Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(3041,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3380.3041");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.f (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 39x^{16} + 605x^{14} + 4764x^{12} + 20080x^{10} + 43783x^{8} + 43791x^{6} + 14071x^{4} + 378x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3041.17 | ||
Root | \(2.81781i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.3041 |
Dual form | 3380.2.f.j.3041.18 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3380\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(1691\) | \(1861\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.81781 | 1.62686 | 0.813431 | − | 0.581661i | \(-0.197597\pi\) | ||||
0.813431 | + | 0.581661i | \(0.197597\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.974186i | − 0.368208i | −0.982907 | − | 0.184104i | \(-0.941062\pi\) | ||||
0.982907 | − | 0.184104i | \(-0.0589383\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.94004 | 1.64668 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.42555i | − 1.03284i | −0.856335 | − | 0.516421i | \(-0.827264\pi\) | ||||
0.856335 | − | 0.516421i | \(-0.172736\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 2.81781i | − 0.727555i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.283829 | −0.0688387 | −0.0344193 | − | 0.999407i | \(-0.510958\pi\) | ||||
−0.0344193 | + | 0.999407i | \(0.510958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.03105i | − 1.38362i | −0.722081 | − | 0.691809i | \(-0.756814\pi\) | ||||
0.722081 | − | 0.691809i | \(-0.243186\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 2.74507i | − 0.599023i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.91511 | −1.85893 | −0.929465 | − | 0.368911i | \(-0.879731\pi\) | ||||
−0.929465 | + | 0.368911i | \(0.879731\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.46666 | 1.05206 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.461096 | 0.0856233 | 0.0428117 | − | 0.999083i | \(-0.486368\pi\) | ||||
0.0428117 | + | 0.999083i | \(0.486368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 7.96959i | − 1.43138i | −0.698418 | − | 0.715690i | \(-0.746112\pi\) | ||||
0.698418 | − | 0.715690i | \(-0.253888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 9.65254i | − 1.68029i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.974186 | −0.164668 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.95339i | − 0.485535i | −0.970085 | − | 0.242767i | \(-0.921945\pi\) | ||||
0.970085 | − | 0.242767i | \(-0.0780552\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.76466i | 1.36881i | 0.729102 | + | 0.684405i | \(0.239938\pi\) | ||||
−0.729102 | + | 0.684405i | \(0.760062\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.81154 | −1.34375 | −0.671873 | − | 0.740666i | \(-0.734510\pi\) | ||||
−0.671873 | + | 0.740666i | \(0.734510\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4.94004i | − 0.736418i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 10.3775i | − 1.51372i | −0.653578 | − | 0.756859i | \(-0.726733\pi\) | ||||
0.653578 | − | 0.756859i | \(-0.273267\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.05096 | 0.864423 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.799776 | −0.111991 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.96945 | 0.682606 | 0.341303 | − | 0.939953i | \(-0.389132\pi\) | ||||
0.341303 | + | 0.939953i | \(0.389132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.42555 | −0.461901 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 16.9943i | − 2.25096i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.88601i | 1.02667i | 0.858188 | + | 0.513336i | \(0.171590\pi\) | ||||
−0.858188 | + | 0.513336i | \(0.828410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4869 | 1.47075 | 0.735375 | − | 0.677661i | \(-0.237006\pi\) | ||||
0.735375 | + | 0.677661i | \(0.237006\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.81252i | − 0.606320i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.96340i | 0.484206i | 0.970251 | + | 0.242103i | \(0.0778372\pi\) | ||||
−0.970251 | + | 0.242103i | \(0.922163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −25.1211 | −3.02422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.22524i | 0.738801i | 0.929270 | + | 0.369400i | \(0.120437\pi\) | ||||
−0.929270 | + | 0.369400i | \(0.879563\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.94784i | 1.16431i | 0.813079 | + | 0.582153i | \(0.197790\pi\) | ||||
−0.813079 | + | 0.582153i | \(0.802210\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.81781 | −0.325372 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.33712 | −0.380301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.63735 | 0.746760 | 0.373380 | − | 0.927679i | \(-0.378199\pi\) | ||||
0.373380 | + | 0.927679i | \(0.378199\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.583871 | 0.0648745 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.05049i | − 0.773891i | −0.922103 | − | 0.386946i | \(-0.873530\pi\) | ||||
0.922103 | − | 0.386946i | \(-0.126470\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.283829i | 0.0307856i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.29928 | 0.139297 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.66990i | 0.919007i | 0.888176 | + | 0.459504i | \(0.151973\pi\) | ||||
−0.888176 | + | 0.459504i | \(0.848027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 22.4568i | − 2.32866i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.03105 | −0.618773 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.332881i | 0.0337990i | 0.999857 | + | 0.0168995i | \(0.00537953\pi\) | ||||
−0.999857 | + | 0.0168995i | \(0.994620\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 16.9224i | − 1.70076i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0197 | 1.39501 | 0.697506 | − | 0.716579i | \(-0.254293\pi\) | ||||
0.697506 | + | 0.716579i | \(0.254293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.6039 | 1.83310 | 0.916549 | − | 0.399923i | \(-0.130963\pi\) | ||||
0.916549 | + | 0.399923i | \(0.130963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.74507 | −0.267891 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8007 | −1.04414 | −0.522071 | − | 0.852902i | \(-0.674840\pi\) | ||||
−0.522071 | + | 0.852902i | \(0.674840\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 2.87817i | − 0.275679i | −0.990455 | − | 0.137839i | \(-0.955984\pi\) | ||||
0.990455 | − | 0.137839i | \(-0.0440158\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 8.32209i | − 0.789898i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.77628 | 0.919675 | 0.459838 | − | 0.888003i | \(-0.347908\pi\) | ||||
0.459838 | + | 0.888003i | \(0.347908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.91511i | 0.831338i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.276502i | 0.0253469i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.734394 | −0.0667631 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.6971i | 2.22686i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3824 | −1.27623 | −0.638114 | − | 0.769942i | \(-0.720285\pi\) | ||||
−0.638114 | + | 0.769942i | \(0.720285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.8292 | −2.18609 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9106 | 1.47749 | 0.738745 | − | 0.673985i | \(-0.235419\pi\) | ||||
0.738745 | + | 0.673985i | \(0.235419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.87537 | −0.509459 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5.46666i | − 0.470495i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.71889i | 0.659469i | 0.944074 | + | 0.329735i | \(0.106959\pi\) | ||||
−0.944074 | + | 0.329735i | \(0.893041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.7958 | −1.59424 | −0.797120 | − | 0.603821i | \(-0.793644\pi\) | ||||
−0.797120 | + | 0.603821i | \(0.793644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 29.2419i | − 2.46261i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 0.461096i | − 0.0382919i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.0504 | 1.40630 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.52113i | − 0.288462i | −0.989544 | − | 0.144231i | \(-0.953929\pi\) | ||||
0.989544 | − | 0.144231i | \(-0.0460708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 11.0498i | − 0.899217i | −0.893226 | − | 0.449608i | \(-0.851564\pi\) | ||||
0.893226 | − | 0.449608i | \(-0.148436\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.40213 | −0.113355 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.96959 | −0.640133 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.47826 | 0.357404 | 0.178702 | − | 0.983903i | \(-0.442810\pi\) | ||||
0.178702 | + | 0.983903i | \(0.442810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.0029 | 1.11051 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.68498i | 0.684472i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 11.3490i | − 0.888923i | −0.895798 | − | 0.444462i | \(-0.853395\pi\) | ||||
0.895798 | − | 0.444462i | \(-0.146605\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.65254 | −0.751449 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 8.82022i | − 0.682529i | −0.939967 | − | 0.341265i | \(-0.889145\pi\) | ||||
0.939967 | − | 0.341265i | \(-0.110855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 29.7936i | − 2.27838i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.64718 | 0.353319 | 0.176659 | − | 0.984272i | \(-0.443471\pi\) | ||||
0.176659 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.974186i | 0.0736416i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.2213i | 1.67025i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.3186 | 1.89240 | 0.946200 | − | 0.323581i | \(-0.104887\pi\) | ||||
0.946200 | + | 0.323581i | \(0.104887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.32715 | −0.321635 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.3679 | 2.39271 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.95339 | −0.217138 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.972271i | 0.0710995i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 5.32554i | − 0.387376i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.62340 | −0.189823 | −0.0949114 | − | 0.995486i | \(-0.530257\pi\) | ||||
−0.0949114 | + | 0.995486i | \(0.530257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 21.6639i | − 1.55940i | −0.626153 | − | 0.779700i | \(-0.715371\pi\) | ||||
0.626153 | − | 0.779700i | \(-0.284629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.8601i | − 1.48622i | −0.669169 | − | 0.743110i | \(-0.733350\pi\) | ||||
0.669169 | − | 0.743110i | \(-0.266650\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.7819 | −1.61497 | −0.807485 | − | 0.589888i | \(-0.799172\pi\) | ||||
−0.807485 | + | 0.589888i | \(0.799172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.1681i | 0.787736i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.449193i | − 0.0315272i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.76466 | 0.612150 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −44.0410 | −3.06106 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.6597 | −1.42906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9891 | 1.10073 | 0.550366 | − | 0.834923i | \(-0.314488\pi\) | ||||
0.550366 | + | 0.834923i | \(0.314488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.5415i | 1.20193i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.81154i | 0.600942i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.76387 | −0.527046 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.0311i | 1.89417i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.54613i | 0.505326i | 0.967554 | + | 0.252663i | \(0.0813064\pi\) | ||||
−0.967554 | + | 0.252663i | \(0.918694\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.94004 | −0.329336 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.4988i | 1.89153i | 0.324853 | + | 0.945765i | \(0.394685\pi\) | ||||
−0.324853 | + | 0.945765i | \(0.605315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 19.3902i | − 1.28134i | −0.767815 | − | 0.640671i | \(-0.778656\pi\) | ||||
0.767815 | − | 0.640671i | \(-0.221344\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.40337 | −0.618696 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.7622 | 0.836080 | 0.418040 | − | 0.908429i | \(-0.362717\pi\) | ||||
0.418040 | + | 0.908429i | \(0.362717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.3775 | −0.676955 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.7028 | 1.21488 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1424i | 0.720741i | 0.932809 | + | 0.360371i | \(0.117350\pi\) | ||||
−0.932809 | + | 0.360371i | \(0.882650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 5.48277i | − 0.353176i | −0.984285 | − | 0.176588i | \(-0.943494\pi\) | ||||
0.984285 | − | 0.176588i | \(-0.0565061\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7547 | −0.946517 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 6.05096i | − 0.386582i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − 19.8669i | − 1.25901i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.4904 | 1.54582 | 0.772910 | − | 0.634516i | \(-0.218801\pi\) | ||||
0.772910 | + | 0.634516i | \(0.218801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.5392i | 1.91998i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.799776i | 0.0500839i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.7828 | 0.922128 | 0.461064 | − | 0.887367i | \(-0.347468\pi\) | ||||
0.461064 | + | 0.887367i | \(0.347468\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.87715 | −0.178778 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.27783 | 0.140994 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.01732 | 0.186056 | 0.0930279 | − | 0.995664i | \(-0.470345\pi\) | ||||
0.0930279 | + | 0.995664i | \(0.470345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 4.96945i | − 0.305271i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.4301i | 1.49510i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.46709 | −0.516248 | −0.258124 | − | 0.966112i | \(-0.583104\pi\) | ||||
−0.258124 | + | 0.966112i | \(0.583104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7542i | 1.56445i | 0.622994 | + | 0.782227i | \(0.285916\pi\) | ||||
−0.622994 | + | 0.782227i | \(0.714084\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.42555i | 0.206568i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6848 | −0.882322 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 39.3701i | − 2.35703i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.1933i | 1.50290i | 0.659788 | + | 0.751452i | \(0.270646\pi\) | ||||
−0.659788 | + | 0.751452i | \(0.729354\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.3058 | 1.14761 | 0.573807 | − | 0.818991i | \(-0.305466\pi\) | ||||
0.573807 | + | 0.818991i | \(0.305466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.9943 | −1.00666 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.53841 | 0.504006 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9194 | −0.995261 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.937995i | 0.0549862i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.23340i | 0.0720561i | 0.999351 | + | 0.0360281i | \(0.0114706\pi\) | ||||
−0.999351 | + | 0.0360281i | \(0.988529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.88601 | 0.459141 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 18.7263i | − 1.08661i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.58408i | 0.494778i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 39.5048 | 2.26949 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 11.4869i | − 0.657739i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.36503i | 0.420344i | 0.977664 | + | 0.210172i | \(0.0674025\pi\) | ||||
−0.977664 | + | 0.210172i | \(0.932598\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 52.4222 | 2.98220 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.77672 | 0.440977 | 0.220489 | − | 0.975390i | \(-0.429235\pi\) | ||||
0.220489 | + | 0.975390i | \(0.429235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.104459 | 0.00590438 | 0.00295219 | − | 0.999996i | \(-0.499060\pi\) | ||||
0.00295219 | + | 0.999996i | \(0.499060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.81252 | −0.271155 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 32.3972i | − 1.81961i | −0.415040 | − | 0.909803i | \(-0.636232\pi\) | ||||
0.415040 | − | 0.909803i | \(-0.363768\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.57951i | − 0.0884354i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.4342 | −1.69867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.71179i | 0.0952464i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 8.11013i | − 0.448491i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.1096 | −0.557363 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.1973i | 1.05518i | 0.849500 | + | 0.527589i | \(0.176904\pi\) | ||||
−0.849500 | + | 0.527589i | \(0.823096\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 14.5899i | − 0.799520i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.96340 | 0.216543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6042 | 1.17686 | 0.588429 | − | 0.808549i | \(-0.299747\pi\) | ||||
0.588429 | + | 0.808549i | \(0.299747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.5477 | 1.49618 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.3002 | −1.47839 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 12.7141i | − 0.686495i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.1211i | 1.35247i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.4830 | −0.670120 | −0.335060 | − | 0.942197i | \(-0.608757\pi\) | ||||
−0.335060 | + | 0.942197i | \(0.608757\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1232i | 1.39834i | 0.714954 | + | 0.699171i | \(0.246448\pi\) | ||||
−0.714954 | + | 0.699171i | \(0.753552\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.7057i | 1.04883i | 0.851464 | + | 0.524413i | \(0.175715\pi\) | ||||
−0.851464 | + | 0.524413i | \(0.824285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.22524 | 0.330402 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.779130i | 0.0412360i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 6.56325i | − 0.346395i | −0.984887 | − | 0.173198i | \(-0.944590\pi\) | ||||
0.984887 | − | 0.173198i | \(-0.0554099\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3736 | −0.914399 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.06938 | −0.108614 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.94784 | 0.520694 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.1532 | −1.73058 | −0.865291 | − | 0.501270i | \(-0.832866\pi\) | ||||
−0.865291 | + | 0.501270i | \(0.832866\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 43.2978i | 2.25399i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 4.84117i | − 0.251341i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.0243 | 1.55460 | 0.777300 | − | 0.629130i | \(-0.216589\pi\) | ||||
0.777300 | + | 0.629130i | \(0.216589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.81781i | 0.145511i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1570i | 0.573097i | 0.958066 | + | 0.286549i | \(0.0925080\pi\) | ||||
−0.958066 | + | 0.286549i | \(0.907492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.5267 | −2.07625 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.5707i | 0.591233i | 0.955307 | + | 0.295616i | \(0.0955250\pi\) | ||||
−0.955307 | + | 0.295616i | \(0.904475\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.33712i | 0.170076i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −43.5293 | −2.21272 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.6724 | 0.946727 | 0.473363 | − | 0.880867i | \(-0.343040\pi\) | ||||
0.473363 | + | 0.880867i | \(0.343040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.53037 | 0.127966 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 47.6509 | 2.40367 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 6.63735i | − 0.333961i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7838i | 0.741977i | 0.928638 | + | 0.370988i | \(0.120981\pi\) | ||||
−0.928638 | + | 0.370988i | \(0.879019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.5557 | −0.828819 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 13.5374i | − 0.676025i | −0.941142 | − | 0.338012i | \(-0.890245\pi\) | ||||
0.941142 | − | 0.338012i | \(-0.109755\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 0.583871i | − 0.0290128i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.1170 | −0.501481 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 9.79211i | − 0.484189i | −0.970253 | − | 0.242094i | \(-0.922166\pi\) | ||||
0.970253 | − | 0.242094i | \(-0.0778343\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.7504i | 1.07287i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.68244 | 0.378028 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.05049 | −0.346095 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −52.9630 | −2.59361 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.3450 | −0.945065 | −0.472533 | − | 0.881313i | \(-0.656660\pi\) | ||||
−0.472533 | + | 0.881313i | \(0.656660\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 10.8582i | − 0.529199i | −0.964358 | − | 0.264599i | \(-0.914760\pi\) | ||||
0.964358 | − | 0.264599i | \(-0.0852397\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 51.2654i | − 2.49261i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.283829 | 0.0137677 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 11.1904i | − 0.541541i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 8.47538i | − 0.408245i | −0.978945 | − | 0.204122i | \(-0.934566\pi\) | ||||
0.978945 | − | 0.204122i | \(-0.0654341\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.6325 | 0.703193 | 0.351596 | − | 0.936152i | \(-0.385639\pi\) | ||||
0.351596 | + | 0.936152i | \(0.385639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 1.29928i | − 0.0622957i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 53.7675i | 2.57205i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2299 | −0.488245 | −0.244123 | − | 0.969744i | \(-0.578500\pi\) | ||||
−0.244123 | + | 0.969744i | \(0.578500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.8920 | 1.42343 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.89017 | 0.0898045 | 0.0449023 | − | 0.998991i | \(-0.485702\pi\) | ||||
0.0449023 | + | 0.998991i | \(0.485702\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.66990 | 0.410993 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 9.92185i | − 0.469288i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.6031i | 0.500393i | 0.968195 | + | 0.250196i | \(0.0804952\pi\) | ||||
−0.968195 | + | 0.250196i | \(0.919505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.0238 | 1.41376 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 31.1361i | − 1.46290i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2158i | 1.31988i | 0.751319 | + | 0.659939i | \(0.229418\pi\) | ||||
−0.751319 | + | 0.659939i | \(0.770582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.55160 | −0.0724223 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1918i | 0.660976i | 0.943810 | + | 0.330488i | \(0.107213\pi\) | ||||
−0.943810 | + | 0.330488i | \(0.892787\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 18.9826i | − 0.882195i | −0.897459 | − | 0.441098i | \(-0.854589\pi\) | ||||
0.897459 | − | 0.441098i | \(-0.145411\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22.4568 | −1.04141 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.88823 | 0.457573 | 0.228786 | − | 0.973477i | \(-0.426524\pi\) | ||||
0.228786 | + | 0.973477i | \(0.426524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.86109 | 0.178288 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6189 | 0.581447 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.1844i | 1.38788i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.03105i | 0.276724i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.5493 | 1.12403 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.4914i | 1.21042i | 0.796065 | + | 0.605211i | \(0.206911\pi\) | ||||
−0.796065 | + | 0.605211i | \(0.793089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.4726i | 1.11354i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.332881 | 0.0151154 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 34.8349i | − 1.57852i | −0.614058 | − | 0.789261i | \(-0.710464\pi\) | ||||
0.614058 | − | 0.789261i | \(-0.289536\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 31.9793i | − 1.44616i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.113245 | 0.00511068 | 0.00255534 | − | 0.999997i | \(-0.499187\pi\) | ||||
0.00255534 | + | 0.999997i | \(0.499187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.130872 | −0.00589420 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.9224 | −0.760603 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.06455 | 0.272032 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 7.69924i | − 0.344665i | −0.985039 | − | 0.172333i | \(-0.944870\pi\) | ||||
0.985039 | − | 0.172333i | \(-0.0551304\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 24.8537i | − 1.11038i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.09165 | −0.0486742 | −0.0243371 | − | 0.999704i | \(-0.507748\pi\) | ||||
−0.0243371 | + | 0.999704i | \(0.507748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 14.0197i | − 0.623869i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 3.78054i | − 0.167569i | −0.996484 | − | 0.0837847i | \(-0.973299\pi\) | ||||
0.996484 | − | 0.0837847i | \(-0.0267008\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.69105 | 0.428707 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 32.9697i | − 1.45565i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 18.6039i | − 0.819786i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −35.5487 | −1.56343 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.0949 | 0.574800 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.70631 | −0.381430 | −0.190715 | − | 0.981645i | \(-0.561081\pi\) | ||||
−0.190715 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.8023 | −0.516077 | −0.258038 | − | 0.966135i | \(-0.583076\pi\) | ||||
−0.258038 | + | 0.966135i | \(0.583076\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.74507i | 0.119805i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.26200i | 0.0985343i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.4792 | 2.45562 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 38.9572i | 1.69060i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.8007i | 0.466954i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 71.3429 | 3.07867 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 20.7279i | − 0.892813i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 21.0010i | − 0.902902i | −0.892296 | − | 0.451451i | \(-0.850907\pi\) | ||||
0.892296 | − | 0.451451i | \(-0.149093\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.1931 | −0.523255 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.87817 | −0.123287 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6759 | −0.841282 | −0.420641 | − | 0.907227i | \(-0.638195\pi\) | ||||
−0.420641 | + | 0.907227i | \(0.638195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 56.7458 | 2.42185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 2.78089i | − 0.118470i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 6.46601i | − 0.274963i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.32209 | −0.353253 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.5516i | 0.913172i | 0.889679 | + | 0.456586i | \(0.150928\pi\) | ||||
−0.889679 | + | 0.456586i | \(0.849072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.73967i | 0.115669i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.6586 | −0.449205 | −0.224602 | − | 0.974450i | \(-0.572108\pi\) | ||||
−0.224602 | + | 0.974450i | \(0.572108\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 9.77628i | − 0.411291i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 0.568799i | − 0.0238873i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.5445 | −1.15473 | −0.577363 | − | 0.816488i | \(-0.695918\pi\) | ||||
−0.577363 | + | 0.816488i | \(0.695918\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.1038 | 1.76199 | 0.880994 | − | 0.473127i | \(-0.156875\pi\) | ||||
0.880994 | + | 0.473127i | \(0.156875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.39224 | −0.308815 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.91511 | 0.371786 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 33.7205i | − 1.40380i | −0.712274 | − | 0.701901i | \(-0.752335\pi\) | ||||
0.712274 | − | 0.701901i | \(-0.247665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 61.0447i | − 2.53693i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.86849 | −0.284953 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 17.0231i | − 0.705024i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 13.3282i | − 0.550114i | −0.961428 | − | 0.275057i | \(-0.911303\pi\) | ||||
0.961428 | − | 0.275057i | \(-0.0886968\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.0650 | −1.98048 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 58.7797i | − 2.41788i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.07378i | − 0.0440949i | −0.999757 | − | 0.0220474i | \(-0.992982\pi\) | ||||
0.999757 | − | 0.0220474i | \(-0.00701848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.276502 | 0.0113355 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −64.1951 | −2.62733 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3111 | −0.748169 | −0.374085 | − | 0.927395i | \(-0.622043\pi\) | ||||
−0.374085 | + | 0.927395i | \(0.622043\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.14497 | −0.0467043 | −0.0233521 | − | 0.999727i | \(-0.507434\pi\) | ||||
−0.0233521 | + | 0.999727i | \(0.507434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.5793i | 0.797332i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.734394i | 0.0298573i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.3920 | −0.462385 | −0.231193 | − | 0.972908i | \(-0.574263\pi\) | ||||
−0.231193 | + | 0.972908i | \(0.574263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − 1.26574i | − 0.0512904i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 6.51518i | − 0.263146i | −0.991306 | − | 0.131573i | \(-0.957997\pi\) | ||||
0.991306 | − | 0.131573i | \(-0.0420027\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 24.6971 | 0.995884 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.43338i | 0.178481i | 0.996010 | + | 0.0892405i | \(0.0284440\pi\) | ||||
−0.996010 | + | 0.0892405i | \(0.971556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.32341i | 0.0933857i | 0.998909 | + | 0.0466929i | \(0.0148682\pi\) | ||||
−0.998909 | + | 0.0466929i | \(0.985132\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.7359 | −1.95570 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.44610 | 0.338386 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −58.2150 | −2.32488 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.838259i | 0.0334236i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4463i | 1.01300i | 0.862239 | + | 0.506501i | \(0.169061\pi\) | ||||
−0.862239 | + | 0.506501i | \(0.830939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.0541 | 1.79074 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.3824i | 0.570746i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.7530i | 1.21657i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.30285 | −0.367440 | −0.183720 | − | 0.982979i | \(-0.558814\pi\) | ||||
−0.183720 | + | 0.982979i | \(0.558814\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 49.3771i | − 1.94724i | −0.228172 | − | 0.973621i | \(-0.573275\pi\) | ||||
0.228172 | − | 0.973621i | \(-0.426725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.8292i | 0.977649i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.1654 | −1.02867 | −0.514334 | − | 0.857590i | \(-0.671961\pi\) | ||||
−0.514334 | + | 0.857590i | \(0.671961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.0139 | 1.06039 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.8771 | −0.857430 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.5177 | −0.489857 | −0.244929 | − | 0.969541i | \(-0.578765\pi\) | ||||
−0.244929 | + | 0.969541i | \(0.578765\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 16.9106i | − 0.660753i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 49.1427i | 1.91724i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.30544 | −0.362488 | −0.181244 | − | 0.983438i | \(-0.558012\pi\) | ||||
−0.181244 | + | 0.983438i | \(0.558012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 0.778487i | − 0.0302796i | −0.999885 | − | 0.0151398i | \(-0.995181\pi\) | ||||
0.999885 | − | 0.0151398i | \(-0.00481934\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.87537i | 0.227837i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.11072 | −0.159168 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.2635i | 0.822096i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 39.3490i | − 1.51905i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6069 | −0.717243 | −0.358621 | − | 0.933483i | \(-0.616753\pi\) | ||||
−0.358621 | + | 0.933483i | \(0.616753\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.46666 | −0.210412 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.451238 | 0.0173425 | 0.00867125 | − | 0.999962i | \(-0.497240\pi\) | ||||
0.00867125 | + | 0.999962i | \(0.497240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.324288 | 0.0124450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 80.3040i | 3.07726i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3929i | 1.35427i | 0.735858 | + | 0.677136i | \(0.236779\pi\) | ||||
−0.735858 | + | 0.677136i | \(0.763221\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.71889 | 0.294924 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 54.6379i | − 2.08457i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0369i | 1.48503i | 0.669828 | + | 0.742516i | \(0.266368\pi\) | ||||
−0.669828 | + | 0.742516i | \(0.733632\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.4855 | −0.626233 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.7958i | 0.712966i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 2.48767i | − 0.0942270i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.9614 | 1.36019 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0395 | −0.681344 | −0.340672 | − | 0.940182i | \(-0.610655\pi\) | ||||
−0.340672 | + | 0.940182i | \(0.610655\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.8121 | −0.671795 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29.2419 | −1.10131 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 13.6578i | − 0.513654i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 19.7805i | − 0.742871i | −0.928459 | − | 0.371436i | \(-0.878866\pi\) | ||||
0.928459 | − | 0.371436i | \(-0.121134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.7888 | 1.22967 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 71.0498i | 2.66084i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.3971i | 1.17255i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.2849 | 0.383562 | 0.191781 | − | 0.981438i | \(-0.438574\pi\) | ||||
0.191781 | + | 0.981438i | \(0.438574\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 18.1237i | − 0.674961i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 15.4494i | − 0.574569i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.461096 | −0.0171247 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.08016 | 0.262589 | 0.131294 | − | 0.991343i | \(-0.458087\pi\) | ||||
0.131294 | + | 0.991343i | \(0.458087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.3276 | −1.60473 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50097 | 0.0925017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 6.29532i | − 0.232523i | −0.993219 | − | 0.116261i | \(-0.962909\pi\) | ||||
0.993219 | − | 0.116261i | \(-0.0370911\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 17.0504i | − 0.628915i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.5768 | 0.500108 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 33.4301i | − 1.22975i | −0.788626 | − | 0.614873i | \(-0.789207\pi\) | ||||
0.788626 | − | 0.614873i | \(-0.210793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.84274i | 0.140976i | 0.997513 | + | 0.0704882i | \(0.0224557\pi\) | ||||
−0.997513 | + | 0.0704882i | \(0.977544\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.52113 | −0.129004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 34.8297i | − 1.27435i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.5219i | 0.384461i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.7285 | 1.26726 | 0.633630 | − | 0.773636i | \(-0.281564\pi\) | ||||
0.633630 | + | 0.773636i | \(0.281564\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 69.0092 | 2.51483 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.0498 | −0.402142 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.10935 | 0.294739 | 0.147370 | − | 0.989081i | \(-0.452919\pi\) | ||||
0.147370 | + | 0.989081i | \(0.452919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 86.0535i | 3.12354i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.4717i | 0.379598i | 0.981823 | + | 0.189799i | \(0.0607837\pi\) | ||||
−0.981823 | + | 0.189799i | \(0.939216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.80388 | −0.101507 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.40213i | 0.0506940i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.2939i | 1.59728i | 0.601810 | + | 0.798639i | \(0.294446\pi\) | ||||
−0.601810 | + | 0.798639i | \(0.705554\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 41.6552 | 1.50017 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2760i | 0.441537i | 0.975326 | + | 0.220769i | \(0.0708566\pi\) | ||||
−0.975326 | + | 0.220769i | \(0.929143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.96959i | 0.286276i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.10727 | −0.290847 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 52.8601 | 1.89391 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3249 | 0.763064 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.52065 | 0.0900808 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.47826i | − 0.159836i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7.08241i | − 0.252461i | −0.992001 | − | 0.126230i | \(-0.959712\pi\) | ||||
0.992001 | − | 0.126230i | \(-0.0402878\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.50222 | 0.302687 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 9.52392i | − 0.338632i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 14.0029i | − 0.496633i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.6799 | 0.697099 | 0.348550 | − | 0.937290i | \(-0.386674\pi\) | ||||
0.348550 | + | 0.937290i | \(0.386674\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.94544i | 0.104202i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.8296i | 1.51331i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.0768 | 1.20254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.68498 | 0.306105 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.8586 | −0.839864 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.3066 | 0.924890 | 0.462445 | − | 0.886648i | \(-0.346972\pi\) | ||||
0.462445 | + | 0.886648i | \(0.346972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 52.2096i | − 1.83333i | −0.399662 | − | 0.916663i | \(-0.630872\pi\) | ||||
0.399662 | − | 0.916663i | \(-0.369128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 72.5702i | 2.54515i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.3490 | −0.397539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.1428i | 1.85923i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.9551i | 1.70855i | 0.519825 | + | 0.854273i | \(0.325997\pi\) | ||||
−0.519825 | + | 0.854273i | \(0.674003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.3073 | −0.986731 | −0.493366 | − | 0.869822i | \(-0.664233\pi\) | ||||
−0.493366 | + | 0.869822i | \(0.664233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.65254i | 0.336058i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.1223i | 0.386759i | 0.981124 | + | 0.193380i | \(0.0619449\pi\) | ||||
−0.981124 | + | 0.193380i | \(0.938055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.14566 | 0.0397905 | 0.0198952 | − | 0.999802i | \(-0.493667\pi\) | ||||
0.0198952 | + | 0.999802i | \(0.493667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −41.3788 | −1.43542 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.71744 | −0.0595057 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.82022 | −0.305236 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 43.5670i | − 1.50590i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 28.3167i | − 0.977602i | −0.872395 | − | 0.488801i | \(-0.837434\pi\) | ||||
0.872395 | − | 0.488801i | \(-0.162566\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7874 | −0.992669 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 70.9898i | 2.44502i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.715436i | 0.0245827i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.4002 | 1.86701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.3298i | 0.902574i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6180i | 1.01410i | 0.861916 | + | 0.507051i | \(0.169264\pi\) | ||||
−0.861916 | + | 0.507051i | \(0.830736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.7936 | −1.01892 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.3690 | −0.490835 | −0.245417 | − | 0.969418i | \(-0.578925\pi\) | ||||
−0.245417 | + | 0.969418i | \(0.578925\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.17850 | −0.313166 | −0.156583 | − | 0.987665i | \(-0.550048\pi\) | ||||
−0.156583 | + | 0.987665i | \(0.550048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.0596 | 0.819949 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.1458i | 1.09426i | 0.837049 | + | 0.547128i | \(0.184279\pi\) | ||||
−0.837049 | + | 0.547128i | \(0.815721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 4.64718i | − 0.158009i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −47.6757 | −1.61915 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 22.7366i | − 0.771285i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.64445i | 0.0556561i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.974186 | 0.0329335 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.9633i | 0.876720i | 0.898800 | + | 0.438360i | \(0.144440\pi\) | ||||
−0.898800 | + | 0.438360i | \(0.855560\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.47549i | 0.117225i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.1165 | 0.576671 | 0.288335 | − | 0.957529i | \(-0.406898\pi\) | ||||
0.288335 | + | 0.957529i | \(0.406898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3273 | 0.616762 | 0.308381 | − | 0.951263i | \(-0.400213\pi\) | ||||
0.308381 | + | 0.951263i | \(0.400213\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22.2213 | 0.746960 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.2866 | −1.21838 | −0.609192 | − | 0.793023i | \(-0.708506\pi\) | ||||
−0.609192 | + | 0.793023i | \(0.708506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.0111i | 0.469917i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.00008i | − 0.0670051i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −62.5874 | −2.09441 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 25.3186i | − 0.846307i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3.67475i | − 0.122560i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.41047 | −0.0469897 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.1883i | 0.804935i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.32715i | 0.143839i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.7409 | −0.356645 | −0.178323 | − | 0.983972i | \(-0.557067\pi\) | ||||
−0.178323 | + | 0.983972i | \(0.557067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 69.2579 | 2.29714 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.8649 | −1.05573 | −0.527866 | − | 0.849327i | \(-0.677008\pi\) | ||||
−0.527866 | + | 0.849327i | \(0.677008\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.1518 | −0.799308 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 32.3679i | − 1.07005i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 16.4741i | − 0.544023i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.6467 | 0.483149 | 0.241574 | − | 0.970382i | \(-0.422336\pi\) | ||||
0.241574 | + | 0.970382i | \(0.422336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.7532i | 0.683842i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.95339i | 0.0971069i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 91.9040 | 3.01852 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.9334i | 1.86792i | 0.357373 | + | 0.933962i | \(0.383672\pi\) | ||||
−0.357373 | + | 0.933962i | \(0.616328\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 36.4937i | − 1.19603i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.9133 | 0.717409 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.972271 | 0.0317967 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.76516 | 0.123002 | 0.0615012 | − | 0.998107i | \(-0.480411\pi\) | ||||
0.0615012 | + | 0.998107i | \(0.480411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.294346 | 0.00960562 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.9802i | 0.944728i | 0.881404 | + | 0.472364i | \(0.156599\pi\) | ||||
−0.881404 | + | 0.472364i | \(0.843401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 78.1379i | − 2.54452i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.32554 | −0.173240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 9.77047i | − 0.317498i | −0.987319 | − | 0.158749i | \(-0.949254\pi\) | ||||
0.987319 | − | 0.158749i | \(-0.0507460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 91.2890i | − 2.96025i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.3749 | −1.37266 | −0.686330 | − | 0.727291i | \(-0.740779\pi\) | ||||
−0.686330 | + | 0.727291i | \(0.740779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.62340i | 0.0848913i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 4.45075i | − 0.143872i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.51964 | 0.242822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32.5144 | −1.04885 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −53.3558 | −1.71937 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.6639 | −0.697385 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.65301i | 0.181788i | 0.995861 | + | 0.0908942i | \(0.0289725\pi\) | ||||
−0.995861 | + | 0.0908942i | \(0.971027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.82349i | 0.154953i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.0547 | 1.28542 | 0.642709 | − | 0.766111i | \(-0.277811\pi\) | ||||
0.642709 | + | 0.766111i | \(0.277811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.3106i | 0.587012i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 15.7119i | − 0.502668i | −0.967900 | − | 0.251334i | \(-0.919131\pi\) | ||||
0.967900 | − | 0.251334i | \(-0.0808692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.6992 | 0.949190 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 14.2183i | − 0.453955i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.6671i | 1.48845i | 0.667929 | + | 0.744225i | \(0.267181\pi\) | ||||
−0.667929 | + | 0.744225i | \(0.732819\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.8601 | −0.664658 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.4870 | −0.906752 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 78.5558 | 2.49793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.23358 | 0.0391859 | 0.0195930 | − | 0.999808i | \(-0.493763\pi\) | ||||
0.0195930 | + | 0.999808i | \(0.493763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 54.0942i | 1.71663i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.7819i | 0.722236i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9285 | 1.04286 | 0.521428 | − | 0.853295i | \(-0.325400\pi\) | ||||
0.521428 | + | 0.853295i | \(0.325400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 16.1452i | − 0.510811i |
(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 | 3380.2.f.j.3041.17 | 18 | ||
13.5 | odd | 4 | 3380.2.a.r.1.9 | ✓ | 9 | ||
13.8 | odd | 4 | 3380.2.a.s.1.9 | yes | 9 | ||
13.12 | even | 2 | inner | 3380.2.f.j.3041.18 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3380.2.a.r.1.9 | ✓ | 9 | 13.5 | odd | 4 | ||
3380.2.a.s.1.9 | yes | 9 | 13.8 | odd | 4 | ||
3380.2.f.j.3041.17 | 18 | 1.1 | even | 1 | trivial | ||
3380.2.f.j.3041.18 | 18 | 13.12 | even | 2 | inner |