Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.106392688.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 9x^{4} + 12x^{3} + 25x^{2} - 10x - 16 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.80207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | −1.80207 | −1.04043 | −0.520213 | − | 0.854037i | \(-0.674147\pi\) | ||||
−0.520213 | + | 0.854037i | \(0.674147\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.702208 | 0.314037 | 0.157018 | − | 0.987596i | \(-0.449812\pi\) | ||||
0.157018 | + | 0.987596i | \(0.449812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.70221 | 0.643374 | 0.321687 | − | 0.946846i | \(-0.395750\pi\) | ||||
0.321687 | + | 0.946846i | \(0.395750\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.247456 | 0.0824853 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.29079 | −1.74475 | −0.872375 | − | 0.488836i | \(-0.837422\pi\) | ||||
−0.872375 | + | 0.488836i | \(0.837422\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.26543 | −0.326732 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.35325 | −1.54089 | −0.770444 | − | 0.637507i | \(-0.779966\pi\) | ||||
−0.770444 | + | 0.637507i | \(0.779966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.06750 | −0.669383 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.86158 | 1.43074 | 0.715369 | − | 0.698747i | \(-0.246259\pi\) | ||||
0.715369 | + | 0.698747i | \(0.246259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.50690 | −0.901381 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.96028 | 0.954606 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.53107 | 0.284312 | 0.142156 | − | 0.989844i | \(-0.454596\pi\) | ||||
0.142156 | + | 0.989844i | \(0.454596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.26543 | −0.227278 | −0.113639 | − | 0.993522i | \(-0.536251\pi\) | ||||
−0.113639 | + | 0.993522i | \(0.536251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.80207 | −0.313700 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.19530 | 0.202043 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.7097 | 1.92507 | 0.962535 | − | 0.271158i | \(-0.0874067\pi\) | ||||
0.962535 | + | 0.271158i | \(0.0874067\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.3364 | 1.81528 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.31414 | 0.673756 | 0.336878 | − | 0.941548i | \(-0.390629\pi\) | ||||
0.336878 | + | 0.941548i | \(0.390629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.90848 | 1.35853 | 0.679265 | − | 0.733893i | \(-0.262299\pi\) | ||||
0.679265 | + | 0.733893i | \(0.262299\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.173766 | 0.0259034 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.70319 | −1.12363 | −0.561813 | − | 0.827264i | \(-0.689896\pi\) | ||||
−0.561813 | + | 0.827264i | \(0.689896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.10249 | −0.586070 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.4490 | 1.60318 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.91192 | 0.537343 | 0.268672 | − | 0.963232i | \(-0.413415\pi\) | ||||
0.268672 | + | 0.963232i | \(0.413415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.702208 | 0.0946857 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.80207 | 0.238690 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.424525 | −0.0552684 | −0.0276342 | − | 0.999618i | \(-0.508797\pi\) | ||||
−0.0276342 | + | 0.999618i | \(0.508797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.09905 | 0.780904 | 0.390452 | − | 0.920623i | \(-0.372319\pi\) | ||||
0.390452 | + | 0.920623i | \(0.372319\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.421222 | 0.0530689 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.41744 | −0.547916 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.02309 | −0.858007 | −0.429004 | − | 0.903303i | \(-0.641135\pi\) | ||||
−0.429004 | + | 0.903303i | \(0.641135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.3650 | −1.48858 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.952290 | −0.113016 | −0.0565080 | − | 0.998402i | \(-0.517997\pi\) | ||||
−0.0565080 | + | 0.998402i | \(0.517997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.42777 | −0.635272 | −0.317636 | − | 0.948213i | \(-0.602889\pi\) | ||||
−0.317636 | + | 0.948213i | \(0.602889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.12176 | 0.937820 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.70221 | 0.193985 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.61270 | −0.969004 | −0.484502 | − | 0.874790i | \(-0.660999\pi\) | ||||
−0.484502 | + | 0.874790i | \(0.660999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.68113 | −1.07568 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.35338 | 0.477846 | 0.238923 | − | 0.971039i | \(-0.423206\pi\) | ||||
0.238923 | + | 0.971039i | \(0.423206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.46130 | −0.483896 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.75909 | −0.295806 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3417 | 1.09622 | 0.548109 | − | 0.836407i | \(-0.315348\pi\) | ||||
0.548109 | + | 0.836407i | \(0.315348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.7082 | −1.12253 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.28039 | 0.236465 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.702208 | −0.0720450 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.39099 | −0.344303 | −0.172152 | − | 0.985070i | \(-0.555072\pi\) | ||||
−0.172152 | + | 0.985070i | \(0.555072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.247456 | 0.0248703 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.03112 | −0.401111 | −0.200556 | − | 0.979682i | \(-0.564275\pi\) | ||||
−0.200556 | + | 0.979682i | \(0.564275\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.23801 | 0.516116 | 0.258058 | − | 0.966129i | \(-0.416917\pi\) | ||||
0.258058 | + | 0.966129i | \(0.416917\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.15402 | −0.210211 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.2526 | 1.37785 | 0.688924 | − | 0.724833i | \(-0.258083\pi\) | ||||
0.688924 | + | 0.724833i | \(0.258083\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.6462 | 1.69020 | 0.845101 | − | 0.534607i | \(-0.179540\pi\) | ||||
0.845101 | + | 0.534607i | \(0.179540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.1018 | −2.00289 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.58975 | 0.808055 | 0.404028 | − | 0.914747i | \(-0.367610\pi\) | ||||
0.404028 | + | 0.914747i | \(0.367610\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.81826 | 0.449305 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.55669 | −0.143916 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.8145 | −0.991368 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.77439 | −0.700993 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.67582 | −0.597104 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3430 | 1.45021 | 0.725103 | − | 0.688640i | \(-0.241792\pi\) | ||||
0.725103 | + | 0.688640i | \(0.241792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.0537 | −1.41345 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.06687 | −0.442694 | −0.221347 | − | 0.975195i | \(-0.571045\pi\) | ||||
−0.221347 | + | 0.975195i | \(0.571045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.70221 | −0.147600 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.48315 | 0.299781 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.56620 | −0.817296 | −0.408648 | − | 0.912692i | \(-0.634000\pi\) | ||||
−0.408648 | + | 0.912692i | \(0.634000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.60970 | 0.730266 | 0.365133 | − | 0.930955i | \(-0.381024\pi\) | ||||
0.365133 | + | 0.930955i | \(0.381024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.8817 | 1.16905 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.29079 | −0.526062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.07513 | 0.0892846 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.39297 | 0.609762 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5796 | 1.27633 | 0.638166 | − | 0.769898i | \(-0.279693\pi\) | ||||
0.638166 | + | 0.769898i | \(0.279693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.0919 | 1.47230 | 0.736150 | − | 0.676819i | \(-0.236642\pi\) | ||||
0.736150 | + | 0.676819i | \(0.236642\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.57215 | −0.127101 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.888593 | −0.0713735 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.4692 | −1.63362 | −0.816811 | − | 0.576906i | \(-0.804260\pi\) | ||||
−0.816811 | + | 0.576906i | \(0.804260\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.04955 | −0.559066 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.6798 | 0.920500 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.524409 | −0.0410749 | −0.0205374 | − | 0.999789i | \(-0.506538\pi\) | ||||
−0.0205374 | + | 0.999789i | \(0.506538\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.26543 | −0.0985134 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.2266 | 1.95210 | 0.976048 | − | 0.217557i | \(-0.0698088\pi\) | ||||
0.976048 | + | 0.217557i | \(0.0698088\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.5740 | 2.04416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.247456 | −0.0189234 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8618 | 0.825804 | 0.412902 | − | 0.910775i | \(-0.364515\pi\) | ||||
0.412902 | + | 0.910775i | \(0.364515\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.67169 | −0.579925 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.765023 | 0.0575027 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0533 | −0.826164 | −0.413082 | − | 0.910694i | \(-0.635548\pi\) | ||||
−0.413082 | + | 0.910694i | \(0.635548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.36675 | 0.547566 | 0.273783 | − | 0.961791i | \(-0.411725\pi\) | ||||
0.273783 | + | 0.961791i | \(0.411725\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9909 | −0.812472 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.22267 | 0.604543 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.35325 | −0.464595 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.44342 | 0.614169 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.8999 | 1.65698 | 0.828490 | − | 0.560004i | \(-0.189200\pi\) | ||||
0.828490 | + | 0.560004i | \(0.189200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6653 | −1.12762 | −0.563808 | − | 0.825906i | \(-0.690664\pi\) | ||||
−0.563808 | + | 0.825906i | \(0.690664\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.96054 | 0.570066 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.76105 | −0.552952 | −0.276476 | − | 0.961021i | \(-0.589167\pi\) | ||||
−0.276476 | + | 0.961021i | \(0.589167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.28201 | −0.232656 | −0.116328 | − | 0.993211i | \(-0.537112\pi\) | ||||
−0.116328 | + | 0.993211i | \(0.537112\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.6561 | 0.892693 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.60620 | 0.182919 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.02943 | 0.211584 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.69794 | 0.118015 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9296 | 1.71622 | 0.858111 | − | 0.513464i | \(-0.171638\pi\) | ||||
0.858111 | + | 0.513464i | \(0.171638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.71609 | 0.117585 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.25561 | 0.426629 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.15402 | −0.146224 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.78122 | 0.660954 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 39.9669 | 2.68847 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3802 | −1.16387 | −0.581933 | − | 0.813237i | \(-0.697703\pi\) | ||||
−0.581933 | + | 0.813237i | \(0.697703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.11526 | −0.0743507 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.00934827 | −0.000620466 0 | −0.000310233 | − | 1.00000i | \(-0.500099\pi\) | ||||
−0.000310233 | 1.00000i | \(0.500099\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.53526 | 0.365780 | 0.182890 | − | 0.983133i | \(-0.441455\pi\) | ||||
0.182890 | + | 0.983133i | \(0.441455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.06750 | −0.201827 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.5316 | −0.755458 | −0.377729 | − | 0.925916i | \(-0.623295\pi\) | ||||
−0.377729 | + | 0.925916i | \(0.623295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.40924 | −0.352860 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5207 | 1.00818 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6298 | 0.946321 | 0.473161 | − | 0.880976i | \(-0.343113\pi\) | ||||
0.473161 | + | 0.880976i | \(0.343113\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.8974 | 1.28171 | 0.640853 | − | 0.767664i | \(-0.278581\pi\) | ||||
0.640853 | + | 0.767664i | \(0.278581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.56525 | 0.164561 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.88080 | −0.184048 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.29079 | 0.400273 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.84510 | −0.497163 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.7680 | 1.75270 | 0.876352 | − | 0.481672i | \(-0.159970\pi\) | ||||
0.876352 | + | 0.481672i | \(0.159970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.86158 | 0.431384 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.03958 | 0.503458 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −30.5983 | −1.90867 | −0.954334 | − | 0.298743i | \(-0.903433\pi\) | ||||
−0.954334 | + | 0.298743i | \(0.903433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.9324 | 1.23854 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.378872 | 0.0234516 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5937 | 0.838227 | 0.419113 | − | 0.907934i | \(-0.362341\pi\) | ||||
0.419113 | + | 0.907934i | \(0.362341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.74698 | 0.168746 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.6365 | −1.14053 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.37492 | −0.327715 | −0.163857 | − | 0.986484i | \(-0.552394\pi\) | ||||
−0.163857 | + | 0.986484i | \(0.552394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.64658 | −0.585988 | −0.292994 | − | 0.956114i | \(-0.594652\pi\) | ||||
−0.292994 | + | 0.956114i | \(0.594652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.2970 | 1.16791 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.50690 | −0.271777 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.994203 | 0.0597359 | 0.0298679 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298679 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.313138 | −0.0187471 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.0311 | −1.85116 | −0.925579 | − | 0.378554i | \(-0.876422\pi\) | ||||
−0.925579 | + | 0.378554i | \(0.876422\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1143 | 0.601232 | 0.300616 | − | 0.953745i | \(-0.402808\pi\) | ||||
0.300616 | + | 0.953745i | \(0.402808\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.26543 | 0.0749575 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.34357 | 0.433477 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.3638 | 1.37434 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.11081 | 0.358222 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.17773 | 0.477748 | 0.238874 | − | 0.971051i | \(-0.423222\pi\) | ||||
0.238874 | + | 0.971051i | \(0.423222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.298105 | −0.0173563 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.96028 | 0.287824 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −43.1648 | −2.49628 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.1641 | 0.874043 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.26436 | 0.417326 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.28280 | 0.245233 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.25758 | −0.242993 | −0.121496 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121496 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.43926 | −0.536981 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.26758 | 0.0718777 | 0.0359389 | − | 0.999354i | \(-0.488558\pi\) | ||||
0.0359389 | + | 0.999354i | \(0.488558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.73769 | 0.380837 | 0.190418 | − | 0.981703i | \(-0.439016\pi\) | ||||
0.190418 | + | 0.981703i | \(0.439016\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.295785 | 0.0166656 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.5503 | −1.60355 | −0.801773 | − | 0.597628i | \(-0.796110\pi\) | ||||
−0.801773 | + | 0.597628i | \(0.796110\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.53107 | 0.0857234 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.6841 | −1.43355 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.35325 | 0.353504 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.3520 | 1.57269 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.7997 | −1.75853 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.1124 | −0.722912 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.7861 | 1.58223 | 0.791114 | − | 0.611669i | \(-0.209501\pi\) | ||||
0.791114 | + | 0.611669i | \(0.209501\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.89765 | 0.158790 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.93167 | −0.269446 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3296 | 1.43426 | 0.717132 | − | 0.696937i | \(-0.245454\pi\) | ||||
0.717132 | + | 0.696937i | \(0.245454\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.4793 | −0.840722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.26543 | −0.0685268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8987 | −1.02044 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.68283 | −0.467468 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.4283 | −1.47243 | −0.736215 | − | 0.676748i | \(-0.763389\pi\) | ||||
−0.736215 | + | 0.676748i | \(0.763389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.3945 | −1.30581 | −0.652905 | − | 0.757440i | \(-0.726450\pi\) | ||||
−0.652905 | + | 0.757440i | \(0.726450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −31.2041 | −1.66555 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.7352 | 0.571375 | 0.285687 | − | 0.958323i | \(-0.407778\pi\) | ||||
0.285687 | + | 0.958323i | \(0.407778\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.668706 | −0.0354912 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.4886 | 1.03144 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.22396 | −0.328488 | −0.164244 | − | 0.986420i | \(-0.552518\pi\) | ||||
−0.164244 | + | 0.986420i | \(0.552518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.80207 | −0.0945841 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.81142 | −0.199499 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.13049 | −0.111211 | −0.0556054 | − | 0.998453i | \(-0.517709\pi\) | ||||
−0.0556054 | + | 0.998453i | \(0.517709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.06756 | 0.0555750 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.65890 | 0.345713 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2252 | 1.35789 | 0.678944 | − | 0.734190i | \(-0.262438\pi\) | ||||
0.678944 | + | 0.734190i | \(0.262438\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0303 | 0.621242 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.63163 | −0.496054 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.02721 | 0.258230 | 0.129115 | − | 0.991630i | \(-0.458786\pi\) | ||||
0.129115 | + | 0.991630i | \(0.458786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.4512 | −1.50883 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.2243 | −0.777923 | −0.388962 | − | 0.921254i | \(-0.627166\pi\) | ||||
−0.388962 | + | 0.921254i | \(0.627166\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.19530 | 0.0609183 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.20446 | 0.112059 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.6173 | −1.40025 | −0.700127 | − | 0.714019i | \(-0.746873\pi\) | ||||
−0.700127 | + | 0.714019i | \(0.746873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.5933 | −2.20461 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.13085 | 0.460591 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.04790 | −0.304303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.3216 | 1.37123 | 0.685616 | − | 0.727964i | \(-0.259533\pi\) | ||||
0.685616 | + | 0.727964i | \(0.259533\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.06750 | 0.153567 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.892819 | −0.0445852 | −0.0222926 | − | 0.999751i | \(-0.507097\pi\) | ||||
−0.0222926 | + | 0.999751i | \(0.507097\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.96054 | 0.396543 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.79817 | −0.337804 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7097 | 0.580430 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6146 | 1.06877 | 0.534387 | − | 0.845240i | \(-0.320543\pi\) | ||||
0.534387 | + | 0.845240i | \(0.320543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.2390 | 0.850335 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.722629 | −0.0355583 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.05698 | 0.150061 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.5153 | −0.759787 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.3531 | 0.896606 | 0.448303 | − | 0.893882i | \(-0.352029\pi\) | ||||
0.448303 | + | 0.893882i | \(0.352029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3409 | 1.23504 | 0.617521 | − | 0.786555i | \(-0.288137\pi\) | ||||
0.617521 | + | 0.786555i | \(0.288137\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.90620 | −0.0926826 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.6335 | 1.38893 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3819 | 0.502413 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.3364 | 0.547329 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.76336 | 0.229443 | 0.114722 | − | 0.993398i | \(-0.463402\pi\) | ||||
0.114722 | + | 0.993398i | \(0.463402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.9887 | 1.58534 | 0.792668 | − | 0.609653i | \(-0.208691\pi\) | ||||
0.792668 | + | 0.609653i | \(0.208691\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.93746 | −0.0928939 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.86158 | −0.328234 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00329 | −0.191066 | −0.0955332 | − | 0.995426i | \(-0.530456\pi\) | ||||
−0.0955332 | + | 0.995426i | \(0.530456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.01519 | −0.0483422 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.44334 | −0.448666 | −0.224333 | − | 0.974512i | \(-0.572020\pi\) | ||||
−0.224333 | + | 0.974512i | \(0.572020\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.26202 | 0.344253 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.0756 | −1.32793 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.3635 | 0.725047 | 0.362523 | − | 0.931975i | \(-0.381915\pi\) | ||||
0.362523 | + | 0.931975i | \(0.381915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.31414 | 0.203145 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.6029 | −1.53182 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.51940 | −0.352515 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.32292 | 0.108662 | 0.0543308 | − | 0.998523i | \(-0.482697\pi\) | ||||
0.0543308 | + | 0.998523i | \(0.482697\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −31.5139 | −1.47094 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.8685 | 0.692495 | 0.346247 | − | 0.938143i | \(-0.387456\pi\) | ||||
0.346247 | + | 0.938143i | \(0.387456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.89544 | −0.413406 | −0.206703 | − | 0.978404i | \(-0.566273\pi\) | ||||
−0.206703 | + | 0.978404i | \(0.566273\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.60131 | 0.0742589 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.3976 | 0.943889 | 0.471944 | − | 0.881628i | \(-0.343552\pi\) | ||||
0.471944 | + | 0.881628i | \(0.343552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.9548 | −0.552020 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.8870 | 1.69966 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.90848 | 0.409612 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.50690 | 0.206791 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.968027 | 0.0443229 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.9259 | −0.681983 | −0.340992 | − | 0.940066i | \(-0.610763\pi\) | ||||
−0.340992 | + | 0.940066i | \(0.610763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −73.6635 | −3.35877 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.0479 | −0.957712 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.38118 | −0.108124 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.3362 | −1.55592 | −0.777961 | − | 0.628312i | \(-0.783746\pi\) | ||||
−0.777961 | + | 0.628312i | \(0.783746\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.945021 | 0.0427353 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.7975 | 1.34474 | 0.672371 | − | 0.740214i | \(-0.265276\pi\) | ||||
0.672371 | + | 0.740214i | \(0.265276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.72726 | −0.438094 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.173766 | 0.00781018 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.62100 | −0.0727116 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.65166 | −0.297769 | −0.148885 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148885 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.4601 | −2.03101 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.7511 | −1.14819 | −0.574093 | − | 0.818790i | \(-0.694645\pi\) | ||||
−0.574093 | + | 0.818790i | \(0.694645\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.83068 | −0.125964 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −47.8883 | −2.12679 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.4332 | 0.684063 | 0.342031 | − | 0.939689i | \(-0.388885\pi\) | ||||
0.342031 | + | 0.939689i | \(0.388885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.23919 | −0.408718 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.96028 | −0.219002 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.67817 | 0.162080 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.70319 | −0.338786 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.5736 | −0.859187 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.7970 | −0.954946 | −0.477473 | − | 0.878646i | \(-0.658447\pi\) | ||||
−0.477473 | + | 0.878646i | \(0.658447\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.9749 | 1.39817 | 0.699083 | − | 0.715040i | \(-0.253592\pi\) | ||||
0.699083 | + | 0.715040i | \(0.253592\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.8249 | 0.603369 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.03958 | 0.350209 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.0813 | 1.04701 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.105051 | −0.00455883 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.1394 | −1.17554 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0083 | 0.432695 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.9189 | 0.859562 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.10249 | −0.176707 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.91147 | −0.125174 | −0.0625870 | − | 0.998040i | \(-0.519935\pi\) | ||||
−0.0625870 | + | 0.998040i | \(0.519935\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.2754 | −0.569702 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.3913 | 0.530786 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.1190 | −0.475416 | −0.237708 | − | 0.971337i | \(-0.576396\pi\) | ||||
−0.237708 | + | 0.971337i | \(0.576396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.50925 | 0.0644131 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.53107 | −0.0652257 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.6606 | −0.623432 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.8178 | −0.628982 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.06544 | −0.214630 | −0.107315 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107315 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −56.0414 | −2.37030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.4490 | 0.483377 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.3188 | −1.06706 | −0.533531 | − | 0.845781i | \(-0.679135\pi\) | ||||
−0.533531 | + | 0.845781i | \(0.679135\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.03179 | 0.253759 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.4793 | −0.692066 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.5225 | −1.02804 | −0.514019 | − | 0.857779i | \(-0.671844\pi\) | ||||
−0.514019 | + | 0.857779i | \(0.671844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.0237 | 1.88418 | 0.942092 | − | 0.335355i | \(-0.108856\pi\) | ||||
0.942092 | + | 0.335355i | \(0.108856\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −41.2673 | −1.72396 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.9245 | −1.28964 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −47.0179 | −1.95738 | −0.978691 | − | 0.205338i | \(-0.934171\pi\) | ||||
−0.978691 | + | 0.205338i | \(0.934171\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.2300 | 1.17320 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.41036 | 0.307433 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.91192 | 0.162015 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.09312 | −0.0451950 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.71061 | −0.276976 | −0.138488 | − | 0.990364i | \(-0.544224\pi\) | ||||
−0.138488 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.26543 | 0.0521410 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.9859 | 0.575305 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.1321 | 0.990988 | 0.495494 | − | 0.868611i | \(-0.334987\pi\) | ||||
0.495494 | + | 0.868611i | \(0.334987\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.59406 | −0.311326 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.91441 | 0.242061 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5383 | 1.20690 | 0.603450 | − | 0.797400i | \(-0.293792\pi\) | ||||
0.603450 | + | 0.797400i | \(0.293792\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.6296 | 0.759917 | 0.379959 | − | 0.925003i | \(-0.375938\pi\) | ||||
0.379959 | + | 0.925003i | \(0.375938\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.73791 | −0.0707730 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.702208 | 0.0285488 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.1050 | −0.491327 | −0.245664 | − | 0.969355i | \(-0.579006\pi\) | ||||
−0.245664 | + | 0.969355i | \(0.579006\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.69655 | −0.190314 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.4592 | 1.96045 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.76374 | −0.192406 | −0.0962029 | − | 0.995362i | \(-0.530670\pi\) | ||||
−0.0962029 | + | 0.995362i | \(0.530670\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.45924 | −0.220138 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.44418 | 0.0983991 | 0.0491995 | − | 0.998789i | \(-0.484333\pi\) | ||||
0.0491995 | + | 0.998789i | \(0.484333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.2057 | −0.450396 | −0.225198 | − | 0.974313i | \(-0.572303\pi\) | ||||
−0.225198 | + | 0.974313i | \(0.572303\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.0353 | 1.36579 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.6037 | 0.705278 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8467 | 0.713868 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.80207 | 0.0719677 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −74.3949 | −2.96632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.2410 | −1.12426 | −0.562129 | − | 0.827050i | \(-0.690017\pi\) | ||||
−0.562129 | + | 0.827050i | \(0.690017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.9248 | −1.78560 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.4762 | 0.455418 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.8079 | 1.02255 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.235650 | −0.00932216 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.6122 | 1.32760 | 0.663801 | − | 0.747909i | \(-0.268942\pi\) | ||||
0.663801 | + | 0.747909i | \(0.268942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.5888 | −0.457017 | −0.228508 | − | 0.973542i | \(-0.573385\pi\) | ||||
−0.228508 | + | 0.973542i | \(0.573385\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.2730 | −0.443875 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.7435 | 1.64110 | 0.820552 | − | 0.571571i | \(-0.193666\pi\) | ||||
0.820552 | + | 0.571571i | \(0.193666\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.424525 | −0.0166641 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.88170 | 0.152136 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.5719 | −0.883307 | −0.441653 | − | 0.897186i | \(-0.645608\pi\) | ||||
−0.441653 | + | 0.897186i | \(0.645608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.55800 | −0.139022 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.34313 | −0.0524007 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.48433 | 0.0578211 | 0.0289106 | − | 0.999582i | \(-0.490796\pi\) | ||||
0.0289106 | + | 0.999582i | \(0.490796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8119 | 0.692801 | 0.346400 | − | 0.938087i | \(-0.387404\pi\) | ||||
0.346400 | + | 0.938087i | \(0.387404\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −72.0232 | −2.79715 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.19530 | −0.0463519 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.5056 | 0.406777 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.3204 | 1.21092 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.09905 | 0.235451 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.9373 | 0.922717 | 0.461358 | − | 0.887214i | \(-0.347362\pi\) | ||||
0.461358 | + | 0.887214i | \(0.347362\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.3555 | −0.860463 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.77350 | −0.221894 | −0.110947 | − | 0.993826i | \(-0.535388\pi\) | ||||
−0.110947 | + | 0.993826i | \(0.535388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.77218 | −0.221516 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0168462 | 0.000645549 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.3560 | −0.511053 | −0.255527 | − | 0.966802i | \(-0.582249\pi\) | ||||
−0.255527 | + | 0.966802i | \(0.582249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.71746 | −0.256661 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.97493 | −0.380567 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.6090 | −0.937530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.6190 | 1.58326 | 0.791631 | − | 0.611000i | \(-0.209232\pi\) | ||||
0.791631 | + | 0.611000i | \(0.209232\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.421222 | 0.0160009 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.04580 | 0.229330 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.4088 | −1.03818 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.7807 | 0.785998 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.25801 | −0.311901 | −0.155950 | − | 0.987765i | \(-0.549844\pi\) | ||||
−0.155950 | + | 0.987765i | \(0.549844\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.7097 | −0.441641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.74783 | 0.367125 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.86180 | −0.258065 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.9299 | −0.898707 | −0.449353 | − | 0.893354i | \(-0.648346\pi\) | ||||
−0.449353 | + | 0.893354i | \(0.648346\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.13126 | −0.0799286 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.68283 | −0.325175 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.41744 | −0.165203 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.3639 | −0.984577 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.0442 | −1.67986 | −0.839932 | − | 0.542691i | \(-0.817405\pi\) | ||||
−0.839932 | + | 0.542691i | \(0.817405\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.91618 | 0.332056 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.8565 | −1.33352 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.90038 | −0.256274 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.6080 | 1.76568 | 0.882841 | − | 0.469673i | \(-0.155628\pi\) | ||||
0.882841 | + | 0.469673i | \(0.155628\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.4206 | 0.904468 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −56.5978 | −2.09334 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.1137 | −1.22308 | −0.611541 | − | 0.791213i | \(-0.709450\pi\) | ||||
−0.611541 | + | 0.791213i | \(0.709450\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.19140 | 0.191488 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.02309 | −0.258699 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.5198 | −1.08590 | −0.542951 | − | 0.839764i | \(-0.682693\pi\) | ||||
−0.542951 | + | 0.839764i | \(0.682693\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.3364 | −0.416455 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.03244 | −0.257995 | −0.128998 | − | 0.991645i | \(-0.541176\pi\) | ||||
−0.128998 | + | 0.991645i | \(0.541176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.9401 | 0.400816 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.07727 | 0.0394152 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.2608 | 0.886472 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.0934 | −1.57250 | −0.786250 | − | 0.617909i | \(-0.787980\pi\) | ||||
−0.786250 | + | 0.617909i | \(0.787980\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.0400 | −1.82356 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.7043 | 0.462356 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.3724 | 1.68544 | 0.842718 | − | 0.538356i | \(-0.180954\pi\) | ||||
0.842718 | + | 0.538356i | \(0.180954\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.3650 | −0.448823 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.21015 | 0.188868 | 0.0944339 | − | 0.995531i | \(-0.469896\pi\) | ||||
0.0944339 | + | 0.995531i | \(0.469896\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.0375 | 1.08743 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.10398 | −0.0399143 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.67060 | 0.0964296 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.8860 | 0.861351 | 0.430676 | − | 0.902507i | \(-0.358275\pi\) | ||||
0.430676 | + | 0.902507i | \(0.358275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.1402 | 1.98583 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.6694 | −1.78648 | −0.893242 | − | 0.449575i | \(-0.851575\pi\) | ||||
−0.893242 | + | 0.449575i | \(0.851575\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.70316 | 0.204864 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.9196 | −1.28861 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.31414 | −0.154570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.952290 | −0.0340756 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.59452 | 0.271406 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.3736 | −0.513017 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.7446 | 1.27416 | 0.637079 | − | 0.770799i | \(-0.280143\pi\) | ||||
0.637079 | + | 0.770799i | \(0.280143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.4969 | −0.872112 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.6215 | 0.519882 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.3678 | −1.36248 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.95025 | −0.175567 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.3068 | −1.28605 | −0.643027 | − | 0.765844i | \(-0.722322\pi\) | ||||
−0.643027 | + | 0.765844i | \(0.722322\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.9403 | 1.73138 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.55911 | 0.0904218 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.42777 | −0.191542 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.20167 | 0.289071 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.68598 | 0.340963 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9696 | 0.385672 | 0.192836 | − | 0.981231i | \(-0.438232\pi\) | ||||
0.192836 | + | 0.981231i | \(0.438232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.26695 | 0.149833 | 0.0749164 | − | 0.997190i | \(-0.476131\pi\) | ||||
0.0749164 | + | 0.997190i | \(0.476131\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.3838 | 0.609677 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.368244 | −0.0128990 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.90848 | −0.311668 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.64982 | −0.0925921 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.9986 | −1.84966 | −0.924832 | − | 0.380377i | \(-0.875794\pi\) | ||||
−0.924832 | + | 0.380377i | \(0.875794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.1222 | −1.46829 | −0.734143 | − | 0.678995i | \(-0.762416\pi\) | ||||
−0.734143 | + | 0.678995i | \(0.762416\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.12176 | 0.282763 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.5326 | 0.435802 | 0.217901 | − | 0.975971i | \(-0.430079\pi\) | ||||
0.217901 | + | 0.975971i | \(0.430079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.9201 | −1.80326 | −0.901629 | − | 0.432510i | \(-0.857628\pi\) | ||||
−0.901629 | + | 0.432510i | \(0.857628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.79162 | −0.0621507 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.0641 | 0.903068 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.7143 | 0.613030 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.27687 | −0.216960 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.491736 | −0.0169766 | −0.00848831 | − | 0.999964i | \(-0.502702\pi\) | ||||
−0.00848831 | + | 0.999964i | \(0.502702\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6558 | −0.919167 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.9202 | 1.92599 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.6605 | 0.641940 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.70221 | 0.0584886 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.2267 | −0.625537 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 80.3473 | 2.75427 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.0105 | 0.959062 | 0.479531 | − | 0.877525i | \(-0.340807\pi\) | ||||
0.479531 | + | 0.877525i | \(0.340807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.173766 | −0.00594266 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.6711 | −0.569475 | −0.284738 | − | 0.958605i | \(-0.591906\pi\) | ||||
−0.284738 | + | 0.958605i | \(0.591906\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.3968 | 0.422974 | 0.211487 | − | 0.977381i | \(-0.432169\pi\) | ||||
0.211487 | + | 0.977381i | \(0.432169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.2336 | −0.451001 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.524206 | −0.0178442 | −0.00892209 | − | 0.999960i | \(-0.502840\pi\) | ||||
−0.00892209 | + | 0.999960i | \(0.502840\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.62721 | 0.259333 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −42.1031 | −1.42990 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.61270 | −0.292166 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.1808 | 1.49701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.839122 | −0.0284000 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.3636 | −0.384161 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.8573 | −1.14328 | −0.571640 | − | 0.820504i | \(-0.693693\pi\) | ||||
−0.571640 | + | 0.820504i | \(0.693693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.7368 | −0.497061 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8780 | 0.669705 | 0.334853 | − | 0.942270i | \(-0.391313\pi\) | ||||
0.334853 | + | 0.942270i | \(0.391313\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.9159 | 0.737529 | 0.368765 | − | 0.929523i | \(-0.379781\pi\) | ||||
0.368765 | + | 0.929523i | \(0.379781\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.537205 | 0.0180580 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.3105 | 1.01773 | 0.508863 | − | 0.860847i | \(-0.330066\pi\) | ||||
0.508863 | + | 0.860847i | \(0.330066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.8192 | 0.933025 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.68113 | −0.324330 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.70319 | 0.257777 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.76173 | −0.259446 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 77.7859 | 2.59720 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.93746 | −0.0646178 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.8534 | −0.827986 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.3267 | −0.909377 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.17299 | 0.171956 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.921098 | 0.0305845 | 0.0152923 | − | 0.999883i | \(-0.495132\pi\) | ||||
0.0152923 | + | 0.999883i | \(0.495132\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.997524 | −0.0330858 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.2900 | 1.20234 | 0.601171 | − | 0.799121i | \(-0.294701\pi\) | ||||
0.601171 | + | 0.799121i | \(0.294701\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.35338 | 0.144076 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.71791 | −0.255146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.62487 | −0.284818 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8109 | −0.356618 | −0.178309 | − | 0.983975i | \(-0.557063\pi\) | ||||
−0.178309 | + | 0.983975i | \(0.557063\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.67246 | 0.252816 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.99066 | 0.197185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.7747 | −1.73522 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.29618 | 0.0425720 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.2971 | −0.370647 | −0.185324 | − | 0.982678i | \(-0.559333\pi\) | ||||
−0.185324 | + | 0.982678i | \(0.559333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.10249 | 0.134454 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.28426 | −0.0747834 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.46130 | −0.145900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2407 | −0.334548 | −0.167274 | − | 0.985910i | \(-0.553496\pi\) | ||||
−0.167274 | + | 0.985910i | \(0.553496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.1418 | −0.396232 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.2384 | 1.47473 | 0.737365 | − | 0.675494i | \(-0.236070\pi\) | ||||
0.737365 | + | 0.675494i | \(0.236070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.6018 | 0.963969 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.92904 | 0.192872 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.9969 | −1.36472 | −0.682358 | − | 0.731018i | \(-0.739045\pi\) | ||||
−0.682358 | + | 0.731018i | \(0.739045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.1450 | 1.10839 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51.4497 | 1.66837 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.5331 | −1.89607 | −0.948037 | − | 0.318160i | \(-0.896935\pi\) | ||||
−0.948037 | + | 0.318160i | \(0.896935\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.0805 | 0.520353 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.75909 | −0.0891888 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.2837 | −0.525827 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3987 | −0.948345 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.52688 | 0.113652 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.0003 | −0.354113 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.2213 | 0.811062 | 0.405531 | − | 0.914081i | \(-0.367087\pi\) | ||||
0.405531 | + | 0.914081i | \(0.367087\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.4490 | −0.367795 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.4601 | 0.784961 | 0.392480 | − | 0.919760i | \(-0.371617\pi\) | ||||
0.392480 | + | 0.919760i | \(0.371617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.6555 | 0.469834 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −51.0923 | −1.63626 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.3563 | −0.555276 | −0.277638 | − | 0.960686i | \(-0.589552\pi\) | ||||
−0.277638 | + | 0.960686i | \(0.589552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3417 | 0.330522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.36666 | 0.139417 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.2564 | −0.933135 | −0.466567 | − | 0.884486i | \(-0.654509\pi\) | ||||
−0.466567 | + | 0.884486i | \(0.654509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.44987 | −0.173647 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 23.6295 | 0.752136 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 61.1263 | 1.94370 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0972 | −0.765474 | −0.382737 | − | 0.923857i | \(-0.625018\pi\) | ||||
−0.382737 | + | 0.923857i | \(0.625018\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −51.8746 | −1.64619 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.30465 | −0.0730624 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.12836 | 0.0357357 | 0.0178678 | − | 0.999840i | \(-0.494312\pi\) | ||||
0.0178678 | + | 0.999840i | \(0.494312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 58.0836 | 1.83768 |
(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 | 3344.2.a.z.1.1 | 6 | ||
4.3 | odd | 2 | 1672.2.a.i.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.i.1.6 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.z.1.1 | 6 | 1.1 | even | 1 | trivial |