0.590771\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.151821 | 0.0182771 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.2444 | 1.33446 | 0.667231 | − | 0.744851i | \(-0.267479\pi\) | ||||
0.667231 | + | 0.744851i | \(0.267479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.43916 | −0.987729 | −0.493864 | − | 0.869539i | \(-0.664416\pi\) | ||||
−0.493864 | + | 0.869539i | \(0.664416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.17443 | 0.251082 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.52522 | −0.971539 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3162 | −1.16066 | −0.580332 | − | 0.814380i | \(-0.697077\pi\) | ||||
−0.580332 | + | 0.814380i | \(0.697077\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.13539 | 0.792821 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.86634 | 0.534150 | 0.267075 | − | 0.963676i | \(-0.413943\pi\) | ||||
0.267075 | + | 0.963676i | \(0.413943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.82038 | 0.414378 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.40701 | 0.150847 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.6367 | −1.23348 | −0.616742 | − | 0.787165i | \(-0.711548\pi\) | ||||
−0.616742 | + | 0.787165i | \(0.711548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.81229 | 0.923780 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.46887 | 0.359705 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.08413 | −0.111230 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.79262 | 0.182013 | 0.0910067 | − | 0.995850i | \(-0.470992\pi\) | ||||
0.0910067 | + | 0.995850i | \(0.470992\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.6032 | −1.26667 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.88795 | 0.287362 | 0.143681 | − | 0.989624i | \(-0.454106\pi\) | ||||
0.143681 | + | 0.989624i | \(0.454106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19062 | −0.215848 | −0.107924 | − | 0.994159i | \(-0.534420\pi\) | ||||
−0.107924 | + | 0.994159i | \(0.534420\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.459187 | 0.0448120 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2271 | −1.18204 | −0.591020 | − | 0.806657i | \(-0.701274\pi\) | ||||
−0.591020 | + | 0.806657i | \(0.701274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4503 | −1.09674 | −0.548372 | − | 0.836234i | \(-0.684752\pi\) | ||||
−0.548372 | + | 0.836234i | \(0.684752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.86577 | 0.366923 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.56004 | −0.240829 | −0.120414 | − | 0.992724i | \(-0.538422\pi\) | ||||
−0.120414 | + | 0.992724i | \(0.538422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.174230 | −0.0162471 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.0276 | 1.20440 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.6285 | −1.24933 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.43766 | 0.857969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.64613 | 0.238594 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.13851 | −0.459603 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00412 | 0.798987 | 0.399493 | − | 0.916736i | \(-0.369186\pi\) | ||||
0.399493 | + | 0.916736i | \(0.369186\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.83094 | −0.161205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.08184 | −0.444003 | −0.222001 | − | 0.975046i | \(-0.571259\pi\) | ||||
−0.222001 | + | 0.975046i | \(0.571259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.86747 | 0.335352 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.40934 | 0.121296 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.0117 | 1.45340 | 0.726702 | − | 0.686953i | \(-0.241052\pi\) | ||||
0.726702 | + | 0.686953i | \(0.241052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.58826 | 0.389171 | 0.194586 | − | 0.980886i | \(-0.437664\pi\) | ||||
0.194586 | + | 0.980886i | \(0.437664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.44216 | 0.121452 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.1259 | −1.76663 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.61469 | −0.134093 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.58634 | 0.130840 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.45447 | −0.692617 | −0.346309 | − | 0.938121i | \(-0.612565\pi\) | ||||
−0.346309 | + | 0.938121i | \(0.612565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0737 | 0.982543 | 0.491272 | − | 0.871006i | \(-0.336532\pi\) | ||||
0.491272 | + | 0.871006i | \(0.336532\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.1476 | −1.62884 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.98090 | −0.319753 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.87818 | 0.708556 | 0.354278 | − | 0.935140i | \(-0.384727\pi\) | ||||
0.354278 | + | 0.935140i | \(0.384727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.20207 | 0.174635 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.621538 | 0.0489840 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.29588 | −0.336480 | −0.168240 | − | 0.985746i | \(-0.553808\pi\) | ||||
−0.168240 | + | 0.985746i | \(0.553808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.10082 | −0.0856985 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.83726 | 0.679790 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.71744 | 0.437223 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.589144 | 0.0447918 | 0.0223959 | − | 0.999749i | \(-0.492871\pi\) | ||||
0.0223959 | + | 0.999749i | \(0.492871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.90191 | 0.672921 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.94969 | −0.296877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.6810 | −1.39629 | −0.698143 | − | 0.715958i | \(-0.745990\pi\) | ||||
−0.698143 | + | 0.715958i | \(0.745990\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.55333 | 0.115458 | 0.0577291 | − | 0.998332i | \(-0.481614\pi\) | ||||
0.0577291 | + | 0.998332i | \(0.481614\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.28280 | 0.168749 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.43639 | −0.326170 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.6720 | 2.38921 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.02757 | −0.365702 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.264735 | −0.0191556 | −0.00957778 | − | 0.999954i | \(-0.503049\pi\) | ||||
−0.00957778 | + | 0.999954i | \(0.503049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6341 | −0.909426 | −0.454713 | − | 0.890638i | \(-0.650258\pi\) | ||||
−0.454713 | + | 0.890638i | \(0.650258\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.13789 | 0.0814857 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.3493 | 1.30733 | 0.653666 | − | 0.756783i | \(-0.273230\pi\) | ||||
0.653666 | + | 0.756783i | \(0.273230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.54692 | 0.534987 | 0.267494 | − | 0.963560i | \(-0.413805\pi\) | ||||
0.267494 | + | 0.963560i | \(0.413805\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.12136 | 0.149629 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.76015 | 0.404283 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.03672 | −0.212094 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.918845 | 0.0638641 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.27155 | −0.641327 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.43774 | −0.512035 | −0.256018 | − | 0.966672i | \(-0.582410\pi\) | ||||
−0.256018 | + | 0.966672i | \(0.582410\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.17951 | −0.354894 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.10120 | 0.143301 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.2012 | 0.964039 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.88734 | 0.262682 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.7722 | −2.27176 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.1035 | 1.74802 | 0.874009 | − | 0.485910i | \(-0.161512\pi\) | ||||
0.874009 | + | 0.485910i | \(0.161512\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.1601 | 0.877337 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.56577 | 0.502158 | 0.251079 | − | 0.967967i | \(-0.419215\pi\) | ||||
0.251079 | + | 0.967967i | \(0.419215\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.3347 | −1.54200 | −0.770999 | − | 0.636837i | \(-0.780243\pi\) | ||||
−0.770999 | + | 0.636837i | \(0.780243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.92698 | 0.258376 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.01646 | 0.328639 | 0.164320 | − | 0.986407i | \(-0.447457\pi\) | ||||
0.164320 | + | 0.986407i | \(0.447457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.65503 | −0.107963 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.75196 | 0.308673 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9238 | 1.09471 | 0.547355 | − | 0.836900i | \(-0.315635\pi\) | ||||
0.547355 | + | 0.836900i | \(0.315635\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.454933 | 0.0293048 | 0.0146524 | − | 0.999893i | \(-0.495336\pi\) | ||||
0.0146524 | + | 0.999893i | \(0.495336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2849 | −0.723928 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.82050 | −0.116308 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.58376 | 0.609800 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.24159 | −0.142055 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.3483 | 1.03190 | 0.515948 | − | 0.856620i | \(-0.327440\pi\) | ||||
0.515948 | + | 0.856620i | \(0.327440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.49002 | −0.0936770 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.75978 | −0.110202 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5775 | 0.659807 | 0.329903 | − | 0.944015i | \(-0.392984\pi\) | ||||
0.329903 | + | 0.944015i | \(0.392984\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8261 | 0.983384 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.51547 | 0.527094 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.0632 | 0.805512 | 0.402756 | − | 0.915307i | \(-0.368052\pi\) | ||||
0.402756 | + | 0.915307i | \(0.368052\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.52711 | −0.155239 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.36021 | 0.328039 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0094 | −0.610282 | −0.305141 | − | 0.952307i | \(-0.598704\pi\) | ||||
−0.305141 | + | 0.952307i | \(0.598704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.49026 | 0.576492 | 0.288246 | − | 0.957556i | \(-0.406928\pi\) | ||||
0.288246 | + | 0.957556i | \(0.406928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.05922 | −0.245675 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.3407 | −1.28689 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.81055 | 0.108785 | 0.0543927 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543927 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.9942 | 1.25689 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.7931 | 1.47903 | 0.739515 | − | 0.673140i | \(-0.235055\pi\) | ||||
0.739515 | + | 0.673140i | \(0.235055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.67137 | 0.574903 | 0.287452 | − | 0.957795i | \(-0.407192\pi\) | ||||
0.287452 | + | 0.957795i | \(0.407192\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.499386 | 0.0295811 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.8330 | 0.639451 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.2299 | 2.07235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.825738 | −0.0484056 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.1006 | 1.17429 | 0.587144 | − | 0.809482i | \(-0.300252\pi\) | ||||
0.587144 | + | 0.809482i | \(0.300252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.53270 | 0.263904 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.0527 | 0.699367 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.54020 | 0.0890720 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.49568 | −0.432044 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.33028 | −0.0764225 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.61975 | −0.150007 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.2967 | −1.10132 | −0.550660 | − | 0.834730i | \(-0.685624\pi\) | ||||
−0.550660 | + | 0.834730i | \(0.685624\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00907 | 0.0574039 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.9474 | −1.35793 | −0.678966 | − | 0.734169i | \(-0.737572\pi\) | ||||
−0.678966 | + | 0.734169i | \(0.737572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.7438 | 1.34208 | 0.671041 | − | 0.741420i | \(-0.265848\pi\) | ||||
0.671041 | + | 0.741420i | \(0.265848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.77908 | 0.156583 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.0507140 | 0.00284838 | 0.00142419 | − | 0.999999i | \(-0.499547\pi\) | ||||
0.00142419 | + | 0.999999i | \(0.499547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8089 | −0.773151 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.63219 | 0.314358 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.8216 | −0.824698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.0593 | 1.22363 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.27438 | 0.291674 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.90406 | 0.325501 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.8008 | −1.80289 | −0.901447 | − | 0.432889i | \(-0.857494\pi\) | ||||
−0.901447 | + | 0.432889i | \(0.857494\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.3963 | 1.28211 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.43448 | −0.133010 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.5480 | 1.28274 | 0.641370 | − | 0.767231i | \(-0.278366\pi\) | ||||
0.641370 | + | 0.767231i | \(0.278366\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.17923 | 0.0640472 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.0448 | −1.84363 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6948 | 1.06342 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0802559 | 0.00432083 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0160 | −0.752419 | −0.376210 | − | 0.926535i | \(-0.622773\pi\) | ||||
−0.376210 | + | 0.926535i | \(0.622773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.1235 | −1.61247 | −0.806236 | − | 0.591594i | \(-0.798499\pi\) | ||||
−0.806236 | + | 0.591594i | \(0.798499\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.4585 | −0.664988 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9936 | 0.957701 | 0.478850 | − | 0.877897i | \(-0.341054\pi\) | ||||
0.478850 | + | 0.877897i | \(0.341054\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.94404 | 0.315477 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.27773 | 0.332253 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.7908 | −1.15007 | −0.575036 | − | 0.818128i | \(-0.695012\pi\) | ||||
−0.575036 | + | 0.818128i | \(0.695012\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7940 | −0.778629 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.34728 | −0.228173 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.46114 | −0.233507 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.33533 | −0.330702 | −0.165351 | − | 0.986235i | \(-0.552876\pi\) | ||||
−0.165351 | + | 0.986235i | \(0.552876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.0149 | 0.833700 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.01504 | 0.468038 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.67690 | −0.293939 | −0.146969 | − | 0.989141i | \(-0.546952\pi\) | ||||
−0.146969 | + | 0.989141i | \(0.546952\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.36696 | 0.122229 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.2739 | 0.735144 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.295498 | 0.0151787 | 0.00758935 | − | 0.999971i | \(-0.497584\pi\) | ||||
0.00758935 | + | 0.999971i | \(0.497584\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.14758 | −0.212487 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.9211 | −1.58000 | −0.789998 | − | 0.613109i | \(-0.789919\pi\) | ||||
−0.789998 | + | 0.613109i | \(0.789919\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.50663 | −0.229679 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.0812 | −0.563288 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.4419 | −1.18855 | −0.594275 | − | 0.804262i | \(-0.702561\pi\) | ||||
−0.594275 | + | 0.804262i | \(0.702561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.38198 | −0.120462 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.34085 | 0.118080 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.45338 | −0.274390 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3509 | −0.519498 | −0.259749 | − | 0.965676i | \(-0.583640\pi\) | ||||
−0.259749 | + | 0.965676i | \(0.583640\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.78148 | −0.0891853 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.1228 | 0.655322 | 0.327661 | − | 0.944795i | \(-0.393740\pi\) | ||||
0.327661 | + | 0.944795i | \(0.393740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.1912 | 1.75300 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.77194 | 0.187429 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.9401 | −1.88062 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7190 | 0.727806 | 0.363903 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363903 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.83610 | −0.386526 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.1696 | −0.795656 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.57246 | 0.126277 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.11350 | −0.103498 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.53165 | 0.465651 | 0.232826 | − | 0.972518i | \(-0.425203\pi\) | ||||
0.232826 | + | 0.972518i | \(0.425203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.3126 | −0.941240 | −0.470620 | − | 0.882336i | \(-0.655970\pi\) | ||||
−0.470620 | + | 0.882336i | \(0.655970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.72821 | 0.424380 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.1156 | −1.65485 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.34553 | 0.452262 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.73123 | 0.469828 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.2355 | 1.11921 | 0.559606 | − | 0.828758i | \(-0.310952\pi\) | ||||
0.559606 | + | 0.828758i | \(0.310952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.6576 | −1.52137 | −0.760684 | − | 0.649123i | \(-0.775136\pi\) | ||||
−0.760684 | + | 0.649123i | \(0.775136\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.743778 | 0.0356614 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.675950 | 0.0323351 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.9084 | 1.14109 | 0.570543 | − | 0.821268i | \(-0.306733\pi\) | ||||
0.570543 | + | 0.821268i | \(0.306733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.60084 | 0.457183 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.6729 | −1.02971 | −0.514855 | − | 0.857277i | \(-0.672154\pi\) | ||||
−0.514855 | + | 0.857277i | \(0.672154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.15141 | −0.291605 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.89439 | 0.184198 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.1288 | 1.65783 | 0.828915 | − | 0.559374i | \(-0.188959\pi\) | ||||
0.828915 | + | 0.559374i | \(0.188959\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.9701 | −1.22289 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.56152 | −0.261303 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.65839 | 0.218388 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.6679 | 1.06036 | 0.530181 | − | 0.847885i | \(-0.322124\pi\) | ||||
0.530181 | + | 0.847885i | \(0.322124\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.2676 | 0.899335 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.831182 | −0.0387120 | −0.0193560 | − | 0.999813i | \(-0.506162\pi\) | ||||
−0.0193560 | + | 0.999813i | \(0.506162\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0478 | −0.699331 | −0.349665 | − | 0.936875i | \(-0.613705\pi\) | ||||
−0.349665 | + | 0.936875i | \(0.613705\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.83372 | 0.0850369 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.9603 | 1.71032 | 0.855160 | − | 0.518364i | \(-0.173459\pi\) | ||||
0.855160 | + | 0.518364i | \(0.173459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.68461 | 0.401018 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.08956 | −0.188437 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.9695 | 0.826240 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.68122 | 0.444205 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3273 | 0.610216 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.0720 | 0.962802 | 0.481401 | − | 0.876500i | \(-0.340128\pi\) | ||||
0.481401 | + | 0.876500i | \(0.340128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.2177 | 1.78817 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.286300 | −0.0130271 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.947623 | 0.0430293 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9444 | −0.631880 | −0.315940 | − | 0.948779i | \(-0.602320\pi\) | ||||
−0.315940 | + | 0.948779i | \(0.602320\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.97882 | 0.0894852 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.9232 | −0.899124 | −0.449562 | − | 0.893249i | \(-0.648420\pi\) | ||||
−0.449562 | + | 0.893249i | \(0.648420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.0751 | −0.994214 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.66234 | −0.299450 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.2044 | −0.951146 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.6053 | 0.967186 | 0.483593 | − | 0.875293i | \(-0.339332\pi\) | ||||
0.483593 | + | 0.875293i | \(0.339332\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.460631 | −0.0205795 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.69154 | 0.253773 | 0.126887 | − | 0.991917i | \(-0.459502\pi\) | ||||
0.126887 | + | 0.991917i | \(0.459502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.52664 | 0.0679344 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.07072 | −0.180787 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.3992 | 0.682559 | 0.341279 | − | 0.939962i | \(-0.389140\pi\) | ||||
0.341279 | + | 0.939962i | \(0.389140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.9144 | 0.704010 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.46770 | −0.241405 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.15801 | −0.0510282 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.1539 | −0.622488 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.271378 | −0.0119122 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.4568 | 1.46577 | 0.732885 | − | 0.680353i | \(-0.238174\pi\) | ||||
0.732885 | + | 0.680353i | \(0.238174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.0006 | −1.09320 | −0.546600 | − | 0.837394i | \(-0.684078\pi\) | ||||
−0.546600 | + | 0.837394i | \(0.684078\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.10049 | −0.178960 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −54.4245 | −2.37077 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8914 | −0.995277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.9042 | −1.03736 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.8446 | 1.16277 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.46354 | −0.279443 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.60506 | 0.371336 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.5690 | −0.670603 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.2501 | −1.55851 | −0.779257 | − | 0.626704i | \(-0.784403\pi\) | ||||
−0.779257 | + | 0.626704i | \(0.784403\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.715513 | −0.0307056 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.05292 | −0.259279 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 45.5824 | 1.94896 | 0.974480 | − | 0.224473i | \(-0.0720661\pi\) | ||||
0.974480 | + | 0.224473i | \(0.0720661\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.8159 | 0.589648 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.26442 | 0.266873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.4540 | 0.827270 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.04354 | 0.0867433 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.6207 | 1.55167 | 0.775835 | − | 0.630936i | \(-0.217329\pi\) | ||||
0.775835 | + | 0.630936i | \(0.217329\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.5746 | −0.785624 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.0497 | −0.635400 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.00687 | −0.126725 | −0.0633623 | − | 0.997991i | \(-0.520182\pi\) | ||||
−0.0633623 | + | 0.997991i | \(0.520182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.35330 | −0.0569337 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.4557 | −0.565088 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.3071 | −1.77361 | −0.886804 | − | 0.462146i | \(-0.847080\pi\) | ||||
−0.886804 | + | 0.462146i | \(0.847080\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.85312 | −0.328643 | −0.164321 | − | 0.986407i | \(-0.552543\pi\) | ||||
−0.164321 | + | 0.986407i | \(0.552543\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.121945 | 0.00509433 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.55586 | 0.0648839 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.80955 | −0.325116 | −0.162558 | − | 0.986699i | \(-0.551974\pi\) | ||||
−0.162558 | + | 0.986699i | \(0.551974\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.81968 | 0.241858 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.17683 | −0.380719 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.6119 | −0.895075 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.88668 | 0.284729 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.9133 | 1.27593 | 0.637964 | − | 0.770066i | \(-0.279777\pi\) | ||||
0.637964 | + | 0.770066i | \(0.279777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.4444 | 0.636376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.45225 | −0.347679 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.1986 | −1.44543 | −0.722716 | − | 0.691145i | \(-0.757106\pi\) | ||||
−0.722716 | + | 0.691145i | \(0.757106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.20437 | −0.295350 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.47635 | −0.142277 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.4328 | −1.81548 | −0.907738 | − | 0.419538i | \(-0.862192\pi\) | ||||
−0.907738 | + | 0.419538i | \(0.862192\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0351 | −1.22516 | −0.612578 | − | 0.790410i | \(-0.709867\pi\) | ||||
−0.612578 | + | 0.790410i | \(0.709867\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.8388 | 0.522837 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.98897 | 0.202830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.5148 | −1.11679 | −0.558395 | − | 0.829575i | \(-0.688583\pi\) | ||||
−0.558395 | + | 0.829575i | \(0.688583\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.65330 | −0.107517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.6305 | 0.591888 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.13449 | −0.328549 | −0.164275 | − | 0.986415i | \(-0.552528\pi\) | ||||
−0.164275 | + | 0.986415i | \(0.552528\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.39881 | 0.0564053 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.8846 | −0.599232 | −0.299616 | − | 0.954060i | \(-0.596858\pi\) | ||||
−0.299616 | + | 0.954060i | \(0.596858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.59265 | 0.345368 | 0.172684 | − | 0.984977i | \(-0.444756\pi\) | ||||
0.172684 | + | 0.984977i | \(0.444756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.878710 | −0.0352614 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.9441 | 0.879173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8864 | 0.835458 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.27076 | 0.170558 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −60.6516 | −2.41834 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2593 | −1.24441 | −0.622207 | − | 0.782853i | \(-0.713764\pi\) | ||||
−0.622207 | + | 0.782853i | \(0.713764\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.42605 | 0.136173 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.75979 | 0.188886 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.0932 | 0.637638 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.3473 | −1.24008 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.2323 | −1.23360 | −0.616800 | − | 0.787120i | \(-0.711571\pi\) | ||||
−0.616800 | + | 0.787120i | \(0.711571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.1159 | −1.73976 | −0.869880 | − | 0.493263i | \(-0.835804\pi\) | ||||
−0.869880 | + | 0.493263i | \(0.835804\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.967879 | −0.0381102 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.15533 | 0.320619 | 0.160310 | − | 0.987067i | \(-0.448751\pi\) | ||||
0.160310 | + | 0.987067i | \(0.448751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.7638 | 1.52161 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.54151 | −0.256382 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.81732 | 0.110250 | 0.0551252 | − | 0.998479i | \(-0.482444\pi\) | ||||
0.0551252 | + | 0.998479i | \(0.482444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.68638 | −0.104966 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.5269 | 0.917870 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.2713 | −1.21816 | −0.609079 | − | 0.793110i | \(-0.708461\pi\) | ||||
−0.609079 | + | 0.793110i | \(0.708461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.2560 | 1.68246 | 0.841231 | − | 0.540675i | \(-0.181831\pi\) | ||||
0.841231 | + | 0.540675i | \(0.181831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.5565 | 0.604164 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.04443 | 0.0792797 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00675 | 0.0389815 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.0241 | −0.464877 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.4042 | −0.864905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.67949 | −0.103287 | −0.0516433 | − | 0.998666i | \(-0.516446\pi\) | ||||
−0.0516433 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.5852 | −0.484406 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.57007 | 0.137209 | 0.0686045 | − | 0.997644i | \(-0.478145\pi\) | ||||
0.0686045 | + | 0.997644i | \(0.478145\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.38049 | −0.129731 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.48503 | −0.133547 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.7566 | −1.55951 | −0.779755 | − | 0.626085i | \(-0.784656\pi\) | ||||
−0.779755 | + | 0.626085i | \(0.784656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.99276 | 0.343596 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7487 | 0.410087 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.3397 | 0.851074 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.3926 | 1.68878 | 0.844388 | − | 0.535733i | \(-0.179965\pi\) | ||||
0.844388 | + | 0.535733i | \(0.179965\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.7668 | 0.902825 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.42546 | 0.0920031 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.5162 | −1.57254 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.31074 | −0.0874001 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.39607 | −0.317115 | −0.158558 | − | 0.987350i | \(-0.550684\pi\) | ||||
−0.158558 | + | 0.987350i | \(0.550684\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.2115 | 0.649145 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.762360 | 0.0287121 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.44602 | −0.204819 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0828 | 0.904448 | 0.452224 | − | 0.891904i | \(-0.350631\pi\) | ||||
0.452224 | + | 0.891904i | \(0.350631\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.7597 | 1.07857 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.48206 | 0.0929539 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.1676 | −0.417646 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.79563 | −0.291133 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.6056 | −1.29057 | −0.645285 | − | 0.763942i | \(-0.723261\pi\) | ||||
−0.645285 | + | 0.763942i | \(0.723261\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.13102 | 0.153847 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.209556 | −0.00779348 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.4191 | 0.535511 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.40361 | 0.0520569 | 0.0260284 | − | 0.999661i | \(-0.491714\pi\) | ||||
0.0260284 | + | 0.999661i | \(0.491714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.2080 | −0.600296 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.7264 | 1.06248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0319 | 0.481345 | 0.240672 | − | 0.970606i | \(-0.422632\pi\) | ||||
0.240672 | + | 0.970606i | \(0.422632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.838579 | 0.0309314 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.8198 | −0.766906 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.84386 | −0.104613 | −0.0523065 | − | 0.998631i | \(-0.516657\pi\) | ||||
−0.0523065 | + | 0.998631i | \(0.516657\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.41458 | −0.162173 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.3233 | 1.11246 | 0.556228 | − | 0.831030i | \(-0.312248\pi\) | ||||
0.556228 | + | 0.831030i | \(0.312248\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.46923 | −0.163740 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.5665 | −0.496372 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.0576 | 0.842506 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.3929 | 0.707656 | 0.353828 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353828 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.53054 | −0.274428 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.38244 | 0.232281 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.7720 | −1.00939 | −0.504696 | − | 0.863297i | \(-0.668395\pi\) | ||||
−0.504696 | + | 0.863297i | \(0.668395\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.686351 | 0.0249130 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.4853 | −1.10509 | −0.552545 | − | 0.833483i | \(-0.686343\pi\) | ||||
−0.552545 | + | 0.833483i | \(0.686343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.5928 | 0.781711 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.6505 | −0.385070 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.0691 | −1.44681 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.3891 | 1.63677 | 0.818386 | − | 0.574669i | \(-0.194869\pi\) | ||||
0.818386 | + | 0.574669i | \(0.194869\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.87233 | −0.175473 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.17984 | 0.0784035 | 0.0392017 | − | 0.999231i | \(-0.487519\pi\) | ||||
0.0392017 | + | 0.999231i | \(0.487519\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.5490 | 1.27696 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.28997 | −0.261526 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.7814 | 0.422111 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.8336 | 1.81897 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.14351 | −0.291025 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.69321 | 0.167508 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.5630 | −1.23204 | −0.616019 | − | 0.787731i | \(-0.711255\pi\) | ||||
−0.616019 | + | 0.787731i | \(0.711255\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.01732 | −0.214222 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.82767 | 0.171652 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.1586 | 0.822388 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.16407 | 0.0412851 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.3705 | 1.64253 | 0.821264 | − | 0.570549i | \(-0.193270\pi\) | ||||
0.821264 | + | 0.570549i | \(0.193270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.6267 | −0.800473 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.4409 | 1.14624 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.1518 | −1.34635 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.328559 | 0.0115802 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.61062 | 0.162302 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.71862 | −0.0955815 | −0.0477908 | − | 0.998857i | \(-0.515218\pi\) | ||||
−0.0477908 | + | 0.998857i | \(0.515218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.8647 | −0.767773 | −0.383887 | − | 0.923380i | \(-0.625415\pi\) | ||||
−0.383887 | + | 0.923380i | \(0.625415\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.37150 | −0.153315 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.27090 | −0.0795463 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.15189 | −0.285198 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.5671 | −0.858443 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.1656 | −1.64609 | −0.823046 | − | 0.567975i | \(-0.807727\pi\) | ||||
−0.823046 | + | 0.567975i | \(0.807727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0300 | 0.349624 | 0.174812 | − | 0.984602i | \(-0.444068\pi\) | ||||
0.174812 | + | 0.984602i | \(0.444068\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.83019 | 0.342243 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.3947 | −1.19602 | −0.598010 | − | 0.801488i | \(-0.704042\pi\) | ||||
−0.598010 | + | 0.801488i | \(0.704042\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.0071 | −0.903265 | −0.451633 | − | 0.892204i | \(-0.649158\pi\) | ||||
−0.451633 | + | 0.892204i | \(0.649158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.833995 | −0.0289310 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.8888 | −0.862346 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.528623 | 0.0182938 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.0772 | −0.693969 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.0861 | −0.935117 | −0.467559 | − | 0.883962i | \(-0.654866\pi\) | ||||
−0.467559 | + | 0.883962i | \(0.654866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.6699 | −0.678271 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.4204 | −0.393341 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.67158 | 0.160707 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.7973 | −0.611523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.45493 | −0.152893 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.76605 | 0.0948191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.3832 | −1.72509 | −0.862544 | − | 0.505982i | \(-0.831130\pi\) | ||||
−0.862544 | + | 0.505982i | \(0.831130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.02237 | 0.103363 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.9044 | 1.32895 | 0.664474 | − | 0.747312i | \(-0.268656\pi\) | ||||
0.664474 | + | 0.747312i | \(0.268656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.08700 | −0.173566 | −0.0867831 | − | 0.996227i | \(-0.527659\pi\) | ||||
−0.0867831 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.99001 | −0.170059 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.1898 | 1.19787 | 0.598937 | − | 0.800796i | \(-0.295590\pi\) | ||||
0.598937 | + | 0.800796i | \(0.295590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.311435 | 0.0105891 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.2280 | −0.551131 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −46.6375 | −1.58207 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.5209 | 0.729206 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.99751 | −0.169140 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.69008 | 0.327585 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.1941 | −1.72870 | −0.864351 | − | 0.502889i | \(-0.832270\pi\) | ||||
−0.864351 | + | 0.502889i | \(0.832270\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.25895 | −0.312297 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.6653 | −0.696231 | −0.348115 | − | 0.937452i | \(-0.613178\pi\) | ||||
−0.348115 | + | 0.937452i | \(0.613178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.9195 | −1.04052 | −0.520262 | − | 0.854007i | \(-0.674166\pi\) | ||||
−0.520262 | + | 0.854007i | \(0.674166\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.08790 | −0.0701840 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.0054 | 0.537408 | 0.268704 | − | 0.963223i | \(-0.413405\pi\) | ||||
0.268704 | + | 0.963223i | \(0.413405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9797 | −0.569483 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.2577 | 1.08067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.42092 | 0.214868 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.87523 | −0.330093 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.709463 | −0.0236883 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.0027 | 0.767182 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.5492 | −1.15100 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.45274 | 0.114900 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.821128 | 0.0272952 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.8755 | 1.35725 | 0.678624 | − | 0.734486i | \(-0.262577\pi\) | ||||
0.678624 | + | 0.734486i | \(0.262577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.05108 | −0.267037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5013 | −0.944291 | −0.472146 | − | 0.881521i | \(-0.656520\pi\) | ||||
−0.472146 | + | 0.881521i | \(0.656520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.9998 | 0.728086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.20674 | 0.0398936 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.58321 | 0.316466 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.0660 | −1.42062 | −0.710309 | − | 0.703890i | \(-0.751445\pi\) | ||||
−0.710309 | + | 0.703890i | \(0.751445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.88865 | 0.292891 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −52.5454 | −1.72955 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.6165 | 1.30258 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.10706 | 0.200582 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.94430 | 0.0637904 | 0.0318952 | − | 0.999491i | \(-0.489846\pi\) | ||||
0.0318952 | + | 0.999491i | \(0.489846\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.06287 | 0.231476 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.0309 | 0.361136 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.2712 | 0.564827 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.9326 | 1.04319 | 0.521596 | − | 0.853192i | \(-0.325337\pi\) | ||||
0.521596 | + | 0.853192i | \(0.325337\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9371 | −0.356920 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.9641 | 0.357419 | 0.178709 | − | 0.983902i | \(-0.442808\pi\) | ||||
0.178709 | + | 0.983902i | \(0.442808\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.89337 | 0.0616567 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.65769 | −0.0864547 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.7390 | 0.706421 | 0.353211 | − | 0.935544i | \(-0.385090\pi\) | ||||
0.353211 | + | 0.935544i | \(0.385090\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.4365 | 1.28016 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.0233604 | −0.000757513 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.91288 | −0.288717 | −0.144358 | − | 0.989525i | \(-0.546112\pi\) | ||||
−0.144358 | + | 0.989525i | \(0.546112\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.139945 | −0.00452852 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.36081 | 0.205616 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.0802 | −1.03592 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.7113 | 0.829396 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.0870 | 1.09844 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.67870 | −0.214995 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.8796 | 1.37891 | 0.689457 | − | 0.724326i | \(-0.257849\pi\) | ||||
0.689457 | + | 0.724326i | \(0.257849\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.82731 | 0.219325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.9981 | 1.12314 | 0.561571 | − | 0.827429i | \(-0.310197\pi\) | ||||
0.561571 | + | 0.827429i | \(0.310197\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.65243 | −0.277384 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.1612 | −0.325419 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.2187 | −0.934790 | −0.467395 | − | 0.884049i | \(-0.654807\pi\) | ||||
−0.467395 | + | 0.884049i | \(0.654807\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −52.6071 | −1.68133 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.9215 | 1.01918 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.0259 | −1.59558 | −0.797789 | − | 0.602937i | \(-0.793997\pi\) | ||||
−0.797789 | + | 0.602937i | \(0.793997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.69986 | 0.309063 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.71959 | −0.0865655 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.31008 | −0.0416582 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.6908 | 0.720797 | 0.360398 | − | 0.932798i | \(-0.382641\pi\) | ||||
0.360398 | + | 0.932798i | \(0.382641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.1091 | 0.479471 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.98948 | 0.126475 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.7647 | −1.10101 | −0.550505 | − | 0.834832i | \(-0.685565\pi\) | ||||
−0.550505 | + | 0.834832i | \(0.685565\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22.3744 | −0.707894 |
(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 | 1336.2.a.c.1.4 | ✓ | 9 | |
4.3 | odd | 2 | 2672.2.a.m.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.c.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial | |
2672.2.a.m.1.6 | 9 | 4.3 | odd | 2 |