Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 625.2 | ||
Character | \(\chi\) | \(=\) | 1008.625 |
Dual form | 1008.2.q.l.529.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.64138 | − | 0.553060i | −0.947651 | − | 0.319309i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.263002 | − | 0.455533i | −0.117618 | − | 0.203721i | 0.801205 | − | 0.598390i | \(-0.204193\pi\) |
−0.918823 | + | 0.394669i | \(0.870859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.333150 | − | 2.62469i | 0.125919 | − | 0.992041i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.38825 | + | 1.81556i | 0.796083 | + | 0.605187i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.30526 | − | 3.99283i | 0.695062 | − | 1.20388i | −0.275098 | − | 0.961416i | \(-0.588710\pi\) |
0.970160 | − | 0.242466i | \(-0.0779564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.244554 | − | 0.423580i | 0.0678270 | − | 0.117480i | −0.830118 | − | 0.557588i | \(-0.811727\pi\) |
0.897945 | + | 0.440109i | \(0.145060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.179749 | + | 0.893158i | 0.0464110 | + | 0.230613i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.75579 | + | 4.77318i | 0.668378 | + | 1.15767i | 0.978357 | + | 0.206922i | \(0.0663446\pi\) |
−0.309979 | + | 0.950743i | \(0.600322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.83782 | + | 3.18319i | −0.421624 | + | 0.730274i | −0.996099 | − | 0.0882484i | \(-0.971873\pi\) |
0.574475 | + | 0.818522i | \(0.305206\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.99844 | + | 4.12386i | −0.436095 | + | 0.899901i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0269769 | − | 0.0467253i | −0.00562506 | − | 0.00974289i | 0.863199 | − | 0.504864i | \(-0.168457\pi\) |
−0.868824 | + | 0.495121i | \(0.835124\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.36166 | − | 4.09051i | 0.472332 | − | 0.818103i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.91591 | − | 4.30087i | −0.561167 | − | 0.827703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.28471 | − | 5.68929i | −0.609956 | − | 1.05647i | −0.991247 | − | 0.132019i | \(-0.957854\pi\) |
0.381292 | − | 0.924455i | \(-0.375479\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.07640 | −1.09135 | −0.545676 | − | 0.837996i | \(-0.683727\pi\) | ||||
−0.545676 | + | 0.837996i | \(0.683727\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.99208 | + | 5.27879i | −1.04309 | + | 0.918920i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.28325 | + | 0.538539i | −0.216909 | + | 0.0910297i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.223731 | − | 0.387513i | 0.0367811 | − | 0.0637068i | −0.847049 | − | 0.531515i | \(-0.821623\pi\) |
0.883830 | + | 0.467808i | \(0.154956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.635671 | + | 0.560002i | −0.101789 | + | 0.0896721i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.52284 | − | 4.36968i | 0.394001 | − | 0.682430i | −0.598972 | − | 0.800770i | \(-0.704424\pi\) |
0.992973 | + | 0.118340i | \(0.0377574\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.84893 | − | 4.93449i | −0.434458 | − | 0.752503i | 0.562794 | − | 0.826598i | \(-0.309727\pi\) |
−0.997251 | + | 0.0740947i | \(0.976393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.198934 | − | 1.56542i | 0.0296553 | − | 0.233360i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.19621 | 1.34140 | 0.670702 | − | 0.741726i | \(-0.265993\pi\) | ||||
0.670702 | + | 0.741726i | \(0.265993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77802 | − | 1.74883i | −0.968289 | − | 0.249833i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.88345 | − | 9.35871i | −0.263736 | − | 1.31048i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.37138 | − | 7.57145i | −0.600455 | − | 1.04002i | −0.992752 | − | 0.120180i | \(-0.961653\pi\) |
0.392297 | − | 0.919839i | \(-0.371680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.42515 | −0.327008 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.77705 | − | 4.20840i | 0.632735 | − | 0.557416i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.63076 | 0.863252 | 0.431626 | − | 0.902053i | \(-0.357940\pi\) | ||||
0.431626 | + | 0.902053i | \(0.357940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.465625 | −0.0596171 | −0.0298086 | − | 0.999556i | \(-0.509490\pi\) | ||||
−0.0298086 | + | 0.999556i | \(0.509490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.56094 | − | 5.66357i | 0.700612 | − | 0.713542i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.257273 | −0.0319108 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.19358 | −0.634496 | −0.317248 | − | 0.948343i | \(-0.602759\pi\) | ||||
−0.317248 | + | 0.948343i | \(0.602759\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0184374 | + | 0.0916137i | 0.00221960 | + | 0.0110290i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.76328 | −0.209263 | −0.104632 | − | 0.994511i | \(-0.533366\pi\) | ||||
−0.104632 | + | 0.994511i | \(0.533366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.23776 | − | 9.07207i | −0.613034 | − | 1.06181i | −0.990726 | − | 0.135875i | \(-0.956616\pi\) |
0.377692 | − | 0.925931i | \(-0.376718\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.13868 | + | 5.40794i | −0.708834 | + | 0.624456i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.71195 | − | 7.38081i | −1.10678 | − | 0.841121i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.3702 | −1.84179 | −0.920895 | − | 0.389812i | \(-0.872540\pi\) | ||||
−0.920895 | + | 0.389812i | \(0.872540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.40747 | + | 8.67203i | 0.267497 | + | 0.963559i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.49251 | − | 7.78126i | −0.493117 | − | 0.854104i | 0.506851 | − | 0.862034i | \(-0.330809\pi\) |
−0.999969 | + | 0.00792925i | \(0.997476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44956 | − | 2.51071i | 0.157227 | − | 0.272325i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.24494 | + | 11.1549i | 0.240683 | + | 1.19593i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.05145 | + | 12.2135i | −0.747452 | + | 1.29463i | 0.201588 | + | 0.979470i | \(0.435390\pi\) |
−0.949040 | + | 0.315155i | \(0.897944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03029 | − | 0.782994i | −0.108004 | − | 0.0820801i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.97367 | + | 3.36061i | 1.03422 | + | 0.348479i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.93340 | 0.198363 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.22413 | + | 9.04847i | 0.530430 | + | 0.918732i | 0.999370 | + | 0.0355020i | \(0.0113030\pi\) |
−0.468939 | + | 0.883230i | \(0.655364\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.7548 | − | 5.35052i | 1.28190 | − | 0.537748i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.98254 | − | 8.63001i | 0.495781 | − | 0.858718i | −0.504207 | − | 0.863583i | \(-0.668215\pi\) |
0.999988 | + | 0.00486475i | \(0.00154850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.82553 | + | 10.0901i | 0.574006 | + | 0.994208i | 0.996149 | + | 0.0876783i | \(0.0279448\pi\) |
−0.422143 | + | 0.906529i | \(0.638722\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.40415 | − | 0.174231i | 0.234621 | − | 0.0170032i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.45556 | + | 4.25316i | −0.237388 | + | 0.411168i | −0.959964 | − | 0.280123i | \(-0.909625\pi\) |
0.722576 | + | 0.691292i | \(0.242958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.76353 | − | 16.9109i | −0.935177 | − | 1.61977i | −0.774319 | − | 0.632796i | \(-0.781907\pi\) |
−0.160858 | − | 0.986978i | \(-0.551426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.581545 | + | 0.512319i | −0.0551978 | + | 0.0486272i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.48658 | − | 9.50304i | 0.516134 | − | 0.893971i | −0.483690 | − | 0.875239i | \(-0.660704\pi\) |
0.999825 | − | 0.0187317i | \(-0.00596282\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0141899 | + | 0.0245777i | −0.00132322 | + | 0.00229188i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.35309 | − | 0.567611i | 0.125093 | − | 0.0524757i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.4462 | − | 5.64293i | 1.23261 | − | 0.517287i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.12844 | − | 8.88272i | −0.466222 | − | 0.807520i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.55763 | + | 5.77702i | −0.591281 | + | 0.520897i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.11451 | −0.457456 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6107 | 1.47396 | 0.736979 | − | 0.675915i | \(-0.236252\pi\) | ||||
0.736979 | + | 0.675915i | \(0.236252\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.94710 | + | 9.67500i | 0.171433 | + | 0.851836i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.90848 | + | 5.03763i | 0.254115 | + | 0.440140i | 0.964655 | − | 0.263517i | \(-0.0848825\pi\) |
−0.710540 | + | 0.703657i | \(0.751549\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.74263 | + | 5.88418i | 0.671371 | + | 0.510223i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.19230 | + | 2.45943i | −0.102617 | + | 0.211674i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.61313 | − | 7.99017i | 0.394126 | − | 0.682647i | −0.598863 | − | 0.800852i | \(-0.704381\pi\) |
0.992989 | + | 0.118205i | \(0.0377139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.88477 | + | 11.9248i | −0.583959 | + | 1.01145i | 0.411046 | + | 0.911615i | \(0.365164\pi\) |
−0.995004 | + | 0.0998314i | \(0.968170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0945 | − | 5.08606i | −1.27118 | − | 0.428323i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.12752 | − | 1.95292i | −0.0942880 | − | 0.163312i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.72777 | + | 2.99259i | −0.143484 | + | 0.248521i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.1581 | + | 6.61915i | 0.837826 | + | 0.545938i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.15043 | + | 7.18875i | 0.340016 | + | 0.588926i | 0.984435 | − | 0.175747i | \(-0.0562340\pi\) |
−0.644419 | + | 0.764673i | \(0.722901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.24894 | + | 12.5555i | −0.589911 | + | 1.02176i | 0.404333 | + | 0.914612i | \(0.367504\pi\) |
−0.994244 | + | 0.107143i | \(0.965830\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.08447 | + | 16.4028i | −0.168520 | + | 1.32609i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.59811 | + | 2.76800i | 0.128363 | + | 0.222331i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4887 | −0.996705 | −0.498352 | − | 0.866975i | \(-0.666061\pi\) | ||||
−0.498352 | + | 0.866975i | \(0.666061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.98762 | + | 14.8452i | 0.236934 | + | 1.17730i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.131627 | + | 0.0552394i | −0.0103736 | + | 0.00435348i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.48448 | − | 4.30325i | 0.194600 | − | 0.337057i | −0.752169 | − | 0.658970i | \(-0.770993\pi\) |
0.946769 | + | 0.321913i | \(0.104326\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.98060 | + | 1.34126i | 0.309889 | + | 0.104417i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.0088 | − | 17.3357i | 0.774504 | − | 1.34148i | −0.160569 | − | 0.987025i | \(-0.551333\pi\) |
0.935073 | − | 0.354456i | \(-0.115334\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.38039 | + | 11.0512i | 0.490799 | + | 0.850089i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.1684 | + | 4.26558i | −0.777600 | + | 0.326197i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.05485 | 0.688427 | 0.344214 | − | 0.938891i | \(-0.388146\pi\) | ||||
0.344214 | + | 0.938891i | \(0.388146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.94956 | − | 7.56138i | −0.752116 | − | 0.571587i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.8836 | − | 3.66721i | −0.818061 | − | 0.275644i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.69175 | + | 13.3225i | 0.574908 | + | 0.995770i | 0.996052 | + | 0.0887763i | \(0.0282956\pi\) |
−0.421143 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.54973 | −0.709826 | −0.354913 | − | 0.934899i | \(-0.615489\pi\) | ||||
−0.354913 | + | 0.934899i | \(0.615489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.764266 | + | 0.257518i | 0.0564962 | + | 0.0190363i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.235367 | −0.0173045 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.4113 | 1.85826 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.2599 | + | 6.22053i | −0.891776 | + | 0.452477i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0433 | 0.799063 | 0.399531 | − | 0.916720i | \(-0.369173\pi\) | ||||
0.399531 | + | 0.916720i | \(0.369173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.6991 | 1.92185 | 0.960923 | − | 0.276817i | \(-0.0892796\pi\) | ||||
0.960923 | + | 0.276817i | \(0.0892796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.422282 | + | 0.142287i | 0.0302403 | + | 0.0101894i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.8386 | 0.914715 | 0.457357 | − | 0.889283i | \(-0.348796\pi\) | ||||
0.457357 | + | 0.889283i | \(0.348796\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1408 | − | 17.5644i | −0.718864 | − | 1.24511i | −0.961450 | − | 0.274979i | \(-0.911329\pi\) |
0.242586 | − | 0.970130i | \(-0.422004\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.52463 | + | 2.87236i | 0.601281 | + | 0.202601i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0269 | + | 6.72597i | −1.12487 | + | 0.472071i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.65405 | −0.185367 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0204052 | − | 0.160570i | 0.00141826 | − | 0.0111604i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.47329 | + | 14.6762i | 0.586109 | + | 1.01517i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.77903 | + | 8.27752i | −0.329002 | + | 0.569848i | −0.982314 | − | 0.187241i | \(-0.940046\pi\) |
0.653312 | + | 0.757088i | \(0.273379\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.89422 | + | 0.975202i | 0.198308 | + | 0.0668197i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.49855 | + | 2.59556i | −0.102200 | + | 0.177016i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.02435 | + | 15.9487i | −0.137422 | + | 1.08267i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.57975 | + | 17.7875i | 0.241897 | + | 1.20197i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.69576 | 0.181337 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.9155 | − | 20.6383i | −0.797921 | − | 1.38204i | −0.920968 | − | 0.389639i | \(-0.872600\pi\) |
0.123046 | − | 0.992401i | \(-0.460734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.0668 | − | 5.48143i | 0.871121 | − | 0.365429i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.33567 | + | 2.31345i | −0.0886514 | + | 0.153549i | −0.906941 | − | 0.421257i | \(-0.861589\pi\) |
0.818290 | + | 0.574806i | \(0.194922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.16258 | − | 5.47775i | −0.208989 | − | 0.361980i | 0.742407 | − | 0.669949i | \(-0.233684\pi\) |
−0.951396 | + | 0.307969i | \(0.900351\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.8590 | + | 17.4860i | 0.780262 | + | 1.15049i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.63381 | − | 8.02600i | 0.303571 | − | 0.525801i | −0.673371 | − | 0.739305i | \(-0.735154\pi\) |
0.976942 | + | 0.213504i | \(0.0684877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.41862 | − | 4.18918i | −0.157774 | − | 0.273272i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 26.8697 | + | 9.05369i | 1.74537 | + | 0.588100i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.69219 | + | 2.93096i | −0.109459 | + | 0.189588i | −0.915551 | − | 0.402202i | \(-0.868245\pi\) |
0.806092 | + | 0.591790i | \(0.201578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.57982 | + | 11.3966i | −0.423844 | + | 0.734119i | −0.996312 | − | 0.0858082i | \(-0.972653\pi\) |
0.572468 | + | 0.819927i | \(0.305986\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.844585 | − | 15.5656i | 0.0541801 | − | 0.998531i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.985984 | + | 3.54756i | 0.0629922 | + | 0.226645i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.898890 | + | 1.55692i | 0.0571950 | + | 0.0990647i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.07041 | + | 15.2566i | 0.194579 | + | 0.966849i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.30235 | 0.145323 | 0.0726614 | − | 0.997357i | \(-0.476851\pi\) | ||||
0.0726614 | + | 0.997357i | \(0.476851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.248755 | −0.0156391 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.76785 | + | 3.31933i | −0.235952 | + | 0.207865i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.5661 | + | 25.2293i | 0.908610 | + | 1.57376i | 0.815997 | + | 0.578056i | \(0.196189\pi\) |
0.0926132 | + | 0.995702i | \(0.470478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.942567 | − | 0.716324i | −0.0585683 | − | 0.0445102i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.48454 | − | 19.5510i | 0.153789 | − | 1.21018i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.35919 | + | 2.35418i | −0.0838110 | + | 0.145165i | −0.904884 | − | 0.425658i | \(-0.860043\pi\) |
0.821073 | + | 0.570823i | \(0.193376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.29936 | + | 3.98261i | −0.141249 | + | 0.244650i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.3289 | − | 16.1471i | 1.12171 | − | 0.988184i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.80840 | + | 4.86428i | 0.171231 | + | 0.296581i | 0.938850 | − | 0.344325i | \(-0.111892\pi\) |
−0.767620 | + | 0.640906i | \(0.778559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.25164 | − | 12.5602i | 0.440506 | − | 0.762978i | −0.557221 | − | 0.830364i | \(-0.688133\pi\) |
0.997727 | + | 0.0673860i | \(0.0214659\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.25806 | + | 1.85500i | 0.0761412 | + | 0.112270i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.8885 | − | 18.8594i | −0.656600 | − | 1.13726i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.873953 | − | 1.51373i | 0.0525108 | − | 0.0909513i | −0.838575 | − | 0.544786i | \(-0.816611\pi\) |
0.891086 | + | 0.453835i | \(0.149944\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.5119 | − | 11.0321i | −0.868808 | − | 0.660473i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.35657 | + | 9.27786i | 0.319546 | + | 0.553471i | 0.980393 | − | 0.197050i | \(-0.0631361\pi\) |
−0.660847 | + | 0.750521i | \(0.729803\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5967 | 0.748793 | 0.374397 | − | 0.927269i | \(-0.377850\pi\) | ||||
0.374397 | + | 0.927269i | \(0.377850\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.17344 | − | 1.06929i | −0.187978 | − | 0.0633390i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6286 | − | 8.07743i | −0.627386 | − | 0.476796i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.68881 | + | 11.5854i | −0.393459 | + | 0.681491i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.57044 | − | 17.7412i | −0.209303 | − | 1.04001i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.57575 | + | 2.72928i | −0.0920562 | + | 0.159446i | −0.908376 | − | 0.418154i | \(-0.862677\pi\) |
0.816320 | + | 0.577600i | \(0.196011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.74391 | − | 3.02053i | −0.101534 | − | 0.175862i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.8946 | + | 1.72809i | −1.38650 | + | 0.100274i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.0263892 | −0.00152613 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.9006 | + | 5.83364i | −0.801220 | + | 0.336245i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9511 | + | 11.4095i | −0.744024 | + | 0.655457i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.122460 | + | 0.212107i | 0.00701206 | + | 0.0121452i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.3884 | 1.16363 | 0.581813 | − | 0.813322i | \(-0.302343\pi\) | ||||
0.581813 | + | 0.813322i | \(0.302343\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.98146 | − | 19.7836i | −0.226497 | − | 1.12545i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.7014 | −1.28728 | −0.643640 | − | 0.765328i | \(-0.722577\pi\) | ||||
−0.643640 | + | 0.765328i | \(0.722577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.7078 | −0.944380 | −0.472190 | − | 0.881497i | \(-0.656536\pi\) | ||||
−0.472190 | + | 0.881497i | \(0.656536\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.04248 | − | 1.04366i | −0.227768 | − | 0.0588036i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.3280 | 0.580080 | 0.290040 | − | 0.957015i | \(-0.406331\pi\) | ||||
0.290040 | + | 0.957015i | \(0.406331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.2884 | −1.69583 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.38276 | − | 5.62297i | 0.356251 | − | 0.313844i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.2586 | −1.12722 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.15511 | − | 2.00070i | −0.0640738 | − | 0.110979i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.67289 | + | 33.1571i | 0.369012 | + | 1.83359i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.06371 | − | 24.1372i | 0.168908 | − | 1.33073i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.6315 | 1.24394 | 0.621970 | − | 0.783041i | \(-0.286332\pi\) | ||||
0.621970 | + | 0.783041i | \(0.286332\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.23788 | − | 0.519281i | 0.0678354 | − | 0.0284564i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.36592 | + | 2.36585i | 0.0746283 | + | 0.129260i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.78253 | − | 11.7477i | 0.369468 | − | 0.639938i | −0.620014 | − | 0.784590i | \(-0.712873\pi\) |
0.989482 | + | 0.144653i | \(0.0462066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.2613 | + | 12.5637i | −0.774568 | + | 0.682366i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.0077 | + | 24.2620i | −0.758558 | + | 1.31386i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.84824 | + | 17.2076i | −0.369770 | + | 0.929123i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0368840 | − | 0.0324934i | 0.00198577 | − | 0.00174939i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.0262 | 1.77294 | 0.886470 | − | 0.462786i | \(-0.153150\pi\) | ||||
0.886470 | + | 0.462786i | \(0.153150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.1773 | − | 17.6276i | −0.544778 | − | 0.943584i | −0.998621 | − | 0.0525019i | \(-0.983280\pi\) |
0.453842 | − | 0.891082i | \(-0.350053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.53486 | + | 0.183325i | −0.135301 | + | 0.00978514i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.75381 | − | 4.76975i | 0.146571 | − | 0.253868i | −0.783387 | − | 0.621534i | \(-0.786510\pi\) |
0.929958 | + | 0.367666i | \(0.119843\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.463748 | + | 0.803234i | 0.0246132 | + | 0.0426312i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.1912 | + | 1.82563i | −1.33326 | + | 0.0966224i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4656 | − | 18.1270i | 0.552354 | − | 0.956704i | −0.445751 | − | 0.895157i | \(-0.647063\pi\) |
0.998104 | − | 0.0615472i | \(-0.0196035\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.74486 | + | 4.75424i | 0.144467 | + | 0.250223i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.50504 | + | 17.4163i | 0.183967 | + | 0.914116i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.75509 | + | 4.77195i | −0.144208 | + | 0.249775i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.14319 | − | 3.71211i | 0.111873 | − | 0.193770i | −0.804652 | − | 0.593746i | \(-0.797648\pi\) |
0.916526 | + | 0.399976i | \(0.130982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.9586 | − | 5.85552i | 0.726655 | − | 0.304826i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.3290 | + | 8.95110i | −1.10735 | + | 0.464718i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.64461 | + | 9.77675i | 0.292267 | + | 0.506221i | 0.974345 | − | 0.225058i | \(-0.0722571\pi\) |
−0.682079 | + | 0.731279i | \(0.738924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.39485 | + | 2.82863i | 0.433508 | + | 0.146070i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.21316 | −0.165486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.5828 | 1.05727 | 0.528634 | − | 0.848850i | \(-0.322705\pi\) | ||||
0.528634 | + | 0.848850i | \(0.322705\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.2644 | − | 9.18670i | −1.39680 | − | 0.470649i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.8108 | − | 18.7248i | −0.552405 | − | 0.956793i | −0.998100 | − | 0.0616083i | \(-0.980377\pi\) |
0.445696 | − | 0.895184i | \(-0.352956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.807939 | + | 6.36528i | −0.0411764 | + | 0.324405i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.15492 | − | 16.9572i | 0.109541 | − | 0.861983i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.34241 | − | 12.7174i | 0.372275 | − | 0.644799i | −0.617640 | − | 0.786461i | \(-0.711911\pi\) |
0.989915 | + | 0.141662i | \(0.0452446\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.148685 | − | 0.257531i | 0.00751934 | − | 0.0130239i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.98780 | − | 9.87723i | −0.100271 | − | 0.498240i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.30539 | + | 7.45716i | 0.216628 | + | 0.375210i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.13424 | + | 5.42866i | −0.157303 | + | 0.272457i | −0.933895 | − | 0.357547i | \(-0.883613\pi\) |
0.776592 | + | 0.630003i | \(0.216947\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.45428 | − | 13.9403i | −0.473306 | − | 0.697888i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6951 | − | 25.4526i | −0.733836 | − | 1.27104i | −0.955232 | − | 0.295857i | \(-0.904395\pi\) |
0.221396 | − | 0.975184i | \(-0.428939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.48601 | + | 2.57384i | −0.0740232 | + | 0.128212i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.31723 | − | 3.37744i | 0.164834 | − | 0.167827i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.03152 | − | 1.78664i | −0.0511303 | − | 0.0885603i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.63285 | −0.0807392 | −0.0403696 | − | 0.999185i | \(-0.512854\pi\) | ||||
−0.0403696 | + | 0.999185i | \(0.512854\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.9909 | + | 10.5636i | −0.591469 | + | 0.521062i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.20904 | − | 17.4037i | 0.108700 | − | 0.856381i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.36308 | + | 4.09298i | −0.115999 | + | 0.200916i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.8956 | − | 15.7654i | 0.876353 | − | 0.772034i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.01823 | − | 15.6200i | 0.440569 | − | 0.763088i | −0.557162 | − | 0.830404i | \(-0.688110\pi\) |
0.997732 | + | 0.0673151i | \(0.0214433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8278 | + | 29.1465i | 0.820135 | + | 1.42052i | 0.905581 | + | 0.424172i | \(0.139435\pi\) |
−0.0854466 | + | 0.996343i | \(0.527232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.9628 | + | 16.6963i | 1.06787 | + | 0.811801i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.0330 | 1.26279 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.155123 | + | 1.22212i | −0.00750691 | + | 0.0591426i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.770605 | + | 3.82907i | 0.0372051 | + | 0.184869i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.1545 | + | 19.3202i | 0.537295 | + | 0.930622i | 0.999048 | + | 0.0436135i | \(0.0138870\pi\) |
−0.461754 | + | 0.887008i | \(0.652780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.32414 | 0.351976 | 0.175988 | − | 0.984392i | \(-0.443688\pi\) | ||||
0.175988 | + | 0.984392i | \(0.443688\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.49101 | − | 3.95641i | 0.215327 | − | 0.189695i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.198314 | 0.00948664 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.6728 | 1.17757 | 0.588785 | − | 0.808289i | \(-0.299606\pi\) | ||||
0.588785 | + | 0.808289i | \(0.299606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.0125 | − | 16.4826i | −0.619643 | − | 0.784884i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.5363 | −1.45082 | −0.725412 | − | 0.688315i | \(-0.758351\pi\) | ||||
−0.725412 | + | 0.688315i | \(0.758351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.41819 | 0.351656 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.83661 | − | 14.0949i | −0.134167 | − | 0.666666i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.4782 | −1.95748 | −0.978738 | − | 0.205116i | \(-0.934243\pi\) | ||||
−0.978738 | + | 0.205116i | \(0.934243\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.6316 | − | 20.1465i | −0.547710 | − | 0.948662i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.8422 | − | 16.5993i | 0.885285 | − | 0.779903i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0857103 | + | 0.675262i | −0.00401816 | + | 0.0316568i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.6289 | −0.543978 | −0.271989 | − | 0.962300i | \(-0.587681\pi\) | ||||
−0.271989 | + | 0.962300i | \(0.587681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.4932 | − | 25.7705i | 0.583131 | − | 1.20286i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.60886 | − | 9.71483i | −0.261231 | − | 0.452465i | 0.705339 | − | 0.708871i | \(-0.250795\pi\) |
−0.966569 | + | 0.256406i | \(0.917462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9362 | − | 34.5305i | 0.926514 | − | 1.60477i | 0.137405 | − | 0.990515i | \(-0.456124\pi\) |
0.789108 | − | 0.614254i | \(-0.210543\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.09223 | − | 5.42718i | −0.0506508 | − | 0.251680i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7818 | + | 20.4067i | −0.545198 | + | 0.944311i | 0.453397 | + | 0.891309i | \(0.350212\pi\) |
−0.998594 | + | 0.0530016i | \(0.983121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.73024 | + | 13.6315i | −0.0798950 | + | 0.629446i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.4986 | + | 6.90699i | 0.944528 | + | 0.318257i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.2701 | −1.20790 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.68059 | + | 15.0352i | 0.398293 | + | 0.689864i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.30650 | − | 26.0190i | 0.151394 | − | 1.19133i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.11485 | − | 12.3233i | 0.325086 | − | 0.563065i | −0.656444 | − | 0.754375i | \(-0.727940\pi\) |
0.981530 | + | 0.191310i | \(0.0612735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.109428 | − | 0.189536i | −0.00498951 | − | 0.00864208i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.246600 | − | 0.0178713i | 0.0112207 | − | 0.000813173i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.74792 | − | 4.75953i | 0.124776 | − | 0.216119i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.9818 | + | 24.2171i | 0.633574 | + | 1.09738i | 0.986815 | + | 0.161850i | \(0.0517460\pi\) |
−0.353242 | + | 0.935532i | \(0.614921\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.45794 | + | 5.68920i | −0.292038 | + | 0.257275i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.2543 | + | 29.8853i | −0.778676 | + | 1.34871i | 0.154030 | + | 0.988066i | \(0.450775\pi\) |
−0.932705 | + | 0.360639i | \(0.882558\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.1040 | − | 31.3570i | 0.815362 | − | 1.41225i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.79187 | − | 4.40302i | −0.260325 | − | 0.197901i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.587437 | + | 4.62808i | −0.0263502 | + | 0.207598i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1436 | + | 22.7654i | 0.588390 | + | 1.01912i | 0.994443 | + | 0.105272i | \(0.0335712\pi\) |
−0.406054 | + | 0.913849i | \(0.633095\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.0159 | + | 22.9191i | −1.16231 | + | 1.02395i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.09068 | −0.271570 | −0.135785 | − | 0.990738i | \(-0.543356\pi\) | ||||
−0.135785 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.24167 | −0.233251 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.36068 | − | 21.6679i | −0.193665 | − | 0.962304i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.08615 | + | 7.07742i | 0.181116 | + | 0.313701i | 0.942261 | − | 0.334880i | \(-0.108696\pi\) |
−0.761145 | + | 0.648582i | \(0.775363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.5564 | + | 10.7252i | −1.13055 | + | 0.474453i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.0494 | − | 1.37768i | 0.841051 | − | 0.0608260i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.06425 | − | 5.30744i | 0.135027 | − | 0.233874i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1996 | − | 36.7189i | 0.932360 | − | 1.61489i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.8624 | − | 5.00788i | −0.652389 | − | 0.219821i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0485 | + | 22.6007i | 0.571666 | + | 0.990155i | 0.996395 | + | 0.0848346i | \(0.0270362\pi\) |
−0.424729 | + | 0.905321i | \(0.639630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6655 | + | 23.6694i | −0.597553 | + | 1.03499i | 0.395628 | + | 0.918411i | \(0.370527\pi\) |
−0.993181 | + | 0.116581i | \(0.962807\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.1491 | + | 17.9138i | 0.530230 | + | 0.781822i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.7453 | − | 29.0037i | −0.729437 | − | 1.26342i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4985 | − | 19.9161i | 0.499937 | − | 0.865916i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.8359 | + | 12.0386i | 0.687220 | + | 0.522429i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.23394 | − | 2.13725i | −0.0534478 | − | 0.0925744i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.58327 | 0.111685 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.25693 | − | 26.1213i | −0.226853 | − | 1.12722i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.6079 | + | 23.0320i | −0.973790 | + | 0.992057i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.79086 | + | 10.0301i | −0.248969 | + | 0.431226i | −0.963240 | − | 0.268643i | \(-0.913425\pi\) |
0.714271 | + | 0.699869i | \(0.246758\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.6747 | + | 5.28157i | 0.672667 | + | 0.226654i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.13566 | + | 8.89522i | −0.219987 | + | 0.381029i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3651 | − | 35.2734i | −0.870750 | − | 1.50818i | −0.861222 | − | 0.508228i | \(-0.830301\pi\) |
−0.00952755 | − | 0.999955i | \(-0.503033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.11203 | − | 0.845370i | −0.0474602 | − | 0.0360795i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.1468 | 1.02869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.45372 | + | 42.9667i | −0.231916 | + | 1.82713i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.386326 | + | 0.130172i | 0.0163986 | + | 0.00552549i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0085 | + | 17.3353i | 0.424075 | + | 0.734520i | 0.996334 | − | 0.0855533i | \(-0.0272658\pi\) |
−0.572258 | + | 0.820074i | \(0.693932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.78687 | −0.117872 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.7095 | − | 14.0540i | −1.76098 | − | 0.593359i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.9328 | −1.05079 | −0.525396 | − | 0.850858i | \(-0.676083\pi\) | ||||
−0.525396 | + | 0.850858i | \(0.676083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.77193 | −0.242827 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.5635 | − | 3.42978i | 0.989572 | − | 0.144037i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.80025 | −0.410848 | −0.205424 | − | 0.978673i | \(-0.565857\pi\) | ||||
−0.205424 | + | 0.978673i | \(0.565857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.7895 | 1.70699 | 0.853494 | − | 0.521103i | \(-0.174479\pi\) | ||||
0.853494 | + | 0.521103i | \(0.174479\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.1262 | − | 6.10759i | −0.757232 | − | 0.255148i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.254841 | −0.0106276 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2505 | − | 17.7544i | −0.426734 | − | 0.739125i | 0.569846 | − | 0.821751i | \(-0.307003\pi\) |
−0.996581 | + | 0.0826259i | \(0.973669\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −43.8234 | − | 14.7662i | −1.82124 | − | 0.613663i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.9201 | + | 9.19914i | −0.909399 | + | 0.381645i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.3086 | −1.66941 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.614432 | − | 0.467095i | −0.0254036 | − | 0.0193120i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.2916 | + | 33.4141i | 0.796251 | + | 1.37915i | 0.922042 | + | 0.387090i | \(0.126520\pi\) |
−0.125791 | + | 0.992057i | \(0.540147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.1673 | − | 19.3423i | 0.460141 | − | 0.796987i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.0731 | − | 7.10053i | −0.866830 | − | 0.292077i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.26539 | + | 2.19172i | −0.0519634 | + | 0.0900032i | −0.890837 | − | 0.454323i | \(-0.849881\pi\) |
0.838874 | + | 0.544326i | \(0.183215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.10693 | − | 4.64109i | −0.250360 | − | 0.190266i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.93076 | + | 34.4384i | 0.283657 | + | 1.40947i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.0218 | 0.654634 | 0.327317 | − | 0.944915i | \(-0.393855\pi\) | ||||
0.327317 | + | 0.944915i | \(0.393855\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1601 | − | 38.3824i | −0.903929 | − | 1.56565i | −0.822349 | − | 0.568983i | \(-0.807337\pi\) |
−0.0815796 | − | 0.996667i | \(-0.525996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.4036 | − | 9.42926i | −0.505112 | − | 0.383989i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.69758 | + | 4.67235i | −0.109672 | + | 0.189958i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.79607 | − | 8.30704i | −0.194666 | − | 0.337172i | 0.752125 | − | 0.659021i | \(-0.229029\pi\) |
−0.946791 | + | 0.321849i | \(0.895696\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.0261 | − | 2.17602i | 1.21672 | − | 0.0881767i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.24897 | − | 3.89533i | 0.0909835 | − | 0.157588i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.2371 | + | 19.4632i | 0.453861 | + | 0.786110i | 0.998622 | − | 0.0524815i | \(-0.0167131\pi\) |
−0.544761 | + | 0.838591i | \(0.683380\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.35630 | + | 1.46785i | 0.175663 | + | 0.0591893i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7056 | − | 20.2746i | 0.471248 | − | 0.816226i | −0.528211 | − | 0.849113i | \(-0.677137\pi\) |
0.999459 | + | 0.0328875i | \(0.0104703\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.98843 | − | 13.8364i | 0.321082 | − | 0.556131i | −0.659629 | − | 0.751591i | \(-0.729287\pi\) |
0.980712 | + | 0.195460i | \(0.0626201\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.122297 | + | 0.252271i | −0.00490762 | + | 0.0101233i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.7074 | + | 22.5768i | 1.19020 | + | 0.904521i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4632 | − | 18.1227i | −0.418527 | − | 0.724910i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.79107 | − | 28.7754i | −0.231273 | − | 1.14918i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.46622 | 0.0983348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.882517 | 0.0351324 | 0.0175662 | − | 0.999846i | \(-0.494408\pi\) | ||||
0.0175662 | + | 0.999846i | \(0.494408\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.4222 | − | 10.9435i | 0.493736 | − | 0.434963i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.36864 | − | 7.56671i | −0.173364 | − | 0.300276i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.39836 | + | 2.44335i | −0.0950265 | + | 0.0968090i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.21116 | − | 3.20135i | −0.166591 | − | 0.126644i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.2141 | + | 35.0118i | −0.798408 | + | 1.38288i | 0.122244 | + | 0.992500i | \(0.460991\pi\) |
−0.920652 | + | 0.390384i | \(0.872342\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.99047 | + | 5.17964i | −0.117932 | + | 0.204265i | −0.918948 | − | 0.394378i | \(-0.870960\pi\) |
0.801016 | + | 0.598643i | \(0.204293\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.89519 | − | 3.43152i | 0.153373 | − | 0.135116i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.4743 | + | 28.5343i | 0.647672 | + | 1.12180i | 0.983677 | + | 0.179941i | \(0.0575906\pi\) |
−0.336005 | + | 0.941860i | \(0.609076\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2856 | − | 26.4755i | 0.600014 | − | 1.03925i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.1433 | − | 25.0582i | 0.475933 | − | 0.982109i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.0166 | − | 22.5455i | −0.509380 | − | 0.882272i | −0.999941 | − | 0.0108653i | \(-0.996541\pi\) |
0.490561 | − | 0.871407i | \(-0.336792\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.52987 | − | 2.64982i | 0.0597771 | − | 0.103537i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.96183 | − | 31.1759i | 0.154566 | − | 1.21629i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.91651 | − | 8.51565i | −0.191520 | − | 0.331722i | 0.754234 | − | 0.656606i | \(-0.228008\pi\) |
−0.945754 | + | 0.324883i | \(0.894675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.51520 | −0.214516 | −0.107258 | − | 0.994231i | \(-0.534207\pi\) | ||||
−0.107258 | + | 0.994231i | \(0.534207\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.42477 | − | 1.49092i | −0.171844 | − | 0.0579024i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.644111 | − | 5.07458i | 0.0249776 | − | 0.196784i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.177222 | + | 0.306958i | −0.00686208 | + | 0.0118855i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.14366 | + | 40.4652i | 0.314852 | + | 1.56447i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.07339 | + | 1.85916i | −0.0414376 | + | 0.0717720i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6176 | + | 33.9788i | 0.756205 | + | 1.30978i | 0.944773 | + | 0.327725i | \(0.106282\pi\) |
−0.188569 | + | 0.982060i | \(0.560385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.4792 | + | 1.77037i | −0.942203 | + | 0.0681415i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.1632 | −1.42830 | −0.714149 | − | 0.699994i | \(-0.753186\pi\) | ||||
−0.714149 | + | 0.699994i | \(0.753186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.4899 | − | 10.6973i | 0.978211 | − | 0.410523i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.47181 | − | 3.05854i | 0.133040 | − | 0.117203i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.10586 | + | 8.84360i | 0.195370 | + | 0.338391i | 0.947022 | − | 0.321169i | \(-0.104076\pi\) |
−0.751652 | + | 0.659560i | \(0.770743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85305 | −0.185426 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.16147 | + | 10.7402i | 0.0824651 | + | 0.409763i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.27615 | −0.162908 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.0761 | 1.33436 | 0.667179 | − | 0.744897i | \(-0.267501\pi\) | ||||
0.667179 | + | 0.744897i | \(0.267501\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.79424 | − | 35.2598i | −0.372052 | − | 1.33941i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.24284 | 0.274737 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.8097 | 1.05337 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.0447 | + | 10.6109i | −0.455572 | + | 0.401342i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.2500 | 0.651522 | 0.325761 | − | 0.945452i | \(-0.394379\pi\) | ||||
0.325761 | + | 0.945452i | \(0.394379\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.822352 | + | 1.42436i | 0.0310156 | + | 0.0537206i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.65301 | + | 8.21367i | 0.0622560 | + | 0.309345i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.9912 | − | 15.9527i | −0.789455 | − | 0.599964i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.5147 | −0.545110 | −0.272555 | − | 0.962140i | \(-0.587869\pi\) | ||||
−0.272555 | + | 0.962140i | \(0.587869\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.0961 | − | 29.7211i | −1.46622 | − | 1.11463i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.163922 | + | 0.283921i | 0.00613893 | + | 0.0106329i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.593081 | + | 1.02725i | −0.0221800 | + | 0.0384168i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.39852 | − | 3.87493i | 0.164266 | − | 0.144712i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.4295 | − | 38.8491i | 0.836480 | − | 1.44883i | −0.0563403 | − | 0.998412i | \(-0.517943\pi\) |
0.892820 | − | 0.450414i | \(-0.148723\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.4242 | − | 11.9287i | 1.05857 | − | 0.444248i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.1030 | − | 15.0671i | 0.636067 | − | 0.560351i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.0295 | −1.15241 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.22039 | + | 3.84582i | 0.0823496 | + | 0.142634i | 0.904259 | − | 0.426985i | \(-0.140424\pi\) |
−0.821909 | + | 0.569619i | \(0.807091\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.99497 | + | 25.0819i | −0.370184 | + | 0.928958i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.7021 | − | 27.1969i | 0.580764 | − | 1.00591i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1360 | + | 33.1445i | 0.706803 | + | 1.22422i | 0.966037 | + | 0.258405i | \(0.0831968\pi\) |
−0.259233 | + | 0.965815i | \(0.583470\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.343640 | − | 6.36820i | 0.0126753 | − | 0.234895i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.9725 | + | 20.7370i | −0.441014 | + | 0.763859i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.59381 | + | 4.49261i | 0.0954148 | + | 0.165263i | 0.909782 | − | 0.415087i | \(-0.136249\pi\) |
−0.814367 | + | 0.580350i | \(0.802916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.614347 | − | 3.05264i | −0.0225686 | − | 0.112142i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.3351 | + | 28.2932i | −0.599276 | + | 1.03798i | 0.393653 | + | 0.919259i | \(0.371211\pi\) |
−0.992928 | + | 0.118716i | \(0.962122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.18314 | − | 3.78132i | 0.0799842 | − | 0.138537i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.39812 | − | 26.7400i | 0.124331 | − | 0.978366i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3452 | + | 7.86203i | 0.378004 | + | 0.287272i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.06106 | − | 13.9622i | −0.294152 | − | 0.509487i | 0.680635 | − | 0.732623i | \(-0.261704\pi\) |
−0.974787 | + | 0.223136i | \(0.928371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.77902 | − | 1.27334i | −0.137715 | − | 0.0464030i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.62595 | 0.277537 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.6421 | 1.65889 | 0.829444 | − | 0.558589i | \(-0.188657\pi\) | ||||
0.829444 | + | 0.558589i | \(0.188657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.408301 | + | 0.137576i | 0.0148204 | + | 0.00499370i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.11500 | − | 10.5915i | −0.221669 | − | 0.383942i | 0.733646 | − | 0.679532i | \(-0.237817\pi\) |
−0.955315 | + | 0.295590i | \(0.904484\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −47.6387 | + | 19.9924i | −1.72464 | + | 0.723773i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.02026 | − | 3.36444i | 0.289973 | − | 0.121642i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.62158 | − | 2.80866i | 0.0585518 | − | 0.101415i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.17344 | − | 5.49656i | 0.114437 | − | 0.198211i | −0.803117 | − | 0.595821i | \(-0.796827\pi\) |
0.917555 | + | 0.397610i | \(0.130160\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.95523 | − | 49.4667i | −0.358529 | − | 1.78150i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.4515 | + | 42.3512i | 0.879459 | + | 1.52327i | 0.851936 | + | 0.523646i | \(0.175428\pi\) |
0.0275225 | + | 0.999621i | \(0.491238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.3504 | + | 24.8556i | −0.515481 | + | 0.892839i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.15094 | + | 1.69706i | 0.0412897 | + | 0.0608815i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.27302 | + | 16.0613i | 0.332240 | + | 0.575457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.06483 | + | 7.04049i | −0.145451 | + | 0.251928i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.8910 | + | 30.7165i | −0.532160 | + | 1.09772i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.28455 | + | 5.68900i | 0.117231 | + | 0.203049i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.1498 | 0.825201 | 0.412600 | − | 0.910912i | \(-0.364621\pi\) | ||||
0.412600 | + | 0.910912i | \(0.364621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.53294 | − | 3.11239i | 0.125776 | − | 0.110804i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.1147 | − | 17.5665i | −0.821864 | − | 0.624594i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.113870 | + | 0.197229i | −0.00404365 | + | 0.00700381i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.97675 | − | 5.26529i | 0.211974 | − | 0.186741i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.2284 | − | 41.9648i | 0.858214 | − | 1.48647i | −0.0154170 | − | 0.999881i | \(-0.504908\pi\) |
0.873631 | − | 0.486589i | \(-0.161759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.3429 | + | 43.8951i | 0.896566 | + | 1.55290i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −39.0149 | + | 16.3665i | −1.37853 | + | 0.578281i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.2976 | −1.70439 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0597815 | + | 0.0454323i | 0.00210702 | + | 0.00160128i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.91940 | − | 9.53734i | −0.0675661 | − | 0.335730i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.2647 | − | 17.7791i | −0.360889 | − | 0.625078i | 0.627218 | − | 0.778844i | \(-0.284193\pi\) |
−0.988107 | + | 0.153765i | \(0.950860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7882 | −0.975776 | −0.487888 | − | 0.872906i | \(-0.662233\pi\) | ||||
−0.487888 | + | 0.872906i | \(0.662233\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.8492 | + | 16.6055i | −0.661071 | + | 0.582379i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.61370 | −0.0915539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.9432 | 0.732711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.03902 | − | 3.74055i | −0.0363064 | − | 0.130705i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.5586 | −0.577901 | −0.288950 | − | 0.957344i | \(-0.593306\pi\) | ||||
−0.288950 | + | 0.957344i | \(0.593306\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4704 | −0.887843 | −0.443922 | − | 0.896066i | \(-0.646413\pi\) | ||||
−0.443922 | + | 0.896066i | \(0.646413\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.44174 | + | 36.9774i | 0.259088 | + | 1.28739i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.0798 | −1.25462 | −0.627309 | − | 0.778771i | \(-0.715844\pi\) | ||||
−0.627309 | + | 0.778771i | \(0.715844\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.3539 | + | 38.7180i | 0.776381 | + | 1.34473i | 0.934015 | + | 0.357234i | \(0.116280\pi\) |
−0.157633 | + | 0.987498i | \(0.550386\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.27167 | + | 2.00126i | −0.0788035 | + | 0.0694229i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.3314 | − | 37.1721i | −0.357960 | − | 1.28794i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.5293 | −0.364383 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.7182 | + | 26.1338i | 0.612431 | + | 0.903316i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.86805 | + | 13.6279i | 0.271635 | + | 0.470486i | 0.969281 | − | 0.245957i | \(-0.0791022\pi\) |
−0.697645 | + | 0.716443i | \(0.745769\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.07866 | + | 12.2606i | −0.244092 | + | 0.422779i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.66095 | − | 18.1910i | −0.126090 | − | 0.626531i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.35611 | − | 5.81296i | 0.115454 | − | 0.199972i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.0230 | + | 10.5013i | −0.859799 | + | 0.360829i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.6759 | − | 6.96670i | −0.709594 | − | 0.239097i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0241422 | −0.000827584 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2010 | + | 24.5968i | 0.486231 | + | 0.842177i | 0.999875 | − | 0.0158264i | \(-0.00503792\pi\) |
−0.513643 | + | 0.858004i | \(0.671705\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.61744 | + | 3.51021i | 0.157913 | + | 0.120046i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.48867 | − | 7.77461i | 0.153330 | − | 0.265575i | −0.779120 | − | 0.626875i | \(-0.784334\pi\) |
0.932450 | + | 0.361300i | \(0.117667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.471450 | − | 0.816575i | −0.0160857 | − | 0.0278612i | 0.857871 | − | 0.513866i | \(-0.171787\pi\) |
−0.873956 | + | 0.486005i | \(0.838454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.9782 | + | 19.1364i | 0.442297 | + | 0.652166i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.0488 | − | 22.6011i | 0.444185 | − | 0.769351i | −0.553810 | − | 0.832643i | \(-0.686827\pi\) |
0.997995 | + | 0.0632920i | \(0.0201600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.38145 | − | 4.12478i | −0.0809716 | − | 0.140247i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3863 | − | 15.3166i | 0.590468 | − | 0.520180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.7375 | + | 65.3633i | −1.28016 | + | 2.21730i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.27011 | + | 2.19989i | −0.0430360 | + | 0.0745405i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.95152 | + | 31.0947i | −0.133739 | + | 1.05240i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.70390 | + | 13.4240i | −0.0576022 | + | 0.453814i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.1794 | + | 22.8275i | 0.445038 | + | 0.770829i | 0.998055 | − | 0.0623413i | \(-0.0198567\pi\) |
−0.553017 | + | 0.833170i | \(0.686523\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.09586 | − | 3.60829i | 0.138150 | − | 0.121705i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.6077 | −1.53656 | −0.768281 | − | 0.640113i | \(-0.778888\pi\) | ||||
−0.768281 | + | 0.640113i | \(0.778888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.1575 | 0.880271 | 0.440136 | − | 0.897931i | \(-0.354930\pi\) | ||||
0.440136 | + | 0.897931i | \(0.354930\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.19187 | + | 5.92232i | 0.0400644 | + | 0.199077i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.5963 | + | 32.2097i | 0.624401 | + | 1.08149i | 0.988656 | + | 0.150196i | \(0.0479904\pi\) |
−0.364255 | + | 0.931299i | \(0.618676\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.53384 | − | 43.5979i | 0.185599 | − | 1.46223i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.1758 | + | 10.3787i | 1.34594 | + | 0.347699i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.9009 | + | 29.2733i | −0.565568 | + | 0.979593i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.04589 | − | 7.00769i | 0.135239 | − | 0.234241i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0433146 | + | 0.0145948i | 0.00144623 | + | 0.000487306i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.9592 | + | 34.5704i | 0.665677 | + | 1.15299i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0932 | − | 41.7307i | 0.802662 | − | 1.39025i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.0426 | − | 1.88733i | 0.866643 | − | 0.0628063i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.51160 | + | 4.35022i | 0.0834884 | + | 0.144606i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9231 | − | 22.3834i | 0.429103 | − | 0.743229i | −0.567691 | − | 0.823242i | \(-0.692163\pi\) |
0.996794 | + | 0.0800134i | \(0.0254963\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.5679 | − | 11.5645i | 0.914368 | − | 0.383570i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.41211 | + | 4.17790i | 0.0799169 | + | 0.138420i | 0.903214 | − | 0.429191i | \(-0.141201\pi\) |
−0.823297 | + | 0.567611i | \(0.807868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41.4256 | −1.37099 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0836956 | − | 0.415877i | −0.00276689 | − | 0.0137485i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.1912 | − | 5.95558i | 0.468635 | − | 0.196670i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.58183 | + | 16.5962i | −0.316075 | + | 0.547459i | −0.979666 | − | 0.200638i | \(-0.935699\pi\) |
0.663590 | + | 0.748096i | \(0.269032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.4651 | − | 11.2760i | −1.10271 | − | 0.371557i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.431218 | + | 0.746891i | −0.0141937 | + | 0.0245842i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05675 | − | 1.83035i | −0.0347458 | − | 0.0601815i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.40641 | + | 34.6743i | −0.144725 | + | 1.13885i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 54.0914 | 1.77468 | 0.887340 | − | 0.461115i | \(-0.152550\pi\) | ||||
0.887340 | + | 0.461115i | \(0.152550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0236 | − | 18.3617i | 0.590700 | − | 0.601781i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.2617 | + | 12.5553i | 1.21989 | + | 0.411041i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.68322 | − | 11.5757i | −0.218565 | − | 0.378565i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.6345 | −0.543426 | −0.271713 | − | 0.962378i | \(-0.587590\pi\) | ||||
−0.271713 | + | 0.962378i | \(0.587590\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.4238 | + | 9.24041i | 0.894942 | + | 0.301549i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.89912 | −0.0945085 | −0.0472543 | − | 0.998883i | \(-0.515047\pi\) | ||||
−0.0472543 | + | 0.998883i | \(0.515047\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.272233 | −0.00886512 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.05804 | + | 3.94878i | 0.197068 | + | 0.128454i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.7311 | 1.87601 | 0.938004 | − | 0.346625i | \(-0.112672\pi\) | ||||
0.938004 | + | 0.346625i | \(0.112672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.12366 | −0.166321 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.9522 | − | 5.71202i | −0.549713 | − | 0.185225i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.4070 | 0.661046 | 0.330523 | − | 0.943798i | \(-0.392775\pi\) | ||||
0.330523 | + | 0.943798i | \(0.392775\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.90440 | − | 5.03057i | −0.0939843 | − | 0.162786i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.7148 | + | 16.7513i | 1.60705 | + | 0.541494i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.4349 | − | 14.7700i | −0.627585 | − | 0.476947i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.92259 | 0.191051 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.5864 | + | 5.69937i | −0.437814 | + | 0.183660i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.02193 | − | 12.1623i | −0.226044 | − | 0.391519i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.26365 | + | 7.38486i | −0.137110 | + | 0.237481i | −0.926401 | − | 0.376537i | \(-0.877115\pi\) |
0.789292 | + | 0.614019i | \(0.210448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.2520 | + | 11.2042i | 1.06821 | + | 0.359931i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.42651 | + | 16.3272i | −0.302511 | + | 0.523965i | −0.976704 | − | 0.214590i | \(-0.931158\pi\) |
0.674193 | + | 0.738555i | \(0.264492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.0052 | + | 22.0431i | 0.929864 | + | 0.706671i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.789458 | + | 3.92275i | 0.0252829 | + | 0.125629i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.611299 | 0.0195572 | 0.00977859 | − | 0.999952i | \(-0.496887\pi\) | ||||
0.00977859 | + | 0.999952i | \(0.496887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.5108 | + | 56.3104i | 1.03905 | + | 1.79969i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.38510 | − | 58.1138i | 0.235788 | − | 1.85543i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.62584 | + | 6.28013i | −0.115646 | + | 0.200305i | −0.918038 | − | 0.396493i | \(-0.870227\pi\) |
0.802392 | + | 0.596798i | \(0.203561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.37659 | − | 5.84842i | −0.107587 | − | 0.186346i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.3780 | + | 37.9239i | −0.584980 | + | 1.20713i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.153710 | + | 0.266234i | −0.00488770 | + | 0.00846575i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.49266 | + | 4.31741i | 0.0791819 | + | 0.137147i | 0.902897 | − | 0.429857i | \(-0.141436\pi\) |
−0.823715 | + | 0.567004i | \(0.808103\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −37.1469 | − | 12.5166i | −1.17882 | − | 0.397202i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.33412 | + | 9.23896i | −0.169103 | + | 0.292895i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.59172 | − | 2.75694i | 0.0504104 | − | 0.0873133i | −0.839719 | − | 0.543021i | \(-0.817280\pi\) |
0.890130 | + | 0.455708i | \(0.150614\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.31902 | + | 0.167715i | −0.0733706 | + | 0.00530627i |
(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 | 1008.2.q.l.625.2 | 22 | ||
3.2 | odd | 2 | 3024.2.q.l.2305.7 | 22 | |||
4.3 | odd | 2 | 504.2.q.c.121.10 | yes | 22 | ||
7.4 | even | 3 | 1008.2.t.l.193.6 | 22 | |||
9.2 | odd | 6 | 3024.2.t.k.289.5 | 22 | |||
9.7 | even | 3 | 1008.2.t.l.961.6 | 22 | |||
12.11 | even | 2 | 1512.2.q.d.793.7 | 22 | |||
21.11 | odd | 6 | 3024.2.t.k.1873.5 | 22 | |||
28.11 | odd | 6 | 504.2.t.c.193.6 | yes | 22 | ||
36.7 | odd | 6 | 504.2.t.c.457.6 | yes | 22 | ||
36.11 | even | 6 | 1512.2.t.c.289.5 | 22 | |||
63.11 | odd | 6 | 3024.2.q.l.2881.7 | 22 | |||
63.25 | even | 3 | inner | 1008.2.q.l.529.2 | 22 | ||
84.11 | even | 6 | 1512.2.t.c.361.5 | 22 | |||
252.11 | even | 6 | 1512.2.q.d.1369.7 | 22 | |||
252.151 | odd | 6 | 504.2.q.c.25.10 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.10 | ✓ | 22 | 252.151 | odd | 6 | ||
504.2.q.c.121.10 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.c.193.6 | yes | 22 | 28.11 | odd | 6 | ||
504.2.t.c.457.6 | yes | 22 | 36.7 | odd | 6 | ||
1008.2.q.l.529.2 | 22 | 63.25 | even | 3 | inner | ||
1008.2.q.l.625.2 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.l.193.6 | 22 | 7.4 | even | 3 | |||
1008.2.t.l.961.6 | 22 | 9.7 | even | 3 | |||
1512.2.q.d.793.7 | 22 | 12.11 | even | 2 | |||
1512.2.q.d.1369.7 | 22 | 252.11 | even | 6 | |||
1512.2.t.c.289.5 | 22 | 36.11 | even | 6 | |||
1512.2.t.c.361.5 | 22 | 84.11 | even | 6 | |||
3024.2.q.l.2305.7 | 22 | 3.2 | odd | 2 | |||
3024.2.q.l.2881.7 | 22 | 63.11 | odd | 6 | |||
3024.2.t.k.289.5 | 22 | 9.2 | odd | 6 | |||
3024.2.t.k.1873.5 | 22 | 21.11 | odd | 6 |