Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.40418\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | −1.40418 | −0.810703 | −0.405351 | − | 0.914161i | \(-0.632851\pi\) | ||||
−0.405351 | + | 0.914161i | \(0.632851\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.61567 | 1.61698 | 0.808489 | − | 0.588511i | \(-0.200286\pi\) | ||||
0.808489 | + | 0.588511i | \(0.200286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.02828 | −0.342761 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.64929 | −1.70333 | −0.851663 | − | 0.524090i | \(-0.824406\pi\) | ||||
−0.851663 | + | 0.524090i | \(0.824406\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.54345 | 1.81483 | 0.907414 | − | 0.420238i | \(-0.138053\pi\) | ||||
0.907414 | + | 0.420238i | \(0.138053\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.07705 | −1.31089 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.39066 | 0.822356 | 0.411178 | − | 0.911555i | \(-0.365118\pi\) | ||||
0.411178 | + | 0.911555i | \(0.365118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.19738 | 1.19236 | 0.596181 | − | 0.802850i | \(-0.296684\pi\) | ||||
0.596181 | + | 0.802850i | \(0.296684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.81011 | −0.585948 | −0.292974 | − | 0.956120i | \(-0.594645\pi\) | ||||
−0.292974 | + | 0.956120i | \(0.594645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.07310 | 1.61462 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65643 | 1.08858 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.17600 | 0.404072 | 0.202036 | − | 0.979378i | \(-0.435244\pi\) | ||||
0.202036 | + | 0.979378i | \(0.435244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.26055 | 1.12443 | 0.562214 | − | 0.826992i | \(-0.309950\pi\) | ||||
0.562214 | + | 0.826992i | \(0.309950\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.93262 | 1.38089 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.641460 | 0.105455 | 0.0527277 | − | 0.998609i | \(-0.483208\pi\) | ||||
0.0527277 | + | 0.998609i | \(0.483208\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.18818 | −1.47129 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.44365 | −0.677650 | −0.338825 | − | 0.940849i | \(-0.610029\pi\) | ||||
−0.338825 | + | 0.940849i | \(0.610029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.71793 | −0.554237 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.69641 | 0.976772 | 0.488386 | − | 0.872628i | \(-0.337586\pi\) | ||||
0.488386 | + | 0.872628i | \(0.337586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.76109 | −0.666686 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.95277 | 0.680316 | 0.340158 | − | 0.940368i | \(-0.389519\pi\) | ||||
0.340158 | + | 0.940368i | \(0.389519\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.4260 | −2.75424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.29805 | −0.966651 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0289 | −1.43584 | −0.717922 | − | 0.696124i | \(-0.754906\pi\) | ||||
−0.717922 | + | 0.696124i | \(0.754906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0389 | −1.54143 | −0.770713 | − | 0.637182i | \(-0.780100\pi\) | ||||
−0.770713 | + | 0.637182i | \(0.780100\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.6590 | 2.93454 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5842 | 1.29306 | 0.646531 | − | 0.762888i | \(-0.276219\pi\) | ||||
0.646531 | + | 0.762888i | \(0.276219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.94589 | 0.475030 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.70411 | −1.03299 | −0.516494 | − | 0.856291i | \(-0.672763\pi\) | ||||
−0.516494 | + | 0.856291i | \(0.672763\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.422919 | 0.0494990 | 0.0247495 | − | 0.999694i | \(-0.492121\pi\) | ||||
0.0247495 | + | 0.999694i | \(0.492121\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.3361 | −1.30898 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2265 | −1.60061 | −0.800305 | − | 0.599594i | \(-0.795329\pi\) | ||||
−0.800305 | + | 0.599594i | \(0.795329\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.85779 | −0.539754 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.06521 | 0.555979 | 0.277989 | − | 0.960584i | \(-0.410332\pi\) | ||||
0.277989 | + | 0.960584i | \(0.410332\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.2595 | 1.32973 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.05549 | −0.327583 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.56457 | −0.165844 | −0.0829218 | − | 0.996556i | \(-0.526425\pi\) | ||||
−0.0829218 | + | 0.996556i | \(0.526425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.79093 | −0.911577 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.7920 | 1.92802 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4451 | 1.66975 | 0.834873 | − | 0.550442i | \(-0.185541\pi\) | ||||
0.834873 | + | 0.550442i | \(0.185541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.80907 | 0.583833 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1405 | −1.10852 | −0.554260 | − | 0.832343i | \(-0.686999\pi\) | ||||
−0.554260 | + | 0.832343i | \(0.686999\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00165 | −0.492827 | −0.246414 | − | 0.969165i | \(-0.579252\pi\) | ||||
−0.246414 | + | 0.969165i | \(0.579252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.29287 | −0.801702 | −0.400851 | − | 0.916143i | \(-0.631285\pi\) | ||||
−0.400851 | + | 0.916143i | \(0.631285\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0279 | 1.05629 | 0.528143 | − | 0.849156i | \(-0.322889\pi\) | ||||
0.528143 | + | 0.849156i | \(0.322889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.900725 | −0.0854930 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.26658 | −0.777654 | −0.388827 | − | 0.921311i | \(-0.627120\pi\) | ||||
−0.388827 | + | 0.921311i | \(0.627120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.1604 | −0.947465 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.72852 | −0.622052 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.9145 | 1.90132 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.40418 | 0.126611 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1113 | 0.993828 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.12925 | 0.100205 | 0.0501024 | − | 0.998744i | \(-0.484045\pi\) | ||||
0.0501024 | + | 0.998744i | \(0.484045\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.23967 | 0.549373 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.9249 | 1.65348 | 0.826739 | − | 0.562586i | \(-0.190194\pi\) | ||||
0.826739 | + | 0.562586i | \(0.190194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.4518 | 1.76021 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.36226 | 0.714436 | 0.357218 | − | 0.934021i | \(-0.383725\pi\) | ||||
0.357218 | + | 0.934021i | \(0.383725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.1952 | 1.54330 | 0.771648 | − | 0.636050i | \(-0.219433\pi\) | ||||
0.771648 | + | 0.636050i | \(0.219433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.40296 | −0.791872 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −36.9659 | −3.09124 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.86769 | 0.653376 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0464 | −0.986877 | −0.493438 | − | 0.869781i | \(-0.664260\pi\) | ||||
−0.493438 | + | 0.869781i | \(0.664260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.44182 | 0.442849 | 0.221424 | − | 0.975178i | \(-0.428929\pi\) | ||||
0.221424 | + | 0.975178i | \(0.428929\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.48656 | −0.281871 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.6361 | 1.81818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.9240 | 1.66992 | 0.834960 | − | 0.550311i | \(-0.185491\pi\) | ||||
0.834960 | + | 0.550311i | \(0.185491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.95458 | −0.551534 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0858 | 1.33826 | 0.669132 | − | 0.743144i | \(-0.266666\pi\) | ||||
0.669132 | + | 0.743144i | \(0.266666\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 28.6818 | 2.23287 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0854 | 1.01258 | 0.506289 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506289 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.8168 | 2.29360 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.34438 | −0.408695 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.2270 | 1.46180 | 0.730902 | − | 0.682482i | \(-0.239100\pi\) | ||||
0.730902 | + | 0.682482i | \(0.239100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.4866 | 1.16404 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.73014 | −0.652521 | −0.326261 | − | 0.945280i | \(-0.605789\pi\) | ||||
−0.326261 | + | 0.945280i | \(0.605789\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2949 | −0.839544 | −0.419772 | − | 0.907630i | \(-0.637890\pi\) | ||||
−0.419772 | + | 0.907630i | \(0.637890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.9048 | 1.24964 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.31931 | 0.170519 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.1548 | −1.40074 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.9084 | −1.22345 | −0.611724 | − | 0.791071i | \(-0.709524\pi\) | ||||
−0.611724 | + | 0.791071i | \(0.709524\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.98688 | 0.286982 | 0.143491 | − | 0.989652i | \(-0.454167\pi\) | ||||
0.143491 | + | 0.989652i | \(0.454167\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −33.2215 | −2.37904 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0163 | −0.856124 | −0.428062 | − | 0.903749i | \(-0.640803\pi\) | ||||
−0.428062 | + | 0.903749i | \(0.640803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9253 | −0.774475 | −0.387238 | − | 0.921980i | \(-0.626571\pi\) | ||||
−0.387238 | + | 0.921980i | \(0.626571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.8621 | −1.04829 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.61567 | −0.252530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.88958 | 0.200840 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.3615 | −2.03098 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.98904 | −0.549988 | −0.274994 | − | 0.961446i | \(-0.588676\pi\) | ||||
−0.274994 | + | 0.961446i | \(0.588676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.2221 | 0.837446 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0668 | −1.09575 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.593854 | −0.0401290 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.1866 | 1.49243 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.5999 | 1.84823 | 0.924115 | − | 0.382116i | \(-0.124804\pi\) | ||||
0.924115 | + | 0.382116i | \(0.124804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.30143 | −0.553429 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.3315 | −1.61494 | −0.807468 | − | 0.589911i | \(-0.799163\pi\) | ||||
−0.807468 | + | 0.589911i | \(0.799163\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.109735 | 0.00725149 | 0.00362574 | − | 0.999993i | \(-0.498846\pi\) | ||||
0.00362574 | + | 0.999993i | \(0.498846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.22953 | −0.539134 | −0.269567 | − | 0.962982i | \(-0.586881\pi\) | ||||
−0.269567 | + | 0.962982i | \(0.586881\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.2120 | 1.57942 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.9766 | 1.29762 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.13997 | 0.461846 | 0.230923 | − | 0.972972i | \(-0.425825\pi\) | ||||
0.230923 | + | 0.972972i | \(0.425825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.3191 | 0.793543 | 0.396771 | − | 0.917917i | \(-0.370131\pi\) | ||||
0.396771 | + | 0.917917i | \(0.370131\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.1481 | −0.651000 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.0088 | 2.16393 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.11245 | −0.450734 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.03854 | −0.381149 | −0.190575 | − | 0.981673i | \(-0.561035\pi\) | ||||
−0.190575 | + | 0.981673i | \(0.561035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.8751 | 0.998060 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.2146 | −1.07802 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.5716 | 1.78225 | 0.891123 | − | 0.453763i | \(-0.149919\pi\) | ||||
0.891123 | + | 0.453763i | \(0.149919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.23754 | −0.138500 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.7054 | −1.89338 | −0.946690 | − | 0.322147i | \(-0.895595\pi\) | ||||
−0.946690 | + | 0.322147i | \(0.895595\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.9076 | 1.10006 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.19693 | 0.134450 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.1607 | 0.741451 | 0.370726 | − | 0.928742i | \(-0.379109\pi\) | ||||
0.370726 | + | 0.928742i | \(0.379109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.84160 | 0.354852 | 0.177426 | − | 0.984134i | \(-0.443223\pi\) | ||||
0.177426 | + | 0.984134i | \(0.443223\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −45.6073 | −2.75022 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.7835 | −1.36893 | −0.684463 | − | 0.729047i | \(-0.739963\pi\) | ||||
−0.684463 | + | 0.729047i | \(0.739963\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.43761 | −0.385410 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.36022 | −0.140799 | −0.0703995 | − | 0.997519i | \(-0.522427\pi\) | ||||
−0.0703995 | + | 0.997519i | \(0.522427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0967397 | 0.00575058 | 0.00287529 | − | 0.999996i | \(-0.499085\pi\) | ||||
0.00287529 | + | 0.999996i | \(0.499085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −26.3874 | −1.56305 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.50343 | −0.323731 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.0919 | −1.35367 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.8023 | 1.44897 | 0.724484 | − | 0.689292i | \(-0.242078\pi\) | ||||
0.724484 | + | 0.689292i | \(0.242078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.8770 | −2.32173 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −31.9548 | −1.85421 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.3878 | −1.06339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.6432 | 0.898681 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −43.5288 | −2.49245 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.46391 | −0.197696 | −0.0988480 | − | 0.995103i | \(-0.531516\pi\) | ||||
−0.0988480 | + | 0.995103i | \(0.531516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.02321 | 0.399537 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0188 | 1.47539 | 0.737697 | − | 0.675132i | \(-0.235913\pi\) | ||||
0.737697 | + | 0.675132i | \(0.235913\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.95821 | 0.280255 | 0.140127 | − | 0.990133i | \(-0.455249\pi\) | ||||
0.140127 | + | 0.990133i | \(0.455249\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.0035 | 0.955012 | 0.477506 | − | 0.878629i | \(-0.341541\pi\) | ||||
0.477506 | + | 0.878629i | \(0.341541\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2928 | −0.688267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6447 | 0.649942 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.6226 | 0.980545 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 52.8260 | 2.93026 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.4852 | −0.856334 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2694 | 0.619424 | 0.309712 | − | 0.950830i | \(-0.399767\pi\) | ||||
0.309712 | + | 0.950830i | \(0.399767\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.659602 | −0.0361460 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.2689 | 2.09085 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.7342 | 1.61972 | 0.809862 | − | 0.586620i | \(-0.199542\pi\) | ||||
0.809862 | + | 0.586620i | \(0.199542\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.6077 | 0.630446 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.3677 | −1.91527 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.2671 | 0.768113 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.6670 | 0.733683 | 0.366841 | − | 0.930283i | \(-0.380439\pi\) | ||||
0.366841 | + | 0.930283i | \(0.380439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4570 | −1.14857 | −0.574284 | − | 0.818656i | \(-0.694720\pi\) | ||||
−0.574284 | + | 0.818656i | \(0.694720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.0126 | 1.97559 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.1025 | 1.06995 | 0.534974 | − | 0.844868i | \(-0.320321\pi\) | ||||
0.534974 | + | 0.844868i | \(0.320321\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.4712 | −1.67032 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.7108 | −0.723629 | −0.361814 | − | 0.932250i | \(-0.617843\pi\) | ||||
−0.361814 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.01278 | 0.421725 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.3677 | −1.54140 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52914 | 0.0800388 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.1307 | 1.41621 | 0.708105 | − | 0.706107i | \(-0.249550\pi\) | ||||
0.708105 | + | 0.706107i | \(0.249550\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.02828 | 0.0535302 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.5573 | −0.546636 | −0.273318 | − | 0.961924i | \(-0.588121\pi\) | ||||
−0.273318 | + | 0.961924i | \(0.588121\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.6023 | −0.805699 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.2385 | 0.733322 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9019 | 1.27913 | 0.639563 | − | 0.768739i | \(-0.279115\pi\) | ||||
0.639563 | + | 0.768739i | \(0.279115\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.58567 | −0.0812364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.74847 | 0.447026 | 0.223513 | − | 0.974701i | \(-0.428248\pi\) | ||||
0.223513 | + | 0.974701i | \(0.428248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.56932 | 0.232272 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.28198 | −0.267807 | −0.133903 | − | 0.990994i | \(-0.542751\pi\) | ||||
−0.133903 | + | 0.990994i | \(0.542751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.52812 | −0.481858 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.5740 | −1.34048 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −51.4385 | −2.58815 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.19379 | −0.411235 | −0.205617 | − | 0.978632i | \(-0.565920\pi\) | ||||
−0.205617 | + | 0.978632i | \(0.565920\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.7598 | 0.587256 | 0.293628 | − | 0.955920i | \(-0.405137\pi\) | ||||
0.293628 | + | 0.955920i | \(0.405137\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 40.9656 | 2.04064 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.5642 | −0.872771 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.62380 | −0.179625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.1419 | −0.699274 | −0.349637 | − | 0.936885i | \(-0.613695\pi\) | ||||
−0.349637 | + | 0.936885i | \(0.613695\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.7421 | −0.579196 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.3141 | 0.899006 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.5493 | −1.25115 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.94153 | −0.192556 | −0.0962781 | − | 0.995354i | \(-0.530694\pi\) | ||||
−0.0962781 | + | 0.995354i | \(0.530694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.9273 | −1.40983 | −0.704914 | − | 0.709292i | \(-0.749015\pi\) | ||||
−0.704914 | + | 0.709292i | \(0.749015\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.88580 | −0.334799 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27.3731 | 1.32779 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 51.9067 | 2.50608 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.29158 | 0.206718 | 0.103359 | − | 0.994644i | \(-0.467041\pi\) | ||||
0.103359 | + | 0.994644i | \(0.467041\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.69228 | 0.0813259 | 0.0406629 | − | 0.999173i | \(-0.487053\pi\) | ||||
0.0406629 | + | 0.999173i | \(0.487053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.0476 | −0.529694 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.6052 | −0.698661 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.55266 | −0.217287 | −0.108643 | − | 0.994081i | \(-0.534651\pi\) | ||||
−0.108643 | + | 0.994081i | \(0.534651\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.59951 | 0.218529 | 0.109265 | − | 0.994013i | \(-0.465150\pi\) | ||||
0.109265 | + | 0.994013i | \(0.465150\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.65696 | −0.268166 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.9153 | 0.800064 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.72931 | 0.223190 | 0.111595 | − | 0.993754i | \(-0.464404\pi\) | ||||
0.111595 | + | 0.993754i | \(0.464404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.64929 | 0.266015 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.64128 | −0.359019 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5087 | 0.912581 | 0.456290 | − | 0.889831i | \(-0.349178\pi\) | ||||
0.456290 | + | 0.889831i | \(0.349178\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.1790 | 0.895200 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.57849 | 0.0735178 | 0.0367589 | − | 0.999324i | \(-0.488297\pi\) | ||||
0.0367589 | + | 0.999324i | \(0.488297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.94122 | 0.229638 | 0.114819 | − | 0.993386i | \(-0.463371\pi\) | ||||
0.114819 | + | 0.993386i | \(0.463371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.7851 | −1.47400 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.2577 | 1.07624 | 0.538120 | − | 0.842868i | \(-0.319135\pi\) | ||||
0.538120 | + | 0.842868i | \(0.319135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.3811 | −1.35381 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.1035 | 1.15426 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.9590 | 1.92521 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.09285 | −0.233186 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.5270 | 0.709449 | 0.354724 | − | 0.934971i | \(-0.384575\pi\) | ||||
0.354724 | + | 0.934971i | \(0.384575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.19737 | 0.191383 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59.4601 | 2.69995 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9614 | 0.723279 | 0.361640 | − | 0.932318i | \(-0.382217\pi\) | ||||
0.361640 | + | 0.932318i | \(0.382217\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.9915 | −1.08493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.11148 | −0.185548 | −0.0927742 | − | 0.995687i | \(-0.529573\pi\) | ||||
−0.0927742 | + | 0.995687i | \(0.529573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.37806 | 0.332291 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.0037 | 0.944046 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.15438 | −0.320274 | −0.160137 | − | 0.987095i | \(-0.551194\pi\) | ||||
−0.160137 | + | 0.987095i | \(0.551194\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.3742 | −0.820901 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.71388 | 0.210182 | 0.105091 | − | 0.994463i | \(-0.466487\pi\) | ||||
0.105091 | + | 0.994463i | \(0.466487\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.2804 | −1.79245 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −41.8681 | −1.85943 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.2184 | −0.807516 | −0.403758 | − | 0.914866i | \(-0.632296\pi\) | ||||
−0.403758 | + | 0.914866i | \(0.632296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.3986 | 1.29798 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.0843 | −0.796891 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.8300 | −1.66376 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.9982 | −1.18509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.9519 | 0.479811 | 0.239905 | − | 0.970796i | \(-0.422884\pi\) | ||||
0.239905 | + | 0.970796i | \(0.422884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.6211 | 0.857972 | 0.428986 | − | 0.903311i | \(-0.358871\pi\) | ||||
0.428986 | + | 0.903311i | \(0.358871\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.2274 | 0.924679 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.1033 | −0.656665 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3408 | 0.492151 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.54345 | −0.283428 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.9843 | −1.29633 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.2587 | 0.529001 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.4723 | 0.966160 | 0.483080 | − | 0.875576i | \(-0.339518\pi\) | ||||
0.483080 | + | 0.875576i | \(0.339518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.8601 | 0.680621 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.8734 | 1.70799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.78852 | −0.247499 | −0.123750 | − | 0.992313i | \(-0.539492\pi\) | ||||
−0.123750 | + | 0.992313i | \(0.539492\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.3794 | 0.528340 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.3095 | 0.481800 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.25673 | −0.138240 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.22507 | 0.348507 | 0.174254 | − | 0.984701i | \(-0.444249\pi\) | ||||
0.174254 | + | 0.984701i | \(0.444249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.0768 | −1.22982 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.8968 | 1.13558 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.5297 | −0.865223 | −0.432611 | − | 0.901580i | \(-0.642408\pi\) | ||||
−0.432611 | + | 0.901580i | \(0.642408\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.8892 | −1.25745 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.9665 | −1.00473 | −0.502364 | − | 0.864656i | \(-0.667536\pi\) | ||||
−0.502364 | + | 0.864656i | \(0.667536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.4864 | 1.44321 | 0.721605 | − | 0.692306i | \(-0.243405\pi\) | ||||
0.721605 | + | 0.692306i | \(0.243405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.7424 | 0.991853 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.6863 | −0.946083 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.0357 | −1.70834 | −0.854168 | − | 0.519996i | \(-0.825933\pi\) | ||||
−0.854168 | + | 0.519996i | \(0.825933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.59829 | −0.232657 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.9797 | −1.15880 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.3281 | −1.00584 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.21910 | 0.256690 | 0.128345 | − | 0.991730i | \(-0.459034\pi\) | ||||
0.128345 | + | 0.991730i | \(0.459034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.5385 | 1.34072 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.8730 | 0.694062 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.92318 | −0.120041 | −0.0600204 | − | 0.998197i | \(-0.519117\pi\) | ||||
−0.0600204 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.3411 | 0.627869 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.4830 | −0.550901 | −0.275450 | − | 0.961315i | \(-0.588827\pi\) | ||||
−0.275450 | + | 0.961315i | \(0.588827\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.1493 | −1.43377 | −0.716886 | − | 0.697191i | \(-0.754433\pi\) | ||||
−0.716886 | + | 0.697191i | \(0.754433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.8835 | −0.443211 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 75.6201 | 3.07439 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.7046 | 1.28685 | 0.643425 | − | 0.765509i | \(-0.277513\pi\) | ||||
0.643425 | + | 0.765509i | \(0.277513\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 43.8177 | 1.77267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.747674 | 0.0301983 | 0.0150991 | − | 0.999886i | \(-0.495194\pi\) | ||||
0.0150991 | + | 0.999886i | \(0.495194\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.07705 | 0.204727 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.6618 | 0.670780 | 0.335390 | − | 0.942079i | \(-0.391132\pi\) | ||||
0.335390 | + | 0.942079i | \(0.391132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.0691 | −1.08800 | −0.543999 | − | 0.839086i | \(-0.683091\pi\) | ||||
−0.543999 | + | 0.839086i | \(0.683091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.8952 | −0.637851 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.190547 | −0.00762189 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.2288 | 1.64652 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.17497 | 0.0867219 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1258 | −0.920625 | −0.460312 | − | 0.887757i | \(-0.652263\pi\) | ||||
−0.460312 | + | 0.887757i | \(0.652263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.2180 | 0.445877 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.08301 | 0.162029 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.95028 | 0.354068 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.8551 | 0.547244 | 0.273622 | − | 0.961837i | \(-0.411778\pi\) | ||||
0.273622 | + | 0.961837i | \(0.411778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.61525 | −0.260880 | −0.130440 | − | 0.991456i | \(-0.541639\pi\) | ||||
−0.130440 | + | 0.991456i | \(0.541639\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.5606 | 0.888324 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.04073 | 0.198172 | 0.0990858 | − | 0.995079i | \(-0.468408\pi\) | ||||
0.0990858 | + | 0.995079i | \(0.468408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 62.3056 | 2.44571 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9694 | 0.624931 | 0.312465 | − | 0.949929i | \(-0.398845\pi\) | ||||
0.312465 | + | 0.949929i | \(0.398845\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 68.4263 | 2.67364 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.434881 | −0.0169663 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.81563 | 0.187590 | 0.0937952 | − | 0.995592i | \(-0.470100\pi\) | ||||
0.0937952 | + | 0.995592i | \(0.470100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6400 | −0.880593 | −0.440296 | − | 0.897853i | \(-0.645127\pi\) | ||||
−0.440296 | + | 0.897853i | \(0.645127\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.1540 | −1.20992 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.11478 | −0.236765 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.7553 | −1.49836 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.0114 | 2.62555 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0840 | −0.581446 | −0.290723 | − | 0.956807i | \(-0.593896\pi\) | ||||
−0.290723 | + | 0.956807i | \(0.593896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 45.6649 | 1.75764 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.4473 | 1.13175 | 0.565876 | − | 0.824490i | \(-0.308538\pi\) | ||||
0.565876 | + | 0.824490i | \(0.308538\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.1657 | 1.30923 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.575409 | 0.0220174 | 0.0110087 | − | 0.999939i | \(-0.496496\pi\) | ||||
0.0110087 | + | 0.999939i | \(0.496496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.2352 | 1.15523 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.154087 | −0.00587880 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.4082 | 1.23466 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5440 | −1.42824 | −0.714120 | − | 0.700023i | \(-0.753173\pi\) | ||||
−0.714120 | + | 0.700023i | \(0.753173\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 65.7879 | 2.49548 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.39066 | −0.128430 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5557 | 0.437078 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1046 | −1.17480 | −0.587402 | − | 0.809295i | \(-0.699849\pi\) | ||||
−0.587402 | + | 0.809295i | \(0.699849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.33391 | 0.125741 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.9980 | −1.28044 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.85434 | −0.219864 | −0.109932 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109932 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6289 | 0.548626 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.5928 | −0.658856 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −133.657 | −4.99847 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.0258 | −0.374420 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.7937 | 1.03653 | 0.518264 | − | 0.855220i | \(-0.326578\pi\) | ||||
0.518264 | + | 0.855220i | \(0.326578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.2982 | −0.643328 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.5670 | 0.652423 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5974 | 0.578474 | 0.289237 | − | 0.957257i | \(-0.406598\pi\) | ||||
0.289237 | + | 0.957257i | \(0.406598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.8231 | 1.06752 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.0669 | −0.557269 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.6572 | −1.46477 | −0.732386 | − | 0.680889i | \(-0.761594\pi\) | ||||
−0.732386 | + | 0.680889i | \(0.761594\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −59.7930 | −2.20250 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.9478 | −0.476292 | −0.238146 | − | 0.971229i | \(-0.576540\pi\) | ||||
−0.238146 | + | 0.971229i | \(0.576540\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −47.7545 | −1.75430 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.12957 | −0.188186 | −0.0940929 | − | 0.995563i | \(-0.529995\pi\) | ||||
−0.0940929 | + | 0.995563i | \(0.529995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.5557 | −1.59576 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.20846 | −0.190568 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0378 | 0.694697 | 0.347349 | − | 0.937736i | \(-0.387082\pi\) | ||||
0.347349 | + | 0.937736i | \(0.387082\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.47919 | 0.308999 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.6758 | 0.716077 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.8052 | 1.19233 | 0.596163 | − | 0.802864i | \(-0.296691\pi\) | ||||
0.596163 | + | 0.802864i | \(0.296691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.2915 | −0.809130 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.2671 | 1.49593 | 0.747966 | − | 0.663737i | \(-0.231031\pi\) | ||||
0.747966 | + | 0.663737i | \(0.231031\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.6062 | −0.455780 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −72.1672 | −2.60581 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.2060 | 1.30562 | 0.652811 | − | 0.757520i | \(-0.273589\pi\) | ||||
0.652811 | + | 0.757520i | \(0.273589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.1196 | −1.44487 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.6296 | −0.849898 | −0.424949 | − | 0.905217i | \(-0.639708\pi\) | ||||
−0.424949 | + | 0.905217i | \(0.639708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50.5420 | 1.81552 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.19738 | −0.186216 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.1721 | 1.75951 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.3084 | 0.439865 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 75.6545 | 2.70022 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.23570 | 0.329217 | 0.164609 | − | 0.986359i | \(-0.447364\pi\) | ||||
0.164609 | + | 0.986359i | \(0.447364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 43.1159 | 1.53497 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −78.7761 | −2.79742 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.1455 | −0.891819 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.1963 | 1.45925 | 0.729624 | − | 0.683848i | \(-0.239695\pi\) | ||||
0.729624 | + | 0.683848i | \(0.239695\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.7052 | 0.803254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.60881 | 0.0568447 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.38920 | −0.0843129 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.0758 | −0.601097 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.01458 | 0.141145 | 0.0705725 | − | 0.997507i | \(-0.477517\pi\) | ||||
0.0705725 | + | 0.997507i | \(0.477517\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.1749 | 0.919124 | 0.459562 | − | 0.888146i | \(-0.348006\pi\) | ||||
0.459562 | + | 0.888146i | \(0.348006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.20264 | −0.287679 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 61.7767 | 2.16394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.0953 | −0.808003 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.0484 | −1.39770 | −0.698849 | − | 0.715269i | \(-0.746304\pi\) | ||||
−0.698849 | + | 0.715269i | \(0.746304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.6884 | 0.616577 | 0.308289 | − | 0.951293i | \(-0.400244\pi\) | ||||
0.308289 | + | 0.951293i | \(0.400244\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 64.0408 | 2.22961 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.9098 | 0.970520 | 0.485260 | − | 0.874370i | \(-0.338725\pi\) | ||||
0.485260 | + | 0.874370i | \(0.338725\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 55.4075 | 1.92438 | 0.962191 | − | 0.272377i | \(-0.0878098\pi\) | ||||
0.962191 | + | 0.272377i | \(0.0878098\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.9921 | 1.10979 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 47.3126 | 1.63732 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.4123 | 1.22403 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.1671 | −1.59386 | −0.796932 | − | 0.604069i | \(-0.793545\pi\) | ||||
−0.796932 | + | 0.604069i | \(0.793545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2650 | −0.836726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.31417 | 0.114146 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 107.808 | 3.70870 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.135840 | −0.00466201 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.80257 | −0.0617914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.7110 | −1.59935 | −0.799677 | − | 0.600430i | \(-0.794996\pi\) | ||||
−0.799677 | + | 0.600430i | \(0.794996\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.3235 | −0.660851 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.0091 | 0.956773 | 0.478387 | − | 0.878149i | \(-0.341222\pi\) | ||||
0.478387 | + | 0.878149i | \(0.341222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.73604 | 0.332189 | 0.166095 | − | 0.986110i | \(-0.446884\pi\) | ||||
0.166095 | + | 0.986110i | \(0.446884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.8036 | 0.367759 | 0.183880 | − | 0.982949i | \(-0.441134\pi\) | ||||
0.183880 | + | 0.982949i | \(0.441134\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 69.5187 | 2.36371 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.72780 | 0.262450 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 80.3698 | 2.72636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 69.2570 | 2.34668 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.9102 | −0.572324 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.1267 | 0.477026 | 0.238513 | − | 0.971139i | \(-0.423340\pi\) | ||||
0.238513 | + | 0.971139i | \(0.423340\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −34.8269 | −1.17468 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.6737 | −1.26926 | −0.634630 | − | 0.772816i | \(-0.718847\pi\) | ||||
−0.634630 | + | 0.772816i | \(0.718847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1033 | 0.676531 | 0.338266 | − | 0.941051i | \(-0.390160\pi\) | ||||
0.338266 | + | 0.941051i | \(0.390160\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 55.9944 | 1.88223 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.1332 | −1.48185 | −0.740924 | − | 0.671589i | \(-0.765612\pi\) | ||||
−0.740924 | + | 0.671589i | \(0.765612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.4431 | 0.919377 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.8038 | 1.16466 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.5653 | −1.05511 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.8198 | 0.862097 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.6229 | 0.454350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.7932 | 0.559462 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.8387 | −1.35753 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.85749 | 0.0616770 | 0.0308385 | − | 0.999524i | \(-0.490182\pi\) | ||||
0.0308385 | + | 0.999524i | \(0.490182\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.4556 | 0.379957 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5018 | 0.480466 | 0.240233 | − | 0.970715i | \(-0.422776\pi\) | ||||
0.240233 | + | 0.970715i | \(0.422776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.6148 | −0.947013 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 61.1222 | 2.02064 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.1624 | 0.698082 | 0.349041 | − | 0.937107i | \(-0.386507\pi\) | ||||
0.349041 | + | 0.937107i | \(0.386507\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.86395 | 0.160273 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −56.9549 | −1.87469 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.17857 | 0.170270 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.14311 | 0.168922 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −59.7145 | −1.95917 | −0.979585 | − | 0.201029i | \(-0.935571\pi\) | ||||
−0.979585 | + | 0.201029i | \(0.935571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.5351 | −1.19611 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −69.2576 | −2.26497 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.1335 | −0.396384 | −0.198192 | − | 0.980163i | \(-0.563507\pi\) | ||||
−0.198192 | + | 0.980163i | \(0.563507\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.96221 | −0.227203 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.8135 | 0.417710 | 0.208855 | − | 0.977947i | \(-0.433026\pi\) | ||||
0.208855 | + | 0.977947i | \(0.433026\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.81011 | 0.0915097 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.2252 | −0.559744 | −0.279872 | − | 0.960037i | \(-0.590292\pi\) | ||||
−0.279872 | + | 0.960037i | \(0.590292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.76735 | 0.0898321 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.8760 | −0.774231 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.2346 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −61.1352 | −1.97829 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17.2613 | 0.557980 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.19445 | 0.264337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.52741 | 0.274792 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.4152 | 0.464043 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.5678 | −0.886522 | −0.443261 | − | 0.896393i | \(-0.646179\pi\) | ||||
−0.443261 | + | 0.896393i | \(0.646179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.7452 | −0.794931 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.8096 | −0.346896 | −0.173448 | − | 0.984843i | \(-0.555491\pi\) | ||||
−0.173448 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −74.1771 | −2.37557 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.4703 | −1.35875 | −0.679373 | − | 0.733793i | \(-0.737748\pi\) | ||||
−0.679373 | + | 0.733793i | \(0.737748\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.83869 | 0.282486 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3398 | −0.362053 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 61.6165 | 1.96526 | 0.982630 | − | 0.185576i | \(-0.0594151\pi\) | ||||
0.982630 | + | 0.185576i | \(0.0594151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.4469 | −1.38433 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.4871 | 0.397067 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.2933 | 1.34349 | 0.671745 | − | 0.740782i | \(-0.265545\pi\) | ||||
0.671745 | + | 0.740782i | \(0.265545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.8243 | −0.502169 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.5024 | −1.25231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.3094 | 0.801557 | 0.400778 | − | 0.916175i | \(-0.368740\pi\) | ||||
0.400778 | + | 0.916175i | \(0.368740\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.62837 | 0.114797 |
(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 | 8036.2.a.q.1.6 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.10 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.10 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.10 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.10 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.10 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.6 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.10 | 15 | 7.6 | odd | 2 |