Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(95,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.s (of order \(6\), degree \(2\), 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: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.4 | ||
Character | \(\chi\) | \(=\) | 288.95 |
Dual form | 288.2.s.a.191.4 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.05094 | + | 1.37678i | −0.606762 | + | 0.794884i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.01113 | − | 1.73848i | −1.34662 | − | 0.777470i | −0.358849 | − | 0.933396i | \(-0.616831\pi\) |
−0.987769 | + | 0.155925i | \(0.950164\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.12309 | − | 1.80312i | 1.18042 | − | 0.681515i | 0.224307 | − | 0.974519i | \(-0.427988\pi\) |
0.956111 | + | 0.293004i | \(0.0946548\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.791040 | − | 2.89383i | −0.263680 | − | 0.964610i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.32430 | + | 2.29375i | 0.399290 | + | 0.691591i | 0.993639 | − | 0.112617i | \(-0.0359232\pi\) |
−0.594348 | + | 0.804208i | \(0.702590\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.36304 | − | 4.09290i | 0.655388 | − | 1.13517i | −0.326408 | − | 0.945229i | \(-0.605838\pi\) |
0.981796 | − | 0.189937i | \(-0.0608283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.55802 | − | 2.31862i | 1.43507 | − | 0.598665i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.79223i | − | 0.434681i | −0.976096 | − | 0.217340i | \(-0.930262\pi\) | ||
0.976096 | − | 0.217340i | \(-0.0697381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.55459i | − | 1.04490i | −0.852671 | − | 0.522448i | \(-0.825019\pi\) | ||
0.852671 | − | 0.522448i | \(-0.174981\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.799695 | + | 6.19478i | −0.174508 | + | 1.35181i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.377525 | + | 0.653893i | −0.0787195 | + | 0.136346i | −0.902698 | − | 0.430275i | \(-0.858416\pi\) |
0.823978 | + | 0.566621i | \(0.191750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.54460 | + | 6.13942i | 0.708920 | + | 1.22788i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.81550 | + | 1.95216i | 0.926744 | + | 0.375694i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.19382 | − | 4.15336i | 1.33586 | − | 0.771259i | 0.349669 | − | 0.936873i | \(-0.386294\pi\) |
0.986191 | + | 0.165614i | \(0.0529607\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.94259 | − | 1.12156i | −0.348900 | − | 0.201437i | 0.315301 | − | 0.948992i | \(-0.397895\pi\) |
−0.664201 | + | 0.747554i | \(0.731228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.54974 | − | 0.587334i | −0.792009 | − | 0.102242i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.5387 | −2.11943 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.98496 | −0.655123 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.15160 | + | 7.55478i | 0.504660 | + | 1.20973i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.57798 | − | 3.22045i | −0.871134 | − | 0.502949i | −0.00340902 | − | 0.999994i | \(-0.501085\pi\) |
−0.867725 | + | 0.497045i | \(0.834418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.60601 | + | 4.39133i | −1.15991 | + | 0.669672i | −0.951281 | − | 0.308324i | \(-0.900232\pi\) |
−0.208624 | + | 0.977996i | \(0.566899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.64893 | + | 10.0889i | −0.394879 | + | 1.50396i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.37819 | − | 2.38710i | −0.201030 | − | 0.348194i | 0.747831 | − | 0.663890i | \(-0.231096\pi\) |
−0.948861 | + | 0.315696i | \(0.897762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00247 | − | 5.20044i | 0.428925 | − | 0.742920i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.46751 | + | 1.88353i | 0.345521 | + | 0.263748i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.41211i | − | 0.606050i | −0.952983 | − | 0.303025i | \(-0.902003\pi\) | ||
0.952983 | − | 0.303025i | \(-0.0979966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.20903i | − | 1.24175i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.27067 | + | 4.78662i | 0.830571 | + | 0.634003i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.36081 | + | 2.35700i | −0.177163 | + | 0.306855i | −0.940908 | − | 0.338663i | \(-0.890025\pi\) |
0.763745 | + | 0.645518i | \(0.223359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.19156 | + | 2.06384i | 0.152563 | + | 0.264248i | 0.932169 | − | 0.362023i | \(-0.117914\pi\) |
−0.779606 | + | 0.626271i | \(0.784580\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.68841 | − | 7.61136i | −0.968649 | − | 0.958942i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.2308 | + | 8.21616i | −1.76511 | + | 1.01909i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.78651 | + | 5.07289i | 1.07344 | + | 0.619753i | 0.929120 | − | 0.369778i | \(-0.120566\pi\) |
0.144323 | + | 0.989531i | \(0.453900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.503509 | − | 1.20697i | −0.0606153 | − | 0.145302i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.0730340 | −0.00866754 | −0.00433377 | − | 0.999991i | \(-0.501379\pi\) | ||||
−0.00433377 | + | 0.999991i | \(0.501379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3207 | 1.55907 | 0.779536 | − | 0.626358i | \(-0.215455\pi\) | ||||
0.779536 | + | 0.626358i | \(0.215455\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.1778 | − | 1.57205i | −1.40617 | − | 0.181525i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.27180 | + | 4.77573i | 0.942659 | + | 0.544245i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.51115 | + | 2.60452i | −0.507544 | + | 0.293031i | −0.731824 | − | 0.681494i | \(-0.761331\pi\) |
0.224279 | + | 0.974525i | \(0.427997\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.74851 | + | 4.57827i | −0.860946 | + | 0.508697i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.244846 | − | 0.424085i | −0.0268753 | − | 0.0465494i | 0.852275 | − | 0.523094i | \(-0.175222\pi\) |
−0.879150 | + | 0.476545i | \(0.841889\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.11576 | + | 5.39665i | −0.337951 | + | 0.585349i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.84204 | + | 14.2692i | −0.197488 | + | 1.52982i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.41211i | 0.467683i | 0.972275 | + | 0.233841i | \(0.0751297\pi\) | ||||
−0.972275 | + | 0.233841i | \(0.924870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 17.0433i | − | 1.78663i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.58569 | − | 1.49583i | 0.371818 | − | 0.155110i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.91805 | + | 13.7145i | −0.812375 | + | 1.40708i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.21855 | + | 12.5029i | 0.732933 | + | 1.26948i | 0.955624 | + | 0.294588i | \(0.0951823\pi\) |
−0.222692 | + | 0.974889i | \(0.571484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.59015 | − | 5.64674i | 0.561831 | − | 0.567518i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.88785 | − | 1.08995i | 0.187848 | − | 0.108454i | −0.403127 | − | 0.915144i | \(-0.632077\pi\) |
0.590975 | + | 0.806690i | \(0.298743\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33065 | + | 1.92295i | 0.328179 | + | 0.189474i | 0.655032 | − | 0.755601i | \(-0.272655\pi\) |
−0.326853 | + | 0.945075i | \(0.605988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.1775 | − | 17.2630i | 1.28599 | − | 1.68470i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.4071 | 1.87615 | 0.938077 | − | 0.346426i | \(-0.112605\pi\) | ||||
0.938077 | + | 0.346426i | \(0.112605\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.0941 | −1.25419 | −0.627096 | − | 0.778942i | \(-0.715757\pi\) | ||||
−0.627096 | + | 0.778942i | \(0.715757\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.18796 | − | 5.48640i | 0.397503 | − | 0.520746i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.23482 | − | 0.712921i | −0.116162 | − | 0.0670660i | 0.440793 | − | 0.897609i | \(-0.354697\pi\) |
−0.556955 | + | 0.830543i | \(0.688030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.27355 | − | 1.31264i | 0.212010 | − | 0.122404i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.7134 | − | 3.60058i | −1.26781 | − | 0.332873i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.23161 | − | 5.59731i | −0.296241 | − | 0.513105i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.99248 | − | 3.45107i | 0.181134 | − | 0.313734i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.2960 | − | 4.29514i | 0.928357 | − | 0.387280i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 7.26404i | − | 0.649715i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5554i | 1.20285i | 0.798929 | + | 0.601425i | \(0.205400\pi\) | ||||
−0.798929 | + | 0.601425i | \(0.794600\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.94758 | − | 15.0868i | 0.171475 | − | 1.32832i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.88176 | − | 13.6516i | 0.688632 | − | 1.19275i | −0.283648 | − | 0.958928i | \(-0.591545\pi\) |
0.972280 | − | 0.233818i | \(-0.0751219\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.21247 | − | 14.2244i | −0.712112 | − | 1.23341i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.1063 | − | 14.2498i | −0.955879 | − | 1.22643i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.70126 | − | 3.86897i | 0.572527 | − | 0.330549i | −0.185631 | − | 0.982620i | \(-0.559433\pi\) |
0.758158 | + | 0.652071i | \(0.226100\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.490339 | + | 0.283097i | 0.0415900 | + | 0.0240120i | 0.520651 | − | 0.853770i | \(-0.325689\pi\) |
−0.479061 | + | 0.877782i | \(0.659023\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.73491 | + | 0.611237i | 0.398751 | + | 0.0514755i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5174 | 1.04676 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.8820 | −2.39852 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.00443 | + | 9.59910i | 0.330280 | + | 0.791721i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.19013 | + | 4.72857i | 0.670961 | + | 0.387380i | 0.796441 | − | 0.604716i | \(-0.206714\pi\) |
−0.125479 | + | 0.992096i | \(0.540047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5260 | + | 9.54127i | −1.34486 | + | 0.776458i | −0.987517 | − | 0.157514i | \(-0.949652\pi\) |
−0.357347 | + | 0.933972i | \(0.616319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.18642 | + | 1.41773i | −0.419297 | + | 0.114617i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.89960 | + | 6.75430i | 0.313223 | + | 0.542519i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5680 | − | 18.3043i | 0.843417 | − | 1.46084i | −0.0435713 | − | 0.999050i | \(-0.513874\pi\) |
0.886989 | − | 0.461791i | \(-0.152793\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.07450 | + | 4.63688i | 0.481739 | + | 0.367728i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.72289i | 0.214594i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.6646i | 1.77523i | 0.460586 | + | 0.887615i | \(0.347639\pi\) | ||||
−0.460586 | + | 0.887615i | \(0.652361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.6788 | + | 9.67816i | 0.987043 | + | 0.753444i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.92712 | − | 5.06992i | 0.226507 | − | 0.392322i | −0.730263 | − | 0.683166i | \(-0.760603\pi\) |
0.956771 | + | 0.290844i | \(0.0939359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.66788 | − | 8.08500i | −0.359067 | − | 0.621923i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.1802 | + | 3.60287i | −1.00792 | + | 0.275518i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.11907 | + | 2.95549i | −0.389195 | + | 0.224702i | −0.681811 | − | 0.731528i | \(-0.738808\pi\) |
0.292616 | + | 0.956230i | \(0.405474\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.1402 | + | 12.7827i | 1.67364 | + | 0.966279i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.81493 | − | 4.35061i | −0.136418 | − | 0.327012i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.8823 | −0.962871 | −0.481436 | − | 0.876481i | \(-0.659884\pi\) | ||||
−0.481436 | + | 0.876481i | \(0.659884\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1934 | −0.757672 | −0.378836 | − | 0.925464i | \(-0.623676\pi\) | ||||
−0.378836 | + | 0.925464i | \(0.623676\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.09371 | − | 0.528464i | −0.302616 | − | 0.0390652i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.9992 | + | 6.92775i | 0.882200 | + | 0.509338i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.11093 | − | 2.37345i | 0.300621 | − | 0.173564i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.5592 | − | 2.58614i | 1.34999 | − | 0.188114i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.2960 | − | 19.5653i | −0.817353 | − | 1.41570i | −0.907626 | − | 0.419779i | \(-0.862107\pi\) |
0.0902735 | − | 0.995917i | \(-0.471226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.12935 | + | 1.95610i | −0.0812926 | + | 0.140803i | −0.903805 | − | 0.427944i | \(-0.859238\pi\) |
0.822513 | + | 0.568747i | \(0.192571\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.64392 | − | 28.2274i | 0.260947 | − | 2.02141i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.65685i | 0.403034i | 0.979485 | + | 0.201517i | \(0.0645872\pi\) | ||||
−0.979485 | + | 0.201517i | \(0.935413\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 13.8193i | − | 0.979621i | −0.871829 | − | 0.489811i | \(-0.837066\pi\) | ||
0.871829 | − | 0.489811i | \(-0.162934\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.2184 | + | 6.76576i | −1.14396 | + | 0.477220i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.9780 | − | 25.9426i | 1.05125 | − | 1.82082i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1973 | + | 19.3944i | 0.782056 | + | 1.35456i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.19089 | + | 0.575239i | 0.152278 | + | 0.0399818i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.4471 | − | 6.03163i | 0.722641 | − | 0.417217i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.52413 | + | 3.18936i | 0.380297 | + | 0.219565i | 0.677947 | − | 0.735110i | \(-0.262870\pi\) |
−0.297651 | + | 0.954675i | \(0.596203\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0767545 | − | 0.100552i | 0.00525913 | − | 0.00688968i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 30.5369 | 2.08260 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.08920 | −0.549130 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.9993 | + | 18.3397i | −0.945985 | + | 1.23928i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.33543 | − | 4.23511i | −0.493435 | − | 0.284885i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.25361 | + | 1.30112i | −0.150913 | + | 0.0871296i | −0.573555 | − | 0.819167i | \(-0.694436\pi\) |
0.422642 | + | 0.906297i | \(0.361103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.9625 | − | 15.1140i | 0.997502 | − | 1.00760i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.7192 | + | 18.5663i | 0.711461 | + | 1.23229i | 0.964309 | + | 0.264780i | \(0.0852993\pi\) |
−0.252848 | + | 0.967506i | \(0.581367\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.370558 | + | 0.641825i | −0.0244872 | + | 0.0424130i | −0.878009 | − | 0.478644i | \(-0.841129\pi\) |
0.853522 | + | 0.521057i | \(0.174462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.2683 | + | 6.36943i | −1.00458 | + | 0.419078i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3832i | 1.33535i | 0.744454 | + | 0.667673i | \(0.232710\pi\) | ||||
−0.744454 | + | 0.667673i | \(0.767290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.58381i | 0.625179i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.15512 | − | 8.94806i | 0.0750331 | − | 0.581239i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.78964 | + | 8.29589i | −0.309816 | + | 0.536617i | −0.978322 | − | 0.207090i | \(-0.933601\pi\) |
0.668506 | + | 0.743707i | \(0.266934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.17787 | + | 5.50424i | 0.204705 | + | 0.354559i | 0.950039 | − | 0.312132i | \(-0.101043\pi\) |
−0.745334 | + | 0.666691i | \(0.767710\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.83997 | − | 15.4795i | 0.118034 | − | 0.993010i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.0817 | + | 10.4395i | −1.15520 | + | 0.666953i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.6415 | − | 10.7627i | −1.18613 | − | 0.684812i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.841191 | + | 0.108591i | 0.0533083 | + | 0.00688166i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0938 | −1.71014 | −0.855072 | − | 0.518509i | \(-0.826487\pi\) | ||||
−0.855072 | + | 0.518509i | \(0.826487\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.99982 | −0.125728 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.15551 | − | 9.96127i | −0.260228 | − | 0.623799i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.31700 | − | 1.91507i | −0.206909 | − | 0.119459i | 0.392965 | − | 0.919553i | \(-0.371449\pi\) |
−0.599874 | + | 0.800095i | \(0.704783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.4454 | + | 7.18535i | −0.773319 | + | 0.446476i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.7097 | − | 17.5322i | −1.09620 | − | 1.08522i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.0988 | + | 27.8840i | 0.992697 | + | 1.71940i | 0.600819 | + | 0.799385i | \(0.294841\pi\) |
0.391878 | + | 0.920017i | \(0.371826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.67035 | + | 13.2854i | −0.471186 | + | 0.816118i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.07450 | − | 4.63688i | −0.371754 | − | 0.283772i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.2601i | 1.66208i | 0.556214 | + | 0.831039i | \(0.312253\pi\) | ||||
−0.556214 | + | 0.831039i | \(0.687747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.48623i | − | 0.515501i | −0.966211 | − | 0.257751i | \(-0.917019\pi\) | ||
0.966211 | − | 0.257751i | \(-0.0829813\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 23.4649 | + | 17.9116i | 1.42016 | + | 1.08406i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.38820 | + | 16.2608i | −0.566130 | + | 0.980565i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.90516 | + | 6.76394i | 0.234638 | + | 0.406405i | 0.959168 | − | 0.282839i | \(-0.0912761\pi\) |
−0.724529 | + | 0.689244i | \(0.757943\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.70892 | + | 6.50873i | −0.102311 | + | 0.389667i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.05260 | − | 3.49447i | 0.361068 | − | 0.208462i | −0.308481 | − | 0.951230i | \(-0.599821\pi\) |
0.669549 | + | 0.742768i | \(0.266487\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.3037 | − | 14.0318i | −1.44471 | − | 0.834101i | −0.446547 | − | 0.894760i | \(-0.647346\pi\) |
−0.998159 | + | 0.0606590i | \(0.980680\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.5604 | − | 25.3145i | −0.625543 | − | 1.49950i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.2274 | −1.37107 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7879 | 0.811053 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.8000 | − | 3.20147i | −1.45380 | − | 0.187674i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.54841 | + | 4.35808i | 0.440983 | + | 0.254602i | 0.704015 | − | 0.710186i | \(-0.251389\pi\) |
−0.263031 | + | 0.964787i | \(0.584722\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.19517 | − | 4.73148i | 0.477141 | − | 0.275478i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.89939 | + | 13.6308i | 0.110214 | + | 0.790939i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.78421 | + | 3.09035i | 0.103184 | + | 0.178719i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.8362 | + | 27.4291i | −0.912782 | + | 1.58099i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.483400 | + | 3.74463i | −0.0277706 | + | 0.215123i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.28599i | − | 0.474454i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.62380i | 0.549259i | 0.961550 | + | 0.274630i | \(0.0885552\pi\) | ||||
−0.961550 | + | 0.274630i | \(0.911445\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.14780 | + | 2.56466i | −0.349736 | + | 0.145898i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.31685 | − | 14.4052i | 0.471606 | − | 0.816845i | −0.527867 | − | 0.849327i | \(-0.677008\pi\) |
0.999472 | + | 0.0324824i | \(0.0103413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3153 | − | 21.3307i | −0.696100 | − | 1.20568i | −0.969808 | − | 0.243868i | \(-0.921584\pi\) |
0.273708 | − | 0.961813i | \(-0.411750\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.91863 | + | 36.2849i | 0.558852 | + | 2.04442i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.8576 | − | 12.0421i | 1.17148 | − | 0.676354i | 0.217452 | − | 0.976071i | \(-0.430226\pi\) |
0.954028 | + | 0.299717i | \(0.0968922\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.0535 | + | 11.0005i | 1.06679 | + | 0.615913i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.3957 | + | 26.7193i | −1.13838 | + | 1.49132i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.16290 | −0.454196 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.5041 | 1.85847 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.7612 | − | 18.0277i | 0.760996 | − | 0.996936i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.60844 | − | 4.97009i | −0.474599 | − | 0.274010i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1084 | − | 6.41343i | 0.610573 | − | 0.352514i | −0.162617 | − | 0.986689i | \(-0.551993\pi\) |
0.773189 | + | 0.634175i | \(0.218660\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.15226 | + | 11.5318i | 0.172743 | + | 0.631938i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.6382 | − | 30.5503i | −0.963678 | − | 1.66914i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0754 | − | 17.4511i | 0.548843 | − | 0.950624i | −0.449511 | − | 0.893275i | \(-0.648402\pi\) |
0.998354 | − | 0.0573495i | \(-0.0182649\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.27925 | − | 0.950829i | 0.123792 | − | 0.0516419i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.94109i | − | 0.321728i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.58839i | 0.193755i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.582163 | + | 4.50969i | −0.0313426 | + | 0.242793i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.50392 | + | 6.06897i | −0.188100 | + | 0.325800i | −0.944617 | − | 0.328175i | \(-0.893566\pi\) |
0.756516 | + | 0.653975i | \(0.226900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.47879 | − | 4.29339i | −0.132687 | − | 0.229820i | 0.792025 | − | 0.610489i | \(-0.209027\pi\) |
−0.924711 | + | 0.380669i | \(0.875694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.3692 | − | 15.0963i | 1.03385 | − | 0.805783i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.05985 | + | 1.76661i | −0.162859 | + | 0.0940270i | −0.579215 | − | 0.815175i | \(-0.696641\pi\) |
0.416355 | + | 0.909202i | \(0.363307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.219915 | + | 0.126968i | 0.0116719 | + | 0.00673875i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.1025 | + | 1.43324i | 0.587607 | + | 0.0758551i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.2054 | 0.802511 | 0.401255 | − | 0.915966i | \(-0.368574\pi\) | ||||
0.401255 | + | 0.915966i | \(0.368574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.74433 | −0.0918070 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.65739 | + | 6.37008i | 0.139477 | + | 0.334343i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.1104 | − | 23.1577i | −2.09947 | − | 1.21213i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.23512 | − | 1.86780i | 0.168872 | − | 0.0974983i | −0.413182 | − | 0.910649i | \(-0.635583\pi\) |
0.582054 | + | 0.813150i | \(0.302249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.90702 | + | 18.6892i | −0.255449 | + | 0.972922i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.95556 | − | 13.7794i | −0.413032 | − | 0.715393i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.760243 | − | 1.31678i | 0.0393639 | − | 0.0681802i | −0.845672 | − | 0.533703i | \(-0.820800\pi\) |
0.885036 | + | 0.465522i | \(0.154134\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0010 | + | 7.63408i | 0.516448 | + | 0.394222i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 39.2581i | − | 2.02190i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.7948i | − | 1.22226i | −0.791531 | − | 0.611129i | \(-0.790716\pi\) | ||
0.791531 | − | 0.611129i | \(-0.209284\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.6628 | − | 14.2460i | −0.956126 | − | 0.729843i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.48499 | + | 2.57208i | −0.0758796 | + | 0.131427i | −0.901468 | − | 0.432845i | \(-0.857510\pi\) |
0.825589 | + | 0.564272i | \(0.190843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.6050 | − | 28.7607i | −0.846268 | − | 1.46578i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.7244 | + | 18.5368i | 0.951816 | + | 0.942278i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.55562 | + | 2.05284i | −0.180277 | + | 0.104083i | −0.587423 | − | 0.809280i | \(-0.699857\pi\) |
0.407146 | + | 0.913363i | \(0.366524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.17193 | + | 0.676614i | 0.0592670 | + | 0.0342178i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.5120 | + | 25.1985i | 0.530259 | + | 1.27110i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18.1116 | 0.911291 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4643 | 0.826319 | 0.413160 | − | 0.910659i | \(-0.364425\pi\) | ||||
0.413160 | + | 0.910659i | \(0.364425\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.2147 | + | 3.64229i | 1.41250 | + | 0.182342i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8460 | + | 15.4996i | 1.34063 | + | 0.774012i | 0.986899 | − | 0.161337i | \(-0.0515805\pi\) |
0.353728 | + | 0.935348i | \(0.384914\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.18083 | + | 5.30056i | −0.457330 | + | 0.264039i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.2910 | − | 0.315173i | 1.55486 | − | 0.0156611i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.27726 | − | 9.14049i | −0.261584 | − | 0.453077i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.24112 | − | 3.88173i | 0.110816 | − | 0.191939i | −0.805283 | − | 0.592890i | \(-0.797987\pi\) |
0.916100 | + | 0.400951i | \(0.131320\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.71591 | + | 13.2922i | −0.0846398 | + | 0.655657i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.81483i | 0.482956i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.70263i | 0.0835791i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.905080 | + | 0.377569i | −0.0443220 | + | 0.0184897i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.48571 | − | 11.2336i | 0.316848 | − | 0.548796i | −0.662981 | − | 0.748636i | \(-0.730709\pi\) |
0.979829 | + | 0.199840i | \(0.0640423\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.21256 | + | 15.9566i | 0.448993 | + | 0.777679i | 0.998321 | − | 0.0579284i | \(-0.0184495\pi\) |
−0.549328 | + | 0.835607i | \(0.685116\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.81765 | + | 5.87654i | −0.282864 | + | 0.285727i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.0033 | − | 6.35275i | 0.533738 | − | 0.308154i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.44270 | + | 4.29704i | 0.360177 | + | 0.207949i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.1551 | + | 17.2337i | −0.635135 | + | 0.832053i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3743 | −1.07773 | −0.538867 | − | 0.842391i | \(-0.681148\pi\) | ||||
−0.538867 | + | 0.842391i | \(0.681148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.857684 | 0.0412177 | 0.0206088 | − | 0.999788i | \(-0.493440\pi\) | ||||
0.0206088 | + | 0.999788i | \(0.493440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.3534 | − | 39.7642i | 1.45533 | − | 1.90655i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.97822 | + | 1.71947i | 0.142467 | + | 0.0822536i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.3089 | − | 5.95187i | 0.492019 | − | 0.284067i | −0.233393 | − | 0.972383i | \(-0.574983\pi\) |
0.725412 | + | 0.688315i | \(0.241649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.4243 | − | 4.57490i | −0.829727 | − | 0.217852i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.99773 | + | 15.5845i | 0.427495 | + | 0.740443i | 0.996650 | − | 0.0817875i | \(-0.0260629\pi\) |
−0.569155 | + | 0.822230i | \(0.692730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.67035 | − | 13.2854i | 0.363610 | − | 0.629790i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.1176 | + | 6.30654i | −0.715036 | + | 0.298289i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 37.0489i | − | 1.74845i | −0.485524 | − | 0.874223i | \(-0.661371\pi\) | ||
0.485524 | − | 0.874223i | \(-0.338629\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 17.0593i | − | 0.803291i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.23162 | − | 32.7799i | 0.198819 | − | 1.54014i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.6294 | + | 51.3197i | −1.38905 | + | 2.40590i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.16540 | + | 7.21469i | 0.194849 | + | 0.337489i | 0.946851 | − | 0.321672i | \(-0.104245\pi\) |
−0.752002 | + | 0.659161i | \(0.770912\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.49873 | − | 8.63051i | 0.163307 | − | 0.402838i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2118 | + | 11.6693i | −0.941356 | + | 0.543492i | −0.890385 | − | 0.455208i | \(-0.849565\pi\) |
−0.0509708 | + | 0.998700i | \(0.516232\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.9990 | − | 17.3199i | −1.39417 | − | 0.804926i | −0.400399 | − | 0.916341i | \(-0.631128\pi\) |
−0.993774 | + | 0.111415i | \(0.964462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.3974 | − | 1.72950i | −0.621291 | − | 0.0802035i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1281 | −0.792595 | −0.396298 | − | 0.918122i | \(-0.629705\pi\) | ||||
−0.396298 | + | 0.918122i | \(0.629705\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.5881 | 1.68948 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.0946 | + | 33.7865i | 0.649446 | + | 1.55680i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.1452 | − | 11.6308i | −0.926278 | − | 0.534787i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.9626 | − | 16.1442i | 1.28301 | − | 0.740747i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.7679 | + | 3.49016i | −0.584602 | + | 0.159803i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.1500 | + | 31.4366i | 0.829293 | + | 1.43638i | 0.898594 | + | 0.438781i | \(0.144590\pi\) |
−0.0693014 | + | 0.997596i | \(0.522077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.41659 | + | 16.3100i | −0.429360 | + | 0.743673i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.74882 | − | 2.86160i | −0.170577 | − | 0.130207i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 50.1971i | − | 2.27933i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00757i | 0.0456575i | 0.999739 | + | 0.0228287i | \(0.00726724\pi\) | ||||
−0.999739 | + | 0.0228287i | \(0.992733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.2042 | − | 23.8192i | −1.41110 | − | 1.07714i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.20416 | + | 9.01387i | −0.234860 | + | 0.406790i | −0.959232 | − | 0.282620i | \(-0.908797\pi\) |
0.724372 | + | 0.689410i | \(0.242130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.44379 | − | 12.8930i | −0.335251 | − | 0.580672i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.6494 | + | 7.28472i | −1.19780 | + | 0.327424i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.228092 | + | 0.131689i | −0.0102313 | + | 0.00590705i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.25233 | + | 1.87773i | 0.145594 | + | 0.0840590i | 0.571028 | − | 0.820931i | \(-0.306545\pi\) |
−0.425433 | + | 0.904990i | \(0.639878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.90393 | + | 9.35819i | 0.174415 | + | 0.418093i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.5980 | 0.918417 | 0.459209 | − | 0.888328i | \(-0.348133\pi\) | ||||
0.459209 | + | 0.888328i | \(0.348133\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.57942 | −0.337280 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.0369 | + | 2.07023i | 0.712225 | + | 0.0919423i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.7984 | − | 6.23445i | −0.478630 | − | 0.276337i | 0.241216 | − | 0.970472i | \(-0.422454\pi\) |
−0.719845 | + | 0.694135i | \(0.755787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.6018 | − | 24.0188i | 1.84036 | − | 1.06253i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.89130 | − | 21.9327i | 0.392561 | − | 0.968351i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.68602 | − | 11.5805i | −0.294621 | − | 0.510299i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.65027 | − | 6.32245i | 0.160539 | − | 0.278061i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.31078 | − | 10.1539i | 0.0575369 | − | 0.445706i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9193i | 0.697438i | 0.937227 | + | 0.348719i | \(0.113383\pi\) | ||||
−0.937227 | + | 0.348719i | \(0.886617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.71297i | − | 0.162357i | −0.996700 | − | 0.0811784i | \(-0.974132\pi\) | ||
0.996700 | − | 0.0811784i | \(-0.0258683\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −40.8670 | + | 17.0483i | −1.78358 | + | 0.744051i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.01009 | + | 3.48158i | −0.0875610 | + | 0.151660i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2149 | + | 19.4249i | 0.487606 | + | 0.844559i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.89721 | + | 2.07348i | 0.342710 | + | 0.0899815i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.3619 | + | 15.2201i | −1.14186 | + | 0.659254i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −58.4373 | − | 33.7388i | −2.52646 | − | 1.45865i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.5386 | − | 17.7361i | 0.584234 | − | 0.765371i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.9047 | 0.685062 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1191 | 0.821994 | 0.410997 | − | 0.911637i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911637i | \(0.365181\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.7127 | − | 14.0341i | 0.459727 | − | 0.602261i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.4282 | + | 22.7639i | 1.68892 | + | 0.975097i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.8869 | − | 13.2137i | 0.978571 | − | 0.564978i | 0.0767328 | − | 0.997052i | \(-0.475551\pi\) |
0.901839 | + | 0.432073i | \(0.142218\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.02983 | − | 5.08075i | 0.214668 | − | 0.216841i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.9169 | − | 32.7650i | −0.805885 | − | 1.39583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.39250 | + | 16.2683i | −0.399410 | + | 0.691798i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.1485 | + | 9.23960i | −0.940150 | + | 0.392199i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.9370i | 1.05662i | 0.849053 | + | 0.528308i | \(0.177173\pi\) | ||||
−0.849053 | + | 0.528308i | \(0.822827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.5075i | 1.75558i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.05264 | + | 8.15421i | −0.0444425 | + | 0.344271i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.2599 | + | 26.4309i | −0.643127 | + | 1.11393i | 0.341604 | + | 0.939844i | \(0.389030\pi\) |
−0.984731 | + | 0.174084i | \(0.944304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.47879 | + | 4.29339i | 0.104284 | + | 0.180624i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.9441 | + | 28.2699i | −0.669591 | + | 1.18722i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.93936 | + | 5.16114i | −0.374758 | + | 0.216366i | −0.675535 | − | 0.737328i | \(-0.736087\pi\) |
0.300777 | + | 0.953694i | \(0.402754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.55903 | − | 4.36421i | −0.316335 | − | 0.182636i | 0.333423 | − | 0.942777i | \(-0.391796\pi\) |
−0.649758 | + | 0.760141i | \(0.725130\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.8086 | + | 5.00987i | 1.62125 | + | 0.209290i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.35270 | −0.223223 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.4398 | 1.43375 | 0.716874 | − | 0.697203i | \(-0.245572\pi\) | ||||
0.716874 | + | 0.697203i | \(0.245572\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.50623 | − | 3.61061i | −0.0625967 | − | 0.150052i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.52935 | − | 0.882972i | −0.0634483 | − | 0.0366319i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.1203 | − | 5.84294i | 0.419139 | − | 0.241990i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.0333 | + | 34.6822i | 1.44845 | + | 1.43393i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.31697 | + | 4.01312i | 0.0956318 | + | 0.165639i | 0.909872 | − | 0.414889i | \(-0.136180\pi\) |
−0.814240 | + | 0.580528i | \(0.802846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.10823 | + | 8.84772i | −0.210481 | + | 0.364564i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.78824 | − | 5.94503i | −0.320365 | − | 0.244546i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.49543i | 0.0614098i | 0.999528 | + | 0.0307049i | \(0.00977521\pi\) | ||||
−0.999528 | + | 0.0307049i | \(0.990225\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.4723i | 0.921275i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.0261 | + | 14.5232i | 0.778685 | + | 0.594397i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.8095 | − | 27.3828i | 0.645957 | − | 1.11883i | −0.338123 | − | 0.941102i | \(-0.609792\pi\) |
0.984080 | − | 0.177728i | \(-0.0568748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.08294 | + | 12.2680i | 0.288919 | + | 0.500423i | 0.973552 | − | 0.228465i | \(-0.0733707\pi\) |
−0.684633 | + | 0.728888i | \(0.740037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.72961 | − | 29.4395i | 0.314774 | − | 1.19887i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.9992 | + | 6.92775i | −0.487837 | + | 0.281653i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.26079 | − | 4.19202i | −0.294706 | − | 0.170149i | 0.345356 | − | 0.938472i | \(-0.387758\pi\) |
−0.640062 | + | 0.768323i | \(0.721092\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.9763 | + | 47.8856i | 0.809479 | + | 1.94042i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0269 | −0.527011 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.9574 | −0.846462 | −0.423231 | − | 0.906022i | \(-0.639104\pi\) | ||||
−0.423231 | + | 0.906022i | \(0.639104\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −38.4695 | − | 4.96609i | −1.55124 | − | 0.200252i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.5516 | − | 14.7522i | −1.02867 | − | 0.593903i | −0.112066 | − | 0.993701i | \(-0.535747\pi\) |
−0.916603 | + | 0.399798i | \(0.869080\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.7743 | + | 18.9222i | −1.31731 | + | 0.760549i | −0.983295 | − | 0.182019i | \(-0.941737\pi\) |
−0.334015 | + | 0.942568i | \(0.608404\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.09448 | + | 2.41183i | −0.124177 | + | 0.0967835i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.95556 | + | 13.7794i | 0.318733 | + | 0.552061i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.09464 | − | 8.82417i | 0.203786 | − | 0.352967i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.67507 | + | 20.7222i | −0.106832 | + | 0.827567i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.14197i | 0.284769i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.9867i | 0.636420i | 0.948020 | + | 0.318210i | \(0.103082\pi\) | ||||
−0.948020 | + | 0.318210i | \(0.896918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.1966 | + | 4.25368i | −0.405278 | + | 0.169068i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.5658 | − | 40.8171i | 0.935180 | − | 1.61978i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.1899 | − | 24.5776i | −0.562225 | − | 0.973802i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0577728 | + | 0.211348i | 0.00228546 | + | 0.00836079i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.3907 | − | 16.3914i | 1.12136 | − | 0.647420i | 0.179616 | − | 0.983737i | \(-0.442515\pi\) |
0.941749 | + | 0.336317i | \(0.109181\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.53896 | + | 2.62057i | 0.178999 | + | 0.103345i | 0.586822 | − | 0.809716i | \(-0.300379\pi\) |
−0.407823 | + | 0.913061i | \(0.633712\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.0925 | + | 42.0426i | −1.26364 | + | 1.65542i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.4906 | −1.19871 | −0.599354 | − | 0.800484i | \(-0.704576\pi\) | ||||
−0.599354 | + | 0.800484i | \(0.704576\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.20848 | −0.282958 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.50128 | − | 11.1370i | 0.333191 | − | 0.436495i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.9758 | + | 12.6877i | 0.859980 | + | 0.496510i | 0.864006 | − | 0.503482i | \(-0.167948\pi\) |
−0.00402567 | + | 0.999992i | \(0.501281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.4660 | + | 27.4045i | −1.85465 | + | 1.07078i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.5372 | − | 38.5479i | −0.411096 | − | 1.50390i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.6127 | − | 28.7740i | −0.647137 | − | 1.12087i | −0.983803 | − | 0.179250i | \(-0.942633\pi\) |
0.336666 | − | 0.941624i | \(-0.390701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9993 | + | 27.7116i | −0.622301 | + | 1.07786i | 0.366755 | + | 0.930317i | \(0.380469\pi\) |
−0.989056 | + | 0.147539i | \(0.952865\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.5399 | − | 5.64841i | 0.525847 | − | 0.219366i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 57.1088i | 2.21458i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.27199i | 0.242852i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.577056 | − | 4.47013i | 0.0223103 | − | 0.172825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.15595 | + | 5.46627i | −0.121834 | + | 0.211023i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.1871 | − | 43.6253i | −0.970891 | − | 1.68163i | −0.692878 | − | 0.721055i | \(-0.743658\pi\) |
−0.278013 | − | 0.960577i | \(-0.589676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.08388 | + | 36.4840i | 0.195679 | + | 1.40427i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.1301 | − | 16.8183i | 1.11956 | − | 0.646379i | 0.178272 | − | 0.983981i | \(-0.442949\pi\) |
0.941289 | + | 0.337603i | \(0.109616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.0884 | + | 26.0318i | 1.73033 | + | 0.999009i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.8269 | − | 4.75405i | −1.41121 | − | 0.182176i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.2382 | −0.468280 | −0.234140 | − | 0.972203i | \(-0.575227\pi\) | ||||
−0.234140 | + | 0.972203i | \(0.575227\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.9045 | −1.02797 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.494216 | − | 1.18470i | −0.0188555 | − | 0.0451990i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.0583 | − | 10.4260i | −0.687967 | − | 0.397198i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.2860 | − | 16.9083i | 1.11409 | − | 0.643222i | 0.174207 | − | 0.984709i | \(-0.444264\pi\) |
0.939886 | + | 0.341487i | \(0.110931\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.27682 | − | 27.7150i | 0.276423 | − | 1.05281i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.984316 | − | 1.70488i | −0.0373372 | − | 0.0646700i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.77180 | + | 9.99704i | −0.218622 | + | 0.378665i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.0631 | − | 21.4216i | −1.06145 | − | 0.810238i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 40.9032i | − | 1.54489i | −0.635079 | − | 0.772447i | \(-0.719033\pi\) | ||
0.635079 | − | 0.772447i | \(-0.280967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.1499i | 0.684535i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.1948 | − | 10.0720i | −0.496945 | − | 0.379335i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.93062 | − | 6.80804i | 0.147826 | − | 0.256043i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.286310 | + | 0.495903i | 0.0107526 | + | 0.0186240i | 0.871352 | − | 0.490659i | \(-0.163244\pi\) |
−0.860599 | + | 0.509283i | \(0.829911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.1055 | + | 10.9942i | 0.416490 | + | 0.412316i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.46676 | − | 0.846832i | 0.0549304 | − | 0.0317141i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.6916 | − | 21.7613i | −1.40959 | − | 0.813825i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.38798 | − | 15.3128i | −0.238564 | − | 0.571866i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.517752 | −0.0193089 | −0.00965445 | − | 0.999953i | \(-0.503073\pi\) | ||||
−0.00965445 | + | 0.999953i | \(0.503073\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8692 | 0.516518 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.9179 | − | 1.40941i | −0.406040 | − | 0.0524164i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 50.9984 | + | 29.4440i | 1.89403 | + | 1.09352i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.28291 | − | 4.20479i | 0.270108 | − | 0.155947i | −0.358829 | − | 0.933403i | \(-0.616824\pi\) |
0.628937 | + | 0.777456i | \(0.283490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.3781 | + | 18.8013i | 0.717709 | + | 0.696344i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.87029 | + | 13.6318i | 0.291093 | + | 0.504188i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.55945 | + | 11.3613i | −0.242279 | + | 0.419639i | −0.961363 | − | 0.275284i | \(-0.911228\pi\) |
0.719084 | + | 0.694923i | \(0.244562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.62997 | − | 35.8657i | 0.170779 | − | 1.32293i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8721i | 0.989845i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.78098i | 0.359799i | 0.983685 | + | 0.179900i | \(0.0575773\pi\) | ||||
−0.983685 | + | 0.179900i | \(0.942423\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 34.4090 | − | 14.3543i | 1.26404 | − | 0.527317i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.703207 | + | 1.21799i | −0.0257982 | + | 0.0446838i | −0.878636 | − | 0.477492i | \(-0.841546\pi\) |
0.852838 | + | 0.522175i | \(0.174879\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.4410 | − | 28.4767i | −0.602352 | − | 1.04330i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.03355 | + | 1.04401i | −0.0378156 | + | 0.0381984i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 60.6102 | − | 34.9933i | 2.21465 | − | 1.27863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.49013 | − | 3.74708i | −0.236828 | − | 0.136733i | 0.376890 | − | 0.926258i | \(-0.376993\pi\) |
−0.613718 | + | 0.789525i | \(0.710327\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.4740 | − | 37.3022i | 1.03765 | − | 1.35937i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 66.3491 | 2.41469 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.6513 | −1.33211 | −0.666057 | − | 0.745901i | \(-0.732019\pi\) | ||||
−0.666057 | + | 0.745901i | \(0.732019\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.10170 | − | 2.75331i | 0.0762868 | − | 0.0999389i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.5513 | − | 17.6388i | −1.10749 | − | 0.639407i | −0.169308 | − | 0.985563i | \(-0.554153\pi\) |
−0.938177 | + | 0.346156i | \(0.887487\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.8942 | + | 23.6103i | −1.48047 | + | 0.854750i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.0817 | + | 4.74750i | 0.653744 | + | 0.171646i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.43130 | + | 11.1393i | 0.232221 | + | 0.402218i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.4694 | + | 33.7219i | −0.702083 | + | 1.21604i | 0.265650 | + | 0.964069i | \(0.414413\pi\) |
−0.967734 | + | 0.251975i | \(0.918920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.12260 | − | 2.55414i | 0.220500 | − | 0.0919853i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.4524i | 1.70674i | 0.521303 | + | 0.853372i | \(0.325446\pi\) | ||||
−0.521303 | + | 0.853372i | \(0.674554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 15.9019i | − | 0.571212i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.18675 | − | 24.6859i | 0.114324 | − | 0.885603i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.6678 | + | 25.4054i | −0.525530 | + | 0.910244i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0967186 | − | 0.167522i | −0.00346086 | − | 0.00599439i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.7499 | − | 5.95699i | 1.52776 | − | 0.212886i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.6432 | + | 36.7444i | −2.27152 | + | 1.31146i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.0786 | + | 11.0150i | 0.680078 | + | 0.392643i | 0.799884 | − | 0.600154i | \(-0.204894\pi\) |
−0.119806 | + | 0.992797i | \(0.538227\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −55.3091 | − | 7.13994i | −1.96906 | − | 0.254189i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.14192 | −0.182826 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.2628 | 0.399953 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.2300 | − | 24.5226i | −0.362821 | − | 0.869727i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.74174 | + | 4.46970i | 0.274227 | + | 0.158325i | 0.630807 | − | 0.775940i | \(-0.282724\pi\) |
−0.356580 | + | 0.934265i | \(0.616057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.27824 | + | 2.47004i | −0.151353 | + | 0.0873838i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.7679 | − | 3.49016i | 0.451132 | − | 0.123319i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.6406 | + | 30.5544i | 0.622522 | + | 1.07824i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.73368 | − | 8.19898i | 0.166840 | − | 0.288976i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.5311 | − | 28.6488i | −1.32116 | − | 1.00849i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 8.93421i | − | 0.314110i | −0.987590 | − | 0.157055i | \(-0.949800\pi\) | ||
0.987590 | − | 0.157055i | \(-0.0502000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1717i | 0.778552i | 0.921121 | + | 0.389276i | \(0.127275\pi\) | ||||
−0.921121 | + | 0.389276i | \(0.872725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.6837 | + | 8.91853i | 0.409764 | + | 0.312787i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.4019 | − | 68.2461i | 1.38019 | − | 2.39056i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.0007 | + | 34.6423i | 0.699737 | + | 1.21198i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −49.3205 | + | 13.4820i | −1.72340 | + | 0.471098i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.83428 | − | 1.05902i | 0.0640167 | − | 0.0369601i | −0.467650 | − | 0.883914i | \(-0.654899\pi\) |
0.531667 | + | 0.846954i | \(0.321566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.3807 | + | 11.7668i | 0.710428 | + | 0.410166i | 0.811219 | − | 0.584742i | \(-0.198804\pi\) |
−0.100792 | + | 0.994908i | \(0.532138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.5211 | − | 30.0147i | −0.435929 | − | 1.04498i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.3293 | 0.533051 | 0.266526 | − | 0.963828i | \(-0.414124\pi\) | ||||
0.266526 | + | 0.963828i | \(0.414124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.88566 | −0.239149 | −0.119574 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119574 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.4165 | − | 1.73196i | −0.465415 | − | 0.0600812i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.32040 | − | 5.38114i | −0.322933 | − | 0.186445i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.6279 | + | 10.1775i | −0.610038 | + | 0.352205i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.16510 | − | 9.19311i | −0.247662 | − | 0.317760i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.1856 | + | 29.7663i | 0.593312 | + | 1.02765i | 0.993783 | + | 0.111337i | \(0.0355134\pi\) |
−0.400470 | + | 0.916310i | \(0.631153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0007 | − | 34.6423i | 0.689681 | − | 1.19456i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.54982 | + | 12.0056i | −0.0533786 | + | 0.413494i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 32.4600i | 1.11666i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 14.3707i | − | 0.493783i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 44.8604 | − | 18.7143i | 1.53961 | − | 0.642272i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50442 | − | 2.60574i | 0.0515709 | − | 0.0893234i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.4800 | − | 49.3288i | −0.975136 | − | 1.68898i | −0.679486 | − | 0.733688i | \(-0.737797\pi\) |
−0.295650 | − | 0.955296i | \(-0.595536\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 45.9509 | + | 12.0648i | 1.57149 | + | 0.412608i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.9801 | − | 7.49405i | 0.443391 | − | 0.255992i | −0.261644 | − | 0.965164i | \(-0.584265\pi\) |
0.705035 | + | 0.709172i | \(0.250931\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.3920 | + | 21.5883i | 1.27580 | + | 0.736583i | 0.976073 | − | 0.217443i | \(-0.0697716\pi\) |
0.299725 | + | 0.954025i | \(0.403105\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.4107 | − | 31.9790i | 0.831913 | − | 1.08984i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.9439 | 1.66607 | 0.833035 | − | 0.553220i | \(-0.186601\pi\) | ||||
0.833035 | + | 0.553220i | \(0.186601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.5522 | 0.698797 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.4903 | + | 18.9829i | −0.492116 | + | 0.644693i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.9482 | − | 6.89830i | −0.405315 | − | 0.234009i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.5257 | − | 23.9749i | 1.40704 | − | 0.812357i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.4711 | − | 30.7796i | 1.03129 | − | 1.04173i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.0979 | − | 22.6863i | −0.442791 | − | 0.766936i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.4280 | + | 24.9901i | −0.487200 | + | 0.843854i | −0.999892 | − | 0.0147181i | \(-0.995315\pi\) |
0.512692 | + | 0.858573i | \(0.328648\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.9331 | + | 5.81241i | −0.469950 | + | 0.196048i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.9613i | − | 0.369294i | −0.982805 | − | 0.184647i | \(-0.940886\pi\) | ||
0.982805 | − | 0.184647i | \(-0.0591143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 23.8707i | − | 0.803313i | −0.915790 | − | 0.401657i | \(-0.868435\pi\) | ||
0.915790 | − | 0.401657i | \(-0.131565\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.09844 | + | 16.2555i | −0.0705384 | + | 0.546421i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.2765 | − | 47.2442i | 0.915854 | − | 1.58631i | 0.110207 | − | 0.993909i | \(-0.464849\pi\) |
0.805647 | − | 0.592397i | \(-0.201818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.4420 | + | 42.3349i | 0.819760 | + | 1.41987i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.7627 | − | 11.7101i | −0.695578 | − | 0.392305i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.8723 | + | 6.27711i | −0.363826 | + | 0.210055i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.7904 | + | 22.3956i | 1.29662 | + | 0.748604i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.12983 | − | 0.791310i | −0.204669 | − | 0.0264211i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.6329 | −0.621442 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.90754 | −0.263438 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.1209 | − | 50.6293i | −0.702858 | − | 1.68484i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.6938 | + | 17.7210i | 1.02029 | + | 0.589068i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.9556 | − | 25.9552i | 1.49273 | − | 0.861827i | 0.492762 | − | 0.870164i | \(-0.335987\pi\) |
0.999965 | + | 0.00833717i | \(0.00265384\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.64750 | − | 4.60092i | −0.154148 | − | 0.152603i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.0141 | + | 46.7897i | 0.895016 | + | 1.55021i | 0.833785 | + | 0.552089i | \(0.186169\pi\) |
0.0612304 | + | 0.998124i | \(0.480498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.648497 | − | 1.12323i | 0.0214621 | − | 0.0371735i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.4080 | + | 8.70809i | 0.377136 | + | 0.287881i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 56.8470i | − | 1.87725i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 26.0348i | − | 0.858808i | −0.903113 | − | 0.429404i | \(-0.858724\pi\) | ||
0.903113 | − | 0.429404i | \(-0.141276\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.2498 | − | 10.1141i | −0.436597 | − | 0.333270i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.172582 | + | 0.298921i | −0.00568060 | + | 0.00983909i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.1251 | − | 24.4653i | −0.464429 | − | 0.804415i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.93002 | − | 11.1595i | 0.0962345 | − | 0.366525i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.1077 | + | 19.1148i | −1.08623 | + | 0.627135i | −0.932570 | − | 0.360989i | \(-0.882439\pi\) |
−0.153659 | + | 0.988124i | \(0.549106\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.6859 | − | 13.6751i | −0.776274 | − | 0.448182i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.0923 | + | 26.5895i | 0.363144 | + | 0.870502i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.5047 | −0.539763 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.6872 | −0.643154 | −0.321577 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321577 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.3103 | + | 5.46190i | 1.38074 | + | 0.178242i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.5374 | − | 15.3214i | −0.865094 | − | 0.499462i | 0.000620548 | − | 1.00000i | \(-0.499802\pi\) |
−0.865715 | + | 0.500537i | \(0.833136\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.21166 | − | 2.43160i | 0.137150 | − | 0.0791838i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −60.3802 | − | 24.4776i | −1.96417 | − | 0.796256i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.8490 | − | 29.1833i | −0.547519 | − | 0.948331i | −0.998444 | − | 0.0557689i | \(-0.982239\pi\) |
0.450925 | − | 0.892562i | \(-0.351094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.4773 | − | 54.5203i | 1.02180 | − | 1.76980i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.34077 | + | 41.3719i | −0.173186 | + | 1.34158i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.8965i | 1.90784i | 0.300054 | + | 0.953922i | \(0.402995\pi\) | ||||
−0.300054 | + | 0.953922i | \(0.597005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 78.5516i | 2.54187i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −35.1695 | + | 14.6715i | −1.13687 | + | 0.474263i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.9524 | − | 24.1663i | 0.450548 | − | 0.780371i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9842 | − | 22.4893i | −0.418846 | − | 0.725462i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.3518 | − | 56.1608i | −0.494705 | − | 1.80976i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.80126 | − | 3.92671i | 0.218940 | − | 0.126405i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.153116 | − | 0.0884018i | −0.00492389 | − | 0.00284281i | 0.497536 | − | 0.867443i | \(-0.334238\pi\) |
−0.502460 | + | 0.864600i | \(0.667572\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.57874 | − | 11.2385i | 0.275589 | − | 0.361033i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.94370 | −0.287017 | −0.143509 | − | 0.989649i | \(-0.545838\pi\) | ||||
−0.143509 | + | 0.989649i | \(0.545838\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.04183 | 0.0654581 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −35.2108 | + | 46.1277i | −1.12765 | + | 1.47727i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.61238 | + | 0.930909i | 0.0515847 | + | 0.0297824i | 0.525571 | − | 0.850750i | \(-0.323852\pi\) |
−0.473986 | + | 0.880532i | \(0.657185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.1203 | + | 5.84294i | −0.323445 | + | 0.186741i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3580 | + | 37.8922i | 0.330705 | + | 1.20981i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.41816 | − | 14.5807i | −0.268498 | − | 0.465052i | 0.699976 | − | 0.714166i | \(-0.253194\pi\) |
−0.968474 | + | 0.249114i | \(0.919861\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.83431 | − | 17.0335i | 0.313347 | − | 0.542733i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.8897 | − | 6.62865i | 0.505774 | − | 0.210992i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6.63136i | − | 0.210865i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.9182i | − | 0.505658i | −0.967511 | − | 0.252829i | \(-0.918639\pi\) | ||
0.967511 | − | 0.252829i | \(-0.0813609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.84440 | + | 22.0340i | −0.0902643 | + | 0.699226i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.0245 | + | 41.6116i | −0.761626 | + | 1.31918i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.40192 | − | 5.89230i | −0.107740 | − | 0.186611i | 0.807114 | − | 0.590395i | \(-0.201028\pi\) |
−0.914854 | + | 0.403784i | \(0.867695\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.1896 | − | 7.77928i | −0.607131 | − | 0.246125i |
(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 | 288.2.s.a.95.4 | ✓ | 24 | |
3.2 | odd | 2 | 864.2.s.a.287.12 | 24 | |||
4.3 | odd | 2 | inner | 288.2.s.a.95.9 | yes | 24 | |
8.3 | odd | 2 | 576.2.s.g.383.4 | 24 | |||
8.5 | even | 2 | 576.2.s.g.383.9 | 24 | |||
9.2 | odd | 6 | inner | 288.2.s.a.191.9 | yes | 24 | |
9.4 | even | 3 | 2592.2.c.c.2591.22 | 24 | |||
9.5 | odd | 6 | 2592.2.c.c.2591.4 | 24 | |||
9.7 | even | 3 | 864.2.s.a.575.11 | 24 | |||
12.11 | even | 2 | 864.2.s.a.287.11 | 24 | |||
24.5 | odd | 2 | 1728.2.s.g.1151.2 | 24 | |||
24.11 | even | 2 | 1728.2.s.g.1151.1 | 24 | |||
36.7 | odd | 6 | 864.2.s.a.575.12 | 24 | |||
36.11 | even | 6 | inner | 288.2.s.a.191.4 | yes | 24 | |
36.23 | even | 6 | 2592.2.c.c.2591.3 | 24 | |||
36.31 | odd | 6 | 2592.2.c.c.2591.21 | 24 | |||
72.5 | odd | 6 | 5184.2.c.m.5183.22 | 24 | |||
72.11 | even | 6 | 576.2.s.g.191.9 | 24 | |||
72.13 | even | 6 | 5184.2.c.m.5183.4 | 24 | |||
72.29 | odd | 6 | 576.2.s.g.191.4 | 24 | |||
72.43 | odd | 6 | 1728.2.s.g.575.2 | 24 | |||
72.59 | even | 6 | 5184.2.c.m.5183.21 | 24 | |||
72.61 | even | 6 | 1728.2.s.g.575.1 | 24 | |||
72.67 | odd | 6 | 5184.2.c.m.5183.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.s.a.95.4 | ✓ | 24 | 1.1 | even | 1 | trivial | |
288.2.s.a.95.9 | yes | 24 | 4.3 | odd | 2 | inner | |
288.2.s.a.191.4 | yes | 24 | 36.11 | even | 6 | inner | |
288.2.s.a.191.9 | yes | 24 | 9.2 | odd | 6 | inner | |
576.2.s.g.191.4 | 24 | 72.29 | odd | 6 | |||
576.2.s.g.191.9 | 24 | 72.11 | even | 6 | |||
576.2.s.g.383.4 | 24 | 8.3 | odd | 2 | |||
576.2.s.g.383.9 | 24 | 8.5 | even | 2 | |||
864.2.s.a.287.11 | 24 | 12.11 | even | 2 | |||
864.2.s.a.287.12 | 24 | 3.2 | odd | 2 | |||
864.2.s.a.575.11 | 24 | 9.7 | even | 3 | |||
864.2.s.a.575.12 | 24 | 36.7 | odd | 6 | |||
1728.2.s.g.575.1 | 24 | 72.61 | even | 6 | |||
1728.2.s.g.575.2 | 24 | 72.43 | odd | 6 | |||
1728.2.s.g.1151.1 | 24 | 24.11 | even | 2 | |||
1728.2.s.g.1151.2 | 24 | 24.5 | odd | 2 | |||
2592.2.c.c.2591.3 | 24 | 36.23 | even | 6 | |||
2592.2.c.c.2591.4 | 24 | 9.5 | odd | 6 | |||
2592.2.c.c.2591.21 | 24 | 36.31 | odd | 6 | |||
2592.2.c.c.2591.22 | 24 | 9.4 | even | 3 | |||
5184.2.c.m.5183.3 | 24 | 72.67 | odd | 6 | |||
5184.2.c.m.5183.4 | 24 | 72.13 | even | 6 | |||
5184.2.c.m.5183.21 | 24 | 72.59 | even | 6 | |||
5184.2.c.m.5183.22 | 24 | 72.5 | odd | 6 |