Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6240,2,Mod(1,6240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("6240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6240.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: | \(49.8266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6240.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.27492 | 1.61577 | 0.807883 | − | 0.589342i | \(-0.200613\pi\) | ||||
0.807883 | + | 0.589342i | \(0.200613\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.27492 | −0.685913 | −0.342957 | − | 0.939351i | \(-0.611428\pi\) | ||||
−0.342957 | + | 0.939351i | \(0.611428\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.27492 | −1.52189 | −0.760945 | − | 0.648816i | \(-0.775265\pi\) | ||||
−0.760945 | + | 0.648816i | \(0.775265\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.27492 | 0.932863 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.274917 | −0.0573242 | −0.0286621 | − | 0.999589i | \(-0.509125\pi\) | ||||
−0.0286621 | + | 0.999589i | \(0.509125\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.27492 | −0.396012 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.27492 | −0.722593 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.27492 | 1.36039 | 0.680194 | − | 0.733032i | \(-0.261896\pi\) | ||||
0.680194 | + | 0.733032i | \(0.261896\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.27492 | 1.29232 | 0.646162 | − | 0.763200i | \(-0.276373\pi\) | ||||
0.646162 | + | 0.763200i | \(0.276373\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.54983 | 1.30384 | 0.651919 | − | 0.758289i | \(-0.273964\pi\) | ||||
0.651919 | + | 0.758289i | \(0.273964\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.2749 | 1.61070 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.27492 | −0.878664 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.27492 | 1.13665 | 0.568324 | − | 0.822805i | \(-0.307592\pi\) | ||||
0.568324 | + | 0.822805i | \(0.307592\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.27492 | 0.306750 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82475 | 1.12989 | 0.564947 | − | 0.825127i | \(-0.308897\pi\) | ||||
0.564947 | + | 0.825127i | \(0.308897\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.27492 | 0.538589 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.274917 | −0.0330961 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.72508 | 0.204730 | 0.102365 | − | 0.994747i | \(-0.467359\pi\) | ||||
0.102365 | + | 0.994747i | \(0.467359\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5498 | −1.46885 | −0.734424 | − | 0.678691i | \(-0.762547\pi\) | ||||
−0.734424 | + | 0.678691i | \(0.762547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.72508 | −1.10828 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.2749 | 1.60605 | 0.803027 | − | 0.595943i | \(-0.203222\pi\) | ||||
0.803027 | + | 0.595943i | \(0.203222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.27492 | 0.680610 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.27492 | −0.877139 | −0.438570 | − | 0.898697i | \(-0.644515\pi\) | ||||
−0.438570 | + | 0.898697i | \(0.644515\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.27492 | 0.448133 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.2749 | 1.44940 | 0.724699 | − | 0.689065i | \(-0.241979\pi\) | ||||
0.724699 | + | 0.689065i | \(0.241979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.27492 | −0.228638 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.0997 | 1.30347 | 0.651733 | − | 0.758449i | \(-0.274042\pi\) | ||||
0.651733 | + | 0.758449i | \(0.274042\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0000 | −1.18240 | −0.591198 | − | 0.806527i | \(-0.701345\pi\) | ||||
−0.591198 | + | 0.806527i | \(0.701345\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.27492 | −0.417189 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2749 | 0.993314 | 0.496657 | − | 0.867947i | \(-0.334561\pi\) | ||||
0.496657 | + | 0.867947i | \(0.334561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.0000 | 1.53252 | 0.766261 | − | 0.642529i | \(-0.222115\pi\) | ||||
0.766261 | + | 0.642529i | \(0.222115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.27492 | 0.785420 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.549834 | −0.0517241 | −0.0258620 | − | 0.999666i | \(-0.508233\pi\) | ||||
−0.0258620 | + | 0.999666i | \(0.508233\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.274917 | 0.0256362 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.8248 | −2.45902 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.82475 | −0.529523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.27492 | 0.746124 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.0997 | −1.87229 | −0.936146 | − | 0.351610i | \(-0.885634\pi\) | ||||
−0.936146 | + | 0.351610i | \(0.885634\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.54983 | 0.752771 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.5498 | −1.62071 | −0.810353 | − | 0.585942i | \(-0.800725\pi\) | ||||
−0.810353 | + | 0.585942i | \(0.800725\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.54983 | −0.741365 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.8248 | 1.93597 | 0.967985 | − | 0.251008i | \(-0.0807620\pi\) | ||||
0.967985 | + | 0.251008i | \(0.0807620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.27492 | −0.190238 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.2749 | 0.929939 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3746 | −1.42338 | −0.711691 | − | 0.702493i | \(-0.752070\pi\) | ||||
−0.711691 | + | 0.702493i | \(0.752070\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.27492 | −0.507297 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.27492 | 0.656244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.17525 | −0.0926225 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7251 | 1.07503 | 0.537516 | − | 0.843254i | \(-0.319363\pi\) | ||||
0.537516 | + | 0.843254i | \(0.319363\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.27492 | 0.177102 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.0997 | −1.75624 | −0.878118 | − | 0.478445i | \(-0.841201\pi\) | ||||
−0.878118 | + | 0.478445i | \(0.841201\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.27492 | 0.323153 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | 0.448461 | 0.224231 | − | 0.974536i | \(-0.428013\pi\) | ||||
0.224231 | + | 0.974536i | \(0.428013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.8248 | 0.953256 | 0.476628 | − | 0.879105i | \(-0.341859\pi\) | ||||
0.476628 | + | 0.879105i | \(0.341859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.82475 | 0.652344 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.27492 | −0.608384 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2749 | 1.04389 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.27492 | 0.310954 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.54983 | 0.329214 | 0.164607 | − | 0.986359i | \(-0.447364\pi\) | ||||
0.164607 | + | 0.986359i | \(0.447364\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.27492 | −0.163752 | −0.0818761 | − | 0.996643i | \(-0.526091\pi\) | ||||
−0.0818761 | + | 0.996643i | \(0.526091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.27492 | −0.577945 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.274917 | −0.0191081 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.54983 | 0.314719 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.72508 | 0.118201 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.54983 | −0.583094 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.0997 | −1.16080 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.5498 | −0.848039 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.27492 | −0.422097 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.45017 | 0.364970 | 0.182485 | − | 0.983209i | \(-0.441586\pi\) | ||||
0.182485 | + | 0.983209i | \(0.441586\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.45017 | 0.494485 | 0.247242 | − | 0.968954i | \(-0.420476\pi\) | ||||
0.247242 | + | 0.968954i | \(0.420476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.0997 | −1.65863 | −0.829316 | − | 0.558779i | \(-0.811270\pi\) | ||||
−0.829316 | + | 0.558779i | \(0.811270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.72508 | −0.639863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.72508 | −0.113014 | −0.0565070 | − | 0.998402i | \(-0.517996\pi\) | ||||
−0.0565070 | + | 0.998402i | \(0.517996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.2749 | 0.927256 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.72508 | 0.111586 | 0.0557932 | − | 0.998442i | \(-0.482231\pi\) | ||||
0.0557932 | + | 0.998442i | \(0.482231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.45017 | −0.0934134 | −0.0467067 | − | 0.998909i | \(-0.514873\pi\) | ||||
−0.0467067 | + | 0.998909i | \(0.514873\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2749 | −0.720328 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.54983 | −0.413422 | −0.206711 | − | 0.978402i | \(-0.566276\pi\) | ||||
−0.206711 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.625414 | 0.0393194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.27492 | 0.392951 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.549834 | 0.0342977 | 0.0171489 | − | 0.999853i | \(-0.494541\pi\) | ||||
0.0171489 | + | 0.999853i | \(0.494541\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 35.3746 | 2.19807 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.4502 | 0.829373 | 0.414686 | − | 0.909964i | \(-0.363891\pi\) | ||||
0.414686 | + | 0.909964i | \(0.363891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.27492 | −0.508324 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.27492 | −0.506417 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.00000 | −0.243884 | −0.121942 | − | 0.992537i | \(-0.538912\pi\) | ||||
−0.121942 | + | 0.992537i | \(0.538912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.6495 | −1.55810 | −0.779048 | − | 0.626964i | \(-0.784297\pi\) | ||||
−0.779048 | + | 0.626964i | \(0.784297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.27492 | 0.258730 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.27492 | −0.137183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.6495 | −1.66130 | −0.830649 | − | 0.556797i | \(-0.812030\pi\) | ||||
−0.830649 | + | 0.556797i | \(0.812030\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0997 | −0.778694 | −0.389347 | − | 0.921091i | \(-0.627299\pi\) | ||||
−0.389347 | + | 0.921091i | \(0.627299\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | 0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.3746 | 2.08810 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.3746 | 1.31615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.2749 | 0.836810 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.5498 | −1.31738 | −0.658688 | − | 0.752416i | \(-0.728888\pi\) | ||||
−0.658688 | + | 0.752416i | \(0.728888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.27492 | −0.132004 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.274917 | −0.0158989 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.5498 | 2.10670 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.0997 | 0.752556 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.82475 | −0.505304 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.37459 | −0.420890 | −0.210445 | − | 0.977606i | \(-0.567491\pi\) | ||||
−0.210445 | + | 0.977606i | \(0.567491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0000 | −0.682656 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.6495 | 1.22763 | 0.613815 | − | 0.789450i | \(-0.289634\pi\) | ||||
0.613815 | + | 0.789450i | \(0.289634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.27492 | −0.240864 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.0997 | −1.29741 | −0.648703 | − | 0.761041i | \(-0.724688\pi\) | ||||
−0.648703 | + | 0.761041i | \(0.724688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.2749 | 0.573490 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.5498 | 0.698291 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.0000 | 0.884802 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.0997 | −0.942735 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0997 | 0.829953 | 0.414976 | − | 0.909832i | \(-0.363790\pi\) | ||||
0.414976 | + | 0.909832i | \(0.363790\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.27492 | 0.453463 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.09967 | 0.386744 | 0.193372 | − | 0.981126i | \(-0.438058\pi\) | ||||
0.193372 | + | 0.981126i | \(0.438058\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.549834 | −0.0298629 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.09967 | 0.492775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2749 | 0.986753 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.274917 | 0.0148010 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2749 | 0.766318 | 0.383159 | − | 0.923682i | \(-0.374836\pi\) | ||||
0.383159 | + | 0.923682i | \(0.374836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5498 | −0.671777 | −0.335889 | − | 0.941902i | \(-0.609037\pi\) | ||||
−0.335889 | + | 0.941902i | \(0.609037\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.6495 | 0.832939 | 0.416470 | − | 0.909150i | \(-0.363267\pi\) | ||||
0.416470 | + | 0.909150i | \(0.363267\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.72508 | −0.0915579 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −26.8248 | −1.41972 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.82475 | −0.305720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.5498 | 0.656888 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.54983 | 0.446298 | 0.223149 | − | 0.974784i | \(-0.428366\pi\) | ||||
0.223149 | + | 0.974784i | \(0.428366\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.27492 | 0.430775 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.3746 | 1.83656 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.900331 | 0.0466174 | 0.0233087 | − | 0.999728i | \(-0.492580\pi\) | ||||
0.0233087 | + | 0.999728i | \(0.492580\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.5498 | −0.952841 | −0.476420 | − | 0.879218i | \(-0.658066\pi\) | ||||
−0.476420 | + | 0.879218i | \(0.658066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.0997 | −1.08097 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.5498 | −1.45883 | −0.729414 | − | 0.684072i | \(-0.760207\pi\) | ||||
−0.729414 | + | 0.684072i | \(0.760207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.72508 | 0.495636 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.54983 | 0.434613 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0997 | 1.06980 | 0.534898 | − | 0.844917i | \(-0.320350\pi\) | ||||
0.534898 | + | 0.844917i | \(0.320350\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.72508 | 0.0872412 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.5498 | −0.935715 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.2749 | −0.718249 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.27492 | 0.415306 | 0.207653 | − | 0.978203i | \(-0.433417\pi\) | ||||
0.207653 | + | 0.978203i | \(0.433417\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.54983 | −0.428027 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.900331 | 0.0449604 | 0.0224802 | − | 0.999747i | \(-0.492844\pi\) | ||||
0.0224802 | + | 0.999747i | \(0.492844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8248 | −0.933108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6495 | 1.36718 | 0.683590 | − | 0.729866i | \(-0.260418\pi\) | ||||
0.683590 | + | 0.729866i | \(0.260418\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0000 | 0.493264 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.0997 | 0.841420 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.8248 | 1.11773 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.0997 | 1.32391 | 0.661953 | − | 0.749546i | \(-0.269728\pi\) | ||||
0.661953 | + | 0.749546i | \(0.269728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.09967 | 0.248543 | 0.124271 | − | 0.992248i | \(-0.460341\pi\) | ||||
0.124271 | + | 0.992248i | \(0.460341\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.00000 | −0.194487 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.27492 | −0.304378 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37.7251 | 1.82564 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.27492 | −0.109834 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.1993 | 1.26198 | 0.630989 | − | 0.775792i | \(-0.282649\pi\) | ||||
0.630989 | + | 0.775792i | \(0.282649\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.549834 | 0.0263021 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7251 | 0.845972 | 0.422986 | − | 0.906136i | \(-0.360982\pi\) | ||||
0.422986 | + | 0.906136i | \(0.360982\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.2749 | 0.536901 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.2749 | 0.678222 | 0.339111 | − | 0.940746i | \(-0.389874\pi\) | ||||
0.339111 | + | 0.940746i | \(0.389874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.27492 | 0.392269 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.3746 | −0.821790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4743 | 1.43817 | 0.719085 | − | 0.694923i | \(-0.244561\pi\) | ||||
0.719085 | + | 0.694923i | \(0.244561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.8248 | −0.886423 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00000 | 0.187936 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.27492 | −0.200411 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.625414 | −0.0292556 | −0.0146278 | − | 0.999893i | \(-0.504656\pi\) | ||||
−0.0146278 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.27492 | −0.292888 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.9244 | −0.834823 | −0.417412 | − | 0.908717i | \(-0.637063\pi\) | ||||
−0.417412 | + | 0.908717i | \(0.637063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.8248 | −1.15370 | −0.576852 | − | 0.816849i | \(-0.695719\pi\) | ||||
−0.576852 | + | 0.816849i | \(0.695719\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.3746 | 1.26674 | 0.633372 | − | 0.773847i | \(-0.281670\pi\) | ||||
0.633372 | + | 0.773847i | \(0.281670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.1993 | 1.57918 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.0000 | −0.645086 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.4502 | −0.894320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | −0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.27492 | 0.378882 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.3746 | 1.79907 | 0.899535 | − | 0.436848i | \(-0.143905\pi\) | ||||
0.899535 | + | 0.436848i | \(0.143905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.27492 | 0.377304 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.17525 | −0.0534757 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.2749 | −0.648191 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.9244 | 1.89978 | 0.949888 | − | 0.312589i | \(-0.101196\pi\) | ||||
0.949888 | + | 0.312589i | \(0.101196\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.7251 | 0.620670 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.09967 | 0.139886 | 0.0699430 | − | 0.997551i | \(-0.477718\pi\) | ||||
0.0699430 | + | 0.997551i | \(0.477718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.27492 | 0.102250 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.37459 | 0.330795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.00000 | −0.268597 | −0.134298 | − | 0.990941i | \(-0.542878\pi\) | ||||
−0.134298 | + | 0.990941i | \(0.542878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.5498 | −0.827096 | −0.413548 | − | 0.910482i | \(-0.635711\pi\) | ||||
−0.413548 | + | 0.910482i | \(0.635711\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.0997 | −0.582928 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.2749 | −1.96245 | −0.981226 | − | 0.192863i | \(-0.938223\pi\) | ||||
−0.981226 | + | 0.192863i | \(0.938223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −53.6495 | −2.37331 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | −0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.0000 | 0.528783 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.09967 | 0.400203 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.0997 | −1.01396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0997 | −1.18726 | −0.593629 | − | 0.804739i | \(-0.702305\pi\) | ||||
−0.593629 | + | 0.804739i | \(0.702305\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.6495 | −1.47139 | −0.735695 | − | 0.677313i | \(-0.763144\pi\) | ||||
−0.735695 | + | 0.677313i | \(0.763144\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.27492 | 0.186573 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.0997 | 1.09336 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9244 | −0.996714 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.27492 | 0.358426 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2749 | −0.444223 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.00000 | 0.258919 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.6495 | −1.10480 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.54983 | −0.367586 | −0.183793 | − | 0.982965i | \(-0.558838\pi\) | ||||
−0.183793 | + | 0.982965i | \(0.558838\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.8248 | 0.550363 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.0000 | −0.685365 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.82475 | 0.376631 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 61.0241 | 2.59501 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.27492 | −0.351251 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.4502 | −1.07836 | −0.539179 | − | 0.842191i | \(-0.681265\pi\) | ||||
−0.539179 | + | 0.842191i | \(0.681265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.54983 | 0.361619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.2749 | 0.602687 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.82475 | −0.119049 | −0.0595245 | − | 0.998227i | \(-0.518958\pi\) | ||||
−0.0595245 | + | 0.998227i | \(0.518958\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.549834 | 0.0231317 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.27492 | 0.179530 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.09967 | −0.129945 | −0.0649724 | − | 0.997887i | \(-0.520696\pi\) | ||||
−0.0649724 | + | 0.997887i | \(0.520696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.8248 | −1.95955 | −0.979777 | − | 0.200090i | \(-0.935876\pi\) | ||||
−0.979777 | + | 0.200090i | \(0.935876\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.54983 | 0.190072 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.274917 | −0.0114648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.62541 | −0.192559 | −0.0962793 | − | 0.995354i | \(-0.530694\pi\) | ||||
−0.0962793 | + | 0.995354i | \(0.530694\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.27492 | −0.0945423 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 51.2990 | 2.12824 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.8248 | −0.779642 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.5498 | −1.01328 | −0.506640 | − | 0.862158i | \(-0.669113\pi\) | ||||
−0.506640 | + | 0.862158i | \(0.669113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | 0.246807 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.7492 | −1.34485 | −0.672424 | − | 0.740166i | \(-0.734747\pi\) | ||||
−0.672424 | + | 0.740166i | \(0.734747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.8248 | 1.09971 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.9244 | −1.22064 | −0.610321 | − | 0.792154i | \(-0.708960\pi\) | ||||
−0.610321 | + | 0.792154i | \(0.708960\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000 | 0.325785 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.82475 | 0.236810 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.6495 | −1.04108 | −0.520541 | − | 0.853837i | \(-0.674270\pi\) | ||||
−0.520541 | + | 0.853837i | \(0.674270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.00000 | −0.161823 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9244 | 0.562402 | 0.281201 | − | 0.959649i | \(-0.409267\pi\) | ||||
0.281201 | + | 0.959649i | \(0.409267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.27492 | −0.333677 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.9003 | −0.519348 | −0.259674 | − | 0.965696i | \(-0.583615\pi\) | ||||
−0.259674 | + | 0.965696i | \(0.583615\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.6495 | 0.950554 | 0.475277 | − | 0.879836i | \(-0.342348\pi\) | ||||
0.475277 | + | 0.879836i | \(0.342348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.274917 | −0.0110320 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.3746 | −1.41725 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.54983 | 0.181703 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −51.9244 | −2.07036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.1993 | −1.36145 | −0.680727 | − | 0.732537i | \(-0.738336\pi\) | ||||
−0.680727 | + | 0.732537i | \(0.738336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.0000 | 0.635943 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.0997 | 0.837315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.2749 | 0.446728 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.72508 | 0.0682432 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.0997 | −1.22836 | −0.614182 | − | 0.789165i | \(-0.710514\pi\) | ||||
−0.614182 | + | 0.789165i | \(0.710514\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.4743 | −0.965170 | −0.482585 | − | 0.875849i | \(-0.660302\pi\) | ||||
−0.482585 | + | 0.875849i | \(0.660302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.54983 | −0.336649 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.72508 | −0.303704 | −0.151852 | − | 0.988403i | \(-0.548524\pi\) | ||||
−0.151852 | + | 0.988403i | \(0.548524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.09967 | −0.357193 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.0997 | −0.670189 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.0997 | −0.747428 | −0.373714 | − | 0.927544i | \(-0.621916\pi\) | ||||
−0.373714 | + | 0.927544i | \(0.621916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.5498 | 0.724802 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.5498 | −0.489616 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.6495 | −0.765436 | −0.382718 | − | 0.923865i | \(-0.625012\pi\) | ||||
−0.382718 | + | 0.923865i | \(0.625012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.45017 | 0.289778 | 0.144889 | − | 0.989448i | \(-0.453718\pi\) | ||||
0.144889 | + | 0.989448i | \(0.453718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.27492 | −0.243698 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.54983 | 0.331548 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.45017 | 0.210716 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.0756 | −0.775009 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.6495 | 1.22000 | 0.609999 | − | 0.792402i | \(-0.291170\pi\) | ||||
0.609999 | + | 0.792402i | \(0.291170\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.4743 | 0.863756 | 0.431878 | − | 0.901932i | \(-0.357851\pi\) | ||||
0.431878 | + | 0.901932i | \(0.357851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 61.0241 | 2.34189 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.45017 | 0.285491 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.7492 | 1.94186 | 0.970932 | − | 0.239357i | \(-0.0769367\pi\) | ||||
0.970932 | + | 0.239357i | \(0.0769367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0000 | −0.382080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.0997 | −0.957612 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.27492 | 0.315249 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.900331 | −0.0342502 | −0.0171251 | − | 0.999853i | \(-0.505451\pi\) | ||||
−0.0171251 | + | 0.999853i | \(0.505451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.72508 | −0.369425 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8248 | −0.865792 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −51.9244 | −1.96678 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.72508 | −0.0652486 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.90033 | 0.109544 | 0.0547720 | − | 0.998499i | \(-0.482557\pi\) | ||||
0.0547720 | + | 0.998499i | \(0.482557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.5498 | −0.624189 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.0000 | 2.10610 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.09967 | −0.0412989 | −0.0206495 | − | 0.999787i | \(-0.506573\pi\) | ||||
−0.0206495 | + | 0.999787i | \(0.506573\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.2749 | 0.535351 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.09967 | 0.0411829 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.27492 | 0.0850771 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.72508 | 0.0644244 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.0997 | −1.68193 | −0.840967 | − | 0.541087i | \(-0.818013\pi\) | ||||
−0.840967 | + | 0.541087i | \(0.818013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −51.2990 | −1.91047 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.45017 | −0.0539322 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4502 | −1.01807 | −0.509035 | − | 0.860746i | \(-0.669998\pi\) | ||||
−0.509035 | + | 0.860746i | \(0.669998\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.6495 | −1.98430 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.2749 | 0.601128 | 0.300564 | − | 0.953762i | \(-0.402825\pi\) | ||||
0.300564 | + | 0.953762i | \(0.402825\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.2749 | −0.415882 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.1993 | −0.670381 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.0000 | 0.956425 | 0.478213 | − | 0.878244i | \(-0.341285\pi\) | ||||
0.478213 | + | 0.878244i | \(0.341285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.6495 | 1.38123 | 0.690613 | − | 0.723224i | \(-0.257341\pi\) | ||||
0.690613 | + | 0.723224i | \(0.257341\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.3746 | 0.636556 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.9244 | 1.60496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.4743 | −1.47693 | −0.738463 | − | 0.674294i | \(-0.764448\pi\) | ||||
−0.738463 | + | 0.674294i | \(0.764448\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.54983 | −0.238689 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.00000 | −0.145575 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.5498 | 1.54650 | 0.773250 | − | 0.634101i | \(-0.218630\pi\) | ||||
0.773250 | + | 0.634101i | \(0.218630\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.625414 | 0.0227011 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0997 | −0.547363 | −0.273681 | − | 0.961820i | \(-0.588241\pi\) | ||||
−0.273681 | + | 0.961820i | \(0.588241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 68.3987 | 2.47620 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.27492 | 0.226870 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | 0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.0997 | 1.55421 | 0.777107 | − | 0.629369i | \(-0.216686\pi\) | ||||
0.777107 | + | 0.629369i | \(0.216686\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.549834 | 0.0198018 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.6495 | 0.419004 | 0.209502 | − | 0.977808i | \(-0.432816\pi\) | ||||
0.209502 | + | 0.977808i | \(0.432816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 35.3746 | 1.26906 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.5498 | −0.592959 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.92442 | −0.140427 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9003 | 0.388555 | 0.194277 | − | 0.980947i | \(-0.437764\pi\) | ||||
0.194277 | + | 0.980947i | \(0.437764\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.4502 | 0.478839 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.35050 | −0.0835740 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.82475 | 0.313376 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.27492 | −0.293481 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.4743 | −0.512704 | −0.256352 | − | 0.966583i | \(-0.582521\pi\) | ||||
−0.256352 | + | 0.966583i | \(0.582521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.0997 | 0.887962 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.27492 | −0.292380 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.5498 | 1.00750 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.17525 | 0.0414221 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.00000 | −0.140807 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.00000 | 0.0703163 | 0.0351581 | − | 0.999382i | \(-0.488807\pi\) | ||||
0.0351581 | + | 0.999382i | \(0.488807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0997 | 0.530221 | 0.265111 | − | 0.964218i | \(-0.414592\pi\) | ||||
0.265111 | + | 0.964218i | \(0.414592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.6495 | −0.899567 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.7251 | −0.480769 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.0997 | −0.598242 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.27492 | 0.149378 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.9244 | −1.32357 | −0.661786 | − | 0.749693i | \(-0.730201\pi\) | ||||
−0.661786 | + | 0.749693i | \(0.730201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.1993 | 1.33155 | 0.665773 | − | 0.746155i | \(-0.268102\pi\) | ||||
0.665773 | + | 0.746155i | \(0.268102\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.27492 | −0.0792025 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.1993 | 1.88470 | 0.942348 | − | 0.334635i | \(-0.108613\pi\) | ||||
0.942348 | + | 0.334635i | \(0.108613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.09967 | −0.107656 | −0.0538280 | − | 0.998550i | \(-0.517142\pi\) | ||||
−0.0538280 | + | 0.998550i | \(0.517142\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.6495 | −0.959151 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −70.7492 | −2.45131 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.8248 | 0.649903 | 0.324951 | − | 0.945731i | \(-0.394652\pi\) | ||||
0.324951 | + | 0.945731i | \(0.394652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.0000 | −0.344418 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.9003 | −0.855586 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0997 | −0.449579 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.27492 | −0.0779832 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.6254 | 0.637722 | 0.318861 | − | 0.947801i | \(-0.396700\pi\) | ||||
0.318861 | + | 0.947801i | \(0.396700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | 0.0683986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.27492 | 0.0777097 | 0.0388548 | − | 0.999245i | \(-0.487629\pi\) | ||||
0.0388548 | + | 0.999245i | \(0.487629\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.1752 | −0.449534 | −0.224767 | − | 0.974413i | \(-0.572162\pi\) | ||||
−0.224767 | + | 0.974413i | \(0.572162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.3746 | 1.20556 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7492 | 1.31904 | 0.659519 | − | 0.751688i | \(-0.270760\pi\) | ||||
0.659519 | + | 0.751688i | \(0.270760\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.0997 | 0.785412 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.3746 | 0.759881 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.4743 | −1.10161 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.2749 | 0.483133 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.27492 | −0.144519 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.09967 | −0.104668 | −0.0523342 | − | 0.998630i | \(-0.516666\pi\) | ||||
−0.0523342 | + | 0.998630i | \(0.516666\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.5498 | −0.760587 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.5498 | −0.759723 | −0.379862 | − | 0.925043i | \(-0.624028\pi\) | ||||
−0.379862 | + | 0.925043i | \(0.624028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.1993 | −1.82395 | −0.911976 | − | 0.410243i | \(-0.865444\pi\) | ||||
−0.911976 | + | 0.410243i | \(0.865444\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.00000 | −0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.9244 | −0.736150 | −0.368075 | − | 0.929796i | \(-0.619983\pi\) | ||||
−0.368075 | + | 0.929796i | \(0.619983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −90.1993 | −3.02519 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.27492 | −0.0762126 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.00000 | 0.267710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | −0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.274917 | −0.00917922 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.9244 | −1.72985 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.5498 | 1.21630 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.8248 | −0.426309 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.54983 | −0.283893 | −0.141946 | − | 0.989874i | \(-0.545336\pi\) | ||||
−0.141946 | + | 0.989874i | \(0.545336\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.0997 | 0.434489 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.6495 | −1.11486 | −0.557429 | − | 0.830225i | \(-0.688212\pi\) | ||||
−0.557429 | + | 0.830225i | \(0.688212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.2990 | −0.903465 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.82475 | −0.291737 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −79.2990 | −2.61868 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8248 | −0.884867 | −0.442433 | − | 0.896801i | \(-0.645885\pi\) | ||||
−0.442433 | + | 0.896801i | \(0.645885\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.37459 | −0.243001 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.72508 | 0.0567818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.27492 | 0.272078 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.0000 | −0.394132 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.8248 | 1.86436 | 0.932180 | − | 0.361996i | \(-0.117904\pi\) | ||||
0.932180 | + | 0.361996i | \(0.117904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.5498 | −0.739041 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.6495 | 0.708773 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.2749 | −0.466840 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.5498 | −1.12869 | −0.564347 | − | 0.825538i | \(-0.690872\pi\) | ||||
−0.564347 | + | 0.825538i | \(0.690872\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.72508 | 0.251831 | 0.125915 | − | 0.992041i | \(-0.459813\pi\) | ||||
0.125915 | + | 0.992041i | \(0.459813\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.27492 | −0.0740815 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.27492 | −0.139063 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.09967 | −0.165717 | −0.0828585 | − | 0.996561i | \(-0.526405\pi\) | ||||
−0.0828585 | + | 0.996561i | \(0.526405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.5498 | −0.407385 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.0997 | −0.749058 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.1752 | −0.945079 | −0.472539 | − | 0.881309i | \(-0.656663\pi\) | ||||
−0.472539 | + | 0.881309i | \(0.656663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.54983 | −0.147229 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.7492 | 1.38044 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.2749 | 0.331105 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.27492 | 0.0732322 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.5498 | 0.596522 | 0.298261 | − | 0.954484i | \(-0.403593\pi\) | ||||
0.298261 | + | 0.954484i | \(0.403593\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.5498 | 0.403159 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.2990 | −1.71045 | −0.855223 | − | 0.518260i | \(-0.826580\pi\) | ||||
−0.855223 | + | 0.518260i | \(0.826580\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 97.5739 | 3.12808 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000 | 0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.0997 | 1.25091 | 0.625455 | − | 0.780261i | \(-0.284914\pi\) | ||||
0.625455 | + | 0.780261i | \(0.284914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8248 | 0.601642 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.0000 | 0.510841 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.19934 | −0.0701480 | −0.0350740 | − | 0.999385i | \(-0.511167\pi\) | ||||
−0.0350740 | + | 0.999385i | \(0.511167\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.0997 | −0.544288 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.35050 | −0.0747414 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.3746 | −1.25077 | −0.625387 | − | 0.780314i | \(-0.715059\pi\) | ||||
−0.625387 | + | 0.780314i | \(0.715059\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.0997 | 0.479174 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.6495 | 0.748987 | 0.374494 | − | 0.927229i | \(-0.377817\pi\) | ||||
0.374494 | + | 0.927229i | \(0.377817\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.27492 | 0.261807 |
(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 | 6240.2.a.bs.1.2 | yes | 2 | |
4.3 | odd | 2 | 6240.2.a.bg.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6240.2.a.bg.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
6240.2.a.bs.1.2 | yes | 2 | 1.1 | even | 1 | trivial |