Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −1.83267 | −1.05809 | −0.529046 | − | 0.848593i | \(-0.677450\pi\) | ||||
−0.529046 | + | 0.848593i | \(0.677450\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.130732 | 0.0584653 | 0.0292326 | − | 0.999573i | \(-0.490694\pi\) | ||||
0.0292326 | + | 0.999573i | \(0.490694\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.665399 | −0.251497 | −0.125749 | − | 0.992062i | \(-0.540133\pi\) | ||||
−0.125749 | + | 0.992062i | \(0.540133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.358681 | 0.119560 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.194392 | −0.0586113 | −0.0293056 | − | 0.999570i | \(-0.509330\pi\) | ||||
−0.0293056 | + | 0.999570i | \(0.509330\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.97689 | 0.548291 | 0.274145 | − | 0.961688i | \(-0.411605\pi\) | ||||
0.274145 | + | 0.961688i | \(0.411605\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.239589 | −0.0618617 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.28864 | −1.28268 | −0.641342 | − | 0.767255i | \(-0.721622\pi\) | ||||
−0.641342 | + | 0.767255i | \(0.721622\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.65240 | 1.06733 | 0.533667 | − | 0.845694i | \(-0.320813\pi\) | ||||
0.533667 | + | 0.845694i | \(0.320813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.21946 | 0.266107 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.84381 | −1.01001 | −0.505003 | − | 0.863118i | \(-0.668508\pi\) | ||||
−0.505003 | + | 0.863118i | \(0.668508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98291 | −0.996582 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.84067 | 0.931587 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.97846 | 1.66726 | 0.833629 | − | 0.552324i | \(-0.186259\pi\) | ||||
0.833629 | + | 0.552324i | \(0.186259\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.34791 | 0.780907 | 0.390454 | − | 0.920623i | \(-0.372318\pi\) | ||||
0.390454 | + | 0.920623i | \(0.372318\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.356256 | 0.0620161 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0869891 | −0.0147038 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.81028 | −0.955204 | −0.477602 | − | 0.878576i | \(-0.658494\pi\) | ||||
−0.477602 | + | 0.878576i | \(0.658494\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.62299 | −0.580142 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.98662 | −1.40347 | −0.701737 | − | 0.712436i | \(-0.747592\pi\) | ||||
−0.701737 | + | 0.712436i | \(0.747592\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.81604 | −1.03944 | −0.519719 | − | 0.854338i | \(-0.673963\pi\) | ||||
−0.519719 | + | 0.854338i | \(0.673963\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0468912 | 0.00699012 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.61972 | 0.673856 | 0.336928 | − | 0.941530i | \(-0.390612\pi\) | ||||
0.336928 | + | 0.941530i | \(0.390612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.55724 | −0.936749 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.69233 | 1.35720 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3018 | 1.41507 | 0.707534 | − | 0.706680i | \(-0.249808\pi\) | ||||
0.707534 | + | 0.706680i | \(0.249808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0254132 | −0.00342672 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.52632 | −1.12934 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.4916 | −1.75645 | −0.878227 | − | 0.478244i | \(-0.841274\pi\) | ||||
−0.878227 | + | 0.478244i | \(0.841274\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.7233 | 1.62906 | 0.814529 | − | 0.580123i | \(-0.196995\pi\) | ||||
0.814529 | + | 0.580123i | \(0.196995\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.238666 | −0.0300691 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.258443 | 0.0320560 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.68629 | 0.816860 | 0.408430 | − | 0.912790i | \(-0.366076\pi\) | ||||
0.408430 | + | 0.912790i | \(0.366076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.87712 | 1.06868 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.25871 | −0.624094 | −0.312047 | − | 0.950067i | \(-0.601015\pi\) | ||||
−0.312047 | + | 0.950067i | \(0.601015\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.23447 | −0.846731 | −0.423366 | − | 0.905959i | \(-0.639151\pi\) | ||||
−0.423366 | + | 0.905959i | \(0.639151\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.13203 | 1.05448 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.129348 | 0.0147406 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5243 | 1.18408 | 0.592041 | − | 0.805908i | \(-0.298322\pi\) | ||||
0.592041 | + | 0.805908i | \(0.298322\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.94739 | −1.10527 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00586 | 0.659229 | 0.329614 | − | 0.944116i | \(-0.393081\pi\) | ||||
0.329614 | + | 0.944116i | \(0.393081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.691396 | −0.0749924 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.4546 | −1.76411 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7725 | −1.56588 | −0.782941 | − | 0.622096i | \(-0.786281\pi\) | ||||
−0.782941 | + | 0.622096i | \(0.786281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.31542 | −0.137894 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.96828 | −0.826273 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.608219 | 0.0624020 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.62962 | 0.470067 | 0.235034 | − | 0.971987i | \(-0.424480\pi\) | ||||
0.235034 | + | 0.971987i | \(0.424480\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0697245 | −0.00700758 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.6604 | −1.75728 | −0.878638 | − | 0.477488i | \(-0.841547\pi\) | ||||
−0.878638 | + | 0.477488i | \(0.841547\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4001 | 1.51741 | 0.758707 | − | 0.651432i | \(-0.225832\pi\) | ||||
0.758707 | + | 0.651432i | \(0.225832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.159422 | 0.0155580 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.53767 | 0.342000 | 0.171000 | − | 0.985271i | \(-0.445300\pi\) | ||||
0.171000 | + | 0.985271i | \(0.445300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.15734 | −0.493983 | −0.246992 | − | 0.969018i | \(-0.579442\pi\) | ||||
−0.246992 | + | 0.969018i | \(0.579442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.6483 | 1.01069 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.0840 | 1.04269 | 0.521347 | − | 0.853344i | \(-0.325430\pi\) | ||||
0.521347 | + | 0.853344i | \(0.325430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.633243 | −0.0590502 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.709073 | 0.0655538 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.51905 | 0.322591 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9622 | −0.996565 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.4695 | 1.48501 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.30509 | −0.116731 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.57646 | 0.672302 | 0.336151 | − | 0.941808i | \(-0.390875\pi\) | ||||
0.336151 | + | 0.941808i | \(0.390875\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4916 | 1.09982 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.28503 | 0.461755 | 0.230878 | − | 0.972983i | \(-0.425840\pi\) | ||||
0.230878 | + | 0.972983i | \(0.425840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.09570 | −0.268432 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.632831 | 0.0544655 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1982 | 0.871292 | 0.435646 | − | 0.900118i | \(-0.356520\pi\) | ||||
0.435646 | + | 0.900118i | \(0.356520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.07106 | −0.430121 | −0.215061 | − | 0.976601i | \(-0.568995\pi\) | ||||
−0.215061 | + | 0.976601i | \(0.568995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.46643 | −0.713002 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.384291 | −0.0321360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.17377 | 0.0974767 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0173 | 0.991168 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.6577 | 1.11888 | 0.559439 | − | 0.828871i | \(-0.311017\pi\) | ||||
0.559439 | + | 0.828871i | \(0.311017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.82325 | 0.148374 | 0.0741868 | − | 0.997244i | \(-0.476364\pi\) | ||||
0.0741868 | + | 0.997244i | \(0.476364\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.89693 | −0.153358 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.568412 | 0.0456560 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.315654 | −0.0251919 | −0.0125960 | − | 0.999921i | \(-0.504010\pi\) | ||||
−0.0125960 | + | 0.999921i | \(0.504010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.8799 | −1.49727 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.22307 | 0.254013 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.04146 | 0.473203 | 0.236602 | − | 0.971607i | \(-0.423966\pi\) | ||||
0.236602 | + | 0.971607i | \(0.423966\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0465741 | 0.00362579 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.3814 | 1.65454 | 0.827272 | − | 0.561801i | \(-0.189891\pi\) | ||||
0.827272 | + | 0.561801i | \(0.189891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.09191 | −0.699377 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.66873 | 0.127611 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.52530 | −0.496109 | −0.248055 | − | 0.968746i | \(-0.579791\pi\) | ||||
−0.248055 | + | 0.968746i | \(0.579791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.31562 | 0.250637 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.7256 | 1.85849 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.2022 | −1.21101 | −0.605503 | − | 0.795843i | \(-0.707028\pi\) | ||||
−0.605503 | + | 0.795843i | \(0.707028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0995 | −1.12234 | −0.561168 | − | 0.827702i | \(-0.689648\pi\) | ||||
−0.561168 | + | 0.827702i | \(0.689648\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.3177 | −1.72369 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.759591 | −0.0558463 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.02807 | 0.0751797 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.22097 | −0.234291 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.89495 | 0.715973 | 0.357987 | − | 0.933727i | \(-0.383463\pi\) | ||||
0.357987 | + | 0.933727i | \(0.383463\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4039 | 0.964832 | 0.482416 | − | 0.875942i | \(-0.339759\pi\) | ||||
0.482416 | + | 0.875942i | \(0.339759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.473641 | −0.0339182 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.4144 | −1.88195 | −0.940975 | − | 0.338475i | \(-0.890089\pi\) | ||||
−0.940975 | + | 0.338475i | \(0.890089\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.12246 | 0.221345 | 0.110673 | − | 0.993857i | \(-0.464700\pi\) | ||||
0.110673 | + | 0.993857i | \(0.464700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.2538 | −0.864314 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.97426 | −0.419311 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.17484 | −0.0820545 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.73738 | −0.120757 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.904388 | −0.0625578 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.11026 | −0.214119 | −0.107059 | − | 0.994253i | \(-0.534144\pi\) | ||||
−0.107059 | + | 0.994253i | \(0.534144\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.63748 | 0.660349 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.891077 | −0.0607710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.89309 | −0.196396 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.2584 | 0.895920 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4551 | −0.703283 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.7967 | 1.19175 | 0.595876 | − | 0.803076i | \(-0.296805\pi\) | ||||
0.595876 | + | 0.803076i | \(0.296805\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.78727 | −0.119152 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.6918 | −1.37336 | −0.686681 | − | 0.726959i | \(-0.740933\pi\) | ||||
−0.686681 | + | 0.726959i | \(0.740933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5042 | 0.958461 | 0.479231 | − | 0.877689i | \(-0.340916\pi\) | ||||
0.479231 | + | 0.877689i | \(0.340916\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.237052 | −0.0155969 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.25667 | 0.540912 | 0.270456 | − | 0.962732i | \(-0.412825\pi\) | ||||
0.270456 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.603947 | 0.0393971 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.2877 | −1.25287 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6277 | 0.752134 | 0.376067 | − | 0.926593i | \(-0.377276\pi\) | ||||
0.376067 | + | 0.926593i | \(0.377276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0048 | 0.902126 | 0.451063 | − | 0.892492i | \(-0.351045\pi\) | ||||
0.451063 | + | 0.892492i | \(0.351045\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.70829 | 0.237887 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.857244 | −0.0547673 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.19729 | 0.585210 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.0068 | −0.697525 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.7401 | 1.94030 | 0.970148 | − | 0.242513i | \(-0.0779719\pi\) | ||||
0.970148 | + | 0.242513i | \(0.0779719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.941597 | 0.0591977 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.26710 | 0.0793489 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.64590 | 0.289803 | 0.144901 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144901 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.86615 | 0.240231 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.22040 | 0.199338 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.8492 | 0.730656 | 0.365328 | − | 0.930879i | \(-0.380957\pi\) | ||||
0.365328 | + | 0.930879i | \(0.380957\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.34678 | 0.0827323 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.0731 | 1.65685 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.5162 | 0.885068 | 0.442534 | − | 0.896752i | \(-0.354080\pi\) | ||||
0.442534 | + | 0.896752i | \(0.354080\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.1680 | −0.982134 | −0.491067 | − | 0.871122i | \(-0.663393\pi\) | ||||
−0.491067 | + | 0.871122i | \(0.663393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.41073 | 0.145904 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.968635 | 0.0584109 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.8283 | 0.710696 | 0.355348 | − | 0.934734i | \(-0.384362\pi\) | ||||
0.355348 | + | 0.934734i | \(0.384362\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.55951 | 0.0933655 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.06946 | 0.0637986 | 0.0318993 | − | 0.999491i | \(-0.489844\pi\) | ||||
0.0318993 | + | 0.999491i | \(0.489844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.1828 | 1.43752 | 0.718759 | − | 0.695260i | \(-0.244711\pi\) | ||||
0.718759 | + | 0.695260i | \(0.244711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.11467 | −0.0660271 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.97969 | 0.352970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.9697 | 0.645276 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.48458 | −0.497375 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.1275 | −0.825340 | −0.412670 | − | 0.910881i | \(-0.635404\pi\) | ||||
−0.412670 | + | 0.910881i | \(0.635404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.76379 | −0.102692 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.940985 | −0.0546015 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.57569 | −0.553776 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.53539 | 0.261415 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.3657 | 1.85936 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.66335 | 0.0952433 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.1243 | 1.83343 | 0.916715 | − | 0.399542i | \(-0.130831\pi\) | ||||
0.916715 | + | 0.399542i | \(0.130831\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.2232 | −1.60556 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.674358 | 0.0382393 | 0.0191197 | − | 0.999817i | \(-0.493914\pi\) | ||||
0.0191197 | + | 0.999817i | \(0.493914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0142 | 0.961698 | 0.480849 | − | 0.876804i | \(-0.340329\pi\) | ||||
0.480849 | + | 0.876804i | \(0.340329\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0312013 | −0.00175800 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 35.2042 | 1.97727 | 0.988634 | − | 0.150344i | \(-0.0480382\pi\) | ||||
0.988634 | + | 0.150344i | \(0.0480382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.74534 | −0.0977201 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.48338 | −0.361867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.6049 | −1.36905 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.85066 | −0.546416 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.45170 | 0.522680 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.07396 | −0.169473 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.96675 | 0.547822 | 0.273911 | − | 0.961755i | \(-0.411683\pi\) | ||||
0.273911 | + | 0.961755i | \(0.411683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.08404 | −0.114205 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.874114 | 0.0477579 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9382 | 0.759262 | 0.379631 | − | 0.925138i | \(-0.376051\pi\) | ||||
0.379631 | + | 0.925138i | \(0.376051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.3133 | −1.10327 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.845197 | −0.0457700 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.02097 | 0.487087 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.16053 | 0.0624806 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.93836 | −0.479836 | −0.239918 | − | 0.970793i | \(-0.577121\pi\) | ||||
−0.239918 | + | 0.970793i | \(0.577121\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.4613 | 1.30938 | 0.654691 | − | 0.755897i | \(-0.272799\pi\) | ||||
0.654691 | + | 0.755897i | \(0.272799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.56947 | 0.510780 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.247057 | −0.0131495 | −0.00657476 | − | 0.999978i | \(-0.502093\pi\) | ||||
−0.00657476 | + | 0.999978i | \(0.502093\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.687483 | −0.0364878 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.44927 | −0.341331 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.23078 | 0.328848 | 0.164424 | − | 0.986390i | \(-0.447423\pi\) | ||||
0.164424 | + | 0.986390i | \(0.447423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.64487 | 0.139203 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.0901 | 1.05446 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.945779 | −0.0495043 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.26507 | 0.274834 | 0.137417 | − | 0.990513i | \(-0.456120\pi\) | ||||
0.137417 | + | 0.990513i | \(0.456120\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.22333 | −0.167800 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.85483 | −0.355885 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 33.0385 | 1.71067 | 0.855334 | − | 0.518077i | \(-0.173352\pi\) | ||||
0.855334 | + | 0.518077i | \(0.173352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.39180 | 0.123512 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.7494 | 0.914142 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.5281 | −0.900356 | −0.450178 | − | 0.892939i | \(-0.648640\pi\) | ||||
−0.450178 | + | 0.892939i | \(0.648640\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.8851 | −0.711358 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.76833 | 0.396943 | 0.198472 | − | 0.980107i | \(-0.436402\pi\) | ||||
0.198472 | + | 0.980107i | \(0.436402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0169099 | 0.000861811 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.44479 | −0.124275 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.68404 | −0.389596 | −0.194798 | − | 0.980843i | \(-0.562405\pi\) | ||||
−0.194798 | + | 0.980843i | \(0.562405\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.6172 | 1.29552 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.68572 | −0.488580 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.37587 | 0.0692276 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.1284 | 0.608706 | 0.304353 | − | 0.952559i | \(-0.401560\pi\) | ||||
0.304353 | + | 0.952559i | \(0.401560\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.67341 | 0.284026 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.5974 | −1.87752 | −0.938762 | − | 0.344568i | \(-0.888026\pi\) | ||||
−0.938762 | + | 0.344568i | \(0.888026\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.59534 | 0.428164 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.30045 | −0.0646196 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.12947 | 0.0559857 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.128039 | −0.00633111 | −0.00316556 | − | 0.999995i | \(-0.501008\pi\) | ||||
−0.00316556 | + | 0.999995i | \(0.501008\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.6900 | −0.921908 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.97728 | 0.441743 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.785160 | 0.0385420 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.29357 | 0.455108 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.22168 | −0.450508 | −0.225254 | − | 0.974300i | \(-0.572321\pi\) | ||||
−0.225254 | + | 0.974300i | \(0.572321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7816 | 1.45147 | 0.725734 | − | 0.687975i | \(-0.241500\pi\) | ||||
0.725734 | + | 0.687975i | \(0.241500\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.65701 | 0.0805664 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.3528 | 1.27830 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.46610 | −0.409703 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.704278 | 0.0340029 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5867 | 0.509945 | 0.254972 | − | 0.966948i | \(-0.417934\pi\) | ||||
0.254972 | + | 0.966948i | \(0.417934\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.5282 | −0.842349 | −0.421175 | − | 0.906980i | \(-0.638382\pi\) | ||||
−0.421175 | + | 0.906980i | \(0.638382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.15114 | −0.103139 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.5354 | −1.07801 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.7944 | −1.46974 | −0.734868 | − | 0.678210i | \(-0.762756\pi\) | ||||
−0.734868 | + | 0.678210i | \(0.762756\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.35196 | −0.111998 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.90445 | −0.375552 | −0.187776 | − | 0.982212i | \(-0.560128\pi\) | ||||
−0.187776 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.93124 | −0.0915497 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.0300 | −1.18388 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.36018 | −0.347348 | −0.173674 | − | 0.984803i | \(-0.555564\pi\) | ||||
−0.173674 | + | 0.984803i | \(0.555564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.74692 | 0.0822594 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.34141 | −0.156993 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.171968 | −0.00806198 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1642 | 1.03680 | 0.518399 | − | 0.855139i | \(-0.326528\pi\) | ||||
0.518399 | + | 0.855139i | \(0.326528\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.6005 | −1.19493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.1989 | −0.614733 | −0.307366 | − | 0.951591i | \(-0.599448\pi\) | ||||
−0.307366 | + | 0.951591i | \(0.599448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6745 | 0.774931 | 0.387466 | − | 0.921884i | \(-0.373351\pi\) | ||||
0.387466 | + | 0.921884i | \(0.373351\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.04171 | −0.0483082 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3937 | 0.619787 | 0.309893 | − | 0.950771i | \(-0.399707\pi\) | ||||
0.309893 | + | 0.950771i | \(0.399707\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.44905 | −0.205438 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.578490 | 0.0266554 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.32498 | 0.0609227 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.1825 | −1.06369 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.69507 | 0.169186 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.5971 | 0.986798 | 0.493399 | − | 0.869803i | \(-0.335754\pi\) | ||||
0.493399 | + | 0.869803i | \(0.335754\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4863 | −0.523730 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.90682 | −0.268770 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.605241 | 0.0274826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.59597 | 0.117634 | 0.0588172 | − | 0.998269i | \(-0.481267\pi\) | ||||
0.0588172 | + | 0.998269i | \(0.481267\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.0720 | −0.500693 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.5376 | 1.06224 | 0.531118 | − | 0.847298i | \(-0.321772\pi\) | ||||
0.531118 | + | 0.847298i | \(0.321772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −47.4838 | −2.13856 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.00911525 | −0.000409700 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.49914 | 0.156958 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.7023 | 1.10583 | 0.552914 | − | 0.833238i | \(-0.313516\pi\) | ||||
0.552914 | + | 0.833238i | \(0.313516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.1851 | −1.75066 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.8849 | −0.485333 | −0.242666 | − | 0.970110i | \(-0.578022\pi\) | ||||
−0.242666 | + | 0.970110i | \(0.578022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.30879 | −0.102740 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.6625 | 0.740006 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.58906 | 0.292055 | 0.146028 | − | 0.989281i | \(-0.453351\pi\) | ||||
0.146028 | + | 0.989281i | \(0.453351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.81381 | 0.212950 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.5207 | 0.994315 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.01329 | 0.0887160 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.898035 | −0.0394955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.9587 | 0.524929 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.2629 | 1.10679 | 0.553394 | − | 0.832919i | \(-0.313332\pi\) | ||||
0.553394 | + | 0.832919i | \(0.313332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.95466 | −0.129198 | −0.0645990 | − | 0.997911i | \(-0.520577\pi\) | ||||
−0.0645990 | + | 0.997911i | \(0.520577\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.07644 | −0.265198 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.9945 | −1.00166 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.462541 | 0.0201105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.83917 | −0.210002 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.7656 | −0.769512 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.462488 | 0.0199951 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.6932 | 1.28136 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.27467 | 0.0549040 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.8713 | 1.37026 | 0.685128 | − | 0.728423i | \(-0.259746\pi\) | ||||
0.685128 | + | 0.728423i | \(0.259746\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.6724 | 1.18754 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.674231 | −0.0288809 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.4371 | −1.68621 | −0.843105 | − | 0.537749i | \(-0.819275\pi\) | ||||
−0.843105 | + | 0.537749i | \(0.819275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.56362 | 0.194771 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.7714 | 1.77952 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.00289 | −0.297793 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.39208 | 0.0590905 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.3533 | 1.28611 | 0.643055 | − | 0.765820i | \(-0.277667\pi\) | ||||
0.643055 | + | 0.765820i | \(0.277667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4746 | −0.569914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.88411 | −0.0795471 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.7866 | 1.63466 | 0.817331 | − | 0.576169i | \(-0.195453\pi\) | ||||
0.817331 | + | 0.576169i | \(0.195453\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.44904 | 0.0609614 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.61898 | 0.277971 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.97210 | −0.376130 | −0.188065 | − | 0.982157i | \(-0.560222\pi\) | ||||
−0.188065 | + | 0.982157i | \(0.560222\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.1013 | 1.38525 | 0.692623 | − | 0.721300i | \(-0.256455\pi\) | ||||
0.692623 | + | 0.721300i | \(0.256455\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.1342 | −0.757566 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.1363 | 1.00655 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.6608 | −1.02664 | −0.513321 | − | 0.858196i | \(-0.671585\pi\) | ||||
−0.513321 | + | 0.858196i | \(0.671585\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.5649 | −1.02088 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.99629 | −0.165794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00259 | −0.0829389 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0926987 | 0.00383262 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.60869 | 0.190221 | 0.0951105 | − | 0.995467i | \(-0.469680\pi\) | ||||
0.0951105 | + | 0.995467i | \(0.469680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.2282 | 0.833490 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 48.4090 | 1.99128 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.5563 | 1.29586 | 0.647930 | − | 0.761700i | \(-0.275635\pi\) | ||||
0.647930 | + | 0.761700i | \(0.275635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.460054 | 0.0188604 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.72243 | −0.234204 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.8145 | 1.29990 | 0.649952 | − | 0.759975i | \(-0.274789\pi\) | ||||
0.649952 | + | 0.759975i | \(0.274789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.5964 | −1.90071 | −0.950354 | − | 0.311170i | \(-0.899279\pi\) | ||||
−0.950354 | + | 0.311170i | \(0.899279\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.39824 | 0.0976641 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.43311 | −0.0582644 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.8926 | 1.90331 | 0.951657 | − | 0.307164i | \(-0.0993801\pi\) | ||||
0.951657 | + | 0.307164i | \(0.0993801\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.9488 | 0.443670 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.13268 | 0.369469 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.6339 | −0.833397 | −0.416698 | − | 0.909045i | \(-0.636813\pi\) | ||||
−0.416698 | + | 0.909045i | \(0.636813\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.15310 | 0.0868212 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.0579 | 0.445175 | 0.222587 | − | 0.974913i | \(-0.428550\pi\) | ||||
0.222587 | + | 0.974913i | \(0.428550\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2019 | −0.972758 | −0.486379 | − | 0.873748i | \(-0.661683\pi\) | ||||
−0.486379 | + | 0.873748i | \(0.661683\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.4473 | −0.940908 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.82961 | 0.393815 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7439 | 0.989757 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.65745 | 0.0661920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.7285 | 1.22522 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.83838 | 0.232422 | 0.116211 | − | 0.993225i | \(-0.462925\pi\) | ||||
0.116211 | + | 0.993225i | \(0.462925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.70007 | 0.226558 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.990487 | 0.0393063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.9630 | −0.513611 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.88620 | −0.0746169 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.66620 | 0.302797 | 0.151398 | − | 0.988473i | \(-0.451622\pi\) | ||||
0.151398 | + | 0.988473i | \(0.451622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.55440 | 0.179608 | 0.0898040 | − | 0.995959i | \(-0.471376\pi\) | ||||
0.0898040 | + | 0.995959i | \(0.471376\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.63305 | 0.0643013 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.0768 | 0.710671 | 0.355335 | − | 0.934739i | \(-0.384367\pi\) | ||||
0.355335 | + | 0.934739i | \(0.384367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.62265 | 0.102948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.30209 | 0.207805 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.1503 | −0.592877 | −0.296439 | − | 0.955052i | \(-0.595799\pi\) | ||||
−0.296439 | + | 0.955052i | \(0.595799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.690924 | 0.0269966 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.59487 | −0.101235 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2205 | 0.982452 | 0.491226 | − | 0.871032i | \(-0.336549\pi\) | ||||
0.491226 | + | 0.871032i | \(0.336549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.22722 | 0.320002 | 0.160001 | − | 0.987117i | \(-0.448850\pi\) | ||||
0.160001 | + | 0.987117i | \(0.448850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.1607 | 0.744139 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.404708 | −0.0156939 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.4900 | −1.68394 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.6154 | −1.26098 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.47331 | −0.0954811 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6843 | −0.566037 | −0.283018 | − | 0.959114i | \(-0.591336\pi\) | ||||
−0.283018 | + | 0.959114i | \(0.591336\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.1206 | −0.928403 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.2263 | −1.62289 | −0.811445 | − | 0.584429i | \(-0.801319\pi\) | ||||
−0.811445 | + | 0.584429i | \(0.801319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.08055 | −0.118221 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.9212 | 1.45314 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.8272 | −0.567346 | −0.283673 | − | 0.958921i | \(-0.591553\pi\) | ||||
−0.283673 | + | 0.958921i | \(0.591553\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.33324 | 0.0509403 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.5813 | −1.01414 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.3656 | 0.775868 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.8949 | −1.82201 | −0.911005 | − | 0.412396i | \(-0.864692\pi\) | ||||
−0.911005 | + | 0.412396i | \(0.864692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0463946 | 0.00176239 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.662951 | −0.0251472 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.5270 | 1.80021 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.1318 | −0.572336 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −52.0331 | −1.96526 | −0.982631 | − | 0.185569i | \(-0.940587\pi\) | ||||
−0.982631 | + | 0.185569i | \(0.940587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.0318 | −1.01952 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.10684 | −0.0416858 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.7512 | 0.441950 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.32991 | −0.125057 | −0.0625287 | − | 0.998043i | \(-0.519916\pi\) | ||||
−0.0625287 | + | 0.998043i | \(0.519916\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.77488 | 0.141569 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.0605 | −0.788721 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0502392 | −0.00187884 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.3098 | −0.795827 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.1038 | −1.42103 | −0.710516 | − | 0.703681i | \(-0.751538\pi\) | ||||
−0.710516 | + | 0.703681i | \(0.751538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2472 | −0.381625 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.6661 | −0.954533 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −44.7389 | −1.66156 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.05611 | 0.187521 | 0.0937604 | − | 0.995595i | \(-0.470111\pi\) | ||||
0.0937604 | + | 0.995595i | \(0.470111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0461 | 0.853559 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.0476 | 1.33327 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.80089 | −0.251197 | −0.125598 | − | 0.992081i | \(-0.540085\pi\) | ||||
−0.125598 | + | 0.992081i | \(0.540085\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.57104 | 0.0579489 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.29976 | −0.0478772 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.4617 | −0.899839 | −0.449919 | − | 0.893069i | \(-0.648547\pi\) | ||||
−0.449919 | + | 0.893069i | \(0.648547\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.8556 | −0.619206 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.4989 | 0.825404 | 0.412702 | − | 0.910866i | \(-0.364585\pi\) | ||||
0.412702 | + | 0.910866i | \(0.364585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.78550 | 0.0654155 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.15419 | 0.0788176 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.35396 | −0.0860119 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −56.3364 | −2.05301 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.238357 | 0.00867470 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3800 | 0.595342 | 0.297671 | − | 0.954669i | \(-0.403790\pi\) | ||||
0.297671 | + | 0.954669i | \(0.403790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.72564 | −0.0626366 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.8712 | 1.33658 | 0.668291 | − | 0.743900i | \(-0.267026\pi\) | ||||
0.668291 | + | 0.743900i | \(0.267026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.43169 | 0.124235 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.247990 | −0.00896611 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.6714 | −0.963048 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.5525 | 1.31812 | 0.659058 | − | 0.752092i | \(-0.270955\pi\) | ||||
0.659058 | + | 0.752092i | \(0.270955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.51439 | −0.306638 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.00250 | 0.287830 | 0.143915 | − | 0.989590i | \(-0.454031\pi\) | ||||
0.143915 | + | 0.989590i | \(0.454031\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.6652 | −0.778238 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.08539 | −0.254187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −41.8094 | −1.49798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.02225 | 0.0365789 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.4617 | 1.55320 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0412662 | −0.00147285 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.6884 | −1.52168 | −0.760838 | − | 0.648942i | \(-0.775212\pi\) | ||||
−0.760838 | + | 0.648942i | \(0.775212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.7158 | −0.773102 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.37528 | −0.262235 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.1527 | 0.893197 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.46821 | −0.0875384 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.3425 | −0.791411 | −0.395706 | − | 0.918377i | \(-0.629500\pi\) | ||||
−0.395706 | + | 0.918377i | \(0.629500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.4320 | −0.864344 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.29862 | −0.187217 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.40632 | 0.0496280 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.421359 | 0.0148510 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.6034 | −0.936484 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.36015 | −0.118137 | −0.0590684 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590684 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7242 | 0.727726 | 0.363863 | − | 0.931452i | \(-0.381458\pi\) | ||||
0.363863 | + | 0.931452i | \(0.381458\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.6305 | 1.03919 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.789813 | 0.0276660 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.7110 | −1.10943 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.471816 | −0.0164866 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.3354 | −0.639911 | −0.319956 | − | 0.947433i | \(-0.603668\pi\) | ||||
−0.319956 | + | 0.947433i | \(0.603668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.1478 | −0.806882 | −0.403441 | − | 0.915006i | \(-0.632186\pi\) | ||||
−0.403441 | + | 0.915006i | \(0.632186\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.77519 | −0.0618042 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.5900 | 0.403023 | 0.201511 | − | 0.979486i | \(-0.435415\pi\) | ||||
0.201511 | + | 0.979486i | \(0.435415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.41376 | −0.326953 | −0.163477 | − | 0.986547i | \(-0.552271\pi\) | ||||
−0.163477 | + | 0.986547i | \(0.552271\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.6775 | −0.751983 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.6789 | 1.20155 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.79524 | 0.0967334 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.0468 | 0.727483 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.460102 | 0.0158845 | 0.00794225 | − | 0.999968i | \(-0.497472\pi\) | ||||
0.00794225 | + | 0.999968i | \(0.497472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.6128 | 1.77975 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.95997 | −0.0675048 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.18861 | −0.0408893 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.29424 | 0.250633 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −44.3191 | −1.52103 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.1439 | 0.964761 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.5659 | 1.45743 | 0.728715 | − | 0.684817i | \(-0.240118\pi\) | ||||
0.728715 | + | 0.684817i | \(0.240118\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.218157 | 0.00746080 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.48824 | 0.187475 | 0.0937374 | − | 0.995597i | \(-0.470119\pi\) | ||||
0.0937374 | + | 0.995597i | \(0.470119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.4623 | 0.425207 | 0.212604 | − | 0.977139i | \(-0.431806\pi\) | ||||
0.212604 | + | 0.977139i | \(0.431806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.9588 | −0.373475 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −57.0707 | −1.94271 | −0.971354 | − | 0.237635i | \(-0.923628\pi\) | ||||
−0.971354 | + | 0.237635i | \(0.923628\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.853067 | −0.0290051 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.1038 | −0.682762 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.04584 | −0.0694005 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.2181 | 0.447877 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.66056 | 0.0562014 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.868404 | 0.0293574 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.6751 | 1.10336 | 0.551679 | − | 0.834056i | \(-0.313987\pi\) | ||||
0.551679 | + | 0.834056i | \(0.313987\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.8911 | 0.873286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.0023 | −1.44879 | −0.724393 | − | 0.689388i | \(-0.757880\pi\) | ||||
−0.724393 | + | 0.689388i | \(0.757880\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.0283 | 1.34706 | 0.673530 | − | 0.739160i | \(-0.264777\pi\) | ||||
0.673530 | + | 0.739160i | \(0.264777\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.23244 | 0.108657 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.67563 | −0.123416 | −0.0617079 | − | 0.998094i | \(-0.519655\pi\) | ||||
−0.0617079 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.04136 | −0.169082 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.93369 | 0.0647810 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.4928 | 0.719230 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.11814 | −0.0708017 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.5491 | 0.585947 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.0375 | 1.30197 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.4827 | −1.81508 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.31187 | −0.276602 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.97399 | −0.0656176 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3684 | 0.609913 | 0.304956 | − | 0.952366i | \(-0.401358\pi\) | ||||
0.304956 | + | 0.952366i | \(0.401358\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.33445 | −0.210101 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.8625 | −0.724338 | −0.362169 | − | 0.932112i | \(-0.617964\pi\) | ||||
−0.362169 | + | 0.932112i | \(0.617964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.16749 | −0.0386382 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.04838 | −0.100776 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.51665 | −0.116130 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.2165 | 0.831817 | 0.415908 | − | 0.909406i | \(-0.363464\pi\) | ||||
0.415908 | + | 0.909406i | \(0.363464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.8732 | −1.93994 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.3959 | −0.342185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.9521 | 0.951939 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.52371 | 0.181422 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.1401 | 1.12010 | 0.560051 | − | 0.828458i | \(-0.310782\pi\) | ||||
0.560051 | + | 0.828458i | \(0.310782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.5070 | −0.999825 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.23588 | −0.0404607 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.134401 | 0.00439540 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.8920 | −1.36855 | −0.684276 | − | 0.729223i | \(-0.739882\pi\) | ||||
−0.684276 | + | 0.729223i | \(0.739882\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.1814 | −1.01757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.8495 | 1.07086 | 0.535432 | − | 0.844578i | \(-0.320149\pi\) | ||||
0.535432 | + | 0.844578i | \(0.320149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.5295 | 1.41752 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.421085 | −0.0136979 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.1594 | 1.33750 | 0.668751 | − | 0.743487i | \(-0.266829\pi\) | ||||
0.668751 | + | 0.743487i | \(0.266829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.3018 | −0.464255 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −64.5178 | −2.09213 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.92982 | −0.159693 | −0.0798463 | − | 0.996807i | \(-0.525443\pi\) | ||||
−0.0798463 | + | 0.996807i | \(0.525443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.29359 | 0.0418596 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.19863 | 0.103397 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.78588 | −0.219127 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.0957 | −0.390184 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.26889 | 0.0408896 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.75232 | 0.0564092 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.5330 | −1.11051 | −0.555253 | − | 0.831681i | \(-0.687379\pi\) | ||||
−0.555253 | + | 0.831681i | \(0.687379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45.0926 | 1.44858 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.7410 | 0.697701 | 0.348850 | − | 0.937178i | \(-0.386572\pi\) | ||||
0.348850 | + | 0.937178i | \(0.386572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.37427 | 0.108174 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.0530 | 0.578159 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.8806 | −0.859985 | −0.429993 | − | 0.902832i | \(-0.641484\pi\) | ||||
−0.429993 | + | 0.902832i | \(0.641484\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.87165 | 0.0917783 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.84984 | −0.0590608 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.2716 | 0.327613 | 0.163807 | − | 0.986492i | \(-0.447623\pi\) | ||||
0.163807 | + | 0.986492i | \(0.447623\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.45322 | −0.110029 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.63355 | 0.179318 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.0157 | 1.04984 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0132 | −0.381612 | −0.190806 | − | 0.981628i | \(-0.561110\pi\) | ||||
−0.190806 | + | 0.981628i | \(0.561110\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.2658 | −0.579647 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.408206 | 0.0129410 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.3475 | 0.549400 | 0.274700 | − | 0.961530i | \(-0.411421\pi\) | ||||
0.274700 | + | 0.961530i | \(0.411421\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.1256 | −0.889856 |
(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 | 6008.2.a.d.1.11 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.d.1.11 | ✓ | 49 | 1.1 | even | 1 | trivial |