Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.98740 | 1.40530 | 0.702652 | − | 0.711534i | \(-0.251999\pi\) | ||||
0.702652 | + | 0.711534i | \(0.251999\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.94976 | 0.974878 | ||||||||
\(5\) | −1.69625 | −0.758588 | −0.379294 | − | 0.925276i | \(-0.623833\pi\) | ||||
−0.379294 | + | 0.925276i | \(0.623833\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.47319 | 0.556812 | 0.278406 | − | 0.960463i | \(-0.410194\pi\) | ||||
0.278406 | + | 0.960463i | \(0.410194\pi\) | |||||||
\(8\) | −0.0998540 | −0.0353037 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.37113 | −1.06605 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.08303 | 0.300378 | 0.150189 | − | 0.988657i | \(-0.452012\pi\) | ||||
0.150189 | + | 0.988657i | \(0.452012\pi\) | |||||||
\(14\) | 2.92781 | 0.782490 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.09796 | −1.02449 | ||||||||
\(17\) | 6.50371 | 1.57738 | 0.788691 | − | 0.614790i | \(-0.210759\pi\) | ||||
0.788691 | + | 0.614790i | \(0.210759\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.99017 | 0.456577 | 0.228288 | − | 0.973594i | \(-0.426687\pi\) | ||||
0.228288 | + | 0.973594i | \(0.426687\pi\) | |||||||
\(20\) | −3.30728 | −0.739531 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.98740 | −0.423715 | ||||||||
\(23\) | 4.59431 | 0.957980 | 0.478990 | − | 0.877820i | \(-0.341003\pi\) | ||||
0.478990 | + | 0.877820i | \(0.341003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.12272 | −0.424544 | ||||||||
\(26\) | 2.15241 | 0.422122 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.87235 | 0.542824 | ||||||||
\(29\) | −5.22348 | −0.969976 | −0.484988 | − | 0.874521i | \(-0.661176\pi\) | ||||
−0.484988 | + | 0.874521i | \(0.661176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.02011 | 0.901638 | 0.450819 | − | 0.892615i | \(-0.351132\pi\) | ||||
0.450819 | + | 0.892615i | \(0.351132\pi\) | |||||||
\(32\) | −7.94458 | −1.40442 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.9255 | 2.21670 | ||||||||
\(35\) | −2.49890 | −0.422391 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.631601 | −0.103835 | −0.0519173 | − | 0.998651i | \(-0.516533\pi\) | ||||
−0.0519173 | + | 0.998651i | \(0.516533\pi\) | |||||||
\(38\) | 3.95527 | 0.641629 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.169378 | 0.0267810 | ||||||||
\(41\) | 4.72010 | 0.737156 | 0.368578 | − | 0.929597i | \(-0.379845\pi\) | ||||
0.368578 | + | 0.929597i | \(0.379845\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.586969 | −0.0895119 | −0.0447559 | − | 0.998998i | \(-0.514251\pi\) | ||||
−0.0447559 | + | 0.998998i | \(0.514251\pi\) | |||||||
\(44\) | −1.94976 | −0.293937 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.13073 | 1.34625 | ||||||||
\(47\) | 5.79589 | 0.845417 | 0.422709 | − | 0.906266i | \(-0.361079\pi\) | ||||
0.422709 | + | 0.906266i | \(0.361079\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.82972 | −0.689960 | ||||||||
\(50\) | −4.21870 | −0.596614 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.11164 | 0.292832 | ||||||||
\(53\) | −11.0820 | −1.52223 | −0.761115 | − | 0.648617i | \(-0.775348\pi\) | ||||
−0.761115 | + | 0.648617i | \(0.775348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.69625 | 0.228723 | ||||||||
\(56\) | −0.147104 | −0.0196575 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.3811 | −1.36311 | ||||||||
\(59\) | 13.9032 | 1.81004 | 0.905019 | − | 0.425371i | \(-0.139856\pi\) | ||||
0.905019 | + | 0.425371i | \(0.139856\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 9.97696 | 1.26707 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.59313 | −0.949141 | ||||||||
\(65\) | −1.83709 | −0.227863 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.913716 | 0.111628 | 0.0558141 | − | 0.998441i | \(-0.482225\pi\) | ||||
0.0558141 | + | 0.998441i | \(0.482225\pi\) | |||||||
\(68\) | 12.6807 | 1.53776 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.96631 | −0.593588 | ||||||||
\(71\) | 10.6391 | 1.26263 | 0.631315 | − | 0.775526i | \(-0.282515\pi\) | ||||
0.631315 | + | 0.775526i | \(0.282515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.55816 | −0.533492 | −0.266746 | − | 0.963767i | \(-0.585949\pi\) | ||||
−0.266746 | + | 0.963767i | \(0.585949\pi\) | |||||||
\(74\) | −1.25524 | −0.145919 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.88035 | 0.445107 | ||||||||
\(77\) | −1.47319 | −0.167885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.39890 | −0.607424 | −0.303712 | − | 0.952764i | \(-0.598226\pi\) | ||||
−0.303712 | + | 0.952764i | \(0.598226\pi\) | |||||||
\(80\) | 6.95119 | 0.777166 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.38072 | 1.03593 | ||||||||
\(83\) | 17.4446 | 1.91479 | 0.957395 | − | 0.288780i | \(-0.0932496\pi\) | ||||
0.957395 | + | 0.288780i | \(0.0932496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.0319 | −1.19658 | ||||||||
\(86\) | −1.16654 | −0.125791 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0998540 | 0.0106445 | ||||||||
\(89\) | 8.43337 | 0.893936 | 0.446968 | − | 0.894550i | \(-0.352504\pi\) | ||||
0.446968 | + | 0.894550i | \(0.352504\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.59550 | 0.167254 | ||||||||
\(92\) | 8.95778 | 0.933913 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.5187 | 1.18807 | ||||||||
\(95\) | −3.37584 | −0.346354 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.31582 | 0.844343 | 0.422172 | − | 0.906516i | \(-0.361268\pi\) | ||||
0.422172 | + | 0.906516i | \(0.361268\pi\) | |||||||
\(98\) | −9.59859 | −0.969604 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.13879 | −0.413879 | ||||||||
\(101\) | 10.8424 | 1.07886 | 0.539429 | − | 0.842031i | \(-0.318640\pi\) | ||||
0.539429 | + | 0.842031i | \(0.318640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.2652 | 1.70119 | 0.850596 | − | 0.525819i | \(-0.176241\pi\) | ||||
0.850596 | + | 0.525819i | \(0.176241\pi\) | |||||||
\(104\) | −0.108145 | −0.0106044 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.0244 | −2.13920 | ||||||||
\(107\) | 6.97016 | 0.673831 | 0.336916 | − | 0.941535i | \(-0.390616\pi\) | ||||
0.336916 | + | 0.941535i | \(0.390616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.70623 | −0.929688 | −0.464844 | − | 0.885393i | \(-0.653890\pi\) | ||||
−0.464844 | + | 0.885393i | \(0.653890\pi\) | |||||||
\(110\) | 3.37113 | 0.321425 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.03706 | −0.570449 | ||||||||
\(113\) | 12.9233 | 1.21572 | 0.607860 | − | 0.794044i | \(-0.292028\pi\) | ||||
0.607860 | + | 0.794044i | \(0.292028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.79312 | −0.726712 | ||||||||
\(116\) | −10.1845 | −0.945609 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 27.6312 | 2.54365 | ||||||||
\(119\) | 9.58118 | 0.878305 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.98740 | 0.179931 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.78798 | 0.878987 | ||||||||
\(125\) | 12.0819 | 1.08064 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3829 | 1.01007 | 0.505033 | − | 0.863100i | \(-0.331480\pi\) | ||||
0.505033 | + | 0.863100i | \(0.331480\pi\) | |||||||
\(128\) | 0.798580 | 0.0705852 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.65103 | −0.320216 | ||||||||
\(131\) | 0.364456 | 0.0318426 | 0.0159213 | − | 0.999873i | \(-0.494932\pi\) | ||||
0.0159213 | + | 0.999873i | \(0.494932\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.93189 | 0.254227 | ||||||||
\(134\) | 1.81592 | 0.156872 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.649422 | −0.0556874 | ||||||||
\(137\) | −12.2799 | −1.04914 | −0.524570 | − | 0.851367i | \(-0.675774\pi\) | ||||
−0.524570 | + | 0.851367i | \(0.675774\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.88780 | −0.160121 | −0.0800605 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800605 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(140\) | −4.87224 | −0.411780 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 21.1442 | 1.77438 | ||||||||
\(143\) | −1.08303 | −0.0905672 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.86036 | 0.735813 | ||||||||
\(146\) | −9.05889 | −0.749719 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.23147 | −0.101226 | ||||||||
\(149\) | −5.45639 | −0.447005 | −0.223503 | − | 0.974703i | \(-0.571749\pi\) | ||||
−0.223503 | + | 0.974703i | \(0.571749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.61465 | −0.131398 | −0.0656992 | − | 0.997839i | \(-0.520928\pi\) | ||||
−0.0656992 | + | 0.997839i | \(0.520928\pi\) | |||||||
\(152\) | −0.198727 | −0.0161189 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.92781 | −0.235930 | ||||||||
\(155\) | −8.51538 | −0.683971 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.70492 | −0.535111 | −0.267556 | − | 0.963542i | \(-0.586216\pi\) | ||||
−0.267556 | + | 0.963542i | \(0.586216\pi\) | |||||||
\(158\) | −10.7298 | −0.853615 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.4760 | 1.06537 | ||||||||
\(161\) | 6.76827 | 0.533415 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.9210 | 1.56033 | 0.780166 | − | 0.625573i | \(-0.215135\pi\) | ||||
0.780166 | + | 0.625573i | \(0.215135\pi\) | |||||||
\(164\) | 9.20304 | 0.718637 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 34.6693 | 2.69086 | ||||||||
\(167\) | −1.84036 | −0.142411 | −0.0712055 | − | 0.997462i | \(-0.522685\pi\) | ||||
−0.0712055 | + | 0.997462i | \(0.522685\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8271 | −0.909773 | ||||||||
\(170\) | −21.9249 | −1.68156 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.14445 | −0.0872632 | ||||||||
\(173\) | 13.1406 | 0.999065 | 0.499532 | − | 0.866295i | \(-0.333505\pi\) | ||||
0.499532 | + | 0.866295i | \(0.333505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.12716 | −0.236391 | ||||||||
\(176\) | 4.09796 | 0.308896 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.7605 | 1.25625 | ||||||||
\(179\) | −14.9918 | −1.12054 | −0.560268 | − | 0.828311i | \(-0.689302\pi\) | ||||
−0.560268 | + | 0.828311i | \(0.689302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.46504 | 0.331884 | 0.165942 | − | 0.986136i | \(-0.446934\pi\) | ||||
0.165942 | + | 0.986136i | \(0.446934\pi\) | |||||||
\(182\) | 3.17090 | 0.235042 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.458760 | −0.0338202 | ||||||||
\(185\) | 1.07136 | 0.0787677 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.50371 | −0.475598 | ||||||||
\(188\) | 11.3006 | 0.824179 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.70914 | −0.486732 | ||||||||
\(191\) | 6.85168 | 0.495770 | 0.247885 | − | 0.968789i | \(-0.420264\pi\) | ||||
0.247885 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.98331 | −0.286725 | −0.143362 | − | 0.989670i | \(-0.545791\pi\) | ||||
−0.143362 | + | 0.989670i | \(0.545791\pi\) | |||||||
\(194\) | 16.5268 | 1.18656 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.41678 | −0.672627 | ||||||||
\(197\) | 7.04258 | 0.501763 | 0.250882 | − | 0.968018i | \(-0.419280\pi\) | ||||
0.250882 | + | 0.968018i | \(0.419280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.78368 | 0.197330 | 0.0986651 | − | 0.995121i | \(-0.468543\pi\) | ||||
0.0986651 | + | 0.995121i | \(0.468543\pi\) | |||||||
\(200\) | 0.211962 | 0.0149880 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.5481 | 1.51612 | ||||||||
\(203\) | −7.69516 | −0.540095 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00649 | −0.559197 | ||||||||
\(206\) | 34.3129 | 2.39069 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.43820 | −0.307734 | ||||||||
\(209\) | −1.99017 | −0.137663 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.15155 | −0.0792758 | −0.0396379 | − | 0.999214i | \(-0.512620\pi\) | ||||
−0.0396379 | + | 0.999214i | \(0.512620\pi\) | |||||||
\(212\) | −21.6072 | −1.48399 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.8525 | 0.946937 | ||||||||
\(215\) | 0.995648 | 0.0679026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.39555 | 0.502043 | ||||||||
\(218\) | −19.2902 | −1.30649 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.30728 | 0.222977 | ||||||||
\(221\) | 7.04369 | 0.473810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4758 | −0.835440 | −0.417720 | − | 0.908576i | \(-0.637171\pi\) | ||||
−0.417720 | + | 0.908576i | \(0.637171\pi\) | |||||||
\(224\) | −11.7038 | −0.781996 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25.6837 | 1.70846 | ||||||||
\(227\) | −11.9482 | −0.793029 | −0.396515 | − | 0.918028i | \(-0.629780\pi\) | ||||
−0.396515 | + | 0.918028i | \(0.629780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.23617 | 0.0816887 | 0.0408444 | − | 0.999166i | \(-0.486995\pi\) | ||||
0.0408444 | + | 0.999166i | \(0.486995\pi\) | |||||||
\(230\) | −15.4880 | −1.02125 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.521586 | 0.0342438 | ||||||||
\(233\) | 7.40871 | 0.485361 | 0.242680 | − | 0.970106i | \(-0.421973\pi\) | ||||
0.242680 | + | 0.970106i | \(0.421973\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.83130 | −0.641323 | ||||||||
\(236\) | 27.1078 | 1.76457 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 19.0416 | 1.23429 | ||||||||
\(239\) | 14.1248 | 0.913656 | 0.456828 | − | 0.889555i | \(-0.348986\pi\) | ||||
0.456828 | + | 0.889555i | \(0.348986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.1006 | 0.715053 | 0.357526 | − | 0.933903i | \(-0.383620\pi\) | ||||
0.357526 | + | 0.933903i | \(0.383620\pi\) | |||||||
\(242\) | 1.98740 | 0.127755 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.94976 | 0.124820 | ||||||||
\(245\) | 8.19244 | 0.523396 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.15541 | 0.137145 | ||||||||
\(248\) | −0.501278 | −0.0318312 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 24.0117 | 1.51863 | ||||||||
\(251\) | −10.9503 | −0.691174 | −0.345587 | − | 0.938387i | \(-0.612320\pi\) | ||||
−0.345587 | + | 0.938387i | \(0.612320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.59431 | −0.288842 | ||||||||
\(254\) | 22.6223 | 1.41945 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.7734 | 1.04833 | ||||||||
\(257\) | −31.7877 | −1.98286 | −0.991432 | − | 0.130623i | \(-0.958302\pi\) | ||||
−0.991432 | + | 0.130623i | \(0.958302\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.930467 | −0.0578164 | ||||||||
\(260\) | −3.58188 | −0.222138 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.724319 | 0.0447486 | ||||||||
\(263\) | 27.8343 | 1.71633 | 0.858167 | − | 0.513371i | \(-0.171603\pi\) | ||||
0.858167 | + | 0.513371i | \(0.171603\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.7979 | 1.15475 | ||||||||
\(266\) | 5.82684 | 0.357267 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.78152 | 0.108824 | ||||||||
\(269\) | 20.4023 | 1.24395 | 0.621974 | − | 0.783038i | \(-0.286331\pi\) | ||||
0.621974 | + | 0.783038i | \(0.286331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.2291 | −1.65405 | −0.827026 | − | 0.562164i | \(-0.809969\pi\) | ||||
−0.827026 | + | 0.562164i | \(0.809969\pi\) | |||||||
\(272\) | −26.6520 | −1.61601 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.4050 | −1.47436 | ||||||||
\(275\) | 2.12272 | 0.128005 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.0515 | −1.56528 | −0.782640 | − | 0.622474i | \(-0.786128\pi\) | ||||
−0.782640 | + | 0.622474i | \(0.786128\pi\) | |||||||
\(278\) | −3.75181 | −0.225019 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.249525 | 0.0149120 | ||||||||
\(281\) | −19.7880 | −1.18046 | −0.590228 | − | 0.807237i | \(-0.700962\pi\) | ||||
−0.590228 | + | 0.807237i | \(0.700962\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.53124 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(284\) | 20.7437 | 1.23091 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.15241 | −0.127274 | ||||||||
\(287\) | 6.95359 | 0.410457 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.2983 | 1.48813 | ||||||||
\(290\) | 17.6091 | 1.03404 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.88731 | −0.520090 | ||||||||
\(293\) | −32.5305 | −1.90045 | −0.950226 | − | 0.311561i | \(-0.899148\pi\) | ||||
−0.950226 | + | 0.311561i | \(0.899148\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.5833 | −1.37307 | ||||||||
\(296\) | 0.0630679 | 0.00366575 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.8440 | −0.628178 | ||||||||
\(299\) | 4.97576 | 0.287756 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.864714 | −0.0498413 | ||||||||
\(302\) | −3.20896 | −0.184655 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.15565 | −0.467759 | ||||||||
\(305\) | −1.69625 | −0.0971272 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.98148 | −0.512600 | −0.256300 | − | 0.966597i | \(-0.582503\pi\) | ||||
−0.256300 | + | 0.966597i | \(0.582503\pi\) | |||||||
\(308\) | −2.87235 | −0.163668 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.9235 | −0.961188 | ||||||||
\(311\) | −21.0590 | −1.19414 | −0.597072 | − | 0.802188i | \(-0.703669\pi\) | ||||
−0.597072 | + | 0.802188i | \(0.703669\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0791 | 1.02189 | 0.510946 | − | 0.859613i | \(-0.329295\pi\) | ||||
0.510946 | + | 0.859613i | \(0.329295\pi\) | |||||||
\(314\) | −13.3254 | −0.751994 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.5265 | −0.592164 | ||||||||
\(317\) | −29.6991 | −1.66807 | −0.834034 | − | 0.551713i | \(-0.813974\pi\) | ||||
−0.834034 | + | 0.551713i | \(0.813974\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.22348 | 0.292459 | ||||||||
\(320\) | 12.8799 | 0.720007 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.4513 | 0.749610 | ||||||||
\(323\) | 12.9435 | 0.720196 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.29896 | −0.127524 | ||||||||
\(326\) | 39.5909 | 2.19274 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.471321 | −0.0260243 | ||||||||
\(329\) | 8.53842 | 0.470739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.68863 | −0.422605 | −0.211303 | − | 0.977421i | \(-0.567771\pi\) | ||||
−0.211303 | + | 0.977421i | \(0.567771\pi\) | |||||||
\(332\) | 34.0127 | 1.86669 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.65752 | −0.200131 | ||||||||
\(335\) | −1.54990 | −0.0846798 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.8639 | 1.19100 | 0.595500 | − | 0.803355i | \(-0.296954\pi\) | ||||
0.595500 | + | 0.803355i | \(0.296954\pi\) | |||||||
\(338\) | −23.5051 | −1.27851 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21.5096 | −1.16652 | ||||||||
\(341\) | −5.02011 | −0.271854 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4274 | −0.940990 | ||||||||
\(344\) | 0.0586112 | 0.00316010 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.1157 | 1.40399 | ||||||||
\(347\) | 13.3499 | 0.716659 | 0.358329 | − | 0.933595i | \(-0.383346\pi\) | ||||
0.358329 | + | 0.933595i | \(0.383346\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.9200 | 0.745119 | 0.372559 | − | 0.928008i | \(-0.378480\pi\) | ||||
0.372559 | + | 0.928008i | \(0.378480\pi\) | |||||||
\(350\) | −6.21492 | −0.332202 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.94458 | 0.423448 | ||||||||
\(353\) | 16.7802 | 0.893118 | 0.446559 | − | 0.894754i | \(-0.352649\pi\) | ||||
0.446559 | + | 0.894754i | \(0.352649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.0466 | −0.957816 | ||||||||
\(356\) | 16.4430 | 0.871479 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.7946 | −1.57469 | ||||||||
\(359\) | −5.31077 | −0.280291 | −0.140146 | − | 0.990131i | \(-0.544757\pi\) | ||||
−0.140146 | + | 0.990131i | \(0.544757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0392 | −0.791538 | ||||||||
\(362\) | 8.87381 | 0.466397 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.11084 | 0.163052 | ||||||||
\(365\) | 7.73180 | 0.404701 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.0741 | −1.41325 | −0.706627 | − | 0.707586i | \(-0.749784\pi\) | ||||
−0.706627 | + | 0.707586i | \(0.749784\pi\) | |||||||
\(368\) | −18.8273 | −0.981441 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.12921 | 0.110693 | ||||||||
\(371\) | −16.3259 | −0.847596 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.5095 | −1.06194 | −0.530971 | − | 0.847390i | \(-0.678173\pi\) | ||||
−0.530971 | + | 0.847390i | \(0.678173\pi\) | |||||||
\(374\) | −12.9255 | −0.668360 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.578743 | −0.0298464 | ||||||||
\(377\) | −5.65717 | −0.291359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.93911 | −0.510538 | −0.255269 | − | 0.966870i | \(-0.582164\pi\) | ||||
−0.255269 | + | 0.966870i | \(0.582164\pi\) | |||||||
\(380\) | −6.58206 | −0.337653 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13.6170 | 0.696707 | ||||||||
\(383\) | −23.3964 | −1.19550 | −0.597751 | − | 0.801682i | \(-0.703939\pi\) | ||||
−0.597751 | + | 0.801682i | \(0.703939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.49890 | 0.127356 | ||||||||
\(386\) | −7.91642 | −0.402935 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.2138 | 0.823132 | ||||||||
\(389\) | 9.75823 | 0.494762 | 0.247381 | − | 0.968918i | \(-0.420430\pi\) | ||||
0.247381 | + | 0.968918i | \(0.420430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.8801 | 1.51110 | ||||||||
\(392\) | 0.482267 | 0.0243582 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.9964 | 0.705129 | ||||||||
\(395\) | 9.15791 | 0.460784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.0300 | −1.50716 | −0.753582 | − | 0.657354i | \(-0.771676\pi\) | ||||
−0.753582 | + | 0.657354i | \(0.771676\pi\) | |||||||
\(398\) | 5.53229 | 0.277309 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.69883 | 0.434942 | ||||||||
\(401\) | 3.91307 | 0.195409 | 0.0977046 | − | 0.995215i | \(-0.468850\pi\) | ||||
0.0977046 | + | 0.995215i | \(0.468850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.43691 | 0.270832 | ||||||||
\(404\) | 21.1400 | 1.05175 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.2934 | −0.758997 | ||||||||
\(407\) | 0.631601 | 0.0313073 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9082 | 0.687717 | 0.343858 | − | 0.939022i | \(-0.388266\pi\) | ||||
0.343858 | + | 0.939022i | \(0.388266\pi\) | |||||||
\(410\) | −15.9121 | −0.785842 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 33.6630 | 1.65846 | ||||||||
\(413\) | 20.4820 | 1.00785 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.5904 | −1.45254 | ||||||||
\(416\) | −8.60419 | −0.421855 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.95527 | −0.193458 | ||||||||
\(419\) | −24.4247 | −1.19322 | −0.596612 | − | 0.802530i | \(-0.703487\pi\) | ||||
−0.596612 | + | 0.802530i | \(0.703487\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4233 | 0.556735 | 0.278368 | − | 0.960475i | \(-0.410207\pi\) | ||||
0.278368 | + | 0.960475i | \(0.410207\pi\) | |||||||
\(422\) | −2.28858 | −0.111407 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.10658 | 0.0537404 | ||||||||
\(425\) | −13.8056 | −0.669668 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.47319 | 0.0712925 | ||||||||
\(428\) | 13.5901 | 0.656903 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.97875 | 0.0954238 | ||||||||
\(431\) | −36.0825 | −1.73803 | −0.869016 | − | 0.494785i | \(-0.835247\pi\) | ||||
−0.869016 | + | 0.494785i | \(0.835247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.63856 | 0.463200 | 0.231600 | − | 0.972811i | \(-0.425604\pi\) | ||||
0.231600 | + | 0.972811i | \(0.425604\pi\) | |||||||
\(434\) | 14.6979 | 0.705523 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.9248 | −0.906333 | ||||||||
\(437\) | 9.14346 | 0.437391 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.32711 | −0.206522 | −0.103261 | − | 0.994654i | \(-0.532928\pi\) | ||||
−0.103261 | + | 0.994654i | \(0.532928\pi\) | |||||||
\(440\) | −0.169378 | −0.00807477 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.9986 | 0.665847 | ||||||||
\(443\) | 17.6111 | 0.836727 | 0.418364 | − | 0.908280i | \(-0.362604\pi\) | ||||
0.418364 | + | 0.908280i | \(0.362604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3051 | −0.678129 | ||||||||
\(446\) | −24.7943 | −1.17405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.1861 | −0.528493 | ||||||||
\(449\) | −13.5885 | −0.641283 | −0.320641 | − | 0.947201i | \(-0.603898\pi\) | ||||
−0.320641 | + | 0.947201i | \(0.603898\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.72010 | −0.222261 | ||||||||
\(452\) | 25.1973 | 1.18518 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.7458 | −1.11445 | ||||||||
\(455\) | −2.70637 | −0.126877 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9343 | 0.838932 | 0.419466 | − | 0.907771i | \(-0.362217\pi\) | ||||
0.419466 | + | 0.907771i | \(0.362217\pi\) | |||||||
\(458\) | 2.45677 | 0.114797 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.1947 | −0.708455 | ||||||||
\(461\) | −1.41379 | −0.0658469 | −0.0329235 | − | 0.999458i | \(-0.510482\pi\) | ||||
−0.0329235 | + | 0.999458i | \(0.510482\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.1184 | 0.795561 | 0.397780 | − | 0.917481i | \(-0.369781\pi\) | ||||
0.397780 | + | 0.917481i | \(0.369781\pi\) | |||||||
\(464\) | 21.4056 | 0.993732 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.7241 | 0.682079 | ||||||||
\(467\) | −35.8427 | −1.65860 | −0.829302 | − | 0.558801i | \(-0.811262\pi\) | ||||
−0.829302 | + | 0.558801i | \(0.811262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.34607 | 0.0621560 | ||||||||
\(470\) | −19.5387 | −0.901254 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.38829 | −0.0639011 | ||||||||
\(473\) | 0.586969 | 0.0269888 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.22458 | −0.193837 | ||||||||
\(476\) | 18.6810 | 0.856241 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.0716 | 1.28396 | ||||||||
\(479\) | 29.9152 | 1.36686 | 0.683430 | − | 0.730016i | \(-0.260488\pi\) | ||||
0.683430 | + | 0.730016i | \(0.260488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.684041 | −0.0311896 | ||||||||
\(482\) | 22.0613 | 1.00487 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.94976 | 0.0886253 | ||||||||
\(485\) | −14.1057 | −0.640509 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.4977 | 0.883525 | 0.441763 | − | 0.897132i | \(-0.354353\pi\) | ||||
0.441763 | + | 0.897132i | \(0.354353\pi\) | |||||||
\(488\) | −0.0998540 | −0.00452018 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.2816 | 0.735530 | ||||||||
\(491\) | 23.3492 | 1.05374 | 0.526868 | − | 0.849947i | \(-0.323366\pi\) | ||||
0.526868 | + | 0.849947i | \(0.323366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.9720 | −1.53002 | ||||||||
\(494\) | 4.28366 | 0.192731 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −20.5722 | −0.923719 | ||||||||
\(497\) | 15.6734 | 0.703048 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7542 | −0.839551 | −0.419776 | − | 0.907628i | \(-0.637891\pi\) | ||||
−0.419776 | + | 0.907628i | \(0.637891\pi\) | |||||||
\(500\) | 23.5569 | 1.05349 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.7625 | −0.971309 | ||||||||
\(503\) | 20.6970 | 0.922833 | 0.461417 | − | 0.887184i | \(-0.347341\pi\) | ||||
0.461417 | + | 0.887184i | \(0.347341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.3914 | −0.818408 | ||||||||
\(506\) | −9.13073 | −0.405910 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.1938 | 0.984691 | ||||||||
\(509\) | 22.8797 | 1.01413 | 0.507063 | − | 0.861909i | \(-0.330731\pi\) | ||||
0.507063 | + | 0.861909i | \(0.330731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.71502 | −0.297055 | ||||||||
\(512\) | 31.7382 | 1.40264 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −63.1749 | −2.78653 | ||||||||
\(515\) | −29.2862 | −1.29050 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.79589 | −0.254903 | ||||||||
\(518\) | −1.84921 | −0.0812496 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.183441 | 0.00804441 | ||||||||
\(521\) | −13.6390 | −0.597534 | −0.298767 | − | 0.954326i | \(-0.596575\pi\) | ||||
−0.298767 | + | 0.954326i | \(0.596575\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8285 | 1.04195 | 0.520974 | − | 0.853572i | \(-0.325569\pi\) | ||||
0.520974 | + | 0.853572i | \(0.325569\pi\) | |||||||
\(524\) | 0.710600 | 0.0310427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 55.3178 | 2.41197 | ||||||||
\(527\) | 32.6493 | 1.42223 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.89233 | −0.0822753 | ||||||||
\(530\) | 37.3589 | 1.62277 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.71648 | 0.247841 | ||||||||
\(533\) | 5.11199 | 0.221425 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.8232 | −0.511160 | ||||||||
\(536\) | −0.0912382 | −0.00394089 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.5474 | 1.74812 | ||||||||
\(539\) | 4.82972 | 0.208031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.6842 | −1.40520 | −0.702602 | − | 0.711583i | \(-0.747979\pi\) | ||||
−0.702602 | + | 0.711583i | \(0.747979\pi\) | |||||||
\(542\) | −54.1151 | −2.32444 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −51.6693 | −2.21530 | ||||||||
\(545\) | 16.4642 | 0.705250 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.32193 | −0.355820 | −0.177910 | − | 0.984047i | \(-0.556934\pi\) | ||||
−0.177910 | + | 0.984047i | \(0.556934\pi\) | |||||||
\(548\) | −23.9428 | −1.02278 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.21870 | 0.179886 | ||||||||
\(551\) | −10.3956 | −0.442869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.95359 | −0.338221 | ||||||||
\(554\) | −51.7747 | −2.19969 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.68075 | −0.156098 | ||||||||
\(557\) | 12.5811 | 0.533077 | 0.266539 | − | 0.963824i | \(-0.414120\pi\) | ||||
0.266539 | + | 0.963824i | \(0.414120\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.635703 | −0.0268874 | ||||||||
\(560\) | 10.2404 | 0.432736 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −39.3267 | −1.65890 | ||||||||
\(563\) | 42.2063 | 1.77878 | 0.889391 | − | 0.457147i | \(-0.151129\pi\) | ||||
0.889391 | + | 0.457147i | \(0.151129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.9212 | −0.922231 | ||||||||
\(566\) | −10.9928 | −0.462061 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.06236 | −0.0445755 | ||||||||
\(569\) | 5.95645 | 0.249707 | 0.124854 | − | 0.992175i | \(-0.460154\pi\) | ||||
0.124854 | + | 0.992175i | \(0.460154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.819100 | −0.0342783 | −0.0171391 | − | 0.999853i | \(-0.505456\pi\) | ||||
−0.0171391 | + | 0.999853i | \(0.505456\pi\) | |||||||
\(572\) | −2.11164 | −0.0882920 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.8196 | 0.576817 | ||||||||
\(575\) | −9.75244 | −0.406705 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8580 | −0.493655 | −0.246827 | − | 0.969059i | \(-0.579388\pi\) | ||||
−0.246827 | + | 0.969059i | \(0.579388\pi\) | |||||||
\(578\) | 50.2777 | 2.09128 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.2755 | 0.717328 | ||||||||
\(581\) | 25.6991 | 1.06618 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.0820 | 0.458970 | ||||||||
\(584\) | 0.455151 | 0.0188343 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −64.6511 | −2.67071 | ||||||||
\(587\) | −28.0996 | −1.15979 | −0.579897 | − | 0.814690i | \(-0.696907\pi\) | ||||
−0.579897 | + | 0.814690i | \(0.696907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.99087 | 0.411667 | ||||||||
\(590\) | −46.8695 | −1.92959 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.58828 | 0.106378 | ||||||||
\(593\) | 18.5874 | 0.763291 | 0.381646 | − | 0.924309i | \(-0.375357\pi\) | ||||
0.381646 | + | 0.924309i | \(0.375357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.2521 | −0.666272 | ||||||||
\(596\) | −10.6386 | −0.435776 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.88882 | 0.404384 | ||||||||
\(599\) | 32.2331 | 1.31701 | 0.658504 | − | 0.752577i | \(-0.271190\pi\) | ||||
0.658504 | + | 0.752577i | \(0.271190\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3221 | −0.828954 | −0.414477 | − | 0.910060i | \(-0.636035\pi\) | ||||
−0.414477 | + | 0.910060i | \(0.636035\pi\) | |||||||
\(602\) | −1.71853 | −0.0700422 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.14818 | −0.128098 | ||||||||
\(605\) | −1.69625 | −0.0689625 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.03349 | 0.123126 | 0.0615628 | − | 0.998103i | \(-0.480392\pi\) | ||||
0.0615628 | + | 0.998103i | \(0.480392\pi\) | |||||||
\(608\) | −15.8111 | −0.641224 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.37113 | −0.136493 | ||||||||
\(611\) | 6.27710 | 0.253944 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.3896 | −1.91405 | −0.957024 | − | 0.290010i | \(-0.906341\pi\) | ||||
−0.957024 | + | 0.290010i | \(0.906341\pi\) | |||||||
\(614\) | −17.8498 | −0.720359 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.147104 | 0.00592697 | ||||||||
\(617\) | 39.3278 | 1.58328 | 0.791638 | − | 0.610990i | \(-0.209229\pi\) | ||||
0.791638 | + | 0.610990i | \(0.209229\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.30861 | 0.213371 | 0.106686 | − | 0.994293i | \(-0.465976\pi\) | ||||
0.106686 | + | 0.994293i | \(0.465976\pi\) | |||||||
\(620\) | −16.6029 | −0.666789 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −41.8526 | −1.67813 | ||||||||
\(623\) | 12.4239 | 0.497754 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.88045 | −0.395218 | ||||||||
\(626\) | 35.9304 | 1.43607 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.0730 | −0.521668 | ||||||||
\(629\) | −4.10775 | −0.163787 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.3358 | −1.20765 | −0.603825 | − | 0.797117i | \(-0.706357\pi\) | ||||
−0.603825 | + | 0.797117i | \(0.706357\pi\) | |||||||
\(632\) | 0.539102 | 0.0214443 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −59.0240 | −2.34414 | ||||||||
\(635\) | −19.3082 | −0.766224 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.23072 | −0.207249 | ||||||||
\(638\) | 10.3811 | 0.410994 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.35459 | −0.0535451 | ||||||||
\(641\) | 11.6197 | 0.458949 | 0.229475 | − | 0.973315i | \(-0.426299\pi\) | ||||
0.229475 | + | 0.973315i | \(0.426299\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.4190 | 1.51510 | 0.757549 | − | 0.652779i | \(-0.226397\pi\) | ||||
0.757549 | + | 0.652779i | \(0.226397\pi\) | |||||||
\(644\) | 13.1965 | 0.520014 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.7239 | 1.01209 | ||||||||
\(647\) | −15.7690 | −0.619942 | −0.309971 | − | 0.950746i | \(-0.600319\pi\) | ||||
−0.309971 | + | 0.950746i | \(0.600319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9032 | −0.545747 | ||||||||
\(650\) | −4.56896 | −0.179209 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 38.8410 | 1.52113 | ||||||||
\(653\) | 39.2465 | 1.53583 | 0.767917 | − | 0.640549i | \(-0.221293\pi\) | ||||
0.767917 | + | 0.640549i | \(0.221293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.618210 | −0.0241555 | ||||||||
\(656\) | −19.3428 | −0.755209 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 16.9693 | 0.661531 | ||||||||
\(659\) | 47.1026 | 1.83486 | 0.917428 | − | 0.397902i | \(-0.130261\pi\) | ||||
0.917428 | + | 0.397902i | \(0.130261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.4570 | 1.18464 | 0.592319 | − | 0.805703i | \(-0.298212\pi\) | ||||
0.592319 | + | 0.805703i | \(0.298212\pi\) | |||||||
\(662\) | −15.2804 | −0.593889 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.74191 | −0.0675992 | ||||||||
\(665\) | −4.97324 | −0.192854 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.9983 | −0.929218 | ||||||||
\(668\) | −3.58825 | −0.138833 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.08026 | −0.119001 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.2546 | 1.74444 | 0.872218 | − | 0.489117i | \(-0.162681\pi\) | ||||
0.872218 | + | 0.489117i | \(0.162681\pi\) | |||||||
\(674\) | 43.4522 | 1.67372 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.0599 | −0.886918 | ||||||||
\(677\) | −18.6511 | −0.716820 | −0.358410 | − | 0.933564i | \(-0.616681\pi\) | ||||
−0.358410 | + | 0.933564i | \(0.616681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2507 | 0.470141 | ||||||||
\(680\) | 1.10158 | 0.0422438 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.97696 | −0.382037 | ||||||||
\(683\) | 4.47064 | 0.171064 | 0.0855322 | − | 0.996335i | \(-0.472741\pi\) | ||||
0.0855322 | + | 0.996335i | \(0.472741\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.8298 | 0.795865 | ||||||||
\(686\) | −34.6352 | −1.32238 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.40538 | 0.0917041 | ||||||||
\(689\) | −12.0021 | −0.457244 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.26763 | −0.200390 | −0.100195 | − | 0.994968i | \(-0.531947\pi\) | ||||
−0.100195 | + | 0.994968i | \(0.531947\pi\) | |||||||
\(692\) | 25.6211 | 0.973967 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.5315 | 1.00712 | ||||||||
\(695\) | 3.20219 | 0.121466 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.6982 | 1.16278 | ||||||||
\(698\) | 27.6645 | 1.04712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.09721 | −0.230453 | ||||||||
\(701\) | −32.7360 | −1.23642 | −0.618210 | − | 0.786013i | \(-0.712142\pi\) | ||||
−0.618210 | + | 0.786013i | \(0.712142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.25700 | −0.0474085 | ||||||||
\(704\) | 7.59313 | 0.286177 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.3489 | 1.25510 | ||||||||
\(707\) | 15.9728 | 0.600721 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9084 | −0.860342 | −0.430171 | − | 0.902748i | \(-0.641547\pi\) | ||||
−0.430171 | + | 0.902748i | \(0.641547\pi\) | |||||||
\(710\) | −35.8659 | −1.34602 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.842106 | −0.0315593 | ||||||||
\(713\) | 23.0639 | 0.863750 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.83709 | 0.0687032 | ||||||||
\(716\) | −29.2303 | −1.09239 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.5546 | −0.393895 | ||||||||
\(719\) | −30.3919 | −1.13343 | −0.566713 | − | 0.823915i | \(-0.691785\pi\) | ||||
−0.566713 | + | 0.823915i | \(0.691785\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.4349 | 0.947245 | ||||||||
\(722\) | −29.8889 | −1.11235 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.70574 | 0.323546 | ||||||||
\(725\) | 11.0880 | 0.411798 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6356 | 0.654067 | 0.327033 | − | 0.945013i | \(-0.393951\pi\) | ||||
0.327033 | + | 0.945013i | \(0.393951\pi\) | |||||||
\(728\) | −0.159317 | −0.00590468 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.3662 | 0.568728 | ||||||||
\(731\) | −3.81747 | −0.141194 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.9843 | 1.25524 | 0.627620 | − | 0.778520i | \(-0.284029\pi\) | ||||
0.627620 | + | 0.778520i | \(0.284029\pi\) | |||||||
\(734\) | −53.8070 | −1.98605 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36.4999 | −1.34540 | ||||||||
\(737\) | −0.913716 | −0.0336572 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5128 | −0.386720 | −0.193360 | − | 0.981128i | \(-0.561939\pi\) | ||||
−0.193360 | + | 0.981128i | \(0.561939\pi\) | |||||||
\(740\) | 2.08888 | 0.0767889 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −32.4460 | −1.19113 | ||||||||
\(743\) | −49.8571 | −1.82908 | −0.914540 | − | 0.404496i | \(-0.867447\pi\) | ||||
−0.914540 | + | 0.404496i | \(0.867447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.25543 | 0.339093 | ||||||||
\(746\) | −40.7605 | −1.49235 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.6807 | −0.463651 | ||||||||
\(749\) | 10.2684 | 0.375197 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7670 | 0.429383 | 0.214692 | − | 0.976682i | \(-0.431125\pi\) | ||||
0.214692 | + | 0.976682i | \(0.431125\pi\) | |||||||
\(752\) | −23.7513 | −0.866122 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.2431 | −0.409448 | ||||||||
\(755\) | 2.73886 | 0.0996773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.5126 | −1.90860 | −0.954301 | − | 0.298848i | \(-0.903398\pi\) | ||||
−0.954301 | + | 0.298848i | \(0.903398\pi\) | |||||||
\(758\) | −19.7530 | −0.717461 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.337091 | 0.0122276 | ||||||||
\(761\) | −21.8952 | −0.793700 | −0.396850 | − | 0.917883i | \(-0.629897\pi\) | ||||
−0.396850 | + | 0.917883i | \(0.629897\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.2991 | −0.517662 | ||||||||
\(764\) | 13.3591 | 0.483315 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −46.4980 | −1.68004 | ||||||||
\(767\) | 15.0575 | 0.543695 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.7637 | −0.676635 | −0.338317 | − | 0.941032i | \(-0.609858\pi\) | ||||
−0.338317 | + | 0.941032i | \(0.609858\pi\) | |||||||
\(770\) | 4.96631 | 0.178973 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.76648 | −0.279522 | ||||||||
\(773\) | 22.6135 | 0.813353 | 0.406676 | − | 0.913572i | \(-0.366688\pi\) | ||||
0.406676 | + | 0.913572i | \(0.366688\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.6563 | −0.382785 | ||||||||
\(776\) | −0.830368 | −0.0298085 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.3935 | 0.695291 | ||||||||
\(779\) | 9.39381 | 0.336568 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.6391 | −0.380697 | ||||||||
\(782\) | 59.3836 | 2.12355 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.7920 | 0.706858 | ||||||||
\(785\) | 11.3733 | 0.405929 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.94959 | 0.283372 | 0.141686 | − | 0.989912i | \(-0.454748\pi\) | ||||
0.141686 | + | 0.989912i | \(0.454748\pi\) | |||||||
\(788\) | 13.7313 | 0.489158 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.2004 | 0.647542 | ||||||||
\(791\) | 19.0384 | 0.676928 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.08303 | 0.0384594 | ||||||||
\(794\) | −59.6817 | −2.11802 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.42751 | 0.192373 | ||||||||
\(797\) | −47.4900 | −1.68218 | −0.841091 | − | 0.540893i | \(-0.818086\pi\) | ||||
−0.841091 | + | 0.540893i | \(0.818086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.6948 | 1.33355 | ||||||||
\(800\) | 16.8641 | 0.596237 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.77683 | 0.274609 | ||||||||
\(803\) | 4.55816 | 0.160854 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.4807 | −0.404642 | ||||||||
\(806\) | 10.8053 | 0.380601 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.08266 | −0.0380877 | ||||||||
\(809\) | 35.5115 | 1.24852 | 0.624259 | − | 0.781217i | \(-0.285401\pi\) | ||||
0.624259 | + | 0.781217i | \(0.285401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.8176 | −1.08215 | −0.541077 | − | 0.840973i | \(-0.681983\pi\) | ||||
−0.541077 | + | 0.840973i | \(0.681983\pi\) | |||||||
\(812\) | −15.0037 | −0.526527 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.25524 | 0.0439963 | ||||||||
\(815\) | −33.7910 | −1.18365 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.16817 | −0.0408690 | ||||||||
\(818\) | 27.6412 | 0.966451 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.6107 | −0.545149 | ||||||||
\(821\) | −14.9903 | −0.523166 | −0.261583 | − | 0.965181i | \(-0.584245\pi\) | ||||
−0.261583 | + | 0.965181i | \(0.584245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.9032 | 0.833212 | 0.416606 | − | 0.909087i | \(-0.363219\pi\) | ||||
0.416606 | + | 0.909087i | \(0.363219\pi\) | |||||||
\(824\) | −1.72400 | −0.0600584 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 40.7058 | 1.41634 | ||||||||
\(827\) | −18.2190 | −0.633536 | −0.316768 | − | 0.948503i | \(-0.602598\pi\) | ||||
−0.316768 | + | 0.948503i | \(0.602598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.8048 | −1.59087 | −0.795433 | − | 0.606041i | \(-0.792757\pi\) | ||||
−0.795433 | + | 0.606041i | \(0.792757\pi\) | |||||||
\(830\) | −58.8080 | −2.04126 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.22356 | −0.285101 | ||||||||
\(833\) | −31.4111 | −1.08833 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.12171 | 0.108031 | ||||||||
\(836\) | −3.88035 | −0.134205 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −48.5416 | −1.67684 | ||||||||
\(839\) | 3.50925 | 0.121153 | 0.0605764 | − | 0.998164i | \(-0.480706\pi\) | ||||
0.0605764 | + | 0.998164i | \(0.480706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.71522 | −0.0591456 | ||||||||
\(842\) | 22.7026 | 0.782382 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.24524 | −0.0772842 | ||||||||
\(845\) | 20.0617 | 0.690143 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.47319 | 0.0506193 | ||||||||
\(848\) | 45.4136 | 1.55951 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −27.4372 | −0.941087 | ||||||||
\(851\) | −2.90177 | −0.0994715 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.5602 | −0.840925 | −0.420462 | − | 0.907310i | \(-0.638132\pi\) | ||||
−0.420462 | + | 0.907310i | \(0.638132\pi\) | |||||||
\(854\) | 2.92781 | 0.100188 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.695999 | −0.0237888 | ||||||||
\(857\) | 28.5171 | 0.974127 | 0.487063 | − | 0.873367i | \(-0.338068\pi\) | ||||
0.487063 | + | 0.873367i | \(0.338068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.1415 | −0.721340 | −0.360670 | − | 0.932693i | \(-0.617452\pi\) | ||||
−0.360670 | + | 0.932693i | \(0.617452\pi\) | |||||||
\(860\) | 1.94127 | 0.0661968 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −71.7103 | −2.44246 | ||||||||
\(863\) | 11.5621 | 0.393579 | 0.196789 | − | 0.980446i | \(-0.436948\pi\) | ||||
0.196789 | + | 0.980446i | \(0.436948\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.2899 | −0.757879 | ||||||||
\(866\) | 19.1557 | 0.650936 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.4195 | 0.489431 | ||||||||
\(869\) | 5.39890 | 0.183145 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.989579 | 0.0335306 | ||||||||
\(872\) | 0.969206 | 0.0328215 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.1717 | 0.614667 | ||||||||
\(875\) | 17.7990 | 0.601715 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.37864 | 0.282926 | 0.141463 | − | 0.989944i | \(-0.454819\pi\) | ||||
0.141463 | + | 0.989944i | \(0.454819\pi\) | |||||||
\(878\) | −8.59969 | −0.290225 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.95119 | −0.234324 | ||||||||
\(881\) | −7.84326 | −0.264246 | −0.132123 | − | 0.991233i | \(-0.542179\pi\) | ||||
−0.132123 | + | 0.991233i | \(0.542179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.5962 | −1.13060 | −0.565301 | − | 0.824885i | \(-0.691240\pi\) | ||||
−0.565301 | + | 0.824885i | \(0.691240\pi\) | |||||||
\(884\) | 13.7335 | 0.461907 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.0002 | 1.17586 | ||||||||
\(887\) | 20.8584 | 0.700356 | 0.350178 | − | 0.936683i | \(-0.386121\pi\) | ||||
0.350178 | + | 0.936683i | \(0.386121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.7691 | 0.562417 | ||||||||
\(890\) | −28.4300 | −0.952977 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.3247 | −0.814452 | ||||||||
\(893\) | 11.5348 | 0.385998 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.4298 | 0.850026 | ||||||||
\(896\) | 1.17646 | 0.0393027 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.0059 | −0.901197 | ||||||||
\(899\) | −26.2224 | −0.874567 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −72.0742 | −2.40114 | ||||||||
\(902\) | −9.38072 | −0.312344 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.29044 | −0.0429194 | ||||||||
\(905\) | −7.57384 | −0.251763 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.1615 | −0.337406 | −0.168703 | − | 0.985667i | \(-0.553958\pi\) | ||||
−0.168703 | + | 0.985667i | \(0.553958\pi\) | |||||||
\(908\) | −23.2961 | −0.773107 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.37865 | −0.178300 | ||||||||
\(911\) | −10.1200 | −0.335291 | −0.167646 | − | 0.985847i | \(-0.553616\pi\) | ||||
−0.167646 | + | 0.985847i | \(0.553616\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.4446 | −0.577331 | ||||||||
\(914\) | 35.6427 | 1.17895 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.41024 | 0.0796366 | ||||||||
\(917\) | 0.536911 | 0.0177304 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.868507 | 0.0286494 | 0.0143247 | − | 0.999897i | \(-0.495440\pi\) | ||||
0.0143247 | + | 0.999897i | \(0.495440\pi\) | |||||||
\(920\) | 0.778174 | 0.0256556 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.80977 | −0.0925349 | ||||||||
\(923\) | 11.5224 | 0.379266 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34071 | 0.0440824 | ||||||||
\(926\) | 34.0211 | 1.11800 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 41.4984 | 1.36225 | ||||||||
\(929\) | −45.3136 | −1.48669 | −0.743346 | − | 0.668907i | \(-0.766762\pi\) | ||||
−0.743346 | + | 0.668907i | \(0.766762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.61198 | −0.315020 | ||||||||
\(932\) | 14.4452 | 0.473168 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −71.2338 | −2.33084 | ||||||||
\(935\) | 11.0319 | 0.360783 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5251 | −0.343841 | −0.171920 | − | 0.985111i | \(-0.554997\pi\) | ||||
−0.171920 | + | 0.985111i | \(0.554997\pi\) | |||||||
\(938\) | 2.67519 | 0.0873480 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.1686 | −0.625212 | ||||||||
\(941\) | 45.3209 | 1.47742 | 0.738710 | − | 0.674024i | \(-0.235436\pi\) | ||||
0.738710 | + | 0.674024i | \(0.235436\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.6856 | 0.706180 | ||||||||
\(944\) | −56.9747 | −1.85437 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.16654 | 0.0379275 | ||||||||
\(947\) | 1.40363 | 0.0456120 | 0.0228060 | − | 0.999740i | \(-0.492740\pi\) | ||||
0.0228060 | + | 0.999740i | \(0.492740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.93661 | −0.160249 | ||||||||
\(950\) | −8.39593 | −0.272400 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.956719 | −0.0310074 | ||||||||
\(953\) | 9.19599 | 0.297887 | 0.148944 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148944 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.6222 | −0.376085 | ||||||||
\(956\) | 27.5399 | 0.890703 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 59.4534 | 1.92085 | ||||||||
\(959\) | −18.0905 | −0.584174 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.79854 | −0.187050 | ||||||||
\(962\) | −1.35946 | −0.0438309 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.6435 | 0.697089 | ||||||||
\(965\) | 6.75670 | 0.217506 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.9062 | 1.21898 | 0.609490 | − | 0.792794i | \(-0.291374\pi\) | ||||
0.609490 | + | 0.792794i | \(0.291374\pi\) | |||||||
\(968\) | −0.0998540 | −0.00320943 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28.0337 | −0.900109 | ||||||||
\(971\) | 2.56099 | 0.0821861 | 0.0410930 | − | 0.999155i | \(-0.486916\pi\) | ||||
0.0410930 | + | 0.999155i | \(0.486916\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.78108 | −0.0891573 | ||||||||
\(974\) | 38.7497 | 1.24162 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.09796 | −0.131173 | ||||||||
\(977\) | −12.0243 | −0.384692 | −0.192346 | − | 0.981327i | \(-0.561610\pi\) | ||||
−0.192346 | + | 0.981327i | \(0.561610\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.43337 | −0.269532 | ||||||||
\(980\) | 15.9733 | 0.510247 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 46.4042 | 1.48082 | ||||||||
\(983\) | 9.71713 | 0.309928 | 0.154964 | − | 0.987920i | \(-0.450474\pi\) | ||||
0.154964 | + | 0.987920i | \(0.450474\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9460 | −0.380631 | ||||||||
\(986\) | −67.5160 | −2.15015 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.20252 | 0.133700 | ||||||||
\(989\) | −2.69671 | −0.0857505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.152915 | 0.00485750 | 0.00242875 | − | 0.999997i | \(-0.499227\pi\) | ||||
0.00242875 | + | 0.999997i | \(0.499227\pi\) | |||||||
\(992\) | −39.8826 | −1.26627 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 31.1493 | 0.987996 | ||||||||
\(995\) | −4.72184 | −0.149692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.30232 | 0.294607 | 0.147304 | − | 0.989091i | \(-0.452941\pi\) | ||||
0.147304 | + | 0.989091i | \(0.452941\pi\) | |||||||
\(998\) | −37.2720 | −1.17982 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.p.1.20 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.m.1.6 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.m.1.6 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.p.1.20 | yes | 25 | 1.1 | even | 1 | trivial |