Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.90388 | −1.09921 | −0.549603 | − | 0.835426i | \(-0.685221\pi\) | ||||
−0.549603 | + | 0.835426i | \(0.685221\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.40322 | −0.627540 | −0.313770 | − | 0.949499i | \(-0.601592\pi\) | ||||
−0.313770 | + | 0.949499i | \(0.601592\pi\) | |||||||
\(6\) | 1.90388 | 0.777255 | ||||||||
\(7\) | −1.81515 | −0.686063 | −0.343032 | − | 0.939324i | \(-0.611454\pi\) | ||||
−0.343032 | + | 0.939324i | \(0.611454\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.624755 | 0.208252 | ||||||||
\(10\) | 1.40322 | 0.443738 | ||||||||
\(11\) | 1.73779 | 0.523962 | 0.261981 | − | 0.965073i | \(-0.415624\pi\) | ||||
0.261981 | + | 0.965073i | \(0.415624\pi\) | |||||||
\(12\) | −1.90388 | −0.549603 | ||||||||
\(13\) | −2.64167 | −0.732668 | −0.366334 | − | 0.930483i | \(-0.619387\pi\) | ||||
−0.366334 | + | 0.930483i | \(0.619387\pi\) | |||||||
\(14\) | 1.81515 | 0.485120 | ||||||||
\(15\) | 2.67156 | 0.689795 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.78392 | 0.432664 | 0.216332 | − | 0.976320i | \(-0.430591\pi\) | ||||
0.216332 | + | 0.976320i | \(0.430591\pi\) | |||||||
\(18\) | −0.624755 | −0.147256 | ||||||||
\(19\) | −2.37686 | −0.545290 | −0.272645 | − | 0.962115i | \(-0.587898\pi\) | ||||
−0.272645 | + | 0.962115i | \(0.587898\pi\) | |||||||
\(20\) | −1.40322 | −0.313770 | ||||||||
\(21\) | 3.45583 | 0.754124 | ||||||||
\(22\) | −1.73779 | −0.370497 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.90388 | 0.388628 | ||||||||
\(25\) | −3.03097 | −0.606194 | ||||||||
\(26\) | 2.64167 | 0.518074 | ||||||||
\(27\) | 4.52218 | 0.870294 | ||||||||
\(28\) | −1.81515 | −0.343032 | ||||||||
\(29\) | 0.0835727 | 0.0155191 | 0.00775953 | − | 0.999970i | \(-0.497530\pi\) | ||||
0.00775953 | + | 0.999970i | \(0.497530\pi\) | |||||||
\(30\) | −2.67156 | −0.487759 | ||||||||
\(31\) | −0.944842 | −0.169699 | −0.0848493 | − | 0.996394i | \(-0.527041\pi\) | ||||
−0.0848493 | + | 0.996394i | \(0.527041\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.30853 | −0.575942 | ||||||||
\(34\) | −1.78392 | −0.305940 | ||||||||
\(35\) | 2.54706 | 0.430532 | ||||||||
\(36\) | 0.624755 | 0.104126 | ||||||||
\(37\) | 11.1027 | 1.82527 | 0.912637 | − | 0.408771i | \(-0.134042\pi\) | ||||
0.912637 | + | 0.408771i | \(0.134042\pi\) | |||||||
\(38\) | 2.37686 | 0.385578 | ||||||||
\(39\) | 5.02942 | 0.805352 | ||||||||
\(40\) | 1.40322 | 0.221869 | ||||||||
\(41\) | −8.01509 | −1.25175 | −0.625874 | − | 0.779925i | \(-0.715257\pi\) | ||||
−0.625874 | + | 0.779925i | \(0.715257\pi\) | |||||||
\(42\) | −3.45583 | −0.533246 | ||||||||
\(43\) | 8.50045 | 1.29631 | 0.648153 | − | 0.761510i | \(-0.275542\pi\) | ||||
0.648153 | + | 0.761510i | \(0.275542\pi\) | |||||||
\(44\) | 1.73779 | 0.261981 | ||||||||
\(45\) | −0.876670 | −0.130686 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −2.06912 | −0.301813 | −0.150906 | − | 0.988548i | \(-0.548219\pi\) | ||||
−0.150906 | + | 0.988548i | \(0.548219\pi\) | |||||||
\(48\) | −1.90388 | −0.274801 | ||||||||
\(49\) | −3.70522 | −0.529317 | ||||||||
\(50\) | 3.03097 | 0.428644 | ||||||||
\(51\) | −3.39637 | −0.475587 | ||||||||
\(52\) | −2.64167 | −0.366334 | ||||||||
\(53\) | −2.56540 | −0.352385 | −0.176193 | − | 0.984356i | \(-0.556378\pi\) | ||||
−0.176193 | + | 0.984356i | \(0.556378\pi\) | |||||||
\(54\) | −4.52218 | −0.615391 | ||||||||
\(55\) | −2.43850 | −0.328807 | ||||||||
\(56\) | 1.81515 | 0.242560 | ||||||||
\(57\) | 4.52526 | 0.599385 | ||||||||
\(58\) | −0.0835727 | −0.0109736 | ||||||||
\(59\) | 0.0652730 | 0.00849782 | 0.00424891 | − | 0.999991i | \(-0.498648\pi\) | ||||
0.00424891 | + | 0.999991i | \(0.498648\pi\) | |||||||
\(60\) | 2.67156 | 0.344897 | ||||||||
\(61\) | 4.73357 | 0.606071 | 0.303035 | − | 0.952979i | \(-0.402000\pi\) | ||||
0.303035 | + | 0.952979i | \(0.402000\pi\) | |||||||
\(62\) | 0.944842 | 0.119995 | ||||||||
\(63\) | −1.13403 | −0.142874 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.70685 | 0.459778 | ||||||||
\(66\) | 3.30853 | 0.407252 | ||||||||
\(67\) | −5.83806 | −0.713232 | −0.356616 | − | 0.934251i | \(-0.616070\pi\) | ||||
−0.356616 | + | 0.934251i | \(0.616070\pi\) | |||||||
\(68\) | 1.78392 | 0.216332 | ||||||||
\(69\) | 1.90388 | 0.229200 | ||||||||
\(70\) | −2.54706 | −0.304432 | ||||||||
\(71\) | 2.32516 | 0.275946 | 0.137973 | − | 0.990436i | \(-0.455941\pi\) | ||||
0.137973 | + | 0.990436i | \(0.455941\pi\) | |||||||
\(72\) | −0.624755 | −0.0736281 | ||||||||
\(73\) | 12.6531 | 1.48094 | 0.740468 | − | 0.672092i | \(-0.234604\pi\) | ||||
0.740468 | + | 0.672092i | \(0.234604\pi\) | |||||||
\(74\) | −11.1027 | −1.29066 | ||||||||
\(75\) | 5.77060 | 0.666331 | ||||||||
\(76\) | −2.37686 | −0.272645 | ||||||||
\(77\) | −3.15435 | −0.359471 | ||||||||
\(78\) | −5.02942 | −0.569470 | ||||||||
\(79\) | 10.2970 | 1.15851 | 0.579253 | − | 0.815148i | \(-0.303345\pi\) | ||||
0.579253 | + | 0.815148i | \(0.303345\pi\) | |||||||
\(80\) | −1.40322 | −0.156885 | ||||||||
\(81\) | −10.4839 | −1.16488 | ||||||||
\(82\) | 8.01509 | 0.885119 | ||||||||
\(83\) | 8.91728 | 0.978799 | 0.489400 | − | 0.872060i | \(-0.337216\pi\) | ||||
0.489400 | + | 0.872060i | \(0.337216\pi\) | |||||||
\(84\) | 3.45583 | 0.377062 | ||||||||
\(85\) | −2.50324 | −0.271514 | ||||||||
\(86\) | −8.50045 | −0.916627 | ||||||||
\(87\) | −0.159112 | −0.0170586 | ||||||||
\(88\) | −1.73779 | −0.185249 | ||||||||
\(89\) | 13.8362 | 1.46663 | 0.733316 | − | 0.679887i | \(-0.237971\pi\) | ||||
0.733316 | + | 0.679887i | \(0.237971\pi\) | |||||||
\(90\) | 0.876670 | 0.0924091 | ||||||||
\(91\) | 4.79504 | 0.502656 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 1.79886 | 0.186534 | ||||||||
\(94\) | 2.06912 | 0.213414 | ||||||||
\(95\) | 3.33526 | 0.342191 | ||||||||
\(96\) | 1.90388 | 0.194314 | ||||||||
\(97\) | −9.35526 | −0.949882 | −0.474941 | − | 0.880018i | \(-0.657531\pi\) | ||||
−0.474941 | + | 0.880018i | \(0.657531\pi\) | |||||||
\(98\) | 3.70522 | 0.374284 | ||||||||
\(99\) | 1.08569 | 0.109116 | ||||||||
\(100\) | −3.03097 | −0.303097 | ||||||||
\(101\) | 3.50973 | 0.349232 | 0.174616 | − | 0.984637i | \(-0.444132\pi\) | ||||
0.174616 | + | 0.984637i | \(0.444132\pi\) | |||||||
\(102\) | 3.39637 | 0.336291 | ||||||||
\(103\) | −2.79158 | −0.275063 | −0.137531 | − | 0.990497i | \(-0.543917\pi\) | ||||
−0.137531 | + | 0.990497i | \(0.543917\pi\) | |||||||
\(104\) | 2.64167 | 0.259037 | ||||||||
\(105\) | −4.84930 | −0.473243 | ||||||||
\(106\) | 2.56540 | 0.249174 | ||||||||
\(107\) | −9.73908 | −0.941512 | −0.470756 | − | 0.882263i | \(-0.656019\pi\) | ||||
−0.470756 | + | 0.882263i | \(0.656019\pi\) | |||||||
\(108\) | 4.52218 | 0.435147 | ||||||||
\(109\) | −10.2798 | −0.984626 | −0.492313 | − | 0.870418i | \(-0.663848\pi\) | ||||
−0.492313 | + | 0.870418i | \(0.663848\pi\) | |||||||
\(110\) | 2.43850 | 0.232502 | ||||||||
\(111\) | −21.1382 | −2.00635 | ||||||||
\(112\) | −1.81515 | −0.171516 | ||||||||
\(113\) | 12.4901 | 1.17497 | 0.587484 | − | 0.809236i | \(-0.300119\pi\) | ||||
0.587484 | + | 0.809236i | \(0.300119\pi\) | |||||||
\(114\) | −4.52526 | −0.423829 | ||||||||
\(115\) | 1.40322 | 0.130851 | ||||||||
\(116\) | 0.0835727 | 0.00775953 | ||||||||
\(117\) | −1.65040 | −0.152579 | ||||||||
\(118\) | −0.0652730 | −0.00600887 | ||||||||
\(119\) | −3.23809 | −0.296835 | ||||||||
\(120\) | −2.67156 | −0.243879 | ||||||||
\(121\) | −7.98010 | −0.725464 | ||||||||
\(122\) | −4.73357 | −0.428557 | ||||||||
\(123\) | 15.2598 | 1.37593 | ||||||||
\(124\) | −0.944842 | −0.0848493 | ||||||||
\(125\) | 11.2692 | 1.00795 | ||||||||
\(126\) | 1.13403 | 0.101027 | ||||||||
\(127\) | −10.9262 | −0.969543 | −0.484772 | − | 0.874641i | \(-0.661097\pi\) | ||||
−0.484772 | + | 0.874641i | \(0.661097\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −16.1838 | −1.42491 | ||||||||
\(130\) | −3.70685 | −0.325112 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −3.30853 | −0.287971 | ||||||||
\(133\) | 4.31437 | 0.374103 | ||||||||
\(134\) | 5.83806 | 0.504331 | ||||||||
\(135\) | −6.34562 | −0.546144 | ||||||||
\(136\) | −1.78392 | −0.152970 | ||||||||
\(137\) | 6.56574 | 0.560949 | 0.280474 | − | 0.959862i | \(-0.409508\pi\) | ||||
0.280474 | + | 0.959862i | \(0.409508\pi\) | |||||||
\(138\) | −1.90388 | −0.162069 | ||||||||
\(139\) | 13.0414 | 1.10616 | 0.553078 | − | 0.833129i | \(-0.313453\pi\) | ||||
0.553078 | + | 0.833129i | \(0.313453\pi\) | |||||||
\(140\) | 2.54706 | 0.215266 | ||||||||
\(141\) | 3.93936 | 0.331754 | ||||||||
\(142\) | −2.32516 | −0.195123 | ||||||||
\(143\) | −4.59066 | −0.383890 | ||||||||
\(144\) | 0.624755 | 0.0520629 | ||||||||
\(145\) | −0.117271 | −0.00973883 | ||||||||
\(146\) | −12.6531 | −1.04718 | ||||||||
\(147\) | 7.05429 | 0.581828 | ||||||||
\(148\) | 11.1027 | 0.912637 | ||||||||
\(149\) | 12.2367 | 1.00247 | 0.501236 | − | 0.865310i | \(-0.332879\pi\) | ||||
0.501236 | + | 0.865310i | \(0.332879\pi\) | |||||||
\(150\) | −5.77060 | −0.471167 | ||||||||
\(151\) | 18.6987 | 1.52168 | 0.760838 | − | 0.648942i | \(-0.224788\pi\) | ||||
0.760838 | + | 0.648942i | \(0.224788\pi\) | |||||||
\(152\) | 2.37686 | 0.192789 | ||||||||
\(153\) | 1.11451 | 0.0901031 | ||||||||
\(154\) | 3.15435 | 0.254184 | ||||||||
\(155\) | 1.32582 | 0.106493 | ||||||||
\(156\) | 5.02942 | 0.402676 | ||||||||
\(157\) | 24.4715 | 1.95304 | 0.976519 | − | 0.215430i | \(-0.0691153\pi\) | ||||
0.976519 | + | 0.215430i | \(0.0691153\pi\) | |||||||
\(158\) | −10.2970 | −0.819187 | ||||||||
\(159\) | 4.88422 | 0.387344 | ||||||||
\(160\) | 1.40322 | 0.110934 | ||||||||
\(161\) | 1.81515 | 0.143054 | ||||||||
\(162\) | 10.4839 | 0.823697 | ||||||||
\(163\) | −12.5179 | −0.980475 | −0.490238 | − | 0.871589i | \(-0.663090\pi\) | ||||
−0.490238 | + | 0.871589i | \(0.663090\pi\) | |||||||
\(164\) | −8.01509 | −0.625874 | ||||||||
\(165\) | 4.64261 | 0.361426 | ||||||||
\(166\) | −8.91728 | −0.692115 | ||||||||
\(167\) | 10.8743 | 0.841476 | 0.420738 | − | 0.907182i | \(-0.361771\pi\) | ||||
0.420738 | + | 0.907182i | \(0.361771\pi\) | |||||||
\(168\) | −3.45583 | −0.266623 | ||||||||
\(169\) | −6.02157 | −0.463198 | ||||||||
\(170\) | 2.50324 | 0.191989 | ||||||||
\(171\) | −1.48496 | −0.113558 | ||||||||
\(172\) | 8.50045 | 0.648153 | ||||||||
\(173\) | −5.08665 | −0.386731 | −0.193365 | − | 0.981127i | \(-0.561940\pi\) | ||||
−0.193365 | + | 0.981127i | \(0.561940\pi\) | |||||||
\(174\) | 0.159112 | 0.0120623 | ||||||||
\(175\) | 5.50167 | 0.415887 | ||||||||
\(176\) | 1.73779 | 0.130991 | ||||||||
\(177\) | −0.124272 | −0.00934085 | ||||||||
\(178\) | −13.8362 | −1.03707 | ||||||||
\(179\) | 0.881654 | 0.0658979 | 0.0329490 | − | 0.999457i | \(-0.489510\pi\) | ||||
0.0329490 | + | 0.999457i | \(0.489510\pi\) | |||||||
\(180\) | −0.876670 | −0.0653431 | ||||||||
\(181\) | 0.589412 | 0.0438106 | 0.0219053 | − | 0.999760i | \(-0.493027\pi\) | ||||
0.0219053 | + | 0.999760i | \(0.493027\pi\) | |||||||
\(182\) | −4.79504 | −0.355432 | ||||||||
\(183\) | −9.01214 | −0.666196 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −15.5796 | −1.14543 | ||||||||
\(186\) | −1.79886 | −0.131899 | ||||||||
\(187\) | 3.10007 | 0.226700 | ||||||||
\(188\) | −2.06912 | −0.150906 | ||||||||
\(189\) | −8.20844 | −0.597076 | ||||||||
\(190\) | −3.33526 | −0.241966 | ||||||||
\(191\) | −12.3437 | −0.893157 | −0.446579 | − | 0.894744i | \(-0.647358\pi\) | ||||
−0.446579 | + | 0.894744i | \(0.647358\pi\) | |||||||
\(192\) | −1.90388 | −0.137401 | ||||||||
\(193\) | −0.626953 | −0.0451291 | −0.0225645 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225645 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(194\) | 9.35526 | 0.671668 | ||||||||
\(195\) | −7.05739 | −0.505390 | ||||||||
\(196\) | −3.70522 | −0.264659 | ||||||||
\(197\) | −10.9647 | −0.781204 | −0.390602 | − | 0.920560i | \(-0.627733\pi\) | ||||
−0.390602 | + | 0.920560i | \(0.627733\pi\) | |||||||
\(198\) | −1.08569 | −0.0771567 | ||||||||
\(199\) | −19.4357 | −1.37776 | −0.688881 | − | 0.724875i | \(-0.741898\pi\) | ||||
−0.688881 | + | 0.724875i | \(0.741898\pi\) | |||||||
\(200\) | 3.03097 | 0.214322 | ||||||||
\(201\) | 11.1150 | 0.783988 | ||||||||
\(202\) | −3.50973 | −0.246944 | ||||||||
\(203\) | −0.151697 | −0.0106471 | ||||||||
\(204\) | −3.39637 | −0.237793 | ||||||||
\(205\) | 11.2469 | 0.785521 | ||||||||
\(206\) | 2.79158 | 0.194499 | ||||||||
\(207\) | −0.624755 | −0.0434235 | ||||||||
\(208\) | −2.64167 | −0.183167 | ||||||||
\(209\) | −4.13048 | −0.285711 | ||||||||
\(210\) | 4.84930 | 0.334633 | ||||||||
\(211\) | −10.5751 | −0.728019 | −0.364009 | − | 0.931395i | \(-0.618592\pi\) | ||||
−0.364009 | + | 0.931395i | \(0.618592\pi\) | |||||||
\(212\) | −2.56540 | −0.176193 | ||||||||
\(213\) | −4.42682 | −0.303321 | ||||||||
\(214\) | 9.73908 | 0.665750 | ||||||||
\(215\) | −11.9280 | −0.813484 | ||||||||
\(216\) | −4.52218 | −0.307695 | ||||||||
\(217\) | 1.71503 | 0.116424 | ||||||||
\(218\) | 10.2798 | 0.696236 | ||||||||
\(219\) | −24.0900 | −1.62785 | ||||||||
\(220\) | −2.43850 | −0.164404 | ||||||||
\(221\) | −4.71253 | −0.316999 | ||||||||
\(222\) | 21.1382 | 1.41870 | ||||||||
\(223\) | 7.56649 | 0.506690 | 0.253345 | − | 0.967376i | \(-0.418469\pi\) | ||||
0.253345 | + | 0.967376i | \(0.418469\pi\) | |||||||
\(224\) | 1.81515 | 0.121280 | ||||||||
\(225\) | −1.89361 | −0.126241 | ||||||||
\(226\) | −12.4901 | −0.830828 | ||||||||
\(227\) | 12.4583 | 0.826886 | 0.413443 | − | 0.910530i | \(-0.364326\pi\) | ||||
0.413443 | + | 0.910530i | \(0.364326\pi\) | |||||||
\(228\) | 4.52526 | 0.299693 | ||||||||
\(229\) | 6.08192 | 0.401904 | 0.200952 | − | 0.979601i | \(-0.435596\pi\) | ||||
0.200952 | + | 0.979601i | \(0.435596\pi\) | |||||||
\(230\) | −1.40322 | −0.0925257 | ||||||||
\(231\) | 6.00549 | 0.395132 | ||||||||
\(232\) | −0.0835727 | −0.00548682 | ||||||||
\(233\) | −15.6170 | −1.02310 | −0.511551 | − | 0.859253i | \(-0.670929\pi\) | ||||
−0.511551 | + | 0.859253i | \(0.670929\pi\) | |||||||
\(234\) | 1.65040 | 0.107890 | ||||||||
\(235\) | 2.90344 | 0.189399 | ||||||||
\(236\) | 0.0652730 | 0.00424891 | ||||||||
\(237\) | −19.6043 | −1.27343 | ||||||||
\(238\) | 3.23809 | 0.209894 | ||||||||
\(239\) | −26.8031 | −1.73375 | −0.866874 | − | 0.498527i | \(-0.833875\pi\) | ||||
−0.866874 | + | 0.498527i | \(0.833875\pi\) | |||||||
\(240\) | 2.67156 | 0.172449 | ||||||||
\(241\) | 12.3017 | 0.792421 | 0.396210 | − | 0.918160i | \(-0.370325\pi\) | ||||
0.396210 | + | 0.918160i | \(0.370325\pi\) | |||||||
\(242\) | 7.98010 | 0.512980 | ||||||||
\(243\) | 6.39363 | 0.410152 | ||||||||
\(244\) | 4.73357 | 0.303035 | ||||||||
\(245\) | 5.19925 | 0.332168 | ||||||||
\(246\) | −15.2598 | −0.972927 | ||||||||
\(247\) | 6.27889 | 0.399516 | ||||||||
\(248\) | 0.944842 | 0.0599975 | ||||||||
\(249\) | −16.9774 | −1.07590 | ||||||||
\(250\) | −11.2692 | −0.712729 | ||||||||
\(251\) | 3.33805 | 0.210696 | 0.105348 | − | 0.994435i | \(-0.466404\pi\) | ||||
0.105348 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(252\) | −1.13403 | −0.0714369 | ||||||||
\(253\) | −1.73779 | −0.109254 | ||||||||
\(254\) | 10.9262 | 0.685571 | ||||||||
\(255\) | 4.76586 | 0.298450 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.9560 | 1.05768 | 0.528842 | − | 0.848720i | \(-0.322626\pi\) | ||||
0.528842 | + | 0.848720i | \(0.322626\pi\) | |||||||
\(258\) | 16.1838 | 1.00756 | ||||||||
\(259\) | −20.1531 | −1.25225 | ||||||||
\(260\) | 3.70685 | 0.229889 | ||||||||
\(261\) | 0.0522125 | 0.00323187 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −5.05197 | −0.311518 | −0.155759 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155759 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(264\) | 3.30853 | 0.203626 | ||||||||
\(265\) | 3.59983 | 0.221136 | ||||||||
\(266\) | −4.31437 | −0.264531 | ||||||||
\(267\) | −26.3424 | −1.61213 | ||||||||
\(268\) | −5.83806 | −0.356616 | ||||||||
\(269\) | −24.4299 | −1.48952 | −0.744758 | − | 0.667335i | \(-0.767435\pi\) | ||||
−0.744758 | + | 0.667335i | \(0.767435\pi\) | |||||||
\(270\) | 6.34562 | 0.386182 | ||||||||
\(271\) | 4.99703 | 0.303548 | 0.151774 | − | 0.988415i | \(-0.451501\pi\) | ||||
0.151774 | + | 0.988415i | \(0.451501\pi\) | |||||||
\(272\) | 1.78392 | 0.108166 | ||||||||
\(273\) | −9.12917 | −0.552522 | ||||||||
\(274\) | −6.56574 | −0.396651 | ||||||||
\(275\) | −5.26718 | −0.317623 | ||||||||
\(276\) | 1.90388 | 0.114600 | ||||||||
\(277\) | 12.3510 | 0.742100 | 0.371050 | − | 0.928613i | \(-0.378998\pi\) | ||||
0.371050 | + | 0.928613i | \(0.378998\pi\) | |||||||
\(278\) | −13.0414 | −0.782171 | ||||||||
\(279\) | −0.590295 | −0.0353400 | ||||||||
\(280\) | −2.54706 | −0.152216 | ||||||||
\(281\) | 16.4859 | 0.983468 | 0.491734 | − | 0.870745i | \(-0.336363\pi\) | ||||
0.491734 | + | 0.870745i | \(0.336363\pi\) | |||||||
\(282\) | −3.93936 | −0.234586 | ||||||||
\(283\) | −9.67749 | −0.575267 | −0.287634 | − | 0.957741i | \(-0.592869\pi\) | ||||
−0.287634 | + | 0.957741i | \(0.592869\pi\) | |||||||
\(284\) | 2.32516 | 0.137973 | ||||||||
\(285\) | −6.34994 | −0.376138 | ||||||||
\(286\) | 4.59066 | 0.271451 | ||||||||
\(287\) | 14.5486 | 0.858778 | ||||||||
\(288\) | −0.624755 | −0.0368141 | ||||||||
\(289\) | −13.8176 | −0.812801 | ||||||||
\(290\) | 0.117271 | 0.00688639 | ||||||||
\(291\) | 17.8113 | 1.04412 | ||||||||
\(292\) | 12.6531 | 0.740468 | ||||||||
\(293\) | −5.29165 | −0.309141 | −0.154571 | − | 0.987982i | \(-0.549399\pi\) | ||||
−0.154571 | + | 0.987982i | \(0.549399\pi\) | |||||||
\(294\) | −7.05429 | −0.411415 | ||||||||
\(295\) | −0.0915924 | −0.00533272 | ||||||||
\(296\) | −11.1027 | −0.645332 | ||||||||
\(297\) | 7.85858 | 0.456001 | ||||||||
\(298\) | −12.2367 | −0.708855 | ||||||||
\(299\) | 2.64167 | 0.152772 | ||||||||
\(300\) | 5.77060 | 0.333166 | ||||||||
\(301\) | −15.4296 | −0.889348 | ||||||||
\(302\) | −18.6987 | −1.07599 | ||||||||
\(303\) | −6.68211 | −0.383877 | ||||||||
\(304\) | −2.37686 | −0.136322 | ||||||||
\(305\) | −6.64224 | −0.380334 | ||||||||
\(306\) | −1.11451 | −0.0637125 | ||||||||
\(307\) | −28.1051 | −1.60405 | −0.802023 | − | 0.597293i | \(-0.796243\pi\) | ||||
−0.802023 | + | 0.597293i | \(0.796243\pi\) | |||||||
\(308\) | −3.15435 | −0.179736 | ||||||||
\(309\) | 5.31483 | 0.302350 | ||||||||
\(310\) | −1.32582 | −0.0753016 | ||||||||
\(311\) | 2.01718 | 0.114384 | 0.0571919 | − | 0.998363i | \(-0.481785\pi\) | ||||
0.0571919 | + | 0.998363i | \(0.481785\pi\) | |||||||
\(312\) | −5.02942 | −0.284735 | ||||||||
\(313\) | 19.0306 | 1.07567 | 0.537837 | − | 0.843049i | \(-0.319242\pi\) | ||||
0.537837 | + | 0.843049i | \(0.319242\pi\) | |||||||
\(314\) | −24.4715 | −1.38101 | ||||||||
\(315\) | 1.59129 | 0.0896590 | ||||||||
\(316\) | 10.2970 | 0.579253 | ||||||||
\(317\) | 0.417139 | 0.0234288 | 0.0117144 | − | 0.999931i | \(-0.496271\pi\) | ||||
0.0117144 | + | 0.999931i | \(0.496271\pi\) | |||||||
\(318\) | −4.88422 | −0.273893 | ||||||||
\(319\) | 0.145231 | 0.00813140 | ||||||||
\(320\) | −1.40322 | −0.0784425 | ||||||||
\(321\) | 18.5420 | 1.03492 | ||||||||
\(322\) | −1.81515 | −0.101154 | ||||||||
\(323\) | −4.24014 | −0.235927 | ||||||||
\(324\) | −10.4839 | −0.582441 | ||||||||
\(325\) | 8.00683 | 0.444139 | ||||||||
\(326\) | 12.5179 | 0.693301 | ||||||||
\(327\) | 19.5715 | 1.08231 | ||||||||
\(328\) | 8.01509 | 0.442559 | ||||||||
\(329\) | 3.75578 | 0.207063 | ||||||||
\(330\) | −4.64261 | −0.255567 | ||||||||
\(331\) | −9.12723 | −0.501678 | −0.250839 | − | 0.968029i | \(-0.580706\pi\) | ||||
−0.250839 | + | 0.968029i | \(0.580706\pi\) | |||||||
\(332\) | 8.91728 | 0.489400 | ||||||||
\(333\) | 6.93648 | 0.380117 | ||||||||
\(334\) | −10.8743 | −0.595013 | ||||||||
\(335\) | 8.19208 | 0.447581 | ||||||||
\(336\) | 3.45583 | 0.188531 | ||||||||
\(337\) | 19.1139 | 1.04120 | 0.520600 | − | 0.853801i | \(-0.325708\pi\) | ||||
0.520600 | + | 0.853801i | \(0.325708\pi\) | |||||||
\(338\) | 6.02157 | 0.327530 | ||||||||
\(339\) | −23.7796 | −1.29153 | ||||||||
\(340\) | −2.50324 | −0.135757 | ||||||||
\(341\) | −1.64193 | −0.0889156 | ||||||||
\(342\) | 1.48496 | 0.0802973 | ||||||||
\(343\) | 19.4316 | 1.04921 | ||||||||
\(344\) | −8.50045 | −0.458314 | ||||||||
\(345\) | −2.67156 | −0.143832 | ||||||||
\(346\) | 5.08665 | 0.273460 | ||||||||
\(347\) | 11.4098 | 0.612512 | 0.306256 | − | 0.951949i | \(-0.400924\pi\) | ||||
0.306256 | + | 0.951949i | \(0.400924\pi\) | |||||||
\(348\) | −0.159112 | −0.00852932 | ||||||||
\(349\) | −12.7844 | −0.684334 | −0.342167 | − | 0.939639i | \(-0.611161\pi\) | ||||
−0.342167 | + | 0.939639i | \(0.611161\pi\) | |||||||
\(350\) | −5.50167 | −0.294077 | ||||||||
\(351\) | −11.9461 | −0.637636 | ||||||||
\(352\) | −1.73779 | −0.0926243 | ||||||||
\(353\) | 29.5803 | 1.57440 | 0.787199 | − | 0.616699i | \(-0.211530\pi\) | ||||
0.787199 | + | 0.616699i | \(0.211530\pi\) | |||||||
\(354\) | 0.124272 | 0.00660498 | ||||||||
\(355\) | −3.26271 | −0.173167 | ||||||||
\(356\) | 13.8362 | 0.733316 | ||||||||
\(357\) | 6.16493 | 0.326283 | ||||||||
\(358\) | −0.881654 | −0.0465969 | ||||||||
\(359\) | −20.0212 | −1.05668 | −0.528340 | − | 0.849033i | \(-0.677185\pi\) | ||||
−0.528340 | + | 0.849033i | \(0.677185\pi\) | |||||||
\(360\) | 0.876670 | 0.0462046 | ||||||||
\(361\) | −13.3505 | −0.702659 | ||||||||
\(362\) | −0.589412 | −0.0309788 | ||||||||
\(363\) | 15.1931 | 0.797433 | ||||||||
\(364\) | 4.79504 | 0.251328 | ||||||||
\(365\) | −17.7551 | −0.929346 | ||||||||
\(366\) | 9.01214 | 0.471072 | ||||||||
\(367\) | −18.4759 | −0.964432 | −0.482216 | − | 0.876052i | \(-0.660168\pi\) | ||||
−0.482216 | + | 0.876052i | \(0.660168\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −5.00747 | −0.260679 | ||||||||
\(370\) | 15.5796 | 0.809943 | ||||||||
\(371\) | 4.65660 | 0.241758 | ||||||||
\(372\) | 1.79886 | 0.0932668 | ||||||||
\(373\) | −15.0242 | −0.777923 | −0.388962 | − | 0.921254i | \(-0.627166\pi\) | ||||
−0.388962 | + | 0.921254i | \(0.627166\pi\) | |||||||
\(374\) | −3.10007 | −0.160301 | ||||||||
\(375\) | −21.4552 | −1.10794 | ||||||||
\(376\) | 2.06912 | 0.106707 | ||||||||
\(377\) | −0.220772 | −0.0113703 | ||||||||
\(378\) | 8.20844 | 0.422197 | ||||||||
\(379\) | −15.4821 | −0.795263 | −0.397631 | − | 0.917545i | \(-0.630168\pi\) | ||||
−0.397631 | + | 0.917545i | \(0.630168\pi\) | |||||||
\(380\) | 3.33526 | 0.171095 | ||||||||
\(381\) | 20.8022 | 1.06573 | ||||||||
\(382\) | 12.3437 | 0.631557 | ||||||||
\(383\) | 5.20876 | 0.266155 | 0.133078 | − | 0.991106i | \(-0.457514\pi\) | ||||
0.133078 | + | 0.991106i | \(0.457514\pi\) | |||||||
\(384\) | 1.90388 | 0.0971569 | ||||||||
\(385\) | 4.42625 | 0.225582 | ||||||||
\(386\) | 0.626953 | 0.0319111 | ||||||||
\(387\) | 5.31070 | 0.269958 | ||||||||
\(388\) | −9.35526 | −0.474941 | ||||||||
\(389\) | −5.93386 | −0.300859 | −0.150429 | − | 0.988621i | \(-0.548066\pi\) | ||||
−0.150429 | + | 0.988621i | \(0.548066\pi\) | |||||||
\(390\) | 7.05739 | 0.357365 | ||||||||
\(391\) | −1.78392 | −0.0902168 | ||||||||
\(392\) | 3.70522 | 0.187142 | ||||||||
\(393\) | 1.90388 | 0.0960380 | ||||||||
\(394\) | 10.9647 | 0.552395 | ||||||||
\(395\) | −14.4490 | −0.727008 | ||||||||
\(396\) | 1.08569 | 0.0545580 | ||||||||
\(397\) | −38.9525 | −1.95497 | −0.977486 | − | 0.211001i | \(-0.932328\pi\) | ||||
−0.977486 | + | 0.211001i | \(0.932328\pi\) | |||||||
\(398\) | 19.4357 | 0.974224 | ||||||||
\(399\) | −8.21403 | −0.411216 | ||||||||
\(400\) | −3.03097 | −0.151548 | ||||||||
\(401\) | 8.65563 | 0.432242 | 0.216121 | − | 0.976367i | \(-0.430660\pi\) | ||||
0.216121 | + | 0.976367i | \(0.430660\pi\) | |||||||
\(402\) | −11.1150 | −0.554363 | ||||||||
\(403\) | 2.49596 | 0.124333 | ||||||||
\(404\) | 3.50973 | 0.174616 | ||||||||
\(405\) | 14.7113 | 0.731010 | ||||||||
\(406\) | 0.151697 | 0.00752861 | ||||||||
\(407\) | 19.2941 | 0.956375 | ||||||||
\(408\) | 3.39637 | 0.168145 | ||||||||
\(409\) | −29.6310 | −1.46516 | −0.732579 | − | 0.680682i | \(-0.761684\pi\) | ||||
−0.732579 | + | 0.680682i | \(0.761684\pi\) | |||||||
\(410\) | −11.2469 | −0.555447 | ||||||||
\(411\) | −12.5004 | −0.616598 | ||||||||
\(412\) | −2.79158 | −0.137531 | ||||||||
\(413\) | −0.118480 | −0.00583004 | ||||||||
\(414\) | 0.624755 | 0.0307050 | ||||||||
\(415\) | −12.5129 | −0.614235 | ||||||||
\(416\) | 2.64167 | 0.129519 | ||||||||
\(417\) | −24.8292 | −1.21589 | ||||||||
\(418\) | 4.13048 | 0.202028 | ||||||||
\(419\) | −34.7146 | −1.69592 | −0.847959 | − | 0.530062i | \(-0.822169\pi\) | ||||
−0.847959 | + | 0.530062i | \(0.822169\pi\) | |||||||
\(420\) | −4.84930 | −0.236621 | ||||||||
\(421\) | −8.47369 | −0.412982 | −0.206491 | − | 0.978448i | \(-0.566204\pi\) | ||||
−0.206491 | + | 0.978448i | \(0.566204\pi\) | |||||||
\(422\) | 10.5751 | 0.514787 | ||||||||
\(423\) | −1.29270 | −0.0628530 | ||||||||
\(424\) | 2.56540 | 0.124587 | ||||||||
\(425\) | −5.40701 | −0.262279 | ||||||||
\(426\) | 4.42682 | 0.214480 | ||||||||
\(427\) | −8.59214 | −0.415803 | ||||||||
\(428\) | −9.73908 | −0.470756 | ||||||||
\(429\) | 8.74006 | 0.421974 | ||||||||
\(430\) | 11.9280 | 0.575220 | ||||||||
\(431\) | 15.5452 | 0.748787 | 0.374394 | − | 0.927270i | \(-0.377851\pi\) | ||||
0.374394 | + | 0.927270i | \(0.377851\pi\) | |||||||
\(432\) | 4.52218 | 0.217573 | ||||||||
\(433\) | −22.5906 | −1.08564 | −0.542819 | − | 0.839850i | \(-0.682643\pi\) | ||||
−0.542819 | + | 0.839850i | \(0.682643\pi\) | |||||||
\(434\) | −1.71503 | −0.0823241 | ||||||||
\(435\) | 0.223270 | 0.0107050 | ||||||||
\(436\) | −10.2798 | −0.492313 | ||||||||
\(437\) | 2.37686 | 0.113701 | ||||||||
\(438\) | 24.0900 | 1.15107 | ||||||||
\(439\) | 14.3651 | 0.685607 | 0.342804 | − | 0.939407i | \(-0.388623\pi\) | ||||
0.342804 | + | 0.939407i | \(0.388623\pi\) | |||||||
\(440\) | 2.43850 | 0.116251 | ||||||||
\(441\) | −2.31486 | −0.110231 | ||||||||
\(442\) | 4.71253 | 0.224152 | ||||||||
\(443\) | 6.91936 | 0.328749 | 0.164374 | − | 0.986398i | \(-0.447440\pi\) | ||||
0.164374 | + | 0.986398i | \(0.447440\pi\) | |||||||
\(444\) | −21.1382 | −1.00318 | ||||||||
\(445\) | −19.4152 | −0.920370 | ||||||||
\(446\) | −7.56649 | −0.358284 | ||||||||
\(447\) | −23.2973 | −1.10192 | ||||||||
\(448\) | −1.81515 | −0.0857579 | ||||||||
\(449\) | 28.4327 | 1.34182 | 0.670911 | − | 0.741537i | \(-0.265903\pi\) | ||||
0.670911 | + | 0.741537i | \(0.265903\pi\) | |||||||
\(450\) | 1.89361 | 0.0892658 | ||||||||
\(451\) | −13.9285 | −0.655868 | ||||||||
\(452\) | 12.4901 | 0.587484 | ||||||||
\(453\) | −35.6000 | −1.67263 | ||||||||
\(454\) | −12.4583 | −0.584697 | ||||||||
\(455\) | −6.72850 | −0.315437 | ||||||||
\(456\) | −4.52526 | −0.211915 | ||||||||
\(457\) | 5.71141 | 0.267168 | 0.133584 | − | 0.991037i | \(-0.457351\pi\) | ||||
0.133584 | + | 0.991037i | \(0.457351\pi\) | |||||||
\(458\) | −6.08192 | −0.284189 | ||||||||
\(459\) | 8.06721 | 0.376545 | ||||||||
\(460\) | 1.40322 | 0.0654255 | ||||||||
\(461\) | 42.0478 | 1.95836 | 0.979180 | − | 0.202994i | \(-0.0650671\pi\) | ||||
0.979180 | + | 0.202994i | \(0.0650671\pi\) | |||||||
\(462\) | −6.00549 | −0.279401 | ||||||||
\(463\) | −31.4541 | −1.46180 | −0.730899 | − | 0.682486i | \(-0.760899\pi\) | ||||
−0.730899 | + | 0.682486i | \(0.760899\pi\) | |||||||
\(464\) | 0.0835727 | 0.00387977 | ||||||||
\(465\) | −2.52420 | −0.117057 | ||||||||
\(466\) | 15.6170 | 0.723442 | ||||||||
\(467\) | 11.1868 | 0.517664 | 0.258832 | − | 0.965922i | \(-0.416662\pi\) | ||||
0.258832 | + | 0.965922i | \(0.416662\pi\) | |||||||
\(468\) | −1.65040 | −0.0762897 | ||||||||
\(469\) | 10.5970 | 0.489322 | ||||||||
\(470\) | −2.90344 | −0.133926 | ||||||||
\(471\) | −46.5908 | −2.14679 | ||||||||
\(472\) | −0.0652730 | −0.00300443 | ||||||||
\(473\) | 14.7720 | 0.679216 | ||||||||
\(474\) | 19.6043 | 0.900454 | ||||||||
\(475\) | 7.20420 | 0.330551 | ||||||||
\(476\) | −3.23809 | −0.148418 | ||||||||
\(477\) | −1.60275 | −0.0733848 | ||||||||
\(478\) | 26.8031 | 1.22595 | ||||||||
\(479\) | −17.8540 | −0.815772 | −0.407886 | − | 0.913033i | \(-0.633734\pi\) | ||||
−0.407886 | + | 0.913033i | \(0.633734\pi\) | |||||||
\(480\) | −2.67156 | −0.121940 | ||||||||
\(481\) | −29.3297 | −1.33732 | ||||||||
\(482\) | −12.3017 | −0.560326 | ||||||||
\(483\) | −3.45583 | −0.157246 | ||||||||
\(484\) | −7.98010 | −0.362732 | ||||||||
\(485\) | 13.1275 | 0.596089 | ||||||||
\(486\) | −6.39363 | −0.290021 | ||||||||
\(487\) | −32.0774 | −1.45357 | −0.726783 | − | 0.686867i | \(-0.758986\pi\) | ||||
−0.726783 | + | 0.686867i | \(0.758986\pi\) | |||||||
\(488\) | −4.73357 | −0.214278 | ||||||||
\(489\) | 23.8325 | 1.07774 | ||||||||
\(490\) | −5.19925 | −0.234878 | ||||||||
\(491\) | −20.4438 | −0.922615 | −0.461307 | − | 0.887240i | \(-0.652619\pi\) | ||||
−0.461307 | + | 0.887240i | \(0.652619\pi\) | |||||||
\(492\) | 15.2598 | 0.687963 | ||||||||
\(493\) | 0.149087 | 0.00671455 | ||||||||
\(494\) | −6.27889 | −0.282501 | ||||||||
\(495\) | −1.52346 | −0.0684746 | ||||||||
\(496\) | −0.944842 | −0.0424246 | ||||||||
\(497\) | −4.22052 | −0.189316 | ||||||||
\(498\) | 16.9774 | 0.760777 | ||||||||
\(499\) | −41.0082 | −1.83578 | −0.917890 | − | 0.396834i | \(-0.870109\pi\) | ||||
−0.917890 | + | 0.396834i | \(0.870109\pi\) | |||||||
\(500\) | 11.2692 | 0.503975 | ||||||||
\(501\) | −20.7033 | −0.924955 | ||||||||
\(502\) | −3.33805 | −0.148984 | ||||||||
\(503\) | 4.35733 | 0.194284 | 0.0971419 | − | 0.995271i | \(-0.469030\pi\) | ||||
0.0971419 | + | 0.995271i | \(0.469030\pi\) | |||||||
\(504\) | 1.13403 | 0.0505135 | ||||||||
\(505\) | −4.92493 | −0.219157 | ||||||||
\(506\) | 1.73779 | 0.0772540 | ||||||||
\(507\) | 11.4643 | 0.509149 | ||||||||
\(508\) | −10.9262 | −0.484772 | ||||||||
\(509\) | −24.2532 | −1.07500 | −0.537502 | − | 0.843263i | \(-0.680632\pi\) | ||||
−0.537502 | + | 0.843263i | \(0.680632\pi\) | |||||||
\(510\) | −4.76586 | −0.211036 | ||||||||
\(511\) | −22.9673 | −1.01602 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.7486 | −0.474562 | ||||||||
\(514\) | −16.9560 | −0.747895 | ||||||||
\(515\) | 3.91721 | 0.172613 | ||||||||
\(516\) | −16.1838 | −0.712453 | ||||||||
\(517\) | −3.59569 | −0.158138 | ||||||||
\(518\) | 20.1531 | 0.885477 | ||||||||
\(519\) | 9.68436 | 0.425096 | ||||||||
\(520\) | −3.70685 | −0.162556 | ||||||||
\(521\) | −12.2046 | −0.534692 | −0.267346 | − | 0.963601i | \(-0.586147\pi\) | ||||
−0.267346 | + | 0.963601i | \(0.586147\pi\) | |||||||
\(522\) | −0.0522125 | −0.00228528 | ||||||||
\(523\) | 29.9006 | 1.30746 | 0.653730 | − | 0.756728i | \(-0.273203\pi\) | ||||
0.653730 | + | 0.756728i | \(0.273203\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −10.4745 | −0.457145 | ||||||||
\(526\) | 5.05197 | 0.220276 | ||||||||
\(527\) | −1.68552 | −0.0734225 | ||||||||
\(528\) | −3.30853 | −0.143985 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −3.59983 | −0.156367 | ||||||||
\(531\) | 0.0407796 | 0.00176969 | ||||||||
\(532\) | 4.31437 | 0.187052 | ||||||||
\(533\) | 21.1732 | 0.917115 | ||||||||
\(534\) | 26.3424 | 1.13995 | ||||||||
\(535\) | 13.6661 | 0.590836 | ||||||||
\(536\) | 5.83806 | 0.252166 | ||||||||
\(537\) | −1.67856 | −0.0724353 | ||||||||
\(538\) | 24.4299 | 1.05325 | ||||||||
\(539\) | −6.43888 | −0.277342 | ||||||||
\(540\) | −6.34562 | −0.273072 | ||||||||
\(541\) | −25.7898 | −1.10879 | −0.554395 | − | 0.832253i | \(-0.687050\pi\) | ||||
−0.554395 | + | 0.832253i | \(0.687050\pi\) | |||||||
\(542\) | −4.99703 | −0.214641 | ||||||||
\(543\) | −1.12217 | −0.0481569 | ||||||||
\(544\) | −1.78392 | −0.0764850 | ||||||||
\(545\) | 14.4248 | 0.617892 | ||||||||
\(546\) | 9.12917 | 0.390692 | ||||||||
\(547\) | −9.97587 | −0.426538 | −0.213269 | − | 0.976994i | \(-0.568411\pi\) | ||||
−0.213269 | + | 0.976994i | \(0.568411\pi\) | |||||||
\(548\) | 6.56574 | 0.280474 | ||||||||
\(549\) | 2.95732 | 0.126215 | ||||||||
\(550\) | 5.26718 | 0.224593 | ||||||||
\(551\) | −0.198641 | −0.00846239 | ||||||||
\(552\) | −1.90388 | −0.0810345 | ||||||||
\(553\) | −18.6907 | −0.794808 | ||||||||
\(554\) | −12.3510 | −0.524744 | ||||||||
\(555\) | 29.6616 | 1.25906 | ||||||||
\(556\) | 13.0414 | 0.553078 | ||||||||
\(557\) | 35.8819 | 1.52036 | 0.760182 | − | 0.649710i | \(-0.225110\pi\) | ||||
0.760182 | + | 0.649710i | \(0.225110\pi\) | |||||||
\(558\) | 0.590295 | 0.0249892 | ||||||||
\(559\) | −22.4554 | −0.949762 | ||||||||
\(560\) | 2.54706 | 0.107633 | ||||||||
\(561\) | −5.90216 | −0.249190 | ||||||||
\(562\) | −16.4859 | −0.695417 | ||||||||
\(563\) | 5.19671 | 0.219015 | 0.109508 | − | 0.993986i | \(-0.465073\pi\) | ||||
0.109508 | + | 0.993986i | \(0.465073\pi\) | |||||||
\(564\) | 3.93936 | 0.165877 | ||||||||
\(565\) | −17.5263 | −0.737339 | ||||||||
\(566\) | 9.67749 | 0.406775 | ||||||||
\(567\) | 19.0300 | 0.799183 | ||||||||
\(568\) | −2.32516 | −0.0975616 | ||||||||
\(569\) | −14.9780 | −0.627910 | −0.313955 | − | 0.949438i | \(-0.601654\pi\) | ||||
−0.313955 | + | 0.949438i | \(0.601654\pi\) | |||||||
\(570\) | 6.34994 | 0.265970 | ||||||||
\(571\) | −37.8406 | −1.58358 | −0.791791 | − | 0.610792i | \(-0.790851\pi\) | ||||
−0.791791 | + | 0.610792i | \(0.790851\pi\) | |||||||
\(572\) | −4.59066 | −0.191945 | ||||||||
\(573\) | 23.5009 | 0.981763 | ||||||||
\(574\) | −14.5486 | −0.607247 | ||||||||
\(575\) | 3.03097 | 0.126400 | ||||||||
\(576\) | 0.624755 | 0.0260315 | ||||||||
\(577\) | 24.8835 | 1.03591 | 0.517957 | − | 0.855407i | \(-0.326693\pi\) | ||||
0.517957 | + | 0.855407i | \(0.326693\pi\) | |||||||
\(578\) | 13.8176 | 0.574737 | ||||||||
\(579\) | 1.19364 | 0.0496061 | ||||||||
\(580\) | −0.117271 | −0.00486941 | ||||||||
\(581\) | −16.1862 | −0.671518 | ||||||||
\(582\) | −17.8113 | −0.738301 | ||||||||
\(583\) | −4.45812 | −0.184637 | ||||||||
\(584\) | −12.6531 | −0.523590 | ||||||||
\(585\) | 2.31587 | 0.0957496 | ||||||||
\(586\) | 5.29165 | 0.218596 | ||||||||
\(587\) | 25.6215 | 1.05751 | 0.528757 | − | 0.848773i | \(-0.322658\pi\) | ||||
0.528757 | + | 0.848773i | \(0.322658\pi\) | |||||||
\(588\) | 7.05429 | 0.290914 | ||||||||
\(589\) | 2.24576 | 0.0925349 | ||||||||
\(590\) | 0.0915924 | 0.00377080 | ||||||||
\(591\) | 20.8755 | 0.858704 | ||||||||
\(592\) | 11.1027 | 0.456319 | ||||||||
\(593\) | −14.3369 | −0.588746 | −0.294373 | − | 0.955691i | \(-0.595111\pi\) | ||||
−0.294373 | + | 0.955691i | \(0.595111\pi\) | |||||||
\(594\) | −7.85858 | −0.322441 | ||||||||
\(595\) | 4.54376 | 0.186276 | ||||||||
\(596\) | 12.2367 | 0.501236 | ||||||||
\(597\) | 37.0032 | 1.51444 | ||||||||
\(598\) | −2.64167 | −0.108026 | ||||||||
\(599\) | −32.8674 | −1.34292 | −0.671462 | − | 0.741039i | \(-0.734333\pi\) | ||||
−0.671462 | + | 0.741039i | \(0.734333\pi\) | |||||||
\(600\) | −5.77060 | −0.235584 | ||||||||
\(601\) | −36.7188 | −1.49779 | −0.748896 | − | 0.662688i | \(-0.769416\pi\) | ||||
−0.748896 | + | 0.662688i | \(0.769416\pi\) | |||||||
\(602\) | 15.4296 | 0.628864 | ||||||||
\(603\) | −3.64736 | −0.148532 | ||||||||
\(604\) | 18.6987 | 0.760838 | ||||||||
\(605\) | 11.1978 | 0.455257 | ||||||||
\(606\) | 6.68211 | 0.271442 | ||||||||
\(607\) | 22.3084 | 0.905468 | 0.452734 | − | 0.891646i | \(-0.350449\pi\) | ||||
0.452734 | + | 0.891646i | \(0.350449\pi\) | |||||||
\(608\) | 2.37686 | 0.0963945 | ||||||||
\(609\) | 0.288813 | 0.0117033 | ||||||||
\(610\) | 6.64224 | 0.268936 | ||||||||
\(611\) | 5.46595 | 0.221128 | ||||||||
\(612\) | 1.11451 | 0.0450516 | ||||||||
\(613\) | −30.3265 | −1.22487 | −0.612437 | − | 0.790519i | \(-0.709811\pi\) | ||||
−0.612437 | + | 0.790519i | \(0.709811\pi\) | |||||||
\(614\) | 28.1051 | 1.13423 | ||||||||
\(615\) | −21.4128 | −0.863449 | ||||||||
\(616\) | 3.15435 | 0.127092 | ||||||||
\(617\) | 12.1516 | 0.489203 | 0.244602 | − | 0.969624i | \(-0.421343\pi\) | ||||
0.244602 | + | 0.969624i | \(0.421343\pi\) | |||||||
\(618\) | −5.31483 | −0.213794 | ||||||||
\(619\) | −42.0680 | −1.69086 | −0.845428 | − | 0.534089i | \(-0.820655\pi\) | ||||
−0.845428 | + | 0.534089i | \(0.820655\pi\) | |||||||
\(620\) | 1.32582 | 0.0532463 | ||||||||
\(621\) | −4.52218 | −0.181469 | ||||||||
\(622\) | −2.01718 | −0.0808816 | ||||||||
\(623\) | −25.1148 | −1.00620 | ||||||||
\(624\) | 5.02942 | 0.201338 | ||||||||
\(625\) | −0.658374 | −0.0263350 | ||||||||
\(626\) | −19.0306 | −0.760616 | ||||||||
\(627\) | 7.86393 | 0.314055 | ||||||||
\(628\) | 24.4715 | 0.976519 | ||||||||
\(629\) | 19.8064 | 0.789731 | ||||||||
\(630\) | −1.59129 | −0.0633985 | ||||||||
\(631\) | 1.89312 | 0.0753640 | 0.0376820 | − | 0.999290i | \(-0.488003\pi\) | ||||
0.0376820 | + | 0.999290i | \(0.488003\pi\) | |||||||
\(632\) | −10.2970 | −0.409593 | ||||||||
\(633\) | 20.1337 | 0.800242 | ||||||||
\(634\) | −0.417139 | −0.0165667 | ||||||||
\(635\) | 15.3319 | 0.608427 | ||||||||
\(636\) | 4.88422 | 0.193672 | ||||||||
\(637\) | 9.78798 | 0.387814 | ||||||||
\(638\) | −0.145231 | −0.00574977 | ||||||||
\(639\) | 1.45266 | 0.0574662 | ||||||||
\(640\) | 1.40322 | 0.0554672 | ||||||||
\(641\) | 7.65598 | 0.302393 | 0.151197 | − | 0.988504i | \(-0.451687\pi\) | ||||
0.151197 | + | 0.988504i | \(0.451687\pi\) | |||||||
\(642\) | −18.5420 | −0.731795 | ||||||||
\(643\) | −21.7473 | −0.857629 | −0.428814 | − | 0.903393i | \(-0.641069\pi\) | ||||
−0.428814 | + | 0.903393i | \(0.641069\pi\) | |||||||
\(644\) | 1.81515 | 0.0715270 | ||||||||
\(645\) | 22.7095 | 0.894185 | ||||||||
\(646\) | 4.24014 | 0.166826 | ||||||||
\(647\) | 19.3773 | 0.761800 | 0.380900 | − | 0.924616i | \(-0.375614\pi\) | ||||
0.380900 | + | 0.924616i | \(0.375614\pi\) | |||||||
\(648\) | 10.4839 | 0.411848 | ||||||||
\(649\) | 0.113430 | 0.00445254 | ||||||||
\(650\) | −8.00683 | −0.314054 | ||||||||
\(651\) | −3.26521 | −0.127974 | ||||||||
\(652\) | −12.5179 | −0.490238 | ||||||||
\(653\) | −43.1557 | −1.68881 | −0.844406 | − | 0.535704i | \(-0.820046\pi\) | ||||
−0.844406 | + | 0.535704i | \(0.820046\pi\) | |||||||
\(654\) | −19.5715 | −0.765306 | ||||||||
\(655\) | 1.40322 | 0.0548284 | ||||||||
\(656\) | −8.01509 | −0.312937 | ||||||||
\(657\) | 7.90510 | 0.308407 | ||||||||
\(658\) | −3.75578 | −0.146415 | ||||||||
\(659\) | 23.3049 | 0.907832 | 0.453916 | − | 0.891045i | \(-0.350027\pi\) | ||||
0.453916 | + | 0.891045i | \(0.350027\pi\) | |||||||
\(660\) | 4.64261 | 0.180713 | ||||||||
\(661\) | 43.1250 | 1.67737 | 0.838685 | − | 0.544617i | \(-0.183325\pi\) | ||||
0.838685 | + | 0.544617i | \(0.183325\pi\) | |||||||
\(662\) | 9.12723 | 0.354740 | ||||||||
\(663\) | 8.97209 | 0.348447 | ||||||||
\(664\) | −8.91728 | −0.346058 | ||||||||
\(665\) | −6.05401 | −0.234765 | ||||||||
\(666\) | −6.93648 | −0.268783 | ||||||||
\(667\) | −0.0835727 | −0.00323595 | ||||||||
\(668\) | 10.8743 | 0.420738 | ||||||||
\(669\) | −14.4057 | −0.556956 | ||||||||
\(670\) | −8.19208 | −0.316488 | ||||||||
\(671\) | 8.22592 | 0.317558 | ||||||||
\(672\) | −3.45583 | −0.133312 | ||||||||
\(673\) | −24.2609 | −0.935188 | −0.467594 | − | 0.883943i | \(-0.654879\pi\) | ||||
−0.467594 | + | 0.883943i | \(0.654879\pi\) | |||||||
\(674\) | −19.1139 | −0.736240 | ||||||||
\(675\) | −13.7066 | −0.527567 | ||||||||
\(676\) | −6.02157 | −0.231599 | ||||||||
\(677\) | −10.5696 | −0.406222 | −0.203111 | − | 0.979156i | \(-0.565105\pi\) | ||||
−0.203111 | + | 0.979156i | \(0.565105\pi\) | |||||||
\(678\) | 23.7796 | 0.913250 | ||||||||
\(679\) | 16.9812 | 0.651679 | ||||||||
\(680\) | 2.50324 | 0.0959947 | ||||||||
\(681\) | −23.7191 | −0.908918 | ||||||||
\(682\) | 1.64193 | 0.0628728 | ||||||||
\(683\) | −47.2330 | −1.80732 | −0.903659 | − | 0.428252i | \(-0.859130\pi\) | ||||
−0.903659 | + | 0.428252i | \(0.859130\pi\) | |||||||
\(684\) | −1.48496 | −0.0567788 | ||||||||
\(685\) | −9.21318 | −0.352018 | ||||||||
\(686\) | −19.4316 | −0.741902 | ||||||||
\(687\) | −11.5792 | −0.441775 | ||||||||
\(688\) | 8.50045 | 0.324077 | ||||||||
\(689\) | 6.77695 | 0.258181 | ||||||||
\(690\) | 2.67156 | 0.101705 | ||||||||
\(691\) | −14.3399 | −0.545516 | −0.272758 | − | 0.962083i | \(-0.587936\pi\) | ||||
−0.272758 | + | 0.962083i | \(0.587936\pi\) | |||||||
\(692\) | −5.08665 | −0.193365 | ||||||||
\(693\) | −1.97069 | −0.0748605 | ||||||||
\(694\) | −11.4098 | −0.433111 | ||||||||
\(695\) | −18.3000 | −0.694157 | ||||||||
\(696\) | 0.159112 | 0.00603114 | ||||||||
\(697\) | −14.2983 | −0.541586 | ||||||||
\(698\) | 12.7844 | 0.483897 | ||||||||
\(699\) | 29.7328 | 1.12460 | ||||||||
\(700\) | 5.50167 | 0.207944 | ||||||||
\(701\) | −9.33296 | −0.352501 | −0.176251 | − | 0.984345i | \(-0.556397\pi\) | ||||
−0.176251 | + | 0.984345i | \(0.556397\pi\) | |||||||
\(702\) | 11.9461 | 0.450877 | ||||||||
\(703\) | −26.3896 | −0.995303 | ||||||||
\(704\) | 1.73779 | 0.0654953 | ||||||||
\(705\) | −5.52780 | −0.208189 | ||||||||
\(706\) | −29.5803 | −1.11327 | ||||||||
\(707\) | −6.37070 | −0.239595 | ||||||||
\(708\) | −0.124272 | −0.00467042 | ||||||||
\(709\) | −36.2182 | −1.36020 | −0.680102 | − | 0.733118i | \(-0.738064\pi\) | ||||
−0.680102 | + | 0.733118i | \(0.738064\pi\) | |||||||
\(710\) | 3.26271 | 0.122447 | ||||||||
\(711\) | 6.43312 | 0.241261 | ||||||||
\(712\) | −13.8362 | −0.518533 | ||||||||
\(713\) | 0.944842 | 0.0353846 | ||||||||
\(714\) | −6.16493 | −0.230717 | ||||||||
\(715\) | 6.44171 | 0.240906 | ||||||||
\(716\) | 0.881654 | 0.0329490 | ||||||||
\(717\) | 51.0299 | 1.90575 | ||||||||
\(718\) | 20.0212 | 0.747185 | ||||||||
\(719\) | −35.6959 | −1.33123 | −0.665617 | − | 0.746294i | \(-0.731831\pi\) | ||||
−0.665617 | + | 0.746294i | \(0.731831\pi\) | |||||||
\(720\) | −0.876670 | −0.0326716 | ||||||||
\(721\) | 5.06715 | 0.188710 | ||||||||
\(722\) | 13.3505 | 0.496855 | ||||||||
\(723\) | −23.4209 | −0.871033 | ||||||||
\(724\) | 0.589412 | 0.0219053 | ||||||||
\(725\) | −0.253306 | −0.00940756 | ||||||||
\(726\) | −15.1931 | −0.563871 | ||||||||
\(727\) | 22.0085 | 0.816250 | 0.408125 | − | 0.912926i | \(-0.366183\pi\) | ||||
0.408125 | + | 0.912926i | \(0.366183\pi\) | |||||||
\(728\) | −4.79504 | −0.177716 | ||||||||
\(729\) | 19.2791 | 0.714042 | ||||||||
\(730\) | 17.7551 | 0.657147 | ||||||||
\(731\) | 15.1641 | 0.560866 | ||||||||
\(732\) | −9.01214 | −0.333098 | ||||||||
\(733\) | −17.5452 | −0.648045 | −0.324023 | − | 0.946049i | \(-0.605035\pi\) | ||||
−0.324023 | + | 0.946049i | \(0.605035\pi\) | |||||||
\(734\) | 18.4759 | 0.681956 | ||||||||
\(735\) | −9.89874 | −0.365120 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −10.1453 | −0.373707 | ||||||||
\(738\) | 5.00747 | 0.184328 | ||||||||
\(739\) | −25.2598 | −0.929198 | −0.464599 | − | 0.885521i | \(-0.653801\pi\) | ||||
−0.464599 | + | 0.885521i | \(0.653801\pi\) | |||||||
\(740\) | −15.5796 | −0.572716 | ||||||||
\(741\) | −11.9542 | −0.439150 | ||||||||
\(742\) | −4.65660 | −0.170949 | ||||||||
\(743\) | 19.3570 | 0.710139 | 0.355069 | − | 0.934840i | \(-0.384457\pi\) | ||||
0.355069 | + | 0.934840i | \(0.384457\pi\) | |||||||
\(744\) | −1.79886 | −0.0659496 | ||||||||
\(745\) | −17.1709 | −0.629091 | ||||||||
\(746\) | 15.0242 | 0.550075 | ||||||||
\(747\) | 5.57112 | 0.203837 | ||||||||
\(748\) | 3.10007 | 0.113350 | ||||||||
\(749\) | 17.6779 | 0.645937 | ||||||||
\(750\) | 21.4552 | 0.783435 | ||||||||
\(751\) | −1.12097 | −0.0409047 | −0.0204523 | − | 0.999791i | \(-0.506511\pi\) | ||||
−0.0204523 | + | 0.999791i | \(0.506511\pi\) | |||||||
\(752\) | −2.06912 | −0.0754532 | ||||||||
\(753\) | −6.35524 | −0.231598 | ||||||||
\(754\) | 0.220772 | 0.00804003 | ||||||||
\(755\) | −26.2384 | −0.954912 | ||||||||
\(756\) | −8.20844 | −0.298538 | ||||||||
\(757\) | 30.0334 | 1.09158 | 0.545792 | − | 0.837921i | \(-0.316229\pi\) | ||||
0.545792 | + | 0.837921i | \(0.316229\pi\) | |||||||
\(758\) | 15.4821 | 0.562336 | ||||||||
\(759\) | 3.30853 | 0.120092 | ||||||||
\(760\) | −3.33526 | −0.120983 | ||||||||
\(761\) | 12.8138 | 0.464501 | 0.232251 | − | 0.972656i | \(-0.425391\pi\) | ||||
0.232251 | + | 0.972656i | \(0.425391\pi\) | |||||||
\(762\) | −20.8022 | −0.753583 | ||||||||
\(763\) | 18.6594 | 0.675516 | ||||||||
\(764\) | −12.3437 | −0.446579 | ||||||||
\(765\) | −1.56391 | −0.0565433 | ||||||||
\(766\) | −5.20876 | −0.188200 | ||||||||
\(767\) | −0.172430 | −0.00622608 | ||||||||
\(768\) | −1.90388 | −0.0687003 | ||||||||
\(769\) | 20.5339 | 0.740471 | 0.370235 | − | 0.928938i | \(-0.379277\pi\) | ||||
0.370235 | + | 0.928938i | \(0.379277\pi\) | |||||||
\(770\) | −4.42625 | −0.159511 | ||||||||
\(771\) | −32.2821 | −1.16261 | ||||||||
\(772\) | −0.626953 | −0.0225645 | ||||||||
\(773\) | −13.2351 | −0.476035 | −0.238017 | − | 0.971261i | \(-0.576497\pi\) | ||||
−0.238017 | + | 0.971261i | \(0.576497\pi\) | |||||||
\(774\) | −5.31070 | −0.190889 | ||||||||
\(775\) | 2.86379 | 0.102870 | ||||||||
\(776\) | 9.35526 | 0.335834 | ||||||||
\(777\) | 38.3691 | 1.37648 | ||||||||
\(778\) | 5.93386 | 0.212739 | ||||||||
\(779\) | 19.0508 | 0.682565 | ||||||||
\(780\) | −7.05739 | −0.252695 | ||||||||
\(781\) | 4.04063 | 0.144585 | ||||||||
\(782\) | 1.78392 | 0.0637929 | ||||||||
\(783\) | 0.377931 | 0.0135061 | ||||||||
\(784\) | −3.70522 | −0.132329 | ||||||||
\(785\) | −34.3389 | −1.22561 | ||||||||
\(786\) | −1.90388 | −0.0679091 | ||||||||
\(787\) | −31.9637 | −1.13938 | −0.569692 | − | 0.821859i | \(-0.692937\pi\) | ||||
−0.569692 | + | 0.821859i | \(0.692937\pi\) | |||||||
\(788\) | −10.9647 | −0.390602 | ||||||||
\(789\) | 9.61834 | 0.342422 | ||||||||
\(790\) | 14.4490 | 0.514072 | ||||||||
\(791\) | −22.6714 | −0.806102 | ||||||||
\(792\) | −1.08569 | −0.0385783 | ||||||||
\(793\) | −12.5045 | −0.444049 | ||||||||
\(794\) | 38.9525 | 1.38237 | ||||||||
\(795\) | −6.85364 | −0.243073 | ||||||||
\(796\) | −19.4357 | −0.688881 | ||||||||
\(797\) | 45.2446 | 1.60265 | 0.801323 | − | 0.598232i | \(-0.204130\pi\) | ||||
0.801323 | + | 0.598232i | \(0.204130\pi\) | |||||||
\(798\) | 8.21403 | 0.290774 | ||||||||
\(799\) | −3.69115 | −0.130584 | ||||||||
\(800\) | 3.03097 | 0.107161 | ||||||||
\(801\) | 8.64423 | 0.305429 | ||||||||
\(802\) | −8.65563 | −0.305641 | ||||||||
\(803\) | 21.9884 | 0.775954 | ||||||||
\(804\) | 11.1150 | 0.391994 | ||||||||
\(805\) | −2.54706 | −0.0897721 | ||||||||
\(806\) | −2.49596 | −0.0879165 | ||||||||
\(807\) | 46.5115 | 1.63728 | ||||||||
\(808\) | −3.50973 | −0.123472 | ||||||||
\(809\) | −23.3171 | −0.819785 | −0.409892 | − | 0.912134i | \(-0.634434\pi\) | ||||
−0.409892 | + | 0.912134i | \(0.634434\pi\) | |||||||
\(810\) | −14.7113 | −0.516902 | ||||||||
\(811\) | −1.88169 | −0.0660751 | −0.0330375 | − | 0.999454i | \(-0.510518\pi\) | ||||
−0.0330375 | + | 0.999454i | \(0.510518\pi\) | |||||||
\(812\) | −0.151697 | −0.00532353 | ||||||||
\(813\) | −9.51374 | −0.333662 | ||||||||
\(814\) | −19.2941 | −0.676259 | ||||||||
\(815\) | 17.5653 | 0.615287 | ||||||||
\(816\) | −3.39637 | −0.118897 | ||||||||
\(817\) | −20.2044 | −0.706863 | ||||||||
\(818\) | 29.6310 | 1.03602 | ||||||||
\(819\) | 2.99572 | 0.104679 | ||||||||
\(820\) | 11.2469 | 0.392761 | ||||||||
\(821\) | 5.55057 | 0.193716 | 0.0968582 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968582 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(822\) | 12.5004 | 0.436000 | ||||||||
\(823\) | 9.48825 | 0.330740 | 0.165370 | − | 0.986232i | \(-0.447118\pi\) | ||||
0.165370 | + | 0.986232i | \(0.447118\pi\) | |||||||
\(824\) | 2.79158 | 0.0972493 | ||||||||
\(825\) | 10.0281 | 0.349132 | ||||||||
\(826\) | 0.118480 | 0.00412246 | ||||||||
\(827\) | −2.79701 | −0.0972616 | −0.0486308 | − | 0.998817i | \(-0.515486\pi\) | ||||
−0.0486308 | + | 0.998817i | \(0.515486\pi\) | |||||||
\(828\) | −0.624755 | −0.0217117 | ||||||||
\(829\) | −19.8838 | −0.690594 | −0.345297 | − | 0.938493i | \(-0.612222\pi\) | ||||
−0.345297 | + | 0.938493i | \(0.612222\pi\) | |||||||
\(830\) | 12.5129 | 0.434330 | ||||||||
\(831\) | −23.5148 | −0.815721 | ||||||||
\(832\) | −2.64167 | −0.0915835 | ||||||||
\(833\) | −6.60982 | −0.229017 | ||||||||
\(834\) | 24.8292 | 0.859766 | ||||||||
\(835\) | −15.2590 | −0.528060 | ||||||||
\(836\) | −4.13048 | −0.142856 | ||||||||
\(837\) | −4.27274 | −0.147688 | ||||||||
\(838\) | 34.7146 | 1.19920 | ||||||||
\(839\) | −8.25551 | −0.285012 | −0.142506 | − | 0.989794i | \(-0.545516\pi\) | ||||
−0.142506 | + | 0.989794i | \(0.545516\pi\) | |||||||
\(840\) | 4.84930 | 0.167317 | ||||||||
\(841\) | −28.9930 | −0.999759 | ||||||||
\(842\) | 8.47369 | 0.292022 | ||||||||
\(843\) | −31.3872 | −1.08103 | ||||||||
\(844\) | −10.5751 | −0.364009 | ||||||||
\(845\) | 8.44960 | 0.290675 | ||||||||
\(846\) | 1.29270 | 0.0444438 | ||||||||
\(847\) | 14.4851 | 0.497714 | ||||||||
\(848\) | −2.56540 | −0.0880963 | ||||||||
\(849\) | 18.4248 | 0.632337 | ||||||||
\(850\) | 5.40701 | 0.185459 | ||||||||
\(851\) | −11.1027 | −0.380596 | ||||||||
\(852\) | −4.42682 | −0.151660 | ||||||||
\(853\) | −8.03199 | −0.275010 | −0.137505 | − | 0.990501i | \(-0.543908\pi\) | ||||
−0.137505 | + | 0.990501i | \(0.543908\pi\) | |||||||
\(854\) | 8.59214 | 0.294017 | ||||||||
\(855\) | 2.08372 | 0.0712619 | ||||||||
\(856\) | 9.73908 | 0.332875 | ||||||||
\(857\) | 51.6112 | 1.76301 | 0.881503 | − | 0.472178i | \(-0.156532\pi\) | ||||
0.881503 | + | 0.472178i | \(0.156532\pi\) | |||||||
\(858\) | −8.74006 | −0.298381 | ||||||||
\(859\) | 30.8266 | 1.05179 | 0.525894 | − | 0.850550i | \(-0.323731\pi\) | ||||
0.525894 | + | 0.850550i | \(0.323731\pi\) | |||||||
\(860\) | −11.9280 | −0.406742 | ||||||||
\(861\) | −27.6988 | −0.943973 | ||||||||
\(862\) | −15.5452 | −0.529473 | ||||||||
\(863\) | 49.1345 | 1.67256 | 0.836279 | − | 0.548305i | \(-0.184727\pi\) | ||||
0.836279 | + | 0.548305i | \(0.184727\pi\) | |||||||
\(864\) | −4.52218 | −0.153848 | ||||||||
\(865\) | 7.13769 | 0.242689 | ||||||||
\(866\) | 22.5906 | 0.767661 | ||||||||
\(867\) | 26.3071 | 0.893436 | ||||||||
\(868\) | 1.71503 | 0.0582120 | ||||||||
\(869\) | 17.8940 | 0.607013 | ||||||||
\(870\) | −0.223270 | −0.00756956 | ||||||||
\(871\) | 15.4222 | 0.522562 | ||||||||
\(872\) | 10.2798 | 0.348118 | ||||||||
\(873\) | −5.84474 | −0.197815 | ||||||||
\(874\) | −2.37686 | −0.0803986 | ||||||||
\(875\) | −20.4554 | −0.691518 | ||||||||
\(876\) | −24.0900 | −0.813926 | ||||||||
\(877\) | −34.8402 | −1.17647 | −0.588236 | − | 0.808690i | \(-0.700177\pi\) | ||||
−0.588236 | + | 0.808690i | \(0.700177\pi\) | |||||||
\(878\) | −14.3651 | −0.484798 | ||||||||
\(879\) | 10.0747 | 0.339810 | ||||||||
\(880\) | −2.43850 | −0.0822018 | ||||||||
\(881\) | 11.9015 | 0.400970 | 0.200485 | − | 0.979697i | \(-0.435748\pi\) | ||||
0.200485 | + | 0.979697i | \(0.435748\pi\) | |||||||
\(882\) | 2.31486 | 0.0779453 | ||||||||
\(883\) | 32.2089 | 1.08392 | 0.541959 | − | 0.840405i | \(-0.317683\pi\) | ||||
0.541959 | + | 0.840405i | \(0.317683\pi\) | |||||||
\(884\) | −4.71253 | −0.158500 | ||||||||
\(885\) | 0.174381 | 0.00586175 | ||||||||
\(886\) | −6.91936 | −0.232460 | ||||||||
\(887\) | −40.3054 | −1.35332 | −0.676661 | − | 0.736295i | \(-0.736574\pi\) | ||||
−0.676661 | + | 0.736295i | \(0.736574\pi\) | |||||||
\(888\) | 21.1382 | 0.709352 | ||||||||
\(889\) | 19.8327 | 0.665168 | ||||||||
\(890\) | 19.4152 | 0.650800 | ||||||||
\(891\) | −18.2189 | −0.610355 | ||||||||
\(892\) | 7.56649 | 0.253345 | ||||||||
\(893\) | 4.91802 | 0.164575 | ||||||||
\(894\) | 23.2973 | 0.779177 | ||||||||
\(895\) | −1.23716 | −0.0413536 | ||||||||
\(896\) | 1.81515 | 0.0606400 | ||||||||
\(897\) | −5.02942 | −0.167928 | ||||||||
\(898\) | −28.4327 | −0.948812 | ||||||||
\(899\) | −0.0789630 | −0.00263356 | ||||||||
\(900\) | −1.89361 | −0.0631205 | ||||||||
\(901\) | −4.57648 | −0.152465 | ||||||||
\(902\) | 13.9285 | 0.463769 | ||||||||
\(903\) | 29.3761 | 0.977576 | ||||||||
\(904\) | −12.4901 | −0.415414 | ||||||||
\(905\) | −0.827075 | −0.0274929 | ||||||||
\(906\) | 35.6000 | 1.18273 | ||||||||
\(907\) | 26.3870 | 0.876167 | 0.438083 | − | 0.898934i | \(-0.355657\pi\) | ||||
0.438083 | + | 0.898934i | \(0.355657\pi\) | |||||||
\(908\) | 12.4583 | 0.413443 | ||||||||
\(909\) | 2.19272 | 0.0727281 | ||||||||
\(910\) | 6.72850 | 0.223048 | ||||||||
\(911\) | −33.3531 | −1.10504 | −0.552519 | − | 0.833500i | \(-0.686333\pi\) | ||||
−0.552519 | + | 0.833500i | \(0.686333\pi\) | |||||||
\(912\) | 4.52526 | 0.149846 | ||||||||
\(913\) | 15.4963 | 0.512854 | ||||||||
\(914\) | −5.71141 | −0.188917 | ||||||||
\(915\) | 12.6460 | 0.418065 | ||||||||
\(916\) | 6.08192 | 0.200952 | ||||||||
\(917\) | 1.81515 | 0.0599416 | ||||||||
\(918\) | −8.06721 | −0.266258 | ||||||||
\(919\) | 36.1660 | 1.19301 | 0.596504 | − | 0.802610i | \(-0.296556\pi\) | ||||
0.596504 | + | 0.802610i | \(0.296556\pi\) | |||||||
\(920\) | −1.40322 | −0.0462628 | ||||||||
\(921\) | 53.5088 | 1.76318 | ||||||||
\(922\) | −42.0478 | −1.38477 | ||||||||
\(923\) | −6.14231 | −0.202177 | ||||||||
\(924\) | 6.00549 | 0.197566 | ||||||||
\(925\) | −33.6520 | −1.10647 | ||||||||
\(926\) | 31.4541 | 1.03365 | ||||||||
\(927\) | −1.74406 | −0.0572823 | ||||||||
\(928\) | −0.0835727 | −0.00274341 | ||||||||
\(929\) | −15.1301 | −0.496403 | −0.248202 | − | 0.968708i | \(-0.579840\pi\) | ||||
−0.248202 | + | 0.968708i | \(0.579840\pi\) | |||||||
\(930\) | 2.52420 | 0.0827719 | ||||||||
\(931\) | 8.80680 | 0.288631 | ||||||||
\(932\) | −15.6170 | −0.511551 | ||||||||
\(933\) | −3.84047 | −0.125731 | ||||||||
\(934\) | −11.1868 | −0.366044 | ||||||||
\(935\) | −4.35009 | −0.142263 | ||||||||
\(936\) | 1.65040 | 0.0539449 | ||||||||
\(937\) | −6.84090 | −0.223482 | −0.111741 | − | 0.993737i | \(-0.535643\pi\) | ||||
−0.111741 | + | 0.993737i | \(0.535643\pi\) | |||||||
\(938\) | −10.5970 | −0.346003 | ||||||||
\(939\) | −36.2320 | −1.18239 | ||||||||
\(940\) | 2.90344 | 0.0946997 | ||||||||
\(941\) | 41.9025 | 1.36598 | 0.682991 | − | 0.730427i | \(-0.260679\pi\) | ||||
0.682991 | + | 0.730427i | \(0.260679\pi\) | |||||||
\(942\) | 46.5908 | 1.51801 | ||||||||
\(943\) | 8.01509 | 0.261007 | ||||||||
\(944\) | 0.0652730 | 0.00212445 | ||||||||
\(945\) | 11.5183 | 0.374689 | ||||||||
\(946\) | −14.7720 | −0.480278 | ||||||||
\(947\) | −9.48720 | −0.308293 | −0.154146 | − | 0.988048i | \(-0.549263\pi\) | ||||
−0.154146 | + | 0.988048i | \(0.549263\pi\) | |||||||
\(948\) | −19.6043 | −0.636717 | ||||||||
\(949\) | −33.4254 | −1.08503 | ||||||||
\(950\) | −7.20420 | −0.233735 | ||||||||
\(951\) | −0.794182 | −0.0257531 | ||||||||
\(952\) | 3.23809 | 0.104947 | ||||||||
\(953\) | 13.3640 | 0.432904 | 0.216452 | − | 0.976293i | \(-0.430552\pi\) | ||||
0.216452 | + | 0.976293i | \(0.430552\pi\) | |||||||
\(954\) | 1.60275 | 0.0518909 | ||||||||
\(955\) | 17.3209 | 0.560492 | ||||||||
\(956\) | −26.8031 | −0.866874 | ||||||||
\(957\) | −0.276503 | −0.00893808 | ||||||||
\(958\) | 17.8540 | 0.576838 | ||||||||
\(959\) | −11.9178 | −0.384846 | ||||||||
\(960\) | 2.67156 | 0.0862243 | ||||||||
\(961\) | −30.1073 | −0.971202 | ||||||||
\(962\) | 29.3297 | 0.945628 | ||||||||
\(963\) | −6.08454 | −0.196072 | ||||||||
\(964\) | 12.3017 | 0.396210 | ||||||||
\(965\) | 0.879754 | 0.0283203 | ||||||||
\(966\) | 3.45583 | 0.111190 | ||||||||
\(967\) | −2.23780 | −0.0719629 | −0.0359815 | − | 0.999352i | \(-0.511456\pi\) | ||||
−0.0359815 | + | 0.999352i | \(0.511456\pi\) | |||||||
\(968\) | 7.98010 | 0.256490 | ||||||||
\(969\) | 8.07271 | 0.259333 | ||||||||
\(970\) | −13.1275 | −0.421498 | ||||||||
\(971\) | −51.6308 | −1.65691 | −0.828455 | − | 0.560056i | \(-0.810780\pi\) | ||||
−0.828455 | + | 0.560056i | \(0.810780\pi\) | |||||||
\(972\) | 6.39363 | 0.205076 | ||||||||
\(973\) | −23.6721 | −0.758893 | ||||||||
\(974\) | 32.0774 | 1.02783 | ||||||||
\(975\) | −15.2440 | −0.488200 | ||||||||
\(976\) | 4.73357 | 0.151518 | ||||||||
\(977\) | 51.8402 | 1.65852 | 0.829258 | − | 0.558866i | \(-0.188763\pi\) | ||||
0.829258 | + | 0.558866i | \(0.188763\pi\) | |||||||
\(978\) | −23.8325 | −0.762079 | ||||||||
\(979\) | 24.0443 | 0.768460 | ||||||||
\(980\) | 5.19925 | 0.166084 | ||||||||
\(981\) | −6.42236 | −0.205050 | ||||||||
\(982\) | 20.4438 | 0.652387 | ||||||||
\(983\) | 29.9246 | 0.954446 | 0.477223 | − | 0.878782i | \(-0.341643\pi\) | ||||
0.477223 | + | 0.878782i | \(0.341643\pi\) | |||||||
\(984\) | −15.2598 | −0.486464 | ||||||||
\(985\) | 15.3859 | 0.490237 | ||||||||
\(986\) | −0.149087 | −0.00474790 | ||||||||
\(987\) | −7.15054 | −0.227604 | ||||||||
\(988\) | 6.27889 | 0.199758 | ||||||||
\(989\) | −8.50045 | −0.270299 | ||||||||
\(990\) | 1.52346 | 0.0484189 | ||||||||
\(991\) | −5.02756 | −0.159706 | −0.0798528 | − | 0.996807i | \(-0.525445\pi\) | ||||
−0.0798528 | + | 0.996807i | \(0.525445\pi\) | |||||||
\(992\) | 0.944842 | 0.0299988 | ||||||||
\(993\) | 17.3771 | 0.551447 | ||||||||
\(994\) | 4.22052 | 0.133867 | ||||||||
\(995\) | 27.2726 | 0.864600 | ||||||||
\(996\) | −16.9774 | −0.537950 | ||||||||
\(997\) | 38.3953 | 1.21599 | 0.607995 | − | 0.793941i | \(-0.291974\pi\) | ||||
0.607995 | + | 0.793941i | \(0.291974\pi\) | |||||||
\(998\) | 41.0082 | 1.29809 | ||||||||
\(999\) | 50.2084 | 1.58852 |
(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 | 6026.2.a.h.1.6 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.h.1.6 | ✓ | 24 | 1.1 | even | 1 | trivial |