Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, 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("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.29150 | 1.59545 | 0.797724 | − | 0.603023i | \(-0.206037\pi\) | ||||
0.797724 | + | 0.603023i | \(0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.645751 | −0.179099 | −0.0895496 | − | 0.995982i | \(-0.528543\pi\) | ||||
−0.0895496 | + | 0.995982i | \(0.528543\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.29150 | 0.984538 | 0.492269 | − | 0.870443i | \(-0.336168\pi\) | ||||
0.492269 | + | 0.870443i | \(0.336168\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.29150 | 1.12815 | ||||||||
\(23\) | −3.64575 | −0.760192 | −0.380096 | − | 0.924947i | \(-0.624109\pi\) | ||||
−0.380096 | + | 0.924947i | \(0.624109\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.645751 | −0.126642 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 5.35425 | 0.994259 | 0.497130 | − | 0.867676i | \(-0.334387\pi\) | ||||
0.497130 | + | 0.867676i | \(0.334387\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.29150 | 0.591171 | 0.295586 | − | 0.955316i | \(-0.404485\pi\) | ||||
0.295586 | + | 0.955316i | \(0.404485\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.35425 | 0.715834 | 0.357917 | − | 0.933753i | \(-0.383487\pi\) | ||||
0.357917 | + | 0.933753i | \(0.383487\pi\) | |||||||
\(38\) | 4.29150 | 0.696174 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.29150 | 0.514046 | 0.257023 | − | 0.966405i | \(-0.417258\pi\) | ||||
0.257023 | + | 0.966405i | \(0.417258\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.64575 | −0.860969 | −0.430485 | − | 0.902598i | \(-0.641657\pi\) | ||||
−0.430485 | + | 0.902598i | \(0.641657\pi\) | |||||||
\(44\) | 5.29150 | 0.797724 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.64575 | −0.537537 | ||||||||
\(47\) | −4.64575 | −0.677652 | −0.338826 | − | 0.940849i | \(-0.610030\pi\) | ||||
−0.338826 | + | 0.940849i | \(0.610030\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.645751 | −0.0895496 | ||||||||
\(53\) | −2.64575 | −0.363422 | −0.181711 | − | 0.983352i | \(-0.558164\pi\) | ||||
−0.181711 | + | 0.983352i | \(0.558164\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.35425 | 0.703047 | ||||||||
\(59\) | 2.70850 | 0.352616 | 0.176308 | − | 0.984335i | \(-0.443584\pi\) | ||||
0.176308 | + | 0.984335i | \(0.443584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.64575 | −0.338754 | −0.169377 | − | 0.985551i | \(-0.554176\pi\) | ||||
−0.169377 | + | 0.985551i | \(0.554176\pi\) | |||||||
\(62\) | 3.29150 | 0.418021 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9373 | 1.33620 | 0.668099 | − | 0.744072i | \(-0.267108\pi\) | ||||
0.668099 | + | 0.744072i | \(0.267108\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.708497 | 0.0840832 | 0.0420416 | − | 0.999116i | \(-0.486614\pi\) | ||||
0.0420416 | + | 0.999116i | \(0.486614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.29150 | −0.619324 | −0.309662 | − | 0.950847i | \(-0.600216\pi\) | ||||
−0.309662 | + | 0.950847i | \(0.600216\pi\) | |||||||
\(74\) | 4.35425 | 0.506171 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.29150 | 0.492269 | ||||||||
\(77\) | −5.29150 | −0.603023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0627461 | −0.00705948 | −0.00352974 | − | 0.999994i | \(-0.501124\pi\) | ||||
−0.00352974 | + | 0.999994i | \(0.501124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.29150 | 0.363486 | ||||||||
\(83\) | −1.64575 | −0.180645 | −0.0903223 | − | 0.995913i | \(-0.528790\pi\) | ||||
−0.0903223 | + | 0.995913i | \(0.528790\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.64575 | −0.608797 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.29150 | 0.564076 | ||||||||
\(89\) | 1.00000 | 0.106000 | 0.0529999 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0529999 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.645751 | 0.0676931 | ||||||||
\(92\) | −3.64575 | −0.380096 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.64575 | −0.479173 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.93725 | −0.298233 | −0.149116 | − | 0.988820i | \(-0.547643\pi\) | ||||
−0.149116 | + | 0.988820i | \(0.547643\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.06275 | 0.105747 | 0.0528736 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528736 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8745 | 1.36710 | 0.683548 | − | 0.729906i | \(-0.260436\pi\) | ||||
0.683548 | + | 0.729906i | \(0.260436\pi\) | |||||||
\(104\) | −0.645751 | −0.0633211 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.64575 | −0.256978 | ||||||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.64575 | 0.349200 | 0.174600 | − | 0.984639i | \(-0.444137\pi\) | ||||
0.174600 | + | 0.984639i | \(0.444137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −12.5830 | −1.18371 | −0.591855 | − | 0.806045i | \(-0.701604\pi\) | ||||
−0.591855 | + | 0.806045i | \(0.701604\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.35425 | 0.497130 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.70850 | 0.249337 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.0000 | 1.54545 | ||||||||
\(122\) | −2.64575 | −0.239535 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.29150 | 0.295586 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.35425 | 0.830055 | 0.415028 | − | 0.909809i | \(-0.363772\pi\) | ||||
0.415028 | + | 0.909809i | \(0.363772\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.06275 | 0.267593 | 0.133797 | − | 0.991009i | \(-0.457283\pi\) | ||||
0.133797 | + | 0.991009i | \(0.457283\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.29150 | −0.372120 | ||||||||
\(134\) | 10.9373 | 0.944835 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 2.35425 | 0.201137 | 0.100569 | − | 0.994930i | \(-0.467934\pi\) | ||||
0.100569 | + | 0.994930i | \(0.467934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5830 | −1.40655 | −0.703276 | − | 0.710917i | \(-0.748280\pi\) | ||||
−0.703276 | + | 0.710917i | \(0.748280\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.708497 | 0.0594558 | ||||||||
\(143\) | −3.41699 | −0.285743 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.29150 | −0.437928 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.35425 | 0.357917 | ||||||||
\(149\) | 22.5203 | 1.84493 | 0.922466 | − | 0.386079i | \(-0.126171\pi\) | ||||
0.922466 | + | 0.386079i | \(0.126171\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.2288 | −1.07654 | −0.538270 | − | 0.842772i | \(-0.680922\pi\) | ||||
−0.538270 | + | 0.842772i | \(0.680922\pi\) | |||||||
\(152\) | 4.29150 | 0.348087 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.29150 | −0.426401 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.35425 | −0.108081 | −0.0540404 | − | 0.998539i | \(-0.517210\pi\) | ||||
−0.0540404 | + | 0.998539i | \(0.517210\pi\) | |||||||
\(158\) | −0.0627461 | −0.00499181 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.64575 | 0.287325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8745 | 0.930083 | 0.465042 | − | 0.885289i | \(-0.346039\pi\) | ||||
0.465042 | + | 0.885289i | \(0.346039\pi\) | |||||||
\(164\) | 3.29150 | 0.257023 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.64575 | −0.127735 | ||||||||
\(167\) | 17.1660 | 1.32835 | 0.664173 | − | 0.747579i | \(-0.268784\pi\) | ||||
0.664173 | + | 0.747579i | \(0.268784\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5830 | −0.967923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.64575 | −0.430485 | ||||||||
\(173\) | −1.64575 | −0.125124 | −0.0625621 | − | 0.998041i | \(-0.519927\pi\) | ||||
−0.0625621 | + | 0.998041i | \(0.519927\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.29150 | 0.398862 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00000 | 0.0749532 | ||||||||
\(179\) | −17.5830 | −1.31422 | −0.657108 | − | 0.753797i | \(-0.728220\pi\) | ||||
−0.657108 | + | 0.753797i | \(0.728220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6458 | 1.68325 | 0.841623 | − | 0.540066i | \(-0.181601\pi\) | ||||
0.841623 | + | 0.540066i | \(0.181601\pi\) | |||||||
\(182\) | 0.645751 | 0.0478663 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.64575 | −0.268768 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.29150 | −0.386953 | ||||||||
\(188\) | −4.64575 | −0.338826 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.5830 | 1.05519 | 0.527595 | − | 0.849496i | \(-0.323094\pi\) | ||||
0.527595 | + | 0.849496i | \(0.323094\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8745 | 1.07069 | 0.535345 | − | 0.844633i | \(-0.320182\pi\) | ||||
0.535345 | + | 0.844633i | \(0.320182\pi\) | |||||||
\(194\) | −2.93725 | −0.210883 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 13.3542 | 0.951451 | 0.475725 | − | 0.879594i | \(-0.342186\pi\) | ||||
0.475725 | + | 0.879594i | \(0.342186\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5203 | −1.24198 | −0.620989 | − | 0.783819i | \(-0.713269\pi\) | ||||
−0.620989 | + | 0.783819i | \(0.713269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.06275 | 0.0747746 | ||||||||
\(203\) | −5.35425 | −0.375795 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.8745 | 0.966683 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.645751 | −0.0447748 | ||||||||
\(209\) | 22.7085 | 1.57078 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.7085 | 1.01257 | 0.506287 | − | 0.862365i | \(-0.331018\pi\) | ||||
0.506287 | + | 0.862365i | \(0.331018\pi\) | |||||||
\(212\) | −2.64575 | −0.181711 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | 0.410152 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.29150 | −0.223442 | ||||||||
\(218\) | 3.64575 | 0.246921 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.645751 | 0.0434379 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.5203 | −1.03931 | −0.519657 | − | 0.854375i | \(-0.673940\pi\) | ||||
−0.519657 | + | 0.854375i | \(0.673940\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.5830 | −0.837009 | ||||||||
\(227\) | 11.6458 | 0.772956 | 0.386478 | − | 0.922299i | \(-0.373692\pi\) | ||||
0.386478 | + | 0.922299i | \(0.373692\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5203 | −1.62034 | −0.810172 | − | 0.586192i | \(-0.800626\pi\) | ||||
−0.810172 | + | 0.586192i | \(0.800626\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.35425 | 0.351524 | ||||||||
\(233\) | 3.64575 | 0.238841 | 0.119421 | − | 0.992844i | \(-0.461896\pi\) | ||||
0.119421 | + | 0.992844i | \(0.461896\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.70850 | 0.176308 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.00000 | 0.0648204 | ||||||||
\(239\) | 19.6458 | 1.27078 | 0.635389 | − | 0.772192i | \(-0.280840\pi\) | ||||
0.635389 | + | 0.772192i | \(0.280840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.93725 | 0.189205 | 0.0946026 | − | 0.995515i | \(-0.469842\pi\) | ||||
0.0946026 | + | 0.995515i | \(0.469842\pi\) | |||||||
\(242\) | 17.0000 | 1.09280 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.64575 | −0.169377 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.77124 | −0.176330 | ||||||||
\(248\) | 3.29150 | 0.209011 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.8745 | 1.75942 | 0.879712 | − | 0.475507i | \(-0.157736\pi\) | ||||
0.879712 | + | 0.475507i | \(0.157736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.2915 | −1.21285 | ||||||||
\(254\) | 9.35425 | 0.586938 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.29150 | −0.517210 | −0.258605 | − | 0.965983i | \(-0.583263\pi\) | ||||
−0.258605 | + | 0.965983i | \(0.583263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.35425 | −0.270560 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.06275 | 0.189217 | ||||||||
\(263\) | 11.8745 | 0.732214 | 0.366107 | − | 0.930573i | \(-0.380690\pi\) | ||||
0.366107 | + | 0.930573i | \(0.380690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.29150 | −0.263129 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.9373 | 0.668099 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.70850 | −0.286021 | −0.143010 | − | 0.989721i | \(-0.545678\pi\) | ||||
−0.143010 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.35425 | 0.142225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.2915 | 1.51962 | 0.759810 | − | 0.650146i | \(-0.225292\pi\) | ||||
0.759810 | + | 0.650146i | \(0.225292\pi\) | |||||||
\(278\) | −16.5830 | −0.994583 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.5203 | −1.40310 | −0.701551 | − | 0.712620i | \(-0.747509\pi\) | ||||
−0.701551 | + | 0.712620i | \(0.747509\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.1660 | −1.79318 | −0.896592 | − | 0.442858i | \(-0.853964\pi\) | ||||
−0.896592 | + | 0.442858i | \(0.853964\pi\) | |||||||
\(284\) | 0.708497 | 0.0420416 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.41699 | −0.202051 | ||||||||
\(287\) | −3.29150 | −0.194291 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.29150 | −0.309662 | ||||||||
\(293\) | 5.52026 | 0.322497 | 0.161248 | − | 0.986914i | \(-0.448448\pi\) | ||||
0.161248 | + | 0.986914i | \(0.448448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.35425 | 0.253086 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.5203 | 1.30456 | ||||||||
\(299\) | 2.35425 | 0.136150 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.64575 | 0.325416 | ||||||||
\(302\) | −13.2288 | −0.761229 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.29150 | 0.246135 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.70850 | −0.382874 | −0.191437 | − | 0.981505i | \(-0.561315\pi\) | ||||
−0.191437 | + | 0.981505i | \(0.561315\pi\) | |||||||
\(308\) | −5.29150 | −0.301511 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7085 | −0.607223 | −0.303612 | − | 0.952796i | \(-0.598193\pi\) | ||||
−0.303612 | + | 0.952796i | \(0.598193\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2288 | 0.804257 | 0.402128 | − | 0.915583i | \(-0.368271\pi\) | ||||
0.402128 | + | 0.915583i | \(0.368271\pi\) | |||||||
\(314\) | −1.35425 | −0.0764247 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0627461 | −0.00352974 | ||||||||
\(317\) | 14.0627 | 0.789843 | 0.394921 | − | 0.918715i | \(-0.370772\pi\) | ||||
0.394921 | + | 0.918715i | \(0.370772\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 28.3320 | 1.58629 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.64575 | 0.203170 | ||||||||
\(323\) | −4.29150 | −0.238786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.8745 | 0.657668 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.29150 | 0.181743 | ||||||||
\(329\) | 4.64575 | 0.256129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.35425 | −0.239331 | −0.119666 | − | 0.992814i | \(-0.538182\pi\) | ||||
−0.119666 | + | 0.992814i | \(0.538182\pi\) | |||||||
\(332\) | −1.64575 | −0.0903223 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.1660 | 0.939282 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1660 | −0.880619 | −0.440309 | − | 0.897846i | \(-0.645131\pi\) | ||||
−0.440309 | + | 0.897846i | \(0.645131\pi\) | |||||||
\(338\) | −12.5830 | −0.684425 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.4170 | 0.943183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.64575 | −0.304399 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.64575 | −0.0884761 | ||||||||
\(347\) | 20.2915 | 1.08930 | 0.544652 | − | 0.838662i | \(-0.316662\pi\) | ||||
0.544652 | + | 0.838662i | \(0.316662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.6458 | −0.783969 | −0.391985 | − | 0.919972i | \(-0.628211\pi\) | ||||
−0.391985 | + | 0.919972i | \(0.628211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.29150 | 0.282038 | ||||||||
\(353\) | −36.4575 | −1.94044 | −0.970219 | − | 0.242230i | \(-0.922121\pi\) | ||||
−0.970219 | + | 0.242230i | \(0.922121\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.00000 | 0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.5830 | −0.929291 | ||||||||
\(359\) | 11.4170 | 0.602566 | 0.301283 | − | 0.953535i | \(-0.402585\pi\) | ||||
0.301283 | + | 0.953535i | \(0.402585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.583005 | −0.0306845 | ||||||||
\(362\) | 22.6458 | 1.19023 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.645751 | 0.0338466 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.9373 | 0.779718 | 0.389859 | − | 0.920874i | \(-0.372524\pi\) | ||||
0.389859 | + | 0.920874i | \(0.372524\pi\) | |||||||
\(368\) | −3.64575 | −0.190048 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.64575 | 0.137361 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.87451 | −0.407727 | −0.203863 | − | 0.978999i | \(-0.565350\pi\) | ||||
−0.203863 | + | 0.978999i | \(0.565350\pi\) | |||||||
\(374\) | −5.29150 | −0.273617 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.64575 | −0.239586 | ||||||||
\(377\) | −3.45751 | −0.178071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2288 | 1.24455 | 0.622274 | − | 0.782800i | \(-0.286209\pi\) | ||||
0.622274 | + | 0.782800i | \(0.286209\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.5830 | 0.746131 | ||||||||
\(383\) | −16.7085 | −0.853764 | −0.426882 | − | 0.904307i | \(-0.640388\pi\) | ||||
−0.426882 | + | 0.904307i | \(0.640388\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.8745 | 0.757093 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.93725 | −0.149116 | ||||||||
\(389\) | 34.3948 | 1.74388 | 0.871942 | − | 0.489609i | \(-0.162861\pi\) | ||||
0.871942 | + | 0.489609i | \(0.162861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.64575 | 0.184374 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.3542 | 0.672777 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.5203 | 1.63215 | 0.816073 | − | 0.577950i | \(-0.196147\pi\) | ||||
0.816073 | + | 0.577950i | \(0.196147\pi\) | |||||||
\(398\) | −17.5203 | −0.878211 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.06275 | −0.452572 | −0.226286 | − | 0.974061i | \(-0.572658\pi\) | ||||
−0.226286 | + | 0.974061i | \(0.572658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.12549 | −0.105878 | ||||||||
\(404\) | 1.06275 | 0.0528736 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.35425 | −0.265727 | ||||||||
\(407\) | 23.0405 | 1.14208 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.2288 | 0.901354 | 0.450677 | − | 0.892687i | \(-0.351183\pi\) | ||||
0.450677 | + | 0.892687i | \(0.351183\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.8745 | 0.683548 | ||||||||
\(413\) | −2.70850 | −0.133276 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.645751 | −0.0316606 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.7085 | 1.11071 | ||||||||
\(419\) | 27.6458 | 1.35058 | 0.675292 | − | 0.737551i | \(-0.264018\pi\) | ||||
0.675292 | + | 0.737551i | \(0.264018\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.5830 | 0.808206 | 0.404103 | − | 0.914713i | \(-0.367584\pi\) | ||||
0.404103 | + | 0.914713i | \(0.367584\pi\) | |||||||
\(422\) | 14.7085 | 0.715998 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.64575 | −0.128489 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.64575 | 0.128037 | ||||||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.12549 | 0.102381 | 0.0511907 | − | 0.998689i | \(-0.483698\pi\) | ||||
0.0511907 | + | 0.998689i | \(0.483698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.2915 | −0.542635 | −0.271317 | − | 0.962490i | \(-0.587459\pi\) | ||||
−0.271317 | + | 0.962490i | \(0.587459\pi\) | |||||||
\(434\) | −3.29150 | −0.157997 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.64575 | 0.174600 | ||||||||
\(437\) | −15.6458 | −0.748438 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.9373 | −1.47655 | −0.738277 | − | 0.674497i | \(-0.764360\pi\) | ||||
−0.738277 | + | 0.674497i | \(0.764360\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.645751 | 0.0307153 | ||||||||
\(443\) | 33.5830 | 1.59558 | 0.797788 | − | 0.602938i | \(-0.206003\pi\) | ||||
0.797788 | + | 0.602938i | \(0.206003\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.5203 | −0.734906 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −18.2288 | −0.860268 | −0.430134 | − | 0.902765i | \(-0.641534\pi\) | ||||
−0.430134 | + | 0.902765i | \(0.641534\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.4170 | 0.820134 | ||||||||
\(452\) | −12.5830 | −0.591855 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.6458 | 0.546562 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.12549 | −0.333316 | −0.166658 | − | 0.986015i | \(-0.553298\pi\) | ||||
−0.166658 | + | 0.986015i | \(0.553298\pi\) | |||||||
\(458\) | −24.5203 | −1.14576 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.5203 | −1.56119 | −0.780597 | − | 0.625035i | \(-0.785085\pi\) | ||||
−0.780597 | + | 0.625035i | \(0.785085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.35425 | 0.0629373 | 0.0314686 | − | 0.999505i | \(-0.489982\pi\) | ||||
0.0314686 | + | 0.999505i | \(0.489982\pi\) | |||||||
\(464\) | 5.35425 | 0.248565 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.64575 | 0.168886 | ||||||||
\(467\) | 39.2915 | 1.81819 | 0.909097 | − | 0.416585i | \(-0.136773\pi\) | ||||
0.909097 | + | 0.416585i | \(0.136773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.9373 | −0.505035 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.70850 | 0.124669 | ||||||||
\(473\) | −29.8745 | −1.37363 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.00000 | 0.0458349 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.6458 | 0.898576 | ||||||||
\(479\) | 12.6458 | 0.577799 | 0.288900 | − | 0.957359i | \(-0.406711\pi\) | ||||
0.288900 | + | 0.957359i | \(0.406711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.81176 | −0.128205 | ||||||||
\(482\) | 2.93725 | 0.133788 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.0000 | 0.772727 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2915 | −0.511667 | −0.255833 | − | 0.966721i | \(-0.582350\pi\) | ||||
−0.255833 | + | 0.966721i | \(0.582350\pi\) | |||||||
\(488\) | −2.64575 | −0.119768 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.8745 | −0.851795 | −0.425897 | − | 0.904772i | \(-0.640042\pi\) | ||||
−0.425897 | + | 0.904772i | \(0.640042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.35425 | −0.241143 | ||||||||
\(494\) | −2.77124 | −0.124684 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.29150 | 0.147793 | ||||||||
\(497\) | −0.708497 | −0.0317805 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.9373 | 1.29541 | 0.647705 | − | 0.761891i | \(-0.275729\pi\) | ||||
0.647705 | + | 0.761891i | \(0.275729\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 27.8745 | 1.24410 | ||||||||
\(503\) | 13.2915 | 0.592639 | 0.296319 | − | 0.955089i | \(-0.404241\pi\) | ||||
0.296319 | + | 0.955089i | \(0.404241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.2915 | −0.857612 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.35425 | 0.415028 | ||||||||
\(509\) | 29.5203 | 1.30846 | 0.654231 | − | 0.756295i | \(-0.272992\pi\) | ||||
0.654231 | + | 0.756295i | \(0.272992\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.29150 | 0.234082 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.29150 | −0.365723 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.5830 | −1.08116 | ||||||||
\(518\) | −4.35425 | −0.191315 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.41699 | 0.368755 | 0.184378 | − | 0.982855i | \(-0.440973\pi\) | ||||
0.184378 | + | 0.982855i | \(0.440973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.7490 | −1.60692 | −0.803461 | − | 0.595357i | \(-0.797011\pi\) | ||||
−0.803461 | + | 0.595357i | \(0.797011\pi\) | |||||||
\(524\) | 3.06275 | 0.133797 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.8745 | 0.517753 | ||||||||
\(527\) | −3.29150 | −0.143380 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.70850 | −0.422109 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.29150 | −0.186060 | ||||||||
\(533\) | −2.12549 | −0.0920653 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.9373 | 0.472417 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.00000 | 0.258678 | ||||||||
\(539\) | 5.29150 | 0.227921 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.35425 | −0.359177 | −0.179589 | − | 0.983742i | \(-0.557477\pi\) | ||||
−0.179589 | + | 0.983742i | \(0.557477\pi\) | |||||||
\(542\) | −4.70850 | −0.202247 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 2.35425 | 0.100569 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.9778 | 0.978886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.0627461 | 0.00266823 | ||||||||
\(554\) | 25.2915 | 1.07453 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.5830 | −0.703276 | ||||||||
\(557\) | 32.5203 | 1.37793 | 0.688964 | − | 0.724796i | \(-0.258066\pi\) | ||||
0.688964 | + | 0.724796i | \(0.258066\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.64575 | 0.154199 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.5203 | −0.992142 | ||||||||
\(563\) | −38.9373 | −1.64101 | −0.820505 | − | 0.571640i | \(-0.806308\pi\) | ||||
−0.820505 | + | 0.571640i | \(0.806308\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −30.1660 | −1.26797 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.708497 | 0.0297279 | ||||||||
\(569\) | −5.16601 | −0.216570 | −0.108285 | − | 0.994120i | \(-0.534536\pi\) | ||||
−0.108285 | + | 0.994120i | \(0.534536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.58301 | −0.359188 | −0.179594 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179594 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(572\) | −3.41699 | −0.142872 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.29150 | −0.137385 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.0000 | 0.666089 | 0.333044 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333044 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(578\) | −16.0000 | −0.665512 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.64575 | 0.0682773 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.0000 | −0.579821 | ||||||||
\(584\) | −5.29150 | −0.218964 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.52026 | 0.228040 | ||||||||
\(587\) | −5.52026 | −0.227845 | −0.113923 | − | 0.993490i | \(-0.536342\pi\) | ||||
−0.113923 | + | 0.993490i | \(0.536342\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.1255 | 0.582031 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.35425 | 0.178959 | ||||||||
\(593\) | −15.0000 | −0.615976 | −0.307988 | − | 0.951390i | \(-0.599656\pi\) | ||||
−0.307988 | + | 0.951390i | \(0.599656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.5203 | 0.922466 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.35425 | 0.0962724 | ||||||||
\(599\) | −8.81176 | −0.360039 | −0.180019 | − | 0.983663i | \(-0.557616\pi\) | ||||
−0.180019 | + | 0.983663i | \(0.557616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.70850 | −0.192064 | −0.0960318 | − | 0.995378i | \(-0.530615\pi\) | ||||
−0.0960318 | + | 0.995378i | \(0.530615\pi\) | |||||||
\(602\) | 5.64575 | 0.230104 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.2288 | −0.538270 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −46.8118 | −1.90003 | −0.950015 | − | 0.312203i | \(-0.898933\pi\) | ||||
−0.950015 | + | 0.312203i | \(0.898933\pi\) | |||||||
\(608\) | 4.29150 | 0.174043 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | 0.121367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.06275 | −0.285262 | −0.142631 | − | 0.989776i | \(-0.545556\pi\) | ||||
−0.142631 | + | 0.989776i | \(0.545556\pi\) | |||||||
\(614\) | −6.70850 | −0.270733 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.29150 | −0.213201 | ||||||||
\(617\) | −20.9373 | −0.842902 | −0.421451 | − | 0.906851i | \(-0.638479\pi\) | ||||
−0.421451 | + | 0.906851i | \(0.638479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.7085 | −0.429372 | ||||||||
\(623\) | −1.00000 | −0.0400642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.2288 | 0.568695 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.35425 | −0.0540404 | ||||||||
\(629\) | −4.35425 | −0.173615 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8118 | 0.788694 | 0.394347 | − | 0.918962i | \(-0.370971\pi\) | ||||
0.394347 | + | 0.918962i | \(0.370971\pi\) | |||||||
\(632\) | −0.0627461 | −0.00249590 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0627 | 0.558503 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.645751 | −0.0255856 | ||||||||
\(638\) | 28.3320 | 1.12168 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.7085 | 0.975927 | 0.487963 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487963 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.29150 | 0.326985 | 0.163492 | − | 0.986545i | \(-0.447724\pi\) | ||||
0.163492 | + | 0.986545i | \(0.447724\pi\) | |||||||
\(644\) | 3.64575 | 0.143663 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.29150 | −0.168847 | ||||||||
\(647\) | 16.6458 | 0.654412 | 0.327206 | − | 0.944953i | \(-0.393893\pi\) | ||||
0.327206 | + | 0.944953i | \(0.393893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.3320 | 0.562581 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.8745 | 0.465042 | ||||||||
\(653\) | 19.8118 | 0.775294 | 0.387647 | − | 0.921808i | \(-0.373288\pi\) | ||||
0.387647 | + | 0.921808i | \(0.373288\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.29150 | 0.128512 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.64575 | 0.181110 | ||||||||
\(659\) | 15.5830 | 0.607028 | 0.303514 | − | 0.952827i | \(-0.401840\pi\) | ||||
0.303514 | + | 0.952827i | \(0.401840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.1660 | 1.52338 | 0.761691 | − | 0.647941i | \(-0.224370\pi\) | ||||
0.761691 | + | 0.647941i | \(0.224370\pi\) | |||||||
\(662\) | −4.35425 | −0.169233 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.64575 | −0.0638675 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5203 | −0.755827 | ||||||||
\(668\) | 17.1660 | 0.664173 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.0000 | −0.540464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.41699 | −0.208810 | −0.104405 | − | 0.994535i | \(-0.533294\pi\) | ||||
−0.104405 | + | 0.994535i | \(0.533294\pi\) | |||||||
\(674\) | −16.1660 | −0.622691 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.5830 | −0.483962 | ||||||||
\(677\) | 1.29150 | 0.0496365 | 0.0248182 | − | 0.999692i | \(-0.492099\pi\) | ||||
0.0248182 | + | 0.999692i | \(0.492099\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.93725 | 0.112721 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.4170 | 0.666931 | ||||||||
\(683\) | −18.5830 | −0.711059 | −0.355529 | − | 0.934665i | \(-0.615699\pi\) | ||||
−0.355529 | + | 0.934665i | \(0.615699\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.64575 | −0.215242 | ||||||||
\(689\) | 1.70850 | 0.0650886 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.2915 | −1.26647 | −0.633234 | − | 0.773960i | \(-0.718273\pi\) | ||||
−0.633234 | + | 0.773960i | \(0.718273\pi\) | |||||||
\(692\) | −1.64575 | −0.0625621 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.2915 | 0.770255 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.29150 | −0.124675 | ||||||||
\(698\) | −14.6458 | −0.554350 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.70850 | 0.102299 | 0.0511493 | − | 0.998691i | \(-0.483712\pi\) | ||||
0.0511493 | + | 0.998691i | \(0.483712\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.6863 | 0.704766 | ||||||||
\(704\) | 5.29150 | 0.199431 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.4575 | −1.37210 | ||||||||
\(707\) | −1.06275 | −0.0399687 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.8745 | −1.12196 | −0.560980 | − | 0.827829i | \(-0.689576\pi\) | ||||
−0.560980 | + | 0.827829i | \(0.689576\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00000 | 0.0374766 | ||||||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.5830 | −0.657108 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.4170 | 0.426078 | ||||||||
\(719\) | −23.3542 | −0.870967 | −0.435483 | − | 0.900197i | \(-0.643422\pi\) | ||||
−0.435483 | + | 0.900197i | \(0.643422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8745 | −0.516714 | ||||||||
\(722\) | −0.583005 | −0.0216972 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.6458 | 0.841623 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.3542 | −0.754897 | −0.377449 | − | 0.926031i | \(-0.623199\pi\) | ||||
−0.377449 | + | 0.926031i | \(0.623199\pi\) | |||||||
\(728\) | 0.645751 | 0.0239331 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.64575 | 0.208816 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.81176 | 0.362406 | 0.181203 | − | 0.983446i | \(-0.442001\pi\) | ||||
0.181203 | + | 0.983446i | \(0.442001\pi\) | |||||||
\(734\) | 14.9373 | 0.551344 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.64575 | −0.134384 | ||||||||
\(737\) | 57.8745 | 2.13183 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.3320 | −1.33649 | −0.668247 | − | 0.743939i | \(-0.732955\pi\) | ||||
−0.668247 | + | 0.743939i | \(0.732955\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.64575 | 0.0971286 | ||||||||
\(743\) | −13.7490 | −0.504402 | −0.252201 | − | 0.967675i | \(-0.581154\pi\) | ||||
−0.252201 | + | 0.967675i | \(0.581154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.87451 | −0.288306 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.29150 | −0.193476 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.41699 | −0.0517069 | −0.0258534 | − | 0.999666i | \(-0.508230\pi\) | ||||
−0.0258534 | + | 0.999666i | \(0.508230\pi\) | |||||||
\(752\) | −4.64575 | −0.169413 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.45751 | −0.125915 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8118 | 0.683725 | 0.341863 | − | 0.939750i | \(-0.388942\pi\) | ||||
0.341863 | + | 0.939750i | \(0.388942\pi\) | |||||||
\(758\) | 24.2288 | 0.880028 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.1660 | 1.60102 | 0.800508 | − | 0.599322i | \(-0.204563\pi\) | ||||
0.800508 | + | 0.599322i | \(0.204563\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.64575 | −0.131985 | ||||||||
\(764\) | 14.5830 | 0.527595 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.7085 | −0.603703 | ||||||||
\(767\) | −1.74902 | −0.0631533 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.0000 | −1.15395 | −0.576975 | − | 0.816762i | \(-0.695767\pi\) | ||||
−0.576975 | + | 0.816762i | \(0.695767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.8745 | 0.535345 | ||||||||
\(773\) | 17.1660 | 0.617418 | 0.308709 | − | 0.951156i | \(-0.400103\pi\) | ||||
0.308709 | + | 0.951156i | \(0.400103\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.93725 | −0.105441 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.3948 | 1.23311 | ||||||||
\(779\) | 14.1255 | 0.506098 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.74902 | 0.134150 | ||||||||
\(782\) | 3.64575 | 0.130372 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.5830 | −1.44663 | −0.723314 | − | 0.690519i | \(-0.757382\pi\) | ||||
−0.723314 | + | 0.690519i | \(0.757382\pi\) | |||||||
\(788\) | 13.3542 | 0.475725 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.5830 | 0.447400 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.70850 | 0.0606705 | ||||||||
\(794\) | 32.5203 | 1.15410 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.5203 | −0.620989 | ||||||||
\(797\) | −50.8118 | −1.79984 | −0.899922 | − | 0.436050i | \(-0.856377\pi\) | ||||
−0.899922 | + | 0.436050i | \(0.856377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.64575 | 0.164355 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.06275 | −0.320017 | ||||||||
\(803\) | −28.0000 | −0.988099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.12549 | −0.0748673 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.06275 | 0.0373873 | ||||||||
\(809\) | −3.41699 | −0.120135 | −0.0600676 | − | 0.998194i | \(-0.519132\pi\) | ||||
−0.0600676 | + | 0.998194i | \(0.519132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.1660 | −0.953928 | −0.476964 | − | 0.878923i | \(-0.658263\pi\) | ||||
−0.476964 | + | 0.878923i | \(0.658263\pi\) | |||||||
\(812\) | −5.35425 | −0.187897 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.0405 | 0.807570 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.2288 | −0.847657 | ||||||||
\(818\) | 18.2288 | 0.637354 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.7712 | −0.724921 | −0.362461 | − | 0.931999i | \(-0.618063\pi\) | ||||
−0.362461 | + | 0.931999i | \(0.618063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.0405 | −1.84888 | −0.924438 | − | 0.381332i | \(-0.875465\pi\) | ||||
−0.924438 | + | 0.381332i | \(0.875465\pi\) | |||||||
\(824\) | 13.8745 | 0.483341 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.70850 | −0.0942407 | ||||||||
\(827\) | 43.5830 | 1.51553 | 0.757765 | − | 0.652528i | \(-0.226291\pi\) | ||||
0.757765 | + | 0.652528i | \(0.226291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.35425 | 0.255424 | 0.127712 | − | 0.991811i | \(-0.459237\pi\) | ||||
0.127712 | + | 0.991811i | \(0.459237\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.645751 | −0.0223874 | ||||||||
\(833\) | −1.00000 | −0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 22.7085 | 0.785390 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.6458 | 0.955007 | ||||||||
\(839\) | 49.8118 | 1.71969 | 0.859846 | − | 0.510553i | \(-0.170559\pi\) | ||||
0.859846 | + | 0.510553i | \(0.170559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.332021 | −0.0114490 | ||||||||
\(842\) | 16.5830 | 0.571488 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.7085 | 0.506287 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.0000 | −0.584127 | ||||||||
\(848\) | −2.64575 | −0.0908555 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8745 | −0.544171 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.3320 | 1.86029 | 0.930146 | − | 0.367189i | \(-0.119680\pi\) | ||||
0.930146 | + | 0.367189i | \(0.119680\pi\) | |||||||
\(854\) | 2.64575 | 0.0905357 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | 0.205076 | ||||||||
\(857\) | −34.2915 | −1.17138 | −0.585688 | − | 0.810537i | \(-0.699175\pi\) | ||||
−0.585688 | + | 0.810537i | \(0.699175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.3320 | −1.17139 | −0.585697 | − | 0.810530i | \(-0.699179\pi\) | ||||
−0.585697 | + | 0.810530i | \(0.699179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.12549 | 0.0723945 | ||||||||
\(863\) | 30.3542 | 1.03327 | 0.516635 | − | 0.856206i | \(-0.327184\pi\) | ||||
0.516635 | + | 0.856206i | \(0.327184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.2915 | −0.383701 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.29150 | −0.111721 | ||||||||
\(869\) | −0.332021 | −0.0112630 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.06275 | −0.239312 | ||||||||
\(872\) | 3.64575 | 0.123461 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.6458 | −0.529225 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.87451 | 0.198368 | 0.0991840 | − | 0.995069i | \(-0.468377\pi\) | ||||
0.0991840 | + | 0.995069i | \(0.468377\pi\) | |||||||
\(878\) | −30.9373 | −1.04408 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.1255 | −0.509591 | −0.254795 | − | 0.966995i | \(-0.582008\pi\) | ||||
−0.254795 | + | 0.966995i | \(0.582008\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.2915 | −1.05304 | −0.526521 | − | 0.850162i | \(-0.676504\pi\) | ||||
−0.526521 | + | 0.850162i | \(0.676504\pi\) | |||||||
\(884\) | 0.645751 | 0.0217190 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33.5830 | 1.12824 | ||||||||
\(887\) | −49.8745 | −1.67462 | −0.837311 | − | 0.546727i | \(-0.815874\pi\) | ||||
−0.837311 | + | 0.546727i | \(0.815874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.35425 | −0.313731 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.5203 | −0.519657 | ||||||||
\(893\) | −19.9373 | −0.667175 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.2288 | −0.608301 | ||||||||
\(899\) | 17.6235 | 0.587777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.64575 | 0.0881428 | ||||||||
\(902\) | 17.4170 | 0.579922 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.5830 | −0.418505 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.2915 | −0.773382 | −0.386691 | − | 0.922209i | \(-0.626382\pi\) | ||||
−0.386691 | + | 0.922209i | \(0.626382\pi\) | |||||||
\(908\) | 11.6458 | 0.386478 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.1660 | −0.966313 | −0.483157 | − | 0.875534i | \(-0.660510\pi\) | ||||
−0.483157 | + | 0.875534i | \(0.660510\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.70850 | −0.288209 | ||||||||
\(914\) | −7.12549 | −0.235690 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.5203 | −0.810172 | ||||||||
\(917\) | −3.06275 | −0.101141 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0405 | −0.826010 | −0.413005 | − | 0.910729i | \(-0.635521\pi\) | ||||
−0.413005 | + | 0.910729i | \(0.635521\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.5203 | −1.10393 | ||||||||
\(923\) | −0.457513 | −0.0150592 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.35425 | 0.0445034 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.35425 | 0.175762 | ||||||||
\(929\) | −20.8745 | −0.684870 | −0.342435 | − | 0.939541i | \(-0.611252\pi\) | ||||
−0.342435 | + | 0.939541i | \(0.611252\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.29150 | 0.140648 | ||||||||
\(932\) | 3.64575 | 0.119421 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.2915 | 1.28566 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2288 | −0.334159 | −0.167079 | − | 0.985943i | \(-0.553434\pi\) | ||||
−0.167079 | + | 0.985943i | \(0.553434\pi\) | |||||||
\(938\) | −10.9373 | −0.357114 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.3542 | 0.337539 | 0.168769 | − | 0.985656i | \(-0.446021\pi\) | ||||
0.168769 | + | 0.985656i | \(0.446021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | −0.390774 | ||||||||
\(944\) | 2.70850 | 0.0881541 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.8745 | −0.971304 | ||||||||
\(947\) | −29.2915 | −0.951846 | −0.475923 | − | 0.879487i | \(-0.657886\pi\) | ||||
−0.475923 | + | 0.879487i | \(0.657886\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.41699 | 0.110920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.00000 | 0.0324102 | ||||||||
\(953\) | −40.1033 | −1.29907 | −0.649536 | − | 0.760331i | \(-0.725037\pi\) | ||||
−0.649536 | + | 0.760331i | \(0.725037\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 19.6458 | 0.635389 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.6458 | 0.408566 | ||||||||
\(959\) | −2.35425 | −0.0760227 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1660 | −0.650516 | ||||||||
\(962\) | −2.81176 | −0.0906548 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.93725 | 0.0946026 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.81176 | −0.0582623 | −0.0291312 | − | 0.999576i | \(-0.509274\pi\) | ||||
−0.0291312 | + | 0.999576i | \(0.509274\pi\) | |||||||
\(968\) | 17.0000 | 0.546401 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.2288 | 0.970087 | 0.485043 | − | 0.874490i | \(-0.338804\pi\) | ||||
0.485043 | + | 0.874490i | \(0.338804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.5830 | 0.531627 | ||||||||
\(974\) | −11.2915 | −0.361803 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.64575 | −0.0846884 | ||||||||
\(977\) | −7.06275 | −0.225957 | −0.112979 | − | 0.993597i | \(-0.536039\pi\) | ||||
−0.112979 | + | 0.993597i | \(0.536039\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.29150 | 0.169117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.8745 | −0.602310 | ||||||||
\(983\) | −50.5203 | −1.61135 | −0.805673 | − | 0.592361i | \(-0.798196\pi\) | ||||
−0.805673 | + | 0.592361i | \(0.798196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.35425 | −0.170514 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.77124 | −0.0881650 | ||||||||
\(989\) | 20.5830 | 0.654501 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0627 | −0.573782 | −0.286891 | − | 0.957963i | \(-0.592622\pi\) | ||||
−0.286891 | + | 0.957963i | \(0.592622\pi\) | |||||||
\(992\) | 3.29150 | 0.104505 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.708497 | −0.0224722 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.45751 | 0.0778302 | 0.0389151 | − | 0.999243i | \(-0.487610\pi\) | ||||
0.0389151 | + | 0.999243i | \(0.487610\pi\) | |||||||
\(998\) | 28.9373 | 0.915993 | ||||||||
\(999\) | 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 | 9450.2.a.eq.1.2 | yes | 2 | |
3.2 | odd | 2 | 9450.2.a.ec.1.1 | ✓ | 2 | ||
5.4 | even | 2 | 9450.2.a.ej.1.2 | yes | 2 | ||
15.14 | odd | 2 | 9450.2.a.et.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9450.2.a.ec.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
9450.2.a.ej.1.2 | yes | 2 | 5.4 | even | 2 | ||
9450.2.a.eq.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
9450.2.a.et.1.1 | yes | 2 | 15.14 | odd | 2 |