Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.203292 | 0.143749 | 0.0718744 | − | 0.997414i | \(-0.477102\pi\) | ||||
0.0718744 | + | 0.997414i | \(0.477102\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.95867 | −0.979336 | ||||||||
\(5\) | 2.16833 | 0.969707 | 0.484853 | − | 0.874596i | \(-0.338873\pi\) | ||||
0.484853 | + | 0.874596i | \(0.338873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.804765 | −0.284527 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.440803 | 0.139394 | ||||||||
\(11\) | −2.03638 | −0.613991 | −0.306996 | − | 0.951711i | \(-0.599324\pi\) | ||||
−0.306996 | + | 0.951711i | \(0.599324\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.83655 | 0.509367 | 0.254684 | − | 0.967024i | \(-0.418029\pi\) | ||||
0.254684 | + | 0.967024i | \(0.418029\pi\) | |||||||
\(14\) | −0.203292 | −0.0543320 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.75374 | 0.938436 | ||||||||
\(17\) | 2.26480 | 0.549294 | 0.274647 | − | 0.961545i | \(-0.411439\pi\) | ||||
0.274647 | + | 0.961545i | \(0.411439\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.79171 | −1.32871 | −0.664354 | − | 0.747418i | \(-0.731293\pi\) | ||||
−0.664354 | + | 0.747418i | \(0.731293\pi\) | |||||||
\(20\) | −4.24705 | −0.949669 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.413979 | −0.0882606 | ||||||||
\(23\) | −2.00013 | −0.417057 | −0.208528 | − | 0.978016i | \(-0.566867\pi\) | ||||
−0.208528 | + | 0.978016i | \(0.566867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.298346 | −0.0596692 | ||||||||
\(26\) | 0.373355 | 0.0732210 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.95867 | 0.370154 | ||||||||
\(29\) | 2.70238 | 0.501819 | 0.250909 | − | 0.968011i | \(-0.419270\pi\) | ||||
0.250909 | + | 0.968011i | \(0.419270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.925459 | 0.166217 | 0.0831086 | − | 0.996540i | \(-0.473515\pi\) | ||||
0.0831086 | + | 0.996540i | \(0.473515\pi\) | |||||||
\(32\) | 2.37263 | 0.419427 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.460414 | 0.0789604 | ||||||||
\(35\) | −2.16833 | −0.366515 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.11408 | 1.16955 | 0.584774 | − | 0.811196i | \(-0.301183\pi\) | ||||
0.584774 | + | 0.811196i | \(0.301183\pi\) | |||||||
\(38\) | −1.17741 | −0.191000 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.74500 | −0.275908 | ||||||||
\(41\) | 3.83498 | 0.598923 | 0.299462 | − | 0.954108i | \(-0.403193\pi\) | ||||
0.299462 | + | 0.954108i | \(0.403193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.434751 | −0.0662989 | −0.0331495 | − | 0.999450i | \(-0.510554\pi\) | ||||
−0.0331495 | + | 0.999450i | \(0.510554\pi\) | |||||||
\(44\) | 3.98860 | 0.601304 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.406610 | −0.0599514 | ||||||||
\(47\) | −4.07454 | −0.594333 | −0.297166 | − | 0.954826i | \(-0.596042\pi\) | ||||
−0.297166 | + | 0.954826i | \(0.596042\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.0606513 | −0.00857738 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.59720 | −0.498842 | ||||||||
\(53\) | 6.46471 | 0.887996 | 0.443998 | − | 0.896028i | \(-0.353560\pi\) | ||||
0.443998 | + | 0.896028i | \(0.353560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.41554 | −0.595391 | ||||||||
\(56\) | 0.804765 | 0.107541 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.549370 | 0.0721359 | ||||||||
\(59\) | −13.7109 | −1.78501 | −0.892504 | − | 0.451040i | \(-0.851053\pi\) | ||||
−0.892504 | + | 0.451040i | \(0.851053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.25010 | −1.18435 | −0.592177 | − | 0.805808i | \(-0.701731\pi\) | ||||
−0.592177 | + | 0.805808i | \(0.701731\pi\) | |||||||
\(62\) | 0.188138 | 0.0238935 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.02515 | −0.878144 | ||||||||
\(65\) | 3.98225 | 0.493937 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.88314 | 0.840909 | 0.420454 | − | 0.907314i | \(-0.361871\pi\) | ||||
0.420454 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(68\) | −4.43599 | −0.537943 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.440803 | −0.0526861 | ||||||||
\(71\) | −14.1463 | −1.67886 | −0.839430 | − | 0.543468i | \(-0.817111\pi\) | ||||
−0.839430 | + | 0.543468i | \(0.817111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.78576 | 0.560131 | 0.280065 | − | 0.959981i | \(-0.409644\pi\) | ||||
0.280065 | + | 0.959981i | \(0.409644\pi\) | |||||||
\(74\) | 1.44623 | 0.168121 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.3441 | 1.30125 | ||||||||
\(77\) | 2.03638 | 0.232067 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8460 | 1.22027 | 0.610135 | − | 0.792297i | \(-0.291115\pi\) | ||||
0.610135 | + | 0.792297i | \(0.291115\pi\) | |||||||
\(80\) | 8.13935 | 0.910007 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.779619 | 0.0860945 | ||||||||
\(83\) | −4.97268 | −0.545822 | −0.272911 | − | 0.962039i | \(-0.587987\pi\) | ||||
−0.272911 | + | 0.962039i | \(0.587987\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.91082 | 0.532654 | ||||||||
\(86\) | −0.0883813 | −0.00953040 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.63881 | 0.174697 | ||||||||
\(89\) | 1.11999 | 0.118719 | 0.0593594 | − | 0.998237i | \(-0.481094\pi\) | ||||
0.0593594 | + | 0.998237i | \(0.481094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.83655 | −0.192523 | ||||||||
\(92\) | 3.91761 | 0.408439 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.828320 | −0.0854347 | ||||||||
\(95\) | −12.5583 | −1.28846 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.04552 | 0.715365 | 0.357682 | − | 0.933843i | \(-0.383567\pi\) | ||||
0.357682 | + | 0.933843i | \(0.383567\pi\) | |||||||
\(98\) | 0.203292 | 0.0205356 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.584362 | 0.0584362 | ||||||||
\(101\) | 10.6965 | 1.06434 | 0.532170 | − | 0.846638i | \(-0.321377\pi\) | ||||
0.532170 | + | 0.846638i | \(0.321377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.9318 | −1.47128 | −0.735638 | − | 0.677375i | \(-0.763118\pi\) | ||||
−0.735638 | + | 0.677375i | \(0.763118\pi\) | |||||||
\(104\) | −1.47799 | −0.144929 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.31422 | 0.127648 | ||||||||
\(107\) | −12.2693 | −1.18612 | −0.593059 | − | 0.805159i | \(-0.702080\pi\) | ||||
−0.593059 | + | 0.805159i | \(0.702080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.53666 | −0.147185 | −0.0735926 | − | 0.997288i | \(-0.523446\pi\) | ||||
−0.0735926 | + | 0.997288i | \(0.523446\pi\) | |||||||
\(110\) | −0.897643 | −0.0855869 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.75374 | −0.354695 | ||||||||
\(113\) | 1.85798 | 0.174784 | 0.0873920 | − | 0.996174i | \(-0.472147\pi\) | ||||
0.0873920 | + | 0.996174i | \(0.472147\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.33695 | −0.404422 | ||||||||
\(116\) | −5.29307 | −0.491449 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.78731 | −0.256593 | ||||||||
\(119\) | −2.26480 | −0.207614 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.85316 | −0.623015 | ||||||||
\(122\) | −1.88047 | −0.170249 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.81267 | −0.162783 | ||||||||
\(125\) | −11.4886 | −1.02757 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −6.17342 | −0.545659 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.809558 | 0.0710029 | ||||||||
\(131\) | −5.09715 | −0.445340 | −0.222670 | − | 0.974894i | \(-0.571477\pi\) | ||||
−0.222670 | + | 0.974894i | \(0.571477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.79171 | 0.502205 | ||||||||
\(134\) | 1.39928 | 0.120880 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.82263 | −0.156289 | ||||||||
\(137\) | 3.51026 | 0.299901 | 0.149951 | − | 0.988693i | \(-0.452088\pi\) | ||||
0.149951 | + | 0.988693i | \(0.452088\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.28843 | −0.278921 | −0.139460 | − | 0.990228i | \(-0.544537\pi\) | ||||
−0.139460 | + | 0.990228i | \(0.544537\pi\) | |||||||
\(140\) | 4.24705 | 0.358941 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.87583 | −0.241334 | ||||||||
\(143\) | −3.73991 | −0.312747 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.85964 | 0.486617 | ||||||||
\(146\) | 0.972905 | 0.0805182 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.9342 | −1.14538 | ||||||||
\(149\) | −14.9074 | −1.22126 | −0.610630 | − | 0.791916i | \(-0.709084\pi\) | ||||
−0.610630 | + | 0.791916i | \(0.709084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.19878 | 0.585828 | 0.292914 | − | 0.956139i | \(-0.405375\pi\) | ||||
0.292914 | + | 0.956139i | \(0.405375\pi\) | |||||||
\(152\) | 4.66096 | 0.378054 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.413979 | 0.0333594 | ||||||||
\(155\) | 2.00670 | 0.161182 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.94517 | −0.793711 | −0.396856 | − | 0.917881i | \(-0.629899\pi\) | ||||
−0.396856 | + | 0.917881i | \(0.629899\pi\) | |||||||
\(158\) | 2.20490 | 0.175412 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.14465 | 0.406721 | ||||||||
\(161\) | 2.00013 | 0.157633 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.0465 | −1.64849 | −0.824244 | − | 0.566235i | \(-0.808399\pi\) | ||||
−0.824244 | + | 0.566235i | \(0.808399\pi\) | |||||||
\(164\) | −7.51147 | −0.586547 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.01090 | −0.0784614 | ||||||||
\(167\) | −9.53253 | −0.737649 | −0.368825 | − | 0.929499i | \(-0.620240\pi\) | ||||
−0.368825 | + | 0.929499i | \(0.620240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.62708 | −0.740545 | ||||||||
\(170\) | 0.998330 | 0.0765684 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.851535 | 0.0649289 | ||||||||
\(173\) | 21.1959 | 1.61150 | 0.805748 | − | 0.592259i | \(-0.201764\pi\) | ||||
0.805748 | + | 0.592259i | \(0.201764\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.298346 | 0.0225528 | ||||||||
\(176\) | −7.64404 | −0.576191 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.227685 | 0.0170657 | ||||||||
\(179\) | 23.4704 | 1.75426 | 0.877130 | − | 0.480253i | \(-0.159455\pi\) | ||||
0.877130 | + | 0.480253i | \(0.159455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4217 | 1.29494 | 0.647471 | − | 0.762090i | \(-0.275827\pi\) | ||||
0.647471 | + | 0.762090i | \(0.275827\pi\) | |||||||
\(182\) | −0.373355 | −0.0276749 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.60964 | 0.118664 | ||||||||
\(185\) | 15.4257 | 1.13412 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.61198 | −0.337262 | ||||||||
\(188\) | 7.98069 | 0.582052 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.55300 | −0.185214 | ||||||||
\(191\) | 10.3025 | 0.745461 | 0.372730 | − | 0.927940i | \(-0.378422\pi\) | ||||
0.372730 | + | 0.927940i | \(0.378422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.54183 | −0.398910 | −0.199455 | − | 0.979907i | \(-0.563917\pi\) | ||||
−0.199455 | + | 0.979907i | \(0.563917\pi\) | |||||||
\(194\) | 1.43230 | 0.102833 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.95867 | −0.139905 | ||||||||
\(197\) | −11.0717 | −0.788825 | −0.394413 | − | 0.918933i | \(-0.629052\pi\) | ||||
−0.394413 | + | 0.918933i | \(0.629052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.3587 | 0.946970 | 0.473485 | − | 0.880802i | \(-0.342996\pi\) | ||||
0.473485 | + | 0.880802i | \(0.342996\pi\) | |||||||
\(200\) | 0.240098 | 0.0169775 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.17450 | 0.152998 | ||||||||
\(203\) | −2.70238 | −0.189670 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.31550 | 0.580780 | ||||||||
\(206\) | −3.03552 | −0.211494 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.89394 | 0.478009 | ||||||||
\(209\) | 11.7941 | 0.815816 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3900 | 1.61023 | 0.805117 | − | 0.593117i | \(-0.202103\pi\) | ||||
0.805117 | + | 0.593117i | \(0.202103\pi\) | |||||||
\(212\) | −12.6622 | −0.869646 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.49425 | −0.170503 | ||||||||
\(215\) | −0.942684 | −0.0642905 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.925459 | −0.0628242 | ||||||||
\(218\) | −0.312390 | −0.0211577 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.64860 | 0.583088 | ||||||||
\(221\) | 4.15941 | 0.279792 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.2201 | −1.62190 | −0.810949 | − | 0.585117i | \(-0.801048\pi\) | ||||
−0.810949 | + | 0.585117i | \(0.801048\pi\) | |||||||
\(224\) | −2.37263 | −0.158528 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.377712 | 0.0251250 | ||||||||
\(227\) | −29.0323 | −1.92694 | −0.963472 | − | 0.267808i | \(-0.913701\pi\) | ||||
−0.963472 | + | 0.267808i | \(0.913701\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.489031 | −0.0323161 | −0.0161580 | − | 0.999869i | \(-0.505143\pi\) | ||||
−0.0161580 | + | 0.999869i | \(0.505143\pi\) | |||||||
\(230\) | −0.881665 | −0.0581353 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.17478 | −0.142781 | ||||||||
\(233\) | −16.2677 | −1.06573 | −0.532866 | − | 0.846200i | \(-0.678885\pi\) | ||||
−0.532866 | + | 0.846200i | \(0.678885\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.83495 | −0.576328 | ||||||||
\(236\) | 26.8552 | 1.74812 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.460414 | −0.0298442 | ||||||||
\(239\) | −18.6270 | −1.20488 | −0.602442 | − | 0.798163i | \(-0.705805\pi\) | ||||
−0.602442 | + | 0.798163i | \(0.705805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.1700 | −1.17043 | −0.585215 | − | 0.810878i | \(-0.698990\pi\) | ||||
−0.585215 | + | 0.810878i | \(0.698990\pi\) | |||||||
\(242\) | −1.39319 | −0.0895577 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.1179 | 1.15988 | ||||||||
\(245\) | 2.16833 | 0.138530 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.6368 | −0.676801 | ||||||||
\(248\) | −0.744777 | −0.0472934 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.33553 | −0.147712 | ||||||||
\(251\) | 28.9466 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.07303 | 0.256069 | ||||||||
\(254\) | −0.203292 | −0.0127557 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.7953 | 0.799706 | ||||||||
\(257\) | 10.2025 | 0.636413 | 0.318207 | − | 0.948021i | \(-0.396919\pi\) | ||||
0.318207 | + | 0.948021i | \(0.396919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.11408 | −0.442048 | ||||||||
\(260\) | −7.79992 | −0.483730 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.03621 | −0.0640172 | ||||||||
\(263\) | −0.138057 | −0.00851293 | −0.00425647 | − | 0.999991i | \(-0.501355\pi\) | ||||
−0.00425647 | + | 0.999991i | \(0.501355\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.0176 | 0.861095 | ||||||||
\(266\) | 1.17741 | 0.0721914 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.4818 | −0.823533 | ||||||||
\(269\) | −0.767771 | −0.0468118 | −0.0234059 | − | 0.999726i | \(-0.507451\pi\) | ||||
−0.0234059 | + | 0.999726i | \(0.507451\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.0186 | −1.51977 | −0.759886 | − | 0.650057i | \(-0.774745\pi\) | ||||
−0.759886 | + | 0.650057i | \(0.774745\pi\) | |||||||
\(272\) | 8.50146 | 0.515477 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.713606 | 0.0431105 | ||||||||
\(275\) | 0.607546 | 0.0366364 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.0594 | −1.44559 | −0.722795 | − | 0.691063i | \(-0.757143\pi\) | ||||
−0.722795 | + | 0.691063i | \(0.757143\pi\) | |||||||
\(278\) | −0.668510 | −0.0400946 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.74500 | 0.104283 | ||||||||
\(281\) | −10.1722 | −0.606825 | −0.303413 | − | 0.952859i | \(-0.598126\pi\) | ||||
−0.303413 | + | 0.952859i | \(0.598126\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.1780 | −1.73445 | −0.867227 | − | 0.497913i | \(-0.834100\pi\) | ||||
−0.867227 | + | 0.497913i | \(0.834100\pi\) | |||||||
\(284\) | 27.7080 | 1.64417 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.760293 | −0.0449571 | ||||||||
\(287\) | −3.83498 | −0.226372 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8707 | −0.698276 | ||||||||
\(290\) | 1.19122 | 0.0699506 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.37374 | −0.548557 | ||||||||
\(293\) | −12.9496 | −0.756522 | −0.378261 | − | 0.925699i | \(-0.623478\pi\) | ||||
−0.378261 | + | 0.925699i | \(0.623478\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −29.7298 | −1.73093 | ||||||||
\(296\) | −5.72516 | −0.332768 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.03054 | −0.175555 | ||||||||
\(299\) | −3.67335 | −0.212435 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.434751 | 0.0250586 | ||||||||
\(302\) | 1.46345 | 0.0842122 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −21.7406 | −1.24691 | ||||||||
\(305\) | −20.0573 | −1.14848 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.02772 | −0.515239 | −0.257620 | − | 0.966246i | \(-0.582938\pi\) | ||||
−0.257620 | + | 0.966246i | \(0.582938\pi\) | |||||||
\(308\) | −3.98860 | −0.227272 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.407945 | 0.0231697 | ||||||||
\(311\) | 24.7431 | 1.40305 | 0.701525 | − | 0.712645i | \(-0.252503\pi\) | ||||
0.701525 | + | 0.712645i | \(0.252503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.8110 | −0.950216 | −0.475108 | − | 0.879928i | \(-0.657591\pi\) | ||||
−0.475108 | + | 0.879928i | \(0.657591\pi\) | |||||||
\(314\) | −2.02177 | −0.114095 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.2438 | −1.19505 | ||||||||
\(317\) | 3.14053 | 0.176389 | 0.0881947 | − | 0.996103i | \(-0.471890\pi\) | ||||
0.0881947 | + | 0.996103i | \(0.471890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.50306 | −0.308112 | ||||||||
\(320\) | −15.2328 | −0.851542 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.406610 | 0.0226595 | ||||||||
\(323\) | −13.1170 | −0.729851 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.547928 | −0.0303936 | ||||||||
\(326\) | −4.27857 | −0.236968 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.08626 | −0.170410 | ||||||||
\(329\) | 4.07454 | 0.224637 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.2551 | −1.11332 | −0.556660 | − | 0.830740i | \(-0.687917\pi\) | ||||
−0.556660 | + | 0.830740i | \(0.687917\pi\) | |||||||
\(332\) | 9.73985 | 0.534544 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.93788 | −0.106036 | ||||||||
\(335\) | 14.9249 | 0.815435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.4420 | 0.623283 | 0.311641 | − | 0.950200i | \(-0.399121\pi\) | ||||
0.311641 | + | 0.950200i | \(0.399121\pi\) | |||||||
\(338\) | −1.95711 | −0.106452 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.61870 | −0.521647 | ||||||||
\(341\) | −1.88458 | −0.102056 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.349873 | 0.0188639 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.30895 | 0.231651 | ||||||||
\(347\) | 13.6007 | 0.730123 | 0.365061 | − | 0.930983i | \(-0.381048\pi\) | ||||
0.365061 | + | 0.930983i | \(0.381048\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.18545 | 0.331100 | 0.165550 | − | 0.986201i | \(-0.447060\pi\) | ||||
0.165550 | + | 0.986201i | \(0.447060\pi\) | |||||||
\(350\) | 0.0606513 | 0.00324195 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.83158 | −0.257524 | ||||||||
\(353\) | 34.6672 | 1.84515 | 0.922574 | − | 0.385821i | \(-0.126082\pi\) | ||||
0.922574 | + | 0.385821i | \(0.126082\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.6739 | −1.62800 | ||||||||
\(356\) | −2.19370 | −0.116266 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.77134 | 0.252173 | ||||||||
\(359\) | −11.3002 | −0.596400 | −0.298200 | − | 0.954503i | \(-0.596386\pi\) | ||||
−0.298200 | + | 0.954503i | \(0.596386\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5439 | 0.765467 | ||||||||
\(362\) | 3.54168 | 0.186146 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.59720 | 0.188545 | ||||||||
\(365\) | 10.3771 | 0.543163 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3988 | 0.751611 | 0.375806 | − | 0.926698i | \(-0.377366\pi\) | ||||
0.375806 | + | 0.926698i | \(0.377366\pi\) | |||||||
\(368\) | −7.50799 | −0.391381 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.13591 | 0.163028 | ||||||||
\(371\) | −6.46471 | −0.335631 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.8622 | −0.924870 | −0.462435 | − | 0.886653i | \(-0.653024\pi\) | ||||
−0.462435 | + | 0.886653i | \(0.653024\pi\) | |||||||
\(374\) | −0.937577 | −0.0484810 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.27905 | 0.169104 | ||||||||
\(377\) | 4.96305 | 0.255610 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.53256 | 0.438288 | 0.219144 | − | 0.975693i | \(-0.429674\pi\) | ||||
0.219144 | + | 0.975693i | \(0.429674\pi\) | |||||||
\(380\) | 24.5977 | 1.26183 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.09441 | 0.107159 | ||||||||
\(383\) | 29.9038 | 1.52801 | 0.764006 | − | 0.645210i | \(-0.223230\pi\) | ||||
0.764006 | + | 0.645210i | \(0.223230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.41554 | 0.225037 | ||||||||
\(386\) | −1.12661 | −0.0573428 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.7999 | −0.700582 | ||||||||
\(389\) | 8.18046 | 0.414766 | 0.207383 | − | 0.978260i | \(-0.433505\pi\) | ||||
0.207383 | + | 0.978260i | \(0.433505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.52989 | −0.229087 | ||||||||
\(392\) | −0.804765 | −0.0406468 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.25078 | −0.113393 | ||||||||
\(395\) | 23.5177 | 1.18330 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.31342 | −0.0659188 | −0.0329594 | − | 0.999457i | \(-0.510493\pi\) | ||||
−0.0329594 | + | 0.999457i | \(0.510493\pi\) | |||||||
\(398\) | 2.71570 | 0.136126 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.11991 | −0.0559957 | ||||||||
\(401\) | −33.1873 | −1.65730 | −0.828648 | − | 0.559770i | \(-0.810889\pi\) | ||||
−0.828648 | + | 0.559770i | \(0.810889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.69965 | 0.0846657 | ||||||||
\(404\) | −20.9509 | −1.04235 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.549370 | −0.0272648 | ||||||||
\(407\) | −14.4870 | −0.718092 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.9044 | −1.47868 | −0.739340 | − | 0.673333i | \(-0.764862\pi\) | ||||
−0.739340 | + | 0.673333i | \(0.764862\pi\) | |||||||
\(410\) | 1.69047 | 0.0834864 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 29.2466 | 1.44087 | ||||||||
\(413\) | 13.7109 | 0.674669 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7824 | −0.529288 | ||||||||
\(416\) | 4.35746 | 0.213642 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.39764 | 0.117273 | ||||||||
\(419\) | −33.5181 | −1.63747 | −0.818734 | − | 0.574173i | \(-0.805324\pi\) | ||||
−0.818734 | + | 0.574173i | \(0.805324\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.0936 | −1.61288 | −0.806442 | − | 0.591314i | \(-0.798610\pi\) | ||||
−0.806442 | + | 0.591314i | \(0.798610\pi\) | |||||||
\(422\) | 4.75499 | 0.231469 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.20257 | −0.252659 | ||||||||
\(425\) | −0.675693 | −0.0327759 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.25010 | 0.447643 | ||||||||
\(428\) | 24.0315 | 1.16161 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.191640 | −0.00924169 | ||||||||
\(431\) | 1.90178 | 0.0916053 | 0.0458026 | − | 0.998951i | \(-0.485415\pi\) | ||||
0.0458026 | + | 0.998951i | \(0.485415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.4641 | −1.07956 | −0.539778 | − | 0.841807i | \(-0.681492\pi\) | ||||
−0.539778 | + | 0.841807i | \(0.681492\pi\) | |||||||
\(434\) | −0.188138 | −0.00903091 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.00981 | 0.144144 | ||||||||
\(437\) | 11.5842 | 0.554147 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.36163 | 0.303624 | 0.151812 | − | 0.988409i | \(-0.451489\pi\) | ||||
0.151812 | + | 0.988409i | \(0.451489\pi\) | |||||||
\(440\) | 3.55347 | 0.169405 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.845574 | 0.0402198 | ||||||||
\(443\) | 11.7960 | 0.560444 | 0.280222 | − | 0.959935i | \(-0.409592\pi\) | ||||
0.280222 | + | 0.959935i | \(0.409592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.42851 | 0.115122 | ||||||||
\(446\) | −4.92374 | −0.233146 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.02515 | 0.331907 | ||||||||
\(449\) | −26.8230 | −1.26586 | −0.632928 | − | 0.774211i | \(-0.718147\pi\) | ||||
−0.632928 | + | 0.774211i | \(0.718147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.80947 | −0.367734 | ||||||||
\(452\) | −3.63917 | −0.171172 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.90203 | −0.276996 | ||||||||
\(455\) | −3.98225 | −0.186691 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.2927 | −0.481470 | −0.240735 | − | 0.970591i | \(-0.577388\pi\) | ||||
−0.240735 | + | 0.970591i | \(0.577388\pi\) | |||||||
\(458\) | −0.0994160 | −0.00464540 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.49466 | 0.396066 | ||||||||
\(461\) | −35.1566 | −1.63741 | −0.818703 | − | 0.574217i | \(-0.805307\pi\) | ||||
−0.818703 | + | 0.574217i | \(0.805307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.3381 | −1.64230 | −0.821150 | − | 0.570712i | \(-0.806667\pi\) | ||||
−0.821150 | + | 0.570712i | \(0.806667\pi\) | |||||||
\(464\) | 10.1440 | 0.470924 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.30709 | −0.153198 | ||||||||
\(467\) | −7.24322 | −0.335176 | −0.167588 | − | 0.985857i | \(-0.553598\pi\) | ||||
−0.167588 | + | 0.985857i | \(0.553598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.88314 | −0.317834 | ||||||||
\(470\) | −1.79607 | −0.0828466 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.0341 | 0.507884 | ||||||||
\(473\) | 0.885318 | 0.0407070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.72793 | 0.0792830 | ||||||||
\(476\) | 4.43599 | 0.203323 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.78672 | −0.173201 | ||||||||
\(479\) | 9.85957 | 0.450495 | 0.225248 | − | 0.974302i | \(-0.427681\pi\) | ||||
0.225248 | + | 0.974302i | \(0.427681\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0654 | 0.595730 | ||||||||
\(482\) | −3.69380 | −0.168248 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.4231 | 0.610141 | ||||||||
\(485\) | 15.2770 | 0.693694 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.37567 | 0.107652 | 0.0538259 | − | 0.998550i | \(-0.482858\pi\) | ||||
0.0538259 | + | 0.998550i | \(0.482858\pi\) | |||||||
\(488\) | 7.44415 | 0.336981 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.440803 | 0.0199135 | ||||||||
\(491\) | 28.4513 | 1.28399 | 0.641995 | − | 0.766709i | \(-0.278107\pi\) | ||||
0.641995 | + | 0.766709i | \(0.278107\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.12033 | 0.275646 | ||||||||
\(494\) | −2.16237 | −0.0972894 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.47393 | 0.155984 | ||||||||
\(497\) | 14.1463 | 0.634549 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.8574 | −0.575575 | −0.287787 | − | 0.957694i | \(-0.592920\pi\) | ||||
−0.287787 | + | 0.957694i | \(0.592920\pi\) | |||||||
\(500\) | 22.5023 | 1.00633 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.88459 | 0.262642 | ||||||||
\(503\) | 5.24764 | 0.233981 | 0.116990 | − | 0.993133i | \(-0.462675\pi\) | ||||
0.116990 | + | 0.993133i | \(0.462675\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.1935 | 1.03210 | ||||||||
\(506\) | 0.828013 | 0.0368096 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.95867 | 0.0869020 | ||||||||
\(509\) | −23.4333 | −1.03866 | −0.519332 | − | 0.854572i | \(-0.673819\pi\) | ||||
−0.519332 | + | 0.854572i | \(0.673819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.78576 | −0.211710 | ||||||||
\(512\) | 14.9480 | 0.660616 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.07408 | 0.0914837 | ||||||||
\(515\) | −32.3771 | −1.42671 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.29731 | 0.364915 | ||||||||
\(518\) | −1.44623 | −0.0635438 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.20477 | −0.140539 | ||||||||
\(521\) | 8.39413 | 0.367754 | 0.183877 | − | 0.982949i | \(-0.441135\pi\) | ||||
0.183877 | + | 0.982949i | \(0.441135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3043 | −0.756663 | −0.378331 | − | 0.925670i | \(-0.623502\pi\) | ||||
−0.378331 | + | 0.925670i | \(0.623502\pi\) | |||||||
\(524\) | 9.98365 | 0.436138 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0280657 | −0.00122372 | ||||||||
\(527\) | 2.09597 | 0.0913021 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.9995 | −0.826064 | ||||||||
\(530\) | 2.84966 | 0.123781 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.3441 | −0.491827 | ||||||||
\(533\) | 7.04313 | 0.305072 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.6039 | −1.15019 | ||||||||
\(536\) | −5.53931 | −0.239262 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.156081 | −0.00672915 | ||||||||
\(539\) | −2.03638 | −0.0877130 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.60112 | −0.240811 | −0.120406 | − | 0.992725i | \(-0.538419\pi\) | ||||
−0.120406 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(542\) | −5.08607 | −0.218465 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.37353 | 0.230388 | ||||||||
\(545\) | −3.33198 | −0.142726 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.16434 | 0.0925407 | 0.0462703 | − | 0.998929i | \(-0.485266\pi\) | ||||
0.0462703 | + | 0.998929i | \(0.485266\pi\) | |||||||
\(548\) | −6.87544 | −0.293704 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.123509 | 0.00526644 | ||||||||
\(551\) | −15.6514 | −0.666771 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.8460 | −0.461219 | ||||||||
\(554\) | −4.89107 | −0.207802 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.44096 | 0.273157 | ||||||||
\(557\) | 34.6728 | 1.46914 | 0.734568 | − | 0.678535i | \(-0.237385\pi\) | ||||
0.734568 | + | 0.678535i | \(0.237385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.798442 | −0.0337705 | ||||||||
\(560\) | −8.13935 | −0.343950 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.06793 | −0.0872304 | ||||||||
\(563\) | 15.0614 | 0.634762 | 0.317381 | − | 0.948298i | \(-0.397197\pi\) | ||||
0.317381 | + | 0.948298i | \(0.397197\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.02871 | 0.169489 | ||||||||
\(566\) | −5.93165 | −0.249326 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.3845 | 0.477682 | ||||||||
\(569\) | 17.9482 | 0.752426 | 0.376213 | − | 0.926533i | \(-0.377226\pi\) | ||||
0.376213 | + | 0.926533i | \(0.377226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.27764 | 0.179014 | 0.0895069 | − | 0.995986i | \(-0.471471\pi\) | ||||
0.0895069 | + | 0.995986i | \(0.471471\pi\) | |||||||
\(572\) | 7.32526 | 0.306285 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.779619 | −0.0325407 | ||||||||
\(575\) | 0.596732 | 0.0248854 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.9224 | 1.62036 | 0.810180 | − | 0.586182i | \(-0.199370\pi\) | ||||
0.810180 | + | 0.586182i | \(0.199370\pi\) | |||||||
\(578\) | −2.41321 | −0.100376 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.4771 | −0.476561 | ||||||||
\(581\) | 4.97268 | 0.206302 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.1646 | −0.545222 | ||||||||
\(584\) | −3.85141 | −0.159373 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.63254 | −0.108749 | ||||||||
\(587\) | −24.3999 | −1.00709 | −0.503546 | − | 0.863968i | \(-0.667972\pi\) | ||||
−0.503546 | + | 0.863968i | \(0.667972\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.35999 | −0.220854 | ||||||||
\(590\) | −6.04381 | −0.248820 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26.7044 | 1.09755 | ||||||||
\(593\) | −20.7529 | −0.852219 | −0.426110 | − | 0.904672i | \(-0.640116\pi\) | ||||
−0.426110 | + | 0.904672i | \(0.640116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.91082 | −0.201324 | ||||||||
\(596\) | 29.1986 | 1.19602 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.746760 | −0.0305373 | ||||||||
\(599\) | 35.5562 | 1.45279 | 0.726393 | − | 0.687280i | \(-0.241195\pi\) | ||||
0.726393 | + | 0.687280i | \(0.241195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.85431 | 0.198011 | 0.0990057 | − | 0.995087i | \(-0.468434\pi\) | ||||
0.0990057 | + | 0.995087i | \(0.468434\pi\) | |||||||
\(602\) | 0.0883813 | 0.00360215 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.1000 | −0.573723 | ||||||||
\(605\) | −14.8599 | −0.604141 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.55179 | 0.103574 | 0.0517869 | − | 0.998658i | \(-0.483508\pi\) | ||||
0.0517869 | + | 0.998658i | \(0.483508\pi\) | |||||||
\(608\) | −13.7416 | −0.557296 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.07747 | −0.165092 | ||||||||
\(611\) | −7.48310 | −0.302734 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.2815 | 1.66734 | 0.833672 | − | 0.552259i | \(-0.186234\pi\) | ||||
0.833672 | + | 0.552259i | \(0.186234\pi\) | |||||||
\(614\) | −1.83526 | −0.0740651 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.63881 | −0.0660294 | ||||||||
\(617\) | −7.93093 | −0.319287 | −0.159644 | − | 0.987175i | \(-0.551034\pi\) | ||||
−0.159644 | + | 0.987175i | \(0.551034\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.93425 | 0.158131 | 0.0790655 | − | 0.996869i | \(-0.474806\pi\) | ||||
0.0790655 | + | 0.996869i | \(0.474806\pi\) | |||||||
\(620\) | −3.93047 | −0.157851 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.03006 | 0.201687 | ||||||||
\(623\) | −1.11999 | −0.0448715 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.4193 | −0.936770 | ||||||||
\(626\) | −3.41754 | −0.136592 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.4793 | 0.777310 | ||||||||
\(629\) | 16.1119 | 0.642425 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.666745 | 0.0265427 | 0.0132713 | − | 0.999912i | \(-0.495775\pi\) | ||||
0.0132713 | + | 0.999912i | \(0.495775\pi\) | |||||||
\(632\) | −8.72848 | −0.347200 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.638443 | 0.0253558 | ||||||||
\(635\) | −2.16833 | −0.0860475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.83655 | 0.0727668 | ||||||||
\(638\) | −1.11873 | −0.0442908 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.3860 | −0.529129 | ||||||||
\(641\) | −16.8540 | −0.665692 | −0.332846 | − | 0.942981i | \(-0.608009\pi\) | ||||
−0.332846 | + | 0.942981i | \(0.608009\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0458 | −0.987709 | −0.493854 | − | 0.869545i | \(-0.664412\pi\) | ||||
−0.493854 | + | 0.869545i | \(0.664412\pi\) | |||||||
\(644\) | −3.91761 | −0.154375 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.66658 | −0.104915 | ||||||||
\(647\) | 6.04381 | 0.237607 | 0.118803 | − | 0.992918i | \(-0.462094\pi\) | ||||
0.118803 | + | 0.992918i | \(0.462094\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.9206 | 1.09598 | ||||||||
\(650\) | −0.111389 | −0.00436904 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 41.2232 | 1.61442 | ||||||||
\(653\) | −22.8710 | −0.895010 | −0.447505 | − | 0.894282i | \(-0.647687\pi\) | ||||
−0.447505 | + | 0.894282i | \(0.647687\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.0523 | −0.431849 | ||||||||
\(656\) | 14.3955 | 0.562051 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.828320 | 0.0322913 | ||||||||
\(659\) | 41.9778 | 1.63522 | 0.817612 | − | 0.575770i | \(-0.195298\pi\) | ||||
0.817612 | + | 0.575770i | \(0.195298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.3913 | 0.870920 | 0.435460 | − | 0.900208i | \(-0.356586\pi\) | ||||
0.435460 | + | 0.900208i | \(0.356586\pi\) | |||||||
\(662\) | −4.11769 | −0.160039 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.00184 | 0.155301 | ||||||||
\(665\) | 12.5583 | 0.486991 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.40511 | −0.209287 | ||||||||
\(668\) | 18.6711 | 0.722407 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.03411 | 0.117218 | ||||||||
\(671\) | 18.8367 | 0.727183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7915 | −0.878550 | −0.439275 | − | 0.898353i | \(-0.644765\pi\) | ||||
−0.439275 | + | 0.898353i | \(0.644765\pi\) | |||||||
\(674\) | 2.32605 | 0.0895962 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.8563 | 0.725242 | ||||||||
\(677\) | −2.11742 | −0.0813790 | −0.0406895 | − | 0.999172i | \(-0.512955\pi\) | ||||
−0.0406895 | + | 0.999172i | \(0.512955\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.04552 | −0.270382 | ||||||||
\(680\) | −3.95206 | −0.151555 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.383120 | −0.0146704 | ||||||||
\(683\) | −48.9058 | −1.87133 | −0.935665 | − | 0.352889i | \(-0.885199\pi\) | ||||
−0.935665 | + | 0.352889i | \(0.885199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.61139 | 0.290816 | ||||||||
\(686\) | −0.203292 | −0.00776171 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.63194 | −0.0622173 | ||||||||
\(689\) | 11.8728 | 0.452316 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.85867 | −0.298958 | −0.149479 | − | 0.988765i | \(-0.547760\pi\) | ||||
−0.149479 | + | 0.988765i | \(0.547760\pi\) | |||||||
\(692\) | −41.5159 | −1.57820 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.76490 | 0.104954 | ||||||||
\(695\) | −7.13040 | −0.270471 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.68545 | 0.328985 | ||||||||
\(698\) | 1.25745 | 0.0475952 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.584362 | −0.0220868 | ||||||||
\(701\) | 37.9287 | 1.43255 | 0.716274 | − | 0.697819i | \(-0.245846\pi\) | ||||
0.716274 | + | 0.697819i | \(0.245846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.2027 | −1.55399 | ||||||||
\(704\) | 14.3059 | 0.539173 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.04755 | 0.265238 | ||||||||
\(707\) | −10.6965 | −0.402282 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.3664 | −0.577096 | −0.288548 | − | 0.957465i | \(-0.593172\pi\) | ||||
−0.288548 | + | 0.957465i | \(0.593172\pi\) | |||||||
\(710\) | −6.23575 | −0.234023 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.901330 | −0.0337788 | ||||||||
\(713\) | −1.85104 | −0.0693220 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.10936 | −0.303273 | ||||||||
\(716\) | −45.9708 | −1.71801 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.29723 | −0.0857318 | ||||||||
\(719\) | −20.3461 | −0.758783 | −0.379392 | − | 0.925236i | \(-0.623867\pi\) | ||||
−0.379392 | + | 0.925236i | \(0.623867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9318 | 0.556090 | ||||||||
\(722\) | 2.95665 | 0.110035 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −34.1233 | −1.26818 | ||||||||
\(725\) | −0.806243 | −0.0299431 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.2751 | 1.15993 | 0.579965 | − | 0.814641i | \(-0.303066\pi\) | ||||
0.579965 | + | 0.814641i | \(0.303066\pi\) | |||||||
\(728\) | 1.47799 | 0.0547780 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.10958 | 0.0780790 | ||||||||
\(731\) | −0.984623 | −0.0364176 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.8273 | −1.10170 | −0.550848 | − | 0.834606i | \(-0.685696\pi\) | ||||
−0.550848 | + | 0.834606i | \(0.685696\pi\) | |||||||
\(734\) | 2.92716 | 0.108043 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.74558 | −0.174925 | ||||||||
\(737\) | −14.0167 | −0.516311 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.0703 | 1.80508 | 0.902539 | − | 0.430607i | \(-0.141701\pi\) | ||||
0.902539 | + | 0.430607i | \(0.141701\pi\) | |||||||
\(740\) | −30.2138 | −1.11068 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.31422 | −0.0482466 | ||||||||
\(743\) | −14.4447 | −0.529925 | −0.264962 | − | 0.964259i | \(-0.585360\pi\) | ||||
−0.264962 | + | 0.964259i | \(0.585360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.3241 | −1.18426 | ||||||||
\(746\) | −3.63124 | −0.132949 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.03336 | 0.330292 | ||||||||
\(749\) | 12.2693 | 0.448310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.1877 | −1.42998 | −0.714989 | − | 0.699136i | \(-0.753568\pi\) | ||||
−0.714989 | + | 0.699136i | \(0.753568\pi\) | |||||||
\(752\) | −15.2948 | −0.557743 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.00895 | 0.0367437 | ||||||||
\(755\) | 15.6093 | 0.568082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1509 | 0.914125 | 0.457063 | − | 0.889435i | \(-0.348902\pi\) | ||||
0.457063 | + | 0.889435i | \(0.348902\pi\) | |||||||
\(758\) | 1.73460 | 0.0630034 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1065 | 0.366602 | ||||||||
\(761\) | 14.0558 | 0.509521 | 0.254760 | − | 0.967004i | \(-0.418003\pi\) | ||||
0.254760 | + | 0.967004i | \(0.418003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.53666 | 0.0556308 | ||||||||
\(764\) | −20.1792 | −0.730057 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.07919 | 0.219650 | ||||||||
\(767\) | −25.1808 | −0.909225 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.79434 | −0.136827 | −0.0684137 | − | 0.997657i | \(-0.521794\pi\) | ||||
−0.0684137 | + | 0.997657i | \(0.521794\pi\) | |||||||
\(770\) | 0.897643 | 0.0323488 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.8546 | 0.390667 | ||||||||
\(773\) | −3.70140 | −0.133130 | −0.0665651 | − | 0.997782i | \(-0.521204\pi\) | ||||
−0.0665651 | + | 0.997782i | \(0.521204\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.276107 | −0.00991805 | ||||||||
\(776\) | −5.66999 | −0.203541 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.66302 | 0.0596221 | ||||||||
\(779\) | −22.2111 | −0.795795 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.8073 | 1.03081 | ||||||||
\(782\) | −0.920889 | −0.0329309 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.75374 | 0.134062 | ||||||||
\(785\) | −21.5644 | −0.769667 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.4190 | −1.11997 | −0.559983 | − | 0.828504i | \(-0.689192\pi\) | ||||
−0.559983 | + | 0.828504i | \(0.689192\pi\) | |||||||
\(788\) | 21.6858 | 0.772525 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.78095 | 0.170099 | ||||||||
\(791\) | −1.85798 | −0.0660621 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.9883 | −0.603271 | ||||||||
\(794\) | −0.267008 | −0.00947576 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.1652 | −0.927402 | ||||||||
\(797\) | 1.53832 | 0.0544901 | 0.0272450 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272450 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.22800 | −0.326463 | ||||||||
\(800\) | −0.707866 | −0.0250268 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.74671 | −0.238234 | ||||||||
\(803\) | −9.74562 | −0.343916 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.33695 | 0.152857 | ||||||||
\(806\) | 0.345525 | 0.0121706 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.60815 | −0.302834 | ||||||||
\(809\) | −8.97381 | −0.315502 | −0.157751 | − | 0.987479i | \(-0.550424\pi\) | ||||
−0.157751 | + | 0.987479i | \(0.550424\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.0991 | 1.51341 | 0.756707 | − | 0.653754i | \(-0.226807\pi\) | ||||
0.756707 | + | 0.653754i | \(0.226807\pi\) | |||||||
\(812\) | 5.29307 | 0.185750 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.94508 | −0.103225 | ||||||||
\(815\) | −45.6357 | −1.59855 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.51795 | 0.0880920 | ||||||||
\(818\) | −6.07932 | −0.212559 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.2873 | −0.568779 | ||||||||
\(821\) | 24.2970 | 0.847971 | 0.423985 | − | 0.905669i | \(-0.360631\pi\) | ||||
0.423985 | + | 0.905669i | \(0.360631\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.3470 | 0.813825 | 0.406913 | − | 0.913467i | \(-0.366605\pi\) | ||||
0.406913 | + | 0.913467i | \(0.366605\pi\) | |||||||
\(824\) | 12.0166 | 0.418618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.78731 | 0.0969830 | ||||||||
\(827\) | −53.3817 | −1.85626 | −0.928131 | − | 0.372253i | \(-0.878585\pi\) | ||||
−0.928131 | + | 0.372253i | \(0.878585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.5788 | −1.58302 | −0.791509 | − | 0.611157i | \(-0.790704\pi\) | ||||
−0.791509 | + | 0.611157i | \(0.790704\pi\) | |||||||
\(830\) | −2.19197 | −0.0760845 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.9020 | −0.447298 | ||||||||
\(833\) | 2.26480 | 0.0784705 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.6697 | −0.715303 | ||||||||
\(836\) | −23.1008 | −0.798958 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.81396 | −0.235384 | ||||||||
\(839\) | 41.0272 | 1.41642 | 0.708208 | − | 0.706004i | \(-0.249504\pi\) | ||||
0.708208 | + | 0.706004i | \(0.249504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6972 | −0.748178 | ||||||||
\(842\) | −6.72765 | −0.231850 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −45.8133 | −1.57696 | ||||||||
\(845\) | −20.8747 | −0.718111 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.85316 | 0.235477 | ||||||||
\(848\) | 24.2668 | 0.833327 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.137363 | −0.00471150 | ||||||||
\(851\) | −14.2291 | −0.487768 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.58986 | 0.0544359 | 0.0272179 | − | 0.999630i | \(-0.491335\pi\) | ||||
0.0272179 | + | 0.999630i | \(0.491335\pi\) | |||||||
\(854\) | 1.88047 | 0.0643483 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.87390 | 0.337483 | ||||||||
\(857\) | −15.7373 | −0.537578 | −0.268789 | − | 0.963199i | \(-0.586623\pi\) | ||||
−0.268789 | + | 0.963199i | \(0.586623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.73832 | 0.127550 | 0.0637749 | − | 0.997964i | \(-0.479686\pi\) | ||||
0.0637749 | + | 0.997964i | \(0.479686\pi\) | |||||||
\(860\) | 1.84641 | 0.0629620 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.386615 | 0.0131682 | ||||||||
\(863\) | −22.7338 | −0.773869 | −0.386934 | − | 0.922107i | \(-0.626466\pi\) | ||||
−0.386934 | + | 0.922107i | \(0.626466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 45.9597 | 1.56268 | ||||||||
\(866\) | −4.56677 | −0.155185 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.81267 | 0.0615260 | ||||||||
\(869\) | −22.0866 | −0.749235 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6412 | 0.428332 | ||||||||
\(872\) | 1.23665 | 0.0418782 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.35497 | 0.0796580 | ||||||||
\(875\) | 11.4886 | 0.388384 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.9098 | −1.34766 | −0.673828 | − | 0.738888i | \(-0.735351\pi\) | ||||
−0.673828 | + | 0.738888i | \(0.735351\pi\) | |||||||
\(878\) | 1.29327 | 0.0436456 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.5748 | −0.558737 | ||||||||
\(881\) | 50.9994 | 1.71821 | 0.859106 | − | 0.511798i | \(-0.171020\pi\) | ||||
0.859106 | + | 0.511798i | \(0.171020\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.228422 | −0.00768700 | −0.00384350 | − | 0.999993i | \(-0.501223\pi\) | ||||
−0.00384350 | + | 0.999993i | \(0.501223\pi\) | |||||||
\(884\) | −8.14693 | −0.274011 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.39802 | 0.0805632 | ||||||||
\(887\) | 27.4320 | 0.921078 | 0.460539 | − | 0.887639i | \(-0.347656\pi\) | ||||
0.460539 | + | 0.887639i | \(0.347656\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 0.493696 | 0.0165487 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 47.4392 | 1.58838 | ||||||||
\(893\) | 23.5985 | 0.789695 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.8916 | 1.70112 | ||||||||
\(896\) | 6.17342 | 0.206240 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.45289 | −0.181965 | ||||||||
\(899\) | 2.50094 | 0.0834109 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.6412 | 0.487770 | ||||||||
\(902\) | −1.58760 | −0.0528613 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.49524 | −0.0497308 | ||||||||
\(905\) | 37.7759 | 1.25571 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.4064 | −0.511562 | −0.255781 | − | 0.966735i | \(-0.582333\pi\) | ||||
−0.255781 | + | 0.966735i | \(0.582333\pi\) | |||||||
\(908\) | 56.8649 | 1.88713 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.809558 | −0.0268366 | ||||||||
\(911\) | −52.7023 | −1.74610 | −0.873052 | − | 0.487627i | \(-0.837863\pi\) | ||||
−0.873052 | + | 0.487627i | \(0.837863\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.1263 | 0.335130 | ||||||||
\(914\) | −2.09241 | −0.0692108 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.957852 | 0.0316483 | ||||||||
\(917\) | 5.09715 | 0.168323 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.5827 | 1.63558 | 0.817792 | − | 0.575514i | \(-0.195198\pi\) | ||||
0.817792 | + | 0.575514i | \(0.195198\pi\) | |||||||
\(920\) | 3.49022 | 0.115069 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.14704 | −0.235375 | ||||||||
\(923\) | −25.9804 | −0.855156 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.12246 | −0.0697860 | ||||||||
\(926\) | −7.18394 | −0.236079 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.41175 | 0.210476 | ||||||||
\(929\) | −43.3260 | −1.42148 | −0.710740 | − | 0.703455i | \(-0.751640\pi\) | ||||
−0.710740 | + | 0.703455i | \(0.751640\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.79171 | −0.189816 | ||||||||
\(932\) | 31.8631 | 1.04371 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.47249 | −0.0481812 | ||||||||
\(935\) | −10.0003 | −0.327045 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.45956 | 0.178356 | 0.0891780 | − | 0.996016i | \(-0.471576\pi\) | ||||
0.0891780 | + | 0.996016i | \(0.471576\pi\) | |||||||
\(938\) | −1.39928 | −0.0456882 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17.3048 | 0.564419 | ||||||||
\(941\) | 13.6724 | 0.445708 | 0.222854 | − | 0.974852i | \(-0.428463\pi\) | ||||
0.222854 | + | 0.974852i | \(0.428463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.67047 | −0.249785 | ||||||||
\(944\) | −51.4672 | −1.67511 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.179978 | 0.00585158 | ||||||||
\(947\) | −2.37187 | −0.0770756 | −0.0385378 | − | 0.999257i | \(-0.512270\pi\) | ||||
−0.0385378 | + | 0.999257i | \(0.512270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.78929 | 0.285313 | ||||||||
\(950\) | 0.351274 | 0.0113968 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.82263 | 0.0590717 | ||||||||
\(953\) | −23.0787 | −0.747591 | −0.373796 | − | 0.927511i | \(-0.621944\pi\) | ||||
−0.373796 | + | 0.927511i | \(0.621944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.3392 | 0.722878 | ||||||||
\(956\) | 36.4843 | 1.17999 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.00437 | 0.0647582 | ||||||||
\(959\) | −3.51026 | −0.113352 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1435 | −0.972372 | ||||||||
\(962\) | 2.65608 | 0.0856355 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.5890 | 1.14624 | ||||||||
\(965\) | −12.0165 | −0.386825 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.81160 | 0.315520 | 0.157760 | − | 0.987477i | \(-0.449573\pi\) | ||||
0.157760 | + | 0.987477i | \(0.449573\pi\) | |||||||
\(968\) | 5.51518 | 0.177265 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.10569 | 0.0997177 | ||||||||
\(971\) | −15.2562 | −0.489594 | −0.244797 | − | 0.969574i | \(-0.578721\pi\) | ||||
−0.244797 | + | 0.969574i | \(0.578721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.28843 | 0.105422 | ||||||||
\(974\) | 0.482953 | 0.0154748 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −34.7225 | −1.11144 | ||||||||
\(977\) | 3.90224 | 0.124844 | 0.0624219 | − | 0.998050i | \(-0.480118\pi\) | ||||
0.0624219 | + | 0.998050i | \(0.480118\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.28073 | −0.0728924 | ||||||||
\(980\) | −4.24705 | −0.135667 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.78392 | 0.184572 | ||||||||
\(983\) | 53.3262 | 1.70084 | 0.850420 | − | 0.526104i | \(-0.176348\pi\) | ||||
0.850420 | + | 0.526104i | \(0.176348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0071 | −0.764929 | ||||||||
\(986\) | 1.24421 | 0.0396238 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.8339 | 0.662816 | ||||||||
\(989\) | 0.869560 | 0.0276504 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.5111 | 0.619790 | 0.309895 | − | 0.950771i | \(-0.399706\pi\) | ||||
0.309895 | + | 0.950771i | \(0.399706\pi\) | |||||||
\(992\) | 2.19578 | 0.0697159 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.87583 | 0.0912158 | ||||||||
\(995\) | 28.9660 | 0.918283 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.8824 | 1.45311 | 0.726556 | − | 0.687108i | \(-0.241120\pi\) | ||||
0.726556 | + | 0.687108i | \(0.241120\pi\) | |||||||
\(998\) | −2.61379 | −0.0827382 | ||||||||
\(999\) | 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 | 8001.2.a.z.1.17 | yes | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.16 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.16 | ✓ | 32 | 3.2 | odd | 2 | inner | |
8001.2.a.z.1.17 | yes | 32 | 1.1 | even | 1 | trivial |