Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [416,2,Mod(15,416)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(416, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("416.15");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 416 = 2^{5} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 416.bk (of order \(12\), degree \(4\), 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: | \(3.32177672409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 104) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 15.2 | ||
Character | \(\chi\) | \(=\) | 416.15 |
Dual form | 416.2.bk.a.111.2 |
$q$-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 \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(287\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.49630 | − | 2.59167i | −0.863890 | − | 1.49630i | −0.868145 | − | 0.496311i | \(-0.834688\pi\) |
0.00425488 | − | 0.999991i | \(-0.498646\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.40823 | + | 1.40823i | 0.629781 | + | 0.629781i | 0.948013 | − | 0.318232i | \(-0.103089\pi\) |
−0.318232 | + | 0.948013i | \(0.603089\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02175 | + | 3.81323i | 0.386186 | + | 1.44126i | 0.836290 | + | 0.548288i | \(0.184720\pi\) |
−0.450104 | + | 0.892976i | \(0.648613\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97784 | + | 5.15776i | −0.992612 | + | 1.71925i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.756644 | + | 2.82384i | −0.228137 | + | 0.851418i | 0.752987 | + | 0.658036i | \(0.228612\pi\) |
−0.981123 | + | 0.193382i | \(0.938054\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.47643 | + | 2.62055i | −0.686837 | + | 0.726811i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.54254 | − | 5.75682i | 0.398281 | − | 1.48640i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.373696 | + | 0.215754i | 0.0906347 | + | 0.0523280i | 0.544632 | − | 0.838675i | \(-0.316669\pi\) |
−0.453998 | + | 0.891003i | \(0.650003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.960219 | + | 3.58359i | 0.220289 | + | 0.822131i | 0.984237 | + | 0.176853i | \(0.0565918\pi\) |
−0.763948 | + | 0.645278i | \(0.776742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.35378 | − | 8.35378i | 1.82294 | − | 1.82294i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.264259 | − | 0.457711i | −0.0551019 | − | 0.0954393i | 0.837159 | − | 0.546960i | \(-0.184215\pi\) |
−0.892261 | + | 0.451521i | \(0.850882\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.03375i | − | 0.206751i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.84516 | 1.70225 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.96425 | − | 1.13406i | 0.364752 | − | 0.210590i | −0.306411 | − | 0.951899i | \(-0.599128\pi\) |
0.671163 | + | 0.741310i | \(0.265795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.525538 | + | 0.525538i | 0.0943894 | + | 0.0943894i | 0.752725 | − | 0.658335i | \(-0.228739\pi\) |
−0.658335 | + | 0.752725i | \(0.728739\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.45062 | − | 2.26434i | 1.47106 | − | 0.394170i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.93105 | + | 6.80878i | −0.664469 | + | 1.15089i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.50702 | + | 1.20765i | 0.740950 | + | 0.198537i | 0.609500 | − | 0.792786i | \(-0.291370\pi\) |
0.131450 | + | 0.991323i | \(0.458037\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.4971 | + | 2.49694i | 1.68088 | + | 0.399831i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.02295 | − | 0.274098i | −0.159757 | − | 0.0428069i | 0.178054 | − | 0.984021i | \(-0.443020\pi\) |
−0.337811 | + | 0.941214i | \(0.609687\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.78795 | − | 3.34168i | −0.882654 | − | 0.509601i | −0.0111217 | − | 0.999938i | \(-0.503540\pi\) |
−0.871533 | + | 0.490337i | \(0.836874\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.4568 | + | 3.06985i | −1.70788 | + | 0.457626i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.10880 | − | 3.10880i | 0.453465 | − | 0.453465i | −0.443038 | − | 0.896503i | \(-0.646099\pi\) |
0.896503 | + | 0.443038i | \(0.146099\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.43454 | + | 4.29233i | −1.06208 | + | 0.613191i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.29133i | − | 0.180822i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.89363i | 0.809552i | 0.914416 | + | 0.404776i | \(0.132650\pi\) | ||||
−0.914416 | + | 0.404776i | \(0.867350\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.04215 | + | 2.91109i | −0.679884 | + | 0.392531i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.85070 | − | 7.85070i | 1.03985 | − | 1.03985i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.50874 | − | 1.47606i | 0.717176 | − | 0.192167i | 0.118265 | − | 0.992982i | \(-0.462267\pi\) |
0.598911 | + | 0.800815i | \(0.295600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.67379 | − | 2.69841i | −0.598417 | − | 0.345496i | 0.170002 | − | 0.985444i | \(-0.445623\pi\) |
−0.768419 | + | 0.639948i | \(0.778956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −22.7103 | − | 6.08522i | −2.86123 | − | 0.766665i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.17774 | + | 0.202965i | −0.890290 | + | 0.0251747i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.76688 | − | 0.473433i | −0.215858 | − | 0.0578391i | 0.149269 | − | 0.988797i | \(-0.452308\pi\) |
−0.365127 | + | 0.930958i | \(0.618975\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.790823 | + | 1.36975i | −0.0952040 | + | 0.164898i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.80671 | − | 1.28795i | 0.570452 | − | 0.152852i | 0.0379481 | − | 0.999280i | \(-0.487918\pi\) |
0.532504 | + | 0.846428i | \(0.321251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.61849 | − | 8.61849i | −1.00872 | − | 1.00872i | −0.999962 | − | 0.00875645i | \(-0.997213\pi\) |
−0.00875645 | − | 0.999962i | \(-0.502787\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.67915 | + | 1.54681i | −0.309361 | + | 0.178610i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.5410 | −1.31522 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.5395i | 1.97334i | 0.162727 | + | 0.986671i | \(0.447971\pi\) | ||||
−0.162727 | + | 0.986671i | \(0.552029\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.30151 | − | 7.45044i | −0.477946 | − | 0.827827i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.64657 | − | 9.64657i | 1.05885 | − | 1.05885i | 0.0606926 | − | 0.998157i | \(-0.480669\pi\) |
0.998157 | − | 0.0606926i | \(-0.0193309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.222420 | + | 0.830084i | 0.0241249 | + | 0.0900352i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.87822 | − | 3.39379i | −0.630211 | − | 0.363853i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.41190 | + | 9.00133i | −0.255661 | + | 0.954139i | 0.712061 | + | 0.702118i | \(0.247762\pi\) |
−0.967722 | + | 0.252022i | \(0.918905\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5231 | − | 6.76562i | −1.31277 | − | 0.709230i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.575658 | − | 2.14838i | 0.0596929 | − | 0.222777i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.69432 | + | 6.39874i | −0.379029 | + | 0.656497i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.871452 | + | 3.25230i | 0.0884825 | + | 0.330221i | 0.995951 | − | 0.0898992i | \(-0.0286545\pi\) |
−0.907468 | + | 0.420120i | \(0.861988\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.3115 | − | 12.3115i | −1.23735 | − | 1.23735i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.895975 | + | 1.55187i | 0.0891529 | + | 0.154417i | 0.907153 | − | 0.420800i | \(-0.138251\pi\) |
−0.818000 | + | 0.575218i | \(0.804917\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.26322 | 0.617133 | 0.308567 | − | 0.951203i | \(-0.400151\pi\) | ||||
0.308567 | + | 0.951203i | \(0.400151\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23.5282 | 2.29611 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.81015 | + | 6.59937i | 0.368341 | + | 0.637985i | 0.989306 | − | 0.145853i | \(-0.0465926\pi\) |
−0.620965 | + | 0.783838i | \(0.713259\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4705 | + | 12.4705i | 1.19445 | + | 1.19445i | 0.975803 | + | 0.218650i | \(0.0701653\pi\) |
0.218650 | + | 0.975803i | \(0.429835\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.61403 | − | 13.4877i | −0.343028 | − | 1.28020i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.82301 | − | 10.0857i | 0.547783 | − | 0.948787i | −0.450643 | − | 0.892704i | \(-0.648805\pi\) |
0.998426 | − | 0.0560833i | \(-0.0178612\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.272425 | − | 1.01670i | 0.0254037 | − | 0.0948080i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.14181 | − | 20.5764i | −0.567810 | − | 1.90229i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.440893 | + | 1.64544i | −0.0404166 | + | 0.150837i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.12474 | + | 1.22672i | 0.193159 | + | 0.111520i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.820266 | + | 3.06127i | 0.0739609 | + | 0.276026i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.49694 | − | 8.49694i | 0.759989 | − | 0.759989i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.77681 | − | 16.9339i | −0.867552 | − | 1.50264i | −0.864491 | − | 0.502648i | \(-0.832359\pi\) |
−0.00306091 | − | 0.999995i | \(-0.500974\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.0006i | 1.76096i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.1468 | 1.41075 | 0.705375 | − | 0.708834i | \(-0.250778\pi\) | ||||
0.705375 | + | 0.708834i | \(0.250778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.6839 | + | 7.32306i | −1.09984 | + | 0.634990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.4561 | + | 12.4561i | 1.07205 | + | 1.07205i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8147 | + | 3.43369i | −1.09483 | + | 0.293360i | −0.760660 | − | 0.649151i | \(-0.775124\pi\) |
−0.334175 | + | 0.942511i | \(0.608458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.07441 | − | 10.5212i | 0.515225 | − | 0.892396i | −0.484619 | − | 0.874725i | \(-0.661042\pi\) |
0.999844 | − | 0.0176705i | \(-0.00562500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.7087 | − | 3.40528i | −1.07026 | − | 0.286776i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.52624 | − | 8.97585i | −0.462127 | − | 0.750598i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.36315 | + | 1.16910i | 0.362340 | + | 0.0970886i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 22.2486 | + | 12.8453i | 1.83504 | + | 1.05946i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.0487 | − | 2.96049i | 0.905146 | − | 0.242533i | 0.223921 | − | 0.974607i | \(-0.428114\pi\) |
0.681225 | + | 0.732074i | \(0.261448\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.47584 | + | 4.47584i | −0.364239 | + | 0.364239i | −0.865371 | − | 0.501132i | \(-0.832917\pi\) |
0.501132 | + | 0.865371i | \(0.332917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.22561 | + | 1.28496i | −0.179930 | + | 0.103883i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.48016i | 0.118889i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.29073i | 0.182820i | 0.995813 | + | 0.0914101i | \(0.0291374\pi\) | ||||
−0.995813 | + | 0.0914101i | \(0.970863\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.2743 | − | 8.81864i | 1.21133 | − | 0.699364i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.47535 | − | 1.47535i | 0.116274 | − | 0.116274i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.8514 | + | 5.05123i | −1.47656 | + | 0.395643i | −0.905175 | − | 0.425040i | \(-0.860260\pi\) |
−0.571385 | + | 0.820682i | \(0.693594\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.0892 | + | 8.71173i | 1.17469 | + | 0.678208i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.6986 | + | 5.27823i | 1.52433 | + | 0.408442i | 0.921163 | − | 0.389177i | \(-0.127240\pi\) |
0.603162 | + | 0.797618i | \(0.293907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.734614 | − | 12.9792i | −0.0565087 | − | 0.998402i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.3427 | − | 5.71875i | −1.63211 | − | 0.437324i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5483 | − | 20.0022i | 0.877999 | − | 1.52074i | 0.0244651 | − | 0.999701i | \(-0.492212\pi\) |
0.853534 | − | 0.521038i | \(-0.174455\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.94194 | − | 1.05624i | 0.297982 | − | 0.0798441i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0682 | − | 12.0682i | −0.907101 | − | 0.907101i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.55591 | + | 4.93976i | −0.639499 | + | 0.369215i | −0.784421 | − | 0.620228i | \(-0.787040\pi\) |
0.144923 | + | 0.989443i | \(0.453707\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.6104 | −1.08598 | −0.542991 | − | 0.839738i | \(-0.682708\pi\) | ||||
−0.542991 | + | 0.839738i | \(0.682708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.1505i | 1.19388i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.64629 | + | 8.04760i | 0.341602 | + | 0.591672i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.892008 | + | 0.892008i | −0.0652301 | + | 0.0652301i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.03755 | + | 33.7286i | 0.657385 | + | 2.45339i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.51822 | − | 5.49535i | −0.688714 | − | 0.397629i | 0.114416 | − | 0.993433i | \(-0.463500\pi\) |
−0.803130 | + | 0.595804i | \(0.796834\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.07308 | + | 4.00480i | −0.0772422 | + | 0.288272i | −0.993732 | − | 0.111785i | \(-0.964343\pi\) |
0.916490 | + | 0.400057i | \(0.131010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.2661 | + | 18.2986i | 0.806781 | + | 1.31039i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.39832 | + | 12.6827i | −0.242120 | + | 0.903606i | 0.732688 | + | 0.680564i | \(0.238265\pi\) |
−0.974809 | + | 0.223042i | \(0.928401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.83125 | + | 11.8321i | −0.484255 | + | 0.838754i | −0.999836 | − | 0.0180866i | \(-0.994243\pi\) |
0.515582 | + | 0.856840i | \(0.327576\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.41680 | + | 5.28756i | 0.0999332 | + | 0.372956i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.33140 | + | 6.33140i | 0.444377 | + | 0.444377i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.05455 | − | 1.82654i | −0.0736533 | − | 0.127571i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.14769 | 0.218779 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.8460 | −0.750234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.28662 | − | 7.42464i | −0.295103 | − | 0.511133i | 0.679906 | − | 0.733299i | \(-0.262021\pi\) |
−0.975009 | + | 0.222166i | \(0.928687\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.5302 | − | 10.5302i | −0.721521 | − | 0.721521i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.44493 | − | 12.8567i | −0.234942 | − | 0.876816i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.46703 | + | 2.54096i | −0.0995882 | + | 0.172492i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.44043 | + | 35.2322i | −0.637925 | + | 2.38077i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.49083 | + | 0.444993i | −0.100284 | + | 0.0299335i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.481305 | − | 1.79626i | 0.0322306 | − | 0.120286i | −0.947936 | − | 0.318460i | \(-0.896834\pi\) |
0.980167 | + | 0.198174i | \(0.0635010\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.33186 | + | 3.07835i | 0.355457 | + | 0.205223i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.15967 | − | 19.2561i | −0.342459 | − | 1.27808i | −0.895552 | − | 0.444956i | \(-0.853219\pi\) |
0.553093 | − | 0.833119i | \(-0.313447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.88318 | + | 5.88318i | −0.388772 | + | 0.388772i | −0.874249 | − | 0.485478i | \(-0.838646\pi\) |
0.485478 | + | 0.874249i | \(0.338646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.2689 | + | 29.9105i | 1.13621 | + | 1.96797i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.9520i | − | 0.979537i | −0.871853 | − | 0.489768i | \(-0.837081\pi\) | ||
0.871853 | − | 0.489768i | \(-0.162919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.75583 | 0.571167 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 45.4565 | − | 26.2443i | 2.95272 | − | 1.70475i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.11437 | − | 2.11437i | −0.136767 | − | 0.136767i | 0.635409 | − | 0.772176i | \(-0.280832\pi\) |
−0.772176 | + | 0.635409i | \(0.780832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8151 | − | 3.70175i | 0.889911 | − | 0.238451i | 0.215233 | − | 0.976563i | \(-0.430949\pi\) |
0.674678 | + | 0.738112i | \(0.264282\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.395012 | − | 0.684181i | 0.0253400 | − | 0.0438902i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.5142 | − | 4.42496i | −1.05505 | − | 0.282701i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.7689 | − | 6.35819i | −0.748837 | − | 0.404562i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −39.4349 | − | 10.5666i | −2.49909 | − | 0.669628i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.77498 | − | 2.75684i | −0.301394 | − | 0.174010i | 0.341675 | − | 0.939818i | \(-0.389006\pi\) |
−0.643069 | + | 0.765808i | \(0.722339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.49245 | − | 0.399901i | 0.0938295 | − | 0.0251415i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.81850 | − | 1.81850i | 0.113879 | − | 0.113879i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.7355 | − | 14.2811i | 1.54296 | − | 0.890828i | 0.544310 | − | 0.838884i | \(-0.316792\pi\) |
0.998650 | − | 0.0519442i | \(-0.0165418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.4202i | 1.14458i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.5082i | 0.836136i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.3279 | − | 12.8910i | 1.37680 | − | 0.794896i | 0.385027 | − | 0.922905i | \(-0.374192\pi\) |
0.991773 | + | 0.128009i | \(0.0408588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.29960 | + | 8.29960i | −0.509841 | + | 0.509841i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.9374 | − | 7.21786i | 1.64854 | − | 0.441726i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1981 | + | 7.61995i | 0.804704 | + | 0.464596i | 0.845113 | − | 0.534587i | \(-0.179533\pi\) |
−0.0404091 | + | 0.999183i | \(0.512866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.30836 | − | 0.618524i | −0.140223 | − | 0.0375727i | 0.188025 | − | 0.982164i | \(-0.439791\pi\) |
−0.328248 | + | 0.944592i | \(0.606458\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.20401 | + | 42.5791i | 0.0728698 | + | 2.57700i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.91915 | + | 0.782184i | 0.176031 | + | 0.0471675i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.66247 | + | 16.7359i | −0.580561 | + | 1.00556i | 0.414852 | + | 0.909889i | \(0.363834\pi\) |
−0.995413 | + | 0.0956726i | \(0.969500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.27557 | + | 1.14563i | −0.255971 | + | 0.0685873i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.9119 | + | 21.9119i | 1.30715 | + | 1.30715i | 0.923462 | + | 0.383691i | \(0.125347\pi\) |
0.383691 | + | 0.923462i | \(0.374653\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.50892 | − | 5.48998i | 0.565247 | − | 0.326345i | −0.190002 | − | 0.981784i | \(-0.560849\pi\) |
0.755249 | + | 0.655438i | \(0.227516\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 22.1112 | 1.30976 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.18079i | − | 0.246784i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.40690 | − | 14.5612i | −0.494524 | − | 0.856540i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.12494 | − | 7.12494i | 0.417671 | − | 0.417671i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.28916 | − | 4.81120i | −0.0753133 | − | 0.281073i | 0.917991 | − | 0.396601i | \(-0.129811\pi\) |
−0.993304 | + | 0.115528i | \(0.963144\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.83623 | + | 5.67895i | 0.572687 | + | 0.330641i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.69264 | + | 24.9773i | −0.388346 | + | 1.44933i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.85388 | + | 0.440981i | 0.107212 | + | 0.0255026i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.82872 | − | 25.4851i | 0.393601 | − | 1.46894i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.68130 | − | 4.64414i | 0.154037 | − | 0.266799i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.78179 | − | 10.3818i | −0.159285 | − | 0.594459i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.32161 | − | 9.32161i | −0.532013 | − | 0.532013i | 0.389158 | − | 0.921171i | \(-0.372766\pi\) |
−0.921171 | + | 0.389158i | \(0.872766\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.37166 | − | 16.2322i | −0.533135 | − | 0.923418i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.84329 | −0.444752 | −0.222376 | − | 0.974961i | \(-0.571381\pi\) | ||||
−0.222376 | + | 0.974961i | \(0.571381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5938 | 0.994462 | 0.497231 | − | 0.867618i | \(-0.334350\pi\) | ||||
0.497231 | + | 0.867618i | \(0.334350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.4121 | − | 40.5509i | −1.31912 | − | 2.28478i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.7327 | − | 14.7327i | −0.827472 | − | 0.827472i | 0.159695 | − | 0.987166i | \(-0.448949\pi\) |
−0.987166 | + | 0.159695i | \(0.948949\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.71616 | + | 6.40480i | 0.0960865 | + | 0.358600i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.4023 | − | 19.7493i | 0.636412 | − | 1.10230i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.414342 | + | 1.54634i | −0.0230546 | + | 0.0860409i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.70901 | + | 2.56002i | 0.150269 | + | 0.142004i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.6598 | − | 50.9789i | 0.755386 | − | 2.81914i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0310 | + | 8.67813i | 0.828684 | + | 0.478441i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.45117 | + | 9.14790i | 0.134729 | + | 0.502814i | 0.999999 | + | 0.00150826i | \(0.000480094\pi\) |
−0.865270 | + | 0.501306i | \(0.832853\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.6500 | + | 19.6500i | −1.07681 | + | 1.07681i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.82147 | − | 3.15488i | −0.0995176 | − | 0.172370i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.1551i | 1.15239i | 0.817312 | + | 0.576196i | \(0.195463\pi\) | ||||
−0.817312 | + | 0.576196i | \(0.804537\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −34.8519 | −1.89290 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.88168 | + | 1.08639i | −0.101899 | + | 0.0588311i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.42357 | − | 4.42357i | −0.238850 | − | 0.238850i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.04259 | + | 0.815259i | −0.163807 | + | 0.0438921i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.19610 | − | 14.1961i | 0.439990 | − | 0.762085i | −0.557698 | − | 0.830044i | \(-0.688315\pi\) |
0.997688 | + | 0.0679589i | \(0.0216487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.13248 | − | 1.37525i | −0.274736 | − | 0.0736152i | 0.118821 | − | 0.992916i | \(-0.462089\pi\) |
−0.393556 | + | 0.919301i | \(0.628755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.9044 | + | 23.1792i | −1.16917 | + | 1.23722i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.04366 | + | 1.61939i | 0.321671 | + | 0.0861916i | 0.416042 | − | 0.909346i | \(-0.363417\pi\) |
−0.0943702 | + | 0.995537i | \(0.530084\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.58272 | + | 4.95524i | 0.455523 | + | 0.262997i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.92414 | − | 1.31942i | 0.260613 | − | 0.0698310i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.28036 | + | 9.28036i | −0.489799 | + | 0.489799i | −0.908243 | − | 0.418444i | \(-0.862576\pi\) |
0.418444 | + | 0.908243i | \(0.362576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.53441 | − | 2.61794i | 0.238653 | − | 0.137787i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.34218i | − | 0.385365i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 24.2737i | − | 1.27054i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.4767 | + | 12.3996i | −1.12107 | + | 0.647252i | −0.941675 | − | 0.336524i | \(-0.890749\pi\) |
−0.179399 | + | 0.983776i | \(0.557415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.45990 | − | 4.45990i | 0.232173 | − | 0.232173i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.4737 | + | 6.02182i | −1.16678 | + | 0.312637i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91414 | + | 1.10513i | 0.0991107 | + | 0.0572216i | 0.548736 | − | 0.835996i | \(-0.315109\pi\) |
−0.449625 | + | 0.893217i | \(0.648443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −34.7352 | − | 9.30728i | −1.79372 | − | 0.480626i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.89246 | + | 7.95584i | −0.0974664 | + | 0.409747i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.5125 | + | 3.08477i | 0.591358 | + | 0.158454i | 0.542074 | − | 0.840331i | \(-0.317639\pi\) |
0.0492842 | + | 0.998785i | \(0.484306\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.2581 | + | 50.6765i | −1.49894 | + | 2.59624i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.5153 | + | 6.30090i | −1.20158 | + | 0.321961i | −0.803451 | − | 0.595370i | \(-0.797005\pi\) |
−0.398124 | + | 0.917332i | \(0.630339\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.2525 | − | 16.2525i | −0.828302 | − | 0.828302i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.4712 | − | 19.9019i | 1.75227 | − | 1.01167i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.5350 | −1.04117 | −0.520584 | − | 0.853811i | \(-0.674286\pi\) | ||||
−0.520584 | + | 0.853811i | \(0.674286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.228060i | − | 0.0115335i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.1604 | − | 41.8471i | −1.21873 | − | 2.11091i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.6997 | + | 24.6997i | −1.24277 | + | 1.24277i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.08669 | − | 26.4479i | −0.355671 | − | 1.32738i | −0.879638 | − | 0.475643i | \(-0.842215\pi\) |
0.523967 | − | 0.851738i | \(-0.324451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 37.9579 | + | 21.9150i | 1.90027 | + | 1.09712i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.38519 | − | 5.16959i | 0.0691729 | − | 0.258157i | −0.922676 | − | 0.385576i | \(-0.874003\pi\) |
0.991849 | + | 0.127419i | \(0.0406694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.67866 | + | 0.0757443i | −0.133433 | + | 0.00377309i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.43443 | − | 16.5495i | 0.220348 | − | 0.822352i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.82043 | + | 11.8133i | −0.338076 | + | 0.585565i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.27483 | − | 30.8821i | −0.409164 | − | 1.52702i | −0.796245 | − | 0.604974i | \(-0.793183\pi\) |
0.387081 | − | 0.922046i | \(-0.373483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.0737 | + | 28.0737i | 1.38477 | + | 1.38477i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.2571 | + | 19.4979i | 0.553926 | + | 0.959428i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.1693 | 1.33369 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −36.3566 | −1.78039 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.06151 | − | 7.03474i | −0.198418 | − | 0.343670i | 0.749598 | − | 0.661894i | \(-0.230247\pi\) |
−0.948016 | + | 0.318224i | \(0.896914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.7134 | + | 23.7134i | 1.15572 | + | 1.15572i | 0.985387 | + | 0.170333i | \(0.0544844\pi\) |
0.170333 | + | 0.985387i | \(0.445516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.77696 | + | 25.2919i | 0.329507 | + | 1.22974i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.223036 | − | 0.386310i | 0.0108188 | − | 0.0187388i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.51421 | − | 20.5793i | 0.266851 | − | 0.995902i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.9935 | + | 27.7528i | −0.723894 | + | 1.33992i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.20438 | + | 30.6192i | −0.395191 | + | 1.47487i | 0.426263 | + | 0.904599i | \(0.359830\pi\) |
−0.821455 | + | 0.570274i | \(0.806837\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.7664 | − | 9.68007i | −0.805740 | − | 0.465194i | 0.0397341 | − | 0.999210i | \(-0.487349\pi\) |
−0.845474 | + | 0.534016i | \(0.820682\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.49866 | − | 13.0572i | −0.167748 | − | 0.626043i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.38650 | − | 1.38650i | 0.0663252 | − | 0.0663252i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.29759 | − | 16.1039i | −0.443750 | − | 0.768597i | 0.554214 | − | 0.832374i | \(-0.313019\pi\) |
−0.997964 | + | 0.0637766i | \(0.979685\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 51.1275i | − | 2.43464i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.81566 | 0.181288 | 0.0906439 | − | 0.995883i | \(-0.471108\pi\) | ||||
0.0906439 | + | 0.995883i | \(0.471108\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0725 | + | 9.27946i | −0.761910 | + | 0.439889i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.2048 | − | 24.2048i | −1.14485 | − | 1.14485i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.39494 | + | 1.98147i | −0.348989 | + | 0.0935112i | −0.429055 | − | 0.903278i | \(-0.641153\pi\) |
0.0800665 | + | 0.996790i | \(0.474487\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.54801 | − | 2.68124i | 0.0728931 | − | 0.126255i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.2971 | + | 4.90269i | 0.859673 | + | 0.230349i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.10782 | − | 27.1630i | −0.380100 | − | 1.27342i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.5841 | + | 4.71165i | 0.822550 | + | 0.220402i | 0.645461 | − | 0.763793i | \(-0.276665\pi\) |
0.177089 | + | 0.984195i | \(0.443332\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.30540 | + | 1.90838i | 0.154283 | + | 0.0890754i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.90436 | − | 1.04617i | 0.181844 | − | 0.0487250i | −0.166748 | − | 0.986000i | \(-0.553327\pi\) |
0.348592 | + | 0.937275i | \(0.386660\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0778804 | − | 0.0778804i | 0.00361941 | − | 0.00361941i | −0.705295 | − | 0.708914i | \(-0.749185\pi\) |
0.708914 | + | 0.705295i | \(0.249185\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.83609 | − | 2.21477i | 0.177894 | − | 0.102707i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.605322i | 0.0280110i | 0.999902 | + | 0.0140055i | \(0.00445823\pi\) | ||||
−0.999902 | + | 0.0140055i | \(0.995542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7.22123i | − | 0.333445i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.93682 | − | 3.42762i | 0.273554 | − | 0.157937i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.8158 | − | 13.8158i | 0.635249 | − | 0.635249i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.70455 | − | 0.992630i | 0.169976 | − | 0.0455450i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.3979 | − | 17.5503i | −1.39183 | − | 0.803571i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.3267 | + | 4.10679i | 0.700297 | + | 0.187644i | 0.591364 | − | 0.806405i | \(-0.298590\pi\) |
0.108933 | + | 0.994049i | \(0.465257\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3260 | + | 8.82024i | −0.653211 | + | 0.402168i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.03118 | − | 1.61605i | −0.274428 | − | 0.0735328i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.35279 | + | 5.80721i | −0.152243 | + | 0.263692i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.60788 | − | 0.430831i | 0.0728601 | − | 0.0195228i | −0.222205 | − | 0.975000i | \(-0.571325\pi\) |
0.295065 | + | 0.955477i | \(0.404659\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 41.2986 | + | 41.2986i | 1.86759 | + | 1.86759i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.1677 | + | 11.0665i | −0.865026 | + | 0.499423i | −0.865692 | − | 0.500577i | \(-0.833121\pi\) |
0.000666399 | 1.00000i | \(0.499788\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.978711 | 0.0440789 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 34.6750i | − | 1.55852i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.82253 | + | 17.0131i | 0.440601 | + | 0.763143i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.15371 | − | 5.15371i | 0.230712 | − | 0.230712i | −0.582278 | − | 0.812990i | \(-0.697838\pi\) |
0.812990 | + | 0.582278i | \(0.197838\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.7957 | − | 58.9502i | −0.705698 | − | 2.63370i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.9365 | + | 21.9026i | 1.69150 | + | 0.976590i | 0.953307 | + | 0.302003i | \(0.0976553\pi\) |
0.738196 | + | 0.674586i | \(0.235678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.923660 | + | 3.44715i | −0.0411023 | + | 0.153396i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.5387 | + | 21.3247i | −1.44509 | + | 0.947064i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.64040 | + | 6.12207i | −0.0727096 | + | 0.271356i | −0.992704 | − | 0.120575i | \(-0.961526\pi\) |
0.919995 | + | 0.391931i | \(0.128193\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0583 | − | 41.6702i | 1.06428 | − | 1.84338i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.49329 | + | 31.6974i | 0.374988 | + | 1.39947i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.82008 | + | 8.82008i | 0.388659 | + | 0.388659i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.42648 | + | 11.1310i | 0.282636 | + | 0.489540i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −69.1188 | −3.03398 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.1087 | 1.01241 | 0.506206 | − | 0.862413i | \(-0.331048\pi\) | ||||
0.506206 | + | 0.862413i | \(0.331048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.4715 | + | 18.1372i | 0.457887 | + | 0.793083i | 0.998849 | − | 0.0479636i | \(-0.0152731\pi\) |
−0.540962 | + | 0.841047i | \(0.681940\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.63575 | − | 8.63575i | −0.376895 | − | 0.376895i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0830048 | + | 0.309778i | 0.00361575 | + | 0.0134942i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3603 | − | 19.6767i | 0.493928 | − | 0.855508i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.79094 | + | 32.8082i | −0.381494 | + | 1.42376i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.25154 | − | 2.00190i | 0.140840 | − | 0.0867121i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.92788 | + | 14.6590i | −0.169817 | + | 0.633766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.6044 | + | 14.7827i | 1.10491 | + | 0.637922i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.49554 | − | 24.2417i | −0.279783 | − | 1.04416i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.4938 | − | 22.4938i | 0.967084 | − | 0.967084i | −0.0323917 | − | 0.999475i | \(-0.510312\pi\) |
0.999475 | + | 0.0323917i | \(0.0103124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.8616 | + | 37.8653i | 0.938170 | + | 1.62496i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.1227i | 1.50449i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.1772 | 0.606172 | 0.303086 | − | 0.952963i | \(-0.401983\pi\) | ||||
0.303086 | + | 0.952963i | \(0.401983\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.8355 | − | 16.0709i | 1.18799 | − | 0.685887i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.95011 | + | 5.95011i | 0.253483 | + | 0.253483i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −66.8819 | + | 17.9209i | −2.84411 | + | 0.762076i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.9045 | − | 24.0833i | 0.590213 | − | 1.02228i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.2083 | − | 3.00327i | −0.474913 | − | 0.127253i | 0.0134200 | − | 0.999910i | \(-0.495728\pi\) |
−0.488333 | + | 0.872657i | \(0.662395\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.0905 | − | 6.89223i | 0.976624 | − | 0.291510i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.64651 | + | 0.977078i | 0.153956 | + | 0.0412523i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.60923 | + | 4.97054i | 0.362836 | + | 0.209483i | 0.670324 | − | 0.742069i | \(-0.266155\pi\) |
−0.307488 | + | 0.951552i | \(0.599488\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.4033 | − | 6.00293i | 0.942512 | − | 0.252545i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.0151 | − | 24.0151i | 1.00854 | − | 1.00854i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.2898 | + | 18.0652i | −1.31174 | + | 0.757332i | −0.982384 | − | 0.186875i | \(-0.940164\pi\) |
−0.329353 | + | 0.944207i | \(0.606831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.28225i | 0.137358i | 0.997639 | + | 0.0686790i | \(0.0218784\pi\) | ||||
−0.997639 | + | 0.0686790i | \(0.978122\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.8908i | 1.37403i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.473160 | + | 0.273179i | −0.0197321 | + | 0.0113924i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.55694 | + | 7.55694i | −0.314600 | + | 0.314600i | −0.846689 | − | 0.532089i | \(-0.821407\pi\) |
0.532089 | + | 0.846689i | \(0.321407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.9848 | − | 3.21131i | 0.498070 | − | 0.133458i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 46.6410 | + | 26.9282i | 1.93499 | + | 1.11717i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.6426 | − | 4.45938i | −0.689267 | − | 0.184689i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 20.3273 | − | 37.6255i | 0.840431 | − | 1.55562i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0208 | − | 3.75688i | −0.578702 | − | 0.155063i | −0.0424176 | − | 0.999100i | \(-0.513506\pi\) |
−0.536285 | + | 0.844037i | \(0.680173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.37868 | + | 2.38794i | −0.0568075 | + | 0.0983934i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37.9543 | − | 10.1698i | 1.56123 | − | 0.418331i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.71248 | − | 2.71248i | −0.111388 | − | 0.111388i | 0.649216 | − | 0.760604i | \(-0.275097\pi\) |
−0.760604 | + | 0.649216i | \(0.775097\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.93804 | + | 1.69628i | −0.120448 | + | 0.0695406i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 40.8865 | 1.67337 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 20.2262i | − | 0.826421i | −0.910635 | − | 0.413211i | \(-0.864407\pi\) | ||
0.910635 | − | 0.413211i | \(-0.135593\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.9818 | + | 36.3415i | 0.855865 | + | 1.48240i | 0.875840 | + | 0.482601i | \(0.160308\pi\) |
−0.0199752 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.70333 | − | 7.70333i | 0.313704 | − | 0.313704i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.26463 | + | 4.71965i | 0.0514144 | + | 0.191881i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4059 | + | 8.31726i | 0.584718 | + | 0.337587i | 0.763006 | − | 0.646391i | \(-0.223723\pi\) |
−0.178288 | + | 0.983978i | \(0.557056\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.93522 | − | 25.8826i | 0.281029 | − | 1.04882i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.448062 | + | 15.8455i | 0.0181267 | + | 0.641040i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.326274 | + | 1.21767i | −0.0131781 | + | 0.0491812i | −0.972202 | − | 0.234145i | \(-0.924771\pi\) |
0.959024 | + | 0.283326i | \(0.0914378\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.15586 | + | 5.46612i | −0.127257 | + | 0.220415i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.14320 | − | 22.9267i | −0.247316 | − | 0.922995i | −0.972205 | − | 0.234130i | \(-0.924776\pi\) |
0.724889 | − | 0.688865i | \(-0.241891\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.13833 | − | 7.13833i | −0.286914 | − | 0.286914i | 0.548945 | − | 0.835859i | \(-0.315030\pi\) |
−0.835859 | + | 0.548945i | \(0.815030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.33742 | − | 4.04852i | −0.0937973 | − | 0.162462i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.7885 | −1.47390 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.7626 | 0.750503 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.2289 | + | 28.1093i | 0.648119 | + | 1.12258i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.42370 | + | 1.42370i | 0.0567668 | + | 0.0567668i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0485313 | + | 0.181121i | 0.00193200 | + | 0.00721032i | 0.966885 | − | 0.255212i | \(-0.0821453\pi\) |
−0.964953 | + | 0.262422i | \(0.915479\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.8281 | + | 22.2190i | −0.509873 | + | 0.883126i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.0789 | − | 37.6150i | 0.399969 | − | 1.49271i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.16281 | − | 30.1123i | 0.283801 | − | 1.19309i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.67064 | + | 28.6272i | −0.303446 | + | 1.13248i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.5562 | − | 6.67195i | −0.456441 | − | 0.263526i | 0.254106 | − | 0.967176i | \(-0.418219\pi\) |
−0.710546 | + | 0.703650i | \(0.751552\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.41461 | + | 12.7435i | 0.134659 | + | 0.502554i | 0.999999 | + | 0.00136906i | \(0.000435785\pi\) |
−0.865340 | + | 0.501185i | \(0.832898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −28.1656 | + | 28.1656i | −1.10902 | + | 1.10902i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.24409 | + | 7.35098i | 0.166852 | + | 0.288997i | 0.937312 | − | 0.348492i | \(-0.113306\pi\) |
−0.770459 | + | 0.637489i | \(0.779973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.6726i | 0.654457i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.78045 | 0.344133 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.7745 | + | 22.9638i | −1.55649 | + | 0.898643i | −0.558907 | + | 0.829230i | \(0.688779\pi\) |
−0.997588 | + | 0.0694122i | \(0.977888\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.7384 | + | 22.7384i | 0.888464 | + | 0.888464i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 70.1166 | − | 18.7877i | 2.73551 | − | 0.732978i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.3199 | − | 21.3386i | 0.479913 | − | 0.831234i | −0.519821 | − | 0.854275i | \(-0.674001\pi\) |
0.999735 | + | 0.0230408i | \(0.00733476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.80194 | + | 1.28668i | 0.186774 | + | 0.0500459i | 0.350993 | − | 0.936378i | \(-0.385844\pi\) |
−0.164220 | + | 0.986424i | \(0.552511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.38400 | + | 3.19789i | 0.131424 | + | 0.124196i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.1745 | − | 7.54934i | −1.09256 | − | 0.292751i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.03814 | − | 0.599372i | −0.0401971 | − | 0.0232078i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.37548 | + | 1.44036i | −0.207828 | + | 0.0556874i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1563 | − | 11.1563i | 0.430683 | − | 0.430683i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.9947 | + | 10.9666i | −0.732193 | + | 0.422732i | −0.819224 | − | 0.573474i | \(-0.805596\pi\) |
0.0870306 | + | 0.996206i | \(0.472262\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 9.14371i | − | 0.351942i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.2466i | 1.04717i | 0.851972 | + | 0.523587i | \(0.175406\pi\) | ||||
−0.851972 | + | 0.523587i | \(0.824594\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.5114 | + | 6.64608i | −0.441765 | + | 0.255053i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.1852 | + | 42.1852i | −1.61654 | + | 1.61654i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.4710 | + | 9.77237i | −1.39552 | + | 0.373929i | −0.876735 | − | 0.480974i | \(-0.840283\pi\) |
−0.518788 | + | 0.854903i | \(0.673617\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.8816 | − | 13.2107i | −0.874259 | − | 0.504754i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.0503 | + | 6.44425i | 0.917576 | + | 0.245864i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.4446 | − | 14.5951i | −0.588391 | − | 0.556030i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.76976 | − | 0.742154i | −0.105367 | − | 0.0282329i | 0.205751 | − | 0.978604i | \(-0.434036\pi\) |
−0.311117 | + | 0.950372i | \(0.600703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 34.3673 | − | 59.5259i | 1.30551 | − | 2.26120i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.3705 | − | 6.26211i | 0.886494 | − | 0.237535i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.323134 | − | 0.323134i | −0.0122396 | − | 0.0122396i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −38.7506 | + | 22.3727i | −1.46568 | + | 0.846212i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.5968 | 1.49555 | 0.747775 | − | 0.663952i | \(-0.231122\pi\) | ||||
0.747775 | + | 0.663952i | \(0.231122\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.3109i | 0.652894i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.1014 | − | 22.6922i | −0.493426 | − | 0.854639i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.00219 | + | 5.00219i | −0.188127 | + | 0.188127i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.979951 | − | 3.65723i | −0.0368028 | − | 0.137350i | 0.945080 | − | 0.326839i | \(-0.105984\pi\) |
−0.981883 | + | 0.189489i | \(0.939317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −90.4644 | − | 52.2296i | −3.39268 | − | 1.95876i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.101666 | − | 0.379422i | 0.00380742 | − | 0.0142095i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.85786 | − | 20.4223i | 0.181674 | − | 0.763752i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.31601 | + | 8.64346i | −0.0864930 | + | 0.322796i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.2355 | + | 33.3168i | −0.717363 | + | 1.24251i | 0.244678 | + | 0.969604i | \(0.421318\pi\) |
−0.962041 | + | 0.272904i | \(0.912016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.39945 | + | 23.8831i | 0.238328 | + | 0.889452i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.2653 | − | 30.2653i | −1.12558 | − | 1.12558i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.17234 | − | 2.03055i | −0.0435396 | − | 0.0754127i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.98457 | 0.184867 | 0.0924337 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924337 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.1733 | −1.04346 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.44196 | − | 2.49754i | −0.0533327 | − | 0.0923750i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.68903 | + | 7.68903i | 0.284001 | + | 0.284001i | 0.834702 | − | 0.550701i | \(-0.185640\pi\) |
−0.550701 | + | 0.834702i | \(0.685640\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.2422 | + | 49.4204i | 0.488444 | + | 1.82290i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.67379 | − | 4.63115i | 0.0984905 | − | 0.170591i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.25679 | + | 12.1545i | −0.119803 | + | 0.447111i | −0.999601 | − | 0.0282364i | \(-0.991011\pi\) |
0.879798 | + | 0.475347i | \(0.157678\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.13150 | + | 40.0149i | 0.0415666 | + | 1.46998i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.24991 | − | 4.66472i | 0.0458547 | − | 0.171132i | −0.939201 | − | 0.343368i | \(-0.888432\pi\) |
0.985056 | + | 0.172235i | \(0.0550990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.7282 | + | 11.3901i | 0.722787 | + | 0.417301i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.0288 | + | 78.4807i | 0.769405 | + | 2.87146i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.2719 | + | 21.2719i | −0.777257 | + | 0.777257i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.3389 | − | 28.2997i | −0.596213 | − | 1.03267i | −0.993374 | − | 0.114923i | \(-0.963338\pi\) |
0.397161 | − | 0.917749i | \(-0.369995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.5002i | 0.601302i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.6061 | −0.458781 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.9250 | + | 12.6584i | −0.796879 | + | 0.460079i | −0.842379 | − | 0.538886i | \(-0.818845\pi\) |
0.0454994 | + | 0.998964i | \(0.485512\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.26957 | − | 3.26957i | −0.118678 | − | 0.118678i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.5595 | + | 3.36531i | −0.455282 | + | 0.121993i | −0.479170 | − | 0.877722i | \(-0.659062\pi\) |
0.0238877 | + | 0.999715i | \(0.492396\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.8110 | + | 60.2944i | −1.26024 | + | 2.18280i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.94371 | − | 1.32466i | −0.178740 | − | 0.0478933i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.77389 | + | 18.0913i | −0.352915 | + | 0.653239i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.5222 | + | 12.7335i | 1.71369 | + | 0.459183i | 0.976325 | − | 0.216308i | \(-0.0694014\pi\) |
0.737369 | + | 0.675490i | \(0.236068\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −74.0236 | − | 42.7376i | −2.66590 | − | 1.53916i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.85399 | + | 1.30062i | −0.174586 | + | 0.0467802i | −0.345053 | − | 0.938583i | \(-0.612139\pi\) |
0.170467 | + | 0.985363i | \(0.445472\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.543276 | − | 0.543276i | 0.0195151 | − | 0.0195151i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 47.7391 | − | 27.5622i | 1.71263 | − | 0.988789i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3.92901i | − | 0.140771i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.5479i | 0.520564i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.3741 | − | 10.0309i | 0.620900 | − | 0.358477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.22588 | + | 3.22588i | −0.115137 | + | 0.115137i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.4229 | − | 12.1710i | 1.61915 | − | 0.433851i | 0.668400 | − | 0.743802i | \(-0.266979\pi\) |
0.950752 | + | 0.309951i | \(0.100313\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −66.8187 | − | 38.5778i | −2.37881 | − | 1.37341i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.4089 | + | 11.8993i | 1.57900 | + | 0.423091i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.6456 | − | 5.56549i | 0.662126 | − | 0.197636i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.9285 | + | 9.09113i | 1.20332 | + | 0.322429i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.4500 | − | 40.6165i | 0.830641 | − | 1.43871i | −0.0668904 | − | 0.997760i | \(-0.521308\pi\) |
0.897531 | − | 0.440951i | \(-0.145359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.83248 | − | 0.491012i | 0.0648285 | − | 0.0173708i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.2445 | − | 39.2445i | −1.38664 | − | 1.38664i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.8583 | − | 17.8161i | 1.08897 | − | 0.628715i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.15527 | 0.146454 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 45.6069i | − | 1.60544i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.37324 | − | 9.30673i | −0.188913 | − | 0.327207i | 0.755975 | − | 0.654600i | \(-0.227163\pi\) |
−0.944888 | + | 0.327393i | \(0.893830\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3668 | − | 13.3668i | 0.469372 | − | 0.469372i | −0.432339 | − | 0.901711i | \(-0.642312\pi\) |
0.901711 | + | 0.432339i | \(0.142312\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.85100 | + | 6.90802i | 0.0649173 | + | 0.242275i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.6606 | − | 19.4339i | −1.17908 | − | 0.680741i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.41748 | − | 23.9504i | 0.224519 | − | 0.837917i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 72.1871 | − | 44.4441i | 2.52242 | − | 1.55300i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.83338 | − | 14.3064i | 0.133786 | − | 0.499295i | −0.866214 | − | 0.499673i | \(-0.833454\pi\) |
1.00000 | 0.000377692i | \(0.000120223\pi\) | ||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.8317 | − | 32.6174i | 0.656431 | − | 1.13697i | −0.325102 | − | 0.945679i | \(-0.605399\pi\) |
0.981533 | − | 0.191292i | \(-0.0612679\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.34077 | − | 8.73586i | −0.0814950 | − | 0.304144i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.55841 | + | 2.55841i | 0.0889646 | + | 0.0889646i | 0.750189 | − | 0.661224i | \(-0.229963\pi\) |
−0.661224 | + | 0.750189i | \(0.729963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.90712 | + | 6.76733i | 0.135700 | + | 0.235039i | 0.925865 | − | 0.377855i | \(-0.123338\pi\) |
−0.790165 | + | 0.612895i | \(0.790005\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 57.8319 | 2.00616 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.70435 | −0.128348 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.3073 | + | 35.1733i | 0.702763 | + | 1.21722i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.64846 | + | 4.64846i | 0.160674 | + | 0.160674i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.70458 | − | 28.7539i | −0.265991 | − | 0.992694i | −0.961641 | − | 0.274312i | \(-0.911550\pi\) |
0.695649 | − | 0.718382i | \(-0.255117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.9278 | + | 20.6596i | −0.411304 | + | 0.712399i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.0016 | − | 89.5751i | 0.826658 | − | 3.08513i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.2433 | − | 19.3123i | 0.593187 | − | 0.664363i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.50681 | + | 9.35554i | −0.0861349 | + | 0.321460i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.4564 | − | 16.4293i | −0.976622 | − | 0.563853i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.638268 | − | 2.38205i | −0.0218795 | − | 0.0816555i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.62369 | − | 7.62369i | 0.261030 | − | 0.261030i | −0.564442 | − | 0.825473i | \(-0.690909\pi\) |
0.825473 | + | 0.564442i | \(0.190909\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0021 | − | 38.1088i | −0.752457 | − | 1.30329i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 56.9565i | − | 1.94560i | −0.231650 | − | 0.972799i | \(-0.574412\pi\) | ||
0.231650 | − | 0.972799i | \(-0.425588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7259 | 0.434201 | 0.217101 | − | 0.976149i | \(-0.430340\pi\) | ||||
0.217101 | + | 0.976149i | \(0.430340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.8352 | + | 6.25572i | −0.369263 | + | 0.213194i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.5737 | + | 28.5737i | 0.972660 | + | 0.972660i | 0.999636 | − | 0.0269758i | \(-0.00858770\pi\) |
−0.0269758 | + | 0.999636i | \(0.508588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.4304 | − | 11.9051i | 1.51068 | − | 0.404786i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.1585 | + | 43.5758i | −0.854428 | + | 1.47991i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.5285 | − | 13.2711i | −1.68014 | − | 0.450192i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.61620 | − | 3.45777i | 0.190298 | − | 0.117162i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.3696 | − | 5.19008i | −0.655563 | − | 0.175658i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.0825 | + | 23.7190i | 1.38884 | + | 0.801848i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.32275 | − | 1.96212i | 0.247272 | − | 0.0662562i | −0.133054 | − | 0.991109i | \(-0.542478\pi\) |
0.380326 | + | 0.924853i | \(0.375812\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.5401 | + | 10.5401i | −0.355508 | + | 0.355508i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.2464 | + | 16.8854i | −0.985336 | + | 0.568884i | −0.903877 | − | 0.427793i | \(-0.859291\pi\) |
−0.0814588 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.0864i | 1.11345i | 0.830698 | + | 0.556723i | \(0.187942\pi\) | ||||
−0.830698 | + | 0.556723i | \(0.812058\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 33.9897i | − | 1.14255i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.41849 | + | 3.12837i | −0.181935 | + | 0.105040i | −0.588202 | − | 0.808714i | \(-0.700164\pi\) |
0.406266 | + | 0.913755i | \(0.366831\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.5835 | − | 54.5835i | 1.83067 | − | 1.83067i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.2935 | − | 6.50943i | 0.813864 | − | 0.218074i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.1258 | + | 8.15552i | 0.472701 | + | 0.272914i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.0051 | − | 5.09239i | −0.635269 | − | 0.170220i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.63108 | − | 5.46447i | −0.0544601 | − | 0.182453i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.62828 | + | 0.436296i | 0.0543061 | + | 0.0145513i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.27157 | + | 2.20243i | −0.0423622 | + | 0.0733735i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −76.2669 | + | 20.4357i | −2.53800 | + | 0.680056i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.5749 | − | 20.5749i | −0.683932 | − | 0.683932i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.7698 | + | 22.9611i | −1.32053 | + | 0.762410i | −0.983814 | − | 0.179195i | \(-0.942651\pi\) |
−0.336719 | + | 0.941605i | \(0.609317\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.6723 | −0.353977 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9298i | 1.35607i | 0.735032 | + | 0.678033i | \(0.237167\pi\) | ||||
−0.735032 | + | 0.678033i | \(0.762833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.9413 | + | 34.5394i | 0.659961 | + | 1.14309i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.7438 | + | 22.7438i | −0.751885 | + | 0.751885i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4980 | + | 61.5713i | 0.544811 | + | 2.03326i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.79881 | − | 3.92529i | −0.224272 | − | 0.129484i | 0.383655 | − | 0.923477i | \(-0.374665\pi\) |
−0.607927 | + | 0.793993i | \(0.707999\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.2106 | + | 38.1065i | −0.336451 | + | 1.25565i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.52832 | + | 15.7858i | −0.280713 | + | 0.519595i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.24842 | − | 4.65915i | 0.0410477 | − | 0.153192i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.6508 | + | 32.3042i | −0.612574 | + | 1.06101i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.88675 | + | 21.9696i | 0.193138 | + | 0.720800i | 0.992741 | + | 0.120272i | \(0.0383766\pi\) |
−0.799603 | + | 0.600529i | \(0.794957\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.5207 | − | 22.5207i | −0.738087 | − | 0.738087i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.7359 | + | 20.3272i | 0.384217 | + | 0.665483i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.51231 | −0.0821614 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.1246 | 1.14747 | 0.573735 | − | 0.819041i | \(-0.305494\pi\) | ||||
0.573735 | + | 0.819041i | \(0.305494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.3257 | − | 45.5974i | −0.859106 | − | 1.48801i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.4717 | − | 33.4717i | −1.09115 | − | 1.09115i | −0.995406 | − | 0.0957410i | \(-0.969478\pi\) |
−0.0957410 | − | 0.995406i | \(-0.530522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.144866 | + | 0.540646i | 0.00471748 | + | 0.0176059i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −34.7708 | + | 60.2247i | −1.13109 | + | 1.95911i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.87571 | + | 25.6605i | −0.223430 | + | 0.833854i | 0.759597 | + | 0.650394i | \(0.225396\pi\) |
−0.983027 | + | 0.183460i | \(0.941270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.9283 | − | 1.24216i | 1.42597 | − | 0.0403222i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.1378 | + | 60.2269i | −0.523303 | + | 1.95299i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.5794 | − | 10.7268i | −0.601845 | − | 0.347475i | 0.167922 | − | 0.985800i | \(-0.446294\pi\) |
−0.769767 | + | 0.638325i | \(0.779628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.66515 | − | 21.1426i | −0.183320 | − | 0.684159i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.0312 | − | 14.0312i | 0.453565 | − | 0.453565i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.1869 | − | 45.3570i | −0.845618 | − | 1.46465i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 30.4476i | − | 0.982181i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.3840 | −1.46248 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.15085 | + | 4.12854i | −0.230194 | + | 0.132903i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.4651 | − | 28.4651i | −0.915375 | − | 0.915375i | 0.0813132 | − | 0.996689i | \(-0.474089\pi\) |
−0.996689 | + | 0.0813132i | \(0.974089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.62759 | − | 1.23996i | 0.148660 | − | 0.0398333i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.57471 | − | 4.45954i | 0.0826265 | − | 0.143113i | −0.821751 | − | 0.569847i | \(-0.807002\pi\) |
0.904377 | + | 0.426734i | \(0.140336\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46.3262 | + | 12.4131i | 1.48515 | + | 0.397945i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.58122 | − | 10.8514i | 0.0826653 | − | 0.347523i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.7613 | − | 3.41938i | −0.408270 | − | 0.109396i | 0.0488381 | − | 0.998807i | \(-0.484448\pi\) |
−0.457108 | + | 0.889411i | \(0.651115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.5933 | − | 13.6216i | −0.754046 | − | 0.435349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −101.455 | + | 27.1847i | −3.23920 | + | 0.867941i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.17750 | − | 6.17750i | 0.197032 | − | 0.197032i | −0.601695 | − | 0.798726i | \(-0.705508\pi\) |
0.798726 | + | 0.601695i | \(0.205508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.6459 | + | 13.0746i | −0.721557 | + | 0.416591i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 51.9404i | − | 1.65328i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.53228i | 0.112320i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.9402 | − | 13.8219i | 0.760486 | − | 0.439067i | −0.0689844 | − | 0.997618i | \(-0.521976\pi\) |
0.829470 | + | 0.558551i | \(0.188643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0406 | − | 20.0406i | 0.635971 | − | 0.635971i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.2823 | + | 7.04233i | −0.833206 | + | 0.223257i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −52.0747 | − | 30.0653i | −1.64922 | − | 0.952179i | −0.977382 | − | 0.211483i | \(-0.932171\pi\) |
−0.671840 | − | 0.740696i | \(-0.734496\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.8653 | + | 10.6819i | 1.26128 | + | 0.337960i |
(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 | 416.2.bk.a.15.2 | 48 | ||
4.3 | odd | 2 | 104.2.u.a.67.2 | yes | 48 | ||
8.3 | odd | 2 | inner | 416.2.bk.a.15.1 | 48 | ||
8.5 | even | 2 | 104.2.u.a.67.5 | yes | 48 | ||
12.11 | even | 2 | 936.2.ed.d.379.11 | 48 | |||
13.7 | odd | 12 | inner | 416.2.bk.a.111.1 | 48 | ||
24.5 | odd | 2 | 936.2.ed.d.379.8 | 48 | |||
52.7 | even | 12 | 104.2.u.a.59.5 | yes | 48 | ||
104.59 | even | 12 | inner | 416.2.bk.a.111.2 | 48 | ||
104.85 | odd | 12 | 104.2.u.a.59.2 | ✓ | 48 | ||
156.59 | odd | 12 | 936.2.ed.d.163.8 | 48 | |||
312.293 | even | 12 | 936.2.ed.d.163.11 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
104.2.u.a.59.2 | ✓ | 48 | 104.85 | odd | 12 | ||
104.2.u.a.59.5 | yes | 48 | 52.7 | even | 12 | ||
104.2.u.a.67.2 | yes | 48 | 4.3 | odd | 2 | ||
104.2.u.a.67.5 | yes | 48 | 8.5 | even | 2 | ||
416.2.bk.a.15.1 | 48 | 8.3 | odd | 2 | inner | ||
416.2.bk.a.15.2 | 48 | 1.1 | even | 1 | trivial | ||
416.2.bk.a.111.1 | 48 | 13.7 | odd | 12 | inner | ||
416.2.bk.a.111.2 | 48 | 104.59 | even | 12 | inner | ||
936.2.ed.d.163.8 | 48 | 156.59 | odd | 12 | |||
936.2.ed.d.163.11 | 48 | 312.293 | even | 12 | |||
936.2.ed.d.379.8 | 48 | 24.5 | odd | 2 | |||
936.2.ed.d.379.11 | 48 | 12.11 | even | 2 |