Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(961,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.bg (of order \(3\), degree \(2\), 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.29428272.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.3 | ||
Root | \(-2.56022 + 0.667305i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.961 |
Dual form | 1680.2.bg.v.1201.3 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56022 | + | 0.667305i | 0.967671 | + | 0.252218i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.65581 | − | 4.59999i | −0.800756 | − | 1.38695i | −0.919119 | − | 0.393979i | \(-0.871098\pi\) |
0.118364 | − | 0.992970i | \(-0.462235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.71602 | −1.58534 | −0.792670 | − | 0.609651i | \(-0.791309\pi\) | ||||
−0.792670 | + | 0.609651i | \(0.791309\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.76242 | − | 6.51670i | −0.912521 | − | 1.58053i | −0.810491 | − | 0.585751i | \(-0.800800\pi\) |
−0.102030 | − | 0.994781i | \(-0.532534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.702205 | + | 2.55086i | 0.153234 | + | 0.556644i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.06022 | − | 3.56840i | 0.429585 | − | 0.744062i | −0.567252 | − | 0.823545i | \(-0.691993\pi\) |
0.996836 | + | 0.0794821i | \(0.0253266\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.71602 | −0.504353 | −0.252176 | − | 0.967681i | \(-0.581146\pi\) | ||||
−0.252176 | + | 0.967681i | \(0.581146\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.91823 | − | 5.05452i | −0.524129 | − | 0.907818i | −0.999605 | − | 0.0280895i | \(-0.991058\pi\) |
0.475476 | − | 0.879728i | \(-0.342276\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.65581 | − | 4.59999i | 0.462317 | − | 0.800756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.85801 | − | 1.88356i | 0.314061 | − | 0.318380i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.45360 | + | 4.24976i | −0.403370 | + | 0.698657i | −0.994130 | − | 0.108190i | \(-0.965494\pi\) |
0.590761 | + | 0.806847i | \(0.298828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.85801 | − | 4.95022i | −0.457648 | − | 0.792670i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.12043 | −1.26820 | −0.634099 | − | 0.773252i | \(-0.718629\pi\) | ||||
−0.634099 | + | 0.773252i | \(0.718629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.31161 | −0.657515 | −0.328757 | − | 0.944414i | \(-0.606630\pi\) | ||||
−0.328757 | + | 0.944414i | \(0.606630\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.41823 | − | 9.38464i | 0.790330 | − | 1.36889i | −0.135433 | − | 0.990786i | \(-0.543243\pi\) |
0.925763 | − | 0.378105i | \(-0.123424\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.10941 | + | 3.41689i | 0.872773 | + | 0.488127i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.76242 | − | 6.51670i | 0.526844 | − | 0.912521i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.29780 | + | 3.97990i | 0.315626 | + | 0.546681i | 0.979570 | − | 0.201101i | \(-0.0644520\pi\) |
−0.663944 | + | 0.747782i | \(0.731119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.31161 | −0.716218 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.35801 | + | 12.7444i | 0.957931 | + | 1.65919i | 0.727513 | + | 0.686094i | \(0.240676\pi\) |
0.230419 | + | 0.973092i | \(0.425990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.85801 | + | 1.88356i | −0.234087 | + | 0.237306i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.85801 | + | 4.95022i | −0.354493 | + | 0.613999i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.15581 | + | 3.73397i | 0.263374 | + | 0.456177i | 0.967136 | − | 0.254259i | \(-0.0818315\pi\) |
−0.703763 | + | 0.710435i | \(0.748498\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.12043 | 0.496042 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3337 | 1.22638 | 0.613190 | − | 0.789936i | \(-0.289886\pi\) | ||||
0.613190 | + | 0.789936i | \(0.289886\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.439784 | − | 0.761729i | −0.0514729 | − | 0.0891536i | 0.839141 | − | 0.543914i | \(-0.183058\pi\) |
−0.890614 | + | 0.454760i | \(0.849725\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.72984 | − | 13.5492i | −0.425055 | − | 1.54407i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.51382 | + | 6.08611i | −0.395335 | + | 0.684741i | −0.993144 | − | 0.116898i | \(-0.962705\pi\) |
0.597809 | + | 0.801639i | \(0.296038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.71602 | 0.298122 | 0.149061 | − | 0.988828i | \(-0.452375\pi\) | ||||
0.149061 | + | 0.988828i | \(0.452375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.52484 | −0.816184 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.35801 | − | 2.35214i | −0.145594 | − | 0.252176i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.95360 | + | 3.38374i | −0.207081 | + | 0.358675i | −0.950794 | − | 0.309824i | \(-0.899730\pi\) |
0.743713 | + | 0.668500i | \(0.233063\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.6342 | − | 3.81433i | −1.53409 | − | 0.399850i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.91823 | − | 5.05452i | 0.302606 | − | 0.524129i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.500000 | − | 0.866025i | −0.0512989 | − | 0.0888523i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.31161 | 0.533837 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.237580 | − | 0.411500i | −0.0236401 | − | 0.0409458i | 0.853963 | − | 0.520333i | \(-0.174192\pi\) |
−0.877603 | + | 0.479387i | \(0.840859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.87183 | − | 15.3665i | 0.874167 | − | 1.51410i | 0.0165200 | − | 0.999864i | \(-0.494741\pi\) |
0.857647 | − | 0.514238i | \(-0.171925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.56022 | + | 0.667305i | 0.249851 | + | 0.0651223i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.16683 | + | 5.48511i | −0.306149 | + | 0.530266i | −0.977516 | − | 0.210859i | \(-0.932374\pi\) |
0.671368 | + | 0.741125i | \(0.265707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.51382 | − | 11.2823i | −0.623911 | − | 1.08064i | −0.988750 | − | 0.149574i | \(-0.952210\pi\) |
0.364840 | − | 0.931070i | \(-0.381124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.90720 | −0.465771 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.61764 | 0.716607 | 0.358304 | − | 0.933605i | \(-0.383355\pi\) | ||||
0.358304 | + | 0.933605i | \(0.383355\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.06022 | − | 3.56840i | −0.192116 | − | 0.332755i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.85801 | − | 4.95022i | 0.264223 | − | 0.457648i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.28398 | − | 19.1948i | −0.484381 | − | 1.75959i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.60661 | + | 14.9071i | −0.782419 | + | 1.35519i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.06022 | − | 7.03250i | −0.366097 | − | 0.634099i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.33366 | −0.295814 | −0.147907 | − | 0.989001i | \(-0.547254\pi\) | ||||
−0.147907 | + | 0.989001i | \(0.547254\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.15581 | − | 3.73397i | −0.189808 | − | 0.328757i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.702205 | − | 1.21625i | 0.0613519 | − | 0.106265i | −0.833718 | − | 0.552190i | \(-0.813792\pi\) |
0.895070 | + | 0.445926i | \(0.147125\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.85801 | − | 1.88356i | 0.161110 | − | 0.163325i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.79005 | − | 16.9569i | −0.836421 | − | 1.44872i | −0.892868 | − | 0.450318i | \(-0.851311\pi\) |
0.0564475 | − | 0.998406i | \(-0.482023\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.21323 | −0.611818 | −0.305909 | − | 0.952061i | \(-0.598960\pi\) | ||||
−0.305909 | + | 0.952061i | \(0.598960\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8365 | 0.912594 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.1806 | + | 26.2937i | 1.26947 | + | 2.19879i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.35801 | + | 2.35214i | −0.112777 | + | 0.195335i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0955907 | + | 6.99935i | 0.00788419 | + | 0.577296i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.43204 | − | 9.40858i | 0.445010 | − | 0.770781i | −0.553043 | − | 0.833153i | \(-0.686533\pi\) |
0.998053 | + | 0.0623724i | \(0.0198667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.19118 | + | 3.79524i | 0.178316 | + | 0.308852i | 0.941304 | − | 0.337561i | \(-0.109602\pi\) |
−0.762988 | + | 0.646413i | \(0.776268\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.52484 | 0.608347 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.83645 | −0.468795 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.53866 | − | 16.5214i | −0.761268 | − | 1.31855i | −0.942197 | − | 0.335058i | \(-0.891244\pi\) |
0.180930 | − | 0.983496i | \(-0.442089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.29780 | + | 3.97990i | −0.182227 | + | 0.315626i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.65581 | − | 7.76108i | 0.603362 | − | 0.611658i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | − | 6.92820i | 0.313304 | − | 0.542659i | −0.665771 | − | 0.746156i | \(-0.731897\pi\) |
0.979076 | + | 0.203497i | \(0.0652307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.65581 | − | 4.59999i | −0.206754 | − | 0.358109i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.50279 | −0.657966 | −0.328983 | − | 0.944336i | \(-0.606706\pi\) | ||||
−0.328983 | + | 0.944336i | \(0.606706\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.6729 | 1.51330 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | + | 0.866025i | 0.0382360 | + | 0.0662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5387 | − | 18.2535i | 0.801239 | − | 1.38779i | −0.117561 | − | 0.993066i | \(-0.537508\pi\) |
0.918801 | − | 0.394722i | \(-0.129159\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.702205 | − | 2.55086i | −0.0530817 | − | 0.192827i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.35801 | + | 12.7444i | −0.553062 | + | 0.957931i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.82264 | + | 4.88895i | 0.210974 | + | 0.365417i | 0.952020 | − | 0.306037i | \(-0.0990032\pi\) |
−0.741046 | + | 0.671454i | \(0.765670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.2685 | 1.87819 | 0.939096 | − | 0.343654i | \(-0.111665\pi\) | ||||
0.939096 | + | 0.343654i | \(0.111665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.45360 | + | 4.24976i | 0.180392 | + | 0.312449i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.9845 | + | 34.6142i | −1.46141 | + | 2.53124i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.56022 | − | 0.667305i | −0.186228 | − | 0.0485393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.43204 | − | 11.1406i | 0.465406 | − | 0.806107i | −0.533813 | − | 0.845602i | \(-0.679242\pi\) |
0.999220 | + | 0.0394948i | \(0.0125749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.87183 | + | 17.0985i | 0.710590 | + | 1.23078i | 0.964636 | + | 0.263585i | \(0.0849051\pi\) |
−0.254046 | + | 0.967192i | \(0.581762\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.71602 | −0.409333 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.7437 | −1.33543 | −0.667715 | − | 0.744417i | \(-0.732728\pi\) | ||||
−0.667715 | + | 0.744417i | \(0.732728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8365 | + | 20.5013i | 0.839064 | + | 1.45330i | 0.890678 | + | 0.454634i | \(0.150230\pi\) |
−0.0516143 | + | 0.998667i | \(0.516437\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.15581 | + | 3.73397i | −0.152059 | + | 0.263374i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.95360 | − | 1.81242i | −0.488047 | − | 0.127207i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.06022 | + | 7.03250i | −0.283578 | + | 0.491171i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.06022 | + | 3.56840i | 0.143195 | + | 0.248021i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.31161 | −0.367412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.64527 | −0.664008 | −0.332004 | − | 0.943278i | \(-0.607725\pi\) | ||||
−0.332004 | + | 0.943278i | \(0.607725\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.16683 | + | 8.94921i | 0.354025 | + | 0.613190i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.15581 | + | 3.73397i | −0.147025 | + | 0.254654i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.09838 | − | 14.8880i | −0.278216 | − | 1.01066i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.439784 | − | 0.761729i | 0.0297179 | − | 0.0514729i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.5061 | + | 37.2496i | 1.44666 | + | 2.50568i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.56796 | −0.439823 | −0.219911 | − | 0.975520i | \(-0.570577\pi\) | ||||
−0.219911 | + | 0.975520i | \(0.570577\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.16683 | − | 3.75306i | −0.143818 | − | 0.249099i | 0.785114 | − | 0.619352i | \(-0.212605\pi\) |
−0.928931 | + | 0.370252i | \(0.879271\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.08177 | − | 5.33779i | 0.203649 | − | 0.352731i | −0.746052 | − | 0.665887i | \(-0.768053\pi\) |
0.949702 | + | 0.313156i | \(0.101386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.86903 | − | 10.0047i | 0.649335 | − | 0.658263i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.71602 | − | 2.97224i | 0.112420 | − | 0.194718i | −0.804325 | − | 0.594189i | \(-0.797473\pi\) |
0.916746 | + | 0.399472i | \(0.130806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.41823 | − | 9.38464i | −0.353446 | − | 0.612187i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.02763 | −0.456494 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.8641 | 1.86706 | 0.933531 | − | 0.358496i | \(-0.116710\pi\) | ||||
0.933531 | + | 0.358496i | \(0.116710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.29780 | − | 14.3722i | −0.534508 | − | 0.925795i | −0.999187 | − | 0.0403158i | \(-0.987164\pi\) |
0.464679 | − | 0.885479i | \(-0.346170\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.01382 | − | 3.58246i | 0.384209 | − | 0.228875i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.85801 | + | 4.95022i | −0.181851 | + | 0.314975i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.35801 | + | 2.35214i | 0.0860604 | + | 0.149061i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1260 | 0.702268 | 0.351134 | − | 0.936325i | \(-0.385796\pi\) | ||||
0.351134 | + | 0.936325i | \(0.385796\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.8861 | −1.37597 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.76242 | − | 6.51670i | −0.235612 | − | 0.408092i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.54919 | + | 11.3435i | −0.408527 | + | 0.707590i | −0.994725 | − | 0.102578i | \(-0.967291\pi\) |
0.586198 | + | 0.810168i | \(0.300624\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.11764 | + | 9.24301i | −0.566542 | + | 0.574333i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.35801 | − | 2.35214i | 0.0840588 | − | 0.145594i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.71602 | + | 4.70429i | 0.167477 | + | 0.290079i | 0.937532 | − | 0.347899i | \(-0.113105\pi\) |
−0.770055 | + | 0.637977i | \(0.779771\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.59559 | 0.282305 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.90720 | −0.239117 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.12043 | + | 5.40475i | 0.190256 | + | 0.329533i | 0.945335 | − | 0.326101i | \(-0.105735\pi\) |
−0.755079 | + | 0.655634i | \(0.772402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4044 | − | 18.0210i | 0.632023 | − | 1.09470i | −0.355115 | − | 0.934823i | \(-0.615558\pi\) |
0.987138 | − | 0.159873i | \(-0.0511085\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.01382 | − | 14.5808i | −0.242927 | − | 0.882470i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.65581 | + | 4.59999i | −0.160151 | + | 0.277390i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4674 | + | 23.3263i | 0.809179 | + | 1.40154i | 0.913433 | + | 0.406988i | \(0.133421\pi\) |
−0.104255 | + | 0.994551i | \(0.533246\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.83645 | 0.349419 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.41000 | 0.501698 | 0.250849 | − | 0.968026i | \(-0.419290\pi\) | ||||
0.250849 | + | 0.968026i | \(0.419290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.84419 | + | 11.8545i | 0.406845 | + | 0.704676i | 0.994534 | − | 0.104410i | \(-0.0332955\pi\) |
−0.587689 | + | 0.809087i | \(0.699962\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.500000 | − | 0.866025i | 0.0296174 | − | 0.0512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.7901 | − | 5.41880i | −1.22720 | − | 0.319862i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.8116 | + | 34.3147i | −1.16539 | + | 2.01851i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000 | + | 6.92820i | 0.234484 | + | 0.406138i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.97237 | −0.348909 | −0.174455 | − | 0.984665i | \(-0.555816\pi\) | ||||
−0.174455 | + | 0.984665i | \(0.555816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.7160 | 0.856800 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.65581 | + | 4.59999i | 0.154106 | + | 0.266919i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.7762 | + | 20.3970i | −0.681037 | + | 1.17959i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0387 | − | 2.87716i | −0.636258 | − | 0.165837i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.237580 | − | 0.411500i | 0.0136486 | − | 0.0236401i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.9789 | −1.88221 | −0.941104 | − | 0.338119i | \(-0.890209\pi\) | ||||
−0.941104 | + | 0.338119i | \(0.890209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.7437 | 1.00940 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3856 | − | 17.9885i | −0.588916 | − | 1.02003i | −0.994375 | − | 0.105919i | \(-0.966222\pi\) |
0.405459 | − | 0.914113i | \(-0.367112\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.77344 | + | 3.07169i | −0.100241 | + | 0.173622i | −0.911784 | − | 0.410670i | \(-0.865295\pi\) |
0.811543 | + | 0.584293i | \(0.198628\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.702205 | + | 2.55086i | 0.0395648 | + | 0.143725i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.64199 | − | 6.30811i | 0.204554 | − | 0.354299i | −0.745436 | − | 0.666577i | \(-0.767759\pi\) |
0.949991 | + | 0.312278i | \(0.101092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.21323 | + | 12.4937i | 0.403863 | + | 0.699512i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.33366 | −0.353510 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.52484 | −0.418693 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.85801 | + | 4.95022i | 0.158534 | + | 0.274589i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.51382 | − | 11.2823i | 0.360215 | − | 0.623911i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.1342 | − | 20.4111i | 1.11004 | − | 1.12530i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0525 | + | 19.1434i | −0.607499 | + | 1.05222i | 0.384152 | + | 0.923270i | \(0.374494\pi\) |
−0.991651 | + | 0.128949i | \(0.958840\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.45360 | − | 4.24976i | −0.134457 | − | 0.232886i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.31161 | 0.235569 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −36.1701 | −1.97031 | −0.985156 | − | 0.171663i | \(-0.945086\pi\) | ||||
−0.985156 | + | 0.171663i | \(0.945086\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.80882 | + | 6.59707i | 0.206867 | + | 0.358304i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.5005 | + | 26.8476i | −0.839399 | + | 1.45388i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.3613 | + | 12.8248i | 0.721442 | + | 0.692475i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.06022 | − | 3.56840i | 0.110918 | − | 0.192116i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.21323 | − | 7.29752i | −0.226178 | − | 0.391752i | 0.730494 | − | 0.682919i | \(-0.239290\pi\) |
−0.956672 | + | 0.291167i | \(0.905956\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.6729 | −1.05307 | −0.526533 | − | 0.850155i | \(-0.676508\pi\) | ||||
−0.526533 | + | 0.850155i | \(0.676508\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.71602 | 0.305099 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.0740 | − | 27.8410i | −0.855534 | − | 1.48183i | −0.876148 | − | 0.482042i | \(-0.839895\pi\) |
0.0206139 | − | 0.999788i | \(-0.493438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16683 | − | 8.94921i | 0.274227 | − | 0.474975i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9812 | − | 14.1735i | 0.739965 | − | 0.750140i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.79005 | − | 8.29662i | 0.252809 | − | 0.437879i | −0.711489 | − | 0.702697i | \(-0.751979\pi\) |
0.964298 | + | 0.264819i | \(0.0853121\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.2132 | −0.903460 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.879569 | −0.0460387 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.6668 | − | 23.6716i | −0.713403 | − | 1.23565i | −0.963572 | − | 0.267448i | \(-0.913820\pi\) |
0.250170 | − | 0.968202i | \(-0.419514\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.06022 | − | 7.03250i | 0.211366 | − | 0.366097i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.22705 | + | 11.7227i | 0.167540 | + | 0.608614i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.1127 | + | 24.4439i | −0.730727 | + | 1.26566i | 0.225845 | + | 0.974163i | \(0.427486\pi\) |
−0.956573 | + | 0.291494i | \(0.905848\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.5248 | 0.799570 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.86409 | 0.506684 | 0.253342 | − | 0.967377i | \(-0.418470\pi\) | ||||
0.253342 | + | 0.967377i | \(0.418470\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.66683 | − | 2.88703i | −0.0853943 | − | 0.147907i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.48898 | − | 12.9713i | 0.382669 | − | 0.662802i | −0.608774 | − | 0.793344i | \(-0.708338\pi\) |
0.991443 | + | 0.130542i | \(0.0416717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.5989 | − | 3.54447i | −0.693063 | − | 0.180643i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.15581 | − | 3.73397i | 0.109586 | − | 0.189808i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.45081 | + | 4.24492i | 0.124261 | + | 0.215226i | 0.921444 | − | 0.388512i | \(-0.127011\pi\) |
−0.797183 | + | 0.603738i | \(0.793677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.0056 | −1.56802 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.40441 | 0.0708431 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.51382 | + | 6.08611i | 0.176799 | + | 0.306225i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.46742 | + | 2.54164i | −0.0736476 | + | 0.127561i | −0.900497 | − | 0.434861i | \(-0.856797\pi\) |
0.826850 | + | 0.562423i | \(0.190131\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.56022 | + | 0.667305i | 0.128171 | + | 0.0334070i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.72984 | + | 16.8526i | −0.485885 | + | 0.841577i | −0.999868 | − | 0.0162226i | \(-0.994836\pi\) |
0.513983 | + | 0.857800i | \(0.328169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.6806 | + | 28.8917i | 0.830922 | + | 1.43920i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.0652 | 1.29200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.7547 | + | 22.0918i | 0.630678 | + | 1.09237i | 0.987413 | + | 0.158161i | \(0.0505566\pi\) |
−0.356735 | + | 0.934206i | \(0.616110\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.79005 | − | 16.9569i | 0.482908 | − | 0.836421i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.3337 | + | 37.5386i | 0.508486 | + | 1.84715i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.35801 | − | 2.35214i | 0.0666621 | − | 0.115462i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.60661 | − | 6.24684i | −0.176617 | − | 0.305909i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.83087 | 0.480269 | 0.240135 | − | 0.970740i | \(-0.422808\pi\) | ||||
0.240135 | + | 0.970740i | \(0.422808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.26291 | 0.402710 | 0.201355 | − | 0.979518i | \(-0.435466\pi\) | ||||
0.201355 | + | 0.979518i | \(0.435466\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.41823 | + | 9.38464i | 0.263443 | + | 0.456297i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.76242 | + | 6.51670i | −0.182504 | + | 0.316107i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.1806 | + | 26.2937i | −0.732929 | + | 1.26947i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.12043 | + | 8.86885i | 0.246642 | + | 0.427197i | 0.962592 | − | 0.270955i | \(-0.0873393\pi\) |
−0.715950 | + | 0.698152i | \(0.754006\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.11484 | −0.101633 | −0.0508164 | − | 0.998708i | \(-0.516182\pi\) | ||||
−0.0508164 | + | 0.998708i | \(0.516182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.71602 | −0.130223 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.06022 | − | 3.56840i | −0.0985535 | − | 0.170700i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.50279 | − | 6.06702i | 0.167179 | − | 0.289563i | −0.770248 | − | 0.637745i | \(-0.779867\pi\) |
0.937427 | + | 0.348182i | \(0.113201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.01382 | + | 3.58246i | −0.286372 | + | 0.170593i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.71602 | + | 4.70429i | −0.129042 | + | 0.223507i | −0.923306 | − | 0.384066i | \(-0.874524\pi\) |
0.794264 | + | 0.607573i | \(0.207857\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.95360 | + | 3.38374i | 0.0926096 | + | 0.160405i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.8641 | 0.513854 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.21882 | 0.435063 | 0.217531 | − | 0.976053i | \(-0.430200\pi\) | ||||
0.217531 | + | 0.976053i | \(0.430200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.5663 | + | 37.3539i | 1.01552 | + | 1.75893i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.19118 | + | 3.79524i | −0.102951 | + | 0.178316i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.6204 | + | 10.7665i | −0.497893 | + | 0.504740i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3039 | − | 33.4353i | 0.902997 | − | 1.56404i | 0.0794135 | − | 0.996842i | \(-0.474695\pi\) |
0.823584 | − | 0.567195i | \(-0.191971\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.76242 | + | 6.51670i | 0.175615 | + | 0.304174i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2840 | −1.17759 | −0.588796 | − | 0.808282i | \(-0.700398\pi\) | ||||
−0.588796 | + | 0.808282i | \(0.700398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.57452 | 0.166122 | 0.0830611 | − | 0.996544i | \(-0.473530\pi\) | ||||
0.0830611 | + | 0.996544i | \(0.473530\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.91823 | − | 5.05452i | −0.135330 | − | 0.234398i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.0276 | − | 32.9568i | 0.880494 | − | 1.52506i | 0.0297012 | − | 0.999559i | \(-0.490544\pi\) |
0.850793 | − | 0.525501i | \(-0.176122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.02763 | + | 10.9983i | 0.139803 | + | 0.507856i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.53866 | − | 16.5214i | 0.439518 | − | 0.761268i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.4508 | + | 19.8334i | 0.526509 | + | 0.911940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.59559 | −0.210418 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.40441 | + | 16.2889i | 0.429698 | + | 0.744260i | 0.996846 | − | 0.0793565i | \(-0.0252865\pi\) |
−0.567148 | + | 0.823616i | \(0.691953\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.0248 | − | 24.2917i | 0.639478 | − | 1.10761i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.5492 | + | 2.74958i | 0.480005 | + | 0.125110i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.00000 | − | 6.92820i | 0.181631 | − | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.24860 | + | 14.2870i | 0.373780 | + | 0.647406i | 0.990144 | − | 0.140056i | \(-0.0447282\pi\) |
−0.616364 | + | 0.787462i | \(0.711395\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.81441 | 0.352659 | 0.176330 | − | 0.984331i | \(-0.443578\pi\) | ||||
0.176330 | + | 0.984331i | \(0.443578\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.2188 | + | 17.6995i | 0.460232 | + | 0.797146i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.65581 | − | 4.59999i | 0.119370 | − | 0.206754i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.4564 | + | 6.89570i | 1.18673 | + | 0.309315i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.5415 | − | 25.1865i | 0.650965 | − | 1.12750i | −0.331924 | − | 0.943306i | \(-0.607698\pi\) |
0.982889 | − | 0.184198i | \(-0.0589688\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.25140 | − | 7.36364i | −0.189938 | − | 0.328983i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.2409 | −1.34837 | −0.674187 | − | 0.738561i | \(-0.735506\pi\) | ||||
−0.674187 | + | 0.738561i | \(0.735506\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.475159 | −0.0211443 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.83645 | + | 17.0372i | 0.436852 | + | 0.756650i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.7160 | − | 20.2927i | 0.519304 | − | 0.899460i | −0.480445 | − | 0.877025i | \(-0.659525\pi\) |
0.999748 | − | 0.0224351i | \(-0.00714192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.617637 | − | 2.24366i | −0.0273227 | − | 0.0992537i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.500000 | + | 0.866025i | −0.0220755 | + | 0.0382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.87183 | − | 15.3665i | −0.390939 | − | 0.677127i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.5590 | −2.53144 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0773 | 0.925191 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.865752 | − | 1.49953i | −0.0379293 | − | 0.0656954i | 0.846438 | − | 0.532488i | \(-0.178743\pi\) |
−0.884367 | + | 0.466793i | \(0.845409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9923 | − | 32.8956i | 0.830474 | − | 1.43842i | −0.0671897 | − | 0.997740i | \(-0.521403\pi\) |
0.897663 | − | 0.440682i | \(-0.145263\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.85801 | − | 1.88356i | 0.0810902 | − | 0.0822053i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.9592 | + | 38.0344i | −0.956557 | + | 1.65681i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.01102 | + | 5.21525i | 0.130914 | + | 0.226750i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.7160 | −0.638621 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.4166 | 2.01052 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.16683 | + | 5.48511i | 0.136914 | + | 0.237142i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.82264 | + | 4.88895i | −0.121806 | + | 0.210974i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.507741 | − | 37.1778i | −0.0218699 | − | 1.60136i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.51382 | − | 7.81816i | 0.194064 | − | 0.336129i | −0.752529 | − | 0.658559i | \(-0.771166\pi\) |
0.946593 | + | 0.322430i | \(0.104500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6342 | + | 21.8832i | 0.542187 | + | 0.939096i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.0276 | −0.558043 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.8144 | 0.505148 | 0.252574 | − | 0.967578i | \(-0.418723\pi\) | ||||
0.252574 | + | 0.967578i | \(0.418723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.35801 | + | 2.35214i | −0.0578532 | + | 0.100205i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.0574 | + | 13.2370i | −0.555258 | + | 0.562893i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.45360 | + | 4.24976i | −0.104150 | + | 0.180392i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.77295 | + | 3.07085i | 0.0751225 | + | 0.130116i | 0.901140 | − | 0.433529i | \(-0.142732\pi\) |
−0.826017 | + | 0.563645i | \(0.809399\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.6453 | 1.04238 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.9690 | −1.68749 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.6729 | − | 25.4142i | −0.618389 | − | 1.07108i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) |
0.371390 | − | 0.928477i | \(-0.378881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.80882 | − | 6.59707i | 0.160238 | − | 0.277541i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.702205 | − | 2.55086i | −0.0294898 | − | 0.107126i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0602 | + | 24.3530i | −0.589435 | + | 1.02093i | 0.404872 | + | 0.914374i | \(0.367316\pi\) |
−0.994307 | + | 0.106558i | \(0.966017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.51382 | + | 13.0143i | 0.314443 | + | 0.544632i | 0.979319 | − | 0.202322i | \(-0.0648488\pi\) |
−0.664876 | + | 0.746954i | \(0.731515\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8641 | 0.537405 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.12043 | −0.171834 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3690 | + | 21.4238i | 0.514930 | + | 0.891884i | 0.999850 | + | 0.0173259i | \(0.00551529\pi\) |
−0.484920 | + | 0.874558i | \(0.661151\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.87183 | + | 17.0985i | −0.410259 | + | 0.710590i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.95360 | + | 1.81242i | 0.288484 | + | 0.0751917i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.2050 | − | 21.1397i | 0.505479 | − | 0.875516i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.85801 | − | 4.95022i | −0.118164 | − | 0.204666i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.9625 | −0.741391 | −0.370695 | − | 0.928755i | \(-0.620881\pi\) | ||||
−0.370695 | + | 0.928755i | \(0.620881\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.83645 | −0.240487 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.37183 | − | 16.2325i | −0.385505 | − | 0.667715i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.1668 | + | 17.6095i | −0.417502 | + | 0.723134i | −0.995687 | − | 0.0927710i | \(-0.970428\pi\) |
0.578186 | + | 0.815905i | \(0.303761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19.2652 | − | 5.02136i | −0.789797 | − | 0.205856i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.8365 | + | 20.5013i | −0.484434 | + | 0.839064i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.3613 | − | 24.8745i | −0.586787 | − | 1.01634i | −0.994650 | − | 0.103301i | \(-0.967059\pi\) |
0.407864 | − | 0.913043i | \(-0.366274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.0717 | 1.18586 | 0.592930 | − | 0.805254i | \(-0.297971\pi\) | ||||
0.592930 | + | 0.805254i | \(0.297971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.31161 | −0.175582 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.60661 | + | 14.9071i | 0.349909 | + | 0.606060i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.7873 | − | 22.1482i | 0.519019 | − | 0.898967i | −0.480737 | − | 0.876865i | \(-0.659631\pi\) |
0.999756 | − | 0.0221022i | \(-0.00703591\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.90720 | − | 6.92820i | −0.0772838 | − | 0.280745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.9707 | + | 53.6428i | −1.25294 | + | 2.17016i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.82264 | − | 10.0851i | −0.235174 | − | 0.407333i | 0.724149 | − | 0.689643i | \(-0.242233\pi\) |
−0.959323 | + | 0.282310i | \(0.908899\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.12043 | −0.327447 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.6232 | −1.47440 | −0.737198 | − | 0.675677i | \(-0.763851\pi\) | ||||
−0.737198 | + | 0.675677i | \(0.763851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.02484 | − | 12.1674i | −0.282352 | − | 0.489048i | 0.689611 | − | 0.724180i | \(-0.257781\pi\) |
−0.971964 | + | 0.235131i | \(0.924448\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.06022 | + | 3.56840i | −0.0826736 | + | 0.143195i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.25963 | + | 7.35945i | −0.290851 | + | 0.294850i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.65581 | − | 4.59999i | −0.106063 | − | 0.183706i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.9259 | 1.47233 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0553 | −0.798388 | −0.399194 | − | 0.916867i | \(-0.630710\pi\) | ||||
−0.399194 | + | 0.916867i | \(0.630710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.82264 | − | 8.35305i | −0.191683 | − | 0.332004i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.66683 | + | 2.88703i | −0.0661461 | + | 0.114568i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.9215 | − | 19.5310i | −1.38364 | − | 0.773847i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.16683 | + | 8.94921i | −0.204397 | + | 0.354025i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.93978 | + | 5.09186i | 0.116115 | + | 0.201116i | 0.918225 | − | 0.396060i | \(-0.129623\pi\) |
−0.802110 | + | 0.597176i | \(0.796289\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.35571 | 0.250645 | 0.125322 | − | 0.992116i | \(-0.460004\pi\) | ||||
0.125322 | + | 0.992116i | \(0.460004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.31161 | −0.169770 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.06022 | − | 5.30045i | −0.120309 | − | 0.208382i | 0.799580 | − | 0.600559i | \(-0.205055\pi\) |
−0.919890 | + | 0.392177i | \(0.871722\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.0829 | − | 67.6936i | 1.53414 | − | 2.65721i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.8442 | − | 10.9933i | 0.425017 | − | 0.430862i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.2514 | − | 35.0764i | 0.792498 | − | 1.37265i | −0.131917 | − | 0.991261i | \(-0.542113\pi\) |
0.924416 | − | 0.381387i | \(-0.124553\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.702205 | − | 1.21625i | −0.0274374 | − | 0.0475230i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.879569 | 0.0343152 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.7282 | −1.62550 | −0.812749 | − | 0.582613i | \(-0.802030\pi\) | ||||
−0.812749 | + | 0.582613i | \(0.802030\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.2298 | − | 17.7186i | −0.397895 | − | 0.689174i | 0.595571 | − | 0.803302i | \(-0.296926\pi\) |
−0.993466 | + | 0.114129i | \(0.963592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.5061 | + | 37.2496i | −0.835227 | + | 1.44666i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.702205 | − | 2.55086i | −0.0272303 | − | 0.0989183i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.59559 | + | 9.69185i | −0.216662 | + | 0.375270i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.28398 | − | 5.68802i | −0.126966 | − | 0.219911i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.30602 | 0.0503436 | 0.0251718 | − | 0.999683i | \(-0.491987\pi\) | ||||
0.0251718 | + | 0.999683i | \(0.491987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.628172 | + | 1.08803i | −0.0241426 | + | 0.0418162i | −0.877844 | − | 0.478946i | \(-0.841019\pi\) |
0.853702 | + | 0.520762i | \(0.174352\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.4817 | + | 5.33844i | 0.786016 | + | 0.204871i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.16683 | − | 3.75306i | 0.0830331 | − | 0.143818i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.28726 | − | 9.15780i | −0.202311 | − | 0.350414i | 0.746961 | − | 0.664867i | \(-0.231512\pi\) |
−0.949273 | + | 0.314454i | \(0.898179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5801 | −0.748118 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.16355 | 0.235154 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.1342 | − | 22.7492i | −0.500375 | − | 0.866675i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.25189 | + | 14.2927i | −0.313917 | + | 0.543719i | −0.979207 | − | 0.202866i | \(-0.934975\pi\) |
0.665290 | + | 0.746585i | \(0.268308\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.5989 | + | 3.54447i | 0.516578 | + | 0.134643i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.60661 | + | 6.24684i | −0.136807 | + | 0.236956i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.5525 | + | 52.9184i | 1.15726 | + | 2.00443i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.43204 | 0.129812 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9072 | 0.449729 | 0.224864 | − | 0.974390i | \(-0.427806\pi\) | ||||
0.224864 | + | 0.974390i | \(0.427806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45360 | + | 4.24976i | 0.0925393 | + | 0.160283i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.41823 | − | 9.38464i | 0.204062 | − | 0.353446i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.333659 | − | 1.21207i | −0.0125485 | − | 0.0455845i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.24086 | − | 7.34539i | 0.159269 | − | 0.275862i | −0.775336 | − | 0.631549i | \(-0.782420\pi\) |
0.934605 | + | 0.355687i | \(0.115753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.51382 | − | 6.08611i | −0.131778 | − | 0.228247i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.0487 | −0.900631 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.3613 | 1.13545 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.4320 | + | 24.9970i | 0.538975 | + | 0.933531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3337 | − | 23.0946i | 0.497262 | − | 0.861282i | −0.502733 | − | 0.864441i | \(-0.667672\pi\) |
0.999995 | + | 0.00315917i | \(0.00100560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.9679 | − | 33.4212i | 1.22779 | − | 1.24467i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.29780 | − | 14.3722i | 0.308598 | − | 0.534508i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.35801 | + | 2.35214i | 0.0504353 | + | 0.0873564i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.5689 | −0.688684 | −0.344342 | − | 0.938844i | \(-0.611898\pi\) | ||||
−0.344342 | + | 0.938844i | \(0.611898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.2221 | + | 28.0975i | 0.599996 | + | 1.03922i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.114355 | − | 0.198068i | 0.00422378 | − | 0.00731581i | −0.863906 | − | 0.503653i | \(-0.831989\pi\) |
0.868130 | + | 0.496338i | \(0.165322\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.10941 | + | 3.41689i | 0.225349 | + | 0.126034i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.4508 | − | 19.8334i | 0.421796 | − | 0.730572i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.4072 | + | 24.9540i | 0.529978 | + | 0.917948i | 0.999388 | + | 0.0349682i | \(0.0111330\pi\) |
−0.469411 | + | 0.882980i | \(0.655534\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.71602 | −0.209983 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.5581 | 1.19444 | 0.597220 | − | 0.802078i | \(-0.296272\pi\) | ||||
0.597220 | + | 0.802078i | \(0.296272\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.43204 | − | 9.40858i | −0.199015 | − | 0.344704i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.35801 | + | 2.35214i | −0.0496870 | + | 0.0860604i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.7680 | + | 11.9298i | −0.429994 | + | 0.435906i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4210 | − | 38.8343i | 0.818155 | − | 1.41709i | −0.0888857 | − | 0.996042i | \(-0.528331\pi\) |
0.907040 | − | 0.421044i | \(-0.138336\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.56301 | + | 9.63542i | 0.202727 | + | 0.351134i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.38236 | 0.159491 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.8641 | 1.04908 | 0.524542 | − | 0.851385i | \(-0.324237\pi\) | ||||
0.524542 | + | 0.851385i | \(0.324237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.9431 | − | 18.9539i | −0.397208 | − | 0.687985i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.39387 | − | 16.2707i | 0.340528 | − | 0.589811i | −0.644003 | − | 0.765023i | \(-0.722728\pi\) |
0.984531 | + | 0.175212i | \(0.0560610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.14807 | − | 33.2317i | −0.331182 | − | 1.20307i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.76242 | − | 6.51670i | 0.136031 | − | 0.235612i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.0586 | − | 72.8475i | −1.51865 | − | 2.63037i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.7226 | 1.21607 | 0.608034 | − | 0.793911i | \(-0.291959\pi\) | ||||
0.608034 | + | 0.793911i | \(0.291959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.0984 | −0.471727 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.87462 | − | 15.3713i | −0.319198 | − | 0.552867i | 0.661123 | − | 0.750278i | \(-0.270080\pi\) |
−0.980321 | + | 0.197410i | \(0.936747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.91823 | + | 5.05452i | −0.104826 | + | 0.181564i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.5635 | − | 3.27460i | −0.450713 | − | 0.117476i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.06022 | + | 7.03250i | −0.145472 | + | 0.251965i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.4442 | − | 47.5347i | −0.982031 | − | 1.70093i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.71602 | 0.0970627 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.0773 | −0.680899 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.5028 | − | 28.5837i | −0.588261 | − | 1.01890i | −0.994460 | − | 0.105113i | \(-0.966479\pi\) |
0.406199 | − | 0.913785i | \(-0.366854\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.71602 | + | 4.70429i | −0.0966929 | + | 0.167477i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.5028 | + | 5.08329i | 0.693440 | + | 0.180741i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.29780 | + | 3.97990i | 0.0814944 | + | 0.141152i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.0122 | −1.59441 | −0.797206 | − | 0.603707i | \(-0.793690\pi\) | ||||
−0.797206 | + | 0.603707i | \(0.793690\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −81.5426 | −2.88477 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.95360 | − | 3.38374i | −0.0690271 | − | 0.119558i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.33596 | + | 4.04601i | −0.0824344 | + | 0.142781i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.89339 | − | 10.5107i | −0.101978 | − | 0.370452i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.12043 | + | 5.40475i | −0.109844 | + | 0.190256i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.8503 | + | 22.2573i | 0.451791 | + | 0.782526i | 0.998497 | − | 0.0547989i | \(-0.0174518\pi\) |
−0.546706 | + | 0.837325i | \(0.684118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0332 | 0.598117 | 0.299059 | − | 0.954235i | \(-0.403327\pi\) | ||||
0.299059 | + | 0.954235i | \(0.403327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.8088 | 0.729797 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.15581 | + | 3.73397i | −0.0754221 | + | 0.130635i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.6204 | − | 10.7665i | 0.371108 | − | 0.376211i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.64199 | − | 16.7004i | 0.336508 | − | 0.582848i | −0.647266 | − | 0.762265i | \(-0.724088\pi\) |
0.983773 | + | 0.179416i | \(0.0574208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.68839 | + | 13.3167i | 0.268000 | + | 0.464190i | 0.968345 | − | 0.249614i | \(-0.0803038\pi\) |
−0.700345 | + | 0.713805i | \(0.746971\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.31161 | −0.184927 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.43204 | −0.119344 | −0.0596719 | − | 0.998218i | \(-0.519005\pi\) | ||||
−0.0596719 | + | 0.998218i | \(0.519005\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.18016 | + | 5.50820i | 0.110451 | + | 0.191308i | 0.915952 | − | 0.401287i | \(-0.131437\pi\) |
−0.805501 | + | 0.592595i | \(0.798104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4674 | + | 23.3263i | −0.467180 | + | 0.809179i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.719305 | − | 52.6690i | −0.0249224 | − | 1.82487i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.25140 | + | 7.36364i | −0.147126 | + | 0.254829i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.91823 | + | 5.05452i | 0.100869 | + | 0.174710i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5304 | 0.777837 | 0.388918 | − | 0.921272i | \(-0.372849\pi\) | ||||
0.388918 | + | 0.921272i | \(0.372849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.6232 | −0.745628 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.20500 | + | 7.28327i | 0.144828 | + | 0.250849i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.83645 | − | 17.0372i | 0.338384 | − | 0.586099i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.9824 | + | 32.4221i | −1.09893 | + | 1.11404i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.84419 | + | 11.8545i | −0.234892 | + | 0.406845i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1099 | + | 17.5109i | 0.346563 | + | 0.600264i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.7216 | −1.59972 | −0.799859 | − | 0.600188i | \(-0.795092\pi\) | ||||
−0.799859 | + | 0.600188i | \(0.795092\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.54919 | − | 2.68328i | −0.0529194 | − | 0.0916591i | 0.838352 | − | 0.545129i | \(-0.183519\pi\) |
−0.891272 | + | 0.453470i | \(0.850186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.55247 | − | 14.8133i | 0.291807 | − | 0.505424i | −0.682430 | − | 0.730951i | \(-0.739077\pi\) |
0.974237 | + | 0.225527i | \(0.0724103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.70220 | − | 20.7141i | −0.194331 | − | 0.705935i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.7795 | + | 30.7950i | −0.605222 | + | 1.04828i | 0.386794 | + | 0.922166i | \(0.373582\pi\) |
−0.992016 | + | 0.126109i | \(0.959751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.5387 | − | 18.2535i | −0.358325 | − | 0.620637i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.6232 | −1.34568 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.3281 | 1.26627 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.3226 | − | 21.3434i | −0.417537 | − | 0.723195i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | + | 6.92820i | −0.135379 | + | 0.234484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.56022 | − | 0.667305i | −0.0865511 | − | 0.0225590i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.2270 | − | 41.9625i | 0.818089 | − | 1.41697i | −0.0889991 | − | 0.996032i | \(-0.528367\pi\) |
0.907088 | − | 0.420940i | \(-0.138300\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.98618 | − | 5.17222i | −0.100721 | − | 0.174455i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −49.3182 | −1.66157 | −0.830786 | − | 0.556592i | \(-0.812109\pi\) | ||||
−0.830786 | + | 0.556592i | \(0.812109\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7437 | −1.60670 | −0.803351 | − | 0.595506i | \(-0.796952\pi\) | ||||
−0.803351 | + | 0.595506i | \(0.796952\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.35801 | + | 12.7444i | 0.247337 | + | 0.428400i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.97565 | − | 15.5463i | 0.301373 | − | 0.521993i | −0.675074 | − | 0.737750i | \(-0.735888\pi\) |
0.976447 | + | 0.215757i | \(0.0692218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.53489 | − | 2.22457i | −0.286251 | − | 0.0746096i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.65581 | + | 4.59999i | −0.0889729 | + | 0.154106i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.41823 | − | 9.38464i | −0.181314 | − | 0.314045i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.64527 | 0.188701 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.5525 | −0.786394 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.92597 | + | 13.7282i | 0.264346 | + | 0.457860i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.2905 | − | 29.9481i | 0.576032 | − | 0.997716i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.02763 | − | 10.9983i | −0.100753 | − | 0.366002i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.6342 | − | 21.8832i | 0.419977 | − | 0.727421i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.0630 | + | 39.9463i | 0.765795 | + | 1.32640i | 0.939825 | + | 0.341655i | \(0.110987\pi\) |
−0.174031 | + | 0.984740i | \(0.555679\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.475159 | 0.0157600 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.71043 | −0.321721 | −0.160861 | − | 0.986977i | \(-0.551427\pi\) | ||||
−0.160861 | + | 0.986977i | \(0.551427\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.21323 | − | 12.4937i | −0.238723 | − | 0.413480i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.60941 | − | 2.64529i | 0.0861702 | − | 0.0873551i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.01661 | + | 8.68903i | −0.165483 | + | 0.286624i | −0.936827 | − | 0.349794i | \(-0.886252\pi\) |
0.771344 | + | 0.636419i | \(0.219585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.4895 | − | 28.5606i | −0.543346 | − | 0.941104i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −59.0674 | −1.94423 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.90720 | 0.161348 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.87183 | + | 15.3665i | 0.291389 | + | 0.504701i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.20828 | + | 14.2172i | −0.269305 | + | 0.466450i | −0.968683 | − | 0.248303i | \(-0.920127\pi\) |
0.699378 | + | 0.714752i | \(0.253461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.01382 | − | 3.58246i | 0.197095 | − | 0.117410i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3856 | − | 17.9885i | 0.340011 | − | 0.588916i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.9845 | + | 34.6142i | 0.653564 | + | 1.13201i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.0895 | 1.47301 | 0.736504 | − | 0.676433i | \(-0.236475\pi\) | ||||
0.736504 | + | 0.676433i | \(0.236475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.54689 | −0.115748 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.14478 | + | 12.3751i | 0.232913 | + | 0.403418i | 0.958664 | − | 0.284540i | \(-0.0918408\pi\) |
−0.725751 | + | 0.687958i | \(0.758508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.7298 | + | 28.9769i | −0.544799 | + | 0.943619i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.85801 | + | 1.88356i | −0.0604411 | + | 0.0612722i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.1513 | − | 36.6352i | 0.687326 | − | 1.19048i | −0.285373 | − | 0.958416i | \(-0.592118\pi\) |
0.972700 | − | 0.232068i | \(-0.0745491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.51382 | + | 4.35406i | 0.0816020 | + | 0.141339i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.28398 | 0.236199 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.0609 | 1.58924 | 0.794619 | − | 0.607109i | \(-0.207671\pi\) | ||||
0.794619 | + | 0.607109i | \(0.207671\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.43204 | − | 11.1406i | −0.208136 | − | 0.360502i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.21323 | + | 12.4937i | −0.233171 | + | 0.403863i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.7492 | − | 49.9462i | −0.443986 | − | 1.61285i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.53209 | + | 2.65366i | −0.0494223 | + | 0.0856020i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.16683 | − | 5.48511i | −0.102050 | − | 0.176755i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.7437 | 0.635571 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.9292 | 0.833828 | 0.416914 | − | 0.908946i | \(-0.363112\pi\) | ||||
0.416914 | + | 0.908946i | \(0.363112\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.76242 | − | 6.51670i | −0.120866 | − | 0.209347i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.2767 | + | 48.9767i | −0.907443 | + | 1.57174i | −0.0898399 | + | 0.995956i | \(0.528636\pi\) |
−0.817603 | + | 0.575782i | \(0.804698\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.4674 | − | 4.81342i | −0.592038 | − | 0.154311i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.85801 | + | 4.95022i | −0.0915296 | + | 0.158534i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.1945 | − | 21.1214i | −0.390135 | − | 0.675734i | 0.602332 | − | 0.798246i | \(-0.294238\pi\) |
−0.992467 | + | 0.122512i | \(0.960905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.7535 | 0.663286 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.0276 | 0.415940 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.06022 | − | 10.4966i | −0.193291 | − | 0.334790i | 0.753048 | − | 0.657966i | \(-0.228583\pi\) |
−0.946339 | + | 0.323176i | \(0.895249\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.37183 | + | 16.2325i | −0.298611 | + | 0.517210i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.7437 | + | 7.23122i | 0.883090 | + | 0.230172i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.88285 | + | 15.3856i | −0.282458 | + | 0.489232i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.24532 | + | 2.15696i | 0.0395589 | + | 0.0685180i | 0.885127 | − | 0.465350i | \(-0.154071\pi\) |
−0.845568 | + | 0.533868i | \(0.820738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22.1049 | −0.701479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.6729 | 0.750482 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.9646 | + | 34.5797i | 0.632286 | + | 1.09515i | 0.987083 | + | 0.160208i | \(0.0512166\pi\) |
−0.354797 | + | 0.934943i | \(0.615450\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.45360 | − | 4.24976i | 0.0776285 | − | 0.134457i |
(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 | 1680.2.bg.v.961.3 | 6 | ||
4.3 | odd | 2 | 840.2.bg.j.121.1 | ✓ | 6 | ||
7.4 | even | 3 | inner | 1680.2.bg.v.1201.3 | 6 | ||
12.11 | even | 2 | 2520.2.bi.n.1801.1 | 6 | |||
28.11 | odd | 6 | 840.2.bg.j.361.1 | yes | 6 | ||
28.19 | even | 6 | 5880.2.a.bu.1.1 | 3 | |||
28.23 | odd | 6 | 5880.2.a.bv.1.1 | 3 | |||
84.11 | even | 6 | 2520.2.bi.n.361.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.bg.j.121.1 | ✓ | 6 | 4.3 | odd | 2 | ||
840.2.bg.j.361.1 | yes | 6 | 28.11 | odd | 6 | ||
1680.2.bg.v.961.3 | 6 | 1.1 | even | 1 | trivial | ||
1680.2.bg.v.1201.3 | 6 | 7.4 | even | 3 | inner | ||
2520.2.bi.n.361.1 | 6 | 84.11 | even | 6 | |||
2520.2.bi.n.1801.1 | 6 | 12.11 | even | 2 | |||
5880.2.a.bu.1.1 | 3 | 28.19 | even | 6 | |||
5880.2.a.bv.1.1 | 3 | 28.23 | odd | 6 |