Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(2.93317\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.93317 | 1.31175 | 0.655877 | − | 0.754867i | \(-0.272299\pi\) | ||||
0.655877 | + | 0.754867i | \(0.272299\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.35675 | −0.512805 | −0.256402 | − | 0.966570i | \(-0.582537\pi\) | ||||
−0.256402 | + | 0.966570i | \(0.582537\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0643015 | 0.0193876 | 0.00969382 | − | 0.999953i | \(-0.496914\pi\) | ||||
0.00969382 | + | 0.999953i | \(0.496914\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.07209 | −0.574696 | −0.287348 | − | 0.957826i | \(-0.592774\pi\) | ||||
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.93317 | −0.757342 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.73736 | −0.421372 | −0.210686 | − | 0.977554i | \(-0.567570\pi\) | ||||
−0.210686 | + | 0.977554i | \(0.567570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.35449 | −1.68724 | −0.843618 | − | 0.536943i | \(-0.819579\pi\) | ||||
−0.843618 | + | 0.536943i | \(0.819579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.35675 | 0.296068 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.641526 | 0.133767 | 0.0668837 | − | 0.997761i | \(-0.478694\pi\) | ||||
0.0668837 | + | 0.997761i | \(0.478694\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.60351 | 0.720701 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.65476 | 0.678672 | 0.339336 | − | 0.940665i | \(-0.389798\pi\) | ||||
0.339336 | + | 0.940665i | \(0.389798\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.92456 | 0.704871 | 0.352436 | − | 0.935836i | \(-0.385354\pi\) | ||||
0.352436 | + | 0.935836i | \(0.385354\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0643015 | −0.0111935 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.97960 | −0.672674 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.28523 | 1.36208 | 0.681041 | − | 0.732245i | \(-0.261527\pi\) | ||||
0.681041 | + | 0.732245i | \(0.261527\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.07209 | 0.331801 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.55401 | 0.242696 | 0.121348 | − | 0.992610i | \(-0.461278\pi\) | ||||
0.121348 | + | 0.992610i | \(0.461278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.77619 | 0.423364 | 0.211682 | − | 0.977339i | \(-0.432106\pi\) | ||||
0.211682 | + | 0.977339i | \(0.432106\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.93317 | 0.437252 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.51709 | 0.658886 | 0.329443 | − | 0.944176i | \(-0.393139\pi\) | ||||
0.329443 | + | 0.944176i | \(0.393139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.15922 | −0.737031 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.73736 | 0.243279 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.55065 | −0.212998 | −0.106499 | − | 0.994313i | \(-0.533964\pi\) | ||||
−0.106499 | + | 0.994313i | \(0.533964\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.188608 | 0.0254318 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.35449 | 0.974127 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0736 | −1.44165 | −0.720827 | − | 0.693115i | \(-0.756238\pi\) | ||||
−0.720827 | + | 0.693115i | \(0.756238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4007 | 1.71578 | 0.857892 | − | 0.513830i | \(-0.171774\pi\) | ||||
0.857892 | + | 0.513830i | \(0.171774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.35675 | −0.170935 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.07781 | −0.753860 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.50770 | −0.550703 | −0.275352 | − | 0.961344i | \(-0.588794\pi\) | ||||
−0.275352 | + | 0.961344i | \(0.588794\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.641526 | −0.0772307 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2267 | −1.21369 | −0.606843 | − | 0.794822i | \(-0.707564\pi\) | ||||
−0.606843 | + | 0.794822i | \(0.707564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.16638 | −0.721720 | −0.360860 | − | 0.932620i | \(-0.617517\pi\) | ||||
−0.360860 | + | 0.932620i | \(0.617517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.60351 | −0.416097 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0872414 | −0.00994208 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.51122 | −0.282534 | −0.141267 | − | 0.989972i | \(-0.545118\pi\) | ||||
−0.141267 | + | 0.989972i | \(0.545118\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.74485 | −0.191523 | −0.0957613 | − | 0.995404i | \(-0.530529\pi\) | ||||
−0.0957613 | + | 0.995404i | \(0.530529\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.09598 | −0.552736 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.65476 | −0.391831 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.4735 | −1.85219 | −0.926095 | − | 0.377291i | \(-0.876856\pi\) | ||||
−0.926095 | + | 0.377291i | \(0.876856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.81132 | 0.294707 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.92456 | −0.406958 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.5720 | −2.21324 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.6851 | 1.79565 | 0.897824 | − | 0.440354i | \(-0.145147\pi\) | ||||
0.897824 | + | 0.440354i | \(0.145147\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0643015 | 0.00646255 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0244 | 0.997464 | 0.498732 | − | 0.866756i | \(-0.333799\pi\) | ||||
0.498732 | + | 0.866756i | \(0.333799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.08730 | −0.599800 | −0.299900 | − | 0.953971i | \(-0.596953\pi\) | ||||
−0.299900 | + | 0.953971i | \(0.596953\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.97960 | 0.388369 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5950 | −1.21760 | −0.608801 | − | 0.793323i | \(-0.708349\pi\) | ||||
−0.608801 | + | 0.793323i | \(0.708349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.0536 | −1.63343 | −0.816717 | − | 0.577038i | \(-0.804208\pi\) | ||||
−0.816717 | + | 0.577038i | \(0.804208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.28523 | −0.786399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3676 | −1.06937 | −0.534686 | − | 0.845051i | \(-0.679570\pi\) | ||||
−0.534686 | + | 0.845051i | \(0.679570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.88171 | 0.175470 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.07209 | −0.191565 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.35717 | 0.216081 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9959 | −0.999624 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.55401 | −0.140120 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.09616 | −0.366372 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.85124 | −0.430478 | −0.215239 | − | 0.976561i | \(-0.569053\pi\) | ||||
−0.215239 | + | 0.976561i | \(0.569053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.77619 | −0.244430 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1490 | 1.14884 | 0.574419 | − | 0.818562i | \(-0.305228\pi\) | ||||
0.574419 | + | 0.818562i | \(0.305228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.97824 | 0.865223 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.93317 | −0.252447 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.39248 | 0.802454 | 0.401227 | − | 0.915979i | \(-0.368584\pi\) | ||||
0.401227 | + | 0.915979i | \(0.368584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.71091 | 0.569212 | 0.284606 | − | 0.958645i | \(-0.408137\pi\) | ||||
0.284606 | + | 0.958645i | \(0.408137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.51709 | −0.380408 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.133239 | −0.0111420 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7200 | 0.890251 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.15922 | 0.425525 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.09023 | −0.498931 | −0.249466 | − | 0.968384i | \(-0.580255\pi\) | ||||
−0.249466 | + | 0.968384i | \(0.580255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3009 | 1.08241 | 0.541206 | − | 0.840890i | \(-0.317968\pi\) | ||||
0.541206 | + | 0.840890i | \(0.317968\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.73736 | −0.140457 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.5114 | 0.924618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.4309 | −1.71037 | −0.855186 | − | 0.518322i | \(-0.826557\pi\) | ||||
−0.855186 | + | 0.518322i | \(0.826557\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.55065 | 0.122974 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.870393 | −0.0685966 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.4013 | −1.28465 | −0.642324 | − | 0.766433i | \(-0.722030\pi\) | ||||
−0.642324 | + | 0.766433i | \(0.722030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.188608 | −0.0146831 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.70642 | −0.669725 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.35449 | −0.562412 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.77119 | −0.590833 | −0.295416 | − | 0.955369i | \(-0.595458\pi\) | ||||
−0.295416 | + | 0.955369i | \(0.595458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.88907 | −0.369579 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0736 | 0.832339 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.5631 | −1.53696 | −0.768479 | − | 0.639875i | \(-0.778986\pi\) | ||||
−0.768479 | + | 0.639875i | \(0.778986\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.27861 | −0.466686 | −0.233343 | − | 0.972395i | \(-0.574966\pi\) | ||||
−0.233343 | + | 0.972395i | \(0.574966\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.4007 | −0.990608 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.3020 | 1.78672 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.111715 | −0.00816940 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.35675 | 0.0986894 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4618 | 0.756991 | 0.378495 | − | 0.925603i | \(-0.376442\pi\) | ||||
0.378495 | + | 0.925603i | \(0.376442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.93031 | 0.282910 | 0.141455 | − | 0.989945i | \(-0.454822\pi\) | ||||
0.141455 | + | 0.989945i | \(0.454822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.07781 | 0.435241 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.96631 | −0.710070 | −0.355035 | − | 0.934853i | \(-0.615531\pi\) | ||||
−0.355035 | + | 0.934853i | \(0.615531\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.2537 | 1.64841 | 0.824205 | − | 0.566291i | \(-0.191622\pi\) | ||||
0.824205 | + | 0.566291i | \(0.191622\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.50770 | 0.317949 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.95861 | −0.348026 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.55818 | 0.318357 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.641526 | 0.0445892 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.472905 | −0.0327115 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.84912 | 0.127298 | 0.0636492 | − | 0.997972i | \(-0.479726\pi\) | ||||
0.0636492 | + | 0.997972i | \(0.479726\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.2267 | 0.700722 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.14303 | 0.555350 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.32466 | −0.361462 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.16638 | 0.416685 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.59997 | 0.242160 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.7420 | −1.32202 | −0.661010 | − | 0.750377i | \(-0.729872\pi\) | ||||
−0.661010 | + | 0.750377i | \(0.729872\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.60351 | 0.240234 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.07103 | 0.270204 | 0.135102 | − | 0.990832i | \(-0.456864\pi\) | ||||
0.135102 | + | 0.990832i | \(0.456864\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.3832 | 1.08263 | 0.541315 | − | 0.840820i | \(-0.317926\pi\) | ||||
0.541315 | + | 0.840820i | \(0.317926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0872414 | 0.00574006 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.9192 | −0.977392 | −0.488696 | − | 0.872454i | \(-0.662527\pi\) | ||||
−0.488696 | + | 0.872454i | \(0.662527\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.2494 | 0.864297 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.51122 | 0.163121 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0543 | 0.650362 | 0.325181 | − | 0.945652i | \(-0.394575\pi\) | ||||
0.325181 | + | 0.945652i | \(0.394575\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.4465 | 1.12383 | 0.561915 | − | 0.827195i | \(-0.310065\pi\) | ||||
0.561915 | + | 0.827195i | \(0.310065\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.1329 | −0.966804 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.2392 | 0.969648 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.74485 | 0.110576 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.90197 | 0.625007 | 0.312504 | − | 0.949917i | \(-0.398832\pi\) | ||||
0.312504 | + | 0.949917i | \(0.398832\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0412511 | 0.00259344 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.09598 | 0.319123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.8372 | −1.23741 | −0.618704 | − | 0.785624i | \(-0.712342\pi\) | ||||
−0.618704 | + | 0.785624i | \(0.712342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.2410 | −0.698483 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.65476 | 0.226224 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.8242 | −0.667447 | −0.333723 | − | 0.942671i | \(-0.608305\pi\) | ||||
−0.333723 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.54832 | −0.279401 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.4735 | 1.06936 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.67721 | −0.529059 | −0.264530 | − | 0.964378i | \(-0.585217\pi\) | ||||
−0.264530 | + | 0.964378i | \(0.585217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.8503 | −1.14507 | −0.572536 | − | 0.819879i | \(-0.694040\pi\) | ||||
−0.572536 | + | 0.819879i | \(0.694040\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.81132 | −0.170149 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.231711 | 0.0139727 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.13118 | 0.308303 | 0.154151 | − | 0.988047i | \(-0.450736\pi\) | ||||
0.154151 | + | 0.988047i | \(0.450736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.92456 | 0.234957 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.8779 | −1.06650 | −0.533252 | − | 0.845956i | \(-0.679030\pi\) | ||||
−0.533252 | + | 0.845956i | \(0.679030\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0771 | −0.777351 | −0.388676 | − | 0.921375i | \(-0.627067\pi\) | ||||
−0.388676 | + | 0.921375i | \(0.627067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 21.5720 | 1.27782 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.10841 | −0.124456 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9816 | −0.822446 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.6851 | −1.03672 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.1704 | 0.944682 | 0.472341 | − | 0.881416i | \(-0.343409\pi\) | ||||
0.472341 | + | 0.881416i | \(0.343409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.4806 | −1.89110 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0643015 | −0.00373115 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.32930 | −0.0768756 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.76660 | −0.217103 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0244 | −0.575886 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 39.3066 | 2.25069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.5563 | −0.716623 | −0.358312 | − | 0.933602i | \(-0.616647\pi\) | ||||
−0.358312 | + | 0.933602i | \(0.616647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.08730 | 0.346295 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.18454 | 0.123874 | 0.0619368 | − | 0.998080i | \(-0.480272\pi\) | ||||
0.0619368 | + | 0.998080i | \(0.480272\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.7286 | 1.68036 | 0.840179 | − | 0.542310i | \(-0.182450\pi\) | ||||
0.840179 | + | 0.542310i | \(0.182450\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.97960 | −0.224225 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.6910 | 1.38678 | 0.693392 | − | 0.720561i | \(-0.256116\pi\) | ||||
0.693392 | + | 0.720561i | \(0.256116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.235007 | 0.0131578 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5950 | 0.702983 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.7774 | 0.710954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.46680 | −0.414184 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.0536 | 0.943064 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.12859 | −0.337880 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.3306 | −1.39230 | −0.696148 | − | 0.717899i | \(-0.745104\pi\) | ||||
−0.696148 | + | 0.717899i | \(0.745104\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.28523 | 0.454028 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.2219 | −0.722387 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00882 | 0.0549542 | 0.0274771 | − | 0.999622i | \(-0.491253\pi\) | ||||
0.0274771 | + | 0.999622i | \(0.491253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3676 | 0.617402 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.252355 | 0.0136658 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4971 | 0.890758 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.88171 | −0.101308 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.37742 | 0.288675 | 0.144337 | − | 0.989529i | \(-0.453895\pi\) | ||||
0.144337 | + | 0.989529i | \(0.453895\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.8774 | −1.86694 | −0.933471 | − | 0.358653i | \(-0.883236\pi\) | ||||
−0.933471 | + | 0.358653i | \(0.883236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.07209 | 0.110600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.1276 | −1.92288 | −0.961438 | − | 0.275020i | \(-0.911315\pi\) | ||||
−0.961438 | + | 0.275020i | \(0.911315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.9967 | −1.59206 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.35717 | −0.124755 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1328 | 1.22090 | 0.610451 | − | 0.792054i | \(-0.290988\pi\) | ||||
0.610451 | + | 0.792054i | \(0.290988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.0886 | 1.84677 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9959 | 0.577133 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.0871 | −0.946720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.93252 | −0.466274 | −0.233137 | − | 0.972444i | \(-0.574899\pi\) | ||||
−0.233137 | + | 0.972444i | \(0.574899\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.55401 | 0.0808986 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.10385 | 0.109226 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2017 | 0.838891 | 0.419445 | − | 0.907781i | \(-0.362225\pi\) | ||||
0.419445 | + | 0.907781i | \(0.362225\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.09616 | 0.211525 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.57301 | −0.390030 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.95663 | 0.151872 | 0.0759361 | − | 0.997113i | \(-0.475806\pi\) | ||||
0.0759361 | + | 0.997113i | \(0.475806\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.85124 | 0.248536 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.0666 | −0.514381 | −0.257191 | − | 0.966361i | \(-0.582797\pi\) | ||||
−0.257191 | + | 0.966361i | \(0.582797\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.255894 | −0.0130416 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.77619 | 0.141121 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.7618 | 0.697749 | 0.348874 | − | 0.937170i | \(-0.386564\pi\) | ||||
0.348874 | + | 0.937170i | \(0.386564\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.11456 | −0.0563658 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.1490 | −0.663281 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.36584 | −0.370615 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.8647 | −1.49887 | −0.749433 | − | 0.662081i | \(-0.769674\pi\) | ||||
−0.749433 | + | 0.662081i | \(0.769674\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.97824 | −0.499537 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.3485 | −1.26584 | −0.632922 | − | 0.774215i | \(-0.718145\pi\) | ||||
−0.632922 | + | 0.774215i | \(0.718145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.13205 | −0.405086 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.93317 | 0.145751 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.532753 | 0.0264076 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.5335 | 0.570293 | 0.285147 | − | 0.958484i | \(-0.407958\pi\) | ||||
0.285147 | + | 0.958484i | \(0.407958\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.39248 | −0.463297 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.0241 | 0.739287 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.11796 | −0.251231 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.71091 | −0.328635 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.1036 | −1.47066 | −0.735328 | − | 0.677711i | \(-0.762972\pi\) | ||||
−0.735328 | + | 0.677711i | \(0.762972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.97021 | 0.144759 | 0.0723795 | − | 0.997377i | \(-0.476941\pi\) | ||||
0.0723795 | + | 0.997377i | \(0.476941\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.51709 | 0.219629 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.26059 | −0.303683 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.1815 | −0.879862 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.133239 | 0.00643283 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.290617 | 0.0139985 | 0.00699927 | − | 0.999976i | \(-0.497772\pi\) | ||||
0.00699927 | + | 0.999976i | \(0.497772\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.66027 | −0.416186 | −0.208093 | − | 0.978109i | \(-0.566726\pi\) | ||||
−0.208093 | + | 0.978109i | \(0.566726\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.7200 | −0.513987 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.71810 | −0.225697 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.4829 | −1.74123 | −0.870616 | − | 0.491963i | \(-0.836279\pi\) | ||||
−0.870616 | + | 0.491963i | \(0.836279\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.15922 | −0.245677 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.6330 | 1.83551 | 0.917754 | − | 0.397149i | \(-0.130000\pi\) | ||||
0.917754 | + | 0.397149i | \(0.130000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −51.2529 | −2.42962 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.09023 | 0.288058 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.1961 | −1.23627 | −0.618136 | − | 0.786071i | \(-0.712112\pi\) | ||||
−0.618136 | + | 0.786071i | \(0.712112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0999253 | 0.00470530 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.3009 | −0.624931 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.24610 | 0.386583 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.98759 | 0.280088 | 0.140044 | − | 0.990145i | \(-0.455276\pi\) | ||||
0.140044 | + | 0.990145i | \(0.455276\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.73736 | 0.0810930 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.6863 | −1.56893 | −0.784464 | − | 0.620174i | \(-0.787062\pi\) | ||||
−0.784464 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.4825 | 0.719532 | 0.359766 | − | 0.933043i | \(-0.382857\pi\) | ||||
0.359766 | + | 0.933043i | \(0.382857\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.5114 | −0.533829 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.98854 | 0.230842 | 0.115421 | − | 0.993317i | \(-0.463178\pi\) | ||||
0.115421 | + | 0.993317i | \(0.463178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.11584 | 0.282403 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.4309 | 0.987483 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.178513 | 0.00820804 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.5020 | −1.21599 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.55065 | −0.0709993 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.2655 | −0.697499 | −0.348749 | − | 0.937216i | \(-0.613394\pi\) | ||||
−0.348749 | + | 0.937216i | \(0.613394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.1678 | −0.782783 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.870393 | 0.0396043 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 51.8734 | 2.35545 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.7295 | −1.34717 | −0.673587 | − | 0.739108i | \(-0.735247\pi\) | ||||
−0.673587 | + | 0.739108i | \(0.735247\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.4013 | 0.741692 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.9213 | 1.71136 | 0.855682 | − | 0.517502i | \(-0.173138\pi\) | ||||
0.855682 | + | 0.517502i | \(0.173138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.34963 | −0.285973 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.188608 | 0.00847728 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.8751 | 0.622384 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.26368 | −0.0565699 | −0.0282850 | − | 0.999600i | \(-0.509005\pi\) | ||||
−0.0282850 | + | 0.999600i | \(0.509005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.1166 | −0.495665 | −0.247833 | − | 0.968803i | \(-0.579718\pi\) | ||||
−0.247833 | + | 0.968803i | \(0.579718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.4033 | 1.30843 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.70642 | 0.386666 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 36.4271 | 1.61460 | 0.807301 | − | 0.590140i | \(-0.200927\pi\) | ||||
0.807301 | + | 0.590140i | \(0.200927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.36626 | 0.370102 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.35449 | 0.324709 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.8551 | −0.786790 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.290456 | 0.0127742 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.77119 | 0.341118 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.0491 | −1.22885 | −0.614427 | − | 0.788974i | \(-0.710613\pi\) | ||||
−0.614427 | + | 0.788974i | \(0.710613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.4652 | 1.55078 | 0.775392 | − | 0.631481i | \(-0.217553\pi\) | ||||
0.775392 | + | 0.631481i | \(0.217553\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.88907 | 0.213377 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.81837 | −0.297013 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5884 | −0.982106 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0736 | −0.480551 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.22006 | −0.139476 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.9432 | −1.59720 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.5631 | 0.887363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.331746 | −0.0142893 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.84741 | 0.337387 | 0.168693 | − | 0.985669i | \(-0.446045\pi\) | ||||
0.168693 | + | 0.985669i | \(0.446045\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.27861 | 0.269441 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −50.0210 | −2.14267 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0303 | 1.11297 | 0.556487 | − | 0.830856i | \(-0.312149\pi\) | ||||
0.556487 | + | 0.830856i | \(0.312149\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.4007 | 0.571928 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.8789 | −1.14508 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.40711 | 0.144885 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.3020 | −1.03156 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.5772 | 0.998999 | 0.499499 | − | 0.866314i | \(-0.333517\pi\) | ||||
0.499499 | + | 0.866314i | \(0.333517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.75252 | −0.243306 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.111715 | 0.00471661 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.45924 | −0.0614997 | −0.0307498 | − | 0.999527i | \(-0.509790\pi\) | ||||
−0.0307498 | + | 0.999527i | \(0.509790\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.3431 | −1.40275 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.35675 | −0.0569783 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4501 | −0.773470 | −0.386735 | − | 0.922191i | \(-0.626397\pi\) | ||||
−0.386735 | + | 0.922191i | \(0.626397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.0806 | −1.13329 | −0.566644 | − | 0.823963i | \(-0.691758\pi\) | ||||
−0.566644 | + | 0.823963i | \(0.691758\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.4618 | −0.437049 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.31174 | 0.0964063 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7436 | 0.488894 | 0.244447 | − | 0.969663i | \(-0.421394\pi\) | ||||
0.244447 | + | 0.969663i | \(0.421394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.93031 | −0.163338 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.36734 | 0.0982138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0997091 | −0.00412953 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.07781 | −0.251287 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.5381 | 0.723874 | 0.361937 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361937 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.8631 | −1.18928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.96631 | 0.409959 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.8036 | −0.936433 | −0.468216 | − | 0.883614i | \(-0.655103\pi\) | ||||
−0.468216 | + | 0.883614i | \(0.655103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.91399 | 0.283446 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.2537 | −0.951710 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.3655 | 0.872971 | 0.436485 | − | 0.899711i | \(-0.356223\pi\) | ||||
0.436485 | + | 0.899711i | \(0.356223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.09186 | −0.0853288 | −0.0426644 | − | 0.999089i | \(-0.513585\pi\) | ||||
−0.0426644 | + | 0.999089i | \(0.513585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.50770 | −0.183568 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.2528 | −1.31126 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.887942 | −0.0360405 | −0.0180202 | − | 0.999838i | \(-0.505736\pi\) | ||||
−0.0180202 | + | 0.999838i | \(0.505736\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.95861 | 0.200933 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.35984 | −0.378659 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.2654 | 1.26280 | 0.631399 | − | 0.775458i | \(-0.282481\pi\) | ||||
0.631399 | + | 0.775458i | \(0.282481\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.55818 | −0.183804 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7468 | 0.794975 | 0.397488 | − | 0.917608i | \(-0.369882\pi\) | ||||
0.397488 | + | 0.917608i | \(0.369882\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.73668 | 0.0698032 | 0.0349016 | − | 0.999391i | \(-0.488888\pi\) | ||||
0.0349016 | + | 0.999391i | \(0.488888\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.641526 | −0.0257436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.7073 | 0.949812 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.0323 | −1.20129 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.472905 | 0.0188860 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.3944 | −0.573943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.51023 | 0.139740 | 0.0698700 | − | 0.997556i | \(-0.477742\pi\) | ||||
0.0698700 | + | 0.997556i | \(0.477742\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.84912 | −0.0734958 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.2295 | −0.564681 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.6904 | 0.423569 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.2267 | −0.404562 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.8251 | −1.09902 | −0.549512 | − | 0.835486i | \(-0.685186\pi\) | ||||
−0.549512 | + | 0.835486i | \(0.685186\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8299 | 0.545399 | 0.272700 | − | 0.962099i | \(-0.412084\pi\) | ||||
0.272700 | + | 0.962099i | \(0.412084\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.14303 | −0.320632 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.6414 | 0.654241 | 0.327120 | − | 0.944983i | \(-0.393922\pi\) | ||||
0.327120 | + | 0.944983i | \(0.393922\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.712046 | −0.0279503 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.32466 | 0.208690 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.1625 | 1.02382 | 0.511909 | − | 0.859040i | \(-0.328938\pi\) | ||||
0.511909 | + | 0.859040i | \(0.328938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 38.5684 | 1.50699 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.16638 | −0.240573 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.9458 | 1.63398 | 0.816989 | − | 0.576653i | \(-0.195642\pi\) | ||||
0.816989 | + | 0.576653i | \(0.195642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.6903 | −0.999236 | −0.499618 | − | 0.866246i | \(-0.666526\pi\) | ||||
−0.499618 | + | 0.866246i | \(0.666526\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.59997 | −0.139811 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.2679 | 1.13496 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.34462 | 0.0907842 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.7420 | 0.763269 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.861686 | 0.0332650 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.468458 | −0.0180577 | −0.00902887 | − | 0.999959i | \(-0.502874\pi\) | ||||
−0.00902887 | + | 0.999959i | \(0.502874\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.60351 | −0.138699 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.12748 | 0.197065 | 0.0985325 | − | 0.995134i | \(-0.468585\pi\) | ||||
0.0985325 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.9943 | −0.920817 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.07103 | −0.156002 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.24490 | 0.0476349 | 0.0238174 | − | 0.999716i | \(-0.492418\pi\) | ||||
0.0238174 | + | 0.999716i | \(0.492418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.5498 | 1.05262 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3832 | −0.625057 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.21309 | 0.122409 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.8788 | 0.489934 | 0.244967 | − | 0.969531i | \(-0.421223\pi\) | ||||
0.244967 | + | 0.969531i | \(0.421223\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0872414 | −0.00331403 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.6843 | 0.746666 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.69988 | −0.102265 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.9192 | 0.564298 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0111 | −0.453654 | −0.226827 | − | 0.973935i | \(-0.572835\pi\) | ||||
−0.226827 | + | 0.973935i | \(0.572835\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −60.9337 | −2.29816 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.2494 | −0.499002 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.6006 | −0.511505 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.333173 | 0.0125126 | 0.00625628 | − | 0.999980i | \(-0.498009\pi\) | ||||
0.00625628 | + | 0.999980i | \(0.498009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.51122 | −0.0941780 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.51771 | 0.0942889 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.390813 | −0.0146156 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.0543 | −0.375486 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.69923 | 0.175252 | 0.0876258 | − | 0.996153i | \(-0.472072\pi\) | ||||
0.0876258 | + | 0.996153i | \(0.472072\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.25898 | 0.307580 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.4465 | −0.648843 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.1699 | 0.489119 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9255 | −0.627733 | −0.313866 | − | 0.949467i | \(-0.601624\pi\) | ||||
−0.313866 | + | 0.949467i | \(0.601624\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.82323 | −0.178394 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.7928 | 0.767998 | 0.383999 | − | 0.923333i | \(-0.374547\pi\) | ||||
0.383999 | + | 0.923333i | \(0.374547\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15.1329 | 0.558185 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.289852 | −0.0106768 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.1583 | −1.40368 | −0.701838 | − | 0.712336i | \(-0.747637\pi\) | ||||
−0.701838 | + | 0.712336i | \(0.747637\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.2392 | −0.559826 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.00712 | −0.0369476 | −0.0184738 | − | 0.999829i | \(-0.505881\pi\) | ||||
−0.0184738 | + | 0.999829i | \(0.505881\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.8637 | −0.654475 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.74485 | −0.0638409 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.0883 | 0.624392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4846 | 0.382589 | 0.191295 | − | 0.981533i | \(-0.438731\pi\) | ||||
0.191295 | + | 0.981533i | \(0.438731\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.90197 | −0.360848 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.0139 | 1.41986 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.4109 | 0.814537 | 0.407269 | − | 0.913308i | \(-0.366481\pi\) | ||||
0.407269 | + | 0.913308i | \(0.366481\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0412511 | −0.00149732 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.38127 | 0.0863211 | 0.0431606 | − | 0.999068i | \(-0.486257\pi\) | ||||
0.0431606 | + | 0.999068i | \(0.486257\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.1375 | 0.837633 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.09598 | −0.184245 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.9454 | 0.828512 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.71515 | 0.242154 | 0.121077 | − | 0.992643i | \(-0.461365\pi\) | ||||
0.121077 | + | 0.992643i | \(0.461365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8372 | 0.714418 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7417 | −0.674091 | −0.337046 | − | 0.941488i | \(-0.609428\pi\) | ||||
−0.337046 | + | 0.941488i | \(0.609428\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.1422 | 0.508002 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.2410 | 0.403269 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4290 | −0.409485 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.657593 | −0.0235305 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.65476 | −0.130610 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.8605 | −2.24359 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.60078 | 0.270939 | 0.135469 | − | 0.990782i | \(-0.456746\pi\) | ||||
0.135469 | + | 0.990782i | \(0.456746\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.8242 | 0.385351 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.4230 | 0.548379 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.7675 | −0.986054 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.54832 | 0.161312 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.3082 | 0.719352 | 0.359676 | − | 0.933077i | \(-0.382887\pi\) | ||||
0.359676 | + | 0.933077i | \(0.382887\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.84782 | −0.277636 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.4735 | −0.617397 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.396508 | −0.0139925 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.55301 | −0.0899819 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.67721 | 0.305452 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.84896 | −0.170480 | −0.0852402 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852402 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.215265 | 0.00755897 | 0.00377948 | − | 0.999993i | \(-0.498797\pi\) | ||||
0.00377948 | + | 0.999993i | \(0.498797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.8503 | 0.661108 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −48.1078 | −1.68514 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.4174 | −0.714316 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.81132 | 0.0982356 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.6835 | −0.791659 | −0.395829 | − | 0.918324i | \(-0.629543\pi\) | ||||
−0.395829 | + | 0.918324i | \(0.629543\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.75812 | −0.340147 | −0.170073 | − | 0.985431i | \(-0.554400\pi\) | ||||
−0.170073 | + | 0.985431i | \(0.554400\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.231711 | −0.00806714 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6125 | 1.02973 | 0.514863 | − | 0.857272i | \(-0.327843\pi\) | ||||
0.514863 | + | 0.857272i | \(0.327843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.3806 | −1.50667 | −0.753336 | − | 0.657636i | \(-0.771557\pi\) | ||||
−0.753336 | + | 0.657636i | \(0.771557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.13118 | −0.177999 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.96342 | 0.310564 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.93317 | −0.101507 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.92456 | −0.135653 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.6211 | 1.36787 | 0.683936 | − | 0.729542i | \(-0.260267\pi\) | ||||
0.683936 | + | 0.729542i | \(0.260267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6427 | −0.539405 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.8779 | 0.615746 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.5375 | −0.878515 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.9187 | 0.512612 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.0771 | 0.448804 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.31519 | 0.182202 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.6643 | −1.18688 | −0.593442 | − | 0.804877i | \(-0.702231\pi\) | ||||
−0.593442 | + | 0.804877i | \(0.702231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.5720 | −0.737747 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.6878 | 0.672522 | 0.336261 | − | 0.941769i | \(-0.390838\pi\) | ||||
0.336261 | + | 0.941769i | \(0.390838\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.1405 | −0.380108 | −0.190054 | − | 0.981774i | \(-0.560866\pi\) | ||||
−0.190054 | + | 0.981774i | \(0.560866\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.10841 | 0.0718545 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.5360 | 0.971377 | 0.485688 | − | 0.874132i | \(-0.338569\pi\) | ||||
0.485688 | + | 0.874132i | \(0.338569\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.7943 | −0.775028 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.9816 | 0.474839 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.161475 | −0.00547767 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.34038 | 0.316487 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.6851 | 0.598549 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.55748 | 0.187877 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.5568 | 1.13313 | 0.566566 | − | 0.824016i | \(-0.308272\pi\) | ||||
0.566566 | + | 0.824016i | \(0.308272\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.1704 | −0.545413 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.9200 | −1.17648 | −0.588242 | − | 0.808685i | \(-0.700180\pi\) | ||||
−0.588242 | + | 0.808685i | \(0.700180\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.89129 | 0.130952 | 0.0654761 | − | 0.997854i | \(-0.479143\pi\) | ||||
0.0654761 | + | 0.997854i | \(0.479143\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.4806 | 1.09182 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.7256 | −0.628745 | −0.314372 | − | 0.949300i | \(-0.601794\pi\) | ||||
−0.314372 | + | 0.949300i | \(0.601794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.58194 | 0.220751 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0643015 | 0.00215418 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.2209 | −1.11170 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −60.3151 | −2.01611 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.32930 | 0.0443841 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.3433 | 0.478376 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.69403 | 0.0897513 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.76660 | 0.125345 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.4163 | −0.612177 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.23006 | −0.140457 | −0.0702285 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702285 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0244 | 0.332488 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.4195 | 1.07411 | 0.537053 | − | 0.843549i | \(-0.319538\pi\) | ||||
0.537053 | + | 0.843549i | \(0.319538\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.112197 | −0.00371317 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.3066 | −1.29944 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.8400 | −0.589129 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.50842 | −0.247680 | −0.123840 | − | 0.992302i | \(-0.539521\pi\) | ||||
−0.123840 | + | 0.992302i | \(0.539521\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.5563 | 0.413743 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.1907 | 0.697500 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.8559 | 0.981655 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.08730 | −0.199933 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.6459 | 0.480516 | 0.240258 | − | 0.970709i | \(-0.422768\pi\) | ||||
0.240258 | + | 0.970709i | \(0.422768\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.9434 | 1.24355 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.18454 | −0.0715185 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.327679 | −0.0107163 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.5660 | −1.09655 | −0.548277 | − | 0.836297i | \(-0.684716\pi\) | ||||
−0.548277 | + | 0.836297i | \(0.684716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.7286 | −0.970155 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.09313 | −0.296428 | −0.148214 | − | 0.988955i | \(-0.547352\pi\) | ||||
−0.148214 | + | 0.988955i | \(0.547352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.996939 | 0.0324648 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.97960 | 0.129456 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.3348 | 1.08323 | 0.541617 | − | 0.840625i | \(-0.317812\pi\) | ||||
0.541617 | + | 0.840625i | \(0.317812\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.7773 | 0.414769 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.6910 | −0.800660 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.3126 | −0.852349 | −0.426174 | − | 0.904641i | \(-0.640139\pi\) | ||||
−0.426174 | + | 0.904641i | \(0.640139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.6863 | 0.992987 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.235007 | −0.00759669 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.7433 | −0.411502 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5978 | −0.503156 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.5950 | −0.405867 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.5283 | 0.371109 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.3925 | −1.78130 | −0.890651 | − | 0.454687i | \(-0.849751\pi\) | ||||
−0.890651 | + | 0.454687i | \(0.849751\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.7774 | −0.410469 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.9200 | 0.542990 | 0.271495 | − | 0.962440i | \(-0.412482\pi\) | ||||
0.271495 | + | 0.962440i | \(0.412482\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.10505 | −0.291895 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.46680 | 0.239129 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.54245 | −0.177319 | −0.0886594 | − | 0.996062i | \(-0.528258\pi\) | ||||
−0.0886594 | + | 0.996062i | \(0.528258\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.12357 | −0.0359096 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.0536 | −0.544478 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.9074 | −0.666842 | −0.333421 | − | 0.942778i | \(-0.608203\pi\) | ||||
−0.333421 | + | 0.942778i | \(0.608203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.2329 | −0.931438 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.12859 | 0.195075 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.78100 | 0.0566324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.9402 | −1.45934 | −0.729669 | − | 0.683800i | \(-0.760326\pi\) | ||||
−0.729669 | + | 0.683800i | \(0.760326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.3306 | 0.803842 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 68.2071 | 2.16231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.5386 | −0.935498 | −0.467749 | − | 0.883861i | \(-0.654935\pi\) | ||||
−0.467749 | + | 0.883861i | \(0.654935\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.28523 | −0.262133 |
(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 | 8016.2.a.bf.1.10 | 12 | ||
4.3 | odd | 2 | 4008.2.a.l.1.10 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.10 | ✓ | 12 | 4.3 | odd | 2 | ||
8016.2.a.bf.1.10 | 12 | 1.1 | even | 1 | trivial |